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This numerical investigation explores supersonic flow over a wall-mounted cylinder using Large Eddy Simulations (LES), unsteady Reynolds Averaged Navier-Stokes (RANS), Delayed Detached Eddy Simulation (DDES), and hybrid RANS/LES approaches. The LES was obtained using a well-validated high-order Navier-Stokes flow solver employing a hybrid 6-order compact spatial discretization and 2-order Roe scheme. An 8-order low-pass spatial filter was used to regularize the flow. The RANS and hybrid RANS/LES solutions were obtained with a 2-order k − turbulence model in conjunction with the high-order flow solver employed in the LES. Additional RANS and DDES results were obtained using a 5-order WENO scheme available in the OVERFLOW code. Results compare the characteristics of both time-mean and instantaneous solutions using the four turbulence modeling approaches. Overall, RANS solutions display favorable agreement with time-mean LES flow field structure and boundary layer characteristics. Unfortunately, both the DDES and hybrid RANS/LES approaches developed significantly longer separation regions upstream of the cylinder. In the hybrid RANS/LES approach, the length of the upstream separation shock was driven by the location chosen to transition from the RANS to hybrid RANS/LES model. For the DDES approach, the upstream separation shock shifted to a location very near the inflow boundary. Both the DDES and hybrid RANS/LES methodologies developed larger transitional/laminar separation regions because the upstream shock-wave/boundary-layer interaction was unable to force the development of small-scale turbulence structures necessary to overcome the reduction in eddy viscosity.

This work investigates the coupling of a very high-order finite-difference algorithm for the solution of conservation laws on general curvilinear meshes with overset-grid techniques originally developed to address complex geometric configurations. The solver portion of the algorithm is based on Pade-type compact finite-differences of up to sixth-order, with up to 10th-order filters employed to remove spurious waves generated by grid non-uniformities, boundary conditions and flow non-linearities. The overset-grid approach is utilized as both a domain-decomposition paradigm for implementation of the algorithm on massively parallel machines and as a means for handling geometric complexity in the computational domain. Two key features have been implemented in the current work; the ability of the high-order algorithm to accommodate holes cut in grids by the overset-grid approach, and the use of high-order interpolation at non-coincident grid overlaps. Several high-order/high-accuracy interpolation methods were considered, and a high-order, explicit, non-optimized Lagrangian method was found to be the most accurate and robust for this application. Several two-dimensional benchmark problems were examined to validate the interpolation methods and the overall algorithm. These included grid-to-grid interpolation of analytic test functions, the inviscid convection of a vortex, laminar flow over single- and double-cylinder configurations, and the scattering of acoustic waves from one- and three-cylinder configurations. The employment of the overset-grid techniques, coupled with high-order interpolation at overset boundaries, was found to be an effective way of employing the high-order algorithm for more complex geometries than was previously possible.

A general analytic method for calculating the scattering of sound by multiple rigid circular cylinders arranged in an arbitrary parallel configuration is presented. The sound scattered by this collection of cylinders is generated by a time-periodic, spatially distributed, axisymmetric source located within the domain of interest. A Hankel transform method is used to calculate the incident field, while separation of variables is used to obtain the scattered fields from each cylinder in the collection. The unknown scattering coefficients are determined through the use of general addition theorems that allows the various fields to be readily transformed between coordinate systems. The method is validated using various two-, three-, and four-cylinder configurations, and the number of coefficients that must be retained in the truncated series is examined. Benchmark configurations consisting of two- and three-cylinder systems with cylinders of varying radii are also presented. These solutions have been used to validate computational aeroacoustic solvers developed for complex geometries.

An uncertainty-based simulation work flow is used to automate the prediction of steadystate aerodynamic loads for a design variant of the HIFiRE-6 hypersonic flight research vehicle. Tools distributed with the Chimera Grid Tools (CGT) framework are exercised to perform overset mesh generation and verify domain connectivity. OVERFLOW is used to compute Reynolds-Averaged Navier-Stokes estimates of static aerodynamic loads at different points within a design space representative of the vehicle’s planned flight test environment. Sensitivity analysis of a design space composed of Mach number, angle of attack, sideslip angle, and dynamic pressure is performed to assess the suitability of using secondorder central-composite statistical designs to capture modest variations in customer-defined system response quantities. Within the specified bounds, automated simulation analytics suggest that for the fixed vehicle being analyzed, variations in axial and normal force coefficients are driven by perturbations in angle of attack and Mach number. Perturbations in sideslip angle induce the most variation in side force coefficient. Perturbations in an interaction term involving sideslip angle and angle of attack, and sideslip angle are the primary drivers impacting variation in rolling moment coefficient. Perturbations in angle of attack and Mach number are predicted to be the primary drivers of variations in pitching moment coefficient. Perturbations in sideslip angle and Mach number are predicted to be the primary drivers for variations in yawing moment. Perturbations in dynamic pressure were determined to be statistically insignificant for the design space analyzed. Analysis of variation results of the design indicate that second-order surrogates, based on a small number of independent simulations, are able to capture 90 to 100% of the variations in steady-state aerodynamic loads predicted by simulation associated with a vehicle at a fixed point along its trajectory. We expect these automated techniques and observations to be useful for future design, testing, and evaluation activities involving high-speed vehicles.

The Application Support Team in the Computational Sciences Branch of AFRL/RQ is currently employing structured overset-grid grid generation methods in conjunction with the NASA flow solver OVERFLOW in order to perform aerodynamic analysis of complex configurations. This paper discusses some process-related issues associated with the gridgeneration and domain connectivity steps in the simulation workflow. The process for performing script-based grid generation is discussed, and additional macros that have been identified and developed based on the repeated need for certain functionality are presented. A process for dividing watertight surface triangulations into components suitable for overset grid generation using the functionality present in Chimera Grids tools is presented. Issues associated with projection onto surface triangulations are discussed, and a categorization of orphan points and steps to take to remove each class are listed. Some grid systems developed for recent applications analyzed by the Application Support Team are shown.

This paper presents recent work that the U.S. Air Force has conducted to better understand the range of potential rocketback trajectories that could meet future launch needs. Various vision architectures were considered to meet a variety of reference mission requirements. These trajectories were compared against each other to determine ranges of critical flight conditions of interest for detailed aerodynamic analysis. Computational Fluid Dynamics (CFD) analysis is presented to show where the most uncertainty in flight conditions appears. This analysis presents a starting point for determining the flight conditions requiring flight testing to validate CFD models.

In this work, the ow elds associated with two canonical turret geometries, a fully exposed hemisphere on a at plate and a 50% submerged hemisphere on a at plate, were simulated using the OVERFLOW 2 ow solver. Both turret geometries utilize a at-window aperture with an aperture ratio (ratio of the aperture diameter to the turret diameter) of 0.295 and an elevation angle of 57 . The forward eld of regard was the particular focus in this study, and both symmetric (azimuth angle of 0 ) and asymmetric (azimuth of 45 ) window orientations were examined. Two ight conditions were also studied; a subsonic case with M = 0:45 and ReD = 6:30 10 and a transonic case with M = 0:85 and ReD = 9:53 10. The ow eld was simulated using the Delayed Detached Eddy Simulation capability of OVERFLOW in conjunction with the spatially fth-order Weighted Essentially Non-Oscillatory (WENO) scheme to capture the o -body vortical structures The incoming boundary layer was set a the same height for both geometries, which corresponded to a quarter of the height of the fully exposed hemisphere and half of the height of the submerged turret. The impact of the turret aerodynamics on the performance of the turrets for directed energy applications is inferred through consideration of the ow features, density and pressure uctuations, and forces on the turrets.

A process is developed to automate external aerodynamic investigations of xed-wing aircraft con gurations using structured overset meshing and analysis technology. Since it has been established by many researchers that mesh generation is often a bottleneck that may prevent the generation of timely results, e ort is devoted to identifying characteristic topologies that occur on xed-wing aircraft that readily lend themselves to e cient automation. A script-based mesh generation process is presented for xed-wing aircraft, and applied to a series of aero-optical use cases designed to predict total aerodynamic performance as a result of a design change, and model potentially relevant interactions between aircraft components. It is demonstrated that improvements in automation e ciency can be achieved with existing tools. However, certain topologies exist that are resistant to automation e orts, requiring sustained expert user intervention to achieve a suitable mesh using established best practices. The current maturity level of this capability for xedwing aircraft is a semi-automated process that is easily transitioned to a broader range of xed-wing aircraft analyses, where many mesh generation tasks may be completed without intervention by the user. Veri cation of domain connectivity using available tools remains an activity that requires manual intervention by an expert user.

A method for minimizing the Δv required for interplanetary missions in heliocentric space is presented. The method is developed by decomposing the orbital transfer into three phases; an initial powered-flight phase, an intermediate free-flight phase, and a terminal powered-flight phase. The free-flight phase is governed by standard two-body orbital mechanics, and the appropriate equations are presented. Assumptions are made regarding the nature of the powered-flight phases, and the results are examined to check the validity of the assumptions. Preliminary results obtained from the optimization code are also presented.

Work has been performed in and coordinated by the Computational Sciences Branch to develop an in-house aero-optics predictive capability. This interim report summarizes the first two years of this effort. The work during this period has focused on acquiring high-quality experimental databases consisting of both aerodynamic and aero-optical measurements for future code validation, and the evaluation and improvement of the unstructured flow solver AVUS to solve representative flow fields.

The flow-field around a “1303” UCAV configuration is computationally simulated using a high-order overset-grid algorithm for a variety of Reynolds numbers and angles of attack. The high-order spatial scheme used here is based on a compact, sixth-order finitedifferencing with a tenth-order, adjustable, Pade-type filter. Turbulence modeling is provided by an implicit large-eddy simulation technique whereby the discriminating filter is used to regularize unresolved scales in the computation. Overset-grid techniques, including high-order interpolation and one-sided operators at hole and computational boundaries, are employed to simplify grid generation and provide a domain decomposition capability for parallel processing. Results are obtained at Reynolds numbers based on the mean aerodynamic chord of Remac = 17927, 29879, and 59758 and at angles of attack of 6 ◦, 12◦, and 15◦. The computations are compared to experimental PIV-data recently obtained at these conditions. Particular focus is placed on the validation of the computational approach by comparing mean stream-wise velocity and span-wise normal vorticity between computation and experiment at a variety of span-wise and stream-wise locations.

In order to meet the demanding accuracy requirements in the simulation of wave propagation phenomena, a numerical approach based on high-resolution spatial schemes is presented. The time-domain AFRL code, FDL3DI, solves either the time-dependent Maxwell's equations (for CEM) or the Euler equations (for acoustics) employing 6th-order accurate compact-differences and low-pass spatial filters of up to 10th-order accuracy. The solver has been made applicable to general curvilinear grids through the incorporation of a careful treatment of the coordinate transformation metrics. In addition, the method has been extended to multi-body scattering applications through the use of overset grids and high-order interpolation. A robust absorbing boundary condition exploiting the transfer function of the low-pass filter has been developed. To evaluate the solver, several benchmark problems have been considered. Application to communication through weakly ionized plasma has also been studied.

Simulating the flow around a maneuvering unmanned combat air vehicle (UCAV) requires a computational method capable of modeling such complex flow features as massive separation, transition from laminar to turbulent flow, and nonlinear vortex dynamics. In the present paper, a parallel, high-order, overset-grid solver is used to compute these challenging flowfields. Turbulence modeling is accomplished using an implicit Large Eddy Simulation (LES) approach, which exploits the characteristics of the sixth-order accurate computational scheme coupled with high-order, low pass filtering. This scheme provides a unified computational approach for the laminar/transitional/turbulent flowfields encountered by maneuvering UCAVs. A general overset- grid capability, including high-order interpolation and the ability to handle holes while maintaining high-order accuracy, has been incorporated into the flow solver. This high-order method is applied to the simulation of a canonical low sweep delta wing and a generic, tailless, low-sweep wing UCAV configuration. Computations performed for the low sweep delta wing at moderate Reynolds numbers demonstrate the ability of the implicit large-eddy simulation (ILES) approach to capture important Reynolds number effects for these complicated transitional flowfields. Groundbreaking high-order computations for the generic UCAV configuration are then presented with the fundamental aerodynamic phenomena of the configuration being examined using the improved accuracy of the high-order overset method. Comparisons with available experimental measurements are made to demonstrate the ability of this high-fidelity modeling approach to capture the complex flow physics involved.

A parallel, high-order, overset-grid method is validated for use in large eddy simulation (LES) through its application to turbulent flow problems. The current method employs a high-order, compact finite-difference approach to evaluate spatial derivatives, with up-to-tenth-order low-pass filters used to remove high-frequency spurious wave content. These filters have also been found to be effective in modeling the dissipation that occurs at the unresolved scales in the flow for LES simulations. Temporal integration is based on an implicit, approximately-factored and diagonalized, second-order algorithm, which reduces the time-step constraints present in explicit time-marching methods for wall-bounded viscous flows. Parallelization, geometric complexity, and local grid refinement are all addressed through the use of an overset-grid approach, with grid communication provided by high-order Lagrangian interpolation. Problems demonstrating this approach include fully turbulent channel flow and flows over a single circular cylinder, a general delta-wing configuration, and a realistic UAV geometry.

In this paper a high-order computational method for the highly unsteady, complex vortical flows over unmanned combat air vehicle (UCAV) like configurations is presented. A sixth-order compact difference scheme with an eighth-order low pass filter is used to solve the Navier-Stokes equations. An implicit large-eddy simulation (ILES) method which exploits the high-order accuracy of the compact difference scheme and uses the discriminating higher-order filter to regularize the flow is used to model the transition and turbulence in these highly separated flows. This computational approach is applied to the detailed characterization of the flowfield over a low sweep delta wing at moderate Reynolds numbers and both low and moderate freestream Mach numbers. Computations exploring the control of the vortical flows above a swept delta wing by use of a dialectric-barrier-discharge (DBD) actuator are also presented. With the actuator located near the apex, significant movement of the vortex breakdown location and a dramatic transformation of the shear-layer sub-structures are demonstrated.

A new preprocessing code BELLERO has been developed to automate many of the tasks associated with domain decomposition for the parallel, high-order overset-grid (HOOG) flow solver FDL3DI. The previous approach required considerable user involvement as well as manual modifications to the code to set up problems for processing using the parallel HO-OG algorithm. Highlighted capabilities of BELLERO include; (1) automatic generation of the grid indices for the domain decomposition, taking into account minimum stencil requirements for the high-order algorithm, (2) automatic generation of the blocklevel connectivity including periodic boundary conditions, (3) automated decomposition of the grid-level boundary conditions, thus eliminating the need to manually specify blocklevel boundaries in the code, and (4) calculation of high-order interpolation coecients and management of hole points to fully implement the HO-OG approach. Improvements have also been made to the FDL3DI solver itself in order to further enhance the overall flexibility of the HO-OG implementation. The new capability is validated using the benchmark problems of acoustic scattering from three circular cylinders and electromagnetic scattering from a single sphere.

A parallel, high-order, overset-grid method is examined for use in ∞uid dynamics and aeroacoustics. This approach, which couples the accuracy and decreased grid-point requirements of high-order methods with the geometric ∞exibility of oversetgrid methods, is demonstrated by its application on three benchmark-type problems. These include the inviscid convection of a vortex in an otherwise uniform mean ∞ow, the scattering of acoustic waves by a conflguration of three circular cylinders, and the viscous, laminar ∞ow over two circular cylinders in close proximity at a Reynolds number of 100. Particular attention is paid to the efiect that the one-sided difierencing and flltering algorithms employed near computational boundaries has on the overall solution accuracy. The impact that the order of the interpolation used at overset grid boundaries has on the solution accuracy is also investigated. The results obtained here show that high-order one-sided fllters and interpolation methods are required to obtain the maximum beneflt from the high-order overset-grid approach.

The accuracy of two general interpolation methods was investigated within the context of developing a high-order overset grid flow solver. The two methods, a generalized Lagrangian method and a basisspline method, were examined using a one-dimensional Fourier error analysis. The local and integrated error was reduced for both implicit and explicit Lagrangian methods by optimizing the coefficients at the expense of reducing formal order of accuracy. For the stencil sizes investigated here, the optimized implicit interpolation methods were shown to possess integrated errors many orders of magnitude lower than the basis-spline, non-optimized or optimized explicit methods. The generalized Lagrangian interpolation method was chosen for implementation with an established high-order flow solver to produce a high-order overset grid capability. A two-dimensional benchmark problem of an inviscid, connecting vortex was solved using this capability on an overset grid system consisting of both Cartesian and curvilinear grids. Initial results showed substantial improvement in the computed solution for the optimized implicit interpolation method when compared to the bilinear interpolation method. The optimized implicit method reduced the maximum difference between the computed and exact solutions by a factor of 9.4 when compared to the bilinear method. INTRODUCTION High-order compact finite-difference schemes continue to mature as a means of simulating various wavepropagation phenomena. Recent works by Rizzetta et * Research Aerospace Engineer. Member AIAA '''Associate Professor. Associate Fellow AIAA This paper is a -work of the U.S. Government and is not subject to copyright protection in the United States. al.' in the field of turbulent flow simulation, Visbal and Gaitonde in aeroacoustics, and Gaitonde et al.' and Shang in electromagnetics have demonstrated the ability to solve increasingly complex multidisciplinary problems using high-order methods on generalized curvilinear grids. These methods are based on Lele's Pade-type, implicit tridiagonal, fourthand sixth-order compact finite differences. Because these schemes are centered, they are non-dissipative hi nature, and thus high-order filters are employed to remove spurious frequencies from the solution. These filters include an adjustable parameter that controls spectral response by shifting the frequency cut-off to higher or lower wavenumbers as well as modifying its sharpness.' Thus, the characteristics of the filter may be easily modified depending upon the quality and resolution of the computational grid as well as the inherent nonlinearities or other destabilizing features of the particular problem being examined. This technology was further developed by Gaitonde and Visbal'' by introducing high-order, one-sided filters to maintain accuracy and stability near boundaries. This enhancement allowed the extension of the approach to multi-domain problems with coincident, overlapping grid points at the domain interfaces. Overset grid methods also continue to develop as an effective means of simulating physical phenomenon for geometrically complex problems or problems with multiple bodies in relative motion. Blake and Shang used an overset grid approach to simulate electromagnetic scattering from a full B-1B aircraft, while Chan and Gomez have developed an automated overset grid generation procedure and examined surface pressures on an X-38 Crew Return Vehicle. Meakin, Meakin and Wissink, and Wang et al. have investigated issues and solved complex flow problems