S. Scott Collis

Monitoring unresolved scales in multiscale turbulence modeling

This paper extends the two-level variational multiscale (VMS) method for large-eddy simulation, introduced by Hughes et al. [Comput. Visual. Sci. 3, 47 (2000)], to a three-level approach that clarifies the role of unresolved scales of motion on the resolved scales. It is shown that the multiscale framework does not obviate modeling on the large scales, but that VMS allows for different modeling assumptions to be used on each scale range. In particular, one can choose to neglect the effect of the unresolved scales on the large scales which is reasonable for sufficiently large-scale separation.

A better consistency for low-order stabilized finite element methods

Abstract The standard implementation of stabilized finite element methods with a piece-wise function space of order lower than the highest derivative present in the partial differential equation often suffers from a weak consistency that can lead to reduced accuracy. The popularity of these low-order elements motivates the development of a new stabilization operator which globally reconstructs the derivatives not present in the local element function space. This new method is seen to engender a stronger consistency leading to better convergence and improved accuracy. Applications to the Navier—Stokes equations are given which illustrate the improvement at a negligible additional cost.

The influence of control on proper orthogonal decomposition of wall-bounded turbulent flows

This paper explores the effects of several wall-based, turbulence control strategies on the structure of the basis functions determined using the proper orthogonal decomposition (POD). This research is motivated by the observation that the POD basis functions are only optimal for the flow for which they were created. Under the action of control, the POD basis may be significantly altered so that the common assumption that effective reduced-order models for predictive control can be constructed from the POD basis of an uncontrolled flow may be suspect. This issue is explored for plane, incompressible, turbulent channel flow at Reynolds number, Reτ=180. Based on well- resolved large eddy simulations, POD bases are constructed for three flows: no control; opposition control, which achieves a 25% drag reduction; and optimal control, which gives a 40% drag reduction. Both controlled flows use wall transpiration as the control mechanism and only differ in the technique used to predict the control. For both cont...

Receptivity to surface roughness near a swept leading edge

The formation of stationary cross flow vortices in a three-dimensional boundary layer due to surface roughness located near the leading edge of a swept wing is investigated using numerical solutions of the compressible Navier–Stokes equations. The numerical solutions are used to evaluate the accuracy of theoretical receptivity predictions which are based on the parallel-flow approximation. By reformulating the receptivity theory to include the effect of surface curvature, it is shown that convex surface curvature enhances receptivity. Comparisons of the parallel-flow predictions with Navier–Stokes solutions demonstrate that non-parallel effects strongly reduce the initial amplitude of stationary cross flow vortices. The curvature and non-parallel effects tend to counteract one another; but, for the cases considered here, the non-parallel effect dominates leading to significant over-prediction of receptivity by parallel-flow receptivity theory. We conclude from these results that receptivity theories must account for non-parallel effects in order to accurately predict the amplitude of stationary crossflow instability waves near the leading edge of a swept wing.

Viscous effects in control of near-wall turbulence

Prior studies of wall bounded turbulence control have utilized direct numerical simulation (DNS) which has limited investigations to low Reynolds numbers where viscous effects may play an important role. The current paper utilizes large eddy simulation (LES) with the dynamic subgrid-scale model to explore the influence of viscosity on one popular turbulence control strategy, opposition control, that has been extensively studied using low Reynolds number DNS. Exploiting the efficiency of LES, opposition control is applied to fully developed turbulent flow in a planar channel for turbulent Reynolds numbers in the range Reτ=80–720. At Reτ=80, opposition control completely suppresses turbulent fluctuations returning the flow to the laminar state. For higher Reynolds numbers, the flow remains turbulent and the predicted drag reduction drops from 26% at Reτ=100 to 19% at Reτ=720. Furthermore, the ratio of power saved to power input drops by more than a factor of 4 when Reynolds number increases over this range,...

The DG/VMS Method for Unified Turbulence Simulation

The high cost of wind tunnel testing and the ongoing reduction in national wind tunnel facilities are forcing the aerospace engineering community to increasingly rely on computational fluid dynamics (CFD) to predict the performance of new aircraft designs. However, most aerospace applications are characterized by flows that exhibit large-scale unsteady turbulence and the accurate prediction of these flows is often critical to predicting overall performance. Unfortunately, the turbulence modeling approaches used in existing industrial CFD simulation tools often do not accurately predict large-scale turbulent flows which limits their utility. This paper introduces a new paradigm, called the DG/VMS method, for CFD that is specifically designed to accurately and efficiently predict complex flows dominated by large-scale turbulence. Here, the DG/VMS formulation is presented along with results for several laminar validation tests. Our future work will apply the DG/VMS to turbulent flows.

Turbulence control simulation using the variational multiscale method

The capabilities of the variational multiscale (VMS) method are explored in the context of turbulence control by applying VMS to the simulation of a simple opposition-control strategy for turbulent channel flow with the results compared to prior direct numerical simulations and large-eddy simulations based on the dynamic subgrid-scale model. In all cases, the VMS method is found to be more efficient and more accurate than the dynamic model, and the simplicity, accuracy, and generality of VMS makes it particularly attractive for turbulence control investigations

Large eddy simulation and turbulence control

This paper reviews LES methods, based on the dynamic subgrid-scale model, that greatly improve the efficiency of turbulence control simulations in the context of drag reduction for plane turbulent channel flow. We begin by performing simulations of opposition control at Reynolds numbers in the range Reτ = 100 to 590 which demonstrate a decrease in effectiveness of this control strategy with increased Reynolds number. We then review techniques for optimal control of turbulent flows and discuss our implementation using an instantaneous control framework where the flow sensitivity is computed from the adjoint LES equations. Detailed optimal control results are presented that demonstrate excellent agreement with available DNS at a fraction of the computational expense. Given the added efficiency of LES, a receding horizon control framework is also explored that results in increased drag reduction along with improved control distributions. Results are also presented for a hybrid LES/DNS method where optimization is performed using LES but the flow is advanced using DNS. This approach demonstrates that even coarse grid LES can serve as a viable reduced order model for DNS. In our ongoing efforts to seek greater model reductions for predictive control, we also explore the influence of control on the basis functions obtained from proper orthogonal decomposition.

A computational approach to swept leading-edge receptivity

Computational techniques developed to simulate receptivity mechanisms near a swept-wing leading edge are presented. The method is based on hybrid finite-difference and spectral approximations to the compressible Navier-Stokes equations in a generalized coordinate system. Particular attention is paid to boundary treatments in an effort to reduce the generation of spurious waves which can mask the physical receptivity mechanisms. Model problems verifying the accuracy of the method are presented, including Tollmien-Schlichting waves in a parallel boundary layer and acoustic scattering from a circular cylinder. Mean flow and receptivity results for a flat plate with superellipse leading edge at M = 0.1 are presented and compare favorably to previous incompressible calculations. Results for the same geometry are also obtained at M = 0.8 and show a significant increase in instability. (Author)

Partition selection in multiscale turbulence modeling

The variational multiscale (VMS) method for large-eddy simulation (LES) is a promising new approach that employs variational projection to achieve a priori scale separation in lieu of traditional spatial filtering. However, depending on the numerical method used, VMS may not be convenient in all spatial directions. We apply the VMS methodology to a numerical method that does not support explicit scale separation in the wall-normal direction for turbulent channel flow. Similar to the common LES practice of filtering only in the planes, variational projection is performed only in the planes and this strategy is found to be as successful as the full VMS method. However, in all VMS approaches, the partition between the large and small scales and the overall resolution are crucial parameters for obtaining quality solutions. By applying scale separation in just one of the coordinate directions, we have developed a consistent method for partition and resolution selection in channel flow that is related to the ph...