A calculation method of heat exchanger convection heat transfer coefficient based on global optimization

Abstract

This invention relates to the field of heat exchanger technology, and provides a method for calculating the convective heat transfer coefficient of a heat exchanger based on global optimization, including: Step 1, model construction and calculation processing; Step 2, preprocessing: preprocessing the Reynolds number; Step 3, dimensionality reduction and distribution solution: decomposing the two-dimensional fitting problem into a one-dimensional variable search problem, first assuming a value m for one unknown quantity, and then solving for another unknown quantity C. A value of C can be obtained for each set of operating conditions. When the C values ​​for each set of operating conditions are basically equal, the value of m is the optimal solution; Step 4, global scanning optimization: performing global scanning optimization on the value of m, gradually shortening the calculation step size as needed, and finally solving for the optimal values ​​of m and C. Through the method for calculating the convective heat transfer coefficient of a heat exchanger based on global optimization described in this invention, the method settings can be optimized, the operational threshold of the solution method can be reduced, the applicability of the solution method can be broadened, the calculation accuracy of the method can be improved, and the calculation cost of the method can be reduced.

Description

Technical Field

[0001] This invention relates to the field of heat exchange equipment technology, and more specifically, to a method for calculating the convective heat transfer coefficient of a heat exchanger based on global optimization. Background Technology

[0002] The convective heat transfer coefficient is a core parameter characterizing the intensity of fluid convective heat transfer. Accurately obtaining this parameter is crucial for conducting research on heat exchanger performance, structural optimization, and operational condition verification. Printed Circuit Heat Exchangers (PCHEs) are a novel type of microchannel compact heat exchanger, characterized by small channel dimensions, thin plate walls, and high structural integration. However, due to hardware limitations, it is impossible to directly measure the channel wall temperature; traditional wall temperature measurement methods are difficult to implement on such devices.

[0003] Currently, the separation method, Wilson graphical method, and equal Reynolds number method are commonly used in engineering to indirectly solve the convective heat transfer coefficient of the fluids on both sides. However, all of these methods have certain limitations: the separation method is only applicable to working conditions where the convective heat transfer coefficients on both sides of the heat transfer surface are significantly different, and its applicable range is narrow; the Wilson graphical method requires a constant mass flow rate of the hot fluid during the test and strict control of the fluid's qualitative temperature fluctuations, which places high demands on the accuracy of the test system and measuring instruments, and imposes many additional constraints; the equal Reynolds number method requires that the Reynolds numbers of the fluids on both sides be equal during the test.

[0004] In summary, existing methods for calculating convective heat transfer coefficients are not very practical and have poor adaptability to operating conditions, making it difficult to efficiently and accurately calculate the convective heat transfer coefficients of printed circuit board heat exchangers. Therefore, it is of great significance to study how to lower the solution threshold and achieve calculation methods with wide applicability and high accuracy.

[0005] Patent CN115270657B discloses a verification method for plate-fin heat exchangers that considers the axial heat conduction effect of baffles and fins. The method includes first giving parameters, then simplifying and initializing the model, then fitting the physical properties, then calculating the pressure field distribution, then calculating the temperature field of the fins and baffles, then calculating the fluid temperature field, and then judging the temperature residual. The calculated results are used for the design of plate-fin heat exchangers. This method can take into account the axial heat conduction effect in the baffles and fins of counter-flow plate-fin heat exchangers. It is suitable for the accurate calculation of low-temperature counter-flow plate-fin heat exchangers with straight fins or perforated fins with small porosity in the channel. However, its calculation method is relatively complex and can easily lead to high calculation costs. Summary of the Invention

[0006] In view of this, the present invention aims to propose a method for calculating the convective heat transfer coefficient of a heat exchanger based on global optimization, in order to solve the problems of weak operability, poor adaptability to operating conditions, and difficulty in efficiently and accurately calculating the convective heat transfer coefficient of printed circuit board heat exchangers in existing technologies. This invention aims to optimize the method settings, lower the operational threshold of the solution method, broaden the applicability of the solution method, improve the calculation accuracy of the method, and reduce the calculation cost of the method.

[0007] To achieve the above objectives, the technical solution of the present invention is implemented as follows:

[0008] This invention relates to a method for calculating the convective heat transfer coefficient of a heat exchanger based on global optimization, the method comprising the following steps:

[0009] Step 1: Model Construction and Calculation: Based on the basic theory of convective heat transfer and the heat transfer mechanism of heat exchangers, a calculation model for the convective heat transfer coefficient is constructed, and the calculation of the convective heat transfer coefficient is organized into solving for the values ​​of unknown constants C and m.

[0010] Step 2: Preprocessing: The Reynolds number is preprocessed to be b×10. e The form is: ; where b is a positive number.

[0011] Step 3, Dimension Reduction and Distribution Solution: Decompose the two-dimensional fitting problem into a one-dimensional variable search problem. First, assume the value of a certain unknown quantity m, and then solve for the other unknown quantity C. A value of C can be solved for each set of working conditions. When the value of C for each set of working conditions is basically equal, the value of m is the optimal solution.

[0012] Step 4: Global Scan Optimization: Perform a global scan optimization on the value of m, gradually shortening the calculation step size as needed, and finally solving for the optimal values ​​of m and C.

[0013] Furthermore, step one includes:

[0014] Step S11: Model building and calculation: Based on the basic theory of convective heat transfer and the heat transfer mechanism of heat exchangers, the heat transfer power Q of the printed circuit board heat exchanger PCHE is calculated using the first formula.

[0015] Step S12: Calculate the overall heat transfer coefficient h of the printed circuit board heat exchanger PCHE using the second formula;

[0016] Step S13: Calculate the cold-side convective heat transfer coefficient α of the printed circuit board heat exchanger (PCHE) using formulas 5 and 6 respectively. c The convective heat transfer coefficient a on the hot side h ;

[0017] Step S14: Calculate the Reynolds numbers of the cold and hot sides of the printed circuit board heat exchanger (PCHE) using the seventh and eighth formulas, respectively.

[0018] Step S15: Express the overall heat transfer coefficient h and the cold-side convective heat transfer coefficient a using the ninth formula. c The convective heat transfer coefficient a on the hot side h The relationship between them;

[0019] Step S16: Combine the fifth, sixth and ninth formulas to construct the tenth formula as the calculation model for the convective heat transfer coefficient, thereby simplifying the calculation of the convective heat transfer coefficient into solving for the values ​​of the unknown constants C and m.

[0020] Furthermore, the first formula in step S11 is:

[0021] ;

[0022] In the formula, m c m h These represent the mass flow rates of the cold and hot sides, respectively, in kg / s; t c_in t c_out t h_in t h_out These are the cold-side fluid inlet temperature, cold-side fluid outlet temperature, and hot-side fluid inlet temperature of the printed circuit board heat exchanger (PCHE), respectively, in °C. p_c C p_h These are the isobaric specific heat capacities of the cold and hot sides, respectively, in kJ / (kg·℃).

[0023] Furthermore, the second formula is:

[0024] ;

[0025] In the formula, A represents the heat transfer area of ​​the printed circuit board heat exchanger (PCHE), in m². 2 ;∆t m It is the logarithmic mean temperature difference between the cold and hot sides of the fluid, in °C.

[0026] Furthermore, in step S13, the fifth formula is: The sixth formula is: ;

[0027] In the formula, C and m are unknown constants; Re c Re h Reynolds numbers for the cold and hot sides, respectively, Pr c Pr h Prandtl numbers for the cold and hot sides, respectively, λ c , λ hd represents the thermal conductivity of the fluid on the cold and hot sides, respectively, in W / (m·℃). c d h These are the equivalent diameters of the cold and hot side channels, respectively, in meters (m).

[0028] Furthermore, in step S14, the seventh formula is: The eighth formula is: ;

[0029] In the formula, ρ c ρ h These are the fluid densities on the cold and hot sides, respectively, in kg / m³. 3 μ c μ h These are the dynamic viscosity of the cold / hot side fluids, respectively, in kg / (m·s), v c v h These represent the fluid velocities on the cold and hot sides, respectively, in m / s.

[0030] Furthermore, in step S15, the ninth formula is: ;

[0031] In the formula, δ is the wall thickness between the cold and hot passages of the printed circuit board heat exchanger (PCHE), in meters; λ w It is the thermal conductivity of the wall between the cold and hot aisles, expressed in W / (m·℃).

[0032] Furthermore, in step S16, the tenth formula is:

[0033] .

[0034] Furthermore, step two includes:

[0035] Step S21: Preprocess the calculated Reynolds numbers of the cold and hot sides of the printed circuit board heat exchanger (PCHE) using formulas eleven and twelfth respectively.

[0036] Step S22: Combine the tenth, eleventh, and twelfth formulas to rearrange the equations and obtain the thirteenth formula.

[0037] Furthermore, in step S21, the eleventh formula is: The twelfth formula is: In the formula, e is on the order of the minimum Reynolds number;

[0038] In step S22, the thirteenth formula is:

[0039] .

[0040] Compared with existing technologies, the method for calculating the convective heat transfer coefficient of a heat exchanger based on global optimization described in this invention has the following advantages:

[0041] By setting the method described above, the method settings can be optimized, the operational threshold of the solution method can be lowered, the applicability of the solution method can be broadened, the calculation accuracy of the method can be improved, and the calculation cost of the method can be reduced.

[0042] Specifically, this method overcomes the limitations of traditional wall temperature measurement, separation, equal Reynolds number, and Wilson graphical methods. It eliminates the need to measure heat exchanger wall temperature, does not require a significant difference in convective heat transfer coefficients on both sides of the heat exchange surface, and does not require strict control of the test flow rate and temperature. This method only requires that the hot and cold channels be geometrically similar and that the fluid flow be in the same flow pattern. It is simple to operate and applicable to a wide range of working conditions.

[0043] This method first performs scaling preprocessing on the independent variables, effectively solving the numerical ill-conditioning problem caused by large numerical calculations and improving the stability of the numerical solution process; it transforms the two-dimensional unknown parameter solution problem into a one-dimensional parameter global traversal optimization problem, and adopts a coarse-to-fine variable step size search strategy, which has high parameter identification accuracy and the obtained convective heat transfer coefficient results are accurate and reliable.

[0044] This method can complete the calculations using only operating condition data collected from conventional experiments. The experimental conditions are simple, effectively reducing the cost and difficulty of experiment setup, operating condition adjustment, and precision measurement. The entire calculation process is highly standardized, easy to program, and can be extended to similar parameter solving scenarios. Attached Figure Description

[0045] The accompanying drawings, which constitute a part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings:

[0046] Figure 1 This is a flowchart illustrating the method;

[0047] Figure 2 A three-dimensional structural diagram of a PCHE heat exchanger;

[0048] Figure 3 A schematic diagram showing the heat exchange channel division of a PCHE heat exchanger;

[0049] Figure 4 This is a schematic diagram of the heat exchange in the PCHE unit. Detailed Implementation

[0050] The inventive concepts of this disclosure will be described below using terminology commonly used by those skilled in the art to communicate the essence of their work to others skilled in the art. However, these inventive concepts may be embodied in many different forms and should not be construed as limited to the embodiments described herein.

[0051] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0052] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0053] To address the problems of existing methods for calculating the convective heat transfer coefficient being inefficient and unsuitable for various operating conditions, thus hindering efficient and accurate calculation of the convective heat transfer coefficient for printed circuit board heat exchangers, this embodiment proposes a method for calculating the convective heat transfer coefficient of a heat exchanger based on global optimization, wherein the heat exchanger is a printed circuit board heat exchanger. The method includes the following steps:

[0054] Step 1: Model Construction and Calculation: Based on the basic theory of convective heat transfer and the heat transfer mechanism of heat exchangers, a calculation model for the convective heat transfer coefficient is constructed, and the calculation of the convective heat transfer coefficient is organized into solving for the values ​​of unknown constants C and m.

[0055] Step 2: Preprocessing: The Reynolds number is preprocessed to be b×10. e The form is used to solve the ill-conditioning of large numbers and improve the convergence of the computation method; where b is a positive number.

[0056] Step 3, Dimension Reduction and Distribution Solution: Decompose the two-dimensional fitting problem into a one-dimensional variable search problem. First, assume the value of a certain unknown quantity m, and then solve for the other unknown quantity C. A value of C can be solved for each set of working conditions. When the value of C for each set of working conditions is basically equal, the value of m is the optimal solution.

[0057] Step 4: Global Scan Optimization: Perform a global scan optimization on the value of m, gradually shortening the calculation step size as needed, and finally solve for the optimal values ​​of m and C. Preferably, the calculation step size can be gradually shortened from 0.5, 0.1, 0.01, to 0.001.

[0058] The calculation method for heat transfer parameters of the printed circuit board heat exchanger (PCHE) described in this application optimizes the method settings, lowers the operational threshold of the solution method, broadens its applicability, improves calculation accuracy, and reduces computational costs. Specifically, the method described in this application effectively improves calculation accuracy while ensuring fast calculation speed. By employing data dimensionality reduction and global optimization, the calculation method for the convection heat transfer coefficients on the hot and cold sides of the PCHE can be obtained using easily acquired experimental data.

[0059] Step one includes:

[0060] Step S11: Model building and calculation: Based on the basic theory of convective heat transfer and the heat transfer mechanism of heat exchangers, the heat transfer power Q of the printed circuit board heat exchanger PCHE is calculated using the first formula.

[0061] Step S12: Calculate the overall heat transfer coefficient h of the printed circuit board heat exchanger PCHE using the second formula;

[0062] Step S13: Calculate the cold-side convective heat transfer coefficient α of the printed circuit board heat exchanger (PCHE) using formulas 5 and 6 respectively. c The convective heat transfer coefficient a on the hot side h ;

[0063] Step S14: Calculate the Reynolds numbers of the cold and hot sides of the printed circuit board heat exchanger (PCHE) using the seventh and eighth formulas, respectively.

[0064] Step S15: Express the overall heat transfer coefficient h and the cold-side convective heat transfer coefficient a using the ninth formula. c The convective heat transfer coefficient a on the hot side h The relationship between them. Among them, the ninth formula is the heat transfer thermal resistance equation.

[0065] Step S16: Combine the fifth, sixth and ninth formulas to construct the tenth formula as the calculation model for the convective heat transfer coefficient, thereby simplifying the calculation of the convective heat transfer coefficient into solving for the values ​​of the unknown constants C and m.

[0066] The first formula in step S11 is:

[0067] ;

[0068] In the formula, m c m h These represent the mass flow rates of the cold and hot sides, respectively, in kg / s. c and m h It can be measured by flow meters arranged in the cold and hot side circuits. t c_in t c_out t h_in t h_out These are the cold-side fluid inlet temperature, cold-side fluid outlet temperature, hot-side fluid inlet temperature, and hot-side fluid outlet temperature of the printed circuit board heat exchanger (PCHE), respectively, in °C. The fluid inlet / outlet temperatures can be measured using thermocouples located at the PCHE inlet / outlet. p_c C p_h These are the isobaric specific heat capacities of the cold and hot sides, respectively, in kJ / (kg·℃). The isobaric specific heat capacity can be found in a property table.

[0069] The second formula in step S12 is:

[0070] ;

[0071] In the formula, A represents the heat transfer area of ​​the printed circuit board heat exchanger (PCHE), in m². 2 ;∆t m It is the logarithmic mean temperature difference between the cold and hot sides of the fluid, in °C.

[0072] The logarithmic mean temperature difference ∆t is calculated using the third formula. m The third formula is:

[0073] ;

[0074] In the third formula, ∆t max ∆t is the temperature difference between the inlet temperature of the hot-side fluid and the outlet temperature of the cold-side fluid. min This represents the temperature difference between the hot-side fluid outlet temperature and the cold-side fluid inlet temperature.

[0075] In step S13, the fifth and sixth formulas are derived from the fourth formula. The fourth formula is: Nu is the heat transfer coefficient, Re is the fluid Reynolds number, Pr is the fluid Prandtl number, and C, m, and n are all constants.

[0076] For a printed circuit board heat exchanger (PCHE) with geometric similarity between hot and cold channels, if the fluids on both sides are in the same flow state, the convective heat transfer coefficients of the fluids in the hot and cold channels are described by the same criterion equation, namely the fourth formula.

[0077] The fifth formula is: The sixth formula is: ;

[0078] In the formula, C and m are unknown constants; Re c Re h These represent the Reynolds numbers for the cold and hot sides of the fluid, respectively. The Reynolds number can be calculated using a formula. c Pr h These are the Prandtl numbers for the cold and hot sides of the fluid, respectively. The Prandtl numbers can be found in property tables. λ c , λ h These are the thermal conductivity coefficients of the cold and hot sides of the fluid, respectively, expressed in W / (m·℃). These thermal conductivity coefficients can be found in a property table. c d h These are the equivalent diameters of the cold and hot side channels, respectively, in meters (m).

[0079] In step S14, the seventh formula is: The eighth formula is: .

[0080] In the formula, ρ c ρ h These are the fluid densities on the cold and hot sides, respectively, in kg / m³. 3 Fluid density can be found in the property table; μ c μ h These are the dynamic viscosities of the cold and hot sides, respectively, in kg / (m·s). The dynamic viscosities can be found in a property table; v c v h These represent the fluid velocities on the cold and hot sides, respectively, in m / s.

[0081] In step S15, the ninth formula is: ;

[0082] In the formula, δ is the wall thickness between the cold and hot passages of the printed circuit board heat exchanger (PCHE), in meters; λ w It is the thermal conductivity of the wall between the cold and hot aisles, expressed in W / (m·℃).

[0083] In step S16, the tenth formula is:

[0084] ;

[0085] In the formula, h, δ, λ w Re c Re h Pr c Pr h , λ c , λ h d c d h All of these are known quantities calculated from the inlet / outlet temperature, inlet / outlet pressure, and cold / hot side flow rate data measured by the printed circuit board heat exchanger (PCHE), or known quantities obtained from the property table; C and m are unknown quantities.

[0086] By constructing the model and organizing the calculation formulas in step one, the limitations of traditional wall temperature measurement methods, separation methods, equal Reynolds number methods, and Wilson graphical methods can be overcome. It eliminates the need to measure the heat exchanger wall temperature, does not require a significant difference in the convective heat transfer coefficients on both sides of the heat exchange surface, and does not require strict control over the test flow rate and temperature. The method in this application only requires geometric similarity between the hot and cold channels and that the fluid flow is in the same flow pattern; it is simple to operate and applicable to a wide range of operating conditions.

[0087] Step two includes:

[0088] Step S21: Preprocess the calculated Reynolds numbers of the cold and hot sides of the printed circuit board heat exchanger (PCHE) using formulas eleven and twelfth respectively.

[0089] Step S22: Combine the tenth, eleventh, and twelfth formulas to rearrange the equations and obtain the thirteenth formula.

[0090] In step S21, the eleventh formula is: The twelfth formula is: In the formula, e is on the order of the minimum Reynolds number.

[0091] In step S22, the thirteenth formula is:

[0092] .

[0093] By setting the steps in step two, the independent variables can be pre-scaled, effectively solving the numerical ill-conditioned problem caused by large numerical calculations and improving the stability of the numerical solution process.

[0094] Step three includes:

[0095] Step S31: Rearrange the thirteenth equation to obtain the seventeenth equation.

[0096] Step S32: Dimensionality reduction distribution solution: The seventeenth formula is rearranged to obtain the eighteenth formula.

[0097] Step S31 includes:

[0098] Step S311: Based on the thirteenth formula, redefine the first variable y and the cold-side variable b. c Thermal variable b h This leads to the fourteenth, fifteenth, and sixteenth formulas.

[0099] Specifically, let the fourteenth formula be... The fifteenth formula is The sixteenth formula is .

[0100] Step S312: Combine the first variable y and the cold-side variable b c Thermal variable b h Substituting into the thirteenth formula, we obtain the simplified seventeenth formula.

[0101] The seventeenth formula is: .

[0102] The eighteenth formula in step S32 is: .

[0103] In the formula, the eighteenth formula contains two unknowns, C and m, where m is the Reynolds number power with a value range of [0-2]. First, assume m is a known quantity and give it a value, then solve for the unknown quantity C. At least three different operating conditions, C1, C2, and C3, need to be calculated.

[0104] By setting the steps in step three, the problem of solving two-dimensional unknown parameters can be transformed into a one-dimensional parameter global traversal optimization problem. Combined with the coarse-to-fine variable step size search strategy adopted in step four, the method is simplified while also improving the computational accuracy and reliability of the method.

[0105] Step four includes:

[0106] Step S41: Global optimization, perform global scan optimization on the value of m, with a scan step size of 0.5;

[0107] Step S42: Determine whether the C deviation value meets the accuracy requirements; if yes, proceed to step S44; if no, proceed to step S43.

[0108] Step S43: Reduce the scanning step size and perform scanning optimization on the m value until the C deviation value meets the accuracy requirements, then proceed to step S44;

[0109] Step S44: Output the calculated values ​​of C and m.

[0110] By setting the steps in step four, a coarse-to-fine variable step size search strategy can be adopted to improve the accuracy of parameter identification and obtain accurate and reliable convective heat transfer coefficient results.

[0111] Step S41 includes: assuming m=0, calculating the average values ​​of C1, C2, and C3 for the three selected different working conditions, and the deviation values ​​D1, D2, and D3 corresponding to C under different working conditions. The calculation formulas for D1, D2, and D3 are as follows:

[0112] ; ; ; .

[0113] Step S42 includes: determining whether the absolute values ​​of D1, D2, and D3 are less than a preset precision f%. If yes, then m and C are at their optimal values, and step S44 is executed; otherwise, the absolute values ​​of D1, D2, and D3 are greater than or equal to f%, and the values ​​of D1, D2, and D3 are recalculated based on the current value of m. Here, f is a positive number. The value of f is adjusted according to the precision requirements; preferably, f is 1.

[0114] Step S43 includes:

[0115] Step S431: Based on the fact that the previous stage of full-domain scanning did not yield satisfactory values ​​for m and C, select the value of m that minimizes the deviation calculated in the previous stage. Within the range of [m - previous stage scan step size, m + previous stage scan step size], reduce the scan step size as needed to optimize the value of m. Recalculate the deviation values ​​D1, D2, and D3 according to the current stage scan step size, and execute step S432. The previous stage includes step S41, and the previous stage where, even after reducing the scan step size, the accuracy requirements are still not met, and the process returns to step S43 where the scan step size needs to be further reduced.

[0116] Step S432: Determine whether the absolute values ​​of D1, D2, and D3 are less than the preset precision f%. If yes, then m and C are the optimal values, and proceed to step S44; otherwise, the absolute values ​​of D1, D2, and D3 are greater than or equal to f%. Then, adjust the value of m according to the current value, recalculate the values ​​of D1, D2, and D3, and return to step S431.

[0117] In this embodiment, step S43 includes:

[0118] Step S431': Based on the fact that the values ​​of m and C that meet the requirements were not obtained in step S41, select the value of m that has the smallest deviation value calculated in step S41. Within the range of [m-0.5, m+0.5], reduce the scanning step size as needed, optimize the value of m, and recalculate the deviation values ​​D1, D2, and D3 according to the current scanning step size of 0.1. Then execute step S432.

[0119] Step 432': Determine whether the current C value meets the precision requirements; if yes, proceed to step S44; if no, proceed to step S431''.

[0120] Step S431'': Based on the fact that the values ​​of m and C that meet the requirements were not obtained in step S431', select the value of m that has the smallest deviation value calculated in step S431', within the range of [m-0.1, m+0.1], reduce the scanning step size as needed, optimize the value of m, and recalculate the deviation values ​​D1, D2, and D3 according to the current scanning step size of 0.01, and execute step S432''.

[0121] Step S432'': Determine whether the current C value meets the precision requirements; if yes, proceed to step S44; if no, proceed to step S431''';

[0122] Step S431''': Based on the fact that the values ​​of m and C that meet the requirements were not obtained in step S431'', select the value of m that has the smallest deviation value calculated in step S431'', within the range of [m-0.01, m+0.01], reduce the scanning step size as needed, optimize the value of m, and recalculate the deviation values ​​D1, D2, and D3 according to the current scanning step size of 0.001, and execute step S432'''.

[0123] Step S432''': Determine whether the current C value meets the accuracy requirements; if yes, proceed to step S44; if no, step S431''' still not finding m and C values ​​that meet the requirements, you can try changing the accuracy requirements or selecting the m and C values ​​corresponding to the smallest deviation as the optimal values.

[0124] In the field of heat exchanger design, a value of m to three decimal places is already a fairly accurate value, and there is no need to pursue further precision.

[0125] The method described in this application can complete the calculation using only operating condition data collected from conventional experiments. The experimental conditions are simple, effectively reducing the cost and difficulty of experimental setup, operating condition adjustment, and precision measurement. The entire calculation process is highly standardized, easy to implement in a program, and can be extended to similar parameter solving scenarios.

[0126] Example 1:

[0127] The PCHE water-to-water heat exchange test case is used as an example for illustration, but it is not limited to this. This calculation method is a general calculation method. It is necessary to ensure that the number of unknown variables does not exceed two, so it can also be used in many other situations.

[0128] Example 1 Calculation: To test the feasibility of this calculation method, a set of experimental data was randomly generated according to the Dittus-Boelter formula (where C=0.023, m=0.8). The calculation method of this application can be judged to accurately calculate the values ​​of C and m using the experimental data. Data measured and obtained under different operating conditions, as well as structural parameters of the printed circuit board heat exchanger (PCHE), are shown in Table 1.

[0129] Table 1

[0130]

[0131] This example uses a method for calculating the convective heat transfer coefficient of a heat exchanger based on global optimization, as described in this application. The method includes the following steps:

[0132] Step 1: Based on the basic theory of convective heat transfer and the heat transfer mechanism of heat exchangers, construct a calculation model for the convective heat transfer coefficient, and organize the calculation of the convective heat transfer coefficient into solving for the values ​​of unknown constants C and m;

[0133] Step 2: Preprocess the Reynolds number to a.bcd×10 e This approach addresses the ill-conditioning of large numbers and improves the convergence of computational methods.

[0134] Step 3: Dimensionality reduction and distribution solution. The two-dimensional fitting problem is decomposed into a one-dimensional variable search problem. First, assume the value of a certain unknown quantity m, and then solve for another unknown quantity C. A value of C can be solved for each set of working conditions. When the value of C for each set of working conditions is basically equal, the value of m is the optimal solution.

[0135] Step 4: Perform a global scan to optimize the value of m, gradually shortening the calculation step size from 0.5, 0.1, 0.01, to 0.001, and finally solve for the optimal values ​​of m and C.

[0136] Step one specifically includes:

[0137] Step S11: Calculate the PCHE heat transfer power Q;

[0138] The PCHE heat exchange power Q can be calculated using the following formula:

[0139] ;

[0140] In the formula, m c m h These represent the mass flow rates of the cold and hot sides, respectively, in kg / s; t c_in t c_out t h_in t h_out These are the PCHE cold-side fluid inlet temperature, cold-side fluid outlet temperature, hot-side fluid inlet temperature, and hot-side fluid outlet temperature, respectively, in °C; C p_c C p_h These represent the isobaric specific heat capacities of the cold and hot side fluids, respectively, in kJ / (kg·℃). Among them, such as... Figure 4 As shown, P c_in P c_out P h_in P h_out These are the operating pressures of the cold-side fluid inlet, cold-side fluid outlet, hot-side fluid inlet, and hot-side fluid outlet of the PCHE (Printed Circuit Board Type Heat Exchanger), respectively, in MPa.

[0141] The calculated heat exchange power Q of PCHE under different operating conditions is shown in Table 2 below:

[0142] Table 2

[0143]

[0144] Step S12: Calculate the overall heat transfer coefficient h of the PCHE;

[0145] The overall heat transfer coefficient h of PCHE can be calculated using the following formula:

[0146] ;

[0147] In the formula, A is the heat transfer area of ​​the PCHE, in m². 2 ;∆t m It is the logarithmic mean temperature difference between the cold and hot sides of the fluid, in °C.

[0148] In step S12, the logarithmic mean temperature difference ∆t m It can be calculated using the following formula:

[0149] ;

[0150] The calculated PCHE overall heat transfer coefficient h is shown in Table 3 below:

[0151] Table 3

[0152]

[0153] Step S13: Calculate the cold / hot Reynolds number Re of the PCHE c and Re h ;

[0154] The cold / hot Reynolds numbers can be calculated using the following formulas respectively:

[0155] ;

[0156] .

[0157] In the formula, ρ c ρ h These are the fluid densities on the cold and hot sides, respectively, in kg / m³. 3 μ c μ h These are the dynamic viscosity of the cold / hot side fluids, respectively, in kg / (m·s); v c v h These represent the fluid velocities on the cold and hot sides, respectively, in m / s.

[0158] PCHE cold / hot Reynolds number Re c and Re h The calculated data is shown in Table 4 below:

[0159] Table 4

[0160]

[0161] Step S14: Construct the PCHE cold-side convective heat transfer coefficient a c The convective heat transfer coefficient a on the hot sideh Computational model;

[0162] For a PCHE heat exchanger with geometrically similar hot and cold channels, if the fluids on both sides are in the same flow state, the convective heat transfer coefficients of the fluids in the hot and cold channels are described by the same criterion equation: ;

[0163] PCHE cold-side convection heat transfer coefficient a c The convective heat transfer coefficient a on the hot side h The following formula can be used for calculation:

[0164] ;

[0165] ;

[0166] In the formula, Re c Re h These represent the Reynolds numbers for the cold and hot sides of the fluid, respectively. The Reynolds number can be calculated using a formula. c Pr h These are the Prandtl numbers for the cold and hot sides of the fluid, respectively. The Prandtl numbers can be found in property tables. λ c , λ h These are the thermal conductivity coefficients of the cold and hot sides of the fluid, respectively, expressed in W / (m·℃). These thermal conductivity coefficients can be found in a property table. c d h These are the equivalent diameters of the cold and hot side channels, respectively, in meters (m).

[0167] Furthermore, the overall heat transfer coefficient h and the convective heat transfer coefficients a on the cold and hot sides... c a h The relationship between them can be expressed by the heat transfer thermal resistance equation;

[0168] The heat transfer resistance equation is: In the formula, δ represents the wall thickness between the cold and hot aisles of the PCHE, in meters (m); λ w It is the thermal conductivity of the wall between the cold and hot aisles, expressed in W / (m·℃).

[0169] Furthermore, joint a c a h And from the heat transfer and thermal resistance equations, we can obtain the tenth formula:

[0170] ;

[0171] In the formula, h, δ, λ w Re c Re h Pr c Pr h , λc , λ h d c d h All of these are known quantities calculated from the inlet / outlet temperature, inlet / outlet pressure, and cold / hot side flow rate data measured by the printed circuit board heat exchanger (PCHE), or known quantities obtained from the property table; C and m are unknown quantities.

[0172] Furthermore, step 2 includes:

[0173] Step S21: Preprocess for different Reynolds numbers;

[0174] ; In the formula, e is taken as 3. The calculations for different working conditions yield the following results. , The specific data is shown in Table 5 below:

[0175] Table 5

[0176]

[0177] Step S22: Combining the formula in step S21 with the formula in step S10, the equation is rearranged to obtain the thirteenth formula:

[0178] .

[0179] Step three includes:

[0180] Step S31: Rectify the equation of formula thirteen: Let the equation in formula thirteen, , , The calculations yielded b under different operating conditions. c b h The data for y are shown in Table 6 below:

[0181] Table 6

[0182]

[0183] Combining the thirteenth formula with the formulas in step S31, we obtain the seventeenth formula:

[0184] .

[0185] Step S32: Dimensionality Reduction and Distribution Solution: The seventeenth formula is rearranged as follows:

[0186] .

[0187] Step four includes:

[0188] Step S41: Global optimization, scan step size 0.5; within the range of m [0,2], with a step size of 0.5, calculate the values ​​of C1, C2, and C3, as well as their deviations D1, D2, and D3. D1, D2, and D3 are calculated using the following formula:

[0189] ; ; ; .

[0190] The calculation results are shown in Table 7:

[0191] Table 7

[0192]

[0193] Step S43: Global optimization, reduce the scan step size to 0.1; In step S41, the required values ​​of m and C were not found. The deviation value is the smallest when m=1, which is 11.2%. Recalculate the deviation values ​​D1, D2, and D3 within the range of [0.5, 1.5] with a step size of 0.1. The calculation results are shown in Table 8 below. Determine whether they meet the accuracy requirements.

[0194] Table 8

[0195]

[0196] When m=0.8, the values ​​of C1, C2, and C3 are completely consistent and without deviation. Therefore, m=0.8 and C=0.023 is the optimal solution for the test data of operating conditions one, two, and three. This corresponds perfectly to the initially assumed values ​​of m and C in the test data.

[0197] By applying the method of this application to actual experimental conditions in Example 1, it can be seen that the method of this application has low computational difficulty, simple overall experimental conditions, can effectively reduce the cost and difficulty of experimental setup and measurement, and can also facilitate the improvement of the accuracy of the method.

[0198] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for calculating the convective heat transfer coefficient of a heat exchanger based on global optimization, characterized in that, The method includes the following steps: Step 1: Model Construction and Calculation: Based on the basic theory of convective heat transfer and the heat transfer mechanism of heat exchangers, a calculation model for the convective heat transfer coefficient is constructed, and the calculation of the convective heat transfer coefficient is organized into solving for the values ​​of unknown constants C and m. Step 2: Preprocessing: The Reynolds number is preprocessed to be b×10. e The form is: ; where b is a positive number; Step 3, Dimension Reduction and Distribution Solution: Decompose the two-dimensional fitting problem into a one-dimensional variable search problem. First, assume the value of a certain unknown quantity m, and then solve for the other unknown quantity C. A value of C can be solved for each set of working conditions. When the value of C for each set of working conditions is basically equal, the value of m is the optimal solution. Step 4: Global Scan Optimization: Perform a global scan optimization on the value of m, gradually shortening the calculation step size as needed, and finally solving for the optimal values ​​of m and C.

2. The method for calculating the convective heat transfer coefficient of a heat exchanger based on global optimization according to claim 1, characterized in that, Step one includes: Step S11: Model building and calculation: Based on the basic theory of convective heat transfer and the heat transfer mechanism of heat exchangers, the heat transfer power Q of the printed circuit board heat exchanger PCHE is calculated using the first formula. Step S12: Calculate the overall heat transfer coefficient h of the printed circuit board heat exchanger PCHE using the second formula; Step S13: Calculate the cold-side convective heat transfer coefficient α of the printed circuit board heat exchanger (PCHE) using formulas 5 and 6 respectively. c The convective heat transfer coefficient a on the hot side h ; Step S14: Calculate the Reynolds numbers of the cold and hot sides of the printed circuit board heat exchanger (PCHE) using the seventh and eighth formulas, respectively. Step S15: Express the overall heat transfer coefficient h and the cold-side convective heat transfer coefficient a using the ninth formula. c The convective heat transfer coefficient a on the hot side h The relationship between them; Step S16: Combine the fifth, sixth and ninth formulas to construct the tenth formula as the calculation model for the convective heat transfer coefficient, thereby simplifying the calculation of the convective heat transfer coefficient into solving for the values ​​of the unknown constants C and m.

3. The method for calculating the convective heat transfer coefficient of a heat exchanger based on global optimization according to claim 2, characterized in that, The first formula in step S11 is: ； In the formula, m c m h These represent the mass flow rates of the cold and hot sides, respectively, in kg / s; t c_in t c_out t h_in t h_out These are the cold-side fluid inlet temperature, cold-side fluid outlet temperature, and hot-side fluid inlet temperature of the printed circuit board heat exchanger (PCHE), respectively, in °C. p_c C p_h These are the isobaric specific heat capacities of the cold and hot sides, respectively, in kJ / (kg·℃).

4. The method for calculating the convective heat transfer coefficient of a heat exchanger based on global optimization according to claim 3, characterized in that, The second formula is: ； In the formula, A represents the heat transfer area of ​​the printed circuit board heat exchanger (PCHE), in m². 2 ;∆t m It is the logarithmic mean temperature difference between the cold and hot sides of the fluid, in °C.

5. The method for calculating the convective heat transfer coefficient of a heat exchanger based on global optimization according to claim 4, characterized in that, In step S13, the fifth formula is: The sixth formula is: ; In the formula, C and m are unknown constants; Re c Re h Reynolds numbers for the cold and hot sides, respectively, Pr c Pr h Prandtl numbers for the cold and hot sides, respectively, λ c , λ h d represents the thermal conductivity of the fluid on the cold and hot sides, respectively, in W / (m·℃). c d h These are the equivalent diameters of the cold and hot side channels, respectively, in meters (m).

6. The method for calculating the convective heat transfer coefficient of a heat exchanger based on global optimization according to claim 5, characterized in that, In step S14, the seventh formula is: The eighth formula is: ; In the formula, ρ c ρ h These are the fluid densities on the cold and hot sides, respectively, in kg / m³. 3 μ c μ h These are the dynamic viscosity of the cold / hot side fluids, respectively, in kg / (m·s), v c v h These represent the fluid velocities on the cold and hot sides, respectively, in m / s.

7. The method for calculating the convective heat transfer coefficient of a heat exchanger based on global optimization according to claim 6, characterized in that, In step S15, the ninth formula is: ; In the formula, δ is the wall thickness between the cold and hot passages of the printed circuit board heat exchanger (PCHE), in meters. λ w It is the thermal conductivity of the wall between the cold and hot aisles, expressed in W / (m·℃).

8. The method for calculating the convective heat transfer coefficient of a heat exchanger based on global optimization according to claim 7, characterized in that, In step S16, the tenth formula is: 。 9. The method for calculating the convective heat transfer coefficient of a heat exchanger based on global optimization according to claim 8, characterized in that, Step two includes: Step S21: Preprocess the calculated Reynolds numbers of the cold and hot sides of the printed circuit board heat exchanger (PCHE) using formulas eleven and twelfth respectively. Step S22: Combine the tenth, eleventh, and twelfth formulas to rearrange the equations and obtain the thirteenth formula.

10. The method for calculating the convective heat transfer coefficient of a heat exchanger based on global optimization according to claim 9, characterized in that, In step S21, the eleventh formula is: The twelfth formula is: In the formula, e is on the order of the minimum Reynolds number; In step S22, the thirteenth formula is: 。

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