A method for designing and optimizing the flow channels of a liquid cooling plate based on topology optimization
Through topological optimization design of liquid-cooled plate runners, the problems of poor temperature consistency and high pressure drop in traditional designs are solved, and more efficient thermal management of battery modules is achieved to meet the operating conditions requirements of the enterprise.
Patent Information
- Application Number
- CN202411040914.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-07-31
- Publication Date
- 2025-07-29
- Estimated Expiration
- 2044-07-31
AI Technical Summary
The traditional liquid-cooled plate runner design has problems such as poor temperature consistency, high temperature difference and high pressure drop of the battery module. The design is subjective and has a long cycle, so it is impossible to obtain an ideal runner design.
The liquid-cooled plate runner is designed using topology optimization method. By building the design domain in the physics simulation software, the runner topology optimization is performed using SIMP interpolation model and Helmholtz filter, and the runner structure is optimized by combining additive manufacturing technology.
It improves the temperature consistency of the battery module, reduces the temperature difference and runner pressure drop, achieves better heat dissipation effect and design freedom, and complies with the standards under enterprise drive durability conditions.
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Figure CN118965765B_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of battery thermal management, and relates to a liquid cooling plate flow channel design and optimization method. Background Art
[0002] With the expansion of battery capacity and system power density, a large amount of heat is generated during the charging and discharging of the battery system. The thermal safety and grouped thermal life problems of lithium batteries restrict the development of the battery system. However, lithium batteries are sensitive to the working temperature and have strict requirements for the working temperature range. Therefore, efficient battery thermal management technology is crucial for the safe operation, long cycle service life and reduction of the overall cost of lithium batteries, and is of great significance for promoting the large-scale application of lithium batteries. The main function of the battery thermal management system is to ensure that the maximum temperature of the battery is lower than the safety temperature of 40 °C when the battery is working; at the same time, it is necessary to maintain the consistency of the battery temperature and ensure that the temperature range of the battery module is controlled within 5 °C. At present, the power battery thermal management solutions are mainly divided into four categories: air cooling, liquid cooling, phase change materials and heat pipe cooling. Among them, liquid cooling is a method of cooling by taking away the heat generated by the battery through the convective heat transfer of the liquid, and it is a battery thermal management system with high thermal conductivity and good cooling effect.
[0003] At the present stage, the main method of liquid cooling is indirect cooling. The liquid cooling plate is in contact with the battery, and the coolant is passed through the liquid cooling plate for heat dissipation. Therefore, the liquid cooling plate flow channel design has a direct impact on the heat dissipation performance of the battery thermal management. In the traditional liquid cooling plate flow channel design, research is mainly carried out on the optimization of the liquid cooling plate flow channel size and shape to achieve better heat dissipation effect. The traditional liquid cooling plate flow channel design has the disadvantages of poor temperature consistency of the battery module, high temperature difference and high pressure drop. This method also has the disadvantages of strong design subjectivity, long design cycle and strong randomness, and an ideal liquid cooling plate flow channel design cannot be obtained. Using the topology optimization method to design the liquid cooling plate flow channel has great freedom. By arranging the inlet and outlet positions and quantities in the design domain, a more novel flow channel can be designed, and combined with additive manufacturing technology, rapid prototyping of the topology optimization flow channel with complex geometric parameters can be realized. Summary of the Invention
[0004] The technical problem to be solved by the present invention is: how to design a better flow channel by performing topology optimization flow channel design on the liquid cooling plate in the battery module, improving the temperature consistency of the battery module, reducing the temperature difference of the battery module, and reducing the flow channel pressure drop.
[0005] A liquid cooling plate flow channel design and optimization method based on topology optimization includes the following steps:
[0006] Step 1: Determine the geometric parameters of the liquid cooling plate according to the specific dimensions of the used battery module, and use the solid heat transfer physical field in the physical field simulation software to construct the design domain of the liquid cooling plate;
[0007] Step 2: Set the boundaries of the design domain according to the material parameters of the liquid cooling plate, the volume heat source of the battery module, and the working conditions;
[0008] The material parameters include the density, thermal conductivity, and specific heat capacity of the material;
[0009] Step 3: Define a material unit with variable thermal conductivity to fill the design domain, and define a variable θ p representing the material phase in the design domain. Control the changes of the entity and the flow channel through the variable θ p and determine the thermal conductivity based on the material phase corresponding to the variable θ p ;
[0010] The variable θ p takes values in the interval (0, 1). Taking 0 represents the entity, and taking 1 represents the flow channel. The thermal conductivity expression is as follows:
[0011] K = θ p ×k0
[0012] where K is the actual thermal conductivity, θ p is the design variable, and k0 is the initial thermal conductivity;
[0013] Step 4: Use the SIMP interpolation model to interpolate the thermal conductivity, and establish a flow channel topology optimization mathematical model with the minimum average temperature in the design domain as the objective function and the volume fraction as the constraint condition according to the control equation;
[0014] The objective function of the topology optimization is to minimize the average temperature in the design domain. The objective function expression is:
[0015]
[0016] where φ is the average temperature in the design domain, Ω is the design domain, and T is the temperature;
[0017] Step 5: Based on the flow channel topology optimization mathematical model obtained in Step 4, use the Helmholtz filter for density filtering, project according to the hyperbolic tangent function, and then use the optimization solver to solve and output the finally converged topology optimization result;
[0018] Step 6: Construct a three-dimensional flow channel model in a 3D modeling tool according to the two-dimensional flow channel model after topology optimization, and construct a battery pack thermal management structure in combination with the components in the battery module;
[0019] Step 7: Set the boundary conditions of each component of the battery pack thermal management structure under the driving durability condition, and test the heat dissipation performance of the topology-optimized flow channel on the battery pack in the CFD solver;
[0020] Step 8: Judge whether the maximum temperature, temperature difference of the battery pack and the pressure drop of the flow channel in the simulation meet the standards. If they meet the standards, complete the topology-optimized flow channel design. If they do not meet the standards, continue to repeat Steps 1 - 8 until they meet the standards;
[0021] Step 9: Further optimize the topology-optimized flow channel design obtained in Step 8, use experimental design and data analysis software for experimental design, study the influence laws of multi-factors such as flow channel volume fraction, coolant inlet temperature, and coolant flow rate on the temperature and pressure drop of the battery module, and determine the best solution for multi-objective optimization with the above multi-factors as the maximum temperature, temperature difference, and flow channel pressure drop as the objective functions.
[0022] Furthermore, the SIMP interpolation model used in Step 4 is as follows:
[0023] 0 ≤ θ c ≤ 1 (1)
[0024] θ f =θ c (2)
[0025] θ=θ f (3)
[0026]
[0027] Among them, θ p is the penalty material volume factor, θ min is the minimum penalty volume fraction, p simp is the simp index; θ c is the variable initial value, θ f is the intermediate variable used to calculate the design variable based on the variable initial value, and θ is the parameter used to calculate the design variable based on the intermediate variable θ f representation.
[0028] Furthermore, the control equation is a fixed heat transfer equation, specifically as follows:
[0029]
[0030] Among them, ρ is the average density of the battery, C p is the average specific heat capacity of the battery, T is the temperature, is the gradient operator, K is the thermal conductivity, q v is the heat source applied to the design domain.
[0031] Furthermore, the constraint conditions for establishing the mathematical model of the runner topology optimization are as follows:
[0032] The limiting condition for topology optimization is the runner volume fraction, and its expression is:
[0033] ∫ Ω θ p d Ω ≤WV
[0034] where W is the runner volume fraction and V is the area of the design domain.
[0035] Furthermore, during the process of density filtering using the Helmholtz filter and projection according to the hyperbolic tangent function, the expression for density filtering using the Helmholtz filter is as follows:
[0036]
[0037] where θ f is the material volume factor for filtering, θ c is the control material volume factor, and R min is the filtering radius;
[0038] The expression for projection according to the hyperbolic tangent function is as follows:
[0039]
[0040] where β is the projection slope and θ β is the projection point.
[0041] Furthermore, during the process of using the optimization solver to solve through iterative loops, the MMA algorithm is used in the optimization solver to optimize and solve the mathematical model of topology optimization. The condition for topology optimization convergence is:
[0042] max|θ pi -θ pi-1 |≤E
[0043] where θ pi is the value of the design variable in the current iteration process, θ pi-1 is the value of the design variable in the previous iteration process; E is the optimization tolerance.
[0044] Furthermore, during the process of constructing a three-dimensional runner model in a 3D modeling tool based on the two-dimensional runner model after topology optimization, first, the liquid cooling plate runner profile is obtained by fitting the topology optimization results, and then it is stretched in the 3D modeling tool to obtain the three-dimensional runner model.
[0045] Further, the boundary conditions under the driving durability working condition described in step 7 are that the battery module is in an environment temperature of 40°C, the initial temperature of the battery module is 40°C, the coolant at the water inlet is a 30% ethylene glycol solution, the flow rate is 10 L / min, and the temperature is 25°C.
[0046] Further, the specific process of step 9 includes the following steps:
[0047] Design a three-factor and three-level experiment using the Box-Behnken response surface method. The flow channel volume fractions are respectively selected as three types: 0.2, 0.3, and 0.4; the coolant inlet temperatures are respectively selected as 20°C, 25°C, and 30°C; the coolant flow rates are respectively selected as 8, 10, and 12 L / min.
[0048] According to the data obtained from the response surface test, the flow channel volume fraction is used as the variable x1, the coolant inlet temperature is used as the variable x2, and the coolant flow rate is used as the variable x3; the highest temperature of the battery module is used as the objective function M, the temperature difference is used as the objective function N, and the pressure drop is used as the objective function O.
[0049] Multi-objective optimization is carried out with the goals of the lowest highest temperature, the lowest temperature difference, and the lowest pressure drop for optimization. The multi-objective optimization mathematical model is:
[0050]
[0051] Among them, m is the highest temperature, N is the temperature difference, O is the pressure drop; W is the flow channel volume fraction, B is the inlet temperature, and C is the flow rate.
[0052] Further, the objective function M, the objective function N, and the objective function O are as follows:
[0053] M = 7.4835 + 15.6575x1 + 1.462x2 - 1.23688x3 - 0.225x1x2 - 3.125x1x3 + 0.00275x2x3 + 31.05x1 2 - 0.00968x2 2 + 0.092625x3 2
[0054] N = 6.22925 + 7.035x1 + 0.22525x2 - 0.730625x3 - 0.14x1x2 - 1.825x1x3 + 0.00175x2x3 + 19.025x1 2 - 0.00489x2 2 + 0.055688x3 2
[0055] O = 207.5 - 992.5x1 - 3.28×10 -13x2 - 10.625x3 + 3.77×10 -13 x1x2 + 100x1x3 + 6×10 - 16 x2x3 + 1000x1 2 + 3.86×10 -15 x2 2 + 5.375x3 2 。
[0056] Beneficial effects:
[0057] Compared with the traditional liquid cooling plate flow channel optimization method, the topology optimization design method of the present invention is carried out before the structure is determined, has greater freedom, can break through the flow channel structure limitation of the traditional heat exchange plate, and achieve better heat exchange effect; the topology optimization result is related to the heat source, coolant inlet parameters and coolant inlet and outlet positions, and can optimize the design of the liquid cooling plate flow channel according to the working conditions of the actual battery module under driving durability; finally, through the response surface experimental design, study the influence laws of multi-factors such as flow channel volume fraction, coolant inlet temperature, coolant flow rate, etc. on the temperature and pressure drop of the battery module, and determine the best solution for multi-objective optimization with the above multi-factors as the objective functions of the highest temperature, temperature difference, and flow channel pressure drop. The topology optimization-based liquid cooling plate flow channel design and optimization research method of the present invention can effectively reduce the temperature difference of the battery module, improve the temperature consistency of the battery module, and reduce the flow channel pressure drop. Brief description of the drawings
[0058] Figure 1 is a flow schematic diagram of a topology optimization-based liquid cooling plate flow channel design and optimization research method;
[0059] Figure 2 is a schematic diagram of the topology optimization design of the liquid cooling plate two-dimensional model;
[0060] Figure 3 is a schematic diagram of the two-dimensional flow channel structure after topology optimization with different volume factors;
[0061] Figure 4 is a schematic diagram of the three-dimensional flow channel structure after topology optimization with different volume factors;
[0062] Figure 5 is a schematic diagram of the battery pack thermal management structure; in the figure, 1 - battery module, 2 - thermal conductive adhesive, 3 - end plate, 4 - foam, 5 - liquid cooling plate, 6 - box body;
[0063] Figure 6 is a cloud map of the battery temperature distribution of the topology optimization flow channel thermal management system with different volume factors;
[0064] Figure 7It is the contour map of the battery temperature distribution under the optimal solution; under the optimal solution, the highest temperature of the battery module is 34.03 °C, the lowest temperature is 29.24 °C, the temperature difference is 4.79 °C, and the pressure drop in the flow channel is 611 Pa, meeting the standard requirements under the enterprise driving durability working conditions. Detailed implementation manners
[0065] Detailed implementation manner 1: Combining Figure 1 to illustrate this implementation manner,
[0066] This implementation manner is a method for the design and optimization of the flow channel of a liquid cooling plate based on topology optimization, including the following steps:
[0067] Step 1: Determine the geometric parameters of the liquid cooling plate according to the specific dimensions of the battery module used by the enterprise, and use the solid heat transfer physical field in COMSOL to construct the design domain of the liquid cooling plate.
[0068] The geometric parameters of the liquid cooling plate refer to the two-dimensional dimensions of the liquid cooling plate, including the length, width, inlet and outlet dimensions, inlet and outlet positions, and the number of inlets and outlets.
[0069] Step 2: Set the boundaries of the design domain according to the material parameters of the liquid cooling plate, the volume heat source of the battery module, and the working conditions. The schematic diagram of the topology optimization design of the two-dimensional model of the liquid cooling plate is as Figure 2 shown.
[0070] The material parameters include the density, thermal conductivity, and specific heat capacity of the material;
[0071] The volume heat source of the battery module is obtained by converting according to the heat generation power and volume of a single battery; the specific geometric dimensions of a single battery are 148 mm in length, 53 mm in width, and 100 mm in height; the heat generation power of a single battery is 11.337 W; the volume heat source is equal to the heat generation power divided by the volume, and the battery volume heat source is obtained as 14453 W / m 3
[0072] Driving durability working conditions (working conditions in three dimensions): The battery module is in an environment temperature of 40 °C, the initial temperature of the battery module is 40 °C, and the coolant temperature is 25 °C.
[0073] The specific boundary settings of the design domain are: The material of the liquid cooling plate is AL(3003), the density is 2730 kg / m 3 , the thermal conductivity is 163 W / kg, and the specific heat capacity is 893 J / kg·K; the volume heat source of the battery module is 14453 W / m 3 ; the working conditions are: Set the initial temperature of the design domain to 40 °C, the heat dissipation boundary temperature to 25 °C, and the remaining boundaries are set as thermal insulation, and assign the volume heat source of 14453 W / m 3 .
[0074] Step 3: Define a material unit filling design domain with variable thermal conductivity and define the variable θ p represents the material phase within the design domain. Based on the variable θ p control the changes of the entity and the flow channel. Based on the variable θ p determine the thermal conductivity corresponding to the material phase.
[0075] The variable θ p has a value defined within the interval (0, 1). Taking 0 represents the entity, and taking 1 represents the flow channel. The thermal conductivity expression is as follows:
[0076] K = θ p × k0
[0077] where K is the actual thermal conductivity, θ p is the design variable, and k0 is the initial thermal conductivity.
[0078] Step 4: Use the interpolation function to interpolate the thermal conductivity. Based on the control equation, establish a mathematical model for flow channel topology optimization with minimizing the average temperature in the design domain as the objective function and the volume fraction as the constraint condition.
[0079] The interpolation function is the SIMP interpolation model. In topology optimization, this interpolation model is a non - linear interpolation model with a penalty effect on intermediate variables, and its expression is:
[0080] 0 ≤ θ c ≤ 1 (1)
[0081] θ f = θ c (2)
[0082] θ = θ f (3)
[0083]
[0084] where, θ p is the penalty material volume factor, θ min is the minimum penalty volume fraction, p simp is the simp exponent; θ c is the initial value of the variable, θ f is the intermediate variable used to calculate the design variable based on the initial value of the variable, and θ is the parameter used to calculate the design variable based on the intermediate variable θ f indicated.
[0085] Formula (1) defines the initial value range of the variable θ c as the interval from 0 to 1; Formulas (2) - (4) perform interpolation on the variable using the SIMP interpolation function, and finally output the variable θ p ; Based on the variable θ output by the SIMP interpolation modelp Determine the thermal conductivity \(K = \theta\) p \(\times k_0\) to achieve interpolation of the thermal conductivity;
[0086] The governing equation is a fixed heat transfer equation, specifically as follows:
[0087]
[0088] where \(\rho\) is the average density of the battery, \(C\) p is the average specific heat capacity of the battery, \(T\) is the temperature, \(\nabla\) is the gradient operator, \(K\) is the thermal conductivity, \(q\) v is the heat source applied to the design domain.
[0089] The objective function of the topology optimization is to minimize the average temperature within the design domain, and the expression of the objective function is:
[0090]
[0091] where \(\varphi\) is the average temperature within the design domain, \(\Omega\) is the design domain, and \(T\) is the temperature.
[0092] The constraint condition of the topology optimization is the channel volume fraction, and its expression is:
[0093] \(\int\) Ω \(\theta\) p \(d\) Ω \(\leq WV\)
[0094] where \(W\) is the channel volume fraction and \(V\) is the area of the design domain.
[0095] The mathematical model of the channel topology optimization is as follows:
[0096] Find: \(\theta\) pi , \(i = 1, 2, \ldots, n\)
[0097]
[0098] Subject to: \(\theta\) p \(= [0, 1]\)
[0099]
[0100] \(\int\) Ω \(\theta\) p \(d\) Ω \(\leq WV\)
[0101] where \(\theta\) p is the penalty material volume factor and is the design variable of the topology optimization, \(\theta\) pi is the \(i\)-th design variable in \(\theta\) p , and the subscript \(i\) is used to represent a specific design variable; \(q\) vis the heat source applied to the design domain, K is the thermal conductivity, W is the flow channel volume fraction, and V is the area of the design domain.
[0102] Step 5: Based on the flow channel topology optimization mathematical model obtained in Step 4, use the Helmholtz filter for density filtering, eliminate the gray-scale elements according to the hyperbolic tangent function, and use the optimization solver to solve and output the finally converged topology optimization result.
[0103] Use the Helmholtz filter to perform density filtering on the intermediate variable, and its expression is:
[0104]
[0105] where, θ f is the filtered material volume factor, θ c is the control material volume factor, and R min is the filtering radius.
[0106] Selecting the projection based on the hyperbolic tangent function to eliminate the intermediate density can obtain a clearer topology image, and its expression is:
[0107]
[0108] where, β is the projection slope, and θ β is the projection point.
[0109] Equation (5) is for density filtering of the initial variable; Equation (6) is for hyperbolic sine projection of the variable after density filtering; and then according to the final output variable θ p , determine the thermal conductivity K = θ p × k0.
[0110] Use the optimization solver to solve and output the finally converged topology optimization result through iterative loops. In the optimization solver, use the MMA algorithm to optimize and solve the topology optimization mathematical model. The condition for topology optimization convergence is:
[0111] max|θ pi -θ pi-1 | ≤ E
[0112] where, θ pi is the value of the design variable in the current iteration process, and θ pi-1 is the value of the design variable in the previous iteration process. E is the optimization tolerance.
[0113] Step 6: Construct a three-dimensional flow channel model in the Space claim according to the two-dimensional flow channel model after topology optimization, and construct a battery pack thermal management structure in combination with the other components in the battery module.
[0114] In the process of constructing a three-dimensional flow channel model in SpaceClaim based on the topologically optimized two-dimensional flow channel model, first, the flow channel profile of the liquid cooling plate is obtained by fitting the topological optimization result, and then it is stretched in SpaceClaim to obtain the three-dimensional flow channel model. Schematic diagrams of the two-dimensional flow channel structures optimized with different volume factors are as shown in Figure 3 shown, and schematic diagrams of the three-dimensional flow channel structures optimized with different volume factors are as shown in Figure 4 shown;
[0115] The remaining components of the battery module include batteries, thermal conductive adhesives, foams, end plates, and boxes. All components are integrated to construct a battery pack thermal management structure in SpaceClaim. A schematic diagram of the battery pack thermal management structure is as shown in Figure 5 shown.
[0116] Step 7: Set the boundary conditions of each component of the battery pack thermal management structure under the driving durability condition, and test the heat dissipation performance of the topologically optimized flow channel for the battery pack in Star-ccm.
[0117] The boundary conditions under the driving durability condition are that the battery module is in an ambient temperature of 40°C, the initial temperature of the battery module is 40°C, the inlet coolant is a 30% ethylene glycol solution, the flow rate is 10 L / min, and the temperature is 25°C.
[0118] Step 8: Determine whether the maximum temperature, temperature difference of the battery pack, and pressure drop of the flow channel in the simulation meet the enterprise standards. If they meet, the design of the topologically optimized flow channel is completed; if not, repeat Steps 1 - 8 until the enterprise standards are met.
[0119] The enterprise standards are that the safe operating temperature of electric vehicles is 20°C - 40°C, the driving durability condition requires that the maximum temperature of the battery module does not exceed 40°C, the temperature difference in the battery module does not exceed 5°C, and the total pressure drop in the system does not exceed 3000 Pa.
[0120] Step 9: Further optimize the topologically optimized flow channel design obtained in Step 8. Use the DESIGN EXPERT 13.0 experimental design software for experimental design to study the influence laws of multi-factors such as the flow channel volume fraction, coolant inlet temperature, and coolant flow rate on the temperature and pressure drop of the battery module, and determine the best solution for multi-objective optimization with the above multi-factors as the objective functions for the maximum temperature, temperature difference, and flow channel pressure drop:
[0121] Design a three-factor and three-level experiment using the Box-Behnken response surface method. The flow channel volume fractions are respectively selected as three types: 0.2, 0.3, and 0.4; the coolant inlet temperatures are respectively selected as 20°C, 25°C, and 30°C; the coolant flow rates are respectively selected as 8, 10, and 12 L / min.
[0122] Based on the data obtained from the response surface experiment, the flow channel volume fraction is taken as variable x1, the coolant inlet temperature is taken as variable x2, and the coolant flow rate is taken as variable x3; the highest temperature of the battery module is taken as the objective function M, the temperature difference is taken as the objective function N, and the pressure drop is taken as the objective function O. The expressions of each objective function are as follows:
[0123] M = 7.4835 + 15.6575x1 + 1.462x2 - 1.23688x3 - 0.225x1x2 - 3.125x1x3 + 0.00275x2x3 + 31.05x1 2 - 0.00968x2 2 + 0.092625x3 2
[0124] N = 6.22925 + 7.035x1 + 0.22525x2 - 0.730625x3 - 0.14x1x2 - 1.825x1x3 + 0.00175x2x3 + 19.025x1 2 - 0.00489x2 2 + 0.055688x3 2
[0125] O = 207.5 - 992.5x1 - 3.28×10 -13 x2 - 10.625x3 + 3.77×10 -13 x1x2 + 100x1x3 + 6×10 - 16 x2x3 + 1000x1 2 + 3.86×10 -15 x2 2 + 5.375x3 2
[0126] Multi-objective optimization is carried out with the lowest highest temperature, the lowest temperature difference, and the lowest pressure drop as the objectives. The multi-objective optimization mathematical model is:
[0127]
[0128] where M is the highest temperature, N is the temperature difference, and O is the pressure drop; W is the flow channel volume fraction, B is the inlet temperature, and C is the flow rate.
[0129] The cloud diagram of the battery temperature distribution of the flow channel thermal management system with different volume factor topology optimizations is as Figure 6 shown, Figure 7 which is the cloud diagram of the battery temperature distribution under the optimal scheme; under the optimal scheme, the highest temperature of the battery module is 34.03 °C, the lowest temperature is 29.24 °C, the temperature difference is 4.79 °C, and the pressure drop in the flow channel is 611 Pa, meeting the standard requirements under the enterprise driving durability working conditions.
[0130] Step 10: Process the liquid cooling plate using additive manufacturing technology and conduct experimental verification according to the optimal solution.
[0131] The present invention may also have many other embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art can make various corresponding changes and deformations according to the present invention. However, these corresponding changes and deformations should all fall within the protection scope of the appended claims of the present invention.
Claims
1. A method for designing and optimizing the flow channels of a liquid cooling plate based on topology optimization, characterized in that, It includes the following steps: Step 1: Determine the geometric parameters of the liquid-cooling plate according to the specific size of the battery module used, and thus construct the design domain of the liquid-cooling plate in the physical field simulation software using the solid heat transfer physical field; Step 2: Set the boundaries of the design domain according to the material parameters of the liquid-cooling plate, the volume heat source of the battery module, and the working conditions; The material parameters include the density, thermal conductivity, and specific heat capacity of the material; Step 3: Define a material unit with variable thermal conductivity to fill the design domain and define the variable θ p represents the material phase within the design domain. Based on the variable θ p control the changes of the solid and the flow channel. Based on the variable θ p determine the thermal conductivity corresponding to the material phase; Variable θ p The value range is defined in the interval (0, 1). Taking 0 represents the entity, and taking 1 represents the flow channel. The expression of the thermal conductivity is as follows: K = θ p × k0 where K is the actual thermal conductivity, θ p is the design variable, and k0 is the initial thermal conductivity; Step 4: Use the SIMP interpolation model to interpolate the thermal conductivity, and establish a mathematical model for channel topology optimization with the average temperature in the design domain minimized as the objective function and the volume fraction as the constraint condition according to the control equation; The objective function of topology optimization is to minimize the average temperature in the design domain, and the expression of the objective function is: where, φ is the average temperature in the design domain, Ω is the design domain, and T is the temperature; Step 5: Based on the mathematical model for channel topology optimization obtained in Step 4, use the Helmholtz filter for density filtering, project according to the hyperbolic tangent function, and then use the optimization solver to solve and output the finally converged topology optimization result; Step 6: Construct a three-dimensional channel model in a 3D modeling tool according to the two-dimensional channel model after topology optimization, and construct a battery pack thermal management structure in combination with the components in the battery module; Step 7: Set the boundary conditions of each component of the battery pack thermal management structure under the driving durability condition, and test the heat dissipation performance of the topology-optimized channel for the battery pack in the CFD solver; Step 8: Judge whether the maximum temperature, temperature difference of the battery pack and the pressure drop of the channel in the simulation meet the standards. If they meet the standards, complete the design of the topology-optimized channel. If they do not meet the standards, continue to repeat Steps 1 - 8 until they meet the standards; Step 9: Further optimize the topology-optimized channel design obtained in Step 8, use experimental design and data analysis software for experimental design, study the influence laws of multiple factors such as the channel volume fraction, coolant inlet temperature, and coolant flow rate on the temperature and pressure drop of the battery module, and determine the best solution for multi-objective optimization with the above multiple factors as the objective functions for the maximum temperature, temperature difference, and channel pressure drop; The specific process of Step 9 includes the following steps: Adopt the Box-Behnken response surface method to design a three-factor and three-level experiment. The channel volume fractions are respectively selected as three types: 0.2, 0.3, and 0.4; the coolant inlet temperatures are respectively selected as 20°C, 25°C, and 30°C; the coolant flow rates are respectively selected as 8, 10, and 12 L / min; According to the data obtained from the response surface experiment, take the channel volume fraction as the variable x1, the coolant inlet temperature as the variable x2, and the coolant flow rate as the variable x3; take the maximum temperature of the battery module as the objective function M, the temperature difference as the objective function N, and the pressure drop as the objective function O; The multi-objective optimization searches for the optimal solution with the lowest maximum temperature, lowest temperature difference, and lowest pressure drop as the objectives, and the multi-objective optimization mathematical model is: where, M is the maximum temperature, N is the temperature difference, O is the pressure drop; W is the channel volume fraction, B is the inlet temperature, and C is the flow rate; The objective function M, the objective function N, and the objective function O are as follows: M = 7.4835 + 15.6575x1 + 1.462x2 - 1.23688x3 - 0.225x1x2 - 3.125x1x3 + 0.00275x2x3 + 31.05x1 2 - 0.00968x2 2 + 0.092625x32 N = 6.22925 + 7.035x1 + 0.22525x2 - 0.730625x3 - 0.14x1x2 - 1.825x1x3 + 0.00175x2x3 + 19.025x1 2 - 0.00489x2 2 + 0.055688x3 2 O = 207.5 - 992.5x1 - 3.28×10 -13 x2 - 10.625x3 + 3.77×10 -13 x1x2 + 100x1x3 + 6×10 -16 x2x3 + 1000x1 2 + 3.86×10 -15 x2 2 + 5.375x3 2 。 2. The method for designing and optimizing the flow channel of a liquid cooling plate based on topology optimization according to claim 1, characterized in that, The SIMP interpolation model used in Step 4 is as follows: 0 ≤ θ c ≤ 1 (1) θ f = θ c (2) θ = θ f (3) where, θ p is the penalty material volume factor, θ min is the minimum penalty volume fraction, p simp is the simp index; θ c is the initial value of the variable, θ f is the intermediate variable for calculating the design variable represented based on the initial value of the variable, θ is the parameter for calculating the design variable represented based on the intermediate variable θ f representation.
3. A method for designing and optimizing the flow channels of a liquid cooling plate based on topology optimization according to claim 2, characterized in that, The control equation is the fixed heat transfer equation, which is specifically as follows: where ρ is the average density of the battery, C p is the average specific heat capacity of the battery, T is the temperature, is the gradient operator, K is the thermal conductivity, q v is the heat source applied to the design domain.
4. A method for designing and optimizing the flow channels of a liquid cooling plate based on topology optimization according to claim 3, characterized in that, The constraint conditions for establishing the mathematical model of the runner topology optimization are as follows: The limiting condition for topology optimization is the runner volume fraction, and its expression is: ∫ Ω θ p d Ω ≤WV Among them, W is the runner volume fraction, and V is the area of the design domain.
5. A method for designing and optimizing the flow channels of a liquid cooling plate based on topology optimization according to any one of claims 2 to 4, characterized in that, During the process of density filtering using the Helmholtz filter and projection according to the hyperbolic tangent function, the expression for density filtering using the Helmholtz filter is as follows: Among them, θ f is the filtered material volume factor, θ c is the control material volume factor, R min is the filtration radius; The expression for projection according to the hyperbolic tangent function is as follows: Among them, β is the projection slope, and θ β is the projection point.
6. A method for designing and optimizing the flow channels of a liquid cooling plate based on topology optimization, characterized in that, During the process of solving through cyclic iteration using the optimization solver, the MMA algorithm is used in the optimization solver to optimize and solve the mathematical model of topology optimization. The condition for topology optimization convergence is: max|θ pi -θ pi-1 |≤E where, θ pi is the value of the design variable in the current iteration process, and θ pi-1 is the value of the design variable in the previous iteration process; E is the optimization tolerance.
7. A method for designing and optimizing the flow channels of a liquid cooling plate based on topology optimization, characterized in that, During the process of constructing a three-dimensional runner model in a 3D modeling tool based on the two-dimensional runner model after topology optimization, first, the runner profile of the liquid cooling plate is obtained by fitting the topology optimization result, and then it is stretched in the 3D modeling tool to obtain the three-dimensional runner model.
8. A method for designing and optimizing the flow channels of a liquid cooling plate based on topology optimization, characterized in that, The boundary conditions under the driving durability condition described in step 7 are that the battery module is in an ambient temperature of 40°C, the initial temperature of the battery module is 40°C, the inlet coolant is a 30% ethylene glycol solution, the flow rate is 10 L / min, and the temperature is 25°C.
Citation Information
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Multi-heat-source cold plate runner optimization method based on topological optimization
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