Abstract
An a priori reduced order method based on the proper generalised decomposition (PGD) is proposed to compute parametric solutions involving turbulent incompressible flows of interest in an industrial context, using OpenFOAM. The PGD framework is applied for the first time to the incompressible Navier-Stokes equations in the turbulent regime, to compute a generalised solution for velocity, pressure and turbulent viscosity, explicitly depending on the design parameters of the problem. In order to simulate flows of industrial interest, a minimally intrusive implementation based on OpenFOAM SIMPLE algorithm applied to the Reynolds-averaged Navier-Stokes equations with the Spalart-Allmaras turbulence model is devised. The resulting PGD strategy is applied to parametric flow control problems and achieves both qualitative and quantitative agreement with the full order OpenFOAM solution for convection-dominated fully-developed turbulent incompressible flows, with Reynolds number up to one million.
Highlights
Parametric studies involving flows of industrial interest require robust computational fluid dynamics (CFD) solvers and efficient strategies to simulate multiple queries of the same problem.Finite volume (FV) methods represent the most common approach in industry to perform flow simulations [1,2,3,4,5,6,7,8] and different strategies have been proposed to simulate flows in the turbulent regime [9,10,11]
A widespread approach is represented by the Reynolds-averaged Navier-Stokes (RANS) equations [12] coupled with the one-equation Spalart-Allmaras (SA) turbulence model [13]
It is known that numerical difficulties arise when reduced basis (RB) and proper orthogonal decomposition (POD) techniques are applied to convection-dominated problems [17,18,19]
Summary
Parametric studies involving flows of industrial interest require robust computational fluid dynamics (CFD) solvers and efficient strategies to simulate multiple queries of the same problem. It is known that numerical difficulties arise when reduced basis (RB) and proper orthogonal decomposition (POD) techniques are applied to convection-dominated problems [17,18,19] This is especially critical in the context of flow simulations when the Reynolds number is increased and turbulent phenomena need to be accounted for. To foster the application of a priori model order reduction techniques to problems of industrial interest, a non-intrusive PGD implementation in the CFD software OpenFOAM has been recently proposed in [45] to solve parametrised incompressible Navier-Stokes equations in the laminar regime. The proposed PGD strategy considers the one-equation SA turbulence model and it constructs a separated representation of velocity, pressure and eddy viscosity to solve the RANS-SA equations in OpenFOAM. 1 + cb , σ g := r + cw2(r6 − r), r := ν , S κ 2d2 where ·, · F denotes the Frobenius inner product and the scalar constants σ =2/3, κ=0.41, cb1=0.1355, cb2=0.622, cv1=7.1, cw2=0.3 and cw3=2 are selected [13]
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