Computational sensitivity analysis of wall-bounded flows

Computational sensitivity analysis methods have been implemented in the context of an unsteady computational fluid dynamics algorithm that is finite volume based and uses fractional-step methods solved on a staggered grid. The computational algorithms have been developed for computing primitive variables as well as sensitivity parameters (or coefficients) in two- and three-dimensional wall-bounded flows. The flow fields investigated in the current work are pressure-driven flows in plane channels and include, specifically, two-dimensional laminar and three-dimensional turbulent channel flow.;Next, SEM has been implemented in direct numerical simulations (DNS) for the case of smooth-wall turbulent channel flow to quantify Reynolds number effects on the mean flow field. In the present study, sensitivity coefficients represent the rate of change of the primitive variables with respect to the Reynolds number, and are determined directly by numerically solving the discretized continuous sensitivity equations concurrently with the discretized Navier-Stokes equations. Simulations have been performed at Reynolds numbers of 100 and 180, based on the friction velocity and channel half-width. The SEM results correctly predict the expected change in both the mean streamwise velocity and Reynolds shear stress profiles with increasing Reynolds number. Furthermore, the mean SEM results correctly predict the local slope of the skin friction coefficient versus Reynolds number curve.;Finally, complex step differentiation has been implemented in the context of the aforementioned DNS of turbulent channel flow to explore Reynolds number effects on the instantaneous velocity field and near-wall turbulent structures. The sensitivity results predict the expected changes in both the instantaneous velocity field and coherent structures (i.e., low-speed streaks and quasi-streamwise vortices). The current results also show that a portion of the Reynolds number sensitivity in wall-bounded flows can be directly correlated to local shear layers in the instantaneous velocity field when viewed from a convective frame of reference. Additional computational grid resolution requirements necessary to run the computational sensitivity simulations in this context are also discussed.;Verification of the numerical code is performed for the case of low Reynolds number, laminar channel flow in two-dimensions. This case has an exact steady-state solution to the Navier-Stokes equations. The exact steady-state solution allows for verification of the numerical algorithm for both the primitive variables and the sensitivity coefficients. The sensitivity of the flow to parameters associated with the exact solution is considered and three computational sensitivity analysis methods are compared in terms of numerical error relative to the exact solution and computational expense. The methods investigated are finite difference, complex step differentiation, and the sensitivity equation method (SEM).