Prediction method for heat transfer characteristics of wall particle deposition based on porous equivalent model

Abstract

This invention discloses a method for predicting the heat transfer characteristics of particle deposition on a wall surface based on a porous equivalent model. The method includes establishing a mesh model; establishing an attached particle deposition judgment model considering wall shear stress, combining the critical wall shear rate deposition criterion with the wall shear stress criterion to determine stable particle deposition; obtaining depositional characteristic parameters such as deposition thickness and deposition rate based on the model; and establishing a fluid-structure interaction numerical method based on an equivalent porous medium. This method utilizes a porous medium framework during continuous phase solving, identifies the equivalent depositional region based on local wall deposition thickness and normal information, and modulates the region's porosity, drag coefficient, and thermal properties to perturb the near-wall flow field. By iteratively updating the depositional characteristics and equivalent region range, the method achieves coupled prediction of depositional layer growth evolution and convective heat transfer, thereby obtaining the synchronous evolution results of wall temperature distribution and depositional morphology under depositional conditions.

Description

Technical Field

[0001] This invention belongs to the field of heat transfer technology, specifically relating to a method for predicting the heat transfer characteristics of wall particle deposition based on a porous equivalent model. Background Technology

[0002] This invention proposes a numerical simulation-based method to characterize the disturbance effect of particle deposition on the near-wall flow field and further predict the impact of this disturbance on near-wall flow heat transfer. Simultaneously, the evolution of the near-wall flow field, in turn, influences particle flow and deposition processes, thereby altering subsequent deposition trends. This method uses only a deposition model and a porous equivalent model to simulate and predict the coupling effect between sedimentary layer growth and the near-wall flow field in a watershed. Compared to traditional dynamic mesh implementation strategies, it effectively avoids the problem of sedimentary morphology distortion and achieves effective prediction of temperature distribution in the flat plate sedimentary morphology domain while maintaining high accuracy. This method provides a foundation for analyzing the evolution of particle deposition trends under fluid-structure interaction and significantly reduces computational resource requirements.

[0003] The near-wall gas-thermal-structure coupling calculation under the influence of particle deposition is a complex problem. The growth of the deposited layer significantly disturbs the near-wall flow field, and the evolved near-wall flow field, in turn, affects the subsequent trend of particle deposition. In this coupling process, the proportions of convective heat transfer, heat resistance of the deposited layer, and heat transfer of the substrate cooling structure in the heat transfer path are constantly changing. Taking typical cooling structures such as film vents as an example, the gradually growing deposited layer may block the film vents, leading to localized deterioration of heat transfer performance and subsequently substrate ablation. Therefore, predicting and controlling the wall deposition characteristics is of great significance for maintaining the reliable operation of heat exchange components.

[0004] However, while existing numerical methods for particle deposition based on DPM (Discrete Phase Model) can calculate information such as deposition quality, deposition rate, and deposition thickness on the deposition surface, this information is usually only recorded on the face in the form of user-defined memories (UDMs). This recorded result is not transformed into a new geometric boundary or property region in the computational domain. Therefore, it is difficult to reflect the influence of the deposition layer on the near-wall flow structure and convective heat transfer in the continuous phase solution. Summary of the Invention

[0005] This invention proposes a method for predicting the heat transfer characteristics of particle deposition on a porous surface based on a porous equivalent model. It develops a particle deposition judgment model that considers wall shear stress and, by analogy, treats the deposited layer as a porous medium with low porosity and high viscous resistance, thereby constructing an equivalent fluid-structure interaction calculation method. This method can predict the growth and evolution of the deposited layer in real time and map the deposition characteristics to the fluid domain, realizing the coupled heat transfer between the flow field, the deposited layer, and the substrate. Comparison with actual modeling and calculation results shows that the maximum relative error of this method is 1.64%.

[0006] To achieve the above objectives, the present invention employs the following technical solution: a method for predicting the heat transfer characteristics of wall particle deposition based on a porous equivalent model, comprising: Step 1: Establish the mesh model: Based on the shape and size of the heat exchange surface, use ICEM (The Integrated Computer Engineering and Manufacturing) software to establish a physical model of the heat exchange surface and divide it into a structured mesh; Step 2: Combine the particle peeling model that considers wall shear stress with the critical wall shear rate model, and load it through UDF compilation; Step 3: Initialize the equivalent porous model and parameters. Preset the fluid domain as a pure flow region (unmarked region), and input the porosity, viscous drag, and thermal properties of the pure fluid. At the same time, input the actual porosity, viscous drag, and thermal properties of the sediment layer (marked region) in case the fluid domain mesh properties change during calculation. Finally, compile and load the model using a UDF (User Defined Function). Step 4: Perform steady-state calculations on the flow field. Once the flow field is stable and filled with particles, activate the particle deposition model. Step 5: When particles are deposited and the wall deposit layer begins to grow, obtain characteristic information such as the deposit layer thickness and deposition rate through the local grid area, activate the porous equivalent model and input the local deposit layer thickness; Step 6: Based on the local sedimentary surface normal vector, sedimentary layer thickness, and corresponding fluid domain grid centroid coordinates, find and mark all fluid domain grids below the sedimentary layer thickness along the direction of the local sedimentary surface normal vector. This determines the marking method for sedimentary layer grids within the fluid domain. Considering that computational domain grid data is difficult to transfer across cores during parallel computing, a global data aggregation and broadcast communication method is adopted to ensure real-time sharing of computational domain data. Step 7: After the fluid domain mesh is marked as a deposition layer, the host process changes the porosity, viscous resistance, and thermal property parameters of the marked fluid domain mesh in step 6 in real time, so that it is equivalent to the high porosity and low resistance fluid element and the low porosity and high resistance deposition layer element, thereby realizing the coupling effect of the deposition layer on near-wall flow and convective heat transfer, and finally updating the temperature field distribution of the computational domain.

[0007] Furthermore, in step 1, the mesh model undergoes mesh independence verification and satisfies the requirement that the minimum mesh quality is higher than 0.25.

[0008] Furthermore, in step 2, the particle peeling model considering wall shear stress can be described as follows: when the shear rate experienced by the wall-adhered particles exceeds the critical wall shear rate, the particles enter the mainstream. The critical wall shear rate can be expressed as: ; In the formula, The critical wall shear rate of the fluid is denoted as . For Cunningham correction factor, The work done by particle adhesion is given by ρ, where ρ is the fluid density. For composite Young's modulus, D p The particle radius is consistent with the parameters of the critical wall shear rate model.

[0009] In the formula, It can be described as: ; ; In the formula, It is the Knudsen number, which represents the relative magnitude of the free path of gas molecules and the particle size. The mean air path, described by the average distance between two adjacent collisions of a spherical molecule with diameter d, is the mean free path of the molecule, expressed as: ; In the formula, d1 is the effective diameter of the molecule, which is 3.5 × 10⁻⁶. -10 m, Let n be the temperature and n be the number of molecules per unit volume. Using the ideal gas law, the result is: ; In the formula, For pressure, Boltzmann constant K B 1.38×10 -23 J / K.

[0010] The shear rate experienced by the adherent particles is: ; In the formula, ρ is the wall shear stress, and ρ is the fluid density.

[0011] The critical wall shear velocity deposition model used in this invention can be described as follows: ; ; ; In the above formula, V cr E is the critical wall shear rate. s E represents the surface Young's modulus. p Let be the Young's modulus of the particle. For surface Poisson's ratio, For the particle Poisson's ratio, D p Where is the particle radius, Particle density, It is an intermediate variable.

[0012] Furthermore, in step 3, the porosity parameter of the undeposited region in the fluid domain is set as follows: porosity =1, viscous drag coefficient =0, where For penetration rate, subscript Unmarked regions (undeposited regions) within the fluid domain. The density, specific heat, and thermal conductivity of the undeposited regions are determined by the selected working fluid material. The porosity parameter of the equivalent region of the sedimentary layer is: porosity. Take actual sedimentary layer data, viscosity drag coefficient Extremely large, where the subscript The fluid domain is marked as a region (sediment layer), with a cutoff upper limit of 10. 12 The density, specific heat, and thermal conductivity of the sediment layer are taken from the actual physical properties.

[0013] Further, in step 5, the deposition layer thickness of the local grid... With sedimentation rate The calculation method is as follows: ; ; In the formula This represents the total mass of particles deposited on the local grid. For the local grid area, Particle density, This represents the cumulative deposition time.

[0014] Further, in step 6, the method for determining the fluid domain meshes that need to be marked is as follows: First, the first layer of near-wall mesh cells are marked; then, all face elements are traversed on the deposition surface where deposition occurs; for each face, its fluid-side adjacent meshes (C0-side fluid meshes) are obtained as candidate cell elements; and the local deposition layer thickness H corresponding to that face is read. dep Calculate the centroid x of the adjacent meshes on the current fluid side. cell With face centroid x face Distance h proj When H dep h proj If the grid is found to be inside the sediment layer, it is marked; otherwise, no action is taken.

[0015] After marking the first layer of candidate elements, the remaining elements within the fluid domain are further evaluated. For any candidate element, its centroid x is taken. cell With the centroid x of the deposition surface face positional difference r=x cell -x face。 After determining the direction of the unit outward normal vector of the face, the normal projection thickness is calculated using this unit outward normal vector n. ; And normal offset distance: ; When 0 is satisfied <h proj <H dep And h prep When the value is less than δ, the candidate cell is determined as an equivalent region cell of the deposition layer and marked; where δ is a threshold used to limit the lateral deviation of the mesh relative to the face.

[0016] Furthermore, regarding parallel and consistent data communication, to avoid inconsistent acquisition of the parameters required for labeling determination due to candidate meshes and deposition faces belonging to different computational cores, a global data aggregation and broadcast communication method is adopted: First, each computational node packages its local data related to labeling determination (including but not limited to coordinates, temperature field data, and deposition data stored in UDMs) and aggregates it to the master node (node0). Then, the master node submits the aggregated global data to the host process (host). Subsequently, the host process uniformly organizes the received data and stores it in a global shared cache. Finally, the host process broadcasts the global shared cache to each computational node, enabling each node to obtain consistent global determination parameters. As the deposition layer updates over time, the above communication process is executed synchronously with the iteration to ensure the consistency and real-time performance of the labeling results across the parallel cores.

[0017] Furthermore, in step 7, the real-time modification of the physical properties of the deposition region in the flow field is achieved as follows: each iteration of the host process changes the marked fluid domain mesh viscous resistance, porosity, thermal conductivity, and specific heat to the physical properties corresponding to the deposition layer. Simultaneously, to ensure the consistency of execution timing among the cores, all cores are forced to begin calculations uniformly only after receiving broadcast information.

[0018] The method for predicting the heat transfer characteristics of wall particle deposition based on a porous equivalent model, as proposed in this invention, has the following advantages: (1) The wall particle deposition heat transfer characteristics prediction method based on the porous equivalent model proposed in this invention couples the critical wall shear rate deposition criterion with the wall shear stress peeling criterion. The stability determination of attached particle peeling is realized through Ansys Fluent user-defined function (UDF). In the numerical calculation, the deposition characteristic parameters such as deposition thickness and deposition rate are updated in real time, thus realizing the prediction of the spatiotemporal evolution characteristics of the deposition layer.

[0019] (2) In view of the dilemma that the deposition features in the existing numerical methods of particle deposition are only recorded on the wall surface elements as UDMs data and cannot affect the flow field, the present invention proposes a mapping mechanism that the deposition feature parameters affect the changes in the physical properties of the fluid domain grid elements. This enables the deposition thickness and other results to be transformed into an equivalent region in the computational domain that can participate in the solution of the control equations, thereby improving the efficiency of wall temperature and heat transfer degradation prediction under deposition conditions and reducing computational requirements.

[0020] (3) The deposition layer evolution and near-wall flow field disturbance coupling calculation method constructed by the present invention treats the deposition layer as a porous medium region with low porosity and high viscosity resistance in the fluid domain, and marks and modifies the properties of the deposition region according to the local deposition thickness and normal information of the wall, thereby realizing the real-time influence of the deposition layer on the near-wall flow structure and heat transfer path.

[0021] (4) This invention does not use the traditional dynamic mesh method to express the geometric growth of the sedimentary layer, thus avoiding the calculation divergence problem caused by mesh distortion during the growth of the sedimentary layer and simplifying the calculation process. At the same time, this method is compatible with parallel computing and iterative update processes, which can reduce the consumption of computing resources and improve the efficiency of engineering simulation while ensuring the accuracy of prediction. It is suitable for the rapid evaluation and optimization design of complex heat transfer structures such as film pores under particle deposition conditions. Attached Figure Description

[0022] Figure 1 This is a flowchart illustrating the implementation of a method for predicting the heat transfer characteristics of wall particle deposition based on a porous equivalent model, as described in this invention. Figure 2 This is a flowchart of the particle stabilization deposition process of the present invention; Figure 3 This is a schematic diagram of the deposition thickness values ​​stored in the UDMs of the present invention; Figure 4 This is a schematic diagram of the marked fluid domain grid cell of the present invention; Figure 5 This is a schematic diagram of a sweep model for verification purposes of the present invention; Figure 6 This is a schematic diagram illustrating the verification of the mesh independence of the sweep model, a verification example of the present invention. Figure 7 This is a diagram showing the mesh generation result of a verification example of the present invention; Figure 8 The flow field temperature and streamline distribution diagrams are shown in the verification example of the present invention for the direct modeling method. Figure 9 The flow field temperature and streamline distribution diagrams of the porous equivalent model in the verification example of this invention are shown. Figure 10 These are temperature distribution diagrams of the substrate surface under two deposition modeling methods in the verification examples of this invention. Figure 11 A schematic diagram of the reserved air film pore structure prepared by CMC in an embodiment of the present invention; Figure 12 This is a flow channel model diagram in an embodiment of the present invention; Figure 13 This is a model diagram of a flat plate containing two air film holes in an embodiment of the present invention; Figure 14 This is a grid independence verification diagram in an embodiment of the present invention; Figure 15 This is a schematic diagram illustrating the marking and judgment principle in an embodiment of the present invention; Figure 16 This is a temperature contour map before and after deposition in an embodiment of the present invention; Figure 17 This is a schematic diagram of the streamlines, temperature field distribution, and deposition morphology of the YZ section in an embodiment of the present invention; Detailed Implementation

[0023] The following is in conjunction with the appendix Figure 1 The process shown in the diagram provides a further explanation of the present invention.

[0024] Step 1: Establish the mesh model: Based on the shape and size of the heat exchange surface, use ICEM software to establish a physical model of the heat exchange surface and divide it into a structured mesh.

[0025] Step 2: Combine the particle stripping model that considers wall shear stress with the critical wall shear rate model, and load it through UDF compilation.

[0026] Step 3: Initialize the porous equivalent model and parameters. Preset the fluid domain as a pure flow region (unmarked region), and input the porosity, viscous drag, and thermal properties of the pure fluid. At the same time, input the actual porosity, viscous drag, and thermal properties of the sediment layer (marked region) in case the fluid domain mesh properties change during calculation. Finally, compile and load the model using UDF.

[0027] Step 4: Perform steady-state calculations on the flow field. Once the flow field is stable and filled with particles, activate the particle deposition model.

[0028] Step 5: When particles are deposited and the wall deposit layer begins to grow, obtain characteristic information such as the deposit layer thickness and deposition rate through the local grid area, activate the porous equivalent model and input the local deposit layer thickness.

[0029] Step 6: Based on the local sedimentary surface normal vector, sedimentary layer thickness, and corresponding fluid domain grid centroid coordinates, find and mark all fluid domain grids below the sedimentary layer thickness along the direction of the local sedimentary surface normal vector. This determines the marking method for sedimentary layer grids within the fluid domain. Considering that computational domain grid data is difficult to transfer across cores during parallel computing, a global data aggregation and broadcast communication method is adopted to ensure real-time sharing of computational domain data.

[0030] Step 7: After the fluid domain mesh is marked as a deposition layer, the host process will change the porosity, viscous drag and thermal properties of the marked mesh in step 6 in real time, so that it is equivalent to the fluid element with high porosity and low drag being transformed into the deposition layer element with low porosity and high drag. This realizes the coupling effect of the deposition layer on near-wall flow and convective heat transfer, and finally updates the temperature field distribution of the computational domain.

[0031] After the above steps are completed, the entire particle deposition method will be simulated and compared to verify the accuracy of the model.

[0032] In step 1, a flat plate model is created and divided into a structured mesh.

[0033] In step 2, the flowchart for determining stable particle deposition is as follows: Figure 2 As shown, the critical wall shear velocity model studies the elastic properties of particles and uses the normal velocity of the particles when they collide with the wall as the criterion. When the normal velocity of the particles is greater than the critical wall shear velocity, the particles will bounce back and not deposit. When the normal velocity of the particles is less than the critical wall shear velocity, the particles will adhere to the wall. ; ; ; ; In the above formula, V crHere, E is the critical wall shear rate, and E is the composite Young's modulus. s E represents the surface Young's modulus. p The Young's modulus of the particles satisfies the following condition with temperature. , For surface Poisson's ratio, For the particle Poisson's ratio, D p Where is the particle radius, Particle density, It is an intermediate variable.

[0034] A particle stripping model considering wall shear stress is used to determine whether particles can be stably deposited. The reason for using an additional criterion is that when the wall stripping shear rate experienced by the adherent particles in the boundary layer exceeds the critical wall shear rate, the adherent particles will detach from the wall and rejoin the mainstream. ; In the above formula, The critical wall shear rate of the fluid is denoted as . For Cunningham correction factor, For the work of particle adhesion, The composite Young's modulus, ρ is the fluid density, and D is the fluid density. p The particle radius is consistent with the parameters of the critical wall shear rate model.

[0035] in, It can be described as: ; ; In the above formula, It is the Knudsen number, which represents the relative magnitude of the free path of gas molecules and the particle size. The mean air path, described by the average distance between two adjacent collisions of a spherical molecule with diameter d, is the mean free path of the molecule, expressed as: ; In the above formula, d1 is the effective diameter of the molecule, which is 3.5 × 10⁻⁶. -10 m and n are the number of molecules per unit volume, which can be calculated using the ideal gas law as follows: ; In the above formula, For pressure, Boltzmann constant K B 1.38×10 -23 J / K.

[0036] In this example, W A The particle adhesion work is a parameter for silicon particles, taken as 0.039 J / m. 3 .

[0037] The shear rate received by the adhering particles is: ; In the above formula, ρ is the wall shear stress, and ρ is the fluid density.

[0038] In step 3, the drag source term of the continuous phase momentum equation can be expressed as: ; In the above formula, The momentum source considering the loss in the porous medium is represented by the direction, where i = 0, 1, 2 represent the x, y, and z directions, respectively. It is inertial resistance. It's penetration rate. It is fluid viscosity. It is fluid density. It is the velocity modulus. Let represent the velocity components in each direction. For flows with low Reynolds numbers, viscous losses typically dominate, while the inertial drag coefficient can usually be set to 0. For turbulent flows, inertial losses typically dominate, while the viscous drag coefficient can usually be set to 0. However, for the unlabeled mesh elements in this example, the momentum loss in the porous medium is 0, from which we can deduce: ; ; ; In the above formula, The porosity of the pure fluid region. The coefficient of viscosity resistance. This is the inertial drag coefficient.

[0039] For the porosity and other equivalent parameters of the sedimentary layer, the local sedimentary volume can be expressed as: ; In the above formula, A is the area of ​​the local grid face, and H... dep This represents the thickness of the local sedimentary layer. The compact density of the local sedimentary layer can be determined by its grain density. Provided.

[0040] The local packing density of the sedimentary layer, taking porosity into account, is: ; The porosity of the sedimentary layer is then expressed as: ; Based on the results, the porosity of the sedimentary layer can be approximated as 0.

[0041] Similarly, according to the linear pressure drop term in the Ergun equation that characterizes viscous shear dominance: ; The viscous resistance of the sedimentary layer is a maximum value. In engineering applications, an upper cutoff value is taken, so the viscous resistance of the sedimentary layer is approximately 10. 12 .

[0042] The thermal conductivity of the deposited layer is directly based on the commonly used 1.78 W / (m·K) in existing studies.

[0043] In step 5, the thickness of the deposition layer of the local grid is... With sedimentation rate The calculation method is as follows: ; ; In the formula This represents the total mass of particles deposited on the local grid. For the local grid area, Particle density, This represents the cumulative deposition time. A schematic diagram of the UDMs (User Defined Memories) data stored on the deposition surface is shown below. Figure 3 As shown.

[0044] All the depositional features calculated above are stored in user-defined memory UDMs for use by the porous equivalent model.

[0045] In step 6, the method for determining the fluid domain meshes that need to be marked is as follows: First, the first layer of near-wall mesh cells are marked. Then, all face elements on the deposition surface where deposition occurs are traversed. For each face, its fluid-side adjacent meshes (C0-side fluid meshes) are taken as candidate cell elements. The local deposition layer thickness H corresponding to that face is then read. dep Calculate the centroid x of the candidate mesh. cell With face centroid x face Distance h proj When H dep h proj If the grid is found to be inside the sediment layer, it is marked; otherwise, no action is taken.

[0046] After marking the first layer of candidate elements, the remaining elements within the fluid domain are further evaluated. For any candidate element, its centroid x is taken. cell With the centroid x of the deposition surface face positional difference r=x cell -x faceAfter determining the direction of the unit outward normal vector of the face, the normal projection thickness is calculated using this unit outward normal vector n: ; And normal offset distance: ; When 0 is satisfied <h proj <H dep And h prep When the value is less than δ, the candidate cell is determined as an equivalent region cell of the deposition layer and marked; where δ is a threshold used to limit the lateral deviation of the mesh relative to the face.

[0047] It is important to note that for parallel and consistent data communication, to avoid inconsistent acquisition of the parameters required for labeling and determination due to candidate meshes and deposition faces belonging to different computational cores, a global data aggregation and broadcast communication method is adopted: First, each computational node packages its local data related to labeling and determination (including but not limited to coordinates, temperature field data, and deposition data stored in UDMs) and aggregates it to the master node (node0). Then, the master node submits the aggregated global data to the host process (host). Subsequently, the host process uniformly organizes the received data and stores it in a global shared cache. Finally, the host process broadcasts the global shared cache to each computational node, ensuring that each node obtains consistent global determination parameters. As the deposition layer updates over time, the above communication process is executed synchronously with the iteration to ensure the consistency and real-time performance of the labeling results across the parallel cores. The fluid domain deposition layer mesh cells after labeling are as follows: Figure 4 As shown.

[0048] In step 7, the real-time modification of the physical properties of the deposition region in the flow field is achieved as follows: Each iteration of the host process changes the marked fluid domain mesh viscous resistance, porosity, thermal conductivity, and specific heat to the physical properties corresponding to the deposition layer. Simultaneously, to ensure the consistency of execution timing among the cores, all cores are forced to begin calculations uniformly only after receiving broadcast information.

[0049] The present invention provides a verification example and an embodiment.

[0050] The specific verification examples include: (1) Constructing a realistic sedimentary layer model and a physical model suitable for the porous equivalent model: Two verification sweep models were constructed. One model establishes a 2.1 mm thick and 5 mm long deposition layer in the center of the physical model. The corresponding physical model applicable to the porous equivalent model does not establish an actual deposition layer model, but only establishes a completely identical flow channel. The specific flow channel model is as follows: Figure 5 As shown, the flow channel is 300mm long and 50mm high. The substrate thickness is 10mm.

[0051] (2) Mesh independence verification: Mesh generation has a significant impact on computational results. To eliminate this influence, mesh independence verification was performed before numerical calculations. Since particle temperature and trajectory depend on the flow field, and the deposition criterion of the deposition model depends on particle temperature, velocity, and the surface temperature of the impacted wall, the accuracy of wall temperature or overall cooling effect calculations can represent the data accuracy of particle motion and deposition calculations. In this study, Ansys Mesh was used to mesh the computational model, and the mesh at the fluid-solid interface was refined. The first layer height was set to 0.0082 mm, with a growth rate of 1.1, and a total of 17 layers were set to ensure mesh density near the wall.

[0052] To ensure mesh independence, five groups of tetrahedral meshes with different sparsity were used for numerical calculations. When the mesh count is further increased or decreased while the average surface temperature of a specified cross-section remains essentially unchanged, the mesh independence requirement can be considered met. Figure 6 It can be seen that as the number of grid cells gradually increases, the interface temperature between the sediment and the thermal barrier coating first rises and then falls. However, when the number of grid cells is around 125,000, the average cross-sectional temperature remains essentially constant. Therefore, this grid was selected for subsequent numerical studies. The specific grid division results are as follows: Figure 7 As shown.

[0053] (3) Verification results: To visually demonstrate the impact of sediment-boundary layer interaction on flow and heat transfer, a velocity vector distribution map of the flow field near the sedimentary region was plotted when the local sediment thickness was 2.1 mm. Under the realistic modeling method, a clear separation—a swirling vortex—formed between the upstream and downstream surfaces of the sediment, with a sharp decrease in local velocity, as shown in the image. Figure 8 As shown. The porous equivalent model, due to the need for numerical interpolation during labeling to maintain surface smoothness, exhibits a smaller "sediment" deformation angle, resulting in weaker equivalent solid resistance compared to the fluid resistance experienced in the actual model, and smoother streamlines, as shown. Figure 9 As shown, the realistic modeling method more realistically reproduces the microscopic effects of sediments on flow separation. The porous equivalent model replaces the solid wall with a drag model, which suppresses some small eddies and results in a more uniform streamline distribution, but can also better reproduce the macroscopic effects of boundary layer uplift and eddies.

[0054] Furthermore, Figure 10The calculation differences between the two methods were compared from a quantitative perspective. The surface temperature of the substrate generally showed a decreasing trend along the flow direction. Abrupt changes occurred in the temperature curve in the region where deposits were present, which is related to the deposits altering the characteristic height of the flow channel and the surface heat transfer characteristics. The presence of deposits enhanced local heat conduction to some extent, but also disturbed the flow boundary layer, changing the surface heat transfer characteristics. Overall, the temperature distribution of the coating surface obtained by the two modeling methods showed little difference, with a maximum temperature difference of 5.11 K (at X=0.1569 m), corresponding to an error of 1.64%.

[0055] The specific implementation examples include: (1) Constructing a CMC (Ceramic Matrix Composites) film cooling plate with film cooling pores: The structure of the CMC substrate is as follows: Figure 11 As shown, this includes a set of 45° inclined circular air-film pores with a diameter of 0.8 mm. The red area represents the weft yarns, with an adjacent weft yarn spacing of 4.66 mm; the yellow area represents the warp yarns, with a weaving angle of 20° and an adjacent warp yarn spacing of 0.6 mm; the gray area represents the air-film pores, with a hexagonal cross-section of the fiber bundle and a cross-sectional dimension S1 = 0.34375 mm. 2 The axial thermal conductivity of the fiber bundle is K. FA =9.66 W / (m·K), transverse thermal conductivity K FT =1.48 W / (m·K).

[0056] To simulate the working environment of a real turbine blade, the main flow channel is designed with a 45° incident angle, and the angle between the pressure surface and the incoming flow direction is as follows: Figure 12 The purple area indicates a channel width of 86 mm. The blue area represents a secondary flow channel with a height of 7 times the plate thickness. To capture the deposition characteristics between film pores, the model includes two adjacent sets of film pores, as shown... Figure 13 As shown. The plate is 50 mm long, 6.68 mm wide, with a lateral spacing of 3.34 mm between the air film vents and a distance of 9 mm from the vent inlet to the front end of the plate. The green part is the substrate, with a thermal conductivity of 0.2 W / (m·K).

[0057] (2) Grid independence verification: Three mesh density schemes were constructed: coarse mesh (4.34 million elements), medium mesh (5.04 million elements), and fine mesh (10.76 million elements) to evaluate the impact of mesh size on simulation results. During particle deposition, particle temperature and trajectory are primarily regulated by the flow field, while deposition behavior is controlled by the interaction between particles and the wall surface. The criteria for particle deposition behavior depend on particle temperature, velocity, and the surface temperature impacting the wall. Therefore, the computational reliability of the particle motion and deposition model can be evaluated using the overall wall cooling effect. Figure 14 The graphs show the variation of the overall cooling effect along the flow direction on the downstream centerline of the film air vent under different grid numbers. It can be seen that when the number of grid cells increases from 4.34 million to 5.04 million, the overall cooling effect on the downstream centerline of the film air vent decreases. When the number of grid cells increases again from 5.04 million to 10.76 million, the change in the overall cooling effect on the downstream centerline of the film air vent is relatively small, with the maximum relative change being less than 5%. Considering the limitations of computational speed and storage space, this embodiment adopts a grid partitioning strategy with 5.04 million grid cells.

[0058] (3) Compile the particle deposition model and the porous equivalent model: The particle deposition model that takes into account wall shear stress is written as the corresponding UDF.

[0059] The multi-hole equivalent model considering cross-core data transmission will be used to determine the core, which will be written as the corresponding UDF. A 2D example will be used to illustrate its determination principle. Figure 15 As shown. Its core judgment can be expressed as follows: for any candidate unit, take its centroid x. cell With the centroid x of the deposition surface face positional difference r=x cell -x face After determining the direction of the unit outward normal vector of the face, the normal projection thickness is calculated using this unit outward normal vector n. ; And normal offset distance: ; When 0 is satisfied <h proj <H dep And h prep When the value is less than δ, the candidate cell is determined as an equivalent region cell of the deposition layer and marked; where δ is a threshold used to limit the lateral deviation of the mesh relative to the face.

[0060] (4) Calculation results: Figure 16The diagram shows temperature contour maps of the flat plate surface before deposition when the air-to-gas ratio is 0.25, and temperature contour maps of the same depositional morphology after deposition. Compared to before deposition, the coverage area of ​​the cooling gas flow along the flow direction slightly decreases after particle deposition. When the air-to-gas ratio M = 0.25, the depositional morphology of the flat plate surface is relatively smooth, with a small total deposition volume and insignificant longitudinal undulations, and no obvious accumulation characteristics are formed. This is because the momentum of the cold gas is weak, and small- and medium-sized particles are more easily entrained by the mainstream, thus inhibiting the migration and capture of particles towards the wall, thereby reducing the possibility of deposition. In terms of temperature distribution, the flat plate surface is mainly in a high-temperature state under this condition, with the wall temperature mostly concentrated in the range of 1350~1500K. The low-temperature region downstream of the film vent is limited to a very small area near the film vent, and the transition boundary between the low-temperature and high-temperature regions is steep. The local temperature gradient is concentrated near the film vent, and the overall low-temperature coverage area is small, making it difficult to effectively reduce the temperature of the flat plate surface.

[0061] Figure 17 The streamline structure of the flow field cross section is shown when the blowing ratio is 0.25. The figure reveals a large CRVP (Counter Rotating Vortex Pair) structure downstream of the film pore. Higher CRVPs tend to entrain low-inertia particles near the wall and transport them to regions far from the pore centerline. Simultaneously, the position of the central vortex of the CRVP also changes to some extent due to the influence of particulate sediments. This phenomenon further verifies the reproducibility of the porous equivalent model in sediment modeling studies and its impact on the flow field.

[0062] This invention is based on a porous equivalent model, treating the undeposited fluid domain as having a porosity close to 1 and resistance consistent with pure fluid flow. When deposition occurs and a local deposition thickness H is obtained at the wall surface... dep Subsequently, based on the wall normal and thickness information, a specific mesh marking method was used to identify the mesh cells corresponding to the deposition layer within the fluid domain, and these cells were equivalent to a porous medium region with near-zero porosity and significantly increased viscous resistance (viscous resistance was taken as 10). 12 The equivalent region is assigned values ​​for parameters such as thermal conductivity and specific heat based on the thermal properties of the deposited material. The near-wall flow field is dynamically updated during the iteration process as the deposition thickness increases. This method can realize the continuous influence of deposition layer growth on flow blockage and convective heat transfer without introducing a realistic depositional geometry model and a dynamic mesh method. A coupled model of particle deposition and flow field disturbance is established, enabling real-time prediction of depositional morphology and wall temperature.

Claims

1. A method for predicting the heat transfer characteristics of wall particle deposition based on a porous equivalent model, characterized in that, include: Step 1: Establish the mesh model: Based on the shape and size of the heat exchange surface, use ICEM software to establish a physical model of the heat exchange surface and divide it into a structured mesh; Step 2: Combine the particle peeling model that considers wall shear stress with the critical wall shear rate model, and load it through UDF compilation; Step 3: Initialize the porous equivalent model and parameters. Preset the fluid domain as a pure flow region, which is an unmarked region. Input the porosity, viscous drag, and thermal properties of the pure fluid. At the same time, input the actual porosity, viscous drag, and thermal properties of the sediment layer in case the fluid domain mesh properties are changed during calculation. Finally, compile and load the UDF, with the sediment layer as the marked region. Step 4: Perform steady-state calculations on the flow field. Once the flow field is stable and filled with particles, activate the particle deposition model. Step 5: When particles are deposited and the wall deposit layer begins to grow, obtain the deposit layer thickness and deposition rate characteristics through the local grid area, activate the porous equivalent model and input the local deposit layer thickness. Step 6: Based on the local sedimentary surface normal vector, sedimentary layer thickness and corresponding fluid domain grid centroid coordinates, find and mark all fluid domain grids below the sedimentary layer thickness along the direction of the local sedimentary surface normal vector. The marking method of sedimentary layer grids in the fluid domain is determined. The communication method of global data aggregation and broadcasting ensures real-time sharing of computational domain data. Step 7: After the fluid domain mesh is marked as a deposition layer, the host process will change the porosity, viscous drag and thermal properties of the marked fluid domain mesh in step 6 in real time, so that it is equivalent to the high porosity and low drag fluid element and the low porosity and high drag deposition layer element, thereby realizing the coupling effect of the deposition layer on near-wall flow and convective heat transfer, and finally update the temperature field distribution of the computational domain.

2. The method for predicting the heat transfer characteristics of wall particle deposition based on a porous equivalent model according to claim 1, characterized in that, In step 1, the mesh model is verified to be mesh-independent and meets the requirement that the minimum mesh quality is higher than 0.

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3. The method for predicting the heat transfer characteristics of wall particle deposition based on a porous equivalent model according to claim 1, characterized in that, In step 2, the particle peeling model considering wall shear stress is expressed as follows: when the shear rate experienced by the wall-adhered particles exceeds the critical wall shear rate, the particles enter the mainstream; where the critical wall shear rate is expressed as: ； In the formula, The critical wall shear rate of the fluid is denoted as . For Cunningham correction factor, The work done by particle adhesion is given by ρ, where ρ is the fluid density. For composite Young's modulus, D p The radius of the particle; The shear rate experienced by the particle is: ； In the formula This refers to the wall shear stress. The critical wall shear rate deposition model used is described as follows: ； ； ； In the formula, V cr E is the critical wall shear rate. s E represents the surface Young's modulus. p Let be the Young's modulus of the particle. For surface Poisson's ratio, For particles, Poisson's ratio Particle density, It is an intermediate variable.

4. The method for predicting the heat transfer characteristics of wall particle deposition based on a porous equivalent model according to claim 1, characterized in that, In step 3, the porosity parameter of the unmarked region in the fluid domain is set as follows: porosity =1, viscous drag coefficient =0, where For penetration rate, subscript Unmarked regions within the fluid domain; the density, specific heat, and thermal conductivity of unmarked regions are determined by the selected working fluid material; The porosity parameter of the equivalent region of the sedimentary layer is: porosity. Take actual sedimentary layer data, viscosity drag coefficient Extremely large, where the subscript The fluid domain is marked with an upper cutoff limit of 10. 12 The density, specific heat, and thermal conductivity of the sediment layer are taken from the actual physical properties.

5. The method for predicting the heat transfer characteristics of wall particle deposition based on a porous equivalent model according to claim 1, characterized in that, In step 5, the thickness of the deposition layer of the local grid is... With sedimentation rate The calculation method is as follows: ； ； In the formula This represents the total mass of particles deposited on the local grid. For the local grid area, Particle density, This represents the cumulative deposition time. All calculated depositional features are stored in UDMs for use by porous equivalent models.

6. The method for predicting heat transfer characteristics of wall particle deposition based on a porous equivalent model according to claim 1, characterized in that, In step 6, the method for determining the fluid domain meshes that need to be marked is as follows: First, mark the first layer of mesh cells near the wall. Then, traverse all face elements on the deposition surface where deposition occurs. For each face, obtain its fluid-side adjacent mesh cells and read the local deposition layer thickness H corresponding to that face. dep ; Calculate the centroid x of the adjacent meshes on the current fluid side cell With face centroid x face Distance h proj When H dep h proj If the grid is found to be inside the sediment layer, it is marked; otherwise, no action is taken. After marking the first layer of candidate units, the remaining units in the fluid domain are further evaluated. For any candidate unit, take its centroid x cell With the centroid x of the deposition surface face positional difference r=x cell -x face After determining the direction of the unit outward normal vector of the face, the normal projection thickness is calculated using this unit outward normal vector n. and normal offset distance : ； ； When 0 is satisfied <h proj <H dep And h prep When the value is less than δ, the candidate cell is determined as an equivalent region cell of the deposition layer and marked; where δ is a threshold used to limit the lateral deviation of the mesh relative to the face.

7. The method for predicting heat transfer characteristics of wall particle deposition based on a porous equivalent model according to claim 6, characterized in that, Step 6, which employs a global data aggregation and broadcasting communication method, specifically includes the following steps: First, each computing node packages its local data related to labeling and judgment and aggregates it to the master node. Then, the master node submits the aggregated global data to the host process. Subsequently, the host process organizes the received data and stores it in a global shared cache. Finally, the host process broadcasts the global shared cache to each computing node, enabling each node to obtain consistent global judgment parameters. As the deposition layer updates over time, the communication process is executed synchronously with the iteration to ensure the consistency and real-time performance of the labeling results across the parallel cores.

8. The method for predicting the heat transfer characteristics of wall particle deposition based on a porous equivalent model according to claim 1, characterized in that, Step 7 is implemented as follows: Each time the host process iterates, it changes the viscous resistance, porosity, thermal conductivity and specific heat of the marked fluid domain mesh to the physical properties corresponding to the deposition layer; at the same time, in order to ensure the consistency of the execution timing among the cores, all cores are forced to start calculations uniformly after receiving the broadcast information.

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