EVTOL battery pack thermal optimization method and system based on pulsating flow

Abstract

The invention relates to the technical field of battery pack thermal management, in particular to an eVTOL battery pack thermal optimization method based on pulsating flow, and the method comprises the steps: determining a battery pack design domain, building a two-dimensional optimization model, and discretizing the design domain; selecting optimization parameters, control equations and other conditions, constructing a topological optimization mathematical model, and obtaining and describing the relationship between related parameters and the unit material density; establishing a two-dimensional cold plate topological optimization model of the battery by taking the average temperature of the surface of the cold plate and the flow dissipated work of fluid as targets, generating an optimal heat dissipation flow channel, and introducing a pulsating flow technology; according to the established battery two-dimensional cold plate topological optimization model, a Helmholtz formula is used for filtering projection, and a preliminary optimization result is output; a pulsating flow and sliding mode control coupling design is adopted, the temperature change of the battery pack is monitored in real time, the frequency and amplitude of the pulsating flow are dynamically adjusted according to temperature feedback to reach an ideal target temperature, and a final optimization result is obtained.

Description

Technical Field

[0001] The present invention relates to the technical field of battery pack thermal management, and in particular to a pulsating flow-based eVTOL battery pack thermal optimization method and system. Background Art

[0002] With the rapid development of urban air mobility (UAM), electric vertical take-off and landing vehicles (eVTOL) have become an important research and development direction in this field due to their significant advantages such as low carbon, environmental protection, and flexible vertical take-off and landing. As the core power source of eVTOL, high-energy-density lithium-ion battery packs generate a large amount of heat during the charging and discharging process. If this heat cannot be dissipated promptly and effectively, it will lead to uneven battery temperature and performance degradation. In severe cases, it may even cause thermal runaway, posing a serious threat to flight safety. As an advanced design method, topology optimization technology can design efficient heat dissipation structures by optimizing material distribution, thus providing a new approach to solving heat dissipation problems. Pulsating flow technology significantly enhances the convective heat transfer effect through periodic flow disturbances, further improving heat dissipation efficiency. In current technical research, there has been no report on the effective combination of topology optimization and pulsating flow technology to achieve collaborative optimization of battery pack thermal management. Summary of the Invention

[0003] In response to the above-mentioned technical deficiencies, the present invention provides an eVTOL battery pack thermal optimization method and system based on pulsating flow to solve the problems of insufficient heat dissipation efficiency and temperature uniformity in the prior art.

[0004] The present invention is achieved through the following technical solutions:

[0005] A pulsating flow-based thermal optimization method for an eVTOL battery pack is provided, the method comprising the following steps:

[0006] Step S10: Determine the shape of the design domain based on the inlet and outlet positions of the battery pack of the electric vertical take-off and landing aircraft and the size of the battery pack, establish a two-dimensional optimization model based on the physical properties of the cold plate material and the thermophysical parameters of the coolant, and discretize the design domain into N finite elements;

[0007] Step S20: Select optimization parameters, control equations, boundary conditions, constraints, and objective functions, build a topology optimization mathematical model, and obtain the relationship between the relevant parameters of the cold plate and the coolant and the unit material density;

[0008] Step S30: Taking the average surface temperature of the cold plate and the dissipated work of the fluid flow as optimization targets, a two-dimensional cold plate topology optimization model for the battery is established. Finite element analysis and sensitivity calculation are used to update the cold plate material density distribution, obtain the optimal heat dissipation flow channel, and introduce pulsating flow technology;

[0009] Step S40: Based on the established two-dimensional battery cold plate topology optimization model, use the Helmholtz formula to perform filtering and projection, and output preliminary optimization results, including the cold plate material density distribution map and temperature gradient map combined with the topology optimization results;

[0010] Step S50: Using the coupling design of pulsating flow and sliding mode control, the temperature change of the battery pack is monitored in real time, and the frequency and amplitude of the pulsating flow are dynamically adjusted according to the temperature feedback to achieve the ideal target temperature, thereby obtaining the final optimization result.

[0011] Preferably, in step S20, optimization parameters, control equations, boundary conditions, constraints and objective functions are selected, and the control equations are the continuity equation, the momentum equation, the energy control equation of the fluid domain and the energy control equation of the solid domain, as shown in formula (1), formula (2), formula (3) and formula (4):

[0012]

[0013] Among them, u, ρ, p and μ are the velocity, density, pressure and dynamic viscosity of the fluid respectively, and F represents the friction force during the flow process. is a differential operator, representing the gradient, T represents the temperature of the fluid; where C pf 、k f and k s are the specific heat capacity of the fluid, the thermal conductivity of the fluid, and the thermal conductivity of the solid, respectively, and Q is the amount of heat in the solid domain.

[0014] Preferably, in step S20, optimization parameters, control equations, boundary conditions, constraints and objective functions are selected, and the boundary conditions include key parameters such as pressure, speed, temperature and heat generation at the cooling inlet of the battery pack of the electric vertical take-off and landing aircraft.

[0015] Preferably, in step S20, optimization parameters, control equations, boundary conditions, constraints and objective functions are selected, and the constraints are mainly the volume ratio of the fluid domain.

[0016] Preferably, the optimization parameters, control equations, boundary conditions, constraints and objective function are determined in step S20. The objective function comprehensively considers four dimensions: maximizing heat transfer, minimizing average temperature, minimizing pressure drop and minimizing liquid flow energy dissipation. The average temperature φ is used. T and fluid power loss φ f Construct the objective function as shown in formula (5):

[0017]

[0018] Among them, φ is the objective function, ω T and ω f They are φT and φ f The temperature weighting coefficient and pressure drop weighting coefficient, φ T,0 and φ f,0 is the normalization factor of the objective function, γ is the design variable, Ω is the design domain, is the target average temperature. In order to reduce the area between the fluid and the solid in the result, hyperbolic tangent projection is used to reduce the intermediate values in the design variables. The calculation formula of the design variable γ after filtering and projection operations is shown in formula (6):

[0019]

[0020] Where β and γβ are the projection slope and projection point respectively, γ fi are the filter design variables.

[0021] Preferably, in step S20, the topology optimization mathematical model is constructed by interpolating material parameters using the Darcy seepage model and the rational approximation model. A density-based topology optimization method is used for design. The design domain is filled with porous medium materials, and their properties are adjusted by a design variable γ that varies continuously in the range of 0 to 1. The reverse permeability α and the effective thermal conductivity k of the porous medium material are both dependent on γ. The relationship between α, k and γ is defined using the Darcy interpolation function, as shown in Equations (6) and (7):

[0022]

[0023] Among them, α f and α s Represent the reverse permeability of the fluid phase and the solid phase respectively. When the design variable γ is 0, the reverse permeability α(γ) is equal to the reverse permeability α of the solid phase. s , so that the flow velocity in this area is close to zero, so that the material behaves locally as a solid. On the contrary, when γ is 1, α(γ) is equal to the reverse permeability α of the fluid phase. f , so that the material behaves as a fluid locally. The parameters q1 and q2 are penalty factors in the Darcy interpolation model, which are used to adjust the values of α and k functions. f and k s Represent the effective thermal conductivity of the fluid phase and the solid phase, respectively. In addition, q1 and q2 can also affect the convergence of the topology optimization process and the value of the design variable γ between 0 and 1. The thermophysical parameters in the porous medium are also affected by the design variable γ.

[0024] The rational approximation model interpolates the thermal conductivity λ, specific heat C, and density, and selects the following interpolation function for calculation, as shown in Equations (8), (9), and (10):

[0025]

[0026] The heat source area for topology optimization is the gap area of the cold plate, specifically the battery area. The goal of topology optimization is to minimize the average temperature of the battery area and the pressure drop of the cold plate. The pressure drop is represented by the fluid power loss. The smaller the fluid power loss, the lower the pressure drop in the cold plate. The calculation formulas for the average temperature ΦT and the fluid power loss Φf are shown in Equations (11) and (12):

[0027]

[0028] in, and Ω represent the battery area and design domain, respectively.

[0029] Preferably, obtaining and describing the relationship between relevant parameters and unit material density in step S20 refers to obtaining the reverse permeability and thermal conductivity of the cold plate and the coolant, and using an interpolation function to describe the relationship between the reverse permeability and the thermal conductivity and the unit material density.

[0030] Preferably, the pulsating flow technology is introduced in step S30 by adding a gas pulsation generator to the optimized flow channel to generate a pulsating flow, and regulating the coolant flow rate by periodic pressure fluctuations, thereby establishing a pulsating flow control equation, as shown in formula (13):

[0031] Q(t)=Q0(1+Asin(2πft)) (13)

[0032] Among them, Q0 is the average flow rate, A is the pulsation amplitude, and f is the optimal pulsation frequency. Combined with computational fluid dynamics (CFD) simulation, the pulsation parameters are optimized to reduce flow resistance and pump power consumption.

[0033] Preferably, the coupling design of pulsating flow and sliding mode control is adopted in step S50 to monitor the temperature change of the battery pack in real time, and to add parameter f to the pulsating flow characteristics. p , as shown in formula (8):

[0034]

[0035] Where ρ is the coolant density, u is the coolant flow rate, t is the unit time, p is the coolant pressure, f p is the pulsation driving force term, which is used to reflect the periodic pressure fluctuations. is a differential operator, representing the gradient. The pulsating flow breaks the laminar stability through periodic velocity changes, promotes vortex generation, and significantly increases turbulent kinetic energy. The heat transfer process equation between the fluid and the battery pack is shown in Equation (15):

[0036]

[0037] Among them, c pis the specific heat capacity, T is the fluid temperature, k is the thermal conductivity; q gen The pulsating flow periodically flushes the wall by alternating acceleration and deceleration, reducing the thickness of the thermal boundary layer (δ T ) thus enhancing the convective heat transfer coefficient h, as shown in formula (16):

[0038]

[0039] The pulsating flow control equation optimizes thermal management performance from the dynamics and energy transfer levels by introducing periodic unsteady terms. Its core lies in using disturbances in the time dimension to break the laminar flow and achieve efficient heat dissipation with lower energy consumption. For high-energy-density battery packs, fluid heat exchange is still the best choice. Its high thermal efficiency and uniformity can effectively ensure flight safety and battery life. Adding a pulsating flow device to the flow channel can form a laminar-turbulent mixed mode to balance energy consumption and heat dissipation requirements.

[0040] Preferably, in step S50, a coupling design of pulsating flow and sliding mode control is adopted, and a sliding mode controller is added to perform sliding mode control on the pulsating controller. In order to simplify the system model and calculation, the dynamics of the coolant flow rate controlled by the pneumatic pulsation generator can be described by a first-order nonlinear model, as shown in formula (17):

[0041]

[0042] Where x(t) is the system state vector, which includes parameters such as flow rate and temperature; u(t) is the control input, that is, the control signal of the pneumatic pulsation generator; d(t) is the external disturbance: the initial temperature change and pressure change of the coolant; f(x, t) and g(x) are nonlinear functions of the system, and the sliding surface is selected as a linear combination of flow rate errors, as shown in Equation (18):

[0043] s=e v +λ∫e v dt (18)

[0044] e v =v d -v is the velocity error, v d is the expected flow rate, and v is the actual flow rate. In order to accurately control the flow rate change, the exponential convergence law is randomly selected to ensure that the system state quickly converges to the sliding mode surface, as shown in Equation (19):

[0045]

[0046] Where ε>0 and k>0 are design parameters used to adjust the convergence speed and system stability; -εsign(s) means forcing the system state to approach the sliding surface; -ks means accelerating convergence and suppressing high-frequency chattering. Based on the sliding surface and the convergence law, the control input u is designed. The control input includes equivalent control terms and switching control terms; the equivalent control term u e It is used to make the system state approach the sliding surface. On the sliding surface, the system should satisfy By solving, we can obtain the equivalent control term, as shown in formula (20):

[0047]

[0048] Switch control u s The system state is kept on the sliding surface and the uncertainty and disturbance of the system are overcome. Combining the equivalent control term and the switching control term, the complete control law is obtained, as shown in Equation (21) and Equation (22):

[0049]

[0050] In order to ensure the stability of the system, Lyapunov stability theory can be used for analysis, and the Lyapunov function can be selected, as shown in Equations (23) and (24):

[0051]

[0052] Since ε>0 and k>0, it means that the system is stable on the sliding film surface. The sliding mode controller designed above is used to control the change of coolant flow rate. This controller ensures that the system state can quickly and stably approach and remain on the sliding surface through the design of sliding surface, reaching law and control law, thereby achieving precise control of coolant flow rate.

[0053] In addition, to achieve the above objectives, the present invention further proposes an eVTOL battery pack thermal optimization system based on pulsating flow, wherein the eVTOL battery pack thermal optimization system based on pulsating flow comprises:

[0054] Design Domain Determination and Discretization Module: This module is used to determine the shape of the design domain based on the inlet and outlet locations and battery pack dimensions of the electric vertical take-off and landing vehicle battery pack, establish a two-dimensional optimization model based on the physical properties of the cold plate material and the thermophysical parameters of the coolant, and discretize the design domain into N finite elements.

[0055] Topology optimization mathematical model construction module: used to select optimization parameters, control equations, boundary conditions, constraints and objective functions, build a topology optimization mathematical model, and obtain the relationship between the relevant parameters of the cold plate and coolant and the unit material density;

[0056] Battery 2D Cold Plate Topology Optimization Model Construction and Pulsating Flow Introduction Module: This module is used to establish a 2D battery cold plate topology optimization model based on the average cold plate surface temperature and fluid flow dissipation work as optimization targets. Finite element analysis and sensitivity calculations are used to update the cold plate material density distribution, obtain the optimal heat dissipation flow path, and introduce pulsating flow technology.

[0057] Filtering projection module: It is used to perform filtering projection based on the established battery two-dimensional cold plate topology optimization model using the Helmholtz formula, and output preliminary optimization results, including the cold plate material density distribution map and temperature gradient map combined with the topology optimization results;

[0058] Pulsating flow and sliding mode control coupling module: used for the coupling design of pulsating flow and sliding mode control, real-time monitoring of battery pack temperature changes, and dynamic adjustment of the pulsating flow frequency and amplitude based on temperature feedback to achieve the ideal target temperature, thereby obtaining the final optimization result.

[0059] The advantages and effects of the present invention are:

[0060] The pulsating flow-based eVTOL battery pack thermal optimization method and system proposed in this invention solve the key problems of eVTOL battery pack thermal management through the combined effect of topology optimization and pulsating flow, providing an efficient and reliable thermal management solution for the development of eVTOL to ensure flight safety and improve the performance and life of the battery pack. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0062] Figure 1 Flowchart of the eVTOL battery pack thermal optimization method based on pulsating flow of the present invention.

[0063] Figure 2 This is a schematic structural diagram of an eVTOL battery pack thermal optimization system based on pulsating flow according to the present invention.

[0064] Figure 3 This is a control diagram of the battery cooling system of the present invention.

[0065] Figure 4 Schematic diagram of the two-dimensional model of the cold plate of the present invention.

[0066] Figure 5 This is a two-dimensional model diagram of the topology optimized cold plate of the present invention.

[0067] Figure 6 This is the velocity gradient diagram of the flow channel after topology optimization of the present invention.

[0068] Figure 7 This is a temperature gradient diagram for different flow rates after topology optimization of the present invention. DETAILED DESCRIPTION

[0069] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0070] like Figure 1 As shown, in one embodiment of the present invention, a method for thermal optimization of an eVTOL battery pack based on pulsating flow includes the following steps:

[0071] Step S10: Determine the shape of the design domain according to the inlet and outlet positions of the battery pack of the electric vertical take-off and landing aircraft and the size of the battery pack, establish a two-dimensional optimization model according to the physical properties of the cold plate material and the thermophysical parameters of the coolant, and discretize the design domain into N finite elements.

[0072] Discretizing the design domain into N finite elements, and transforming the continuous design domain into a collection of finite elements, allows complex physical problems to be transformed into a system of algebraic equations for solution. This allows for numerical calculations to be performed on a computer, analyzing and calculating each element to ultimately obtain an approximate solution for the entire design domain. Compared to directly processing the continuous design domain, discretized calculations are more efficient and accurate, capable of handling a variety of complex boundary conditions and physical phenomena.

[0073] Step S20: Step S20: Select optimization parameters, control equations, boundary conditions, constraints and objective functions, build a topology optimization mathematical model, and obtain the relationship between the relevant parameters of the cold plate and coolant and the unit material density.

[0074] Specifically, in step S20, optimization parameters, control equations, boundary conditions, constraints, and objective functions are selected. The control equations are the continuity equation, the momentum equation, the energy control equation for the fluid domain, and the energy control equation for the solid domain, as shown in Equations (1), (2), (3), and (4):

[0075]

[0076] Among them, u, ρ, p and μ are the velocity, density, pressure and dynamic viscosity of the fluid respectively, and F represents the friction force during the flow process. is a differential operator, representing the gradient, T represents the temperature of the fluid; where C pf 、k f and k s are the specific heat capacity of the fluid, the thermal conductivity of the fluid, and the thermal conductivity of the solid, respectively, and Q is the amount of heat in the solid domain.

[0077] Specifically, in step S20, optimization parameters, control equations, boundary conditions, constraints and objective functions are selected, wherein the boundary conditions include key parameters such as pressure, velocity, temperature and heat generation at the cooling inlet of the battery pack of the electric vertical take-off and landing aircraft.

[0078] Specifically, in step S20 , optimization parameters, control equations, boundary conditions, constraints and objective functions are selected, wherein the constraints are mainly the volume ratio of the fluid domain.

[0079] Specifically, in step S20, the optimization parameters, control equations, boundary conditions, constraints and objective functions are determined. The objective function comprehensively considers four dimensions: maximizing heat transfer, minimizing average temperature, minimizing pressure drop and minimizing liquid flow energy dissipation. The average temperature φ is used. T and fluid power loss φ f Construct the objective function as shown in formula (5):

[0080]

[0081] Among them, φ is the objective function, ω T and ω f They are φ T and φ f The temperature weighting coefficient and pressure drop weighting coefficient, φ T,0 and φ f,0 is the normalization factor of the objective function, γ is the design variable, Ω is the design domain, is the target average temperature. In order to reduce the area between the fluid and the solid in the result, hyperbolic tangent projection is used to reduce the intermediate values in the design variables. The calculation formula of the design variable γ after filtering and projection operations is shown in formula (6):

[0082]

[0083] Where β and γβ are the projection slope and projection point respectively, γ fi are the filter design variables.

[0084] Specifically, in step S20, the topology optimization mathematical model is constructed by interpolating the material parameters using the Darcy seepage model and the rational approximation model. The density-based topology optimization method is used for design. The design domain is filled with porous medium materials, and their properties are adjusted by the design variable γ that varies continuously in the range of 0 to 1. The reverse permeability α and the effective thermal conductivity k of the porous medium material are both dependent on γ. The relationship between α, k and γ is defined using the Darcy interpolation function, as shown in Equations (7) and (8):

[0085]

[0086] Among them, α f and α s Represent the reverse permeability of the fluid phase and the solid phase respectively. When the design variable γ is 0, the reverse permeability α(γ) is equal to the reverse permeability α of the solid phase. s , so that the flow velocity in this area is close to zero, so that the material behaves locally as a solid. On the contrary, when γ is 1, α(γ) is equal to the reverse permeability α of the fluid phase. f , so that the material behaves as a fluid locally. The parameters q1 and q2 are penalty factors in the Darcy interpolation model, which are used to adjust the values of α and k functions. f and k s Represent the effective thermal conductivity of the fluid phase and the solid phase, respectively. In addition, q1 and q2 can also affect the convergence of the topology optimization process and the value of the design variable γ between 0 and 1. The thermophysical parameters in the porous medium are also affected by the design variable γ.

[0087] The rational approximation model interpolates the thermal conductivity λ, specific heat C, and density, and the following interpolation functions are selected for calculation, as shown in Equations (9), (10), and (11):

[0088]

[0089]

[0090] The heat source area for topology optimization is the gap area of the cold plate, specifically the battery area. The goal of topology optimization is to minimize the average temperature of the battery area and the pressure drop of the cold plate. The pressure drop is represented by the fluid power loss. The smaller the fluid power loss, the lower the pressure drop in the cold plate. The calculation formulas for the average temperature ΦT and the fluid power loss Φf are shown in Equations (12) and (13):

[0091]

[0092] in, and Ω represent the battery area and design domain, respectively.

[0093] Specifically, obtaining and describing the relationship between relevant parameters and unit material density in step S20 refers to obtaining the reverse permeability and thermal conductivity of the cold plate and the coolant, and using an interpolation function to describe the relationship between the reverse permeability and the thermal conductivity and the unit material density.

[0094] Step S30: Taking the average surface temperature of the cold plate and the dissipated work of the fluid flow as optimization targets, a two-dimensional cold plate topology optimization model of the battery is established. The cold plate material density distribution is updated through finite element analysis and sensitivity calculation to obtain the optimal heat dissipation flow channel, and pulsating flow technology is introduced.

[0095] Specifically, the pulsating flow technology is introduced in step S30 by adding a gas pulsation generator to the optimized flow channel to generate pulsating flow, and regulating the coolant flow rate through periodic pressure fluctuations, thereby establishing a pulsating flow control equation, as shown in formula (14):

[0096] Q(t)=Q0(1+Asin(2πft)) (14)

[0097] Among them, Q0 is the average flow rate, A is the pulsation amplitude, and f is the optimal pulsation frequency. Combined with computational fluid dynamics (CFD) simulation, the pulsation parameters are optimized to reduce flow resistance and pump power consumption.

[0098] Step S40: Based on the established two-dimensional battery cold plate topology optimization model, use the Helmholtz formula to perform filtering projection and output preliminary optimization results, including the cold plate material density distribution map and temperature gradient map combined with the topology optimization results.

[0099] Step S50: Using the coupling design of pulsating flow and sliding mode control, the temperature change of the battery pack is monitored in real time, and the frequency and amplitude of the pulsating flow are dynamically adjusted according to the temperature feedback to achieve the ideal target temperature, thereby obtaining the final optimization result.

[0100] Specifically, in step S50, a coupling design of pulsating flow and sliding mode control is adopted to monitor the temperature change of the battery pack in the two-dimensional cold plate model of the battery in real time. Based on the unsteady Navier-Stokes equation, the parameter f is added to the pulsating flow characteristics. p , as shown in formula (15):

[0101]

[0102] Where, is the coolant density, u is the coolant flow rate, t is the unit time, p is the coolant pressure, f p is the pulsation driving force term, which is used to reflect the periodic pressure fluctuations. is a differential operator, representing the gradient. The pulsating flow breaks the laminar stability through periodic velocity changes, promotes vortex generation, and significantly increases turbulent kinetic energy. The heat transfer process equation between the fluid and the battery pack is shown in Equation (16):

[0103]

[0104] Among them, c p is the specific heat capacity, T is the fluid temperature, k is the thermal conductivity; q gen The pulsating flow periodically flushes the wall by alternating acceleration and deceleration, reducing the thickness of the thermal boundary layer (δ T ) thereby enhancing the convective heat transfer coefficient h, as shown in Equation (17):

[0105]

[0106] The pulsating flow control equation optimizes thermal management performance from the dynamics and energy transfer levels by introducing periodic unsteady terms. Its core lies in using disturbances in the time dimension to break the laminar flow and achieve efficient heat dissipation with lower energy consumption. For high-energy-density battery packs, fluid heat exchange is still the best choice. Its high thermal efficiency and uniformity can effectively ensure flight safety and battery life. Adding a pulsating flow device to the flow channel can form a laminar-turbulent mixed mode to balance energy consumption and heat dissipation requirements.

[0107] Specifically, in step S50, a coupling design of pulsating flow and sliding mode control is adopted, and a sliding mode controller is added to perform sliding mode control on the pulsating controller. In order to simplify the system model and calculation, the dynamics of the coolant flow rate controlled by the gas pulsation generator can be described by a first-order nonlinear model, as shown in Equation (18):

[0108]

[0109] Where x(t) is the system state vector, which includes parameters such as flow rate and temperature; u(t) is the control input, that is, the control signal of the pneumatic pulsation generator; d(t) is the external disturbance: the initial temperature change and pressure change of the coolant; f(x, t) and g(x) are nonlinear functions of the system, and the sliding surface is selected as a linear combination of flow rate errors, as shown in Equation (19):

[0110] s=e v +λ∫e v dt (19)

[0111] e v =v d -v is the velocity error, v d is the expected flow rate, and v is the actual flow rate. In order to accurately control the flow rate change, the exponential reaching law is randomly selected to ensure that the system state converges quickly to the sliding mode surface, as shown in Equation (20):

[0112]

[0113] Where ε>0 and k>0 are design parameters used to adjust the convergence speed and system stability; -εsign(s) means forcing the system state to approach the sliding surface; -ks means accelerating convergence and suppressing high-frequency chattering. Based on the sliding surface and the convergence law, the control input u is designed. The control input includes equivalent control terms and switching control terms; the equivalent control term u e It is used to make the system state approach the sliding surface. On the sliding surface, the system should satisfy By solving, we can obtain the equivalent control term, as shown in formula (21):

[0114]

[0115] Switch control u s The system state is kept on the sliding surface and the uncertainty and disturbance of the system are overcome. Combining the equivalent control term and the switching control term, the complete control law is obtained, as shown in Equation (22) and Equation (23):

[0116]

[0117] In order to ensure the stability of the system, Lyapunov stability theory can be used for analysis, and the Lyapunov function can be selected, as shown in Equations (24) and (25):

[0118]

[0119] Since ε>0 and k>0, it means that the system is stable on the sliding film surface. The sliding mode controller designed above is used to control the change of coolant flow rate. This controller ensures that the system state can quickly and stably approach and remain on the sliding surface through the design of sliding surface, reaching law and control law, thereby achieving precise control of coolant flow rate.

[0120] In addition, if Figure 2 As shown, in one embodiment of the present invention, a pulsating flow-based eVTOL battery pack thermal optimization system is proposed. The pulsating flow-based eVTOL battery pack thermal optimization system includes:

[0121] Design Domain Determination and Discretization Module: This module is used to determine the shape of the design domain based on the inlet and outlet locations and battery pack dimensions of the electric vertical take-off and landing vehicle battery pack, establish a two-dimensional optimization model based on the physical properties of the cold plate material and the thermophysical parameters of the coolant, and discretize the design domain into N finite elements.

[0122] Topology optimization mathematical model construction module: used to select optimization parameters, control equations, boundary conditions, constraints and objective functions, build a topology optimization mathematical model, and obtain the relationship between the relevant parameters of the cold plate and coolant and the unit material density;

[0123] Battery 2D Cold Plate Topology Optimization Model Construction and Pulsating Flow Introduction Module: This module is used to establish a 2D battery cold plate topology optimization model based on the average cold plate surface temperature and fluid flow dissipation work as optimization targets. Finite element analysis and sensitivity calculations are used to update the cold plate material density distribution, obtain the optimal heat dissipation flow path, and introduce pulsating flow technology.

[0124] Filtering projection module: It is used to perform filtering projection based on the established battery two-dimensional cold plate topology optimization model using the Helmholtz formula, and output preliminary optimization results, including the cold plate material density distribution map and temperature gradient map combined with the topology optimization results;

[0125] Pulsating flow and sliding mode control coupling module: used for the coupling design of pulsating flow and sliding mode control, real-time monitoring of battery pack temperature changes, and dynamic adjustment of the pulsating flow frequency and amplitude based on temperature feedback to achieve the ideal target temperature, thereby obtaining the final optimization result.

[0126] This application provides a pulsating flow-based eVTOL battery pack thermal optimization system. This system utilizes the pulsating flow-based eVTOL battery pack thermal optimization method described in the aforementioned embodiment to address the technical issues of low heat dissipation efficiency and insufficient temperature uniformity in conventional aircraft battery packs. Compared to the prior art, the pulsating flow-based eVTOL battery pack thermal optimization system provided in this application offers the same beneficial effects as the pulsating flow-based eVTOL battery pack thermal optimization method described in the aforementioned embodiment. Other technical features of the pulsating flow-based eVTOL battery pack thermal optimization system are the same as those disclosed in the aforementioned embodiment and are not further detailed here.

[0127] like Figure 3 As shown, it is a schematic diagram of the control of the battery cooling system of the present invention, including a sliding membrane controller, a pneumatic pulsation generator, a topology optimized cold plate and a temperature sensor, and the optimal target temperature is achieved by the battery pack thermal management optimization method of the present invention.

[0128] like Figure 4 The figure shows a case of the present invention, which is a schematic diagram of the topologically optimized cold plate flow channel structure simulated by software. The two-dimensional cold plate model has a size of 240mm×180mm, and the inlet and outlet are on both sides of the cold plate, with a size of 18mm×7.5mm. The solid material of the cold plate is aluminum, and its physical property parameters are k s =202[W / (m*K)] solid thermal conductivity, solid specific heat capacity C s =900[J / kg / K)], solid density P s =2700[kg / m^3] solid density; water is used as the coolant, and its physical parameters are, fluid thermal conductivity k f =0.6[W / m / (K)], fluid specific heat capacity C f=4200[J / kg / K], fluid density ρ f =1000[kg / m^3].

[0129] Figure 5 To simulate the topology optimization flow channel velocity diagram under different flow velocities through software; Figure 6 is the temperature gradient diagram, Figure 7 This is the temperature gradient diagram for different flow rates after topology optimization. As the speed increases from 0.018m / s to 0.02m / s, the average temperature drops by about 5.3°. By comparison, we can see the impact of pulsating flow on the average temperature and power consumption by regulating the coolant flow rate through periodic pressure fluctuations. Through the synergistic effect of structural optimization and flow control, the heat dissipation performance and thermal uniformity are significantly improved.

[0130] The various parts disclosed in this application can be implemented using hardware, software, firmware, or a combination thereof. In the description of the above embodiments, specific features, structures, materials, or characteristics can be combined in any appropriate manner in any one or more embodiments or examples.

[0131] Obviously, those skilled in the art may make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if such changes and modifications fall within the scope of the claims and their equivalents, the present invention is intended to include such changes and modifications.

Claims

1. An eVTOL battery pack thermal optimization method based on pulsating flow, characterized in that: The method comprises the following steps: Step S10: Determine the shape of the design domain based on the inlet and outlet positions of the battery pack of the electric vertical take-off and landing aircraft and the size of the battery pack, establish a two-dimensional optimization model based on the physical properties of the cold plate material and the thermophysical parameters of the coolant, and discretize the design domain into N finite elements; Step S20: Select optimization parameters, control equations, boundary conditions, constraints, and objective functions, build a topology optimization mathematical model, and obtain the relationship between the relevant parameters of the cold plate and the coolant and the unit material density; Step S30: Taking the average surface temperature of the cold plate and the dissipated work of the fluid flow as optimization targets, a two-dimensional cold plate topology optimization model for the battery is established. Finite element analysis and sensitivity calculation are used to update the cold plate material density distribution, obtain the optimal heat dissipation flow channel, and introduce pulsating flow technology; Step S40: Based on the established two-dimensional battery cold plate topology optimization model, use the Helmholtz formula to perform filtering and projection, and output preliminary optimization results, including the cold plate material density distribution map and temperature gradient map combined with the topology optimization results; Step S50: Using the coupling design of pulsating flow and sliding mode control, the temperature change of the battery pack is monitored in real time, and the frequency and amplitude of the pulsating flow are dynamically adjusted according to the temperature feedback to achieve the ideal target temperature, thereby obtaining the final optimization result.

2. The eVTOL battery pack thermal optimization method based on pulsating flow according to claim 1, characterized in that: The control equations are the continuity equation, the momentum equation, the energy control equation of the fluid domain, and the energy control equation of the solid domain, as shown in Equations (1), (2), (3), and (4): Among them, u, ρ, p and μ are the velocity, density, pressure and dynamic viscosity of the fluid respectively, F represents the friction during the flow process, T represents the temperature of the fluid, Is a differential operator, representing the gradient; where C pf 、k f and k s are the specific heat capacity of the fluid, the thermal conductivity of the fluid, and the thermal conductivity of the solid, respectively, and Q is the amount of heat in the solid domain.

3. The eVTOL battery pack thermal optimization method based on pulsating flow according to claim 1, characterized in that: The boundary conditions include pressure, velocity, temperature and heat generation parameters at the cooling inlet of the battery pack of the electric vertical take-off and landing aircraft.

4. The eVTOL battery pack thermal optimization method based on pulsating flow according to claim 1, characterized in that: The constraint condition is the volume ratio of the fluid domain.

5. The eVTOL battery pack thermal optimization method based on pulsating flow according to claim 1, characterized in that: The objective function comprehensively considers the four dimensions of heat transfer maximization, average temperature minimization, pressure drop minimization and liquid flow energy dissipation minimization. T and fluid power loss φ f Construct the objective function as shown in formula (5): oh T +oh f =1 Among them, φ is the objective function, ω T and ω f They are φ T and φ f The temperature weighting coefficient and pressure drop weighting coefficient, φ T,0 and φ f,0 is the normalization factor of the objective function, γ is the design variable, Ω is the design domain, is the target average temperature.

6. The eVTOL battery pack thermal optimization method based on pulsating flow according to claim 1, characterized in that: The topology optimization mathematical model constructed in step S20 is constructed by interpolating material parameters using the Darcy seepage model and the rational approximation model. A density-based topology optimization method is used for design. The design domain is filled with porous medium materials, and their properties are adjusted by a design variable γ that varies continuously in the range of 0 to 1. The reverse permeability α and the effective thermal conductivity k of the porous medium material are both dependent on γ. The relationship between α, k and γ is defined using the Darcy interpolation function, as shown in Equations (6) and (7): Among them, α f and α s Represent the reverse osmosis of the fluid phase and the solid phase respectively. When the design variable γ is 0, the reverse osmosis α(γ) is equal to the reverse osmosis α of the solid phase. s , making the material behave as a solid locally. On the contrary, when γ is 1, α(γ) is equal to the reverse permeability α of the fluid phase. f , so that the material behaves as a fluid locally. The parameters q1 and q2 are penalty factors in the Darcy interpolation model, which are used to adjust the values of α and k functions. In addition, q1 and q2 affect the convergence of the topology optimization process and the value of the design variable γ between 0 and 1. The thermal physical parameters in the porous medium are also affected by the design variable γ, k f and k s represent the effective thermal conductivities of the fluid and solid phases, respectively.

7. The eVTOL battery pack thermal optimization method based on pulsating flow according to claim 1, characterized in that: Acquiring and describing the relationship between relevant parameters and unit material density in step S20 refers to acquiring the reverse permeability and thermal conductivity of the cold plate and coolant, and using an interpolation function to describe the relationship between the reverse permeability and thermal conductivity and the unit material density.

8. The eVTOL battery pack thermal optimization method based on pulsating flow according to claim 1, characterized in that: In step S50, the coupling design of pulsating flow and sliding mode control is adopted to monitor the temperature change of the battery pack in real time, and the parameter f is added to the pulsating flow characteristics. p , as shown in formula (8): Where ρ is the coolant density, u is the coolant flow rate, t is the unit time, p is the coolant pressure, f p is the pulsation driving force term, which is used to reflect the periodic pressure fluctuations. It is a differential operator that represents the gradient. Pulsating flow breaks the laminar stability through periodic velocity changes.

9. An eVTOL battery pack thermal optimization system based on pulsating flow, characterized in that: The eVTOL battery pack thermal optimization system based on pulsating flow includes: Design Domain Determination and Discretization Module: This module is used to determine the shape of the design domain based on the inlet and outlet locations and battery pack dimensions of the electric vertical take-off and landing vehicle battery pack, establish a two-dimensional optimization model based on the physical properties of the cold plate material and the thermophysical parameters of the coolant, and discretize the design domain into N finite elements. Topology optimization mathematical model construction module: used to select optimization parameters, control equations, boundary conditions, constraints and objective functions, build a topology optimization mathematical model, and obtain the relationship between the relevant parameters of the cold plate and coolant and the unit material density; Battery 2D Cold Plate Topology Optimization Model Construction and Pulsating Flow Introduction Module: This module is used to establish a 2D battery cold plate topology optimization model based on the average cold plate surface temperature and fluid flow dissipation work as optimization targets. Finite element analysis and sensitivity calculations are used to update the cold plate material density distribution, obtain the optimal heat dissipation flow path, and introduce pulsating flow technology. Filtering projection module: It is used to perform filtering projection based on the established battery two-dimensional cold plate topology optimization model using the Helmholtz formula, and output preliminary optimization results, including the cold plate material density distribution map and temperature gradient map combined with the topology optimization results; Pulsating flow and sliding mode control coupling module: used for the coupling design of pulsating flow and sliding mode control, real-time monitoring of battery pack temperature changes, and dynamic adjustment of the pulsating flow frequency and amplitude based on temperature feedback to achieve the ideal target temperature, thereby obtaining the final optimization result.

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