Cooling performance fast calculation method for self-suction phase change transpiration cooling structure

Abstract

The application provides a cooling performance rapid calculation method for a self-suction phase change sweating cooling structure, and first establishes a three-dimensional model of the self-suction phase change cooling structure and a grid model for cooling performance calculation; then establishes a transient coolant transport model based on a laminar flow control equation, and performs transient solution on the transient coolant transport model based on a set boundary condition; the liquid level position and the coolant temperature of the liquid phase coolant are used to calculate the coolant inlet boundary pressure of the current time step, the calculated coolant inlet boundary pressure is used as a boundary condition for calculation until a convergence condition is reached, and finally the structure surface steady-state temperature is output. The capillary volume force obtained by calculation in the traditional CSF model is converted into an equivalent pressure difference between the upper and lower surfaces of the coolant as the pressure condition of the coolant inlet boundary, the tracking calculation of the liquid boundary is avoided, the model solving process is simplified, and the calculation complexity is significantly reduced.

Description

Technical Field

[0001] This invention relates to the field of thermal protection technology, specifically to a rapid calculation method for the cooling performance of a self-extraction phase change sweating cooling structure. Background Technology

[0002] Phase change sweating cooling technology utilizes a liquid coolant to undergo a phase change on a high-temperature surface, forming a protective gas film with a thermal blocking effect, effectively reducing the convective heat flux caused by high-speed airflow. Due to its high cooling efficiency, this technology has attracted widespread attention in recent years, with research covering multiple aspects such as cooling structure design, coolant selection, and heat and mass transport mechanisms. However, the engineering application of such systems still faces many challenges. Traditional sweating cooling systems typically rely on coolant storage tanks, pressure pumps, and flow control systems, which not only significantly increase system weight but also lead to a substantial increase in structural complexity, severely restricting its practical application and verification in aircraft. To address these issues, self-regulating self-suction sweating cooling technology has gradually attracted attention. For example, the applicant proposed an active thermal protection flexible skin with fault-tolerant and self-regulating characteristics based on the reticulate leaf vein structure of dicotyledonous plants in Chinese invention patent application publication number CN119037698A. This technology utilizes capillary force generated by micropores in the structure to drive coolant transport and relies on dynamic changes in the gas-liquid interface to achieve adaptive flow regulation, offering advantages such as compact structure and no need for external power supply.

[0003] In evaluating the cooling performance of sweating cooling structures, existing research typically defines cooling efficiency as the primary metric by calculating the temperature field distribution of the structure under steady-state conditions. Numerical prediction methods for the temperature field mainly fall into two categories: one directly models the pore structure to meticulously describe the flow and heat transfer behavior of the coolant within the microchannels; the other treats the entire cooling structure as a porous medium to simplify the flow-heat coupling process and improve computational efficiency. For self-extraction phase-change sweating cooling structures, explicit modeling of the microporous structure is often employed, combined with the VOF (Volume of Fluid) method and the CSF (Continuum Surface Force) model. Capillary forces are calculated using liquid surface tension to track the dynamic evolution of the coolant gas-liquid interface, thus more realistically reflecting the coolant transport process. Despite its high physical accuracy, this method still faces several challenges in engineering applications: First, when there are significant geometric changes in the channel structure along the thickness direction (such as the transition from small aperture to large aperture to small aperture), the internal flow state is complex, the gas-liquid interface fluctuates strongly, and the steady-state solution is difficult to converge stably; Second, in transient simulations, the CSF model needs to solve for the coolant liquid level position in real time, which involves a large amount of computation and is time-consuming, making it difficult to meet the requirements of speed and resource efficiency in actual engineering.

[0004] Therefore, there is an urgent need to develop a computationally efficient and rapid calculation and evaluation method for the self-absorption phase change sweating cooling performance that is adaptable to complex pore structure characteristics, so as to support the engineering design and promotion of this type of active thermal protection technology in extreme flight missions such as cross-domain environments and morphological deformation. Summary of the Invention

[0005] To address the problems of existing methods for calculating and evaluating the cooling performance of self-extraction phase change evaporation cooling structures, such as difficulty in steady-state convergence, high computational cost of transient simulation, and inability to adapt to complex pore structures, especially the low computational efficiency of traditional VOF-CSF model-based methods in dynamic interface tracking and capillary force solution, which makes it difficult to meet the needs of rapid engineering evaluation, this invention proposes a rapid calculation method for the cooling performance of self-extraction phase change evaporation cooling structures.

[0006] This method transforms the capillary volume forces calculated in the traditional CSF model into an equivalent pressure difference between the upper and lower surfaces of the coolant, serving as the pressure condition at the coolant inlet boundary. This avoids the need for tracking calculations of the liquid boundary, simplifies the model solution process, and significantly reduces computational complexity. To accurately reflect the capillary force changes in different regions within complex channels, a marking mechanism for the gas-liquid coolant interface is introduced into the model. Based on the actual position of the liquid coolant surface in the channel, the local capillary pressure is dynamically determined, thereby improving the physical rationality and stability of the simulation results. Simultaneously, this method employs a transient solution strategy and uses the result when the structural surface temperature reaches a steady state as an approximate solution for steady-state cooling performance. This enables rapid prediction of the structural temperature response under different channel structures and thermal boundary conditions, while ensuring evaluation accuracy, and is used for quantitative calculation of cooling efficiency.

[0007] The computational method proposed in this invention has the advantages of fast solution speed, strong adaptability to complex structures, and low computational resource consumption. It can effectively support the rapid design, performance prediction and engineering optimization of thermal protection structures of self-extraction phase change sweating cooling structures in complex flight missions such as cross-domain adaptation and morphological deformation, and fill the gap in the existing technology in the field of efficient cooling performance evaluation methods.

[0008] The technical solution of this invention is as follows:

[0009] A rapid calculation method for the cooling performance of a self-suction phase change evaporation cooling structure includes the following steps:

[0010] Step 1: Establish a three-dimensional model of the self-suction phase change cooling structure, and divide the computational mesh according to the three-dimensional model to establish a mesh model for cooling performance calculation;

[0011] Step 2: Using the mesh model established in Step 1, establish a transient coolant transport model based on the laminar flow control equations; perform transient solution on the transient coolant transport model based on the set boundary conditions to obtain the temperature of the solid material used in the cooling structure at the current time step. Volume fraction of liquid coolant Temperature of the mixture of gaseous and liquid coolant And determined by the volume fraction of the liquid coolant. The liquid level of the liquid coolant was calculated. The boundary condition set is the external flow field heat flux density. Coolant inlet temperature and coolant inlet pressure ;

[0012] Step 3: Use the liquid level of the liquid coolant obtained in Step 2 Temperature of the mixture of gaseous and liquid coolant According to the formula

[0013]

[0014] Calculate the coolant inlet boundary pressure for the current time step. ;in The surface tension coefficient is a temperature-dependent variable. The function, The contact angle between the liquid coolant and the channel wall. The hydraulic radius of the channel is relative to the liquid surface position. The function, External mainstream static pressure;

[0015] The calculated coolant inlet boundary pressure Substitute step 2 as the boundary condition for calculation, and repeat steps 2 and 3 until the convergence condition is met. Finally, output the temperature of the solid material used in the cooling structure. As the steady-state temperature of the structural surface.

[0016] In a further preferred embodiment, the transient coolant transport model includes fluid domain governing equations and solid domain governing equations.

[0017] In a further preferred embodiment, the governing equations of the fluid domain are:

[0018]

[0019]

[0020]

[0021]

[0022] in Indicates time Calculate the partial derivatives. , The numbers represent the volume fractions of the gaseous and liquid phase coolants, respectively. , The densities of the gaseous coolant and the liquid coolant are represented, respectively. , The velocity values ​​of the gaseous coolant and the liquid coolant are represented respectively. This indicates the mass flow rate between the gaseous coolant and the liquid coolant. This represents the latent heat of phase transition between the gaseous and liquid phase coolants. Represents the gradient operator; , , , , The density, velocity, dynamic viscosity, internal energy, and thermal conductivity of the mixture of gaseous and liquid coolants are represented in sequence. This indicates the pressure of the mixture of gaseous and liquid coolant. This represents the gravitational acceleration of the mixture of gaseous and liquid coolant. This indicates the temperature of the mixture of gaseous and liquid coolant.

[0023] In a further preferred embodiment, the density, velocity, dynamic viscosity, internal energy, and thermal conductivity of the mixture of gaseous and liquid coolant are calculated by a weighted average of the volume fractions of the corresponding properties of the gaseous and liquid coolants.

[0024]

[0025]

[0026]

[0027]

[0028]

[0029] in , The dynamic viscosity of the gaseous coolant and the liquid coolant are respectively represented. , These represent the internal energies of the gaseous coolant and the liquid coolant, respectively. , The values ​​represent the thermal conductivity of the gaseous coolant and the liquid coolant, respectively.

[0030] In a further preferred embodiment, the governing equation of the solid domain is:

[0031]

[0032] in , , , The following are the density, specific heat capacity, thermal conductivity, and temperature of the solid materials used in the cooling structure, in that order. For internal energy source terms, Represents the gradient operator. Indicates time Calculate the partial derivatives.

[0033] Further preferred option, liquid level position According to the formula

[0034]

[0035] Calculation, where To calculate the total number of grid cells within the domain; For the first Liquid phase volume fraction per grid cell; For the first The height coordinates of the center point of each grid cell It is a value-finding function. To set a threshold.

[0036] In a further preferred embodiment, in step 1, the self-suction phase change cooling structure consists of a bottom coolant transport layer and a top imitation leaf vein flow channel layer. The coolant transport layer has vertically penetrating channels that are responsible for introducing coolant from the bottom liquid tank into the imitation leaf vein flow channel layer. The internal channels of the imitation leaf vein flow channel layer are arranged in an "X" pattern, with every four channels converging at the bottom to form a junction hole, which connects to the transport channels in the lower coolant transport layer, forming a multi-layer closed network.

[0037] A further optimized approach involves dividing the computational domain into four spaces for each transport channel, based on the bifurcated ducts:

[0038]

[0039] Among them, the first The coordinates of the center point of the transport channel entrance are , These are the coordinates of the center point of the grid cells within a unit cell; one transport channel corresponds to one unit cell. The length of a single cell is constant, and the structural range controlled by one transport channel is [missing information]. , The thickness of a single cell; according to the formula

[0040]

[0041] Calculate the liquid level position ,in For the first Liquid phase volume fraction per grid cell; For the first The height coordinates of the center point of each grid cell It is a value-finding function. To set a threshold.

[0042] In a further preferred embodiment, the method further includes step 4: after obtaining the steady-state temperature of the structural surface, according to the formula...

[0043]

[0044] Calculate cooling efficiency ,in This represents the average steady-state temperature of the structural surface. The initial temperature of the coolant. This refers to the temperature of the adiabatic wall surface.

[0045] A further preferred embodiment, when the external mainstream is a subsonic airflow, is the temperature of the adiabatic wall. Using the mainstream total temperature calculation, when the external mainstream is a supersonic airflow, the temperature of the adiabatic wall surface is... The recovery temperature was used for calculation.

[0046] Beneficial effects:

[0047] Compared with the prior art, the beneficial effects of the present invention are:

[0048] In the numerical calculation of the self-suction phase change sweating cooling structure, in order to avoid the high computational cost and low convergence problem caused by the traditional VOF-CSF method of tracking the gas-liquid interface, this invention proposes a simplified modeling method driven by equivalent capillary pressure. The capillary volume force is converted into an equivalent pressure difference between the upper and lower surfaces of the channel and applied to the fluid inlet boundary, thereby replacing the traditional capillary volume force solution process, simplifying the model solution process and improving computational efficiency.

[0049] Traditional VOF-CSF methods, when dealing with capillary forces, fix the pressure at the coolant inlet to the external atmospheric pressure. In the model, capillary action is achieved by introducing a volume force term into the momentum equation. ,in For surface tension coefficient, Liquid volume fraction, The curvature of the gas-liquid interface is used to apply this volume force directly to the internal mesh of the fluid, thereby characterizing the capillary pressure difference at the interface.

[0050] Clearly, the calculation of this volumetric force depends on the curvature of the gas-liquid interface. The curvature needs to be calculated using the gradient and normal vector of the phase fraction field. This process is highly sensitive to the smoothness of the phase fraction field and has strict requirements on mesh generation and time step size: when the resolution is insufficient or the time step is too large, the interface position is prone to jitter and capillary oscillations are induced, making it difficult for the numerical solution to converge; while when the mesh is too fine or the time step is too small, although the interface resolution can be improved, the computational cost will increase significantly. Furthermore, since the capillary volume force is strongly coupled with the phase fraction distribution, the iteration process involves not only high-order gradient calculations but also continuous updates to the interface morphology, often leading to residual oscillations and low convergence efficiency. Therefore, the traditional VOF-CSF method generally exhibits insufficient numerical stability and low computational efficiency.

[0051] This invention creatively transforms capillary pressure into an equivalent pressure condition at the coolant inlet boundary. Specifically, instead of introducing volume force terms dependent on interface curvature into the fluid domain, it calculates the hydraulic radius corresponding to the coolant surface in real time through a geometric model and liquid surface position determination, and then uses the formula... Obtain the equivalent capillary pressure difference This pressure is different from the mainstream static pressure. After superposition, it is directly applied to the coolant inlet as a boundary condition.

[0052] Unlike traditional methods that rely on interface curvature calculations, this method eliminates the need for high-order gradient solving and precise capture of the gas-liquid interface position at each time step. It relies solely on phase fractional field statistics to obtain the liquid surface position, fundamentally eliminating the excessive sensitivity of numerical calculations to interface smoothness, mesh resolution, and time step size. Furthermore, by introducing capillary driving as pressure as the inlet boundary, it avoids the local oscillations and residual fluctuations easily caused by volume force application, making the numerical process more stable. Therefore, the calculation method of this invention significantly reduces numerical implementation complexity and computational resource consumption while improving iterative convergence and overall computational efficiency, and accurately characterizes the capillary transport mechanism. Thus, this invention can achieve rapid prediction of cooling performance while ensuring computational accuracy, possessing outstanding technical advantages and broad engineering application value.

[0053] Furthermore, this invention introduces a calibration mechanism for the liquid level position. By identifying the changes in the position of the coolant liquid level in the channel in real time and combining the channel geometry, the magnitude of the local capillary force is dynamically adjusted, thereby achieving accurate characterization of the coolant transport behavior in complex non-uniform channel structures and enhancing the model's adaptability to multi-channel non-uniform structures.

[0054] This invention, based on a transient solution strategy, selects the temperature at which the structural surface temperature reaches a steady state as the evaluation criterion, effectively avoiding convergence difficulties that may occur in steady-state simulations and achieving rapid calculation of cooling efficiency. The overall method possesses advantages such as high physical accuracy, high computational efficiency, and good adaptability to structural complexity. It can provide a practical evaluation method for the rapid design and performance evaluation of self-extraction and sweating cooling structures in high heat flux density applications such as cross-domain and variable-structure flight, and is expected to provide technical reference for the engineering application of related technologies.

[0055] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0056] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0057] Figure 1 The following is a flowchart illustrating the logic of using the method proposed in this invention to rapidly calculate and evaluate the cooling performance of a self-absorbing sweating cooling structure in this embodiment.

[0058] Figure 2 : A cross-sectional view and flow channel structure diagram of the self-extraction sweating cooling structure used in the embodiment;

[0059] Figure 3 Specific heat capacity curves of nickel-based superalloys GB4169;

[0060] Figure 4 Thermal conductivity curves of nickel-based superalloys GB4169;

[0061] Figure 5 Steady-state temperature distribution diagram of the structure using the equivalent capillary force model;

[0062] Figure 6 Steady-state temperature distribution diagram of the structure using the VOF-CSF model. Detailed Implementation

[0063] The embodiments of the present invention are described in detail below. These embodiments are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0064] This embodiment provides a rapid calculation method for the cooling performance of self-extraction phase change evaporation cooling structures, addressing the problems of high computational cost and numerical instability inherent in traditional gas-liquid interface tracking models when handling complex pore structures and dynamic phase change processes. This method simplifies capillary force modeling during coolant transport by constructing an equivalent capillary pressure difference model and combining it with a transient heat transfer solution strategy, avoiding gas-liquid interface tracking calculations and significantly improving computational efficiency and stability. Simultaneously, the introduction of a liquid surface position marking mechanism and a local pore parameter correlation strategy enhances the model's adaptability to non-uniform structures, enabling accurate prediction of structural temperature response and cooling performance. The overall solution can serve as a fundamental evaluation tool for the design, optimization, and engineering application of self-extraction phase change evaporation cooling systems.

[0065] like Figure 1 As shown, this embodiment takes a leaf vein-inspired self-suction phase change cooling structure with a channel diameter of 1.4 mm and an inclination angle of 30° as an example, and provides a rapid calculation method for the cooling performance of a self-suction phase change sweating cooling structure. It proposes a modeling and performance prediction process for a typical microchannel cooling structure, covering aspects such as channel geometry parameter modeling, transient simulation of the internal flow field, capillary force equivalent modeling, temperature response extraction, and quantitative evaluation of the cooling effect. Specifically, it includes the following steps:

[0066] Step 1: Establish a three-dimensional model of the self-suction phase change cooling structure, and divide the computational mesh according to the three-dimensional model to establish a mesh model for cooling performance calculation;

[0067] In this embodiment, in order to accurately characterize the transport path and distribution behavior of the coolant in the self-extraction phase change sweating cooling structure, it is necessary to perform parametric modeling of its internal three-dimensional pore structure. For example... Figure 2 As shown, the structure selected in this embodiment draws inspiration from the network vein morphology of dicotyledonous plants. It consists of a bottom coolant transport layer and a top leaf vein-like flow channel layer, featuring closed channels, spatial branching, and multi-path connections. This is beneficial for improving the continuity of coolant transport and the uniformity of temperature response under deformation conditions. For details, please refer to Chinese invention patent application CN119037698A. The structure consists of a lower coolant transport layer and an upper leaf vein-like flow channel layer. The coolant transport layer has vertically penetrating channels responsible for introducing coolant from the bottom liquid tank into the leaf vein-like flow channel layer. The internal channels of the leaf vein-like flow channel layer are arranged in an "X" pattern, with every four channels converging at the bottom to form a junction hole, connecting with the transport channels in the lower coolant transport layer to form a multiple closed network, simulating the loop-like redundant structure of plant leaf veins.

[0068] During the modeling process, the channel geometry is abstracted parametrically, including the following key parameters: transport channel diameter. , diameter of leaf vein channel Bifurcation angle between the channel and the thickness direction Channel layer thickness Leaf vein layer thickness The channels are arranged regularly, exhibiting periodic characteristics, and the unit cell structure is as follows: Figure 2 As shown. Considering that coolant transport in the simulated leaf vein channels is mainly driven by capillary force, the geometric modeling must also ensure that the capillary pressure can overcome the system's friction loss and gravitational potential difference. Therefore, Murray's law is used to optimize the diameter ratio of the transport channel and the branch channels. A bifurcation angle gradient distribution is introduced to match the heat flux density requirements of different regions of the structure, forming a three-dimensional geometric parameter field with spatial variation. In this embodiment, the selected leaf vein-like channel diameter is 0.9 mm, the bifurcation angle is set to 30°, the channel layer thickness is 3 mm, and the leaf vein layer thickness is 10 mm. This parameter combination achieves a balance between structural manufacturability and cooling performance. The 30° bifurcation angle is beneficial for increasing the channel density within a given structural thickness, thereby enhancing the local cooling capacity of the structure in high heat flux regions (such as the leading edge); at the same time, this angle also optimizes the channel spatial layout and improves the coverage uniformity of the coolant transport path. The channel diameter of 0.9 mm not only provides stable capillary driving force and coolant transport effect, but also facilitates the actual structural preparation through 3D printing, with good machinability and forming accuracy. The overall structure, while meeting the functional layout of leaf veins, also takes into account the dynamic adjustment capability of the coolant channels and the feasibility of actual engineering implementation, providing a reliable geometric basis for subsequent numerical modeling.

[0069] Step 2: Using the mesh model established in Step 1, establish a transient coolant transport model based on the laminar flow control equations; the transient coolant transport model includes fluid domain control equations and solid domain control equations.

[0070] Since this embodiment focuses on the heat and mass transfer process of the self-exhausting sweating cooling structure and coolant, the model simplifies the external flow field. An empirical formula for heat flux based on the reference enthalpy method is used to simplify the external flow field into a steady plate heat flux applied to the upper surface of the leaf-vein-like structure. This simplification is based on the incompressible Blasius boundary layer solution, applies the Reynolds analogy to establish the relationship between the friction coefficient and the Stanton number, and uses the Eckert reference enthalpy method to account for compression effects, thereby improving model accuracy and external flow field heat flux density. The calculation formula is as follows:

[0071]

[0072] In the formula, For Stanton numbers, , The following are the inflow density and velocity of the external flow field, respectively. , These are the adiabatic wall enthalpy and the actual wall enthalpy, respectively. In this embodiment, the total airflow temperature is selected as approximately 893 K. After obtaining the adiabatic wall enthalpy using the total airflow temperature, the external flow field heat flux density is calculated to be 170 kW / m² using the above formula. 2 .

[0073] In terms of flow modeling within the cooling structure, to accurately simulate the flow behavior and phase change process of the coolant in microscale channels, and to improve the convergence of the model under complex geometries, this embodiment adopts a transient calculation strategy, using the instantaneous solution when the surface temperature of the structure reaches a steady state as an approximate solution for steady-state cooling performance. The coolant flow section is based on the incompressible Navier-Stokes equations under laminar flow conditions to construct a set of governing equations, and introduces a Volume of Fluid (VOF) multiphase flow model. By solving the continuity equation for the gas-liquid phase volume fraction, dynamic tracking and morphological evolution simulation of the coolant gas-liquid interface are achieved, capturing the distribution characteristics and migration path of the coolant within the channel. Furthermore, to describe the phase change process of the coolant under heated conditions, this embodiment introduces Lee model source terms into the continuity and energy equations to achieve numerical modeling of phase change mass transfer and latent heat release, thereby characterizing the coolant phase change cooling process. The resulting fluid domain governing equations are:

[0074]

[0075]

[0076]

[0077]

[0078] in Indicates time Calculate the partial derivatives. , The numbers represent the volume fractions of the gaseous and liquid phase coolants, respectively. , The densities of the gaseous coolant and the liquid coolant are represented, respectively. , The velocity values ​​of the gaseous coolant and the liquid coolant are represented respectively. This indicates the mass flow rate between the gaseous coolant and the liquid coolant. This represents the latent heat of phase transition between the gaseous and liquid phase coolants. Represents the gradient operator; This indicates the pressure of the mixture of gaseous and liquid coolant. This represents the gravitational acceleration of the mixture of gaseous and liquid coolant. This indicates the temperature of the mixture of gaseous and liquid coolant. , , , , The density, velocity, dynamic viscosity, internal energy, and thermal conductivity of the mixture of gaseous and liquid coolants are represented in order, respectively, and are calculated by weighted average of the volume fractions of the corresponding properties of the gaseous and liquid coolants.

[0079]

[0080]

[0081]

[0082]

[0083]

[0084] in , The dynamic viscosity of the gaseous coolant and the liquid coolant are respectively represented. , These represent the internal energies of the gaseous coolant and the liquid coolant, respectively. , The values ​​represent the thermal conductivity of the gaseous coolant and the liquid coolant, respectively.

[0085] The governing equation for the solid domain of the cooling structure is:

[0086]

[0087] in , , , The following are the density, specific heat capacity, thermal conductivity, and temperature of the solid materials used in the cooling structure, in that order. This is an internal energy source term.

[0088] In this embodiment, the solid material used for the cooling structure is a nickel-based superalloy GB4169, and the material parameters are as follows: Figure 3 and Figure 4 As shown; the cooling medium is liquid water, and the physical properties of liquid water and water vapor are from the NIST database.

[0089] After establishing the transient coolant transport model consisting of the fluid domain governing equations and the solid domain governing equations, the transient coolant transport model is solved transiently based on the set boundary conditions to obtain the temperature of the solid material used in the cooling structure at the current time step. Volume fraction of liquid coolant Temperature of the mixture of gaseous and liquid coolant And determined by the volume fraction of the liquid coolant. The liquid level of the liquid coolant was calculated. The boundary condition set is the external flow field heat flux density. Coolant inlet temperature and coolant inlet pressure During the solution process, the temperature of the solid material used in the cooling structure is considered. Temperature of the mixture of vapor and liquid coolant Initial values ​​need to be set in advance. During the iteration process, as the time steps are continuously solved, the desired result is achieved. and The continuous iteration; and the coolant inlet pressure Initial values ​​should also be set in advance and updated in step 3 at each time step.

[0090] To accurately simulate the dynamic changes in capillary pressure at different heights, this embodiment uses the volume fraction of the liquid coolant. Refine to liquid volume fraction for each grid cell By statistically analyzing grid cells with liquid phase volume fractions within a set range, and combining this with a weighted average of the grid cell height coordinates, the liquid level of the coolant can be determined in real time. In this embodiment, the set range is 0.95 to 1. The specific liquid level of the coolant is determined accordingly. The expression is:

[0091]

[0092] in To calculate the total number of grid cells within the domain; For the first Liquid phase volume fraction per grid cell; For the first The height coordinates of the center point of each grid cell This is a function for retrieving values.

[0093] Step 3: Use the liquid level of the liquid coolant obtained in Step 2 Temperature of the mixture of gaseous and liquid coolant According to the formula

[0094]

[0095] Calculate the coolant inlet boundary pressure for the current time step. ;in The surface tension coefficient is a temperature-dependent variable. The function, The contact angle between the liquid coolant and the channel wall. The hydraulic radius of the channel is relative to the liquid surface position. The function, The external mainstream static pressure. The calculated coolant inlet boundary pressure. Substitute step 2 as the boundary condition for calculation, and repeat steps 2 and 3 until the convergence condition is met. Finally, output the temperature of the solid material used in the cooling structure. The steady-state temperature of the structural surface; the convergence condition is temperature. The change value over multiple time steps is less than a set threshold.

[0096] The theoretical derivation of the above formula is as follows:

[0097] The formula for calculating capillary pressure difference is:

[0098]

[0099] in For surface tension coefficient, The contact angle between the liquid coolant and the channel wall. The hydraulic radius of the channel; these three parameters are set according to the type of coolant, the wetting characteristics of the structural material, and the geometry of the channel. In this embodiment, the cooling structure is a nickel-based high-temperature alloy GB4169, the coolant is liquid water, and the contact angle is... 70°, surface tension coefficient With temperature The changes are shown in Table 1:

[0100] Table 1: Surface tension coefficient of liquid water

[0101]

[0102] The hydraulic radius of the channel Defined as:

[0103]

[0104] in For the cross-sectional area of ​​the channel, Let be the perimeter of the channel's cross-section. Clearly, the cross-sectional area and perimeter of the channel are related to the structure of the cooling channel and the liquid level position. Related. For a well-designed cooling structure, the cross-sectional shape function of its cooling channels... and wetted periodic function It is known that, for the cooling structure with a channel diameter of 0.9 mm and a bifurcation angle of 30° in this embodiment, the corresponding function is:

[0105]

[0106]

[0107] Therefore, based on the instantaneous liquid level position The above function can be used to dynamically calculate the hydraulic radius corresponding to that location. and equivalent capillary pressure difference :

[0108]

[0109]

[0110] Achieve an accurate description of the capillary-driven effect in complex variable cross-section channel structures.

[0111] In the thermo-mass coupling solution process, the equivalent capillary pressure difference is represented by the inlet boundary pressure. The form is applied to the lower boundary of the coolant fluid domain and interacts with the external mainstream static pressure. The pressure difference that together constitutes the driving pressure of the coolant controls the rise, distribution, and phase change process of the coolant, thereby obtaining the final coolant inlet boundary pressure. The expression is:

[0112]

[0113] Furthermore, for cooling structures with multiple independent cooling channels, this embodiment also determines the equivalent capillary pressure boundary conditions for each transport channel based on the spatial correspondence between different channels and transport channels. This enables regional control of local coolant transport behavior, thereby improving the physical rationality and adaptability of the overall numerical modeling. Figure 2 As shown, each transport channel is connected to four orifices, and each orifice further branches into four orifices. When calculating the coolant level, since the orifices have the same structure and are interconnected, this method includes the entire interconnected orifice region in the statistical calculation during the determination of the liquid level to obtain the equivalent capillary pressure of the corresponding transport channel.

[0114] One transport channel corresponds to one unit cell. Let the length of a unit cell be denoted as , and the unit cell have the same length and width. Let the first _____ be the length of a single cell. The coordinates of the center point of the transport channel entrance are The structural range controlled by a transport channel is , The unit cell thickness is 13 mm in this embodiment, and the unit cell length is... The value is 5.95 mm. Based on the bifurcated channels, the corresponding computational domain can be divided into four spaces:

[0115]

[0116] in The coordinates of the grid nodes within the unit cell are given; the liquid surface position is calculated using the formula. for:

[0117]

[0118] liquid level position Substituting the cross-sectional shape function and the wetted perimeter function, the calculation is obtained. Further calculations yielded the inlet boundary pressure:

[0119]

[0120] Step 4: Quantitatively evaluate the thermal response and cooling effect of the cooling structure based on the previously obtained numerical calculation results: Using the temperature distribution at which the structure surface temperature reaches steady state as a basis, extract the temperature response of the structure surface and calculate the cooling efficiency accordingly. Specifically: Cooling efficiency. Defined as the ratio of the actual cooling rate of the structure to the theoretical maximum cooling rate, after obtaining the steady-state temperature of the structure surface, it is calculated using the formula...

[0121]

[0122] Calculate cooling efficiency ,in This represents the average steady-state temperature of the structural surface. The initial temperature of the coolant. The adiabatic wall temperature is the surface temperature of the structure without any cooling fluid injection. When the main external airflow is subsonic, the adiabatic wall temperature is... Using the mainstream total temperature calculation, when the external mainstream is a supersonic airflow, the temperature of the adiabatic wall surface is... Calculated using recovery temperature.

[0123] During the evaluation process, results such as the phase transition region distribution and coolant volume fraction when the structure reaches steady state can be further extracted. This method enables rapid quantitative comparison of cooling performance under different channel structural parameters and boundary conditions, supporting structural design optimization and engineering application evaluation.

[0124] To verify the computational advantages of the method of this invention in rapid evaluation of cooling performance, the constructed models were solved using both the traditional VOF-CSF model and the equivalent capillary force modeling method proposed in this invention. The steady-state response values ​​of the structural surface temperature and the computational resources and time required to reach steady state were compared. All calculations were performed on a high-performance server configured with dual Intel Xeon 7285H 32-core processors and 256GB of memory. The calculation results are shown in Table 2 and... Figure 5 and Figure 6As shown:

[0125] Table 2 Comparison of structural cooling efficiency and calculation kernel time using the VOF-CSF model and the equivalent capillary force model respectively.

[0126]

[0127] The results show that the two methods achieve highly consistent calculations of structural surface temperature and cooling efficiency (relative errors are both less than 0.5%), but the method of this invention has a significant advantage in computational efficiency. The equivalent capillary force modeling method reduces the kernel time from 24,000 in the traditional method to 1,110, reducing computational resource consumption by approximately 95.4%, effectively avoiding the high overhead problem of the traditional VOF-CSF method in interface tracking and capillary force solution. In summary, the rapid calculation and evaluation method for cooling performance proposed in this invention not only has good prediction accuracy but also significantly improves solution efficiency, making it particularly suitable for applications requiring rapid comparison and engineering optimization of different structural parameters or thermal boundary conditions.

[0128] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. A method for rapid calculation of cooling performance of a self-suction phase change transpiration cooling structure, characterized in that: The method comprises the following steps: Step 1: a three-dimensional model of the self-suction phase change cooling structure is established, and a calculation grid is divided according to the three-dimensional model to establish a grid model for cooling performance calculation; Step 2: using the grid model established in step 1, a transient coolant transport model based on a laminar flow control equation is established; the transient coolant transport model includes a fluid domain control equation and a solid domain control equation; based on a set boundary condition, the transient coolant transport model is solved transiently to obtain the temperature of the solid material of the cooling structure at the current time step , the volume fraction of the liquid phase coolant , the temperature of the gas phase coolant and the liquid phase coolant mixture , and the liquid surface position of the liquid phase coolant is calculated from the volume fraction of the liquid phase coolant ; wherein the set boundary condition is an external flow field heat flux , a coolant inlet temperature and a coolant inlet pressure ;​ Liquid level position According to the formula Compute, where is the total number of grid cells in the computational domain; is the liquid volume fraction of the th grid cell; is the height coordinate of the center point of the th grid cell, is the value function, is the set threshold value; Step 3: Liquid level position of the liquid phase coolant obtained from Step 2 temperature of the gas phase coolant and the liquid phase coolant mixture according to the formula calculating a coolant inlet boundary pressure for the current time step ; wherein is a surface tension coefficient, which is a function of temperature , is a contact angle of the liquid coolant with the channel wall, is a hydraulic radius of the channel, which is a function of the liquid level position, is an external main flow static pressure; The calculated coolant inlet boundary pressure Substitute the result of Step 2 as a boundary condition to calculate, and loop Step 2 and Step 3 until a convergence condition is reached, and finally output the temperature of the solid material used for the cooling structure As the steady-state temperature of the structure surface.

2. The method for quick calculation of cooling performance of a self-suction phase-change transpiration cooling structure according to claim 1, characterized in that: The fluid domain control equation is: wherein denotes the time derivative derivative, , denote the volume fractions of the gas and liquid coolants, respectively, , denote the densities of the gas and liquid coolants, respectively, , denote the velocities of the gas and liquid coolants, respectively, denotes the mass flow rate between the gas and liquid coolants, denotes the latent heat of phase change between the gas and liquid coolants, denotes the gradient operator; , , , , denote the density, velocity, dynamic viscosity, internal energy and thermal conductivity of the gas and liquid coolant mixture, respectively; denotes the pressure of the gas and liquid coolant mixture, denotes the gravitational acceleration of the gas and liquid coolant mixture, denotes the temperature of the gas and liquid coolant mixture.

3. The method for quick calculation of cooling performance of a self-suction phase-change transpiration cooling structure according to claim 2, characterized in that: The density, velocity, dynamic viscosity, internal energy and thermal conductivity of the gas-liquid coolant mixture are calculated by volume fraction weighted average of the corresponding properties of the gas coolant and the liquid coolant: wherein 、 successively represent the dynamic viscosity of the gas and liquid phase coolant, respectively; 、 successively represent the internal energy of the gas and liquid phase coolant, respectively; 、 successively represent the thermal conductivity of the gas and liquid phase coolant, respectively.

4. The method for quick calculation of cooling performance of a self-suction phase-change transpiration cooling structure according to claim 1, characterized in that: The solid domain control equation is: wherein 、 、 、 are, in sequence, the density, the specific heat capacity, the thermal conductivity and the temperature of the solid material used for the cooling structure, is the internal energy source term, denotes the gradient operator, denotes the partial derivative with respect to time the partial derivative is calculated.

5. The method for quick calculation of cooling performance of self-suction phase-change transpiration cooling structure according to claim 1, characterized in that: In step 1, the self-suction phase change cooling structure is composed of a bottom coolant transport layer and a top leaf vein flow channel layer. The coolant transport layer is provided with vertical through channels responsible for introducing the coolant from the bottom liquid tank to the leaf vein flow channel layer. The internal channels of the leaf vein flow channel layer are arranged in an "X" type regular cross. Every four channels converge into an intersection hole at the bottom, which is connected with the transport channel in the lower coolant transport layer, forming a multiple closed network.

6. The method for quick calculation of cooling performance of a self-suction phase-change transpiration cooling structure according to claim 5, characterized in that: For each transport channel, the corresponding calculation domain is divided into four spaces according to the branched channels: wherein the first The coordinate of the center point of the inlet of the transport channel is , is the coordinate of the center point of the grid cell in the unit cell, and one transport channel corresponds to one unit cell, is the length of one unit cell, the length and width of the unit cell are consistent, and the structure range controlled by one transport channel is , is the thickness of the unit cell; according to the formula Computing a liquid level position wherein is the liquid volume fraction of the grid cell; is the height coordinate of the grid cell center point, is a value function, is a set threshold value.

7. The method for quick calculation of cooling performance of self-suction phase-change transpiration cooling structure according to claim 1, characterized in that: It also includes step 4: after obtaining the steady-state temperature of the structure surface, the formula is used to calculate the heat transfer coefficient of the structure surface. Computing cooling efficiency wherein is the average value of the steady state temperature of the structure surface, is the initial temperature of the coolant, is the adiabatic wall temperature.

8. The method for quick calculation of cooling performance of a self-suction phase-change transpiration cooling structure according to claim 7, characterized in that: When the outer mainstream is subsonic airflow, the adiabatic wall temperature is calculated by the total temperature of the mainstream When the outer mainstream is supersonic airflow, the adiabatic wall temperature is calculated by the total temperature of the mainstream The recovery temperature is calculated.

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