Numerical analysis method for condensation heat exchange capacity of plate-fin heat exchanger

Abstract

The invention relates to a numerical analysis method for condensation heat exchange capacity of a plate-fin heat exchanger, which comprises the following steps of: constructing a reverse Carnot principle thermodynamic cycle experimental device, and selecting the plate-fin heat exchanger with sawtooth fins; working conditions are designed according to an improved Wilson graphical method, and experimental parameters such as inlet and outlet temperature and flow and fin structure and working medium physical property parameters are obtained; a numerical model is built based on energy conservation and the Newton cooling law, a water side heat exchange coefficient empirical formula and a refrigerant side heat exchange coefficient empirical formula are fitted, the water side adopts an improved Wilson graphical method considering fluid properties, and an equivalent Reynolds number containing gas-liquid two-phase parameters is introduced into the refrigerant side; verification shows that the water side low Reynolds number error is less than or equal to 15%, the high Reynolds number is less than or equal to 10%, and the refrigerant side error is within + / - According to the method, continuous data estimation is realized through numerical fitting, the structure of the power-assisted heat exchanger is optimized, and a rapid and accurate heat exchange performance design tool is provided for an automobile R1234yf system.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of automobile thermal management, in particular to a numerical analysis method for condensation heat exchange capacity of a plate-fin heat exchanger. BACKGROUND

[0002] The increase in global energy consumption in recent years has prompted the development of advanced heat exchange equipment. Compact heat exchangers are improved versions of heat exchange devices, which are applied in many industrial applications such as automobiles, aerospace, cryogenics, oil and gas, etc. In compact heat exchangers, the brazed plate-fin type is widely favored due to its compactness, high efficiency and low weight. Compact heat exchangers usually use flat fins, serrations, perforations, corrugations and louver fins to provide high fin density. The serrated fin surface used in compact heat exchangers has the highest heat transfer capacity relative to pressure drop, and is mainly preferred for various thermal fluid applications. In general, the heat transfer coefficient of the serrated fin surface is 1.5-4 times higher than that of the ordinary fin surface.

[0003] While advanced heat exchange equipment is continuously developing, refrigerants also play a crucial role in reducing global energy demand. Several decades ago, the use of hydrochlorofluorocarbons (HCFCs) and chlorofluorocarbons (CFCs) was widely popularized and used worldwide. With the development of the times, chlorofluorocarbon refrigerant R12 was replaced by HFC R134a, which has zero ozone depletion potential (ODP) because it does not contain chlorine. Although the ODP of R134a is zero, due to its high global warming potential (GWP), it has been replaced by refrigerants such as R1234yf, which has a lower GWP value. The typical working temperature of R1234yf in automobile air conditioner condensers is 30-42℃, while the condensation temperature of traditional refrigerants is usually higher (50-60℃). Although new refrigerants such as R290, carbon dioxide, etc. have begun to gradually enter the automobile market in today's society, R1234yf still occupies a considerable share in the refrigerant market.

[0004] Research on the application of R1234yf in compact heat exchangers (brazed plate serrated fins) will help the design and development of compact condensers and their application in various practical applications to reduce global energy demand. In addition, compared with other uninterrupted fin surfaces, compact condensers using serrated fin surfaces have better performance through phase change heat transfer.

[0005] Therefore, it is urgent to develop a numerical analysis method for condensation heat exchange capacity of a plate-fin heat exchanger for R1234yf refrigerant. SUMMARY

[0006] In view of the problems in the prior art, the present application aims to provide a plate-fin heat exchanger condensation heat exchange capacity numerical analysis method, which can accurately characterize the condensation heat exchange performance of a plate-fin heat exchanger for R1234yf refrigerant, and provide a reliable basis for its structure optimization.

[0007] In order to achieve the above-mentioned purpose, the present application adopts the following technical solutions:

[0008] A plate-fin heat exchanger condensation heat exchange capacity numerical analysis method comprises the following steps:

[0009] Step 1: Construct an inverse Carnot cycle experimental system, wherein the plate-fin heat exchanger is provided with an R1234yf refrigerant loop and a cooling water loop;

[0010] Step 2: Start the refrigerant loop and the cooling water loop, and record the steady-state experimental data after the heat balance error of the refrigerant and the cooling water is ≤±5%;

[0011] Step 3: Use the obtained steady-state experimental data to design an experimental working condition of 30-42℃ according to the improved Wilson graphical method, keep the water side flow constant, change the refrigerant side mass flow and inlet temperature in stages, and obtain an experimental data set of real measured values in the Reynolds number range of 500≤Re≤2000;

[0012] Step 4: Based on the law of conservation of energy and Newton's cooling law, a numerical calculation model of the plate-fin heat exchanger is established, the geometric parameters and working medium physical property parameters of the plate-fin heat exchanger are collected, and these parameters and the experimental data set obtained in step 3 are input into the numerical calculation model to obtain the condensation heat exchange coefficient h refg ;

[0013] Step 5: Fit the h refg obtained in step 4 with the experimental data set in step 3 to obtain a water side heat exchange coefficient empirical formula, so that the prediction error is ≤15% in the low Reynolds number region and ≤10% in the high Reynolds number region;

[0014] Step 6: The water side heat exchange coefficient empirical formula obtained in step 5 is substituted back to the numerical calculation model in step 4, and a refrigerant side heat exchange coefficient empirical formula is obtained by fitting again, so that the prediction error is ≤±15% in the range of 500≤Re≤2000;

[0015] Step 7: Based on the empirical formulas obtained in steps 5 and 6, the plate-fin heat exchanger condensation heat exchange capacity prediction data of R1234yf refrigerant under different working conditions in the range of 30-42℃ is output.

[0016] Further, step 8 is included, which compares the predicted data output from step 7 with the measured values of the corresponding working condition in the experimental data set of step 3, and if the error meets the error range specified in steps 5 and 6, it is confirmed that the numerical analysis method is effective.

[0017] Further, in step 1, the plate-fin heat exchanger is connected in parallel with the standard condenser through a bypass line, and before the experiment, the standard condenser is run to stabilize the equipment state, and after the test parameters are reached, the plate-fin heat exchanger path is switched.

[0018] Further, in step 1, the plate-fin heat exchanger is coated with a polyamide foam heat insulation layer on the outer surface.

[0019] Further, the steady-state experimental data includes the inlet and outlet temperatures, pressures, and flow rates of the refrigerant side and the water side; the geometric parameters and working fluid property parameters of the plate-fin heat exchanger include fin density, fin height, fin thickness, serration length, hydraulic diameter, thermal conductivity, density, and viscosity.

[0020] Further, step 3 includes establishing the expression of X and Y to fit the empirical formula of the water side heat transfer coefficient by introducing a correction parameter reflecting the fluid properties through the improved Wilson graphical method, where X is the ratio of the high-temperature side to the low-temperature side fluid property parameters, and Y is a composite parameter based on the total heat transfer coefficient and fluid properties.

[0021] The expression of X is:

[0022]

[0023] where η c and η h represent the overall fin surface efficiency of the low-temperature side and the high-temperature side, respectively, A h and A c are the heat transfer areas of the high-temperature side and the low-temperature side, respectively, λ w is the thermal conductivity of water, D h is the hydraulic diameter, and Re is the Reynolds number, and Pr is the Prandtl number.

[0024] The expression of Y is:

[0025]

[0026] where U is the total heat transfer coefficient, t is the plate thickness, λ p is the plate thermal conductivity, and A p is the plate area.

[0027] Further, when calculating the condensation heat transfer coefficient h refg in step 4, the fin efficiency η f of the plate-fin heat exchanger is used to correct the three-dimensional heat conduction effect.

[0028] Further, the fin efficiency η f is expressed as,

[0029]

[0030] wherein l is the fin characteristic length, m is the ratio of the heat conduction capacity of the fin to the surface convection heat exchange capacity, and is expressed as,

[0031]

[0032] wherein h is the fin height. h w As the water-side heat exchange coefficient, it is determined by fitting the water-to-water test data.

[0033] Further, the refrigerant-side heat exchange coefficient empirical formula is,

[0034]

[0035] wherein A, b1, b2, and b3 are constants obtained by fitting the experimental data, λ l is the liquid thermal conductivity, D h is the hydraulic diameter, Re eq is the equivalent Reynolds number, Pr l is the liquid Prandtl number.

[0036] Further, the calculation formula of the equivalent Reynolds number Re eq is,

[0037]

[0038] The calculation formula of the Prandtl number Pr l is,

[0039]

[0040] wherein G refg is the refrigerant mass flow rate, x m is the average gas fraction at the inlet and outlet, ρ l and ρ g are the refrigerant liquid and gas phase densities, μ l is the refrigerant liquid phase viscosity, Cp l is the refrigerant liquid phase specific heat.

[0041] Overall, the present application has the following advantages:

[0042] 1) By using the numerical fitting method to utilize the discrete data obtained by experiments, the continuous data of heat exchange under different working conditions are estimated, which is helpful for analyzing the heat exchange performance of the heat exchanger under different flow rates, and saves the experimental cost

[0043] 2) In the study of the mechanism of jumping the fetus, the model can provide more accurate simulation data for the study due to the easy modification of parameters.

[0044] 3) The numerical analysis method used can better characterize the condensation heat transfer performance of the plate-fin heat exchanger, and help to seek the optimization of the structure of the heat exchanger. BRIEF DESCRIPTION OF DRAWINGS

[0045] Figure 1 It is the experimental principle diagram of the embodiment.

[0046] Figure 2 It is the structure diagram of the plate-fin heat exchanger of the embodiment.

[0047] Figure 3 It is the water-side heat transfer coefficient result verification diagram.

[0048] Figure 4 It is the agent-side heat transfer coefficient result verification diagram.

[0049] In the drawings:

[0050] 1-expansion valve, 2-evaporator, 3-superheater, 4-Coriolis flowmeter, 5-compressor, 6-subcooler, 7-plate-fin heat exchanger, 71-refrigerant outlet, 72-cover plate, 73-cooling water outlet, 74-baffle, 75-cooling water inlet, 76-sawtooth fin, 77-baffle, 78-refrigerant inlet, 8-standard condenser, 9-water tank, 10-water pump, 11-turbine flowmeter. DETAILED DESCRIPTION

[0051] The present application uses data fitting method through experimental data, and systematically describes the heat transfer coefficient prediction method based on Reynolds number and Prandtl number. The experimental conditions are designed based on Wilson graphical method, and the Wilson graphical method is improved and optimized by using fluid properties, and the water-agent side heat transfer coefficient of the heat exchanger is fitted. The prediction result of the water-agent side heat transfer coefficient fitting formula is smaller. At the same time, the heat transfer coefficient fitting formula established can provide reference for performance analysis and optimization design of plate-fin heat exchanger 7.

[0052] In order to make the purpose, technical scheme and advantages of the present application more clear and definite, the present application is further described in detail below with examples and drawings.

[0053] (1) Experimental equipment and arrangement principle:

[0054] As Figure 1As shown, the test device is a reverse Carnot principle heat cycle system, and its refrigerant side mainly includes a standard condenser 8, an expansion valve 1, an evaporator 2, a superheater 3, a Coriolis force flowmeter 4, a compressor 5, a subcooler 6, a plate-fin heat exchanger 7, a water tank 9, a water pump 10, a turbine flowmeter 11, etc. In the figure, P is a pressure sensor, and T is a temperature sensor. The cooling liquid side loop is maintained by two water chillers. During the experiment, the plate-fin heat exchanger 7 (i.e., the test condenser) is installed in parallel with the standard condenser 8 through a bypass line. By controlling the flow rate and temperature of the cooling water in other loops, the required state of the refrigerant in the plate-fin heat exchanger 7 is maintained. Before the plate-fin heat exchanger 7 is tested, experiments are performed on the standard condenser 8 in the refrigerant loop to maintain the stability of the test equipment. Once the test parameters are reached, the bypass pipeline is opened to allow the refrigerant to pass through the plate-fin heat exchanger 7, and the passage through the standard condenser 8 is closed.

[0055] The refrigerant used in this embodiment is R1234yf, and its saturation temperature range is 30-42℃.

[0056] (2) Selection of plate-fin heat exchanger 7:

[0057] As shown in Figure 2 , the plate-fin heat exchanger 7 of this embodiment includes a cover plate 72, a barrier plate 77, and a partition plate 74. The plate-fin heat exchanger 7 adopts a cross-flow arrangement, and a refrigerant passage is arranged in the middle single layer between the upper and lower barrier plates 77. The two ends of the refrigerant passage are connected to a refrigerant inlet 78 and a refrigerant outlet 71, respectively. Cooling water passages are arranged on the upper and lower sides of the refrigerant passage, and the two ends of the cooling water passages are connected to a cooling water inlet 75 and a cooling water outlet 73, respectively. A plurality of partition plates 74 are arranged in the refrigerant passage and the cooling water passage. Sawtooth fins 76 are arranged in adjacent partition plates 74. The surface of the plate-fin heat exchanger 7 is coated with a 10mm-thick polyamide foam to achieve a relatively adiabatic environment, avoiding heat exchange between the tested plate-fin heat exchanger 7 and the environment, and affecting the experimental accuracy. The sawtooth fin 76 structure is assembled by vacuum brazing manufacturing process to develop a test condenser assembly, including a separator, a sawtooth fin 76, a side strip, a top and bottom plate, and then welding nozzles and headers to the core.

[0058] (3) Obtain experimental parameters related to the heat exchange and pressure drop performance of the plate-fin heat exchanger 7:

[0059] The operation flow steps are as follows: 1. Turn on the power supply. 2. Turn on the refrigerant circuit of the standard condenser 8 and the cooling water valve. 3. Check whether the pressure and flow of the cooling water are stable. 4. Start the compressor 5. 5. If the state is stable, open the refrigerant valve to the plate-fin heat exchanger 7. 6. Control the parameters of the cooling water in the subcooler 6 to achieve the test conditions. 7. Wait for the plate-fin heat exchanger 7 to reach a steady state condition, and record the data. The test conditions are designed according to the Wilson graphical method, that is, the water side flow is kept constant, and the size of the refrigerant side flow and the change of the inlet temperature are adjusted. The heat balance error between the refrigerant and the cooling water during the experiment is within ±5%.

[0060] (4) Collect the structural parameters of the plate-fin heat exchanger 7 and the physical property parameters of the working medium required for numerical calculation:

[0061] Through the initial values of the plate-fin heat exchanger 7, the geometric parameters related to the heat exchange performance of the plate-fin heat exchanger 7 are obtained, such as fin density, fin height, fin thickness, hydraulic diameter, heat transfer area, etc.

[0062] (5) Build a numerical calculation model of the plate-fin heat exchanger 7:

[0063] From step (3), the initial experimental data related to the plate-fin heat exchanger 7 are obtained, such as inlet and outlet temperatures, working medium flow, inlet and outlet pressures, etc. Using the law of conservation of energy and Newton's cooling law, the initial experimental data are processed to obtain the heat exchange capacity related parameters of the plate-fin heat exchanger 7 under the test conditions.

[0064] Heat exchange rate

[0065]

[0066] Among them, the logarithmic mean temperature difference ΔT ln is given by:

[0067]

[0068] In the formula, Ts is the saturation temperature of the refrigerant, Twi and Two are the temperatures of the inlet and outlet cooling water of the test condenser respectively, C pw is the specific heat of the cooling water, the mass flow rate of the cooling water, and U is the total heat transfer efficiency of the heat exchanger. Without considering the thermal resistance caused by the fouling of the heat exchanger, the average condensation heat transfer coefficient h refg inside the test condenser is determined by:

[0069]

[0070] A p = L f W f (5)

[0071]

[0072] where A w and A refg are the areas in the water passage and refrigerant passage respectively, η orefg and η ow are the overall fin surface efficiencies on the refrigerant side and water side respectively, A p is the plate area, h w is the cooling water heat transfer coefficient. W f and L f are the width and flow length of the test condenser respectively. The fin efficiency is given by η f , f n is the total number of fin layers, and s is the fin pitch. The overall fin surface efficiency η o is given by the following equation:

[0073] η o = 1 - a (1 - η f ) (7)

[0074] where a is the ratio of the fin area to the total area a, and the fin efficiency η f is given by the following equation:

[0075]

[0076] where m is the ratio of the heat conduction ability of the fin to the surface convective heat transfer ability, which comprehensively reflects the competition between heat conduction along the fin and surface heat dissipation, and its expression is as follows,

[0077]

[0078] where h w is the water-side heat transfer coefficient determined by fitting the water-to-water test data.

[0079] (6) Numerical analysis of the water-side heat transfer coefficient of the plate-fin heat exchanger 7:

[0080] The heat transfer coefficient is brought into the empirical formula of the heat resistance of the heat exchanger, and the improved Wilson graphical method is used to obtain the following expressions of X and Y, which are used to fit the water-side heat transfer coefficient of the test piece.

[0081]

[0082] where η c and η h represent the overall fin surface efficiencies on the low-temperature side and the high-temperature side respectively. According to the test parameters obtained at different low-temperature side flow rates, the following empirical formula of the heat transfer coefficient of the low-temperature water side is fitted.

[0083]

[0084] (7) Verification of water-side heat transfer coefficient empirical formula:

[0085] The formula calculated plate-fin heat exchanger 7 heat transfer coefficient and experimental results, as shown in the comparison results in low Reynolds number, that is, Re <160 cases, the error is within 15%, in high Reynolds number conditions, the error is within 10%. Figure 3

[0086] (8) Plate-fin heat exchanger 7 refrigerant-side heat transfer coefficient numerical formula derivation:

[0087] The test results of the refrigerant-side according to different mass flow and Ts derived plate-fin heat exchanger 7 refrigerant-side heat transfer coefficient. Power law expression is used to establish the correlation between the condensation rate and liquid thermal conductivity (λ l ), hydraulic diameter (D h ), equivalent Reynolds number (Re eq ) and liquid Prandtl number (Pr l ). The refrigerant-side heat transfer coefficient h refg is shown as follows:

[0088]

[0089] Wherein, A, b1, b2, b3 are constants obtained by fitting the experimental data. According to the experimental data in the temperature range of 30-42 ℃, the liquid phase thermal conductivity of R1234yf, the liquid phase viscosity is fitted to obtain the constants respectively 2.96×10 -9 , 5.49, 1.66, -2.8.

[0090]

[0091] Wherein, the equivalent Reynolds number Re eq and Prandtl number Pr l are as follows:

[0092]

[0093] Wherein, the average gas fraction x m of the inlet and outlet is represented, the liquid and gas phase density of the refrigerant is represented by ρ l and ρ g respectively, μ l is the liquid phase viscosity of the refrigerant, and the specific heat of the refrigerant liquid phase is represented by Cp l .

[0094] (9) Verification of heat transfer coefficient empirical formula:

[0095] ​The refrigerant of the working condition verified in the embodiment is R1234yf, and the saturation temperature is 30-42℃, which is consistent with the actual operating parameters of the condenser of the automobile air conditioner. The refrigerant-side heat exchange coefficient of the plate-fin heat exchanger 7 calculated by the formula is compared with the experimental results, and the experimental and predicted results under each temperature condition and each same working condition are taken as the horizontal and vertical axes to draw a comparison chart as shown in FIG. 8. The refrigerant-side heat exchange coefficient is predicted within the range of ±15% of the average absolute deviation of the current experimental value in the range of 500-2000 Reynolds numbers. Figure 4

[0096] The embodiment is aimed at the low GWP and high gas-liquid density ratio characteristics of R1234yf, and proposes an equivalent Reynolds number model to solve the problem of phase change heat transfer prediction in the serrated fin 76; through the design of adiabatic coating and bypass switching, the environmental thermal disturbance is reduced, and the experimental repeatability is significantly improved; by improving the Wilson graphical method and coupling the overall fin surface efficiency, the prediction error of the condensation heat exchange coefficient is controlled in a low range; the empirical formula can be extrapolated to a wider working condition, reducing the number of real vehicle tests and development costs, providing a high-precision, wide-working-condition heat exchanger performance prediction tool for the automobile thermal management system using low-GWP refrigerants such as R1234yf, and supporting the lightweight and energy efficiency improvement of the structure.

[0097] The above embodiments are the preferred embodiments of the present application, but the embodiments of the present application are not limited to the above embodiments, and any changes, modifications, substitutions, combinations, simplifications made without departing from the spirit and principles of the present application shall be equivalent replacement methods, and shall be included in the protection scope of the present application.​

Claims

1. A numerical analysis method of condensation heat transfer capacity of a plate-fin heat exchanger, characterized by, The method comprises the following steps: Step 1: Constructing an inverse Carnot cycle experimental system, in which a plate-fin heat exchanger is provided with an R1234yf refrigerant circuit and a cooling water circuit; Step 2: Starting the refrigerant circuit and the cooling water circuit, and recording the steady-state experimental data after the heat balance error of the refrigerant and the cooling water is less than or equal to ±5%; Step 3: Using the obtained steady-state experimental data, designing an experimental condition of 30-42 DEG C according to the improved Wilson graphical method, keeping the water side flow constant, changing the refrigerant side mass flow and inlet temperature in stages, and obtaining an experimental data set of real measured values in the range of 500≤Re≤2000 Reynolds numbers; Step 4: Based on the law of conservation of energy and Newton's cooling law, a numerical calculation model of the plate-fin heat exchanger is established, the geometric parameters and working medium physical property parameters of the plate-fin heat exchanger are collected, and these parameters and the experimental data set obtained in step 3 are input into the numerical calculation model, to obtain the condensation heat exchange coefficient h refg ; Step 5: h refg The experimental data set of step 3 is fitted to obtain an empirical formula of the water-side heat transfer coefficient, so that the prediction error is ≤15% in the low Reynolds number region and ≤10% in the high Reynolds number region. Step 6: Taking the water side heat exchange coefficient empirical formula obtained in step 5 as a known quantity, and substituting it into the numerical calculation model of step 4, and fitting the refrigerant side heat exchange coefficient empirical formula again, so that the prediction error is less than or equal to ±15% in the range of 500≤Re≤2000; Step 7: Based on the empirical formulas obtained in steps 5 and 6, the plate-fin heat exchanger condensing heat exchange capacity prediction data of R1234yf refrigerant in different conditions within 30-42 DEG C is output.

2. The method of analysis according to claim 1, characterized in that: Step 8: Comparing the prediction data output in step 7 with the measured values of the corresponding conditions in the experimental data set in step 3, if the error meets the error range specified in steps 5 and 6, the numerical analysis method is confirmed to be effective.

3. The method of analysis of claim 1, wherein: In step 1, the plate-fin heat exchanger is connected in parallel with a standard condenser through a bypass line, and the standard condenser is run before the experiment to stabilize the equipment state, and the plate-fin heat exchanger passage is switched after the test parameters are reached.

4. The method of analysis of claim 1, wherein: In step 1, the plate-fin heat exchanger is coated with a polyamide foam heat insulation layer on the outer surface.

5. The method of analysis of claim 1, wherein: The steady-state experimental data includes the inlet and outlet temperatures, pressures and flow rates of the refrigerant side and the water side; the geometric parameters and working fluid property parameters of the plate-fin heat exchanger include fin density, fin height, fin thickness, sawtooth length, hydraulic diameter, thermal conductivity, density and viscosity.

6. The method of analysis of claim 1, wherein: Step 3 includes: through the improved Wilson graphical method, a correction parameter reflecting the fluid property is introduced, an expression of X and Y is established to fit the water side heat exchange coefficient empirical formula, wherein X is the ratio of the high-temperature side to the low-temperature side fluid property parameter, and Y is a composite parameter based on the total heat transfer coefficient and the fluid property; The expression of X is: wherein η c and η h represent the overall fin surface efficiency on the low-temperature side and the high-temperature side, respectively, A h and A c are the heat transfer areas on the high-temperature side and the low-temperature side, respectively, λ w is the thermal conductivity of water, D h is the hydraulic diameter, Re is the Reynolds number, and Pr is the Prandtl number; The expression of Y is: where U is the overall heat transfer coefficient, t is the thickness of the panel, λ p is the thermal conductivity of the panel, A p is the area of the panel.

7. The method of analysis of claim 1, wherein: At step 4, the condensing heat transfer coefficient h is calculated refg At step 5, the fin efficiency η of the plate fin heat exchanger is calculated f The three-dimensional heat conduction effect is corrected.

8. The method of analysis according to claim 7, wherein: Fins efficiency η f The expression for, Wherein, h is the water side convective heat transfer coefficient, l is the fin characteristic length, m is the ratio of the fin heat conduction capacity to the surface convective heat transfer capacity, and the expression of m is, where λ is the fin thermal conductivity, h w As the water-side heat transfer coefficient, it is determined by fitting the water-to-water test data.

9. The method of claim 1, wherein: The refrigerant side heat exchange coefficient empirical formula is, wherein A, b1, b2, b3 are constants obtained by fitting experimental data, λ l is the liquid thermal conductivity, D h is the hydraulic diameter, Re eq is the equivalent Reynolds number, Pr l is the liquid Prandtl number.

10. The method of analysis of claim 1, wherein: Equivalent Reynolds number Re eq The calculation formula is, Prandtl number Pr l The calculation formula is, where G refg is the refrigerant mass flow rate, x m is the average gas fraction at the inlet and outlet, p l and p g are the refrigerant liquid and vapor densities, respectively, m l is the refrigerant liquid viscosity, and Cp l is the refrigerant liquid specific heat.

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