Scott M. Murman

Higher-Order Methods for Compressible Turbulent Flows Using Entropy Variables

A higher-order space-time discontinuous Galerkin method is presented for the simulation of compressible ows. The eect of the discrete formulation on the nonlinear stability of the scheme is assessed through numerical simulations. For marginally resolved turbulent simulations at moderate Reynolds number, polynomial dealiasing is shown to be necessary in order to maintain stability at high order. With increasing Reynolds number, the formulation using conservative variables is shown to be unstable at high order even when using polynomial dealiasing. Using an entropy variable formulation consistent with established entropy stability theory ensures nonlinear stability at high and innite Reynolds number. The eect of the numerical ux for underresolved turbulent simulations is investigated. A low-Mach modied ux term is presented to suppress the biased pressure-dilatation term seen with other upwind numerical uxes. Subgrid-scale modeling eects of dierent numerical ux functions on the kinetic energy spectrum are examined in the limit of innite Reynolds number.

DNS of Flows over Periodic Hills using a Discontinuous-Galerkin Spectral-Element Method

ow in a channel. The higher-order method is shown to provide increased accuracy relative to low-order methods at a given number of degrees of freedom. The turbulent ow over a periodic array of hills in a channel is simulated at Reynolds number 10,595 using an 8th-order scheme in space and a 4th-order scheme in time. These results are validated against experiment and compared with previous large eddy simulation (LES) results. A preliminary analysis provides insight into how these detailed simulations can be used to improve Reynolds-averaged Navier-Stokes (RANS) modeling.

On the accuracy of RANS simulations with DNS data

Simulation results conducted for incompressible planar wall-bounded turbulent flows with the Reynolds-Averaged Navier-Stokes (RANS) equations with no modeling involved are presented. Instead, all terms but the molecular diffusion are represented by the data from direct numerical simulation (DNS). In simulations, the transport equations for velocity moments through the second order (and the fourth order where the data are available) are solved in a zero-pressure gradient boundary layer over a flat plate and in a fully-developed channel flow in a wide range of Reynolds numbers using DNS data from Sillero et al. (2013), Lee & Moser (2015), and Jeyapaul et al. (2015). The results obtained demonstrate that DNS data are the significant and dominant source of uncertainty in such simulations (hereafter, RANS-DNS simulations). Effects of the Reynolds number, flow geometry, and the velocity moment order as well as an uncertainty quantification technique used to collect the DNS data on the results of RANS-DNS simulations are analyzed. New criteria for uncertainty quantification in statistical data collected from DNS are proposed to guarantee the data accuracy sufficient for their use in RANS equations and for the turbulence model validation.

COMPUTATIONAL INVESTIGATION OF SLOT BLOWING FOR FUSELAGE FOREBODY FLOW CONTROL

Abstract This paper presents a computational investigation of a tangential slot blowing concept for generating lateral control forces on an aircraft fuselage forebody. This work is aimed at aiding researchers in designing future experimental and computational models of tangential slot blowing. The effects of varying both the jet width and jet exit velocity for a fixed location slot are analyzed. The primary influence on the resulting side force of the forebody is seen to be the jet mass flow rate. This influence is insensitive to different combinations of slot widths and jet velocities over the range of variables considered. Both an actuator plane and an overset grid technique are used to model the tangential slot. The overset method successfully resolves the details of the actual slot geometry, extending the generality of the numerical method. The actuator plane concept predicts side forces similar to those produced by resolving the actual slot geometry.

Tensor-product preconditioners for higher-order space-time discontinuous Galerkin methods

A space-time discontinuous-Galerkin spectral-element discretization is presented for direct numerical simulation of the compressible Navier-Stokes equations. An efficient solution technique based on a matrix-free Newton-Krylov method is developed in order to overcome the stiffness associated with high solution order. The use of tensor-product basis functions is key to maintaining efficiency at high-order. Efficient preconditioning methods are presented which can take advantage of the tensor-product formulation. A diagonalized Alternating-Direction-Implicit (ADI) scheme is extended to the space-time discontinuous Galerkin discretization. A new preconditioner for the compressible Euler/Navier-Stokes equations based on the fast-diagonalization method is also presented. Numerical results demonstrate the effectiveness of these preconditioners for the direct numerical simulation of subsonic turbulent flows.

Coupled numerical simulation of the external and engine inlet flows for the F-18 at large incidence

Abstract This paper presents a numerical simulation of the external and engine inlet flows for the F-18 aircraft at typical high-angle-of-attack flight conditions. Two engine inlet mass flow rates, corresponding to flight idle and maximum power, were computed. This was accomplished using a structured, overset grid technique to couple the external and internal grid systems. Reynolds-averaged Navier–Stokes solutions were obtained using an implicit, finite-differencing scheme. Results show a strong coupling of the external and engine inlet flows, especially at the maximum power setting. Increasing the mass flow rate through the inlet caused the primary vortex breakdown location to move downstream. This trend is also observed in flight tests performed on the F-18. A reversed flow region upstream of the inlet duct is visible in the faired-inlet and flight-idle computations. This flow reversal is not present in the maximum power setting computation. These large-scale changes in flow structure highlight the importance of simulating inlet conditions in high-angle-of-attack aircraft computations.

Analysis of a pneumatic forebody flow control concept about a full aircraft geometry

A full aircraft geometry is used to computationally analyze the effectiveness of a pneumatic forebody flow control concept. An overset grid technique is employed to model the aircraft and slot geometry. Steady-state solutions for both isolated forebody and full aircraft configurations are carried out using a thin-layer Navier-Stokes flow solver. A solution obtained using the full aircraft geometry and a flight sideslip condition investigates the effect of sideslip on the leading edge extention vortex burst point. A no-sideslip blowing solution using the isolated forebody at full-scale wind tunnel test conditions is compared with experimental data to determine the accuracy of the numerical method. A solution employing the full geometry and slot blowing at flight conditions is obtained.

A Space-Time Discontinuous-Galerkin Approach for Separated Flows

The motivation and goals for developing a space-time spectral-element Discontinuous-Galerkin solver for complex separated flows are discussed. The desire for spectral elements in space and time to leverage current and next-generation computing hardware and enable the development of novel subgrid-scale physical models for scaleresolving simulations at practical engineering Reynolds numbers is discussed. Timing results for hardware-optimized kernels are presented and demonstrate the ability of space-time spectral-elements to utilize a significant fraction of the available computing power of an Intel Xeon processor. A dynamic Variational Multiscale Method is developed and applied to the simulation of channel flow at Re� = 544 .

Design of a Variational Multiscale Method for High Reynolds Number Compressible Flows

The ultimate goal of this work is the simulation of separated flow about the threedimensional FAITH bump to support Reynolds-averaged modeling efforts. Given the relatively high Reynolds number of this experimental configuration, numerical efficiency becomes paramount to enable practical simulations. This work describes the progress in the design of a VMM for high-Reynold-number separated flows, focusing on performance vs. accuracy trade-offs of the numerical schemes.

Development of a High-Order Space-Time Matrix-Free Adjoint Solver

The growth in computational power and algorithm development in the past few decades has granted the science and engineering community the ability to simulate flows over complex geometries, thus making Computational Fluid Dynamics (CFD) tools indispensable in analysis and design. Currently, one of the pacing items limiting the utility of CFD for general problems is the prediction of unsteady turbulent ows.1{3 Reynolds-averaged Navier-Stokes (RANS) methods, which predict a time-invariant mean flowfield, struggle to provide consistent predictions when encountering even mild separation, such as the side-of-body separation at a wing-body junction. NASAs Transformative Tools and Technologies project is developing both numerical methods and physical modeling approaches to improve the prediction of separated flows. A major focus of this e ort is efficient methods for resolving the unsteady fluctuations occurring in these flows to provide valuable engineering data of the time-accurate flow field for buffet analysis, vortex shedding, etc. This approach encompasses unsteady RANS (URANS), large-eddy simulations (LES), and hybrid LES-RANS approaches such as Detached Eddy Simulations (DES). These unsteady approaches are inherently more expensive than traditional engineering RANS approaches, hence every e ort to mitigate this cost must be leveraged. Arguably, the most cost-effective approach to improve the efficiency of unsteady methods is the optimal placement of the spatial and temporal degrees of freedom (DOF) using solution-adaptive methods.