• Document: The Adjoint Method Hits the Road: Applications in Car Aerodynamics
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Symposium in Honor of Antony Jameson‘s 80th Birthday, Stanford University 2014 The Adjoint Method Hits the Road: Applications in Car Aerodynamics Dr. Carsten Othmer, Volkswagen AG, Corporate Research, Wolfsburg, Germany Übersicht Adjoint-Based Optimization for Cars: Overview Cooling Flow Control Optimization Vehicle Shape Continuous Aeroacoustic Optimization Adjoint Method Optimization Topology Shape Optimization Optimization of Ducted Flows Acknowledgements • Prof. Giannakoglou‘s team at the National Technical University of Athens • Eugene De Villiers and Thomas Schumacher from Engys, London • E. Stavropoulou, M. Hojjat and Prof. Bletzinger from TU Munich • The Adjoint team at Volkswagen: S. Baumbach, K. Brandes, M. Gregersen, F. Kunze, N. Magoulas, J. Müller, H. Narten, D. Schräder and other supportive colleagues The Adjoint Method: Computation of Sensitivity Maps Surface Sensitivities = ∂J/∂β Volume Sensitivities = ∂J/∂α red: push away from the fluid red: important areas blue: push towards the fluid blue: counterproductive areas Massflow Pressure drop Drag Uniformity The Adjoint Method: Computational Process 1. CFD computation: v , p (“primal field“) 2. Adjoint CFD computation: u , q (“dual field“) 3. Computation of sensitivities: • Volume sensitivities: • Surface sensitivities: Implementation of an Adjoint Solver for Automotive Applications • Platform: Open source code OpenFOAM® chosen in 2006 solve ( fvm::ddt(rho, U) + fvm::div(phi, U) - fvm::laplacian(mu, U) == - fvc::grad(p) ); • Topology optimization [VW, AIAA 2007] • Shape sensitivities [VW, IJNMF 2008] • Low-Re Adjoint turbulence [NTUA + VW, C&F 2009] • Adjoint wall functions [NTUA + VW, JCP 2010, ECCOMAS 2014] • Packaging and further industrialization by Engys [since 2011] • Uptake and improvements by Helgason, Hinterberger, Jakubek, Lincke, Towara, …  Versatile continuous adjoint solver “adjointFoam“ for incompressible steady-state RANS Adjoint-Based Optimization for Cars: Overview Cooling Flow Control Optimization Vehicle Shape Continuous Aeroacoustic Optimization Adjoint Method Optimization Topology Shape Optimization Optimization of Ducted Flows Topology Optimization • Well-developed tool in structure mechanics, wide-spread industrial use Example: Optimal car body topology [Conic, VW] • Transfer to fluid dynamics: Klimetzek [Daimler, 2003], Borrvall and Petersson [2003] Topology Optimization for Fluid Dynamics • Starting point: Entire installation space – Flow solution – Identification of “counter-productive“ cells via a local criterion (v•u) – Punishment of counter-productive cells with porosity • Result: Optimal topology Topology Optimization for Fluid Dynamics • Starting point: Entire installation space – Flow solution – Identification of “counter-productive“ cells via a local criterion (v•u) – Punishment of counter-productive cells with porosity • Result: Optimal topology Topology Optimization for Fluid Dynamics • Starting point: Entire installation space – Flow solution – Identification of “counter-productive“ cells via a local criterion (v•u) – Punishment of counter-productive cells with porosity • Result: Optimal topology Topology Optimization for Fluid Dynamics • Starting point: Entire installation space – Flow solution – Identification of “counter-productive“ cells via a local criterion (v•u) – Punishment of counter-productive cells with porosity • Result: Optimal topology Topo Example 1: From Packaging Space to the Optimal Port Drafting with adjointFoam Packaging space definition adjointFoam + manual CAD iterations [F. Kunze and R. Niederlein] Fina

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