Compressible turbulent fluid topological optimization method based on automatic differentiation

Abstract

The invention discloses a compressible turbulent fluid topological optimization method based on automatic differentiation, and relates to topological optimization. The method comprises the steps: establishing a geometric model corresponding to flow channel topological optimization; acquiring the basic parameters of a topological optimization object, and constructing a CFD topological optimization model; constructing a target function according to the basic parameters, and forming a nonlinear programming problem; deriving a sensitivity equation based on an adjoint method; solving the fluid control equation to obtain a flow field result and a value of a target function, and outputting a new flow field result; building a Jacobian matrix and a gradient vector by using an automatic differential technology; establishing a matrix form adjoint equation to obtain an adjoint multiplier; substituting the new flow field result and the adjoint multiplier into a sensitivity equation to solve the sensitivity; establishing a mathematical model by using an MMA numerical optimization method in combination with a nonlinear programming problem; carrying out optimization solution on the flow channel, updating design variables to obtain an optimal solution, and outputting an optimal two-dimensional topological configuration. And the problems of insufficient flexibility, tedious process, error proneness and the like of manual derivation of a compressible fluid accompanying equation are avoided.

Description

technical field [0001] The invention belongs to the technical field of fluid topology optimization in computational fluid dynamics, in particular to an automatic differential-based compressible turbulent fluid topology optimization method. Background technique [0002] Compressibility is one of the inherent properties of all fluids, which is usually ignored in water and other liquids, but for gases such as air, compressibility is a critical consideration at high speed and high pressure one. High-speed compressible fluid flow widely exists in the aerospace field, and the compressibility of fluid must be considered in aerodynamic design such as engine flow path components, aircraft shape, airfoil profile, and turbomachinery. At the same time, with the development of computer technology, optimization methods for compressible flows have emerged one after another, Cummings et al. ([1]Cummings R M, Yang H T, Oh YH. Supersonic, turbulent flow computation and drag optimization for ...

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Problems solved by technology

[0005] The purpose of the present invention is to provide fluid topology optimization for compressible fluids, and consider the influence of the turbulence model on the optimization, construct the adjoint equation through the automatic differentiation method, and use the characteristics of the automatic differentiation method to generate the Jacobian matrix efficiently and accurately. A topology optimization method for compressible turbulent fluids based on automatic differentiation to avoid problems such as manual derivation of adjoint equations for compressible fluids with insufficient flexibility, tedious process and error-prone

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