Multi-fidelity topological optimization method, system and device for micro-channel flow boiling process and medium

Abstract

A multi-fidelity topological optimization method, system, device and medium for a microchannel flow boiling process, and the method comprises the steps: firstly carrying out low-fidelity topological optimization on a single-phase laminar flow convective heat transfer process to generate a group of candidate topological optimization structures; then calculating the speed, temperature and two-phase distribution in a single-phase heat transfer process and a flow boiling heat transfer process on the basis of a high-fidelity flow boiling numerical model, and constructing a novel objective function capable of reflecting flow boiling heat transfer characteristics on the basis of leading factors of the flow boiling heat transfer problem in the microchannel; and finally, directly generating a topological optimization structure under a low-fidelity condition based on the new objective function. Aiming at the defect that an existing topological optimization algorithm cannot directly optimize the flow boiling heat transfer problem, rapid and accurate multi-fidelity topological optimization is realized by constructing a novel objective function capable of reflecting the flow boiling heat transfer characteristics; according to the designed topological optimization structure, local hot spots are eliminated, thermal resistance is reduced, and temperature uniformity is improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of micro-channel enhanced heat transfer, and particularly relates to a multi-fidelity topology optimization method, system, device and medium for enhancing flow boiling heat transfer in a micro-channel. BACKGROUND

[0002] Micro-channels are widely used in the field of heat dissipation of high-power devices, such as forced convection heat transfer in the micro-channel heat sink of an electronic chip. With the increasing heat generation of high-power devices, single-phase forced convection heat transfer in a micro-channel can no longer meet the heat dissipation requirements. Flow boiling heat transfer is widely used in many fields because it can fully utilize the latent heat of the coolant. However, flow boiling heat transfer still has defects such as flow instability and local hot spots. Improving the micro-channel structure to enhance the flow boiling heat transfer process in it is the key to improving the performance of related devices. Therefore, it is of great significance to optimize the micro-channel in which flow boiling heat transfer occurs efficiently and with high performance. In a micro-channel, the flow boiling process often crosses processes such as nucleate boiling, transition boiling and film boiling, and there is a complex coupling relationship between two-phase flow dynamics and heat transfer. In the optimization process, local micro structures and overall channel configurations need to be designed in coordination, which not only makes full use of the latent heat of the coolant, but also avoids local overheating caused by the low thermal conductivity of the gas film. In the current research on the enhancement of flow boiling heat transfer in a micro-channel, the research process mainly includes size optimization, shape optimization and bionic optimization. Most of the existing optimization results come from the qualitative thinking of designers, and it is difficult to design new structures that break away from human thinking habits.

[0003] Compared with existing micro-channel size, shape and / or biological inspired optimization, topology optimization has the highest degree of design freedom and can generate optimized structures beyond the experience of designers. Topology optimization is a computational design method that can automatically generate structures with optimal performance under specified design conditions. For complex physical problems such as turbulent flow, traditional topology optimization methods are difficult to directly perform, and multi-fidelity topology optimization is a new topology optimization framework. There are two key steps in this method: generating a set of seed structures through low-fidelity topology optimization that can be directly performed; and determining the best structure by modeling the complex process in these structures for high-fidelity evaluation.

[0004] Currently, the topology optimization design of convective heat transfer in microchannels mainly focuses on single-phase flow heat transfer, and there is no direct application of topology optimization to the flow boiling heat transfer process. Even the multi-fidelity topology optimization framework suitable for a variety of complex problems is difficult to optimize the flow boiling heat transfer process. On the one hand, the flow boiling heat transfer process has the characteristics of transient evolution of two-phase interface, and there are other key variables such as velocity, pressure and temperature. This multi-variable non-steady-state process brings great challenges to multi-fidelity topology optimization. On the other hand, even if the topology optimization of such problems achieves a convergent solution, it usually requires high computational resources, and it is easy to diverge, and the solution may fall into a local optimal solution.

[0005] The topology optimization research in existing studies for flow heat transfer problems mainly focuses on the laminar single-phase field. Compared with single-phase flow heat transfer problems, the control equations of gas-liquid phase change flow heat transfer include volume fraction conservation equations, surface tension source terms and phase change source terms, and the control equation set is complex and strongly coupled. On the one hand, the non-steady-state process and dynamic evolution of the gas-liquid interface involved in the flow boiling heat transfer lead to high time consumption, high memory occupation and instability in the topology optimization forward and adjoint equation solving. On the other hand, in the topology optimization process of complex flow boiling heat transfer problems, the two-phase flow dynamics and the distribution of design variables interact with each other, and the dimension of the design solution space is extremely high, making it difficult to converge to the optimal design variable distribution. There is very little research on the topology optimization of complex flow boiling heat transfer problems, which mainly falls into two categories. One is the research idea of Weibel team of Purdue University in the United States, which is supported by the Defense Advanced Research Projects Agency (DARPA) of the United States. Weibel et al. [An approach for topology optimization of heatsinks for two-phase flow boiling: Part 1 - Model formulation and numerical implementation] [An approach for topology optimization of heatsinks for two-phase flow boiling: Part 2 - Model calibration and experimental validation] added a simplified phase change model such as enthalpy method to the topology optimization model, and derived the corresponding adjoint equation and boundary conditions to directly obtain the final topology optimization structure. This approach is subject to the topology optimization method itself, and not only does the phase change model need to be greatly simplified, but it is also difficult to optimize the transient process. While the complex flow boiling heat transfer process is a complex transient two-phase flow heat transfer process, there is a huge deviation between the optimized structure and the actual situation. SUMMARY

[0006] In order to overcome the defects of the prior art, the present application aims to provide a multi-fidelity topology optimization method for micro-channel flow boiling process, based on a new target function with two-phase flow heat transfer characteristics, topology optimization is carried out under low fidelity conditions, and performance evaluation is carried out under high fidelity. Specifically, first, low-fidelity topology optimization is carried out on the single-phase laminar flow heat transfer process, thereby generating a set of candidate topology optimization structures; then, based on the high-fidelity flow boiling numerical model, the velocity, temperature and two-phase distribution in the single-phase heat transfer process and the flow boiling heat transfer process are studied and compared in detail, and based on the dominant factors of the flow boiling heat transfer problem in the micro-channel, a new target function is constructed which can reflect the flow boiling heat transfer characteristics; finally, based on the new target function, topology optimization structure is generated directly under low fidelity conditions; the present application overcomes the shortcomings that the existing topology optimization algorithm cannot directly optimize the flow boiling heat transfer problem, realizes fast and accurate multi-fidelity topology optimization, and the designed topology optimization structure eliminates local hot spots, reduces thermal resistance and improves temperature uniformity.

[0007] In order to achieve the above-mentioned purpose, the technical scheme adopted by the present application is as follows:

[0008] A multi-fidelity topology optimization method for micro-channel flow boiling process, specifically comprising the following steps:

[0009] Step 1, low-fidelity topology optimization is carried out on the single-phase laminar flow heat transfer process, thereby generating a set of candidate topology optimization structures for the laminar single-phase flow heat transfer problem;

[0010] Step 2, based on the high-fidelity flow boiling numerical model, simulate the two-phase flow boiling heat transfer process in the candidate topology optimization structure; calculate the velocity, temperature and two-phase distribution in the single-phase heat transfer process and the flow boiling heat transfer process, and based on the dominant factors of the flow boiling heat transfer problem in the micro-channel, construct a new target function reflecting the flow boiling heat transfer characteristics;

[0011] Step 3, based on the new target function, generate topology optimization structure with high flow boiling heat transfer performance directly under low fidelity conditions.

[0012] 2. The multi-fidelity topology optimization method for micro-channel flow boiling process according to claim 1, wherein the specific method of step 1 is:

[0013] Step 1.1, a low-fidelity convection heat transfer topology optimization model under single-phase laminar steady-state conditions is constructed using a topology optimization method based on the density method; three hierarchical reduced-order models are used to approximate the flow and heat transfer in the three-dimensional microchannel in the two-dimensional model, the three hierarchical reduced-order models include two two-layer (2L) reduced-order models and one single-layer (1L) reduced-order model; both two two-layer (2L) reduced-order models regard the three-dimensional microchannel as two parts including a channel layer and a substrate layer; in the channel layer, there are solid and fluid, and flow and heat transfer are solved; in the substrate layer, all are solid, and heat conduction is solved; wherein the first two-layer (2L) reduced-order model is named 2L reduced-order model I, the control equations of the channel layer thereof include mass conservation equation, momentum conservation equation and energy conservation equation; the mass conservation equation is

[0014]

[0015] the momentum conservation equation is

[0016]

[0017] wherein, u, p, p and mu are the velocity, density, pressure and viscosity of the fluid respectively; fl

[0018] F is the Brinkman volume force term:

[0019] F = - a (y) u (3)

[0020] wherein, a (y) is the inverse permeability, F is used to describe the influence of the solid area on the fluid flow, and the influence becomes stronger with the increase of the flow velocity;

[0021] the three-dimensional microchannel flow is simplified to two-dimensional, specifically, the flow in the three-dimensional microchannel is simplified to parabolic Poiseuille flow, and a 6 / 7 rescaling constant is added to the momentum conservation equation, so that the three-dimensional flow and heat transfer are described in the region of any two-dimensional arranged microchannel, i.e. the calculation domain;

[0022] the energy conservation equation of the channel layer is expressed as:

[0023]

[0024] the energy conservation equation of the substrate layer is expressed as:

[0025]

[0026] wherein, c p,fl is the specific heat capacity of the fluid; T c and T b are the temperatures of the channel layer and the substrate layer respectively; lambda (y) is the effective thermal conductivity; lambda s is the thermal conductivity of the solid; H c and H​b These represent the half-heights of the fluid channel and the solid substrate, respectively; q in The heat flux density at the bottom of the substrate;

[0027] The second two-layer (2L) reduced-order model is named 2L Model II. Its governing equations for the channel layer include the mass conservation equation, momentum conservation equation, and energy conservation equation. The mass conservation equation for 2L Model II is:

[0028]

[0029] The momentum conservation equation for Model II 2L is:

[0030]

[0031] The energy conservation equations for the channel layer and the basal layer in Model II 2L are:

[0032]

[0033] Treating the single-layer (1L) reduced-order model as a microchannel with only a channel layer, and directly incorporating the heat flux density at the bottom of the microchannel as a source term into the energy conservation equation, the governing equations of the single-layer (1L) reduced-order model are as follows:

[0034]

[0035] Step 1.2: Based on the two two-layer (2L) reduction models and one single-layer (1L) reduction model from Step 1.1, the low-fidelity initial topology optimization problem for microchannels is defined as follows:

[0036] min:T max

[0037]

[0038] Among them, T max It is the highest temperature of the radiator, and the lowest temperature is T. max For the highest heat transfer performance, A Ωd It is the design domain Ω d area, f c The fluid volume fraction constraint is used to solve the topology optimization problem described above. The problem will be performed in a given discretized computational domain, which can be any two-dimensional geometry.

[0039] The objective function of the microchannel topology optimization problem is the maximum temperature, i.e., the maximum value, within the computational domain. However, the maximum value itself is not continuous. Therefore, the generalized p-norm is used to continuously calculate the maximum value, i.e., the maximum temperature, resulting in the following optimization objective:

[0040]

[0041] where N is the total number of nodes in the computational domain, i.e. the number of grids, and p is the norm;

[0042] The control equations (1), (2), (4)-(12) are solved by using the finite volume method flow heat transfer solver, and the design variables, i.e. the arrangement of the solid, are filtered by using the Helmholtz density filter to avoid the chessboard problem generated by the solution;

[0043] Step 1.3, low-fidelity flow heat transfer topology optimization: based on the control equations (1), (2), (4)-(12) and the optimization objective (14) in steps 1.1 and 1.2, low-fidelity flow heat transfer topology optimization is performed in a given discretized arbitrary two-dimensional computational domain, and a set of candidate topology optimization structures is generated for the laminar single-phase flow heat transfer problem; specifically:

[0044] Step 1.3.1, the initial design variable distribution is set by using the full fluid arrangement initialization strategy, and the design variable field is the arrangement of the solid in the computational domain;

[0045] Step 1.3.2, based on step 1.3.1, the fluid velocity u and temperature T are obtained by solving equations (1)-(5);

[0046] Step 1.3.3, the adjoint variable u * is obtained by solving the following adjoint equation;

[0047]

[0048] The Lagrange multiplier method is used to introduce the adjoint variable, and the Lagrange function L is obtained, which is a function of the fluid velocity u in step 1.3.2 and the adjoint variable u * in step 1.3.3;

[0049] Step 1.3.4, based on the results of steps 1.3.2 and 1.3.3, the sensitivity , i.e. the gradient of the Lagrange function L with respect to the design variable field γ, is solved:

[0050]

[0051] where γ is the design variable field, and γ is a number between 0 and 1, 0 represents solid and 1 represents fluid; the design variable field is updated in the direction of decreasing sensitivity by the above formula;

[0052] Step 1.3.4, based on the results of steps 1.1.2 and 1.1.3, the fluid velocity u and temperature T and the adjoint variable u * and T * are calculated to obtain the sensitivity, and the design variable field is updated;

[0053] Step 1.3.5. Solving the governing equations (1), (2), (4)-(12) by using the finite volume method flow heat transfer solver as described in Step 1.2, and filtering the design variable field by using the Helmholtz density filter to avoid checkerboard phenomenon;

[0054] Step 1.3.6. Repeating the above Steps 1.3.2-1.3.5 until the design variable field converges, obtaining the low-fidelity flow heat transfer topology optimization structure based on 2L model I;

[0055] Step 1.3.7. Repeating Steps 1.3.2-1.3.6, respectively, to solve equations (6)-(9) and (10)-(12) by using the same solver and filter, obtaining the low-fidelity flow heat transfer topology optimization structures based on 2L model II and 1L model, and the structure is presented as the arrangement of solids in the two-dimensional calculation domain; Steps 1.3.6-1.3.7 obtain a set of candidate topology optimization structures, which are exported in stp, step engineering geometry format.

[0056] 3. The multi-fidelity topology optimization method for micro-channel flow boiling process according to claim 1, wherein the specific method of Step 2 is:

[0057] Step 2.1. Constructing a phase change model based on the volume of fluid method and interface temperature correction, i.e. a high-fidelity flow boiling numerical model, the mass conservation equation, momentum conservation equation, energy conservation equation and volume fraction conservation equation of the fluid are as follows:

[0058]

[0059] Where t, p, u, g, T, ρ, μ, c p , λ are time, pressure, velocity, gravitational acceleration, temperature, density, viscosity, heat capacity and thermal conductivity, respectively, and ρ, μ and λ are volume-averaged fluid properties, and c p is the mass-averaged value, and subscript k represents the kth phase.

[0060] Numerically simulating the candidate topology optimization structure, the two-phase flow flow boiling heat transfer is characterized by the volume fraction control equation, C is the volume fraction of each phase; C1 and C2 are defined as the volume fractions of the primary phase (water) and the secondary phase (vapor), and the body force term F is calculated by the continuous surface force model. E is the energy source term caused by phase change, which is calculated according to the phase change rate

[0061]

[0062] Where h fg is the latent heat. ​Liquid reduction rate and vapor generation rate

[0063]

[0064] Step 2.2, based on the phase change model in step 2.1, evaluate the heat transfer performance of the low-fidelity flow heat transfer topological optimization structure obtained in step 1 under flow boiling conditions:

[0065] Step 2.2.1, stretch the low-fidelity flow heat transfer topological optimization structure obtained in step 1 in the height direction, and add a top plate and a base layer to obtain a three-dimensional geometric model of the microchannel;

[0066] Step 2.2.2, import the three-dimensional geometric model of the microchannel obtained in step 2.2.1 into a mesh drawing software to draw an unstructured mesh of the microchannel;

[0067] Step 2.2.3, for the unstructured mesh obtained in step 2.2.2, give the initial conditions and boundary conditions of the boiling heat transfer process in the microchannel, wherein the inlet is a velocity inlet boundary condition, the outlet is a pressure outlet boundary condition, the bottom wall is a constant heat flow boundary condition, the fluid-solid contact surface is a fluid-solid coupling boundary condition, and the other walls are adiabatic no-slip boundary conditions, solve the mass, momentum, and energy conservation equations of the fluid in step 2.1 and the volume fraction conservation equations (15) to (20), and calculate the two-phase flow distribution field, velocity field, and temperature field in the unstructured mesh region to obtain the two-phase volume fraction, velocity, pressure, and temperature at each position in the calculation domain, which intuitively reflects the heat transfer performance of the low-fidelity flow heat transfer topological optimization structure under flow boiling conditions;

[0068] Step 2.3, for the single-phase heat transfer process and the flow boiling heat transfer process obtained in steps 1 and 2.2, weight the temperature at different positions with the local position coordinates to construct a new objective function (formula 21) reflecting the flow boiling heat transfer characteristics to replace the maximum temperature (formula 14), thereby realizing efficient topological optimization of the flow boiling problem;

[0069] The following is a new objective function reflecting the flow boiling heat transfer characteristics:

[0070]

[0071] where the integral is over the entire bottom element, T max is the highest temperature of the current structure bottom surface. T max,ref is the highest temperature of all structures, Δx is the distance from the current element to the center of the calculation domain, Δx ref is the distance from the center of the calculation region to the corner, which serves as a reference value, Abot is the bottom surface area, the whole objective function (equation 21) is divided into three parts multiplied, the first part describes the temperature uniformity, the second part describes the absolute value of the temperature, the third part describes the influence of the high temperature of the corner.

[0072] The specific method of step 3 is:

[0073] Using the new objective function formula 21 obtained in step 2, the other solving process of step 1 is unchanged, and the low-fidelity topology optimization described in step 1 is carried out based on two two-layer (2L) reduced-order models and one single-layer (1L) reduced-order model, and a high-performance microchannel geometry structure based on the new objective function is generated.

[0074] The system based on the multi-fidelity topology optimization method for the microchannel flow boiling process described above comprises:

[0075] A low-fidelity topology optimization module is used to solve the adjoint equation in a given calculation domain based on the traditional objective function and the new objective function according to the method of step 1, calculate the sensitivity and update the design variable field; In this process, the velocity and temperature distribution of the topology optimization structure under the condition of low-fidelity will also be obtained.

[0076] A high-fidelity flow boiling heat transfer performance evaluation module is used to solve the flow boiling heat transfer process in the microchannel topology optimization structure according to the method of step 2, obtain the internal two-phase flow dynamics behavior, and obtain the velocity and temperature distribution; Then in step 3, the low-fidelity physical quantity distribution obtained in step 1 is compared and analyzed, a new objective function reflecting the characteristics of flow boiling heat transfer is obtained, and the new objective function is returned to the low-fidelity topology optimization module to generate a topology optimization structure with high flow boiling heat transfer performance.

[0077] The device based on the multi-fidelity topology optimization method for the microchannel flow boiling process described above comprises:

[0078] A memory is used to store a computer program;

[0079] A processor is used to realize the multi-fidelity topology optimization method for the microchannel flow boiling process according to the stored computer program.

[0080] A computer storage medium stores a computer program, which can perform multi-fidelity flow boiling topology optimization based on the multi-fidelity topology optimization method for the microchannel flow boiling process according to any one of claims 1 to 4 when executed by a processor.

[0081] Compared with the prior art, the present application has the following beneficial effects:

[0082] 1. Step 2 of this invention employs a phase transition model based on the fluid volume method and phase interface temperature correction for high-fidelity performance evaluation, ensuring accurate acquisition of the flow boiling heat transfer performance of the topology-optimized microchannel structure. Compared to the difficulty in experimental observation, numerical simulation facilitates the extraction of key internal physical fields and the analysis of two-phase flow dynamics characteristics.

[0083] 2. Step 3 of this invention solves the problem that existing topology optimization algorithms cannot directly optimize the flow boiling heat transfer problem. It establishes a mapping between the single-phase flow heat transfer topology optimization problem and the two-phase flow boiling heat transfer topology optimization problem, which can quickly design high-performance flow boiling heat transfer microchannels. At the same time, it can also use a new objective function as an index to quickly evaluate the flow boiling heat transfer performance of the microchannel topology optimization structure.

[0084] 3. Step 3 of this invention, based on a novel objective function, not only promotes flow boiling heat transfer and two-phase flow discharge, but also has good temperature uniformity and robustness. It effectively eliminates the dependence of existing multi-fidelity topology optimization processes on the range of seed parameter selection, and greatly saves computational resources in solving transient problems in existing multi-fidelity topology optimization design processes.

[0085] In summary, this invention addresses the shortcomings of existing topology optimization algorithms that cannot directly optimize the flow boiling heat transfer problem. By constructing a novel objective function that reflects the characteristics of flow boiling heat transfer, it achieves fast and accurate multi-fidelity topology optimization. The designed topology optimization structure eliminates local hot spots, reduces thermal resistance, and improves temperature uniformity. Attached Figure Description

[0086] Figure 1 This is a flowchart of the multi-fidelity topology optimization method for microchannel flow boiling processes according to the present invention; wherein, Figure 1 (a) is a flowchart of the multi-fidelity topology optimization method; Figure 1 (b) is the multi-fidelity topology optimization method using new indices in this invention.

[0087] Figure 2 This invention provides a topology optimization structure diagram and key physical field distribution for high-flow boiling heat transfer performance; wherein, Figure 2 (a) is the topology optimization structure. Figure 2 (b) shows the temperature distribution on the bottom surface. Figure 2 (c) is a two-phase flow distribution. Detailed Implementation

[0088] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are for illustration and explanation only and are not intended to limit the scope of the present disclosure.

[0089] A multi-fidelity topology optimization method for micro-channel flow boiling process, specifically comprising the following steps:

[0090] Step 1, low-fidelity topology optimization is performed on single-phase laminar convection heat transfer process, thereby generating a group of candidate structures;

[0091] Step 2, then based on a high-fidelity flow boiling numerical model, simulating the flow boiling heat transfer process of two-phase flow in the candidate topology optimization structure; the velocity, temperature and two-phase distribution in the single-phase heat transfer process and the flow boiling heat transfer process are studied and compared in detail, and based on the dominant factors of the flow boiling heat transfer problem in the micro-channel, a new type of objective function reflecting the flow boiling heat transfer characteristics is constructed;

[0092] Step 3, based on the new type of objective function, directly generating a topology optimization structure with high flow boiling heat transfer performance under low-fidelity conditions.

[0093] The specific method of step 1 is:

[0094] Step 1.1, using a topology optimization method based on density method to construct a low-fidelity convection heat transfer topology optimization model under single-phase laminar steady-state conditions; using three hierarchical reduced-order models to approximate the flow heat transfer in the three-dimensional micro-channel in the two-dimensional model, the three hierarchical reduced-order models include two two-layer (2L) reduced-order models and one single-layer (1L) reduced-order model; both two two-layer (2L) reduced-order models regard the three-dimensional micro-channel as two parts including the channel layer and the substrate layer; in the channel layer, there are solid and fluid, and the flow heat transfer is solved; in the substrate layer, all are solid, and the heat conduction is solved; wherein the first two-layer (2L) reduced-order model is named 2L reduced-order model I, the control equations of the channel layer thereof include mass conservation equation, momentum conservation equation and energy conservation equation; the mass conservation equation is:

[0095]

[0096] The momentum conservation equation is:

[0097]

[0098] Wherein, u, ρ fl , p, μ are the velocity, density, pressure and viscosity of the fluid. Equation (4) is different from the original Navier-Stokes equation, because the three-dimensional flow in the micro-channel is simplified to two-dimensional, by simplifying the flow in the three-dimensional channel to parabolic Poiseuille flow, a 6 / 7 rescaling constant is added in the momentum equation. F is the Brinkman body force term.

[0099] F = - α (γ) u (3)

[0100] where a (y) is the inverse permeability, which varies in both fluid and solid regions during the topology optimization process.

[0101] The three-dimensional microchannel flow is simplified to two-dimensional, specifically, the flow in three-dimensional microchannels is simplified to parabolic Poiseuille flow, and a 6 / 7 rescaling constant is added to the momentum conservation equation, so that the three-dimensional flow heat transfer is described by reduced order in the region of any two-dimensional arrangement of microchannels, i.e. the calculation domain;

[0102] The energy conservation equations of the channel layer and the substrate layer are expressed as

[0103]

[0104] In the formula, c p,fl is the specific heat capacity of the fluid; T c and T b are the temperatures of the channel layer and the substrate layer, respectively; λ (y) is the effective thermal conductivity; λ s is the solid thermal conductivity; H c and H b are the half-heights of the fluid channel and the solid substrate layer, respectively; q in is the heat flux density at the bottom of the substrate layer.

[0105] The second double-layer model is named 2L model II, and its mass and momentum conservation equations are similar to equations (1) and (2).

[0106]

[0107]

[0108] The single-layer (1L) reduced-order model is regarded as a microchannel with only a channel layer, and the heat flux density at the bottom of the microchannel is directly added to the energy conservation equation as a source term. The control equations of the 1L model are as follows:

[0109] Step 1.2, according to different control equations, the low-fidelity initial topology optimization problem of the microchannel is defined as:

[0110] min: T max

[0111]

[0112] Where T max is the highest temperature of the heat sink, and the minimum T max corresponds to the highest heat transfer performance. A Ωd is the area of the design domain Ω d . f c is the fluid volume fraction constraint condition.

[0113] To obtain a differentiable maximum operator, the maximum temperature in the computational domain is calculated by a generalized p-norm:

[0114]

[0115] where N is the total number of nodes in the computational domain, p is the norm, and is set to 10.

[0116] After the topology optimization problem of the microchannel is successfully defined, the control equations based on different hierarchical reduced-order models need to be solved, where the effective thermal conductivity λ(γ) needs to be interpolated by a reasonable approximation (RAMP) function due to its relationship with the local fluid-solid distribution ratio. To avoid the checkerboard problem, a Helmholtz density filter based on partial differential equations (PDE) is used. To obtain a clearer fluid-solid interface, a hyperbolic tangent projection method is used.

[0117] Step 1.3. Based on the control equations and optimization objectives in steps 1.1 and 1.2, perform low-fidelity topology optimization in the design domain to produce a set of candidate topology optimization structures for the laminar flow single-phase heat transfer problem.

[0118] The specific steps for the topology optimization of the unit cell structure at the pore scale in step 1.3 are as follows:

[0119] Step 1.3.1 Set the initial design variable distribution;

[0120] Step 1.3.2 Based on step 1.3.1, solve equations (1) to (5) to obtain the fluid velocity u and temperature T;

[0121] Step 1.3.3 Then solve the adjoint equations to obtain the adjoint variables u * and T * ;

[0122] Step 1.3.4 Calculate the sensitivity based on the results of step 1.3.2 and step 1.3.3, and update the design variable field;

[0123] Step 1.3.5 Filter and project the design variable field according to the description in step 1.2.

[0124] Step 1.3.6 Repeat the above steps 1.3.2 to 1.3.5 until the design variable field converges, obtaining the low-fidelity flow and heat transfer topology optimization structure based on the 2L model I.

[0125] Step 1.3.7 Repeat steps 1.3.2 to 1.3.6, respectively changing the control equations to (6) to (9) and (10) to (12), to obtain the low-fidelity flow and heat transfer topology optimization structure based on the 2L model II and the 1L model.

[0126] The specific method of step 2 is:

[0127] Step 2.1, build a phase change model based on the fluid volume method and interface temperature correction, i.e. high-fidelity flow boiling numerical model, the mass, momentum and energy conservation equations of fluid are as follows:

[0128]

[0129]

[0130] Where t, p, u, g, T, p, m, c p , l are time, pressure, velocity, gravitational acceleration, temperature, density, viscosity, heat capacity and thermal conductivity, respectively. The fluid properties such as p, m and l are volume-averaged, and c p is mass-averaged. The subscript k represents the kth phase. The two-phase flow simulation uses the volume of fluid method, and C is the volume fraction of each phase. C1 and C2 are defined as the volume fractions of the primary phase (water) and the secondary phase (vapor). The body force term F is calculated by the continuous surface force model. S E is the energy source term caused by phase change, which can be calculated according to the phase change rate :

[0131] Where h fg is the latent heat, which can be used to calculate the liquid reduction rate and the vapor generation rate

[0132]

[0133] Step 2.2, based on the phase change model in step 2.1, evaluate the heat transfer performance of the topological optimization structure obtained in step 1 under flow boiling conditions.

[0134] Step 2.2.1, stretch the two-dimensional topological optimization structure obtained in step 1 in the height direction, and add a top plate and a base layer to obtain a three-dimensional geometric model.

[0135] Step 2.2.2, import the three-dimensional geometric model obtained in step 2.2.1 into a mesh drawing software to draw an unstructured mesh.

[0136] Step 2.2.3, for the unstructured mesh obtained in step 2.2.2, given the initial conditions and boundary conditions of the boiling heat transfer process in the microchannel, the inlet is a velocity inlet boundary condition, the outlet is a pressure outlet boundary condition, the bottom wall is a constant heat flux boundary condition, the fluid-solid contact surface is a fluid-structure coupling boundary condition, and the other walls are adiabatic no-slip boundary conditions, solve (15)-(20) in step 2.1, and perform statistics on the two-phase flow distribution field, velocity field and temperature field in the calculation domain.

[0137] Step 2.3, detailed study and comparison of the velocity, temperature and two-phase distribution field in the single-phase heat transfer process and the flow boiling heat transfer process obtained in steps 1 and 2.2, based on the dominant factors of the flow boiling heat transfer problem in the microchannel, a new target function reflecting the characteristics of flow boiling heat transfer is constructed;

[0138] For example, for a square design domain, it is found that under flow boiling conditions, steam will accumulate in the corners of the design domain, which will cause local high temperature and further worsen the two-phase flow discharge. Therefore, for such design domains, the following new target function reflecting the characteristics of flow boiling heat transfer is proposed:

[0139] Where the integral is over the entire bottom unit. T max is the highest temperature of the current structure bottom. T max,ref is the highest temperature of all structures. Δx is the distance from the current unit to the center of the calculation domain. Δx ref is the distance from the center of the calculation region to the corner, as a reference value. A bot is the bottom area. The entire index is divided into three parts, the first part describes the temperature uniformity, the second part describes the absolute value of the temperature, and the third part describes the influence of the high temperature at the corner. When the high temperature region is not at the corner, the third part can be used as a weight to weaken the influence of the region on the index.

[0140] The step 3 specific method is:

[0141] Step 3.1, directly perform the low-fidelity topology optimization described in step 1 under different seed parameters and generate high-performance structures through the new target function obtained in step 2;

[0142] Step 3.2, extract the flow boiling heat transfer high-performance microchannel geometry based on the new target function obtained in step 3.1 for subsequent application, such as additive manufacturing or numerical simulation.

[0143] Verification of enhanced flow boiling heat transfer performance:

[0144] Figure 2It is shown that for the problem of flow boiling heat transfer in microchannels, the high-performance topological optimization microchannel structure (a) and the corresponding bottom temperature field distribution (b) and two-phase flow distribution (c) are produced by using the multi-fidelity topological optimization method based on the performance objective function capable of reflecting the characteristics of flow boiling heat transfer proposed in the application. The high-performance microchannel structure shown in (a) is obtained, and the enhanced flow boiling heat transfer performance of the microchannel topological optimization structure is verified by using the high-fidelity performance evaluation process in step 2. Figure 2

[0145] The application evaluates the effectiveness of multi-fidelity topological optimization based on a new objective function for enhancing flow boiling heat transfer. Taking the design of a chip-top microchannel heat exchanger as an example, the performance of the generated new structure in terms of thermal resistance, maximum temperature and temperature uniformity is evaluated. It is verified whether the new objective function reflecting the characteristics of flow boiling heat transfer can achieve fast and accurate multi-fidelity topological optimization, and whether the topologically optimized structure can eliminate local hot spots, reduce thermal resistance and improve temperature uniformity.

[0146] For the high-performance microchannel geometry structure based on the new objective function of flow boiling heat transfer obtained in steps 1-3 above, the average temperature of the heating surface is obtained by using post-processing software such as Tecplot; and the same post-processing calculation is performed for the microchannel geometry structure based on the traditional objective function obtained in step 1 to obtain the average temperature. According to the average temperature, common heat exchange performance indicators such as unit thermal resistance are calculated. The unit thermal resistance corresponding to the multi-fidelity topological optimization result based on the new objective function is compared with the unit thermal resistance corresponding to the topological optimization structure based on the traditional objective function. Lower unit thermal resistance corresponds to higher boiling heat transfer performance.

[0147] The comparison results show that the multi-fidelity topological optimization based on the new objective function is effective in enhancing flow boiling heat transfer. The evaluation of the new structure of the chip-top microchannel heat exchanger shows good performance, with specific data as follows: the best structure based on the new objective for topological optimization is 12%, 2% and 36% better than the best structure based on the original objective for topological optimization in terms of thermal resistance, maximum temperature and temperature uniformity, respectively, proving the innovative effect of the application. By constructing a new objective function, fast and accurate multi-fidelity topological optimization is successfully achieved, and the topologically optimized structure can eliminate local hot spots, reduce thermal resistance and improve temperature uniformity, filling the gap that current topological optimization methods cannot be applied to boiling heat transfer problems.

[0148] The preferred embodiments of the application are described in detail above in combination with the drawings, but the application is not limited to the specific details in the above embodiments. Within the technical concept of the application, various simple modifications can be made to the technical solutions of the application, and these simple modifications all belong to the protection scope of the application.​

Claims

1. A method of multifidelity topology optimization for microchannel flow boiling processes, comprising: Specifically comprising the following steps: Step 1, low-fidelity topology optimization is performed on the single-phase laminar convection heat transfer process, so as to generate a set of candidate topology optimization structures for the laminar single-phase flow heat transfer problem; Step 2, based on a high-fidelity flow boiling numerical model, the two-phase flow flow boiling heat transfer process in the candidate topology optimization structure is simulated; The velocity, temperature and two-phase distribution in the single-phase heat transfer process and the flow boiling heat transfer process are calculated, and based on the dominant factors of the flow boiling heat transfer problem in the microchannel, a new type of objective function reflecting the flow boiling heat transfer characteristics is constructed; Step 3, based on the new type of objective function, a topology optimization structure with high flow boiling heat transfer performance is directly generated under low-fidelity conditions.

2. The method of multi-fidelity topology optimization for micro-channel flow boiling process according to claim 1, wherein, The specific method of step 1 is: Step 1.1, a low-fidelity convection heat transfer topology optimization model under single-phase laminar steady-state conditions is constructed using a topology optimization method based on the density method; three hierarchical reduced-order models are used to approximate the flow heat transfer in the three-dimensional microchannel in the two-dimensional model, the three hierarchical reduced-order models include two two-layer (2L) reduced-order models and one single-layer (1L) reduced-order model; both two two-layer (2L) reduced-order models regard the three-dimensional microchannel as two parts including a channel layer and a substrate layer; in the channel layer, there are solids and fluids, and the flow heat transfer is solved; in the substrate layer, all are solids, and the heat conduction is solved; wherein the first two-layer (2L) reduced-order model is named 2L reduced-order model I, the control equations of the channel layer thereof include mass conservation equation, momentum conservation equation and energy conservation equation; the mass conservation equation is: ▽·u＝0 (1) The momentum conservation equation is: where u, p, p, and m are the velocity, density, pressure, and viscosity of the fluid, respectively. fl where u, p, p, and m are the velocity, density, pressure, and viscosity of the fluid, respectively. F is the Brinkman volume force term: F = - alpha (gamma) u (3) Wherein, alpha (gamma) is the inverse permeability, F is used to describe the influence of the solid area on the fluid flow, and the influence becomes stronger with the increase of the flow velocity; The three-dimensional microchannel flow is simplified to two-dimensional, specifically, the flow in the three-dimensional microchannel is simplified to parabolic Poiseuille flow, and a 6 / 7 rescaling constant is added to the momentum conservation equation, so that the three-dimensional flow heat transfer is described in the region of any two-dimensional arranged microchannel, that is, the calculation domain; The energy conservation equation of the channel layer is expressed as: The energy conservation equation of the substrate layer is expressed as: where c p,fl is the fluid specific heat; T c and T b are the temperatures of the channel and base layers, respectively; λ(γ) is the effective thermal conductivity; λ s is the solid thermal conductivity; H c and H b are the half-heights of the fluid channel and solid base layer, respectively; q in is the heat flux at the base of the base layer; The second two-layer (2L) reduced-order model is named 2L model II, the control equations of the channel layer thereof include mass conservation equation, momentum conservation equation and energy conservation equation; the mass conservation equation of the 2L model II is: ▽·u＝0 (6) The momentum conservation equation of the 2L model II is: ρ fl (u · V)u = -Vp + μV 2 u + F (7) The energy conservation equations of the channel layer and the substrate layer of the 2L model II are: The single-layer (1L) reduced-order model is regarded as a microchannel with only a channel layer, and the heat flux density of the microchannel bottom surface is directly added to the energy conservation equation as a source term, and the control equations of the single-layer (1L) reduced-order model are as follows: ▽·u＝0 (10) ρ fl (u · V)u = -Vp + μV 2 u + F (11) Step 1.2, based on the two two-layer (2L) reduced-order models and the single-layer (1L) reduced-order model in step 1.1, the low-fidelity initial topology optimization problem of the microchannel is defined as: min: T max where T max is the maximum temperature of the heat sink, min T max corresponds to the maximum heat transfer performance, A Ωd is the area of the design domain Ω d , f c is the fluid volume fraction constraint condition, and the above topology optimization problem will be performed in a given discretized calculation domain, which is an arbitrary two-dimensional geometric shape. The objective function of the topology optimization problem of the microchannel is the maximum temperature in the calculation domain, that is, the maximum value, and the maximum value itself is not continuous, therefore, the generalized p-norm is used to continuously calculate the maximum value, that is, the maximum temperature, and the following optimization objective formula is obtained: Wherein, N is the total number of nodes in the calculation domain, that is, the number of grids, p is the norm; The finite volume method flow heat solver is used to solve the control equations (1), (2), (4)-(12), and the Helmholtz density filter is used to filter the design variable, that is, the arrangement of the solid, to avoid the chessboard problem in solving; Step 1.3, low-fidelity flow heat topology optimization: based on the control equations (1), (2), (4)-(12) and the optimization objective (14) in steps 1.1 and 1.2, low-fidelity flow heat topology optimization is performed in a given discretized arbitrary two-dimensional calculation domain, and a group of candidate topology optimization structures is generated for the laminar single-phase flow heat transfer problem; Specifically: Step 1.3.1, the initial design variable distribution is set by using the full fluid arrangement initialization strategy, and the design variable field is the arrangement of the solid in the calculation domain; Step 1.3.2, based on step 1.3.1, solve equations (1)-(5) to obtain fluid velocity u and temperature T; Step 1.3.3 Solve the following adjoint equation for the adjoint variable u * ; - p(u - V)u * = - Vp * + mV 2 u * + p(Vu) - u * The Lagrange multiplier method is used to introduce the adjoint variable, obtaining the Lagrangian function L, which is a function of the fluid velocity u in step 1.3.2 and the adjoint variable u in step 1.3.3 * ; Step 1.3.

4. Solve the sensitivity based on the results of Step 1.3.2 and Step 1.3.3 i.e. the gradient of the Lagrangian function L with respect to the design variable field γ: Wherein, γ is the design variable field, γ is a number between 0 and 1, 0 represents solid, and 1 represents fluid; The design variable field is updated in the direction of sensitivity reduction by the above formula; Step 1.3.4 Calculate the sensitivity and update the design variable field based on the results of Step 1.1.2 and Step 1.1.3, combining the fluid velocity u and temperature T and the accompanying variables u * and T * Calculate the sensitivity and update the design variable field; Step 1.3.5, according to the finite volume method flow heat solver for solving the control equations (1), (2), (4)-(12) in step 1.2, and the Helmholtz density filter is used to filter the design variable field, to avoid the chessboard phenomenon; Step 1.3.6, repeat steps 1.3.2 to 1.3.5 above until the design variable field converges, and obtain the low-fidelity flow heat topology optimization structure based on the 2L model I; Step 1.3.7, repeat steps 1.3.2 to 1.3.6, respectively, to solve equations (6)-(9) and (10)-(12) using the same solver and filter, to obtain the low-fidelity flow heat topology optimization structure based on the 2L model II and the 1L model, and the structure presents the arrangement of the solid in the two-dimensional calculation domain; Steps 1.3.6 to 1.3.7 obtain a group of candidate topology optimization structures, and are exported in stp, step engineering geometry format.

3. The method of multi-fidelity topology optimization for micro-channel flow boiling process according to claim 1, wherein, The specific method of step 2 is: Step 2.1, construct a phase change model based on the volume of fluid method and interface temperature correction, that is, a high-fidelity flow boiling numerical model, the mass conservation equation, momentum conservation equation, energy conservation equation and volume fraction conservation equation of the fluid are as follows: where t, p, u, g, T, p, m, c p , and l are time, pressure, velocity, gravitational acceleration, temperature, density, viscosity, heat capacity, and thermal conductivity, respectively, and p, m, and l are volume-averaged values, and c p is a mass-averaged value, and subscript k represents the kth phase. The numerical simulation candidate topology optimization structure, by volume fraction control equation of two-phase flow boiling heat transfer is characterized, C is the volume fraction of each phase; C1 and C2 are defined as the volume fraction of the main phase (water) and the secondary phase (vapor), and the body force term F is calculated by the continuous surface force model. S E Is the energy source term caused by phase transition, according to the phase transition rate Calculation: where h fg is latent heat; may be used to calculate liquid reduction rate and vapor generation rate Step 2.2, based on the phase change model in step 2.1, evaluate the heat transfer performance of the low-fidelity flow heat topology optimization structure obtained in step 1 under flow boiling conditions: Step 2.2.1, stretch the low-fidelity flow heat topology optimization structure obtained in step 1 in the height direction, and add a top plate and a base layer to obtain a three-dimensional geometric model of the microchannel; Step 2.2.2, import the three-dimensional geometric model of the microchannel obtained in step 2.2.1 into a mesh drawing software to draw an unstructured mesh of the microchannel; Step 2.2.3, for the unstructured grid obtained in step 2.2.2, given the initial conditions and boundary conditions of the boiling heat transfer process in the microchannel, wherein the inlet is a velocity inlet boundary condition, the outlet is a pressure outlet boundary condition, the bottom wall is a constant heat flux boundary condition, the fluid-solid contact surface is a fluid-solid coupling boundary condition, and the other walls are adiabatic no-slip boundary conditions, solve the mass, momentum, energy conservation equations and volume fraction conservation equations (15) to (20) of the fluid in step 2.1, and calculate the two-phase flow distribution field, velocity field and temperature field in the unstructured grid area to obtain the two-phase volume fraction, velocity, pressure and temperature at each position in the calculation domain, so as to intuitively reflect the heat transfer performance of the low-fidelity flow heat transfer topology optimization structure under the condition of flow boiling; Step 2.3, for the single-phase heat transfer process and the flow boiling heat transfer process obtained in steps 1 and 2.2, a new type of objective function (formula 21) reflecting the flow boiling heat transfer characteristics is constructed by weighting the temperature at different positions with the local position coordinates to replace the maximum temperature (formula 14), so as to realize high-efficiency topology optimization of the flow boiling problem; The new type of objective function reflecting the flow boiling heat transfer characteristics is as follows: where the integral is over the entire bottom surface of the element, T max is the maximum temperature of the current structure bottom surface. T max,ref is the maximum temperature of all structures, Δx is the distance of the current element to the center of the calculation domain, Δx ref is the distance from the center of the calculation region to the corner, A bot is the bottom surface area, the entire objective function (equation 21) is divided into three parts multiplied, the first part describes the temperature uniformity, the second part describes the absolute value of the temperature, the third part describes the influence of the high temperature of the corner.

4. The method of multi-fidelity topology optimization for micro-channel flow boiling process according to claim 1, wherein, The specific method of step 3 is: Using the new type of objective function formula 21 obtained in step 2, the other solving procedures of step 1 remain unchanged, and based on two two-layer (2L) reduced-order models and one single-layer (1L) reduced-order model, the low-fidelity topology optimization described in step 1 is carried out, and a high-performance microchannel geometry structure based on the new type of objective function is generated.

5. The system based on the above multi-fidelity topology optimization method for microchannel flow boiling process according to any one of claims 1 to 4, characterized in that, It comprises: A low-fidelity topology optimization module for solving the adjoint equation in a given calculation domain based on the traditional objective function and the new type of objective function according to the method of step 1, calculating the sensitivity and updating the design variable field; in this process, the velocity and temperature distribution of the topology optimization structure under the condition of low-fidelity will also be obtained; A high-fidelity flow boiling heat transfer performance evaluation module for solving the flow boiling heat transfer process in the microchannel topology optimization structure according to the method of step 2 to obtain the internal two-phase flow dynamics and the velocity and temperature distribution; then in step 3, the low-fidelity physical quantity distribution obtained in step 1 is compared and analyzed to obtain a new type of objective function reflecting the flow boiling heat transfer characteristics, and then the new type of objective function is returned to the low-fidelity topology optimization module to generate a topology optimization structure with high flow boiling heat transfer performance.

6. The apparatus based on the above-described method of multi-fidelity topological optimization for micro-channel flow boiling process according to any one of claims 1 to 4, characterized in that, It comprises: Memory: for storing computer programs; Processor: for implementing the multi-fidelity topology optimization method for microchannel flow boiling process according to the stored computer programs.

7. A computer storage medium storing a computer program, characterized in that, The computer program can perform multi-fidelity flow boiling topology optimization based on the multi-fidelity topology optimization method for microchannel flow boiling process according to any one of claims 1 to 4 when executed by the processor.

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