A two-dimensional air intake design method based on fluid topology optimization

Abstract

This invention proposes a two-dimensional air intake design method based on fluid topology optimization, comprising: using the total pressure recovery coefficient and the inlet / outlet static pressure ratio as objective functions, the fluid volume in the design domain as constraints, and considering a turbulence model, establishing a corresponding topology optimization model using mathematical methods. Based on this, a geometric model for air intake topology optimization is established, boundary conditions are defined, and the flow field is solved. Based on the flow field calculation results, the adjoint method is used for sensitivity analysis of the objective function, and a moving asymptote optimization algorithm is used for gradient optimization and iterative updates to obtain the final topology optimization result. The air intake design method provided by this invention can not only optimize the shape and size of aerodynamic components but also change their topological layout, potentially leading to a new concept of aerodynamic layout and providing a novel approach to air intake design.

Description

Technical Field

[0001] This invention relates to the field of air intake design, and in particular to a two-dimensional air intake design method based on fluid topology optimization. Background Technology

[0002] As an important component of the propulsion system of supersonic aircraft, the air intake has a significant impact on the performance of the entire propulsion system. In current research, the air intake design methods used are often based on the optimal wave system theory. These methods can only perform shape design to a certain extent and are greatly limited by the designer's inertia and limitations.

[0003] Fluid topology optimization is a research hotspot in the field of optimization design. Unlike traditional aerodynamic optimization methods where design variables are design parameters or boundary geometry information describing the geometric structure, and the structural shape is altered by changing the geometric curves used to fit the boundary or by changing the grid node coordinates using boundary movement methods, fluid topology optimization arranges design variables across the entire design space. This covers almost all possibilities within the design space for component design, enabling optimization not only of the shape and size of aerodynamic components but also alteration of their topological layout. This holds promise for creating new aerodynamic layout concepts, thus addressing the limitations of traditional aerodynamic design methods that restrict the possibility of innovative aerodynamic designs due to design freedom and the limitations of designer thinking. Theoretically, with a sound optimization theory and design methodology, the optimal topological configuration within the design domain can be obtained through fluid topology optimization.

[0004] Based on this, scholars both domestically and internationally have conducted research on fluid topology optimization from multiple perspectives, such as the phase-field method and Boltzmann method based on optimization methods, studies on steady and unsteady flow based on fluid flow states, and studies on whether the flow medium is compressible or incompressible. In practical applications, Sá et al. applied fluid topology optimization based on the variable density method to the design of a small rotary pump considering energy dissipation and vorticity, and experimentally verified the design performance. Shin et al. used a 2D axisymmetric model at medium Reynolds numbers to optimize vortex-type fluid diodes, and Alonso et al. applied density-based optimization to the design of bladeless Tesla-type centrifugal pumps. Lim et al. applied fluid topology optimization to the design of vortex-type passive fluid diode valves for nuclear applications, and Gaymann et al. applied it to the design of two-dimensional and three-dimensional fluid diode valves at medium to high Reynolds numbers.

[0005] Existing technologies are mostly designed for simple flow channel structures, while there is very little optimization of fluid topology structures for complex engineering problems, and there are no solutions for optimizing the design of two-dimensional air intakes using fluid topology optimization methods. Summary of the Invention

[0006] The main objective of this invention is to overcome the aforementioned deficiencies in the prior art and propose a two-dimensional intake design method based on fluid topology optimization. The method establishes an objective function using the total pressure recovery coefficient and the inlet / outlet static pressure ratio, which are the main factors for evaluating intake performance. The fluid volume ratio is used as a constraint, and the intake topology is optimized by comprehensively considering the turbulence model. This method can not only optimize the shape and size of aerodynamic components, but also change their topological layout, thereby obtaining an intake structure that differs from the traditional configuration.

[0007] The present invention adopts the following technical solution:

[0008] S1. Establish the geometric configuration for topology optimization of the two-dimensional air intake and determine the design domain;

[0009] S2, construct a multi-objective topology optimization model with the total pressure recovery coefficient and the inlet / outlet static pressure ratio as objective functions, the fluid volume ratio as constraint, and a turbulence model;

[0010] S3, Solve the initial flow field given the boundary conditions;

[0011] S4, use the adjoint method to solve for the sensitivity of the objective function;

[0012] S5, update design variables using the moving asymptote method;

[0013] S6: Determine if the objective function meets the requirements. If not, repeat S3-S5. If yes, output the topology configuration to obtain the optimized intake duct model.

[0014] S1 has two design methods for the multi-objective topology optimization model. The first design method is to select the design point, total compression angle and number of compression surfaces, calculate the size of each compression angle according to the oblique shock wave relationship, and further determine the lip point, shoulder coordinates and isolation section length. Based on the corresponding parameters, establish the initial model and determine the design domain and entrance / exit positions.

[0015] The second design method is to weaken the spatial constraints, expand the design domain, and determine the design domain and entrance / exit locations based on the configuration obtained from the first design method.

[0016] In S2: The total pressure recovery coefficient σ only involves the boundary value integral, and is specifically expressed as follows:

[0017]

[0018] Where P1 * For total export pressure, Total inlet pressure, Let ρ be the outlet static pressure, ρ be the fluid density, u be the fluid velocity field, and S1 be the outlet boundary region.

[0019] The static pressure ratio η is:

[0020]

[0021] Where P S0 For inlet static pressure, The outlet static pressure is the total pressure; both the inlet total pressure and static pressure are determined by the boundary conditions.

[0022] Fluid volume constraint β V Material density γ needs to be introduced as a design variable to discretize the design region Ω, as shown below:

[0023]

[0024] In the above formula, V0 represents the total volume of the initial design variables in the control domain. When the design variable γ = 0, it indicates that the material is a pure solid. When γ = 1, it indicates that the material is a pure fluid.

[0025] The parameters involved in the multi-objective function are adjusted as follows:

[0026] σ * =n1lgσ;

[0027] η * =n2lgη;

[0028] n1 and n2 are the corresponding coefficients. By adjusting n1 and n2, the corresponding parameters are made to be of the same order of magnitude.

[0029] Based on the total pressure recovery coefficient and the inlet and outlet static pressures, weighting coefficients are selected to obtain the multi-objective function J for inlet topology optimization:

[0030] J=ω1σ * +ω2η * ;

[0031] In the formula, ω1 and ω2 are the weight coefficients of their respective objective functions.

[0032] S3 solves for the initial flow field given the boundary conditions, specifically:

[0033] Output the parameters required for sensitivity analysis, such as J. * Parameters such as u, p, T, μ, μT:

[0034] S4. Using the parameters obtained in S3, construct the sensitivity adjoint equation for the objective function. The specific steps are as follows:

[0035] J(u(γ),γ)=J * +λ T R(u(γ),γ);

[0036] Where λ is the adjoint multiplier in the adjoint equation, R(u(γ),γ) is the governing equation and constraints of the objective function, such as the governing equation and boundary conditions, and u(γ) is an intermediate variable.

[0037] Its total derivative is:

[0038]

[0039] Let the implicit terms in the above equation If the value is zero, find the adjoint multiplier, substitute it into the adjoint equation, and solve for the sensitivity.

[0040] As can be seen from the above description of the present invention, compared with the prior art, the present invention has the following beneficial effects:

[0041] This invention provides a two-dimensional air intake design method based on fluid topology optimization, comprising: S1, establishing the geometric configuration of the two-dimensional air intake topology optimization and determining the design domain; S2, constructing a multi-objective topology optimization model with the total pressure recovery coefficient and inlet / outlet static pressure ratio as objective functions, fluid volume ratio as constraints, and employing a turbulence model; S3, solving the initial flow field given boundary conditions; S4, solving the sensitivity of the objective function using the adjoint method; S5, updating the design variables using the moving asymptote method; S6, determining whether the objective function meets the requirements. If not, repeating S3-S5; if yes, outputting the topology configuration to obtain the optimized air intake model. The method provided by this invention arranges the fluid topology optimization design variables throughout the entire design space, allowing the design of components to cover almost all possibilities within the design space. It not only optimizes the shape and size of aerodynamic components but also changes their topological layout. By optimizing and designing the air intake using the fluid topology optimization method, it is entirely possible to obtain a completely new aerodynamic topology layout within the design space, thereby potentially achieving a significant improvement in air intake performance. Attached Figure Description

[0042] Figure 1 This is a flowchart of a two-dimensional air intake design method based on fluid topology optimization provided by an embodiment of the present invention;

[0043] Figure 2 This is a graph showing the relationship between the permeability coefficient and design variables provided in an embodiment of the present invention;

[0044] Figure 3 Figure (a) is a schematic diagram of the fluid topology optimization design of the air intake provided in the embodiment of the present invention, wherein Figure (b) is the two-dimensional air intake configuration established by the first design method and Figure (a) is the two-dimensional air intake configuration established by the second design method. Detailed Implementation

[0045] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0046] like Figure 1 The present invention provides a flowchart of a two-dimensional air intake design method based on fluid topology optimization, which is as follows:

[0047] S101: Based on actual requirements and objectives, establish the geometric configuration for topology optimization of the two-dimensional air intake and determine the design domain;

[0048] Based on actual requirements and objectives, the required geometric configuration for topology optimization of the two-dimensional inlet is established, and the design domain is determined. The first design method is to adopt the optimal wave system theory for the initial design domain. Taking the inlet under 5mach conditions as an example, the leading edge point of the inlet is selected as the origin of the coordinate system, the number of compression surfaces is 2, and the post-wave Mach number is 3. The first-stage wedge angle is 10.63°, the shock wave angle is 19.97°, the second-stage wedge angle is 13.42°, and the shock wave angle is 25.71°. The coordinates of the inflection point, lip point, and shoulder are (in mm): (187.0, 35.1); (275.2, 100.0); (307.6, 89.0). The length of the isolator is generally 6-10 times the height of the isolator; in this case, it is 6 times. The two-dimensional inlet configuration is established using the corresponding parameters. Based on this, it is appropriately extended outward, and the design domain and inlet / outlet positions are determined. Figure 3 (a) The specific measures are as follows: ensure that the coordinates of the leading edge point, the lip point and the shoulder remain unchanged, use the coordinates of the inflection point as variables, use a suitable arc between the leading edge point and the shoulder to replace the two-stage profile, select the external pressure section and the internal contraction section of the intake as the design domain (the area composed of the blue line segments in the figure), and introduce the far field outside the design domain, use the far field to the left of the leading edge point as the inlet, and use the outlet of the isolation section as the pressure outlet to obtain the initial configuration.

[0049] The second design approach weakens spatial constraints and adopts configurations with higher degrees of freedom, such as... Figure 3 (b) By treating the shoulder and part of the isolation section as variables, the design domain is further expanded, while the entrance and exit positions remain unchanged, resulting in the initial configuration.

[0050] The advantage of the first method is that the optimization objective is very clear. Based on the initial configuration obtained using the optimal wave system theory, certain geometric constraints are applied to guide the design variables to find the optimal configuration near the surface, making it easier to obtain an inlet configuration that meets the optimization objective. The second design approach has a higher degree of freedom. Without an initial configuration and corresponding geometric constraints, it can find the optimal configuration within the entire design space, and is expected to obtain an aerodynamic configuration scheme that differs from the traditional inlet topology layout.

[0051] S102: Construct a multi-objective topology optimization model with the total pressure recovery coefficient and the inlet / outlet static pressure ratio as objective functions, fluid volume ratio as constraint, and turbulence model as consideration;

[0052] The total pressure recovery coefficient and the inlet / outlet static pressure ratio, parameters involved in the objective function, are important parameters for evaluating the performance of the intake duct and are used to measure the losses during the intake flow process. As defined, the total pressure recovery coefficient σ only involves boundary value integrals, specifically expressed as follows:

[0053] A multi-objective topology optimization model is constructed, with the total pressure recovery coefficient and inlet / outlet static pressure as objective functions, fluid volume ratio as constraint, and turbulence model as consideration.

[0054] Specifically defined as:

[0055]

[0056] Where P1 * For total export pressure, Total inlet pressure, Let ρ be the outlet static pressure, ρ be the fluid density, u be the fluid velocity field, and S1 be the outlet boundary region.

[0057] The static pressure ratio η is:

[0058]

[0059] Where P S0 For inlet static pressure, The outlet static pressure is given. The inlet static temperature and static pressure are determined by the boundary conditions, using the operating condition at 30km, with a static temperature of 226.5K and a static pressure of 1197Pa.

[0060] Define fluid volume constraint β V The specific expression is as follows:

[0061]

[0062] In the above formula, V0 represents the total volume of the initial design variables in the control domain. When the design variable γ = 0, it indicates that the material is a pure solid; when γ = 1, it indicates that the material is a pure fluid. The fluid volume occupancy is adjusted according to actual needs.

[0063] To ensure that all parameters involved are of the same order of magnitude, the parameters involved in the multi-objective function are adjusted. The specific steps are as follows:

[0064] σ * =n1lgσ;

[0065] η * =n2lgη;

[0066] n1 and n2 are the corresponding coefficients. By adjusting n1 and n2, the corresponding parameters are made to be of the same order of magnitude.

[0067] Based on the total pressure recovery coefficient and the inlet and outlet static pressures, and considering their interaction, an appropriate weighting coefficient is selected to obtain the multi-objective function J for inlet topology optimization:

[0068] J=ω1σ * +ω2η * ;

[0069] In the formula, ω1 and ω2 are the weight coefficients of their respective objective functions. To comprehensively consider both, the weight coefficients are both 0.5. Finally, the maximum value problem is transformed into a minimum value problem:

[0070] J * =-J

[0071] Based on the obtained multi-objective function, using fluid volume ratio as a constraint and considering the turbulent k-ε model, the steady Navier-Stokes multi-objective topology optimization mathematical model is obtained as follows:

[0072] minJ * =-J=-(ω1σ) * +ω2η * );

[0073]

[0074] F=-α(γ)u

[0075]

[0076] P k =μ t 2S ij

[0077] ω1+ω2=1, 0≤ω1,ω2≤1

[0078] 0≤γ≤1

[0079]

[0080] In the formula, ρ is the fluid density in the region, μ is the dynamic viscosity, μT is the turbulent viscosity obtained from the turbulence model, p is the pressure, T is the temperature, h is the static enthalpy, and h tot Let S be the total enthalpy, k be the model kinetic energy, ε be the energy dissipation rate, and k0 and ε0 represent the magnitudes of turbulent kinetic energy and energy dissipation when the fluid velocity becomes zero, respectively. ijLet F be the Reynolds stress tensor, and F be the source term, characterizing the magnitude of the additional force in the flow field. This paper adopts the Rational Approximation of Material Properties (RAMP) model from the variable density method.

[0081] A larger permeability coefficient α indicates a greater resistance of the porous medium to fluid flow. Wherein, α... max and α min Let α be the minimum and maximum values, respectively. Within the scope of this patent research, let α be... min =0, α max The value of α is related to viscosity and permeability; the smaller the value, the smaller the viscosity, which means the greater the permeability; conversely, the larger the value, the greater the permeability. max The larger the value of α, the smaller the permeability. In principle, to ensure the result is as close to reality as possible, the permeability should be as small as possible. However, since fluid permeability has a significant impact on the variable density method algorithm in topology optimization, α... max The value of q should not be too large, otherwise it will cause numerical instability in the results. Generally, a relatively large real number is chosen. q is a positive real number, and the concavity / convexity of the equation can be controlled by adjusting the value of q. When q approaches positive infinity, the interpolation function becomes a straight line. When q approaches 0, the penalty for certain regions in the design domain is better, which will help to make the convergence of the flow channel structure clearer. For the values ​​of parameters in the penalty terms applied to kinetic energy and energy dissipation in the transport equation, such as α... k max α k min q k The principle for parameter selection is the same as that in the momentum equation.

[0082] The Darcy number is introduced to describe the ratio of viscous force to porous friction, characterizing the permeability of porous media. Its specific expression is:

[0083]

[0084] l represents the characteristic length of the flow channel inlet. The Darcy number reflects, to some extent, the permeability of the porous medium. The larger the Darcy number, the greater the permeability of the porous medium, and the smaller its influence on the strength of the fluid zone, and vice versa.

[0085] The relationship between permeability coefficient and design variables under different interpolation functions is as follows: Figure 2 As shown, the q value should be selected based on the actual situation to avoid the transition region as much as possible, so that the fluid-solid boundary is clear.

[0086] S103: Define the corresponding initial boundary conditions. The inlet is given static temperature, static pressure and Mach number, and the outlet is given static temperature and static pressure. Define the initial design variable value as 1, which represents pure fluid, and perform flow field calculation to obtain the parameters involved in the topology optimization model, such as J*, U, p, T, μ, μT, etc.

[0087] S104: The sensitivity of a multi-objective function to design variables is solved using the adjoint method. The specific solution process is as follows:

[0088] The sensitivity adjoint equation for fluid topology optimization is constructed using the adjoint method:

[0089] J(u(γ),γ)=J * +λ T R(u(γ),γ);

[0090] Where λ is the adjoint multiplier in the adjoint equation, R(u(γ),γ) is the governing equation and constraints of the objective function, such as the governing equation and boundary conditions, and u(γ) is an intermediate variable.

[0091] The total derivative of the objective function with respect to the design variable γ is:

[0092]

[0093] Let the implicit terms in the above equation If the value is zero, find the adjoint multiplier, substitute it into the adjoint equation, and solve for the sensitivity.

[0094] S105: Based on the obtained objective function sensitivity, the two-dimensional air intake is optimized using the moving asymptote method to obtain the optimized configuration. The flow field is then calculated again to update the design variables.

[0095] S106: Determine whether the optimized configuration meets the convergence requirements, such as whether the maximum relative design variable change value of the mesh element before and after the update meets the requirements. If not, continue iterating and repeat steps S103-S105. If convergence is achieved, stop iterating and output the final two-dimensional intake topology optimization configuration.

[0096] This invention provides a two-dimensional air intake design method based on fluid topology optimization, comprising: S1, establishing the geometric configuration of the two-dimensional air intake topology optimization and determining the design domain; S2, constructing a multi-objective topology optimization model with the total pressure recovery coefficient and inlet / outlet static pressure ratio as objective functions, fluid volume ratio as constraints, and employing a turbulence model; S3, solving the initial flow field given boundary conditions; S4, solving the sensitivity of the objective function using the adjoint method; S5, updating the design variables using the moving asymptote method; S6, determining whether the objective function meets the requirements. If not, repeating S3-S5; if yes, outputting the topology configuration to obtain the optimized air intake model. The method provided by this invention arranges the fluid topology optimization design variables throughout the entire design space, allowing the design of components to cover almost all possibilities within the design space. It not only optimizes the shape and size of aerodynamic components but also changes their topological layout. By optimizing and designing the air intake using the fluid topology optimization method, it is entirely possible to obtain a completely new aerodynamic topology layout within the design space, thereby potentially achieving a significant improvement in air intake performance.

[0097] The above are merely specific embodiments of the present invention, but the design concept of the present invention is not limited thereto. Any non-substantial modifications made to the present invention using this concept shall be considered as infringing upon the protection scope of the present invention.

Claims

1. A two-dimensional air intake design method based on fluid topology optimization, characterized in that, include: S1. Establish the geometric configuration for topology optimization of the two-dimensional air intake and determine the design domain; S2, construct a multi-objective topology optimization model with the total pressure recovery coefficient and the inlet / outlet static pressure ratio as objective functions, the fluid volume ratio as constraint, and a turbulence model; S3, Solve the initial flow field given the boundary conditions; S4, use the adjoint method to solve for the sensitivity of the objective function; S5, update design variables using the moving asymptote method; S6, determine whether the objective function meets the requirements. If not, repeat S3-S5. If yes, output the topology configuration to obtain the optimized intake duct model. The total pressure recovery coefficient σ in S2 only involves the boundary value integral, and is specifically expressed as follows: Where P1 * For total export pressure, Total inlet pressure, Let ρ be the outlet static pressure, ρ be the fluid density, u be the fluid velocity field, and S1 be the outlet boundary region. The static pressure ratio η is: Where P S0 For inlet static pressure, The outlet static pressure is the total pressure; both the inlet total pressure and static pressure are determined by the boundary conditions. Fluid volume constraint β V Material density γ needs to be introduced as a design variable to discretize the design region Ω, as shown below: In the above formula, V0 is the total volume of the initial design variables in the control domain. When the design variable γ = 0, it indicates that the material is a pure solid. When γ = 1, it indicates that the material is a pure fluid. The parameters involved in the multi-objective function are adjusted as follows: s * =n1lgσ; or * =n2lgη; n1 and n2 are the corresponding coefficients. By adjusting n1 and n2, the corresponding parameters are made to be of the same order of magnitude. Based on the total pressure recovery coefficient and the inlet and outlet static pressures, weighting coefficients are selected to obtain the multi-objective function J for inlet topology optimization: J=ω1σ * +ω2η * ; In the formula, ω1 and ω2 are the weight coefficients of their respective objective functions.

2. The two-dimensional air intake design method based on fluid topology optimization according to claim 1, characterized in that, Establishing the geometric configuration for topology optimization of the two-dimensional air intake involves two design methods, specifically: The first design method involves selecting the design point, total compression angle, and number of compression surfaces. The magnitude of each compression angle is calculated using the oblique shock wave formula. The lip point, shoulder coordinates, and isolation section length are further determined. An initial model is then established based on these parameters, and the design domain and inlet / outlet locations are determined. The second design method is to weaken the spatial constraints, expand the design domain, determine the design domain and the location of entrances and exits, and obtain the geometric configuration based on the configuration obtained by the first design method.

3. The two-dimensional air intake design method based on fluid topology optimization according to claim 1, characterized in that, S3 provides a solution for the initial flow field given the boundary conditions, specifically: Output the parameters required for sensitivity analysis; S4. Using the parameters obtained in S3, construct the sensitivity adjoint equation for the objective function. The specific steps are as follows: J(u(γ),γ)=J * +λ T R(u(γ),γ); Where λ is the adjoint multiplier in the adjoint equation, R(u(γ),γ) is the governing equation and constraints of the objective function, such as the governing equation and boundary conditions, and u(γ) is an intermediate variable. Its total derivative is: Let the implicit terms in the above equation If the value is zero, find the adjoint multiplier, substitute it into the adjoint equation, and solve for the sensitivity.

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