A Continuous Shape Sensitivity Equation (CSE) method is presented for shape parameters and applied turbulent wall-bounded flows computed using the standard k - e turbulence model with wall functions. Computations are done with an adaptive finite-element code. This paper is an extension of previous works on sensitivity analysis of laminar flows for shape parameters and wall-bounded turbulent flows for value parameters. The differentiation of two-velocity scale wall functions, accounting for their complex dependencies on boundary shape parameters, is presented in details. Flow and sensitivity solutions are first verified on a problem with a closed form solution using the Method of the Manufactured Solution. The problem allows for the Verification of the wall functions and their sensitivities with respect to shape parameters. Then, we present the application of the methodology to sensitivity analysis on a problem of practical engineering complexity. The problem consists in simulating turbulent flows around a square cross-section cylinder in proximity of a solid wall. We investigate the ability of the method to deal with non trivial geometrical changes and to predict important changes in the flow response.
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