Abstract
Fluid topology optimisation has become a popular approach for optimisation of geometries in aero-thermal applications. However, one of the main limitations of current approaches considering turbulent flow is the fidelity of the Reynolds Averaged Navier–Stokes models employed. In response, this paper shows the development of the first data-driven fluid topology optimisation technique based on the continuous adjoint method. The technique first extracts data from a high fidelity simulation of a standard topology-optimised geometry. These data are fed through a symbolic regression-based machine learning algorithm called gene expression programming, to learn an explicit model for the anisotropy tensor. The novel aspect of the work is the derivation of the adjoint form of the generalised explicit algebraic stress model such that the developed turbulence model can be inserted directly into the primal and adjoint system of equations. This allows a second, data-driven optimisation to be performed. Finally, a high fidelity simulation of the resulting geometry is also conducted to allow comparison against the standard geometry. The method is first applied to the back-facing step to verify the approach and then to a 2D u-bend configuration. The data-driven optimisation was able to find geometries exhibiting significant reductions in pressure loss when compared with results from the standard optimisation.
Highlights
Fluid topology optimisation (FTO) is fast gaining traction within multiple industrial sectors including aerospace and automotive for use in the design of parts for additive manufacturing
The turbulence model will be extended to a data-driven explicit algebraic stress models (EASMs), the general form of which will be presented along with a novel derivation of the continuous adjoint system of equations for the EASM
A novel data-driven technique has been developed to improve the treatment of turbulence in fluid topology optimisation
Summary
Fluid topology optimisation (FTO) is fast gaining traction within multiple industrial sectors including aerospace and automotive for use in the design of parts for additive manufacturing. Permeability-based FTO starts with an initial guess for the permeability field and modifies this guess across the domain to optimise some flow-based objective. The approach adopted here is the adjoint method (either continuous or discrete). It is a gradient-based technique which operates by extracting topological sensitivities within a predefined design domain (Othmer 2008). These sensitivities are equivalent to the gradient of the objective function with respect to the chosen design variables. The adjoint method is popular in topology optimisation as it requires the evaluation of just two sets of partial differential equations (primal and adjoint) to compute these sensitivities (Giles and Pierce 2000)
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