Topology optimization of turbulent flows

Abstract

 Users may download and print one copy of any publication from the public portal for the purpose of private study or research.  You may not further distribute the material or use it for any profit-making activity or commercial gain  You may freely distribute the URL identifying the publication in the public portal If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.

Density based topology optimization of turbulent flow heat transfer systems

“…10) is related to the length scale l = √ k/ω of turbulent eddies where ω b ensures that turbulent eddies become infnitesimally small as a wall is approached. During the optimization process, both k and ω are penalized to their wall boundary conditions in the solidified regions [15]. Since a regular mesh is used in the design domain, y 1 does not vary and is defined by the half cell length for penalization of the wall boundary condition ω b inside the design domain.…”

“…The present implementation is based on the PETSc library [8,7,9], which is utilized mainly for its efficient parallel sparse solvers. A verification of the implemented fluid dynamics solver with a detailed explanation of the solution procedure is presented in [15]. The additional heat transfer Equation 11 is discretized similarly, and the details will be omitted here for brevity.…”

“…In [39] a continuous adjoint formulation is presented based on the Spalart-Allmaras (SA) turbulence model [31]. Discrete adjoint formulations based on finite volume method for both the one-equation SA and k − ω turbulence models [36] have been presented only recently in [15]. This work provides the foundation of the current presentation, which is extended further to include heat transport, hence demonstrating the feasibility of the approach for large scale mixed thermo-fluidic topology optimization problems.…”

“…The present article demonstrates turbulent-flow heat-transfer topology optimization problems where the fluid flow is modeled by steady state incompressible Reynolds-averaged Navier-Stokes (RANS) equations. Turbulence closure is achieved utilizing the two-equation k-ω model, and the solution of the problem is obtained using an already developed 3D finite volume framework [15] which employs automatic differentiation [18] for calculating the adjoint equations and exact gradients consistent with the considered turbulence model. To the best of the authors' knowledge, such topology optimization of coupled thermal-fluid problems with turbulent flows has not been previously demonstrated with exact sensitivities obtained within the discrete adjoint approach, and without any simplifying assumptions.…”

Computational design of flow fields for vanadium redox flow batteries via topology optimization

“…For flow field design problems, Borrvall and Petersson [26] proposed a topology optimization method to minimize power dissipation in Stokes flow, and this has been expanded to laminar Navier-Stokes flow problems [27][28][29] and turbulence prob- lems [30,31]. The fluid topology optimization has been applied to multiphysics problems such as fluid-structure interaction problems [32,33], forced convection problems [34][35][36], natural convection problems [37][38][39] and turbulent heat transfer problems [40,41].…”