CN113836651B - Turbine cascade runner topology design method based on fluid topology optimization - Google Patents
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Abstract
A turbine cascade runner topology design method based on fluid topology optimization belongs to the field of turbine pneumatic design. Establishing a geometric model of topological optimization of a turbine cascade runner of the engine, and determining a design domain and an entrance position; constructing three objective functions of energy dissipation of the fluid, momentum of the turbine in the rotation direction and volume fraction of the fluid; adjusting orders of magnitude between objective functions to ensure order of magnitude similarity, so as to construct a modified multi-objective function; defining corresponding boundary conditions, solving a flow field, solving an accompanying flow field by using an accompanying method, outputting an accompanying multiplier, and performing sensitivity analysis and calculation; substituting the objective function value and the sensitivity thereof into an MMA optimization algorithm to optimize, and updating the design variables; and judging whether the objective function is converged, if not, substituting the updated design variable into the MMA optimization algorithm for continuous iteration, and if so, outputting a final topology result. The geometric information and the initial blade profile are not required to be given, and a new idea is provided for the design of the turbine blade cascade configuration of the engine.
Description
Technical Field
The invention belongs to the field of turbine pneumatic design, and particularly relates to a turbine cascade runner topology design method based on fluid topology optimization.
Background
Turbine blades, which are the core components of a turbine section in a gas turbine engine, function to draw a high temperature, high pressure gas stream into a combustion chamber by rotation, and thereby convert the gas stream into mechanical energy to maintain engine operation. The air inlet resistance and the air inlet uniformity are greatly influenced by the aerodynamic design such as the configuration, the size, the arrangement and the like of the blade cascade as a key structure for directly influencing the air flow condition of the runner, so that the aerodynamic performance of the gas turbine engine is directly determined.
In recent years, researches on pneumatic optimization design of turbine blade cascades are favored by researchers at home and abroad. She Tao et al (She Tao, chen Fei. Aerodynamic optimization design of turbocompressor impeller [ J ]. Fluid machinery, 2017,45 (08): 24-28+58) aerodynamic optimization design of impeller using neural network and genetic algorithm; walther et al (NadarajahS, walther b. An adaptation-Based Optimization Method for Multistage turbomachinery.2013) propose a multi-stage turbine aerodynamic profile optimization framework based on gradient constraints; lu et al (Luo J, mcbean I, feng L.optimizations of Endwall Contours of a Turbine Blade Row Using an Adjoint Method [ C ]// Asme Turbo Expo: turbine Technical Conference & Exposition.2011) optimized low cascade ratio turbine cascades using a continuous companion method. However, since the degree of freedom in the design of the aerodynamic configuration of the turbine blade row is very high, it is difficult to cover all possibilities of geometric optimization of the blade profile even by means of a parameterization of the geometric profile.
Fluid topology optimization is a "from nothing to nothing" design method that can change the topology of a conventional design without giving an initial geometry. Based on the method, the turbine engine cascade runner is optimized, so that a turbine cascade runner scheme different from the traditional topological configuration can be obtained, and a brand new design thought is provided for the turbine cascade pneumatic configuration.
When a fluid topology optimization method is first proposed from Borrvall and Petersson et al (Borrvall T, petersson J.morphology optimization of fluids in Stokes flow [ J ]. International Journal for Numerical Methods in Fluids,2003,41 (1): 77-107), the optimization method is applied to the optimization problem of a pipeline runner; olesen et al (Olesen L H, okkels F, bruus H.A high level programming language implementation of topology optimization applied to steady-state Navier-Stokes flow [ J ]. International Journal for Numerical Methods in Engineering,2006,65 (7): 975-1001) propose a program framework for implementing fluid topology optimization, and apply it to topology optimization of Navier-Stokes flow, analyze the influence of different parameters of the optimization algorithm on microchannel optimization; s.a and Novotny (L.E.N.S, novotny A, romero J S, et al design optimization of laminar flow machine rotors based on the topological derivative concept [ J ]. Structural and Multidisciplinary Optimization,2017,56 (4): 1013-1026) apply the topology derivative method to the fluid topology optimization design of radial flow rotary machines; zhang Min (Zhang Min, yang Jinan, liu Yan. Fluid topology optimization method and its application in turbomachinery [ J/OL ]. Propulsion technique 1-16[2021-07-05 ]) the turbine blade tip geometry is profile optimized using the fluid topology optimization method.
However, related researches are directed to relatively simple runner designs, and most of the related researches select energy dissipation to optimize as a single objective function, and a fluid topology optimization method is utilized to optimize a turbine cascade runner of an engine, so that a scheme for designing a cascade configuration is not yet publicly reported.
Disclosure of Invention
The invention aims to provide a turbine blade cascade runner topology design method based on fluid topology optimization aiming at the defects in the prior art. The turbine blade cascade belongs to a key rotating component, energy dissipation needs to be considered seriously during design, the blade cascade rotating mechanical energy predicts the influence of the occupied volume of the blade cascade and the like on turbine efficiency, geometrical profile information does not need to be given, and the fluid topology optimization design of the traditional topology configuration of the turbine blade cascade of the engine is hopefully changed.
The invention comprises the following steps:
1) Establishing a geometric model of topological optimization of a turbine cascade runner of the engine according to the target and the requirement of the topological optimization of the fluid, and determining a design domain and an entrance position;
2) Defining a weighting function according to actual design requirements, and constructing an objective function expression of energy dissipation of the fluid, momentum of the rotation direction of the turbine and the volume fraction of the fluid;
3) Adjusting orders of magnitude between objective functions by using a mathematical method to ensure order of magnitude similarity, so as to construct a modified multi-objective function;
4) Defining corresponding boundary conditions, solving a flow field, solving an accompanying flow field by using an accompanying method, outputting an accompanying multiplier, and performing sensitivity analysis and calculation;
5) Substituting the objective function value and the sensitivity thereof into an MMA optimization algorithm, and iteratively updating the design variables;
6) Judging whether the objective function is converged, if not, substituting the updated design variable into an MMA optimization algorithm for continuous iteration, and if so, outputting a final topology result to complete the topology design of the turbine cascade runner.
In the step 1), the geometric model for topological optimization of the turbine cascade flow channels of the engine is established by designing the turbine cascade of the engine by using a variable density method and determining the topological optimization design area omega of the cascade flow channels and the positions of inlets and outlets of the flow channels.
In step 2), the construction of the multi-objective function of three targets, namely, energy dissipation of the fluid, momentum of the rotation direction of the turbine, and volume fraction occupied by the fluid, is to define a weighting function according to actual design requirements, and the expression of the specific objective function is as follows:
introducing material density gamma as design variable, discretizing design area omega, defining energy dissipation phi of fluid E (u,p,γ)：
Turbine rotational direction momentum J M ：
J M ＝∫ Ω mu n dΩ
Volume fraction beta of fluid V ：
Wherein μ is dynamic viscosity, μ T The turbulence viscosity obtained by solving the turbulence model is u, the fluid velocity field is u n Is the normal velocity of the fluid, i.e. the direction of rotation of the turbine, V 0 The total volume of the initial design variables in the control domain. Since the cascade rotation mechanical energy cannot characterize the cascade rotation direction, the optimization result cannot distinguish the turbine rotation direction, and the cascade rotation direction momentum is adopted to characterize the cascade rotation direction.
In step 3), the specific steps of constructing the modified multi-objective function may be:
(3.1) according to three objective functions of energy dissipation, turbine rotation direction momentum and fluid volume fraction, comprehensively considering interaction relations among the three, selecting a proper weight coefficient, and calculating a multi-objective function J of an engine turbine cascade runner based on fluid topological optimization:
wherein omega is E ,ω M ,ω V The weight coefficients of the corresponding objective functions are added to be 1;
(3.2) step-up function J for determining the momentum of the turbine in the rotational direction M * Stepwise adjusting n 1 Values such that J M * Energy dissipation from fluid Φ E The orders of magnitude are consistent;
wherein n is 1 From beta V * Given as a convergence order at the time of single-objective optimization;
(3.3) determining the step-up function β of the fluid volume fraction V * Stepwise adjusting n 2 Values such that beta V * Energy dissipation from fluid Φ E The orders of magnitude are consistent;
wherein n is 2 From phi E Beta when optimizing as a single objective V * Is given by the convergence magnitude of (2);
(3.4) constructing a modified multi-objective function J according to the objective function after the adjustment level * ；
ρ(u·▽)u+▽p-(μ+μ T )▽·(▽u+▽u T )＝F
F＝-α(γ)u
ω E +ω M +ω V ＝1,0≤ω E ,ω M ,ω V ≤1
0≤γ≤1
Wherein ρ is the fluid density of the region, p is the pressure, T is the temperature, h is the static enthalpy, h tot For total enthalpy, k is thermal conductivity, F is the source term, also referred to herein as darcy force, and characterizes the magnitude of the additional force in the flow field.
In step 4), the specific steps of defining the corresponding boundary conditions and solving the flow field, solving the accompanying flow field by using an accompanying method, outputting the accompanying multiplier, and performing sensitivity analysis and calculation can be as follows:
(4.1) defining corresponding boundary strips given the initial design variable valuesPart, solve control equation, output J * ,u,p,T,μ,μ T Isoparametric parameters;
(4.2) constructing a sensitivity-related equation for fluid topology optimization:
J(u,γ)＝J * +λ T R(u,γ)
wherein λ is the syndrome, and R (u, γ) =0 is the multiple objective function J * N-S equation and boundary constraint conditions;
(4.3) deriving the objective function J (u, γ) based on the syndrome λ:
(4.4) orderThe syndrome λ can be obtained;
(4.5) obtaining sensitivity of the objective function J (u, gamma) to the design variable by using the control flow field parameters and the accompanying multipliers
(4.6) substituting the objective function value and the sensitivity thereof into a moving progressive line method (MMA, the method of moving asymptotes) to perform optimization solution on the flow, and updating the design variables;
in step 6), the determining whether the objective function converges is based on comparing the maximum change value of the relative design variable of each grid cell before and after updating with the set iteration termination condition.
Compared with the prior art, the invention has the beneficial effects that:
on the basis of meeting design requirements, the invention aims at the defect that the traditional turbine blade grid profile optimization method cannot change the topological configuration, and designs and researches the turbine blade grid runner by using the fluid topological optimization method, so that the invention is a 'none-to-none' design method. The method does not need to give geometric information and an initial blade profile, and is hopeful to obtain a turbine blade cascade runner scheme different from the traditional topological configuration, so that a new pneumatic design thought is provided for the turbine blade cascade configuration of the engine.
Drawings
Fig. 1 is a schematic flow chart of an embodiment of the present invention.
FIG. 2 is a schematic diagram of a fluid topology optimization design for a turbine blade in accordance with an embodiment of the present invention.
Fig. 3 is a schematic diagram of a fluid topology optimization design of a turbine cascade runner according to an embodiment of the present invention.
Detailed Description
The detailed description of the embodiments of the present invention is presented below in conjunction with the drawings, and for purposes of explanation and not limitation, specific details are set forth in the following description in order to provide a thorough understanding of the present invention.
Referring to fig. 1, the turbine two-dimensional cascade runner topology design method based on fluid topology optimization in the embodiment of the invention mainly comprises the following steps:
(1) According to the target and the requirement of the fluid topology optimization, a geometric model of the topological optimization of the turbine cascade runner of the engine is established, and the design area omega of the topological optimization of the cascade runner and the inlet and outlet positions of the runner are determined. As shown in fig. 2, which is a schematic diagram of blade fluid topology optimization of a certain axial turbine 1, a blade height direction of a single blade 2 is selected as a design area 4, and a blade height section denoted by 3 in fig. 2 is selected as a blade height section; FIG. 3 is a schematic diagram of a fluid topology optimization design of cascade channels with inlet on the left, outlet on the right, and periodic boundaries on the top and bottom;
(2) Introducing material density gamma as design variable, discretizing design area omega, defining energy dissipation phi of fluid E (u, p, gamma), turbine rotational direction momentum J M Volume fraction beta of fluid V An expression of an objective function;
J M ＝∫ Ω mu n dΩ
wherein μ is dynamic viscosity, μ T The turbulence viscosity obtained by solving the turbulence model is u, the fluid velocity field is u n For the normal velocity of the fluid, i.e. the direction of rotation of the turbine, V 0 The total volume of the initial design variables in the control domain. When γ=0, this indicates that the material is a pure solid, and when γ=1, this indicates that the material is a pure fluid.
Darcy Da describes the ratio of viscous force to porous friction force, and represents the size, mu, of the permeability of a porous medium 0 For dynamic viscosity of incoming flow, l is the characteristic length, expressed as:
the material interpolation function expression is:
where α is the local permeability coefficient of the medium, and the greater the value, the greater the barrier to fluid; q is an interpolation parameter, the smaller the value of q is, the smaller the penalty is for the material density value close to the pure fluid, so that the free evolution of the topological structure is facilitated, the topological optimization convergence process is accelerated, and the topological structure is clearer; however, in the process of performing topological optimization of a fluid by using a variable density method, the medium is required to approach two extremes (pure solid, pure fluid), so q cannot be excessively small, otherwise, the density of a material representing an intermediate state and the density of a material representing an extreme state are easily caused to be not greatly different when the material represents a porous medium, and the optimization result is affected. Alpha max Expressed as permeability coefficient, alpha, at a pure solid medium max The larger the value, the larger the viscous force at the point, the lower the permeability, and the closer to pure solid; conversely, alpha max The smaller the value, the smaller the viscous force at the point, the higher the permeability, the closerPure fluid. At the same time, since the permeability of the pure solid medium is 0, alpha is theoretically max Infinity should be taken, but there is an infinite number in the numerical calculation, which tends to cause the calculation result to be not converged, and a finite value is often taken.
(3) According to three objective functions of energy dissipation, turbine rotation direction momentum and fluid volume fraction, the interaction relation among the three is comprehensively considered, a proper weight coefficient is selected, and a multi-objective function J of an engine turbine cascade runner based on fluid topological optimization is calculated:
wherein omega is E ,ω M ,ω V The weight coefficient of each corresponding objective function can be selected according to design requirements. Omega E The fluid energy dissipation is taken as a main optimization target when the duty ratio is large, and the obtained topological structure tends to be a straight channel; omega M The occupied ratio is large, the momentum in the Y direction is taken as a main optimization target, and the obtained topological structure tends to be curved; omega V And if the ratio is large, the volume fraction occupied by the fluid is taken as a main optimization target, and the obtained topological structure is less influenced by the two.
(4) The order of magnitude is uniformly adjusted according to different orders of magnitude between different objective functions, so that the orders of magnitude of three objective functions are consistent in the optimization process, and a multi-objective function J is obtained * The method comprises the following specific steps:
4.1 Stage function J) for determining the momentum of the turbine in the direction of rotation M * Stepwise adjusting n 1 Values such that J M * And phi is phi E The orders of magnitude are consistent;
wherein n is 1 From beta V * Given as the magnitude of convergence at the time of single-objective optimization.
4.2 Determining fluid volumeFractional tuning function beta V * Stepwise adjusting n 2 Values such that beta V * And phi is phi E The orders of magnitude are consistent;
wherein n is 2 From phi E Beta when optimizing as a single objective V * Is given by the convergence magnitude of (2).
4.3 Constructing a multi-objective function J according to the objective function after the order adjustment * ；
F＝-α(γ)u
ω E +ω M +ω V ＝1,0≤ω E ,ω M ,ω V ≤1
0≤γ≤1
(5) Given the initial design variable value, defining the corresponding boundary condition of the entrance and the exit, further solving the control equation and outputting J * ,u,p,T,μ,μ T Equal parameters for subsequent solving of the accompanying equation and sensitivity;
(6) Computing multiple objective functions J using adjoint * For the sensitivity of the design variable, the step of solving the sensitivity is as follows:
6.1 Construction of sensitivity syndromes for fluid topology optimization using syndromes
J(u,γ)＝J * +λ T R(u,γ)
Wherein λ is the syndrome, and R (u, γ) =0 is the multiple objective function J * N-S equation and boundary constraint conditions;
6.2 Completing the objective function J (u, gamma) based on the syndrome lambda
6.3 Equation order aboveThe syndrome λ can be obtained;
6.4 Using the control flow field parameters and the accompanying multipliers to determine the sensitivity of the objective function J (u, gamma) to the design variables
(7) Substituting the objective function value and the sensitivity thereof into an MMA algorithm to perform optimization solution on the flow channel, and solving and outputting new design variables, so as to update the distribution of the design variables in the control flow field and solve the distribution;
(8) And (3) repeating the steps (5) to (7), judging whether the termination condition is met or not by comparing the maximum relative design variable change value of each grid unit before and after updating with the set iteration termination condition as a convergence basis, substituting the updated design variable into an MMA algorithm to continue iteration if the termination condition is not met, and stopping calculation if the termination condition is met, and outputting the two-dimensional topological configuration of the turbine cascade runner of the engine.
According to the invention, a variable density method is utilized to design a turbine blade cascade of an engine, the optimization problem of a turbine blade cascade runner is converted into a mathematical model, a weighting function is defined according to actual design requirements, and a multi-objective function of three targets such as energy dissipation of fluid, momentum of a turbine rotation direction and volume fraction occupied by the fluid is constructed; adjusting orders of magnitude between objective functions by using a mathematical method to ensure order of magnitude similarity, so as to construct a modified multi-objective function; defining corresponding boundary conditions and solving a flow field; then solving an accompanying flow field by using an accompanying method, and performing sensitivity analysis; and performing gradient optimization updating iteration by using an MMA optimization algorithm to obtain a final topology result. The invention does not need to give geometric information and an initial blade profile, and is hopeful to obtain a turbine blade grid runner scheme different from the traditional topological configuration, thereby providing a new thought for designing the turbine blade grid profile of the engine.
Claims (3)
1. The turbine cascade runner topology design method based on fluid topology optimization is characterized by comprising the following steps of:
1) Establishing a geometric model of topological optimization of a turbine cascade runner of the engine according to the target and the requirement of the topological optimization of the fluid, and determining a design domain and an entrance position;
2) Defining a weighting function according to actual design requirements, and constructing an objective function expression of energy dissipation of the fluid, momentum of the rotation direction of the turbine and the volume fraction of the fluid;
the construction of the objective function expression of the energy dissipation of the fluid, the rotational momentum of the turbine and the volume fraction of the fluid is to define a weighting function according to actual design requirements, and the expression of the specific objective function is as follows:
introducing material density gamma as design variable, discretizing design area omega, defining energy dissipation phi of fluid E (u,p,γ)：
Turbine rotational direction momentum J M ：
J M ＝∫ Ω mu n dΩ
Volume fraction beta of fluid V ：
Wherein μ is dynamic viscosity, μ T The turbulence viscosity obtained by solving the turbulence model is u, the fluid velocity field is u n Is the normal velocity of the fluid, i.e. the direction of rotation of the turbine, V 0 The total volume of the initial design variables in the control domain;
3) Adjusting orders of magnitude between objective functions by using a mathematical method to ensure order of magnitude similarity, so as to construct a modified multi-objective function;
the specific steps of constructing the modified multi-objective function are as follows:
(3.1) according to three objective functions of energy dissipation, turbine rotation direction momentum and fluid volume fraction, comprehensively considering interaction relations among the three, selecting a proper weight coefficient, and calculating a multi-objective function J of an engine turbine cascade runner based on fluid topological optimization:
wherein omega is E ,ω M ,ω V The weight coefficients of the corresponding objective functions are added to be 1;
(3.2) step-up function J for determining the momentum of the turbine in the rotational direction M * Stepwise adjusting n 1 Values such that J M * Energy dissipation from fluid Φ E The orders of magnitude are consistent;
wherein n is 1 From beta V * Given as a convergence order at the time of single-objective optimization;
(3.3) determining the step-up function β of the fluid volume fraction V * Stepwise adjusting n 2 Values such that beta V * Energy dissipation from fluid Φ E The orders of magnitude are consistent;
wherein n is 2 From phi E Beta when optimizing as a single objective V * Is given by the convergence magnitude of (2);
(3.4) constructing a modified multi-objective function J according to the objective function after the adjustment level * ；
F＝-α(γ)u
ω E +ω M +ω V ＝1,0≤ω E ,ω M ,ω V ≤1
0≤γ≤1
Wherein ρ is the fluid density of the design region, p is the pressure, T is the temperature, h is the static enthalpy, h tot For total enthalpy, k is thermal conductivity, F is the source term, also referred to herein as Darcy force, characterizing the attachment in the flow fieldThe magnitude of the applied force;
4) Defining corresponding boundary conditions, solving a flow field, solving an accompanying flow field by using an accompanying method, outputting an accompanying multiplier, and performing sensitivity analysis and calculation, wherein the specific steps are as follows:
(4.1) given the initial design variable value, defining the corresponding boundary condition, solving the control equation, outputting J * ,u,p,T,μ,μ T Parameters;
(4.2) constructing a sensitivity-related equation for fluid topology optimization:
J(u,γ)＝J * +λ T R(u,γ)
wherein λ is the syndrome, and R (u, γ) =0 is the multiple objective function J * N-S equation and boundary constraint conditions;
(4.3) deriving the objective function J (u, γ) based on the syndrome λ:
(4.4) orderFinding a syndrome lambda;
(4.5) obtaining sensitivity of the objective function J (u, gamma) to the design variable by using the control flow field parameters and the accompanying multipliers
(4.6) substituting the objective function value and the sensitivity thereof into an MMA algorithm to perform optimization solution on the flow, and updating the design variables;
5) Substituting the objective function value and the sensitivity thereof into an MMA optimization algorithm, and iteratively updating the design variables;
6) Judging whether the objective function is converged, if not, substituting the updated design variable into an MMA optimization algorithm for continuous iteration, and if so, outputting a final topology result to complete the topology design of the turbine cascade runner.
2. The turbine cascade runner topology design method based on fluid topology optimization as recited in claim 1, wherein in the step 1), the geometric model for establishing the turbine cascade runner topology optimization of the engine is to design the turbine cascade of the engine by using a variable density method, and a design area Ω of the cascade runner topology optimization and an entrance and exit position of the runner are determined.
3. The method of claim 1, wherein in step 6), the determining whether the objective function converges is based on comparing the maximum change value of the relative design variable of each grid cell before and after updating with the set iteration termination condition.
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