| Description |
Nonparametric approaches to computational sensitivity analysis, based on Complex Step Differentiation (CSD) and the Sensitivity Equation Method (SEM), have been used to examine parameter dependence in the incompressible, temporal, planar mixing layer. Both of these sensitivity approaches were implemented numerically in the context of Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES), coupled with standard and dynamic Smagorinsky models, in order to examine the sensitivity of the flow to perturbations in Reynolds number, Prandtl number, initial conditions, and model coefficients. The DNS codes were run over a Reynolds number range 100 ≤ Reδ0 ≤ 1000, where δ0 represents the initial vortex thickness of the mixing layer; while the LES codes were run up to Reδ0 = 2000. In both cases, the partial differential equations governing the behavior of the flow are derived, discretized, and solved using an explicitly, unsteady, finite-volume based fractional step algorithm. The unique aspect of the present work, compared to traditional parametric studies, is the fact that both CSD and SEM yield spatiotemporally resolved sensitivity fields. This allows one to investigate the local, instantaneous response of the flow field to infinitesimal changes in the design/flow parameters of interest, with application toward optimization and active control. In terms of the DNS of the temporal mixing layer, a two-blade pattern, which appears as a dominant feature in the sensitivity solution, provides new information that highlights the physical mechanisms leading to vortex thickness growth and enhanced molecular mixing with increasing Reynolds and Prandtl numbers.Through a "nearby flow" analysis, the sensitivity fields predict faster growth of the mixing layer with an increase the turbulence intensity in the inital conditions. In this study, both a priori and a posteriori studies were conducted in the LES framework. The sensitivity solution allows one to extrapolate low Reynolds number a priori data to estimate the correct value of the model coefficients that should be used at higher Reynolds numbers. Results from the a posteriori study indicate that both CSD and SEM in the context of LES are able to capture the essential, large-scale features of the coherent sensitivity structures at high Reynolds number. |
