convective heat transfer.
Lavrov, Dmitry Alexandrovich
Academic degree:
PhD
Place of defense of the dissertation:
VAK specialty code:
Speciality:
Theoretical foundations of heat engineering
Number of pages:
Introduction.
1. Literature review and research objectives.
1.1. Methods for a comparative quantitative assessment of the energy efficiency of convective heating surfaces.
1.2. Increasing the efficiency of tubular heating surfaces
1.3. Research objectives.
2. Method for calculating the energy efficiency of heat exchangers from smooth-tube and finned tube bundles and devices from profile sheets (plate heat exchangers). Comparison of smooth-tube and finned bundles in the case of "two-sided" and "one-sided" flow around the heating surface.
2.1. Method for calculating the energy efficiency of smooth-tube bundles.
2.2. Method for calculating the energy efficiency of finned beams.
2.3. Determination of the Energy Efficiency of Smooth-Tube and Finned Bundles. Comparison of smooth-tube and finned bundles.
2.4. Method for calculating the energy efficiency of heat exchangers from profile sheets (plate heat exchangers). Calculation of energy efficiency.
3. Experimental study heat and aerodynamic characteristics in supertight chess beams.
3.1. Technique for studying heat transfer and aerodynamic resistance.
3.2. Experimental site.
3.3. Scheme of the experimental setup.
3.4. Technique for processing experimental data.
3.5. Measurements in thermal and aerodynamic experiments.
3.6. Calibration experiments.
3.7. Analysis and generalization of experimental data on heat transfer.
3.8. Analysis and generalization of experimental data on resistance.
3.9. Comparison of the obtained results with the data of other authors.
Introduction to the thesis (part of the abstract) On the topic "Intensification of convective heat transfer"
Heat exchangers, as a rule, are the most metal-intensive and bulky part of power plants in industrial and station power engineering. This applies in particular to heat exchangers operating in low-grade heat recovery systems and operating at small temperature differences. Therefore, the problem of developing efficient heat exchange systems is to a large extent the problem of intensifying heat transfer.
The search and study of methods of intensification, as well as the science of heat transfer in general, has a fairly long history. Based on the intuitive idea of intensive mixing as a means of intensifying heat transfer, many researchers have proposed and tested a variety of turbulent inserts, modified channel shapes, and various artificial forms of surface roughness. On the basis of developed computational models of turbulence and with the use of numerical simulation of complex flows, in relatively recent times, fairly clear ideas about the mechanism of heat transfer intensification, the influence of factors such as fluid properties (Prandtl number), flow regime (Reynolds number), acceleration or flow deceleration (flow in a confuser or diffuser). Methods of various physical influences are being developed to intensify the transfer, such as acoustic and electromagnetic influences.
Convective recuperative heat exchangers such as "gas-gas", "liquid-liquid", "gas-liquid", "gas-two-phase medium", "liquid-two-phase medium" are widely used at present both in industrial (petrochemistry, metallurgy, aviation , marine, refrigeration equipment, etc.), and in the station power industry.
A large amount of metal is consumed in the manufacture of such heat exchangers. Their operation is associated with high energy costs, primarily for pumping coolants. The growth in production volumes is accompanied by an increase in the mass and dimensions of heat exchangers, as well as in energy costs for their operation. Therefore, the task of reducing the mass of heat exchangers (especially "gas - gas" and "gas - liquid"), on the one hand, and operating costs, on the other, is also very relevant here.
These tasks can only be solved by intensifying heat transfer from one or both heat carriers with a moderate increase in hydrodynamic resistance, since the energy efficiency of a heat exchanger is determined by the ratio between the useful effect (heat flow) and material costs (metal and energy consumption).
The problem of increasing the energy efficiency of heat exchangers and methods for comparative evaluation of their efficiency, as noted above, has been studied, in essence, since the appearance of the first devices. The analysis was based on the research of Gukhman A.A. , Kirpicheva M.A. , Buznika V.M. , Zhukauskas A.A. , Migaya V.K. , Kalinina E.K. and Dreitser G.A. . Extensive information on the designs of compact and intensified heat exchangers and methods for their calculation is contained in.
The inconsistency of these requirements is obvious: the intensity of heat transfer, ceteris paribus, increases approximately in proportion to the speed of the coolant to the first degree, and the power expended is proportional to the speed cubed. In addition, the heat flux is generally proportional to the surface area.
Therefore, the solution to the problem of increasing the energy efficiency of the heat exchanger is to create such a physical environment for a given area and average velocity of the coolant, in which heat transfer occurs with the highest possible intensity, and the process of momentum transfer (determining power costs) - with the least.
The complexity of this task is due to two circumstances. First, both transfer processes are carried out by the same elements of the medium, which are simultaneously carriers of both heat and momentum. Secondly, in the general case, one should consider the issues of intensifying heat transfer and reducing the pumping costs for both coolants that have a common separating surface.
It is obvious that the physical situation corresponding to the process scheme described above is very unusual, very complex, and can only be created artificially with well thought out and carefully controlled process development.
In addition, in the practical use of intensification in heat exchangers, one has to face the problems of choosing the right method of intensification and the geometric parameters of intensifying elements, take into account that the manufacture of intensified surfaces requires certain additional costs (taking into account manufacturability and cost), and also take into account cases when the intensified surfaces worked well in the initial period of operation, and then the corresponding effect decreased or disappeared due to the accumulation of thermally harmful deposits, erosive and corrosive wear of the intensifying elements, and then it becomes necessary to choose the optimal method from the standpoint of long-term operation, methods of possible cleaning, etc. ., that is, in general, from the standpoint of the reliability of the heat exchanger.
Increasing the energy efficiency of heat exchangers with smooth-tube, few-row bundles operating on pure gas (heat-recovery boilers, CCGT units, air heaters, hot water gas boilers, dry cooling towers, etc.) can be achieved by reducing the transverse and longitudinal pitch of the bundle, that is, due to increasing the compactness of the beam.
This issue is the subject of the experimental part of the work, in which heat-aerodynamic characteristics of supertight transversely streamlined staggered smooth-tube bundles.
An important issue when considering the problem of intensification of convective heat transfer remains the question of determining quantitative indicators of energy efficiency and the correct comparison of various methods of intensification.
The computational and methodological part of the work is devoted to this issue, in which a methodology and algorithm for calculating the energy efficiency indicators of various convective surfaces with a "one-sided" and "two-sided" flow around the surface are developed. eight
Dissertation conclusion on the topic "Theoretical foundations of heat engineering", Lavrov, Dmitry Aleksandrovich
The range of variation of the parameters under consideration (the energy efficiency indicator for the surface area Kp, the ratio of lengths b21b\ and the ratio of heights b21b\ of the test and reference heat exchangers, the ratio of conjugate Reynolds numbers, the ratio of volumes occupied by surfaces and the compactness factor) depending on the type of profile channel is shown in Table 2.11 .
Table 2.11 shows that the most effective plate surfaces for gas-gas heat exchangers are surfaces with flat channels with spherical recesses (holes) and with biangular channels formed by trapezoidal protrusions. These heat exchangers have a smaller heating surface area than the other three (including the "reference"), with the same transferred heat fluxes, the same power for pumping heat carriers and at the same heat carrier flow rates. At the same time, there is a decrease in the height
92 of the exchange apparatus (reduction in the length of the path of the heat carriers) and an increase in the length of the heat exchanger (the width of the sheets k is taken unchanged, Fig. 2.23). The conjugate values of the Reynolds numbers and, consequently, the velocity of the coolants are also dictated by the comparison conditions. In all cases, the range of Reynolds numbers was controlled, in which the empirical dependences for heat transfer and resistance accepted from the literature are valid.
CONCLUSION
As a result of this work:
1. The existing methods of comparative quantitative assessment of the efficiency of convective heating surfaces are analyzed.
2. Methods for increasing the energy efficiency of tubular heating surfaces are analyzed.
3. A method is proposed for calculating the energy efficiency of smooth-tube and finned tube bundles with “one-sided” and “two-sided” flow around the heating surface, heat exchangers from profiled sheets and heat exchangers with flat mesh-finned channels.
4. An analysis of the energy efficiency of smooth-tube and finned staggered bundles, heat exchangers from profile sheets and heat exchangers with flat mesh-finned channels was carried out.
5. New reliable dependencies for heat transfer and resistance in staggered bundles with axb = 1.051x0.910 have been obtained; 1.027x0.889 and 1.009x0.874 in the range of numbers Nye = (8-100)-10 when changing the rows along the gas 22 from 5 to 3.
6. The indicators of energy efficiency of the studied compact heating surfaces are determined.
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A.A.Konoplev, G.G.Aleksanyan, B.L.Rytov, acad. Al. Al. Berlin, Institute of Chemical Physics. acad. N.N. Semenov of the Russian Academy of Sciences, Moscow
A new effective method for intensifying convective heat transfer in tubular heat exchangers, called the deep profiling method, has been developed, theoretically and experimentally studied. Tests of an experimental laboratory heat exchanger were carried out, the data of which were compared with those for TTAI. All the obtained results are published in scientific periodicals. The possibilities of using the method to create efficient and compact tubular heat exchangers are shown.
The problem of creating modern highly efficient and compact heat exchange equipment is very relevant today, it is of great scientific and practical importance. This problem is closely related to the problem of heat transfer intensification, for the solution of which several different methods have been proposed and, to one degree or another, studied (see, for example, ). Of these, perhaps the most successful, as well as relatively simple and technologically advanced, was the profiling of heat exchange tubes with annular protrusions rolled over their surface. The methods are different, such as, for example, swirling of flows in channels, spiral or longitudinal ribs and inserts, rough surfaces and the imposition of oscillations on heat exchange flows, etc. were not as effective. Also, the use of heat exchange pipes of small diameter contributes to more intensive heat transfer. Thus, shell-and-tube heat exchangers of the TTAI brand manufactured by Teploobmen LLC with close-packed bundles of smooth or knurled thin-walled steel or titanium tubes (approximately 8 mm in diameter and 0.2-0.3 mm thick walls) that appeared relatively recently on the market of heat exchange equipment are placed in the annular space without baffles, significantly surpass all other tubular, and not only, heat exchangers in terms of thermal and weight and size parameters. The disadvantages that appear during their operation are associated precisely with the thin walls of the tubes and their small diameter. These are, for example, deflection and vibrations of the tube bundle, difficulties in mechanical cleaning, etc.
The intensification of heat transfer of the pipe channel when profiling it by knurling is achieved due to additional turbulence of near-wall liquid layers, which leads to an increase in the coefficient of heat transfer to the wall. As found by the authors of the knurling and a number of its researchers, the optimal value is approximately d/D»0.92-0.94. A greater narrowing of the flow section of the pipe channel, although it leads to a greater increase in the coefficient of heat transfer to the wall, is accompanied by a noticeably increasing diffusion of turbulence into the internal volume of the channel, significant energy losses for pumping the coolant, and, according to the now established opinion, is not necessary, because the core of the coolant flow in turbulent mode and so is quite turbulent.
Nevertheless, based on the experience of studying heat and mass transfer during chemical reactions in turbulent flows (see, for example, ), it was assumed at the Institute of Chemical Physics of the Russian Academy of Sciences that turbulization of the entire flow, including its core, can also be used to intensify heat transfer. This additional turbulence can be achieved by changing the size of the flow area more than is considered acceptable for knurling. The proposed method was called the deep profiling method.
Its essence lies in the fact that with intense turbulence of the entire flow as a whole near the wall, in addition to an increase in the transfer coefficient, there is an increase in the temperature gradient (i.e., the temperature difference, which determines, along with the coefficient, the magnitude of the diffusion heat flux to the wall) due to the "flattening" of its radial profile. Studies conducted at the ICP RAS have shown that despite a significant increase in energy losses for pumping the coolant, such values of design and consumption parameters can be found, taking into account that D P~v 2 , and Nu~ v m, where m<1, которые обеспечат приемлемые значения характеристик процесса теплообмена.
The results of our studies have been published, see, for example,. In general, they indicate the applicability of the deep profiling method for practical use, and therefore we would like to acquaint the interested reader with at least their main results. Moreover, in our opinion, it is this method that seems to be the most effective and promising among those known today.
It is clear that the correct choice of one or another method of heat transfer intensification in solving certain technological problems can be made only on the basis of a proper assessment of their properties and parameters. This assessment, often understood as the effectiveness of intensification, should be built on the correlation of the effect of intensification and the costs of its implementation and be of a comparative nature. It can be obtained by comparing the data for the evaluated heat exchanger (or its channel) with already known data, which are most often and most conveniently used for smooth-tube heat exchangers (channels).
However, it must be recognized that today there is not only a generally recognized method for assessing the effectiveness of heat transfer intensification, there is not even a generally recognized definition of it. This problem is often not paid any attention at all, limiting the assessment of the intensification only by bringing the dependencies of the form:
, (1c)
Undoubtedly, dependencies (1) contain all the information necessary for estimating one or another method of intensification, however, for estimates that are quite understandable and important from a practical point of view, only these dependencies are probably not enough.
In some works, the authors propose to evaluate the effectiveness of intensification using the Kirpichev energy criterion E=Q/N, or some modification E¢ = E/D t, assuming that when comparing two heat exchangers, the one in which the heat exchange is intensified in a more efficient way should have a higher value of the corresponding criterion. In this case, the comparison itself should be carried out with the same Re numbers and the number of pipes in the heat exchangers, as well as their lengths. L and diameters D. That is, it is necessary to compare structurally identical heat exchangers under the same conditions, differing only in intensifiers in the pipe channels. The global parameters of heat exchangers, such as the heat exchange surface F, thermal power Q, the power spent on pumping the coolant, N must be obtained during design and evaluated subsequently.
This issue is considered in more detail, and it is also concluded that the coefficient E¢ should not be "...classified as a simple and physically clear, fundamental criterion for evaluating the effectiveness of intensification." When comparing heat exchangers, it is not very informative, and therefore of little use, in our opinion.
Criteria for evaluating the efficiency of heat transfer intensification are also derived, for comparison F and F ch criterion has the form:
, (2a)
However, one inaccuracy should be noted here, which is that if F, Nu/Nu ch, z/z ch are defined in (2a) at the Re number of the intensified channel, then F ch, must be determined at the Reynolds number of the smooth-tube channel Re ch, which at Nu/Nu ch< z/z гл, не совпадает с Re и явным образом из (2а) не следует. Поэтому, использование для оценок выражения (2а) без учета зависимости
is not correct and can lead to errors, and the larger the Re ch, as well as the difference between Nu/Nu ch and z/z ch. Get same dependency (2b) or dependency
, (2c)
is possible only as a result of solving the corresponding system of equations.
Sharing in general the approach to evaluating the efficiency of heat transfer intensification as a comparison of the main parameters of heat exchangers, we would like to introduce some clarifications and additions to it. Indeed, since the goal of heat transfer intensification is to increase it, which ultimately leads to a decrease in the heat exchange surface, it is necessary to evaluate it precisely by this effect, i.e., by reducing the heat transfer surface. However, since, as a rule, the resistance coefficients increase with the intensification of heat transfer, it is necessary to evaluate the efficiency of intensification at the cost of pumping equal to each other, or being in some other, but quite definite ratio. And, finally, in order to obtain estimates of the efficiency of heat transfer intensification, there is no need to make comparisons for any of the parameters of hypothetical heat exchangers, requiring the equality of all the others. For these purposes, it is quite sufficient to compare the specific, i.e., related to the unit mass of the coolant, characteristics.
In other words, comparison of the specific heat transfer surfaces with equal specific costs for pumping heat carriers, total, for the same heat transfer problem, which means the equality of inlet and outlet temperatures for the same heat carriers, the costs of which are also in the same ratio , allows you to compare even different types of heat exchangers (for example, shell-and-tube and plate heat exchangers), including evaluating the method of heat transfer intensification.
We also developed a new technique, see, for example, for processing experimental data, which was then used in all our works. Its essence lies in the fact that when two of the four independent heat transfer variables are fixed, for example, t tr,in and t mt,in, and two other variables, for example, G three G mt, from the experimental data it is possible to find the longitudinal profiles of the heat transfer coefficient K, heat transfer coefficients a tr and a mt, as well as all other heat transfer parameters, approximating them with some suitable function, for example, a polynomial of the second degree. The average values in this case can be obtained by averaging these same profiles. The practice of applying this technique has shown that the values obtained in this way are more accurate than those obtained directly from the relations of the criterion model.
HEAT EXCHANGERS FOR TESTING
Having proposed a deep profiling method for intensifying heat transfer in tubular heat exchangers, we decided to demonstrate its capabilities using a laboratory heat exchanger as an example, comparing the results obtained with data for a TTAI heat exchanger. The results are described in more detail in ; here we present them briefly.
For testing, a heat exchanger with a length L = 0.616 m was made, the inner diameter of the casing D mt of which was changed due to special inserts and amounted to 0.03, 0.032, 0.034 and 0.037 m. In experiments with smooth tubes, a heat exchanger with D mt = 0.04 m was also used. Seven copper tubes were fixed in hexagonal tube sheets, the spacing S of which was proportional to D mt, so that S = D mt /3, the tube bundle was located in the center of the annular space, and, thus, the distance between the casing and the outer tube of the bundle for all its external tubes were the same. During the manufacture of profiled tubes from smooth copper pipes with an outer diameter Dн = 0.01 m and an internal diameter D = 0.008 m, some deformation occurred, as a result of which their dimensions changed and became equal to Dн = 0.0094 m and D = 0.0075 m.
The heat exchanger TTAI-2-25/1450, produced by the manufacturer Teploobmen LLC with serial number 1970, was kindly provided for comparative tests by the General Director of NPO Termek Alexander Lavrentievich Naumov, for which the authors are deeply grateful to him.
According to the passport data, the heated channel of the heat exchanger is a pipe, heated and heating media - fresh water with initial temperatures of 5 ° C and 105 ° C, flow rates - 1.56 and 3.44 t / h, respectively, and the outlet temperature of the heated medium is 60 ° C, heating - 80 °C. The pressure drop in the pipe space does not exceed 0.3, and in the annular space it is 0.25 kgf/cm2. The tube bundle placed under the casing Dmt = 0.0264 contains 6 tubes with a length of the washed part of them 1.39 m, a diameter of 0.008 m and walls 0.2 mm thick, made of Kh17N13M2T steel (calculated value of the thermal conductivity coefficient l = 15 W/m K).
Structurally, the heat exchanger is made with two entrances to the annular space, spaced apart at its ends, and an exit from it in the middle, so that only half of the total flow flows through each cross section of the annulus. Such a flow scheme, due to a 2-fold increase in the flow rate of the heat carrier of the heating channel, allows, while maintaining the energy costs for pumping the heat carrier, to slightly increase the temperature difference of heat exchange and, thus, the thermal power of the apparatus compared to the variant with only one inlet.
We carried out several experiments with the TTAI heat exchanger, in which, assuming that the main goal is to evaluate its heat transfer coefficients, we left only one of the entrances to the annular space, using the other as an exit from it, while closing the exit in the middle. Thus, a purely countercurrent heat exchanger was obtained with the same heat transfer coefficients and energy costs for pumping heat carriers as for the original heat exchanger, namely: K = 8.08 kW/(m 2 K), Gmt = 0.5 × 3.44 t/ h and DP mt = 0.5 kgf/cm2. See details in .
RESULTS AND ITS DISCUSSION
Experiments with a laboratory heat exchanger were carried out in the version with a heated pipe channel, similar to the operating conditions of the TTAI heat exchanger. The methodology for conducting experiments and processing the results obtained is briefly described above, for details see . The results obtained are shown in table 1, and in fig. one.
Table 1. Heat exchangers with HP tubes. one)
| No. p / p | Options | D mt = 0.03 | D mt = 0.032 | D mt = 0.034 | D mt = 0.037 | ||||
| Experiment data | Recalculation for SR conditions | Experiment data | Recalculation for SR conditions | Experiment data | Recalculation for SR conditions | Experiment data | Recalculation for SR conditions | ||
| 1 | G | ||||||||
| 2 | t in | ||||||||
| 3 | t Wed | ||||||||
| 4 | t exit | ||||||||
| 5 | D t | 24.64 | 27.19 | 35.38 | 27.79 | 36.29 | 28.62 | 43.68 | 29.53 |
| 6 | K | 7.09 | 6.96 | 6.15 | 6.57 | 5.70 | 6.08 | 5.44 | 5.56 |
| 7 | a | ||||||||
| 8 | i a | ||||||||
| 9 | v | ||||||||
| 10 | 10 -3 Re | ||||||||
Notes:
1) - in the numerator of the data given in the form of a fraction, the values \u200b\u200bare indicated for the pipe channel, in the denominator - for the annulus;
Rice. Fig. 1. Dependences of heat transfer coefficients on the equivalent diameter: (a, b) – heat transfer enhancement coefficients; (c) is the heat transfer coefficient; 1 - 7-pipe heat exchangers; 2 - 6-pipe heat exchanger; 3 – approximating curve; 4 - average value.
Let's take a closer look at them. Typically, the comparison of different heat exchangers is carried out under the same conditions, which could be called "standard mode" (SR) conditions. Let us take the following values for the SR mode in our case: the inlet temperatures of the heat carriers are equal to t tr, in = 15°С and t mt, in = 60°С, the flow velocity in the pipe channel v tr = 1 m/s, and the ratio G mt / G tr, we will leave the corresponding one-input TTAI (see above), i.e. G mt / G tr = 0.5´3.44/1.56. The obtained experimental data were recalculated to standard conditions under the assumption that the dependence of local heat transfer enhancement coefficients ia = ia(L) can be neglected, and in each specific case their average values ia can be used, which can be found by averaging the corresponding longitudinal distributions (see, For example, ).
On fig. Figure 1 shows the data for ia tr (Fig. 1a), ia mt (Fig. 1b), and K (Fig. 1c) depending on the equivalent diameter de mt. Experimental data (Figs. 1a-1c, curves 1), for K (Fig. 1c) these are the data obtained when recalculated for SR conditions, see Table. 1 are approximated by polynomials of the 2nd degree f(x) = ax 2 + bx + c, (Fig. 1a-1c, curves 3), the coefficients of which are found from the corresponding data. In this case, the relative root-mean-square approximation errors for ia tr, ia mt, and K were 1.6%, 1.8%, and 0.3%, respectively.
For ia tr and ia mt, the average values are also shown (Fig. 1a-1b, curves 4). The relative standard deviations from the mean values were 3.4% and 21.2%, respectively.
Thus, from the given data it follows that the average value of ia tr = 3.84 and the found dependence ia mt = ia mt (de mt) in an acceptable way describe the heat exchange parameters of our profiled heat exchangers.
Experiments were also carried out to determine the coefficients of hydrodynamic resistance. The total pressure drop in the heat exchanger channel is usually represented as the sum of the pressure drops due to frictional resistance during the flow of working media in the channel and the drop due to the inlet/outlet resistance of the channel. To find the pressure drops across the inlet/outlet resistances and from here to determine the local resistance coefficients z tr,loc and z mt,loc, experiments were carried out to determine the pressure loss in heat exchangers with smooth tubes with D n = 0.01 m and D = 0.008 m. However, in this case, for obvious reasons, the heat exchanger with Dmt = 0.03 m was replaced by a heat exchanger with Dmt = 0.04 m.
A series of experiments carried out at different flow rates (velocities) of the working media made it possible to establish that for our heat exchangers the coefficient of local inlet/outlet resistance for the pipe channel can be determined as z tr,loc = 131Re –0.25, and for the annulus channel - z mt, loc = z mt,loc (de mt)Re –0.25 . The values of z mt, lok (de mt) for four experimental heat exchangers, shown in fig. 2a, curve 1, are also approximated by a polynomial of the 2nd degree (Fig. 2a, curve 3). In this case, the relative rms approximation error was 2.2%.
Rice. Fig. 2. Dependences of the hydrodynamic resistance coefficients on the equivalent diameter: (a) heat exchangers with smooth tubes; (b) - heat exchangers with profiled tubes; 1 - 7-pipe heat exchangers; 2 - 6-pipe heat exchanger; 3 – approximating curve.
Assuming the equality of coefficients of local inlet/outlet resistances for heat exchangers with smooth and profiled tubes, friction resistance coefficients in profiled channels, defined as ) mt × z ch,mt, can be found from the results of similar experiments for heat exchangers with shaped tubes. Thus, (z/z ch) mt = 14.9 and the experimental dependence for (z/z ch) mt = (z/z ch) mt (de mt), shown in Fig. 3, were found. 2b, curve 1. An approximation of the latter is also shown in Figs. 2b, curve 3, the relative rms approximation error in this case was 0.5%.
In addition to the experiments described above with 7-pipe heat exchangers, experiments were also carried out with a 6-pipe heat exchanger obtained by removing the central tube from a 7-pipe heat exchanger with Dmt = 0.032 m, and thus the configuration of the tube bundle of our heat exchanger was similar to the configuration of the tube bundle of the TTAI heat exchanger.
The results of experiments carried out with this heat exchanger are shown in fig. 1-2, curves 2, in the form of experimental points plotted on them. Note that there is a fairly good agreement between the results both in terms of heat transfer coefficients and in terms of resistance coefficients, see fig. 1-2. Thus, the relative deviations in absolute value are 0.3% for ia tr (deviations from the mean value, Fig. 1a, curve 4), 5.2% for ia mt (deviations from the approximating curve, Fig. 1b, curve 3), 4.6% for K (Fig. 1c, curve 3), 0.5% for z mt,lok (Fig. 2a, curve 3), and 5.1% for (z/z ch)tr (Fig. 2b, curve 3).
Thus, using the data found in the experiment, it is possible to construct a certain method for calculating heat exchangers with a close-packed bundle of HP tubes (at least 6 and 7 tubes) and compare them with a TTAI heat exchanger. In these calculations, the inlet temperatures of the heat carriers and the ratio of their flow rates corresponded to the passport data for the TTAI, and the results obtained were compared with the results of calculations of the TTAI heat exchanger for its single-input version.
In table. Figure 2 shows the results of calculations obtained for HP tubes similar to TTAI tubes (material, diameter, wall). In option 1 (Table 2), the replacement of TTAI tubes by HP tubes leads to an increase in the specific energy consumption for pumping heat carriers w/w TTAI = 1.51 and an increase in the efficiency coefficient k/k TTAI = 1.34. (in the sense of , in this case k/k TTAI = K/K TTAI). In option 2, reducing the flow rate to G/G TTAI = 0.812 equalizes the unit costs for pumping, while leaving the efficiency factor k/k TTAI = 1.16 still relatively high.
Table 2. Comparison of TTAI and HP tube heat exchangers.
| No. p / p | Options | TTAI 1) | Heat exchangers with HP tubes | |||
| Option 1 2) | Option 2 3) | Option 3 | Option 4 | |||
| 1 | n | 6 | 6 | 6 | 6 | 7 |
| 2 | 10 3 D mt | 26.4 | 26.4 | 26.4 | 25.4 | 27.2 |
| 3 | G 4) | |||||
| 4 | G tr / G tr,ttai | 1 | 1 | 0.812 | 0.788 | 0.911 |
| 5 | w/w TTAI | 1 | 1.51 | 1 | 1 | 1 |
| 6 | L 5) | |||||
| 7 | L/D | 183 | 136 | 128 | 123 | 121 |
| 8 | F 5) | |||||
| 9 | F/V 5) | |||||
| 10 | F/G tr 5) | |||||
| 11 | K 5) | |||||
| 12 | iK | 1.51 | 1.61 | 1.63 | 1.52 | 1.52 |
| 13 | Q/F | 429 | 577 | 497 | 502 | 506 |
| 14 | v 4) | |||||
| 15 | 10 -3 Re 4) | |||||
| 16 | a4) | |||||
| 17 | i a4) | |||||
| 18 | k/k TTAI | 1 | 1.34 | 1.16 | 1.17 | 1.18 |
Notes:
1) - assessment according to the criterion model with correction;
2) - replacement of TTAI tubes with GP tubes;
3) - the same for the case of equality of unit costs for pumping coolants to costs for TTAI;
4) - in the numerator of the fraction, the value for the pipe channel is indicated, in the denominator - for the annulus;
5) - in the numerator of the fraction the value of the quantity is indicated, in the denominator - its relation to the value for TTAI.
In option 3 (Table 2) it is shown that Dmt = 0.0254 m can even be slightly reduced, and in option 4 - that a 7-tube bundle can also be used, while k/k TTAI = 1.17-1.18 even slightly increases. The heat exchange surface per unit volume (F/V)/(F/V) TTAI = 1.08-1.10 increases slightly and the specific surface decreases (F/G)/(F/G) TTAI = 0.854-0.847. At the same time, in all considered variants, the length of the heat exchanger does not exceed L/L TTAI = 0.75 (see Table 2).
Similarly, we will also carry out calculations for heat exchangers with a 7-tube bundle of close-packed HP tubes with dimensions 10/0.8, 12/1 and 16/1 made of copper, brass and steel. The conditions mentioned above for the inlet temperatures of coolants and the ratio of costs Gtr /Gmt = (Gtr /Gmt) TTAI, we will supplement the requirement of equality of specific energy costs for pumping coolants w/w TTAI = 1.
The parameters of the heat exchangers found under these conditions are optimal for each of the considered tubes, the calculation results are presented in Table. 3.
Table 3. Parameters of heat exchangers with HP tubes. one)
| No. p / p | Tube 10/0.8 | Tube 12/1 | Tube 16/1 | |||||||
| 1 | Wall material 2) | copper | brass | steel | copper | brass | steel | copper | brass | Steel |
| 2 | 10 3 D mt | 32.8 | 33 | 39 | 39.4 | 51.5 | 52.2 | |||
| 3 | G 3) | |||||||||
| 4 | G tr / G tr,ttai | 1.20 | 1.17 | 1.03 | 1.64 | 1.60 | 1.38 | 2.71 | 2.66 | 2.36 |
| 5 | L 4) | |||||||||
| 6 | L/D | 104 | 109 | 152 | 98.4 | 105 | 157 | 88.5 | 94.3 | 142 |
| 7 | F 4) | |||||||||
| 8 | F/V 4) | |||||||||
| 9 | F/G tr 4) | |||||||||
| 10 | K 4) | |||||||||
| 11 | iK | 1.65 | 1.60 | 1.37 | 1.82 | 1.73 | 1.40 | 2.17 | 2.01 | 1.51 |
| 12 | Q/F | 577 | 537 | 337 | 582 | 532 | 308 | 574 | 527 | 310 |
| 13 | v 3) | |||||||||
| 14 | 10 -3 Re 3) | |||||||||
| 15 | a 3) | |||||||||
| 16 | i a 3) | |||||||||
| 17 | k/k TTAI | 1.31 | 1.22 | 0.77 | 1.32 | 1.21 | 0.70 | 1.31 | 1.20 | 0.71 |
Notes:
1) - accepted here G mt / G tr = ( G mt / G tr) TTAI, w = w TTAI;
2) - the values of l for copper, brass and steel are taken equal to 390, 110 and 15, respectively;
3) - in the numerator of the fraction, the value for the pipe channel is indicated, in the denominator - for the annulus;
4) - in the numerator of the fraction the value of the quantity is indicated, in the denominator - its relation to the value for TTAI.
For all calculated sizes of brass and copper tubes, the heat transfer efficiency is higher than that of the TTAI heat exchanger - k/k TTAI = K/K TTAI = 1.2-1.3, and remains approximately the same, due to the increase in heat transfer in the annulus a mt, primarily due to with an increase in its intensification ia mt (Table 3). As a result, the specific heat exchange surface F/G tr and the dimensionless length of the heat exchangers L/D decrease, however, due to the large diameters of the tubes, the surface area F/V per unit volume decreases (Table 3). It can also be noted that from those given in Table. It follows from Table 3 that as the tube diameter increases, the ratio of the heat transfer coefficients a mt /a tr increases, approaching unity.
CONCLUSION
Thus, it follows from the experimental and calculated data presented in this work that the use of deeply profiled tubes in a close-packed bundle without baffles in the annular space can lead to the creation of very efficient heat exchangers. Moreover, the diameter of the heat exchange tube has little effect on the thermal parameters, its increase only reduces the content of the heat exchange surface per unit volume of the heat exchanger.
The search for optimal parameters for deep profiling of heat exchange tubes of tubular heat exchangers, in our opinion, is an important task, and it should also be continued.
NOTATION
D- internal diameter, characteristic size, m;
de- equivalent diameter, m;
F- heat exchange surface, m 2 ;
G- coolant flow rate, kg/s;
i a- i a = a/a ch = Nu/Nu ch, heat transfer enhancement parameter;
To- heat transfer coefficient, kW / (m 2 K);
k– efficiency coefficient;
L- heat exchange length, m;
N- power loss for coolant pumping, W;
Q- heat flow, W;
S- distance between the axes of the tubes, m;
s- flow area, m 2;
t- temperature, °C;
t d- profiling step, m;
V- the volume of the heat exchanger, m 3;
v- speed, m/s;
w - w = (N tr + N mt)/ G tr, total specific pumping costs, J/kg;
a is the heat transfer coefficient, kW / (m 2 K);
D p– pressure drop, Pa;
r - density, kg / m 3;
l is the coefficient of thermal conductivity, W/(m K);
z is the coefficient of hydrodynamic resistance;
Nu - Nusselt criterion;
Re - Reynolds criterion.
in – at the entrance to the channel;
out - at the exit from the channel;
km – criterion model;
loc - local value;
mt - interpipe channel;
n - outer (diameter);
cp – average value;
tr - pipe channel;
Literature
1. Dzyubenko B.V., Kuzma-Kichta Yu.A., Leontiev A.I. and others. Intensification of heat and mass transfer on macro-, micro- and nanoscales. M.: FSUE "TsNIATOMINFORM", 2008.
2 Kalinin E.K., Dreitser G.A., Kopp I.Z., Myakochin A.S. Effective heat exchange surfaces. Moscow: Energoatomizdat, 1998.
3. Berlin Al.Al., Minsker K.S., Dyumaev K.M. New unified energy and resource-saving high-performance technologies of increased environmental cleanliness based on tubular turbulent reactors. Moscow: OAO NIITEKHIM, 1996.
4. Konoplev A.A., Aleksanyan G.G., Rytov B.L., Berlin Al.Al. Efficient method of intensification of convective heat transfer. // Theoret. basics of chem. technology. 2004. V. 38. No. 6. S. 634.
5. A. A. Konoplev, G. G. Aleksanyan, B. L. Rytov, Al. Al. Berlin. Convective heat transfer in deeply profiled channels. // Theoret. basics of chem. technology. 2007. V. 41. No. 5. S. 549.
6. A. A. Konoplev, G. G. Aleksanyan, B. L. Rytov, Al. Al. Berlin. Calculation of local parameters of intensified heat transfer. // Theoret. basics of chem. technology. 2007. V. 41. No. 6. S. 692.
7. A. A. Konoplev, G. G. Aleksanyan, B. L. Rytov, Al. Al. Berlin. On the efficiency of heat transfer intensification by deep profiling. // Theoret. basics of chem. technology. 2012. V. 46. No. 1. S. 24.
8. Konoplev A.A., Aleksanyan G.G., Rytov B.L., Berlin Al.Al. On the compactness of tubular heat exchangers. // Theoret. basics of chem. technology. 2012. V. 46. No. 6. S. 639.
9. A. A. Konoplev, G. G. Aleksanyan, B. L. Rytov, Al. Al. Berlin. On efficient tubular heat exchangers. // Theoret. basics of chem. technology. 2015. V. 49. No. 1. S. 65.
Page 1
The intensification of convective heat transfer by increasing the speed of the coolant flow is associated with the expenditure of energy and overcoming resistance as it moves along the surface of the streamlined body. Knowing this resistance makes it possible to select an economically advantageous heat carrier velocity, at which the efficiency of heat exchange and the energy consumption to overcome the resistance create the most economically favorable operating conditions for the heat exchanger.
The intensification of convective heat transfer under conditions of internal (longitudinal flow) and external (transverse flow) problems is the main direction for improving the overall mass characteristics of recuperative heat exchangers. To date, various methods for intensifying heat transfer have been proposed and developed, and studies have been carried out on numerous constructive types and shapes of convective surfaces that implement one or another method of intensification in the flow of gases and liquids.
To intensify convective heat transfer, it is desirable that the thermal boundary layer be as thin as possible. With the development of flow turbulence, the boundary layer becomes so thin that convection begins to have a dominant effect on heat transfer.
To intensify convective heat transfer, it is desirable that the thermal boundary layer be as thin as possible. With the development of flow turbulence, the boundary land becomes so thin that convection begins to have a dominant effect on heat transfer.
To intensify convective heat transfer, it is desirable that the thermal boundary layer be as thin as possible. With the development of flow turbulence, the boundary layer becomes so thin that heat transfer is carried out exclusively by convection.
To intensify convective heat transfer, it is desirable that the thermal boundary layer be as thin as possible. With the development of flow turbulence, the boundary layer becomes so thin that convection begins to have a dominant effect on heat transfer.
A similar mechanism of intensification of convective heat transfer, as shown by experiments using the optical inhomogeneity of the medium, also takes place with free convection. On rough pipes, the separation angle f of the vortices from the upper part of the pipe is larger, the angle P in which they rise upwards is wider, and the thickness b of the column of heated air above the pipe is greater. For water (tfK i & 20 C), the maximum heat transfer intensification by roughness also takes place and occurs at (Gr-Pr) md s 5 10e, which corresponds to a diameter of 10 mm.
In order to intensify convective heat transfer, high gas flow rates1 are desirable. However, an increase in speed is accompanied by an increase in gas resistance and an increase in energy consumption to overcome it.
At present, the intensification of convective heat transfer is considered the most promising and complex problem in the theory of transfer. It is also traditionally believed that this problem is most relevant for coolants, which are characterized by high values of Reynolds numbers.
As is known, the intensification of convective heat transfer is carried out in the directions of achieving the minimum thickness and maximum degree of turbulence of the boundary layer. For this purpose, intermittent or perforated ribs, profile ribs, ribs with turbulators are used. With relatively small values of the parameter h / 2 / ol, these measures must be carried out along the entire height of the rib. Apparently, there is some benefit in heat removal with equal hydraulic losses.
In this field of intensification of convective heat transfer, the works of prominent scientists G.A. Dreitser, E.K. Kalinin, V.K. Blinking, the materials of which are used in this paragraph.
The ultimate goal of applying the method of intensifying convective heat transfer is to build an apparatus with the smallest heat transfer surface area or with a minimum temperature difference at the lowest power consumption for pumping liquid. Since the use of any of the known methods of heat transfer intensification is accompanied, in addition to an increase in heat transfer, by an increase in hydraulic resistance, which increases the power consumption for pumping liquid, one of the main indicators of the apparatus is the efficiency of its convective surfaces.
In some cases, methods are used to intensify convective heat transfer during boiling on a rotating heating surface.
A consequence of the intensification of heat transfer processes is an increase in the heat transfer coefficient, which, with clean heat exchange surfaces, is determined by the heat transfer coefficients from the side of the heating and heated coolants. In many cases, the physicochemical properties of the heat carriers used differ significantly, their pressure and temperature, and heat transfer coefficients are not the same. So, the value of the heat transfer coefficient from the side of water α = 2000 ... 7000 W / (m 2 K), from the side of the gas coolant α ≤ 200 W / (m 2 K), for viscous liquids α = 100 ... 600 W / (m 2 K). It is obvious that the heat transfer intensification should be carried out from the side of the coolant, which has a small value of the heat transfer coefficient. With the same order of values of the heat transfer coefficients of heat carriers, heat transfer intensification can be carried out on both sides of heat transfer, but taking into account operational and technical capabilities.
Usually, the intensification of heat transfer is associated with an increase in energy costs to overcome increasing hydraulic resistance. Therefore, one of the main indicators characterizing the expediency of heat transfer intensification in heat exchangers is its energy efficiency. The increase in the intensity of heat transfer should be commensurate with the increase in hydraulic resistance.
The following main methods of heat transfer intensification are used:
designing rough surfaces and surfaces of complex shape, contributing to the turbulence of the flow in the near-wall layer;
the use of turbulent inserts in the channels;
increase in heat exchange surface area by means of fins;
impact on the coolant flow by electric, magnetic and ultrasonic fields;
turbulence of the near-wall layer by organizing fluctuations in the speed of the oncoming flow and its swirl;
mechanical impact on the heat exchange surface by its rotation and vibration;
the use of a granular nozzle both in a stationary and in a pseudo-moving state;
adding solid particles or gas bubbles to the coolant.
The possibility and expediency of using one or another method of intensification for specific conditions are determined by the technical capabilities and efficiency of this method.
One of the most widely used methods for intensifying heat transfer (increasing the heat flow) is the finning of the outer surface of pipes, provided that a coolant with a low value of the heat transfer coefficient is directed into the annular space.
Schemes of some devices used to intensify heat transfer in pipes are given in Table. 7.1.
7.1. Schemes of devices used for intensification
heat transfer
|
ribbing |
ribbing | ||
|
twisted |
Pipe with helical smoothly defined protrusions |
|
|
|
Continuous screw agitator |
Twisted pipe | ||
|
Annular channel type diffuser-confuser |
Alternating smoothly defined annular protrusions on the inner surface of a smooth pipe |
Vane swirlers, intermittent screw swirlers with a different shape of the central body, etc. are used. It should be noted that simultaneously with an increase in the heat transfer coefficient by 30 ... 40%, there is an increase in hydraulic resistance by 1.5-2.5 times. This is explained by the fact that the dissipation of energy during the disintegration of large-scale vortex structures (they arise when the flow swirls) significantly exceeds the generation of turbulence - to feed the weakening vortices, a continuous supply of energy from the outside is needed.
It has been established that under turbulent and transitional flow regimes, it is advisable to intensify turbulent pulsations not in the flow core, but in the near-wall layer, where the turbulent thermal conductivity is low and the heat flux density is maximum, because this layer accounts for 60 ... 70% of the available temperature difference "wall- liquid". The higher the R number r, the thinner layer it is expedient to influence.
The above recommendations can be implemented by creating in some way, for example, by knurling, alternating smoothly defined annular protrusions on the inner surface of a smooth pipe. For dropping liquids with P r= 2 ... 80 the best results were obtained at t sun /d int = 0.25 ... 0.5 and d sun / d int = 0.94 ... 0.98. So, at R e = 10 5, heat transfer increases by 2.0-2.6 times with an increase in hydraulic resistance by 2.7-5.0 times compared with the heat transfer of a smooth pipe. For air, good results were obtained at t sun /d in = 0.5 ... 1.0 and d sun / d in = 0.9 ... 0.92: in the transition region of the flow (R e = 2000 ... 5000) an increase in heat transfer 2.8 ... 3.5 times with an increase in resistance by 2.8-4.5 times (compared to a smooth pipe).
Methods of mechanical influence on the heat exchange surface and influence on the flow of electric, ultrasonic and magnetic fields have not yet been studied enough.
Copyright JSC "Central Design Bureau "BIBCOM" & LLC "Agency Book-Service" Moscow State Technical University named after N.E. Bauman V.N. Afanasiev, V.L. Trifonov HEAT TRANSFER INTENSIFICATION UNDER FORCED CONVECTION Guidelines for the course research work on the course "Methods of heat transfer intensification" Moscow Publishing house of MSTU im. N.E. Bauman 2007 Copyright OJSC Central Design Bureau BIBCOM & LLC Agency Book-Service UDC 536.24(076) LBC 31.31 A94 Reviewer N.L. Schegolev A94 Afanasiev V.N., Trifonov V.L. Intensification of heat transfer under forced convection: Method. instructions for course research work on the course "Methods of heat transfer intensification". - M .: Publishing house of MSTU im. N.E. Bauman, 2007. - 68 p.: ill. The main provisions of the theory of convective heat transfer and methods for intensifying heat transfer are described. The requirements for the implementation of experimental research and the design of a course research paper are formulated. For students of MSTU named after N.E. Bauman, studying in the specialty "Thermophysics". Il. 14. Bibliography. 24 titles UDC 536.24(076) BBK 31.31 Methodical edition Valery Nikanorovich Afanasyev Valery Lvovich Trifonov HEAT TRANSFER INTENSIFICATION UNDER FORCED CONVECTION Editor A.V. Sakharova Proofreader R.V. Tsareva Computer layout A.Yu. Uralova Signed for publication on 10.05.2007. Format 60×84/16. Offset paper. Pech. l. 4.25. Conv. oven l. 3.95. Uch.-ed. l. 3.45. Circulation 300 copies. Ed. No. 168. Order Publishing house of Moscow State Technical University. N.E. Bauman. 105005, Moscow, 2nd Baumanskaya st., 5. MSTU im. N.E. Bauman, 2007 Copyright OJSC "TsKB "BIBCOM" & LLC "Agency Kniga-Service" INTRODUCTION modern methods of calculating hydrodynamics and heat transfer during the movement of various devices in a viscous non-isothermal medium are impossible. The impossibility of using the equations directly to obtain exact solutions of transport processes in the boundary layer has led to the creation of various methods for their experimental study, including statistical methods. The issues of increasing the amount of heat removed in various technological processes, i.e., the intensification of heat transfer processes, have been and remain the most difficult. A significant increase in the number of publications on this topic indicates its extreme relevance. The basis of this course research work (KRW) is based on the results of fundamental research on heat and mass transfer processes conducted at the Moscow State Technical University. N.E. Bauman at the Department of Thermal Physics for several decades, as well as materials from leading research institutes and the latest achievements of domestic and foreign science in the field of heat and mass transfer. The existing and developed semi-empirical methods for calculating the boundary layer require a deeper experimental study of its structure. There are two approaches: classical (using traditional methods of diagnosing a boundary layer by average characteristics) and statistical (investigating the fluctuating characteristics of a turbulent boundary layer). CRW provides for experimental and theoretical studies of dynamic and thermal boundary layers by traditional methods (according to average characteristics). The work on the study of the boundary layer by classical methods is designed for sixth-year students who have mastered the study of computational heat transfer and hydrodynamics, convective heat transfer and the theory of the boundary layer. When performing work, the student must master modern methods of experimental study of hydrodynamics and heat transfer in laminar and turbulent fluid flow regimes, as well as methods for assessing the reliability of the results obtained. KRW is based on the experimental study of a specific process - the study of hydrodynamics and heat transfer in a forced gradientless flow around a flat plate. Experimental study of many complex processes, which include convective heat transfer, depending on a large number of individual factors, is extremely difficult. One of the means of solving such problems is the application of the theory of similarity, which makes it possible to process and generalize the results of experiments. The final result must be presented in a criterion form, and for this the student must master the theory of similarity well. 4 Copyright OJSC "Central Design Bureau "BIBCOM" & LLC "Agency Kniga-Service" THEORETICAL PART 1. Basic methods of heat transfer body and environment. Therefore, for practical calculations of a steady (constant in time) heat flux supplied (removed) to the surface of a body flown by a liquid or gas, the Newton–Richmann law is usually used: Q = αΔTA, (1) where Q is the heat flux that the body exchanges with the environment environment, W; A is the heat exchange surface, m2; ΔT is the temperature difference between the body and the environment, deg; α is the heat transfer coefficient, W/(m2 deg), indicating the intensity of the heat transfer process between the heat exchange surface and the environment. In fact, formula (1) does not reflect the real dependence of the amount of heat on temperature, physical properties and dimensions of bodies in thermal interaction. In essence, the application of this formula is some formal technique that transfers all the difficulties of calculating heat transfer to determining the heat transfer coefficient α, which usually depends to a lesser extent on the size of the heat exchange surface and on the temperature difference than the heat flux Q. When calculating heat transfer from one liquid medium to another through the wall separating them, in calculation practice, an expression similar to formula (1) is used: Q = kΔTA, (2) deg), which indicates the intensity of the process of heat transfer from one liquid to another through the wall separating them; ΔT is the difference between the average temperatures of liquids, deg. Dependences (1) and (2) show that in each particular case it is necessary to take into account the features characteristic of the heat transfer process under consideration. From the general course of the theory of heat and mass transfer, it is known that there are three main methods of heat transfer: thermal conductivity, convection and radiation. Thermal conductivity is the transfer of heat in a continuous material medium. The basic law of thermal conductivity is the Biot-Fourier law, according to which the heat flux density is directly proportional to the temperature gradient and is inversely directed to it: q = – λ(∂t/∂n), (3) where the thermal conductivity coefficient λ, W/(m deg) , is a thermophysical parameter indicating the ability of a body to conduct heat. The amount of heat per unit time at thermal conductivity Q = q A. When designing machines and apparatuses, it often becomes necessary to strengthen or weaken the transfer of heat through the wall. Reducing the intensity of heat transfer provides a reduction in heat losses through the wall or thermal protection of parts of machines and apparatus adjacent to hot surfaces. This problem can be solved by thermal insulation of hot surfaces. Reducing the size and weight of heat exchangers is associated with the need to intensify heat transfer processes, which can be carried out in various ways, including increasing the heat transfer surface with the help of fins. Convective heat transfer is the transfer of heat in a moving medium. Usually, the Newton-Richmann law (1) is used to determine the amount of heat transferred during convection. The task of increasing the amount of heat removed from the surface of the body, i.e. e. intensification of convective heat transfer6 Copyright OJSC "Central Design Bureau" BIBCOM " & LLC "Agency Kniga-Service" chi, has been and remains the most difficult, but also the most urgent task of the theory of transfer processes in a moving medium. The statement of the problem of heat transfer in a moving medium acquires a special meaning if it is considered in conjunction with the problem of energy consumption for the movement of the coolant. Under normal, practical conditions, the goal is to achieve the highest possible heat transfer rate with the lowest possible energy consumption. The situation, in which the desire to increase the intensification of heat transfer at any cost, is justified, should be considered as completely exceptional. In addition, it is obvious that certain properties of the heat exchange system can lead to intensification, for example, surface roughness obtained during conventional machining, surface vibration due to the rotation of machine parts or flow pulsations, an electric field present in electrical equipment, etc. Radiation is a transfer heat with the help of electromagnetic waves. In engineering practice, to calculate the heat flux in radiation processes, the Stefan–Boltzmann law is usually used: Q = εσ0T 4A, (4) where σ0 is the Stefan–Boltzmann constant, σ0 = 5.67 10–8 W/(m2 K4); ε is the degree of emissivity of the radiating body. It can be seen from formula (4) that the main methods of radiation intensification are aimed at increasing the parameters T, A, and ε. All of the above shows that the amount of heat that a body exchanges with the environment depends on many factors. These factors must be known in order to take them into account when using certain heat transfer processes in various power plants and in order to control them, i.e., intensify heat transfer or reduce heat removal. Thus, the intensification of heat transfer is an increase in the amount of heat removed in heat transfer processes. When considering methods for intensifying heat transfer under conditions of heat conduction, convection, and radiation, it must be remembered that in each specific case, as a rule, combined methods of intensification are used, taking into account the characteristic features of the process under consideration. 7 Copyright OJSC Central Design Bureau BIBCOM & LLC Agency Kniga-Service With the growth of energy capacities and production volumes, the dimensions of the heat exchangers (TOA) used increase significantly, which increases the requirements for the efficiency and reliability of their work. Obviously, by increasing the energy efficiency of thermal power plants by only a few percent by creating more compact heat exchangers, on a national scale, you can get significant savings in material resources: fuel, materials and metals, labor costs, etc. Thus, the development and creation of highly efficient compact cooling systems is an extremely urgent problem closely related to the intensification of heat and mass transfer processes, which is largely determined by the features of the flow around and hydraulic resistance of heat exchange surfaces. Since the invention of the first TOAs, the heat-releasing surfaces in them have been made from small-diameter pipes. Such pipes are still used in large quantities in the manufacture of TOA. However, a square meter of a heat exchange surface made of pipes is several times more expensive than a surface of the same area made of a thin sheet. From the 1960s to the present, the number of papers published on various aspects of heat transfer enhancement, including reports, articles, dissertations and patents, has steadily increased. This shows that heat transfer enhancement is currently an important special area for the study and development of heat transfer. 2. Intensification of convective heat transfer The intensification of convective heat transfer is currently perhaps the most complex and, in any case, the most urgent problem in the theory of transfer processes in a moving medium. It acquires special importance under the conditions of a gaseous coolant, which is characterized by a reduced intensity of exchange processes (in what follows, this particular case is mainly meant). The specificity of this problem lies in the fact that, considered separately on the basis of the study of heat transfer as an independent isolated process, it is essentially meaningless; it receives real content only in conjunction with the problem of energy consumption for the coolant advancement. In this case, under normal, practical conditions, the goal is to achieve the highest possible intensity of heat transfer with the lowest possible energy consumption. It is clear that only a joint analysis of the quantities introduced as a quantitative measure of the intensity of heat transfer and power consumption can provide rational grounds for evaluating the results achieved. However, it would be wrong to think that the matter is thus reduced to the study of two different autonomous and independently formulated problems, followed by a comparison of their solutions. It is extremely important that these problems are closely related to each other, since they characterize different aspects of the same process and their solutions determine quantitatively effects that are outwardly very heterogeneous, but due to a single physical mechanism. The deep similarity of both problems is manifested in the fact that under the simplest conditions, a special kind of relation operates - the Reynolds analogy, which establishes a direct and explicit relationship between the intensity of heat transfer, on the one hand, and the intensity of dissipative effects (responsible for power consumption), on the other. With the complication of the physical environment of the process, the Reynolds analogy loses its force and must be replaced by dependencies that are more mediated in nature and more complex in structure. Unfortunately, there is no theory yet that would make it possible to formulate these dependences for various specific conditions and would make it possible to find a general solution, of which they would become a particular case. However, consideration of the extremely extensive and diverse experimental material accumulated during the operation of various heat exchange devices has already relatively long led to the conclusion that the following trend exists: when the process becomes more complicated (i.e., when the conditions for which the Reynolds analogy is valid) are violated, the ratio between the consumed power and the achieved intensity of heat transfer becomes less favorable. Thus, the Reynolds analogy has acquired the meaning of a special kind of restriction, which establishes the lower, physically possible limit of the power expended at a given intensity of convective heat transfer. Thus, it was believed that it is under these simplest conditions, when the Reynolds analogy is in effect, that the most advantageous relationship between the intensity of heat transfer and the power consumed is realized. A more detailed and deep study of the mechanism of transfer processes showed that such an understanding of the Reynolds analogy is unsatisfactory. In certain cases, it correctly characterizes some aspects of the process under consideration, but it does not fully reflect the influence of the totality of the physical conditions of the process in all their actual complexity and cannot be accepted as a whole. In many cases, which are by no means devoid of practical interest, if the process conditions that satisfy the Reynolds analogy are violated, the relationship between heat transfer and hydrodynamic resistance actually deteriorates. This means that in a changed physical environment, such a mechanism of energy dissipation begins to operate, which is not connected in the same simple and obvious way with the transfer of heat in the direction normal to the surface. However, it does not follow at all from this that a situation leading to the opposite effect, i.e., a significant increase in heat transfer with a relatively insignificant increase (or even decrease) in the intensity of energy dissipation, is fundamentally impossible. In this sense, it is very instructive that in recent decades, under conditions of moderate forcing of heating surfaces, more favorable relationships have been obtained between the intensity of heat transfer and resistance. Thus, the Reynolds analogy cannot be attributed the meaning of the condition that establishes the lower limit of the required power. Even more favorable ratios are actually achievable, in which there are no internal contradictions. The fact that the processes of transfer of heat and momentum are carried out by the same carriers does not yet determine the type of relationship between the intensity of heat transfer and hydrodynamic resistance. Obviously, the temperature and velocity distributions formed within the transfer region should have a significant effect. The relation expressed in the form of the Reynolds analogy (the dimensionless heat transfer coefficient St is equal to the dimensionless friction stress on the surface) is valid only if the temperature field is similar to the velocity field. This requirement can be met with sufficient accuracy for the simplest form of the process – coolant flow along a surface that does not have longitudinal curvature (for example, flow inside straight pipes and channels of constant cross section, longitudinal flow around flat and tubular surfaces at Рr = 1). If the similarity of the fields is violated, the analogy becomes invalid and other relations begin to operate. It is much easier to cause deterioration in process conditions than to improve them. Any changes in the physical environment, due to random causes and leading to a violation of the similarity of temperature and velocity distributions, almost always cause changes in the ratio under consideration in an unfavorable direction. Only certain, specially created influences lead to the desired result. All of the above indicates the great complexity of the problem of intensifying convective heat transfer and convinces us that it would be unreasonable to place any hopes on empirical searches for its solution. It is, of course, possible to accidentally discover one or another intensifying effect, and this has happened many times. However, without a proper understanding of the physical nature of the detected effect, it is hardly possible to find ways to use it expediently and propose such means of reproducing it in a workflow environment that would not serve as a source of negative side effects. In order to distinguish an intensifying physical effect from a variety of heterogeneous phenomena, to determine the conditions and possibilities for its rational use, it is necessary to have a sufficiently detailed physical model of the process, supported to some extent by elements of the quantitative theory. Only in the last period, when the problem of heat transfer intensification turned out to be organically connected with the developing theory of transfer processes, was significant progress achieved. Nevertheless, the available information about the transfer processes is still insufficiently complete and cannot serve as a reliable physical basis for the development of a theory so complex in its specific direction. However, to date, a significant amount of data on intensifying effects has been accumulated, the use of which is quite appropriate. These effects have been carefully studied not only qualitatively, but also quantitatively and comprehended in a certain system of physical representations. Methods for their practical implementation are proposed and experimentally tested. It is not yet possible to create a universal theory explaining the totality of the data obtained so far, but nevertheless, some general considerations can be made that allow us to consider the results of the studies, at least from a qualitative point of view. The main idea is that intensifying effects in the near-wall region cause enhanced renewal of the medium, vigorous replacement of some of its elements by others, which, due to the different nature of the distribution of temperature and velocity, perform the function of heat carriers more efficiently than the function of momentum carriers. The more significant this difference, the more favorable or, conversely, worse the ratio between the intensity of heat transfer and hydrodynamic resistance. It is easy to understand that the physical environment corresponding to such a scheme of the process is very complex and very unusual. With the deepening of knowledge about the structure of the turbulent boundary layer and the mechanism of the transfer processes occurring in it, new possibilities will undoubtedly open up for creating more subtle and effective methods for influencing the properties of the process. Conditions that determine the optimal choice of methods for intensifying convective heat transfer. One of the main tasks in the creation of most modern heat exchange systems is to ensure the minimum dimensions and weight of TOA at given hydraulic resistances, flow rates, and coolant temperatures. Therefore, a very important moment in the design of TOA is the choice of the type of heat exchange surface. Obviously, the best surface will be the one that, under other identical conditions, provides the maximum heat transfer coefficient, i.e., the largest specific heat flux. Therefore, the intensification of heat transfer processes, especially in channels, is the most effective way to reduce the size and weight of heat exchange devices. A significant improvement in the characteristics of heat exchange devices, such as weight and size parameters, metal consumption, surface temperature, reliability and service life, can be achieved using methods of heat transfer intensification that are optimal for a particular case. However, the choice of the optimal method of heat transfer intensification is a difficult task, it is determined by many conditions, the most important of which are as follows. 12 Copyright JSC "Central Design Bureau "BIBCOM" & OOO "Agency Kniga-Service" 1. Goals and objectives of heat transfer enhancement for this particular class of TOA. 2. Permissible energy costs for the intensification of heat transfer and the type of available energy. 3. Hydrodynamic structure of the flow in which it is required to intensify heat transfer; the nature of the distribution of the density of heat fluxes or the temperature field in the coolant; valid ways to control the flow structure. 4. Manufacturability of TOA with heat transfer enhancement, convenience and reliability in operation. Let's consider these conditions in more detail. 1. Goals and objectives of heat transfer enhancement in this particular class of TOA. The tasks of intensifying heat transfer usually come down to reducing the weight and size parameters of the TOA or to reducing the temperature difference in it compared to their values, which are achieved under given conditions in the usual ways (by changing the flow rate and channel sizes, etc., depending on specific conditions). 2. Permissible energy costs for the intensification of heat transfer and the type of energy available for this. The analysis and design studies of the object as a whole make it possible to identify the permissible energy costs for pumping heat carriers through the heat exchange device. The type of energy is also usually known: as a rule, this is (at a given pressure drop) the required power at the pumps for pumping the coolant. There is a need for heat transfer enhancement methods that will ensure a reduction in the overall dimensions of heat exchange devices with constant total pressure losses for pumping the coolant through the TOA. Each type of heat exchange devices has its own criteria for evaluating the chosen method of heat transfer enhancement. The most common assessment of the intensification method is by comparing the ratios between the increase in heat transfer St/St0 and the resistance coefficients Сf /Сf 0: (St/St0) > (Сf /Сf0), where St and Сf are the Stanton number and the resistance coefficient for given conditions, and St0 and Сf0 – for standard conditions, respectively. 13 Copyright OJSC Central Design Bureau BIBCOM & OOO Agency Kniga-Service Intensification methods that ensure the fulfillment of the inequality (St/St0) > (Сf /Сf0) are especially effective, but their implementation is fraught with difficulties. The development of such methods was generally considered impossible for a long time. The final choice of the intensification method should be made on the basis of a complete comparative calculation of TOA, their design study, operational requirements, reliability and economic calculations, i.e. everything that was discussed above. 3. Hydrodynamic structure of the flow in which it is required to intensify heat transfer; the nature of the distribution of the density of heat fluxes or the temperature field in the coolant; valid ways to control the flow structure. Usually, to increase heat transfer, the turbulent regime of the coolant flow is used, therefore, knowledge of the hydrodynamic structure of the turbulent flow and the features of heat transfer in it makes it possible to establish areas in which an increase in the intensity of turbulent pulsations will have the greatest effect on the intensification of heat transfer, and, consequently, will help to choose the places and methods of influencing the flow. As a rule, these are areas that are quite close to the walls. The turbulent thermal conductivity in them is less than in the core of the flow, and the heat flux density is close to the maximum (for heat exchange with the wall). In non-circular channels with narrow angles, for example, in tight bundles of pipes or rods with their longitudinal flow, in triangular channels, etc., the flow structure during transitional and turbulent flow changes not only along the normal to the wall, but also along the channel perimeter . Along with the turbulent flow in the core of the flow and near the wall in the wide parts of the channel and in the corners, there may be zones with weak turbulence or even with a laminar flow regime. These zones account for a significant part of the channel surface. Therefore, when developing methods for intensifying heat transfer in such channels, it is necessary not only to look for ways of additional turbulence of the near-wall region in wide parts of the channel, but also specific ways for flow turbulence in the corner zones. 4. Manufacturability of TOA with heat transfer enhancement, convenience and reliability in operation. The most important conditions for the final choice of the heat transfer intensification method, especially for mass-produced HEAs and heat exchangers, are manufacturability and operational qualities: manufacturability of the production of the heat exchange surfaces themselves, manufacturability of assembly from them TOA, reliability and service life, impact on clogging and scaling compared to conventional base surfaces of these heat exchangers. This, of course, takes into account the economic effect that the use of this method of heat transfer intensification gives: reduction of metal consumption, weight, overall dimensions of TOA, etc. operation of the heat exchange device in real conditions. This is precisely what explains the fact that a considerable time usually elapses from the development of a heat transfer enhancement method to its widespread use in TOA. But on the other hand, only a few of the developed and published methods of heat transfer intensification can satisfy the conditions described above and find wide application, although in some specific cases, the use of some of them may be appropriate. In this regard, of greatest interest are works that not only offer comprehensively justified methods for intensifying heat transfer, but also develop a technology for manufacturing surfaces that intensify this process, as well as a technology for assembling heat exchangers with such surfaces. The main methods of intensification of convective heat transfer. Since in terrestrial conditions the most common method of heat transfer is convective heat transfer, heat transfer intensification is defined as an increase in the heat transfer coefficient by using various types of influence on the flow. However, regardless of the method of intensification, its main task is to reduce the corresponding thermal resistance. With thermal conductivity, a decrease in thermal resistance is achieved by influencing the heat transfer coefficients (under boundary conditions of the third kind) and on the internal thermal resistance of the wall by introducing fins, using a cooling effect, etc. The intensity of thermal conductivity is greatly influenced by the thermophysical properties of the wall materials, insulating materials, the conditions of contact between the individual layers of the wall, the geometric dimensions and shape of the heat exchange surface. When considering intensification processes for radiation, the methods of intensification are most often used by increasing the heat transfer surface and temperature, as well as by affecting the degree of surface emissivity. The largest number of heat transfer intensification methods is proposed for convective heat transfer. The main task in this case is to determine the heat transfer coefficient, which, obviously, explains the definition of intensification given above. No design problem has a ready answer. An engineer participating in the design and creation of new technology samples must clearly understand that one theory, no matter how advanced it is, is not enough and that it must be supported by experience, common sense and, if necessary, the flexibility of a compromise solution, especially when considering the main laws. , underlying simple, reliable and practically expedient methods of heat transfer intensification. The variety of modern technology, and in many cases its high cost, makes the study of these regularities doubly important. Passive and active methods of intensifying heat transfer under conditions of free and forced convection in both single-phase and two-phase media, as well as in the processes of heat conduction and radiative heat transfer, are known. Passive methods (which do not require direct energy input from the outside) include special physical and chemical surface treatment, the use of rough and developed surfaces, devices that provide mixing and swirling of the flow, methods of influencing surface tension, and adding impurities to the coolant. Active methods (requiring direct energy consumption from an external source) include mechanical effects, vibration of heat exchange surfaces, fluid flow pulsations, the use of electrostatic fields, coolant injection and suction, and the use of dispersed substance flows. Since most heat exchangers use a liquid or gaseous coolant that comes into contact with a solid surface during flow, the study of the influence of the latter on convective heat transfer is of great practical interest. Works devoted to various methods of heat transfer intensification show that the main methods are aimed at destruction or artificial turbulence of the boundary layer, since when a heat transfer surface interacts with a gas or liquid flow washing it, it is the boundary layer that grows on this surface that exerts the main resistance to heat transfer. The main task of the intensification of convective heat transfer is such an impact on the boundary layer, which would make it thinner or partially destroy it. An increase in the oncoming flow velocity reduces the thickness of the boundary layer, but is associated with a rapid increase in hydrodynamic resistance. The use of this simplest method of intensification is limited by the increase in energy costs. When flowing around smooth walls that do not have turbulizers near the surface, the Reynolds analogy operates, as already noted, which establishes a direct relationship between the intensity of heat transfer and surface friction. When flowing around heat exchange surfaces with more complex configurations than a smooth wall, the relationship between the power consumed and the heat transfer intensity achieved becomes more complicated. Situations are possible that lead to a significant increase in heat transfer with a slight increase in surface friction. In this sense, the relationship between the intensity of heat transfer and hydrodynamic resistance for surfaces operating on the principle of an external task or transverse flow turns out to be more favorable. A certain system of physical concepts and an understanding of the physical nature of heat transfer intensification make it possible to rationally use intensifying effects in heat exchanger designs. Intensifying influences are favorable when they cause an enhanced renewal of the environment in the boundary layer, an energetic replacement of some volumes of the environment with others. The more significant the difference in the distribution of temperature and velocity of particles of the working medium near the wall, the more favorable (or not more favorable) the ratio between the intensity of heat transfer and hydrodynamic resistance. To date, various methods of near-wall intensification of heat transfer have been developed, which have an important advantage over others: they have high energy efficiency due to turbulization of only the near-wall flow region. The flow is turbulent where the maximum temperature gradient occurs. As a result, the energy costs for pumping the coolant through the path are significantly reduced compared to the costs of turbulizing the entire flow. The intensity and efficiency of the heat transfer process depend on the shape of the heat exchange surface, the equivalent diameter of the channels, the surface roughness, the layout of the channels, which ensures optimal speeds of the working media, the temperature difference, the presence of turbulent elements in the channels, fins and some other design features. The main currently known methods of intensifying convective heat transfer are the following: a) the impact on the flow of the working medium by the shape of the heat exchange surface; b) impact on the flow of additional turbulence by roughness elements; c) an increase in the heat exchange surface area from the side of the working medium with a low heat transfer coefficient; d) mechanical effect on the heat exchange surface (surface vibration, pressure pulsation in the flow, mixing of the working medium); e) impact on the flow by a field (electromagnetic, acoustic); f) injection or suction of the working medium through a permeable heat-releasing surface; g) addition of solid particles or gas bubbles to the flow. The possibility of practical use of one or another method of heat transfer intensification is determined by its technical availability and technical and economic efficiency. An analysis of numerous experimental works devoted to the intensification of heat transfer allows us to conclude that the choice of the type, size and shape of turbulators was carried out (with rare exceptions) without sufficiently compelling justifications, and most importantly, without taking into account those specific conditions for operation in which it was supposed to use one or another type. heat transfer surface. As for attempts to analyze the mechanics of turbulent exchange under conditions of artificial flow turbulence, present a physical model of such a phenomenon and accurately describe it analytically, as far as is known, so far all they remain ineffective. The reason for this lies, in addition to objective difficulties (heat transfer under conditions of vortex, separated flows), mainly in the fact that most authors use the hydrodynamic analogy method to analyze thermal processes, which is obviously completely unacceptable under conditions of separated flows. The most effective are those methods of heat transfer intensification that most fully take into account the features of convective heat transfer, and for this it is necessary to know the structure of the flow in which heat transfer is to be intensified. 3. Analytical and experimental study of the structure of the boundary layer Basic provisions of the theory of convective heat transfer. Convective heat exchange between a moving medium and its interface with another medium (solid, liquid or gas), as already mentioned, is called heat transfer. The heat transfer process is called stationary if the temperature field in the liquid does not depend on time, and non-stationary if the temperature distribution in the flow depends on time. Depending on the cause of the movement of a fluid, free (natural) convection and forced convection are distinguished. Free (natural) convection is a convective heat transfer during the movement of a fluid under the action of an inhomogeneous field of body forces (gravitational, magnetic, electric). Forced convection is a convective heat transfer during the movement of a fluid under the action of external forces applied to the fluid inside the system, or due to the kinetic energy imparted to the fluid outside the system (pump, fan, aircraft). It is known from hydrodynamics that there are two modes of fluid flow: laminar and turbulent. In a laminar flow, fluid particles follow well-defined trajectories in the flow, all the time maintaining movement in the direction of the average flow velocity vector, and random disturbances arising in the flow quickly die out. With a turbulent flow, velocity pulsations occur in the flow, individual volumes of liquid begin to move across the flow, causing intense mixing of the liquid and, as a result, this leads to a significant intensification of metabolic processes (heat - heat transfer, substances - mass transfer). The main task of the theory of convective heat transfer is to establish a relationship between the heat flux density on the heat transfer surface, the temperature of this surface and the temperature of the liquid, in other words, the determination of the heat transfer coefficient, and the intensification of convective heat transfer is defined as any effect on the flow, leading to an increase in the heat transfer coefficient. To obtain quantitative patterns of the processes under study, two research methods are used. The first method is based on the experimental study of a specific process. The experimental study of many complex phenomena, which depend on a large number of individual factors, is an extremely difficult undertaking. Therefore, when setting up an experiment, in addition to a detailed study of the process under consideration, the task is always to obtain data for calculating other processes related to the process under study. One of the means of solving such a problem is the theory of similarity, which makes it possible to process and generalize the results of experiments so that they can be transferred from a model to a full-scale sample, to other initial cases. The similarity theory establishes the conditions for the similarity of physical phenomena and gives the rules for the rational association of physical quantities into dimensionless complexes (similarity criteria), the number of which is significantly less than the number of quantities of which they consist. These complexes reflect the joint influence of the totality of physical quantities on the phenomenon and can be considered as new generalized variables. Reducing the number of variables and using them in a complex form greatly simplifies the experiment and the generalization of its results. Such processes have the same physical nature and are described by the same basic equations and similar uniqueness conditions, and also have numerically equal defining similarity criteria of the same name. The similarity criteria, which include the desired values, are called determined. The similarity criteria, which are composed of values included in the uniqueness condition, are called defining. They can be calculated when the problem is formulated, without its solution or experimental study. Similarity criteria have a certain physical meaning and express the ratio of the scales of two specific effects that are essential for the phenomenon. In this work, the following similarity criteria are used. 1. Stanton number St = α ρu∞ C p or St = qst, ρu∞ C p (T∞ − Tst) where C p is the heat capacity of the liquid at P = const, J/(kg ⋅ K); ρ is the liquid density, kg/m3; u∞ is the fluid velocity at the outer boundary of the boundary layer, m/s; T∞ is the liquid temperature at the outer boundary of the boundary layer, K; Tst is the wall temperature, K. The Stanton number is the ratio of the heat flux into the wall qst to the convective flow that can be transferred by the fluid flow when its temperature decreases from T∞ to Tst. 2. Prandtl number Pr = ν , α where ν is the kinematic viscosity of the liquid, m2/s; α is the coefficient of thermal diffusivity, m2/s. The Prandtl number characterizes the ratio between the rate of exchange of mechanical energy in a fluid flow and the rate of exchange of thermal energy, or the ability of a fluid to transfer heat. The Prandtl number contains only the physical parameters of the medium, therefore it is a dimensionless physical parameter. 3. Reynolds number Re = u∞ l , ν where l is the characteristic length, m. The Reynolds number expresses the relationship between the inertial force and the internal friction force. At a certain critical value of the Reynolds number, the laminar flow of the liquid turns into a turbulent one, which significantly affects the intensity of convective heat transfer and resistance. Therefore, the Reynolds number is one of the main defining criteria in the theory of heat transfer. 4. Drag coefficient Cf /2 = τ st ρ∞ u∞2 . The drag coefficient is the ratio of the friction stress on the wall τst to the velocity head. The second method for obtaining quantitative patterns in the processes under study is a method based on solving a system of equations describing the phenomenon under study. In the case of a plane stationary flow of a compressible fluid, the following differential equations of the theory of convective heat transfer can be written: the continuity equation ∂ ∂ (ρ u) + (ρv) = 0; ∂x ∂y (5) equation of motion ⎥ + ⎢μ ⎥ ; 6 ∂u ⎞ ⎤ ∂ ⎡ ⎛ ∂u ∂v ⎞ ⎤ +v ⎟ =− + − + ρ⎜u ⎢μ 2 ⎥ + ⎢μ ⎥ ; (7) ∂y ⎠ ∂y 3 ∂y ⎣ ⎜⎝ ∂y ∂x ⎟⎠ ⎦ ∂x ⎣ ⎜⎝ ∂y ∂x ⎟⎠ ⎦ ⎝ ∂x Service” energy equation ⎫ ⎡ ∂ ρ ⎢u ⎣ ⎤ ∂P ∂ ∂ P ∂ ⎛ ∂T ⎞ ∂ ⎛ ∂ T ⎞ C T) + v (C T) ⎥ − u − v = ⎜ λ ⎟ + ⎜ λ ⎟ − ⎪ ( . ⎢⎜ ⎟ + ⎜ ⎟ ⎥ + μ ⎜ + ⎟, 3 ⎝ ∂ x ∂y ⎠ ∂x ⎠ ⎝ ∂ ⎠ ⎝ ∂y ∂x ⎠ 2 ⎣ 2⎤ ⎦ 2 ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎭ where u and v are the longitudinal and vertical components of the velocity vector, respectively. The system of equations (5)–(8) is solved jointly with the equation of state, the dependences of physical parameters on the state parameters, and the uniqueness conditions.To single out a specific process from an infinite number of convective heat transfer processes, it is necessary to formulate uniqueness conditions that contain geometric, physical, initial and boundary conditions.Geometric conditions determine the shape and dimensions of a solid body, on the surface of which the parameters q or T should be determined. Some conditions determine the numerical values of the physical parameters of the liquid μ, ρ, Ср, λ, as well as internal sources of heat in the liquid flow. The initial conditions are given in the form of the initial distribution of temperatures and velocities. The boundary conditions determine the conditions on the heat exchange surfaces and at the flow boundaries. The horizontal component of the velocity on the heating surface is assumed to be zero (the condition of the liquid sticking to the wall). The vertical velocity component on the heating surface in the general case can be a non-zero specified value. Thermal boundary conditions usually include setting the temperature on the heating surface or heat fluxes. There are three ways to specify thermal boundary conditions. Under the boundary condition of the first kind, the temperature distribution on the heat exchange surface is given. Under the boundary condition of the second kind, the distribution of the specific heat flux on the heat exchange surface is known. 23 Copyright OJSC Central Design Bureau BIBCOM & LLC Agency Kniga-Service Boundary condition of the III kind connects the temperature of the heat exchange surface with the ambient temperature through a given value of the heat transfer coefficient from the wall to this medium. The analytical solution of the complete system of differential equations (5) - (8) is associated with exceptionally great mathematical difficulties and is possible only for some special cases. Therefore, in 1904, L. Prandtl proposed to simplify the complete system of differential equations (5) - (8). When a viscous fluid with high Reynolds numbers moves, the effect of viscosity manifests itself differently in the immediate vicinity of the streamlined surface and far from it. Near the surface, due to the adhesion of the liquid to the solid wall, significant transverse velocity gradients arise. With distance from the wall, the change in the longitudinal velocity along the normal to the surface of the body decreases: the action of viscous forces becomes vanishingly small already at a relatively small distance from the wall. Therefore, when a fluid moves with large Reynolds numbers, the entire flow can be divided into two regions: the boundary layer region, where the influence of viscosity is significant, and the outer region of potential flow, where the influence of viscosity is very small. Such a division of the flow into the boundary layer and the external flow greatly simplifies the problem, since it allows considering each of the flow regions separately with subsequent merging of the obtained solutions. In addition, under these conditions, inertial forces in the external flow prevail over the forces of viscous friction, and therefore the equations of an ideal fluid can be used to describe the motion. The mathematical description of fluid motion in the boundary layer is also simplified. The fluid layer adjacent to the wall, in which the velocity varies from zero at the wall to some constant value in free flow, is called the dynamic boundary layer. If heat exchange occurs between the fluid flow and the surface of the body, then a thermal boundary layer is formed near the surface of the streamlined body, i.e., a region in the immediate vicinity of the wall in which the temperature changes from the values on the wall to the corresponding value in the external flow. In the boundary layer, the velocity or temperature asymptotically approach the corresponding values in the potential flow; therefore, the boundary layer thickness is taken to be the distance normal to the surface at which the velocity or difference flow temperatures and wall temperatures differ by 1% from the corresponding values in the external flow (Fig. one). Despite its insignificant thickness in comparison with the characteristic external dimensions of a streamlined body, the boundary Fig. 1. The boundary layer plays the main role in the processes of dynamic and thermal interaction of the fluid flow with the surface. All hydrodynamic and thermal resistances are concentrated in the boundary layer. Therefore, in order to intensify heat transfer, leading to an outstripping increase in the heat transfer coefficient compared to the resistance coefficient, it is necessary to have a good understanding of the structure of the boundary layer. If we make a comparative assessment of the terms of the system of differential equations (5) - (8) according to the assumptions of L. Prandtl (that the transverse dimensions and velocities in the boundary layer are small compared to the longitudinal ones) and discard the terms of the second order of smallness, we can obtain approximate differential equations dynamic and thermal boundary layer. For the case of a flat stationary boundary layer, the system of differential equations takes the following form: the continuity equation ∂ ∂ (ρu) + (ρv) = 0; ∂x ∂y (9) y ⎠ ∂x ∂y ⎜⎝ ∂y ⎟⎠ ⎝ ∂x (10) ∂P = 0; ∂y (11) energy equation 2 ⎡ ∂ ⎤ ⎛ ∂u ⎞ ∂ ∂P ∂ ⎛ ∂T ⎞ ρ ⎢u C pT + v C pT ⎥ − u = ⎜λ ⎟ + μ⎜ ⎟ . ∂y ∂x ∂y ⎝ ∂y ⎠ ⎝ ∂y ⎠ ⎣ ∂x ⎦ ( ) ( ) closed. An analysis of equations (9) - (12) makes it possible to detect the similarity between the velocity and temperature distributions in the boundary layer when an incompressible fluid flow with constant physical properties flows around a flat impermeable plate if the Prandtl number is equal to one. In this case, the equations of the dynamic and thermal boundary layers will coincide, and, consequently, the distributions of velocities and temperatures in the boundary layer will also coincide: Т − Т st u = . u∞ T ∞ − T st This result is of great practical importance, since for most gases the Prandtl numbers are close to unity. In this case, one can come to an important conclusion about the analogy in the processes of momentum and heat transfer (Reynolds analogy): Сƒ /2 = St. (13) This analogy is also preserved for Pr ≠ 1. In the case of an incompressible fluid flow with constant physical properties, the dynamic boundary layer equations are solved independently of the equations of the thermal boundary layer. However, despite the fact that the system of differential equations of the boundary layer (9) - (12) is simpler than the corresponding system of complete differential equations (5) - (8), the exact solution of equations (9) - (12) is possible only for a very limited number of assignment laws external flow velocity, when partial differential equations of the boundary layer can be reduced to ordinary differential equations. In this regard, approximate methods for solving differential equations of the boundary layer, based on the use of integral relations between momenta and energy, become of great importance. The approximation of these methods lies in the refusal to satisfy the differential equations for each value of the transverse coordinate of the boundary layer. In the integral methods for solving the boundary layer equations, they are valid only on average over the thickness of the boundary layer when the boundary conditions are satisfied both on the wall and on the outer boundary. Integral equations of momentum and energy are obtained from differential equations of motion, continuity and energy (9) - (12) by integrating them over the thickness of the boundary layer and express the law of conservation of momentum and energy for the entire section of the boundary layer. For the case of a flat stationary boundary layer, the integral relations of momenta and energy have the form ∗ + 1 − M ∞2 ⎥ = St, t ⎢ dx u∞ dx ⎣ ΔT∞ dx ⎦ (15) where the form parameter of the boundary layer is H = δ*/δ**; momentum loss thickness ∞ ρu ⎛ u ⎞ 1− ⎜ ⎟⎠ dy; ρ u u ⎝ ∞ ∞ ∞ 0 δ∗∗ = ∫ (16) ⎝ u∞ ⎠ 0 (17) shape parameter characterizing the aerodynamic flow curvature, f = δ∗∗ du∞ ; u∞ dx Mach number M = u∞ /а; energy loss thickness δ∗∗ t ∞ T − T st ⎞ ρu ⎛ 1− dy; ⎜ ρ u ⎝ Т ∞ − Т st ⎟⎠ 0 ∞ ∞ =∫ (18) temperature difference between flow and wall ΔТ = Т – Тst. The upper limit of integration in the expressions for the parameters δ and δ∗∗ (16) - (17) and in the expression for δ∗∗ t (18) can be replaced by the thickness of the dynamic and thermal boundary layers, respectively, and no significant errors will be introduced into the calculation. The quantities δ∗ , δ∗∗ and δ∗∗ t are important calculated characteristics of the boundary layer. The displacement thickness, as follows from the equality layer due to the braking effect of friction forces during the flow of a real fluid. As can be seen in fig. 2, the displacement thickness δ∗ , in contrast to the thickness of the boundary layer δ, is a quite definite value. The expression for the momentum loss thickness δ∗∗ (16) can be written as ∞ ρ∞ u∞2 δ∗∗ = ∫ ρ u (u∞ − u)dy. 0 By analogy with the displacement thickness, it is possible to determine the momentum loss thickness δ∗∗ as a segment through which, during the flow 2. Determining the displacement thickness δ* of an ideal fluid, a second momentum would pass, equal to the loss of momentum in the boundary layer section due to the braking effect of friction forces. To determine the thickness of energy loss, we rewrite expression (18) in the following form (Fig. 3): = ∫ ρu (T − Tst) dy. 0 Then the thickness of the energy loss can be defined as a segment through which a second amount of energy would pass during the flow of an ideal fluid with a temperature difference (T∞ − Tst), Fig. 3. Determination of the energy loss thickness δ∗∗ t equal to the energy loss in the boundary layer cross section during the flow of a real fluid. The convenience of using the parameters δ∗ , δ∗∗ and δ∗∗ t as scales lies in the fact that, unlike the thicknesses of the boundary layer δ and δt, the integral thicknesses are not related to representations of the boundary layer of finite thickness. In this case, the structure of the energy and momentum equation (13) and (14) shows that the quantities δ∗∗ and δ∗∗ t are of the most significant importance. Therefore, it is convenient to construct the characteristic Reynolds numbers of the dynamic and thermal boundary layers from the above-mentioned thicknesses: Re∗∗ = u∞ δ∗∗ ; ν∞ Re∗∗ t = u∞ δ∗∗ t. ν∞ Introducing them into the integral equations (14) and (15), instead of losing momentum and energy after simple transformations, we obtain: Book-Service» ⎛ Cf dRe∗∗ + f (1 + H) Re L = ⎜ dX ⎝ 2 ⎞ ⎟⎠ Re L ; (19) Re∗∗ dΔT∞ dRe∗∗ t + t = StRe L . ΔT∞ dX dX u∞ L – ν the Reynolds number constructed from the local value of the velocity at the outer boundary of the boundary layer and the characteristic size L of the streamlined surface; ΔT∞ = T∞ - Tst - temperature difference. Equations (14) and (15) were obtained without any assumptions about the nature of the fluid flow in the boundary layer. Therefore, they are valid for both laminar and turbulent boundary layers. Integral relations (14) and (15) can be solved if the so-called laws of friction and heat transfer are known, which in the general case can be represented as Here X = x/L is the dimensionless longitudinal coordinate; Re L = () ~ f = f Re∗∗ ; f; M0; Tst /T ∞ ; . ..; () St = f Re** st; 1/ ∆T∞ ; dΔT∞ / dx; M0; Tst /T ∞ ; ... . The form of these functions depends primarily on the fluid flow regime in the boundary layer. For laminar flow, the laws of friction and heat transfer can be obtained analytically under certain boundary conditions. For a turbulent flow regime, the laws of friction and heat transfer are obtained on the basis of semi-empirical theories of turbulence with the involvement of experimental data. As shown by numerous experimental data obtained by different authors, the laws of friction and heat transfer are conservative when the boundary conditions change. Therefore, the dependences obtained for “standard” conditions, i.e., for the case of a gradientless flow of an incompressible fluid around a plate with a constant temperature on the wall, can be used under more complex conditions. 31 Copyright OJSC Central Design Bureau BIBCOM & OOO Agency Kniga-Service All the variety of boundary conditions is quite fully taken into account when integrating the momentum and energy equations. Heat transfer and friction in a laminar boundary layer. For a flat impermeable plate flown by a stationary incompressible fluid flow with constant physical properties at a constant temperature of the plate surface, the integral momentum and energy relations (14) and (15) take the form dδ∗∗/dx = Сƒ0/2; dRe∗∗/ dRex = Cƒ0/2; (20) dδt∗∗/dx = St0; (21) dRet∗∗/ dRex = St0. For the first time the solution of the dynamic problem for this case was found by Blasius. As a result of the exact solution of equations (5) - (8), he obtained an expression for the distribution of the local value of the friction coefficient along the plate in the form line 1 in Fig. 4) in the form C f0 = 0.44 Re∗∗ (23) . A similar solution of the energy equation gives the dependence of the Stanton number on the Reynolds number, built along the longitudinal coordinate, in the form St 0 = 0.332 Re x 3 Pr 2 . (24) Substituting (24) into (20) and assuming that the boundary layer grows from the leading edge of the plate, after integration we obtain Re∗∗ t = 32 0.664 Pr 2/3 Re x . (25) Copyright JSC "Central Design Bureau "BIBCOM" & LLC "Agency Book-Service" Pic. Fig. 4. Laws of friction in the boundary layer on a flat plate. Fig. 5. Laws of heat transfer in the boundary layer on a flat plate 33 Copyright JSC "Central Design Bureau "BIBCOM" & OOO "Agency Kniga-Service" Substituting (25) into (24), we obtain the law of heat transfer on a flat plate (line 1 in Fig. 5) St 0 = 0.22. 1/3 Re∗∗ t Pr (26) In addition, when the velocity and temperature profiles are represented as an exponential function, they have the form u/u∞ = (y/δ)n, ΔT/ΔT∞ = (y/δт)n , where n = 1/2 for a laminar boundary layer. Heat transfer and friction in a turbulent boundary layer and its structure. As is known, the transition from a laminar flow regime to a turbulent one occurs at a certain value of the Reynolds number, called the critical one. At Reynolds numbers exceeding critical values, the laminar flow becomes unstable to small perturbations and passes into turbulent flow. The laminar or jet-like structure of the flow completely disappears, turbulent eddies form and disintegrate, and the velocity at any point in the flow changes in time both in magnitude and in direction. From the point of view of the flow of exchange processes, the most significant circumstance is that in this case the transfer of momentum, heat, and matter across the main flow is significantly intensified. Based on numerous experiments, it has been established that in the boundary layer the critical Reynolds number depends on many factors: on the change in pressure at the outer boundary of the boundary layer, the degree of turbulence of the external flow, the state of the surface, its heating, etc. So, on a plate with a sharp leading edge , blown by the air flow, the transition of the laminar form of the flow into the turbulent one occurs at a distance x from the leading edge, determined by the equality fluid motion theory of turbulent flow is still in an unsatisfactory state. However, despite this, with the statistical approach, the movement of a fluid is not devoid of a certain degree of order. In statistical analysis, attempts are abandoned to follow the movement of individual fluid particles and, consequently, attempts to determine the turbulent tangent from the equations of motion of individual particles, and focus on the correlation of the series experimental values characterizing the turbulent flow. Only a few characteristics of a turbulent flow can be determined analytically (for example, the thickness of a turbulent boundary layer on the outer surface of a body). All our conclusions regarding turbulent flows will be limited due to the conditions of experimental observations and measurements. First, we will try to describe a turbulent flow (or a turbulent boundary layer) qualitatively, and then, using a simple model of turbulent momentum exchange and experimental data, we will move on to quantitative characteristics. On fig. 6 shows some of the phenomena observed in a turbulent boundary layer. In the area immediately adjacent to the 6. Turbulent flow near the wall, flowing towards the wall, the movement of the fluid is predominantly laminar and the velocity increases steeply. Somewhat farther from the wall, the flow becomes unsteady and finally reaches a region where the entire flow is involved in turbulent motion. Through experimental studies, it was found that the laminar region is not completely unperturbed. Comparatively large fluid elements adjacent to the wall, having a low velocity, periodically break away from the surface and move approximately along the trajectory shown in Fig. 6. Getting into a developed turbulent region, they are destroyed, which leads to a characteristic pattern of turbulence dissipation. The mechanism of this phenomenon is not completely clear yet, but it is probably a consequence of the instability of the fluid in the laminar region. It is also clear that the element of fluid detached from the surface is replaced by a fluid with higher energy flowing from a region remote from the surface. Apparently, it is this liquid that brings the energy necessary to separate the liquid element from the surface. In any case, in the core of the flow, turbulence is generated and maintained by fluid elements that come from the wall. Shown in fig. 6 phenomena occur relatively close to the wall. It is quite probable that the time-averaged local velocity in this region depends mainly on the conditions at a given point and its immediate vicinity and does not depend significantly, for example, on the distance to the opposite wall of the channel or on the shape of its cross section. Therefore, the quantities on which the time-averaged velocity can depend and which can be measured in the experiment are the distance from the wall y, shear stress on the wall τ0, kinematic viscosity ν, and density ρ: u = f(y, τ0, ν, ρ) . With the help of dimensional analysis, this equation is reduced to the following relation between dimensionless groups: u/(τ0/ρ)0.5 = f . (27) To shorten the notation, the dimensionless groups in equation (27) are denoted as u+ and у+ (these are the dimensionless velocity and the dimensionless distance from the wall, respectively): u+ = u/uτ and y+ = y uτ/ν, where the parameter uτ = (τ0 /ρ)0.5 is sometimes called dynamic speed, since it has the dimension of speed. Then equation (27) takes the form u+ = f (y+). (28) If all significant variables were taken into account, then equation (27) will show that when measuring the velocity profile in a turbulent flow in a wide range of Reynolds numbers, the experimental data in the u+, y+ coordinates should fall on one common curve. 36 Copyright OJSC Central Design Bureau BIBCOM & OOO Agency Kniga-Service For a purely laminar flow, it can be easily shown that equation (27) is indeed valid. Indeed, in this case, the shear stress at any point in the flow is determined by Newton's equation: τ = μ (du/dy) = ρν (du/dy), or τ/ρ = ν (du/dy). (29) It is known that in the case of a stabilized gradientless flow, the tangential stresses change linearly from a certain value on the wall to zero in the undisturbed flow. However, in the near-wall region, the shear stress slightly differs from the stress τ0. Therefore, in this region τ0 ≈ ρν (du/dy). We integrate this dependence and reduce it to a dimensionless form: du = (τ0/ρν) dy; u = (τ0/ρν) y + С; u/(τ0/ρ)0.5 = + С. If u = 0 for y = 0, then C = 0 and we get a simple dependence u+ = y+. (30) For a turbulent flow, only the form of the function u+(y+) changes. In a turbulent flow, the main movement is superimposed by a chaotic pulsating movement of individual parts of the fluid. Therefore, to create a mathematical model of turbulent motion, it is usually represented as the sum of the average and fluctuating motions: ui = u + ui′, (31) where u is the average velocity in time for a fixed point in space; ui′ is the fluctuating component of the velocity. The time interval is chosen so large that the time-averaged value of the pulsating velocity component will be zero ui′ = 0. Velocity pulsations cause pulsations in the flow of pressure, density, temperature, concentration, etc. The relationship between the pulsation components and the averaged values of these quantities is determined by formulas similar to expression (31). Substituting into the equations of system (9) - (12) the instantaneous values of the parameters defined by equality (31) and averaging them, we obtain a system of differential equations describing the averaged stationary turbulent flow of a fluid. Carrying out a comparative assessment of the values of the terms included in the resulting system of differential equations and keeping the largest terms of the same order in them, we obtain, as in the case of a laminar boundary layer, the following system of equations for a plane stationary turbulent boundary layer: the continuity equation ∂ ∂ (ρu ) + (ρv) = 0; ∂x ∂y (32) equations of motion ρu ∂u ∂u ∂P ∂ ∂u + ρv =− + (μ − ρu"v"), ∂x ∂y ∂x ∂y ∂y (33) ∂P / ∂ y=0; energy equation ρu ∂x ∂y ∂x ∂y ⎝ ∂y ⎝ ∂y ⎠ ⎠ (34) that additional turbulent friction stresses arise in the turbulent boundary layer τ t = − ρu ′ v ′ (35) qt = − ρС p v" T" , (36) and heat flow called Reynolds. These turbulent transport components cannot be determined by solving the system of equations (32) - (34) and the boundary conditions drawn up for the average values of the quantities. The integral equations of motion and energy of a turbulent boundary layer are derived from equations (32) - (34) in exactly the same way as in the case of a laminar boundary layer, and have the same form (14) - (15). However, for a turbulent boundary layer, the laws of friction and heat transfer cannot be obtained analytically by solving the system of differential equations (32) - (34), since this system is not closed. Therefore, to solve the integral equations (14) and (15), it is necessary to use either the empirical laws of friction and heat transfer obtained on the basis of an analysis of the available experimental data, or the laws obtained using semi-empirical theories of turbulence. Semi-empirical theories of turbulence involve the use of hypotheses relating the turbulent friction stress and heat flow with the parameters of the mean flow, which makes it possible to close the system of equations of the turbulent boundary layer (32) - (34). The hypothesis proposed by Prandtl turned out to be the most effective in calculating turbulent flows in the boundary layer. He suggested that the velocity pulsation normal to the streamlines of the averaged motion is of the same order as the longitudinal velocity pulsation and is proportional to the difference in velocities between the layers of the liquid: u" ≈ v" ≈ l ∂u. ∂y (37) It should be expected that in the region immediately adjacent to the wall, equation (30) is also valid for turbulent flow. The general nature of the turbulent velocity profile in the region far from the wall can be determined using the Prandtl mixing path theory. Despite the fact that this theory is based on a rather crude model of turbulent momentum exchange, it still sheds some light on the actual nature of transport in turbulent flows. There are other theories of turbulent transport, but we will use the Prandtl theory, since it can be used in the most analytical way to obtain the logarithmic velocity profile experimentally observed in almost all turbulent boundary layers. Let us assume that a liquid particle δm moving in the x direction with an average velocity u, due to the pulsation component of the velocity v" has traveled a distance l in the y direction (Fig. 7). Since there is a velocity gradient in the y direction, the average velocity 7. The model of the process of turbulent exchange of momentum in the new position is equal to u + δu Now suppose that on the path l the particle δm does not gain or lose momentum, and after it has traveled the entire distance l, there is a complete exchange of momentum by viscous interaction particles with the surrounding liquid. We will call the distance l the mixing path. In order to satisfy the continuity equation, the other element of the liquid must obviously move in the opposite direction. It is this movement of the elements of the liquid in the direction transverse to the main flow that determines the mechanism of turbulent transfer of momentum, heat and matter.The momentum carried by a liquid particle of mass δm in the x direction is equal to δmδu.If the process the wasp flows in time δθ, the momentum transfer rate is δmδu / δθ. Therefore, according to the momentum theorem, the tangential friction force acting between the fluid layers is F= δm δu. δθ If the area on which this force acts is equal to A, then the turbulent shear stress is τ= F 1 δm = δu. A A δθ If l is small, then δu ≈ l (du dy). The parameter (δm/δθ) is the mass flow rate of the fluid. According to the continuity equation (1/А)(δm/δθ) = |v′| ρ, where |v′| is the corresponding average pulsating velocity component in the positive direction of the y axis. Substituting this dependence into the equation for τ, after transformations we obtain τ/ρ = |v′| δu = (l |v′|)du/dy. (38) Note that this equation is written in the same form as equation (29) for shear stress in laminar flow. Let us determine the kinematic turbulent viscosity νт according to the relation τ/ρ = νт (du/dy). (39) Kinematic turbulent momentum transfer νт is a turbulent analogue of kinematic viscosity ν characterizing molecular momentum transfer. Both quantities have the same dimension. However, an important difference between these quantities is that νt is not a physical constant of the fluid, but depends on the pulsating velocity component and the length of the mixing path, i.e., on the degree and scale of turbulence. If only molecular momentum transfer occurs in the near-wall region, equation (29) should be used to calculate the shear stress. But for all flow points sufficiently remote from the wall, according to the considered model of turbulent momentum exchange, equation (39) is valid. Obviously, there must also be an intermediate region in which both molecular and turbulent momentum transfer occurs simultaneously. In this case, the total shear stress should be equal to the sum of the stresses determined by equations (29) and (39): τ/ρ = (ν + νt) (du/dy). (40) The velocity profile in a turbulent flow can be determined if some assumptions are made regarding the length of the mixing path l and the modulus of the fluctuating velocity component |v′|. Using his assumption (37), Prandtl wrote the transverse velocity fluctuation as |v′| = K1 |u′| and, on the basis of similarity considerations, came to the conclusion that |u′| = K2 δu = K2ldu/dy. After including all the constants in the unknown l, he obtained the expression τ/ρ = (l 2du/dy) (du/dy). (41) Then Prandtl assumed that the length of the mixing path l is directly proportional to the distance from the wall: l = k y. Then equation (41) takes the form 2 ⎛ du ⎞ τ = k 2 y2 ⎜ ⎟ . ρ ⎝ dy ⎠ In this equation, shear stress τ changes from the maximum value on the wall to zero in the core of the flow (in the case of a stabilized flow in a round pipe, near the pipe axis). In the region not too far from the wall, where the main change in velocity occurs, the value of τ differs little from the value on the wall τ0. Then approximately it is possible to write down 42 Copyright OJSC “Central Design Bureau “BIBCOM” & LLC “Agency Kniga-Service” 2 ⎛ du ⎞ τ0 = k 2 y2 ⎜ ⎟ ; ρ ⎝ dy ⎠ du 1 τ0 = . dy ky ρ Introducing u+ and y+ , we have du + 1 = +. + dy ky Integrating this equation, we obtain the following expression for the velocity distribution: u+ = 1 ln y + + C. k (42) The logarithmic dependence of u+ on y+ (42) was also obtained by other researchers, but they relied on somewhat different assumptions . Thus, if the main assumptions of the considered model of turbulent momentum transfer are valid, it can be expected that the measured turbulent velocity profiles in the coordinates u+, y+ form a single universal curve, which is logarithmic in most of the flow cross section and approaches linear in the near-wall region. Similar dependences have indeed been established experimentally. On fig. Figure 8 shows a three-layer scheme approximating numerous experimental data (which are not shown in the figure). Experimental data obtained for flows in round pipes and in turbulent boundary layers on the outer surfaces of bodies give similar results. At very small values of y+, the dependence u+(y+) corresponds to equation (30), while at y+ > 25...30 it is well approximated by equation (42). Recall that equation (42) was obtained under the assumption of a constant shear stress and it cannot be expected that it will be valid for the region near the pipe axis (or in the outer region of the turbulent boundary Fig. 8. Logarithmic velocity profile in a turbulent boundary layer with an external flow around), where the shear stress tends to zero. Therefore, somewhat unexpected is the good agreement between the measured velocity profiles and the logarithmic one over the entire cross section up to the pipe axis. Modern ideas about the structure of a turbulent boundary layer are based on its division into regions that differ from each other in the nature of the fluid flow. In the immediate vicinity of the wall, there is a region of a viscous sublayer with a thickness of about 1% of the total thickness of the boundary layer, in which the processes of molecular transfer play the main role. The viscous sublayer is separated from the fully developed part of the turbulent boundary layer by a transition region, which occupies 2–3% of the thickness of the entire layer. In the transition region of the flow, the laminar friction stress is commensurate with the turbulent one. In a fully developed region of a turbulent boundary layer, turbulent friction is critical. The researchers proposed universal turbulent velocity profiles near the wall in the form of one, two or three algebraic equations. The most commonly used model is described by three equations. In the three-layer scheme at y+< 5 опытные данные хорошо соответствуют уравнению (30). Эту область, где νт = 0, назвали ламинарным подслоем. При у+ >30 experimental data are in good agreement with the logarithmic curve, i.e., equation (42), if we assume that νt >> ν. This region has been called the turbulent core. The area in which the influence of both νt and ν is significant was called the intermediate (buffer) layer. The complete universal velocity profile is described by the following system of equations: y+< 5, u+ = у +; (43) 5 < у + < 30, u + = – 3,05 + 5,00 ln у +; (44) у + >30, u + = 5.2 + 2.5 ln y +. (45) According to the three-layer scheme, the function νт is not continuous and the velocity profile u+ has breaks. However, this model clearly shows the difference between the mechanisms of momentum transfer in each zone. If the shear stress distribution is known or postulated, then using equation (40) it is easy to determine the values of νt in any zone. When developing various methods for enhancing heat transfer, it is very important to know in which part of the boundary layer the main hydrodynamic and thermal resistances are concentrated. According to V.K. Blinking , the fraction of thermal resistance of individual layers in a three-layer scheme with a turbulent flow regime in a pipe at Re ≥ 104 is: for a viscous sublayer (y+ = y uτ/ ν< 5) – 32,3 %; для переходного слоя (y+ = 5...30) – 52 %, для ядра потока – 15,7 %. При турбулентном течении даже в гладких каналах основная часть гидравлических потерь расходуется на порождение турбулентности, которая происходит как раз около стенки в зоне y+ < 50...60. Изучение структуры турбулентного потока и механизма переноса теплоты в нем показали, что в переносе теплоты существенную роль играют крупномасштабные пульсации, направленные из ядра потока к стенке как результат нелинейного взаимодействия ядра потока со стенкой. При этом происходит перенос крупных масс теплоносителя из ядра потока к стенке и об45 Copyright ОАО «ЦКБ «БИБКОМ» & ООО «Aгентство Kнига-Cервис» ратно, возрастает количество выбросов от стенки, стимулирующих порождение турбулентности. Однако крупные турбулентные пульсации возникают в зоне, где y+ >60 due to coolant emissions from the wall into the flow core. Further, large velocity pulsations, alternating with pressure pulsations, break up into smaller ones and transfer their energy to them, which eventually dissipates into the thermal energy of the flow. Since any additional flow turbulence is associated with additional energy costs, the choice of the place and method of additional flow turbulence is decisive in the development of effective methods for heat transfer intensification. Therefore, it is obvious that such an intensification method would be the most effective, which would provide additional turbulence of only near-wall liquid layers under the condition y+ ≤ 30...60, without turbulizing the flow core. It can be expected that just such a method of heat transfer intensification will provide a significant increase in the St number with a moderate increase in the value of Cf, i.e., it will ensure the fulfillment of the inequality (St/St0) > Cf /Cf 0). Laws of friction and heat transfer. In practical calculations, the power dependence of the distribution of velocities and temperatures in the boundary layer is often used: u/u∞ = (y/δ)n, ΔT/ΔT∞ = (y/δт)n (Fig. 9) the sufficiently exact power law of friction (C f0 = B Re∗∗) −m (47) . In the range of Reynolds numbers 5 ⋅ 105< Reх < 107 экспериментальные данные дают значение n, равное 1/7, и закон трения в виде выражения (см. рис. 4, линия 2) (С f0 = B Re∗∗) −m = 0,0252 Re∗∗0,25 . (48) Подставляя (48) в уравнение (19) и интегрируя его, получим для рассматриваемых условий распределение коэффициента трения вдоль обтекаемой пластины С f0 = 0,0576 Re −x 0,2 . 46 (49) Copyright ОАО «ЦКБ «БИБКОМ» & ООО «Aгентство Kнига-Cервис» Рис. 9. Степенной профиль скорости в турбулентном пограничном слое Экспериментальные исследования показывают, что для многоатомных газов (где Pr ≈ 1) в рассматриваемых условиях хорошо выполняется аналогия Рейнольдса (13). Тогда, интегрируя уравнение (20) с учетом соотношений (13) и (49) и считая, что пограничный слой нарастает с переднего края пластины, получим закон теплообмена в виде 0,25 St 0 = 0,0126 Re∗∗− . т (50) Вводя поправочный множитель на число Прандтля согласно экспериментальным данным, окончательно получим (см. рис. 5, линия 2) −0,25 St 0 = 0,0126 Re** Pr −0,75 . т (51) ЭКСПЕРИМЕНТАЛЬНАЯ ЧАСТЬ 1. Основные требования к выполнению курсовой научно-исследовательской работы Одним из основных требований к курсовой научно-исследовательской работе (КНИР) является комплексность, т. е. взаимосвязанность расчетно-теоретической, исследовательской и экспериментальной задач. 47 Copyright ОАО «ЦКБ «БИБКОМ» & ООО «Aгентство Kнига-Cервис» В основу данной КНИР положены результаты фундаментальных исследований структуры пограничных слоев, включая средние, пульсационные и корреляционные характеристики как динамического, так и теплового пограничных слоев при различных граничных условиях. Эти исследования способствовали более глубокому пониманию механизма обменных процессов, происходящих в пограничном слое. Объектом данной КНИР является структура пограничного слоя, развивающегося на плоской пластине при различных гидродинамических и тепловых граничных условиях при ламинарном и турбулентном режимах течения потока, а целью является углубленная проработка различных методов интенсификации конвективного теплообмена. Основные исходные данные для выполнения КНИР и объем работы указываются в задании к КНИР, в котором четко формулируется название темы КНИР, исходные данные и параметры, подлежащие численному и экспериментальному определению. Задание, оформленное на специальном бланке, подписывается и выдается руководителем курсовой работы. Студент, получивший задание, расписывается в получении и указывает дату получения задания. Подписанное задание вставляется в расчетно-пояснительную записку. Образец задания к КНИР приведен в приложении 1. Организационно работа состоит из следующих частей: а) теоретическое исследование методов интенсификации конвективного теплообмена; б) экспериментальное исследование гидродинамики и теплообмена в пограничном слое при безградиентном обтекании пластины; в) экспериментальное исследование гидродинамики и теплообмена в пограничном слое при наличии заданного метода интенсификации теплообмена; г) обработка полученных результатов с использованием вычислительной техники и вручную; д) анализ полученных результатов и оформление расчетнопояснительной записки. Каждый студент получает в индивидуальном задании скорость внешнего потока uω и тепловой поток Q. В задании к экспериментальной части указано, в каких сечениях и какие параметры измеряются, каковы используемые методы определения отдельных параметров. 48 Copyright ОАО «ЦКБ «БИБКОМ» & ООО «Aгентство Kнига-Cервис» В качестве дополнительных указаний по выполнению КНИР может быть задана специальная часть по углубленной проработке какого-либо метода интенсификации конвективного теплообмена. Данная КНИР имеет следующие задачи: 1. Освоить классические методы экспериментальной диагностики динамических и тепловых пограничных слоев, что позволит определить области воздействия на поток с целью интенсификации обменных процессов в пограничном слое. 2. Получить навыки проведения научно-исследовательской работы (НИР): постановки задачи НИР, планирования и выполнения НИР. 3. Провести теоретическое и экспериментальное исследование структуры пограничного слоя как в стандартных условиях, так и при использовании какого-либо метода интенсификации процесса теплообмена. Таким образом, основной целью курсовой работы является подготовка выпускников кафедры «Теплофизика» к самостоятельному планированию, проведению, анализу научных исследований и составлению научной документации. 2. Экспериментальное исследование и обработка эксперимента Каждый студент под наблюдением преподавателя проводит экспериментальное исследование, но перед этим он должен изучить установку, порядок работы на ней, технику безопасности и ознакомиться с классическими методами диагностики пограничного слоя (измерение скорости, температуры, плотности теплового потока, поверхностного трения и т. п.) . Экспериментальная установка. Экспериментальная часть исследования проводится на малой дозвуковой низкотурбулентной аэродинамической трубе открытого типа, работающей по принципу всасывания (рис. 10). Сопло прямоугольного сечения спрофилировано по формуле Витошинского и имеет семикратное поджатие, обеспечивающее пространственно-равномерное поле скоростей и низкую степень турбулентности (ε = 0,002) в ядре потока на входе в рабочий участок. Для разрушения крупномасштабной вихревой структуры всасываемого воздуха и формирования равномерного поля скорости на входе в сопло, в коллекторе устанавливается хонейкомб, представ49 Copyright ОАО «ЦКБ «БИБКОМ» & ООО «Aгентство Kнига-Cервис» ляющий собой сотовую конструкцию с размером ячейки 10×10 мм и длиной 100 мм. Низкая степень турбулентности в ядре потока обеспечивается также при помощи ряда сеток, установленных между хонейкомбом Рис. 10. Аэродинамическая труба: 1 – обтекатель; 2 – фильтр; 3 – хонейкомб; 4 – сетки; 5 – нагреваемая пластина; 6 – ЛАТР; 7 – ваттметр; 8 – манометр; 9 – ампервольтомметр; 10 – сопло; 11 – измерительный зонд; 12 – микровинт; 13 – крышка; 14 – диффузор; 15 – эластичное соединение; 16 – вентилятор; 17 – электродвигатель и соплом. Сетки изготовлены со стороной ячейки 2×2 мм из проволоки диаметром 0,35 мм. На входе в аэродинамическую трубу установлен пылезадерживающий фильтр со стороной ячейки 0,05×0,05 мм, изготовленный из медной проволоки диаметром 0,05 мм. Рабочая часть аэродинамической трубы представляет собой параллелепипед размером 80 × 300 × 1100 мм. Такая форма рабочего участка обеспечивает получение двумерного пограничного слоя на исследуемой поверхности нагреваемой пластины, которая является нижней съемной стенкой рабочего участка. Кроме того, в нижней стенке рабочей части размещена нагревательная панель, позволяющая нагревать исследуемый образец по законам qст = = const и Tст = const. Схема рабочей части экспериментального стенда показана на рис. 11. 50 Copyright ОАО «ЦКБ «БИБКОМ» & ООО «Aгентство Kнига-Cервис» Пластина изготовлена из стеклопластика толщиной 15 мм. По всей поверхности пластины 5, обращенной к потоку, методом го- Рис. 11. Сечение пластины: 1 – электроизоляция; 2 – медная пластина; 3 – электроизоляция; 4 – нагревательный элемент; 5 – стеклопластик рячего прессования нанесен токопроводящий слой 4, представляющий собой стеклоткань, пропитанную порошком графита и прокатанную на валках до толщины 0,4 мм. На нагреватель через тонкий слой электроизоляции 3 уложена медная пластина 2 толщиной 2 мм, которая обеспечивает подвод тепла по закону Тст = = const. Поверхность медной пластины покрыта тонким слоем электроизоляционного лака 1. Подводимая к электронагревателю пластины мощность регулируется с помощью лабораторного автотрансформатора и контролируется ваттметром. Конструкция аэродинамической трубы позволяет получить на входе в рабочую часть аэродинамической трубы плоский профиль скорости (с неоднородностью менее 5 %), формирующий низкотурбулентный изотропный поток, а используемый вентилятор позволяет получать скорость в ядре потока до 20 м/с. Регулирование скорости достигается установкой дополнительного гидравлического сопротивления на выходе из вентилятора. Расположенные на верхней стенке аэродинамической трубы три окна позволяют проводить диагностику течения датчиками различных типов в сечениях пограничного слоя на расстояниях примерно 250, 600 и 900 мм от начала исследуемого образца (пластины). К рабочему участку жестко крепится диффузор. Небольшой угол раскрытия диффузора (около 5о) обеспечивает безотрывное 51 Copyright ОАО «ЦКБ «БИБКОМ» & ООО «Aгентство Kнига-Cервис» торможение потока перед входом в вентилятор. Эластичное соединение диффузора с переходником вентилятора исключает передачу вибраций от вентилятора к рабочей части. О среднем течении в пограничном слое можно судить по распределению скоростей, а о теплопереносе – по профилям температуры. Совместное измерение распределения скоростей и температур в потоке жидкости или газа дает возможность количественно проанализировать и сопоставить теплообмен в различных областях пограничного слоя, включая вязкий подслой при турбулентном течении. С этой целью необходимо очень тщательно провести измерения профилей скорости и температуры вблизи стенки. Такие измерения профилей дают основу для количественного анализа. Распределение средних скоростей и температур в сечениях пограничного слоя фиксируются с помощью специально сконструированного пневмозонда типа Пито–Прандтля (рис. 12), совмещен- Рис. 12. Конструкция измерительного зонда: 1 – микронасадок Пито–Прандтля; 2 – микровинт; 3 – измерительный комплекс ИКД-0,016Дф; 4 – датчики температуры; 5 – рабочий элемент 52 Copyright ОАО «ЦКБ «БИБКОМ» & ООО «Aгентство Kнига-Cервис» ного с микротермопарой. Используемый микронасадок позволяет измерять осредненные значения скорости и температуры, начиная с расстояния 0,2 мм от поверхности. Система перемещения микрозонда, представляющая собой прецизионный микровинт, обеспечивает точность фиксации микронасадка над обтекаемой поверхностью около 0,05 мм. Показания ЭДС термопары регистрируются цифровым ампервольтомметром Ф-30, а перепад давлений (полного и статического) в трубке Пито измеряется интегральным комплексом давлений (ИКД-0,016Дф) и регистрируется цифровым ампервольтомметром Ф-30. Методика проведения эксперимента. Перед началом работы необходимо ознакомиться с руководством к работе, в том числе с правилами техники безопасности (приложение 2), теорией ошибок и методикой теплотехнических измерений . Эксперимент проводится при заданном скоростном режиме. Требуется исследовать динамические и тепловые характеристики пограничного слоя при ламинарном и турбулентном режимах течения. При проведении опытов необходимо соблюдать определенную последовательность операций. 1. Провести тарировку датчика давлений ИКД-0,016Дф с использованием микроманометра МКВ-250 (микроманометр жидкостной компенсационный с микрометрическим винтом, класс точности 0,02) и построить тарировочную зависимость скорости потока от электрического сигнала u = f(e), предварительно определив скорость по перепаду давлений, определенному с использованием микроманометра МКВ-250: u= 2Δhg ρж 2ΔP = = 4,03 2Δ h, ρ ρ где ΔР – разность полного и статического давлений в точке замера, Н/м2; ρ – плотность воздуха, кг/м3; ρж – плотность жидкости в манометре, кг/м3 ; g – ускорение свободного падения, м/с2; Δh – разность уровней жидкости в манометре, м; 2. Установить координатное устройство в первое окно (х = = 0,255 м) на верхней стенке рабочего участка. 3. Включить электродвигатель вентилятора и установить с помощью сеток, расположенных на выходе вентилятора, нужный режим работы аэродинамической трубы (заданную скорость потока). 53 Copyright ОАО «ЦКБ «БИБКОМ» & ООО «Aгентство Kнига-Cервис» 4. Нагреть тепловую пластину. Для этого через автотрансформатор на нагревательный элемент подается электропитание заданной мощности, контроль осуществляется по показанию ваттметра. Стационарный режим работы устанавливается примерно через час, что фиксируется по постоянству температуры нагреваемой поверхности во времени. 5. После выхода установки на стационарный режим работы производятся замеры всех параметров динамического и теплового пограничных слоев за один проход микрозонда (перепада давлений на трубке Пито и термоЭДС на термопаре насадка). Для этого с помощью микрозонда подвести микронасадок к поверхности рабочей пластины до касания с ней. В этом положении микронасадка центр приемного отверстия трубки полного напора и термопара находятся на расстоянии y = 0,2 мм от поверхности пластины. В этом положении необходимо записать показания на шкале микровинта и дальнейший отсчет расстояния вести от этого значения. В журнале наблюдений (готовится заранее или выдается на кафедре) указываются рекомендуемые значения расстояний, на которых производятся замеры перепада давлений и ЭДС термопары. Замеры давления в каждой точке необходимо производить через 20…30 с после установки микрозонда, так как он обладает определенной инерционностью из-за малости диаметров приемных отверстий микронасадка и значительной длины трубок, соединяющих его с манометром. Результаты замеров заносят в журнал наблюдений. Аналогичным образом производят измерения в двух других сечениях аэродинамической трубы (во втором и третьем сечениях). Обработка результатов эксперимента. В результате обработки опытных данных определяются основные характеристики динамического и теплового пограничного слоя и проверяется справедливость законов трения (23) и (48) и теплообмена (26) и (51) в «стандартных» условиях при обтекании плоской пластины. Обработка результатов опыта производится в следующем порядке: 1. Определить скорость потока в точках замера по тарировочной зависимости. 2. Построить график u = f(y) изменения профиля скорости в пограничном слое. 3. Определить графически толщину динамического пограничного слоя δ как расстояние, на котором скорость потока u = 0,99 u∞. 4. Построить график u/u∞ = f(y/δ). 54 Copyright ОАО «ЦКБ «БИБКОМ» & ООО «Aгентство Kнига-Cервис» 5. Определить показатель степени n в зависимости u/u∞ = (y/δ)n и дать заключение по режиму течения. 6. Определить графически толщину вытеснения в случае ρ = const: δ∗ = ∞ ⎛ u ⎞ ∫ ⎜⎝1 − u∞ ⎟⎠ dy. 0 Для этого построить на миллиметровой бумаге график функции (1 – u/u∞) от y и подсчитать площадь под кривой. Толщина вытеснения δ∗ равна произведению величины этой площади на масштабы по осям абсцисс и ординат (см. рис. 2). Сравнить подсчитанную графически величину δ∗ = S My Mu с толщиной вытеснения, рассчитанной аналитически. 7. Определить графически толщину потери импульса δ∗∗ = ∞ ⎛ u ⎞ u ∫ ⎜⎝1 − u∞ ⎟⎠ u∞ dy. 0 Для этого построить на миллиметровой бумаге график функции (1 – u/u∞) (u/u∞) от y и подсчитать площадь под кривой. Толщина потери импульса δ∗∗ равна произведению этой площади на масштабы по осям абсцисс и ординат. Сравнить подсчитанную графически величину δ∗∗ с толщиной потери импульса, рассчитанной аналитически. 8. Определить формпараметр H = δ*/δ** и дать заключение по режиму течения. 9. Вычислить число Рейнольдса, построенное по толщине потери импульса: Re** = (u∞ δ∗∗)/ ν. 10. Определить напряжение трения на стенке τ0 двумя способами: – по наклону профиля скорости у стенки τ0 = μ (du/dy)y = 0; для этого на миллиметровой бумаге для области, характеризуемой значениями y = 0...0,50 мм, в крупном масштабе вычертить график 55 Copyright ОАО «ЦКБ «БИБКОМ» & ООО «Aгентство Kнига-Cервис» u = u(y); тогда (du/dy)y = 0 = Δu/Δy есть тангенс угла между кривой u(y) и осью y; – по методу Клаузера, который часто используется при исследовании турбулентного пограничного слоя . Используя выражение универсального закона для плоской стенки u+ = 5,75 lg y+ + 5,2, найти распределение скорости в логарифмической области турбулентного пограничного слоя: u = 5,75 uτ lg y + 5,75 uτ lg (uτ /ν) + 5,2 uτ. В полулогарифмических координатах u – lg y надо построить сетку кривых по данному уравнению для различных uτ (рис. 13). Рис. 13. Номограмма для определения динамической скорости На этот график наносят экспериментальный профиль скорости, определяют размеры логарифмической области и значения uτ в этой области. Затем определяют напряжение трения на стенке в исследуемом сечении по формуле τ0 = ρuτ2 . 56 Copyright ОАО «ЦКБ «БИБКОМ» & ООО «Aгентство Kнига-Cервис» 11. Определить локальное значение коэффициента трения по соотношению Сf = 2 τ0 / ρu∞2 . 12. Определить локальное значение коэффициента трения по приближенной формуле Сf = 2 δ**/ x. 13. Используя градуировочную таблицу (приложение 3), построить тарировочный график и определить значения ΔТ = Тст – Т в точках замера. 14. Построить график ΔТ = f (y) изменения температурного напора в пограничном слое. 15. Определить графически толщину теплового пограничного слоя δт как расстояние, на котором температурный напор ΔТ = = 0,99 ΔТ∞. 16. Построить график ΔT/ΔT∞ = f(y/δт). 17. Определить показатель степени n в зависимости ΔT/ΔT∞ = = (y/δт)n. 18. Определить температуру стенки Тст = Т∞ + ΔТ∞, где значение Т∞ определяется по показаниям термометра, расположенного в помещении лаборатории. 19. Определить графически толщину потери энергии ∞ δт** = u ⎛ T − Tст ⎞ ∫ u∞ ⎜⎝1 − T∞ − Tст ⎟⎠ dy. 0 Для этого построить на миллиметровой бумаге график функции (1 – ΔТ/ΔТ∞) (u/u∞) от y и подсчитать площадь под кривой (см. рис. 3). Толщина потери энергии δт** равна произведению этой площади на масштабы по осям абсцисс и ординат. Сравнить подсчитанную графически величину δт** с толщиной потери энергии, рассчитанной аналитически. 20. Вычислить число Рейнольдса, построенное по толщине потери энергии: Reт** = (u∞ δт**)/ ν. 57 Copyright ОАО «ЦКБ «БИБКОМ» & ООО «Aгентство Kнига-Cервис» 21. Определить плотность теплового потока на стенке: а) по наклону профиля температуры вблизи стенки (как в п. 10): qст = ⎮λ (dТ/dy)y = 0⎮ = λ (ΔT/Δy)ст; б) при qст = const по соотношению qст = k Qп/ A, где Qп – подведенная к пластине мощность, Вт; A = 0,3 м2 – площадь поверхности нагреваемой пластины, обращенной к потоку; k = 0,7 – коэффициент, учитывающий потери тепла на элементы конструкции аэродинамической трубы. 22. Определить в турбулентном пограничном слое плотность теплового потока на стенке, используя косвенный метод его определения по логарифмической части профиля температуры. 24. Вычислить число Стантона St = qст / (Cp ρ ΔТ∞ u∞). 25. По экспериментально полученным данным построить графики (см. рис. 8): u+ = f(y+). Все экспериментально полученные результаты сравнить с определенными численно и известными законами гидродинамики и теплообмена (рис. 14): Сf = f(Re**); St = f(Reт**). 26. Провести анализ исследований, дать оценку полученных результатов и сделать выводы. Теплофизические свойства воздуха даны в приложении 4. В заключительной части работы проводится сравнение и анализ экспериментально полученных локальных коэффициентов трения и чисел Стантона с известными законами трения и теплообмена при безградиентном обтекании гладкой поверхности неизотермичным потоком. Результаты обработки экспериментальных данных и расчета свести в таблицы, желательно по гидродинамике и теплообмену раздельно. 58 Copyright ОАО «ЦКБ «БИБКОМ» & ООО «Aгентство Kнига-Cервис» Рис. 14. Законы трения и теплообмена в пограничном слое на плоской пластине Расчетно-пояснительная записка. Она должна содержать: – титульный лист (оформляется на бланке установленного в МГТУ им. Н.Э. Баумана образца); – задание; – введение; – результаты обработки экспериментальных исследований и сравнение их с результатами расчета; – описание графического метода определения интегральных характеристик пограничного слоя (исполняется на одном листе формата А4); – графическое сравнение рассчитанных и экспериментально определенных профилей скорости, температуры, коэффициентов трения и плотностей теплового потока, а также сравнение их с известными законами гидродинамики и теплообмена. Графики должны быть предельно четки, ясны и компактны; – спецчасть (например, анализ одного из методов интенсификации конвективного теплообмена); – заключение; – список использованной литературы; – оглавление. 59 Copyright ОАО «ЦКБ «БИБКОМ» & ООО «Aгентство Kнига-Cервис» Объем записки – 20–25 листов формата А4. Записка должна быть вшита в обложку или в скоросшиватель. Графики выполняют на миллиметровой бумаге стандартного формата и вшивают в записку. В расчетно-пояснительной записке помещают все материалы, связанные с теоретическим и экспериментальным исследованием гидродинамики и теплообмена при внешнем обтекании потоком пластины. Она должна включать краткое описание аэродинамической трубы, описание метода интенсификации теплоотдачи, исследовательскую теоретическую и исследовательскую экспериментальную части. Во введении должны быть оговорены актуальность работы, цель и задачи исследования. Материал в записке целесообразно излагать кратко и логически последовательно. Общеизвестные формулы, по которым производится расчет той или иной зависимости или параметра, должны приводиться в пояснительной записке без выводов. Формулы же, полученные самим студентом, даются с последовательными выводами и рассуждениями. Изложение материала в пояснительной записке должно сопровождаться необходимыми схемами и графиками. В заключении должны быть даны выводы по работе и оценка результатов теоретического и экспериментального исследований. Во всех случаях, когда используются какие-либо справочные данные, например по теплофизическим свойствам, используемым при расчете критериев подобия, необходимо в тексте давать ссылку на литературу, из которой они взяты. В квадратных скобках указывается порядковый номер источника по списку литературы и номер страницы. Пояснительную записку нужно писать лаконично, применяя четкие и ясные формулировки, не допускающие нескольких толкований. Результаты однотипных расчетов следует сводить в таблицу. Параметры гидродинамического и теплового пограничных слоев (профили скоростей и температур, интегральные характеристики, коэффициенты трения и плотности тепловых потоков), полученные при аналитическом расчете, необходимо сравнить с экспериментально полученными данными и с известными законами и данными, проанализировать полученные результаты и сделать выводы по ним. 60 Copyright ОАО «ЦКБ «БИБКОМ» & ООО «Aгентство Kнига-Cервис» При проведении аналитических расчетов можно пользоваться работами , при обработке экспериментальных данных – работами . КНИР перед сдачей должна быть подписана студентом. Если КНИР удовлетворяет предъявляемым требованиям, студент допускается к защите. Защита КНИР является завершающим этапом ее выполнения. Защита призвана научить студента всестороннему обоснованию предложенных им решений научных и инженерных задач. Готовясь к защите КНИР, студент должен продумать и написать доклад на 8…10 мин. Защита состоит из короткого доклада студента и ответов на вопросы преподавателей – членов комиссии. Студент должен дать все объяснения по существу работы. Для составления доклада могут быть использованы целиком или частично введение и заключение расчетно-пояснительной записки. В основной части доклада следует описать исследование, проведенное студентом, выводы по нему, кратко изложить суть разработанной (используемой) расчетной модели, а также методику и результаты экспериментального исследования. Весь доклад иллюстрируется чертежами, схемами, графиками, таблицами и ссылками на результаты расчета. По результатам защиты комиссия рекомендует лучшие КНИР к участию в конкурсе. 61 Copyright ОАО «ЦКБ «БИБКОМ» & ООО «Aгентство Kнига-Cервис» Приложение 1 Московский государственный технический университет имени Н.Э. Баумана Факультет Э Кафедра Э-6 ЗАДАНИЕ на курсовую научно-исследовательскую работу (КНИР) по курсу «Методы интенсификации теплообмена» Студент Иванов М.С. (фамилия, инициалы) Э6 – 111 (индекс группы) Руководитель Петров В.Н. (фамилия, инициалы) Срок выполнения курсовой работы по графику: 20 % – к 8-й нед., 40 % – к 10-й нед., 60 % – к 12-й нед., 80 % – к 14-й нед., 100 % – к 16-й нед. Защита КНИР 17-я неделя. I. Тема КНИР. Интенсификация теплообмена при вынужденной конвекции – экспериментальное исследование структуры турбулентного пограничного слоя. II. Техническое задание. 1. Экспериментальное исследование гидродинамики и теплообмена в турбулентном пограничном слое на плоской пластине при: u∞ = … м/с; Q = … Вт. 2. Экспериментальное исследование гидродинамики и теплообмена в турбулентном пограничном слое на плоской пластине при наличии турбулизатора (d = … мм): u∞ = … м/с; Q = … Вт. III. Объем и содержание КНИР (проведение эксперимента, обработка полученных результатов, определение средних и инте62 Copyright ОАО «ЦКБ «БИБКОМ» & ООО «Aгентство Kнига-Cервис» гральных характеристик исследуемого пограничного слоя и их графическое представление (сечение 3), расчетно-пояснительная записка 20 – 25 листов формата А4): 1. Обзор существующих МИТ (вынужденной конвекции) ....10 %. 2. Экспериментальное исследование гидродинамики и теплообмена в турбулентном пограничном слое при безградиентном обтекании пластины и при наличии турбулизатора: u∞ = … м/с; Q = =… Вт; турбулизатор: d = … мм, α = … ................................... 25 %. 3. Обработка результатов и определение средних и интегральных характеристик исследуемого пограничного слоя и графическое их представление................................................................. 55 %. 4. Расчетно-пояснительная записка...................................... 10 %. 63 Copyright ОАО «ЦКБ «БИБКОМ» & ООО «Aгентство Kнига-Cервис» Приложение 2 ПАМЯТКА ПО ТЕХНИКЕ БЕЗОПАСНОСТИ ПРИ РАБОТЕ НА АЭРОДИНАМИЧЕСКОЙ ТРУБЕ Эксперименты должны проводиться лишь после ознакомления студентов с устройством стенда, усвоения ими методики выполнения экспериментальных исследований и изучения настоящей памятки. Перед началом работы студенты должны пройти инструктаж по технике безопасности и расписаться в журнале. Электропитание экспериментальной установки осуществляется от сети переменного тока напряжением 380 В через электрораспределительный щит типа ЩЭ. Включение стенда осуществляется установкой вилки в розетку и включением рубильника. Все металлические конструктивные части установки, которые могут оказаться под напряжением вследствие нарушения изоляции, должны быть заземлены, электроаппаратура и токоведущие части – изолированы и укрыты в корпусе установки. Категорически запрещается открывать панель щита и защитный корпус магнитного пускателя электродвигателя вентилятора при подключенной к электросети установке. Включение электропитания стенда, электродвигателя вентилятора, а также цифровых электроизмерительных приборов осуществляет учебный мастер или преподаватель. В процессе проведения эксперимента необходимо постоянно следить за работой установки и при обнаружении неисправностей немедленно ставить в известность об этом преподавателя или учебного мастера. 64 Copyright ОАО «ЦКБ «БИБКОМ» & ООО «Aгентство Kнига-Cервис» Приложение 3 Градуировочная таблица хромель-алюмелевой термопары ТемпеТемпеТемпеТемпеТемпеЭДС, ЭДС, ЭДС, ЭДС, ЭДС, ратура, ратура, ратура, ратура, ратура, мВ мВ мВ мВ мВ °C °C °C °C °C 0 0 15 0,60 30 1,20 45 1,82 60 2,43 1 0,04 16 0,64 31 1,24 46 1,86 61 2,47 2 0,08 17 0,68 32 1,28 47 1,90 62 2,51 3 0,12 18 0,72 33 1,32 48 1,94 63 2,56 4 0,16 19 0,76 34 1,36 49 1,98 64 2,60 5 0,20 20 0,80 35 1,41 50 2,02 65 2,64 6 0,24 21 0,84 36 1,45 51 2,06 66 2,68 7 0,28 22 0,88 37 1,49 52 2,10 67 2,72 8 0,32 23 0,92 38 1,53 53 2,14 68 2,77 9 0,36 24 0,96 39 1,57 54 2,18 69 2,81 10 0,40 25 1,00 40 1,61 55 2,23 70 2,85 11 0,44 26 1,04 41 1,65 56 2,27 71 2,89 12 0,48 27 1,08 42 1,69 57 2,31 72 2,93 13 0,52 28 1,12 43 1,73 58 2,35 73 2,97 14 0,56 29 1,16 44 1,77 59 2,39 74 3,01 65 Copyright ОАО «ЦКБ «БИБКОМ» & ООО «Aгентство Kнига-Cервис» Приложение 4 Теплофизические параметры воздуха 250 ρ, кг/м3 1,390 Ср, кДж/(кг⋅K) 1,006 λ⋅103, Вт/(м⋅K) 22,1 α⋅106, м2/c 15,80 μ⋅107, Н⋅с/м2 159,6 ν⋅106, м2/с 11,40 0,72 260 1,340 1,006 22,9 16,98 164,6 12,28 0,72 270 1,290 1,006 23,8 18,36 169,6 13,10 0,71 280 1,240 1,006 24,6 19,72 174,6 14,00 0,71 290 1,200 1,006 25,4 21,04 . 179,6 14,95 0,71 300 1,160 1,007 26,2 22,43 184,6 15,90 0,70 310 1,120 1,007 26,9 23,85 189,6 16,87 0,70 320 1,090 1,007 27,7 25,24 194,5 17,90 0,70 330 1,060 1,008 28,5 26,67 199,2 18,90 0,70 340 1,020 1,009 29,2 28,37 203,8 19,90 0,70 350 0,995 1,009 30,0 29,88 208,2 2С,90 0,70 375 0,928 1,012 31,9 33,95 219,2 23,60 0,69 400 0,870 1,014 33,3 38,31 230,1 26,40 0,69 425 0,820 1,017 35,5 42,57 240,4 29,30 0,69 450 0,770 1,021 37,3 47,45 250,7 32,40 0,68 475 0,730 1,025 39,1 52,25 261,1 35,60 0,68 Т, К 66 Рr Copyright ОАО «ЦКБ «БИБКОМ» & ООО «Aгентство Kнига-Cервис» СПИСОК ЛИТЕРАТУРЫ 1. 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Баумана. 1976. №. 222. С. 121–129. 22. Методические указания по выполнению лабораторных работ по курсу «Теория теплообмена» / В.Н. Афанасьев, В.М. Белов, А.И. Кожинов, П.С. Роганов. М.: МВТУ им. Н. Э. Баумана. 1982. 40 с. 23. Клаузер Ф. Турбулентный пограничный слой: Пер с нем. // Проблемы механики. 1959. № 2. С. 297–340. 24. Репик Е.У., Тарасова В.Н. Измерение силы трения в пограничном слое при малых и умеренных числах Рейнольдса // Тр. ЦАГИ. Вып. 1218. 1970. 35 с. ОГЛАВЛЕНИЕ Введение........................................................................................................ Теоретическая часть..................................................................................... 1. Основные способы передачи теплоты............................................ 2. Интенсификация конвективного теплообмена.............................. 3. Аналитическое и экспериментальное исследование структуры пограничного слоя.............................................................................. Экспериментальная часть............................................................................ 1. Основные требования к выполнению курсовой научно-исследовательской работы......................................................................... 2. Экспериментальное исследование и обработка эксперимента......... Приложение 1 ............................................................................................... Приложение 2 ............................................................................................... Приложение 3 ............................................................................................... Приложение 4 ............................................................................................... Список литературы...................................................................................... 68 3 5 5 8 19 47 47 49 62 64 65 66 67
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