Influence of integer design variables in topology optimization of incompressible turbulent flow

Abstract

• Optimize incompressible turbulent flow at bidimensional and tridimensional domains employing the continuous adjoint approach • Analyze the influence of integer design variables in topology optimization of incompressible turbulent fluids • Develop the adjoint near wall distance calculation to treat the adjoint spalart allmaras turbulence model Turbulent fluid flow is a challenging physical problem to be addressed with topology optimization due to the vortex generation and the near wall distance calculation that difficult the calibration of topology optimization parameters when continuous design variables based-optimizers are used. The intrinsic nature of topology optimization inverse permeability interpolation clashes with the accuracy requirements from turbulent fluid flow dynamics. To solve the mentioned challenge, the present paper investigates the influence of an integer continuous variable-based-optimizer, i.e. a [0, 1] binary behaviour, that avoids grey regions during the optimization process. Its influence on the near wall distance calculation is analyzed as it affects the permeability of the fluid domain. The turbulence phenomenon is treated via the Spalart-Allmaras model and its near wall distance calculation is approached by the Hamilton-Jacobi formulation. Permeability independence on the topology optimization formulation constraints is proposed firstly at the continuous adjoint approach to avoid miscalculations in the fluid cells. The finite volume method is employed to solve the Reynolds Averaged Navier-Stokes governing equations and 2D and 3D tests are developed, where discussions on the solid-fluid boundaries definition, the material penalization dependence, objective function comparisons and accuracy of the CFD analysis and the wall distance calculation are presented.