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Eysteinn Helgason
Division of Fluid Dynamics, Department of Applied Mechanics, Chalmers University of Technology, Gothenburg, Sweden

Sinisa Krajnovic
Department of Mechanics and Maritime Sciences (M2), Chalmers University of Technology, Goteborg 41296, Sweden

DOI: 10.1615/TFESC1.cmd.013294
pages 299-309

KEY WORDS: Adjoint method, scalar transport, transport of heat and particles, shape optimization


The continuous adjoint formulation of the steady-state Navier-Stokes equations with scalar transport has been implemented in the open-source framework OpenFOAM®. The flow is solved using a steady-state compressible flow solver. A cost function based on uniform species distribution at a selected region on the surface of the geometry is presented. The continuous adjoint approach is applied to calculate the gradient of the cost function with respect to normal motion of the surface geometry. The main advantage of applying the adjoint method is the considerable decrease in simulation time compared to traditional methods, reducing the total simulation time for the whole sensitivity field to roughly two flow simulations. The current implementation of the adjoint equations with scalar transport is applied to a simple two dimensional channel. The sensitivity of a species distribution at a location at the surface of the channel with respect to the normal motion of the surface is evaluated. The results from the adjoint implementation are validated against gradients approximated using finite difference calculations. The comparison shows close agreement between the gradients obtained using the two methods, implying that the implementation of the adjoint equations can be used as a guideline when improving a design or in an optimization process for this type of flow.

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