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This paper describes selected developments in transonic flow simulation technology that have utilized nonlinear potential methods for external aerodynamic applications. In particular, the research efforts in this field at Ames Research Center are highlighted. Included are a review of the various potential equation forms, the pertinent characteristics associated with key potential equation numerical algorithms, and a variety of numerical results for various aerodynamic applications to highlight key discussion points.

The effect of turbulence models in the off-body grids on the accuracy of solutions for rotor flows in hover has been investigated. Results from the Reynolds-Averaged Navier-Stokes and Laminar Off-Body models are compared. Advection of turbulent eddy viscosity has been studied to find the mechanism leading to inaccurate solutions. A coaxial rotor result is also included.

This paper presents an automated approach for effective extraction, visualization, and quantification of vortex core radii from the Navier-Stokes simulations of a UH-60A rotor in forward flight. We adopt a scaled Q-criterion to determine vortex regions and then perform vortex core profiling in these regions to calculate vortex core radii. This method provides an efficient way of visualizing and quantifying the blade tip vortices. Moreover, the vortices radii are displayed graphically in a plane.

This presentation describes the state of transonic flow simulation using nonlinear potential methods for external aerodynamic applications. The presentation begins with a review of the various potential equation forms (with emphasis on the full potential equation) and includes a discussion of pertinent mathematical characteristics and all derivation assumptions. Impact of the derivation assumptions on simulation accuracy, especially with respect to shock wave capture, is discussed. Key characteristics of all numerical algorithm types used for solving nonlinear potential equations, including steady, unsteady, space marching, and design methods, are described. Both spatial discretization and iteration scheme characteristics are examined. Numerical results for various aerodynamic applications are included throughout the presentation to highlight key discussion points. The presentation ends with concluding remarks and recommendations for future work. Overall. nonlinear potential solvers are efficient, highly developed and routinely used in the aerodynamic design environment for cruise conditions. Published by Elsevier Science Ltd. All rights reserved.

An approximate iterative search algorithm for finding donor cells associated with the chimera zonal grid approach is presented. This new algorithm is both fast and simple. It is used in conjunction with a chimera-based full potential solver for computing transonic flow solutions about wing and wing/fuselage configurations. Within each grid zone a fully implicit approximate factorization scheme is used to advance the solution one iteration. This is followed by the explicit advance of all common intergrid boundaries using a trilinear interpolation of the velocity potential. The presentation is highlighted with numerical result comparisons, a grid refinement study, and parametric variation of pertinent algorithm parameters. The new search algorithm produces donor cells for the two-zone wing problem at a rate in excess of 60,000 cells/s (single processor Cray C90). The approximate nature of the search algorithm, which causes some of the donor cells to be approximated by nearest neighbor cells, does not cause any impact on solution accuracy. Overall the results indicate that the present chimera zonal grid approach is a viable technique for solving the full potential equation for aerodynamic applications

A numerical scheme utilizing a chimera zonal grid approach for solving the three-dimensional fullpotential equation is described. Within each grid zone a new approximate factorization scheme based on the approximation factorization scheme 2 algorithm is utilized to advance the solution one iteration. This is followed by the explicit advance of all common zonal grid boundaries using trilinear interpolation of the velocity potential. Two spatial discretization variations are presented; one using a hybrid e rst-order/ second-order-accurate scheme and the second using a fully second-order-accurate scheme. The presentation is highlighted with a grid ree nement study and a number of transonic wing e owe eld computations.

Numerical simulation of hovering rotorcraft flow fields with emphasis on the accurate capture of the vortical wake is examined. The present approach utilizes the OVERFLOW Navier-Stokes flow solver, which has been enhanced with a solution adaptive grid capability. Regions of the flow within the off-body Cartesian grid that contain concentrated levels of vorticity are systematically refined within the constraints of the overset zonal grid approach. The resulting vortical flow field is captured more accurately relative to solutions that do not use any form of refinement and with significantly fewer grid points relative to solutions that utilize uniform refinement.

A numerical approach is described that simplifies and automates the CFD solution process so that Earth scientists can utilize high-resolution Navier-Stokes flow solvers as a research tool to investigate wind events on the Earth’s surface. The current approach utilizes the OVERFLOW-2 structured overset RANS code. A genetic algorithm is used to obtain an optimal multi-zone overset grid system that reduces the grid size and simulation time by maintaining high resolution over high-gradient land regions and lower resolution over low-gradient water regions. Flow simulations are presented that include flow separation and reattachment over mountainous terrain for coastal islands in Alaska (USA) and British Columbia (Canada).

A study involving four transonic airfoil computer codes, two FP and two Euler, has been performed. The major conclusions of the study are as follows: (1) the FP codes are faster than the Euler codes by about an order of magnitude based on CPU time on the Cray XMP; (2) the FP formulation loses accuracy as transonic flow develops, but entropy corrections yield FP solutions comparable to those of the Euler; (3) grid coarseness and type can be significant in affecting both accuracy and convergence characteristics; (4) the FP formulation must be more tightly converged than the Euler formulation for comparable levels of accuracy in the lift coefficient; and (5) in general, good accuracy for adequate meshes can be obtained with both formulations, irrespective of the solution method.

A probabilistic risk assessment (PRA) approach has been developed and applied to the risk analysis of capsule abort during ascent. The PRA is used to assist in the identification of modeling and simulation applications that can significantly impact the understanding of crew risk during this potentially dangerous maneuver. The PRA approach is also being used to identify the appropriate level of fidelity for the modeling of those critical failure modes. The Apollo launch escape system (LES) was chosen as a test problem for application of this approach. Failure modes that have been modeled and/or simulated to date include explosive overpressure-based failure, explosive fragment-based failure, land landing failures (range limits exceeded either near launch or Mode III trajectories ending on the African continent), capsule-booster re-contact during separation, and failure due to plume-induced instability. These failure modes have been investigated using analysis tools in a variety of technical disciplines at various levels of fidelity. The current paper focuses on the roles and impacts of the higher-fidelity methods on this process and, by association, the roles and impacts of the high performance computing resources of the Columbia supercomputer system at NASA Ames Research Center.

A numerical scheme utilizing a chimera zonal grid approach for solving the full potential equation in two spatial dimensions is described. Within each grid zone a fully-implicit approximate factorization scheme is used to advance the solution one interaction. This is followed by the explicit advance of all common zonal grid boundaries using a bilinear interpolation of the velocity potential. The presentation is highlighted with numerical results simulating the flow about a two-dimensional, nonlifting, circular cylinder. For this problem, the flow domain is divided into two parts: an inner portion covered by a polar grid and an outer portion covered by a Cartesian grid. Both incompressible and compressible (transonic) flow solutions are included. Comparisons made with an analytic solution as well as single grid results indicate that the chimera zonal grid approach is a viable technique for solving the full potential equation.

The field of computational fluid dynamics (CFD) using large-scale supercomputer applications is discussed. Formulational and computational requirements for the various governing equations, including the Euler and Navier-Stokes approaches, are examined for typical problems including the viscous flow field solution about a complete aerospace vehicle. Recent computed results and experimental comparisons are given to highlight the presentation. The future of CFD associated with three-dimensional applications is found to be rapidly expanding across a broad front, including internal and external flows and flows across the entire speed regime. >

A method for aerodynamic shape optimization based on a genetic algorithm approach is demonstrated. The algorithm is coupled with a transonic full potential flow solver and is used to optimize the flow about transonic wings including multi-objective solutions that lead to the generation of pareto fronts. The results indicate that the genetic algorithm is easy to implement, flexible in application and extremely reliable.

A new method for aerodynamic shape optimization using a genetic algorithm with real number encoding is presented. The algorithm is used to optimize three different problems, a simple hill climbing problem, a quasi-one-dimensional nozzle problem using an Euler equation solver and a three-dimensional transonic wing problem using a nonlinear potential solver. Results indicate that the genetic algorithm is easy to implement and extremely reliable, being relatively insensitive to design space noise.

The Computational Aerosciences (CAS) project of the High Performance Computing and Communications program is presented and discussed. The main emphasis of this presentation is on the applications portion of the CAS program, which includes a High-Speed Civil Transport element, a High Performance Aircraft element, a NASP-Derived Vehicle element, and an Aerobraking element. Two major thrusts of this program are the enhancement of simulation capabilities using multidiscipline formulations and the improvement in processing efficiency via massive parallel computer hardware. Current activities in these two areas at Ames, Langley and Lewis, are presented and discussed.

The process of computational fluid dynamics (CFD) validation is described from two perspectives, numerical error validation and physical model validation. Errors associated with time and space discretization, grid refinement, numerical dissipation, and level of solution convergence, are all possible sources of numerical error. The second aspect of CFD code validation is associated with the governing equations and the physical models, e.g., chemistry and turbulence models. This type of validation requires comparisons with carefully conducted experiments and is the primary aspect of the validation process discussed in this paper. Examples of validation are shown for selected Reynolds-averaged Navier-Stokes codes for conditions from transonic through hypersonic. Since code applications are becoming more complex, it no longer suffices to use data from surface or integral quantities alone to provide the required validation. Flow field surveys and experimental boundary condition measurements are emerging as critical data that must be obtained for CFD code validation. Progress in the overall level of validation is shown to be improving. However, future challenges remain, some of which are enumerated.

Large scale Navier-Stokes computations about aircraft components as well as reasonably complete aircraft configurations are presented and discussed. Speed and memory requirements are described for various general problem classes, which in some cases are already being used in the industrial design environment. Recent computed results, with experimental comparisons when available, are included to highlight the presentation. Finally, prospects for the future are described and recommendations for areas of concentrated research are indicated. The future of Navier-Stokes computations is seen to be rapidly expanding across a broad front of applications, which includes the entire subsonic-to-hypersonic speed regime.

Le champ d'ecoulement est divise en plusieurs zones. Les effets de paroi en soufflerie sont modelises. On obtient des solutions en bon accord avec l'experience

A fast, fully implicit approximate factorization algorithm designed to solve the conservative, transonic, full-potential equation in either two or three dimensions is described. The algorithm uses an upwind bias of the density coefficient for stability in supersonic regions. This provides an effective upwind difference of the streamwise terms for any orientation of the velocity vector (i.e., rotated differencing), thereby greatly enhancing the reliability of the present algorithm. A numerical transformation is used to establish an arbitrary body-fitted, finite-difference mesh. Computed results for both airfoils and simplified wings demonstrate substantial improvement in convergence speed for the new algorithm relative to standard successive-line over-relaxation algorithms.

A new spatial differencing scheme for the transonic full-potential equation in conservative form has been developed. Three consistency conditions for the full-potential equations are derived and are satisifed by the new scheme. This scheme guarantees zero truncation error on any curvilinear mesh for freestream flows in either two- or three-space dimensions. Solutions obtained with this new differencing scheme, away from freestream regions, exhibit greatly improved accuracy, especially for nonsmooth or singular meshes. The computing times associated with the new scheme are approximately the same as the less accurate old scheme when computations are performed on the same mesh.

The viscous effects on transonic flow past an airfoil which contains a shallow cavity beneath a porous surface are studied numerically. The porous region occupies a small portion of the total airfoil surface, and is located near the shock. Both an interactive boundary layer (IBL) algorithm and a thin-layer Navier-Stokes (TLNS) algorithm have been modified for use in studying the outer flow, whereas a stream-function formulation has been used to model the inner flow in the small cavity. The coupling procedure at the porous surface is based on Darcy's law and on the assumption of a constant total presusre in the cavity. In addition, a modified Baldwin-Lomax turbulence model is used to consider the transpired turbulent boundary layer in the TLNS approach, and the Cebeci-Smith turbulence model is used in the IBL approach. According to the present analysis, a porous surface can reduce the wave drag appreciably, but it can also increase viscous losses. As has been observed experimentally, the numerical results indicate that the total drag is reduced at higher Mach numbers and increased at lower Mach numbers when the angles of attack are small. Furthermore, the streamline patterns of passive-shock and boundary-layer interaction are revealed in this study.

Transonic flow fields about a low-aspect-ratio advanced technology wing have been computed using a viscous/inviscid zonal approach. The flow field near the wing where viscous effects are important was solved using the 'Reynolds-Averaged Navier-Stokes Equations' in 'thin-layer' form. The Euler equations were used to determine the flow field in regions away from the wing where viscous effects are insignificant. A zonal grid using an H-H topology was generated around the wing by first solving a set of Poisson's equations for the global grid. This grid was then subdivided into separate zones of viscous or inviscid flow as suggested by the flow physics. A series of flow cases were computed and compared with corresponding sets of experimental data. All cases showed good agreement with experiment in terms of the pressure field. Also, a good correlation between computed separated surface flow and experimental oil flow was obtained.

Results from the Viscous Transonic Airfoil Workshop held at the AIAA 25th Aerospace Sciences Meeting at Reno, NV in January 1987, are compared with each other and with experimental data. Test cases used in this workshop include attached and separated transonic flows for three different airfoils: the NACA 0012 airfoil, the RAE 2822 airfoil, and the Jones airfoil. A total of 23 sets of numerical results from 15 different author groups are included. The numerical methods used vary widely and include: 16 Navier-Stokes methods, 2 Euler/boundary-layer methods, and 5 full-potential/boundary-layer methods. The results indicate a high degree of sophistication among the numerical methods with generally good agreement between the various computed and experimental results for attached or moderately-separated cases. The agreement for cases with larger separation is only fair and suggests additional work is required in this area.

Implicit approximate factorization techniques (AF) are investigated for the solution of matrix equations resulting from finite-difference approximations to the full potential equation in conservation form. For transonic flows, an artificial viscosity, required to maintain stability in supersonic regions, is introduced by an upwind bias of the density. Two implicit AF procedures are presented, and their convergence performance is compared with that of the standard transonic solution procedure: successive line overrelaxation (SLOR). Subcritical and supercritical test cases are considered. Results indicate a substantial improvement in convergence rate for AF schemes relative to SLOR.

A fast, fully implicit, approximate factorization algorithm designed to solve the conservative full-potential equation is used to compute lifting-wing flowfields with embedded transonic flow. The computer program (TWING—transonic wing analysis) uses an elliptic-solver numerical grid-generation routine and is capable of analyzing arbitrary wing geometries with sweep, twist, taper, and section variation. Computed flowfield results for several wing geometries are presented; they demonstrate substantial improvement in convergence speed relative to the FLO28 computer code.

A new, implicit approximate factorization (AF) algorithm designed to solve the conservative full-potential equation for the transonic flow past arbitrary airfoils has been developed. The new algorithm uses an upwind bias of the density coefficient to provide stability in supersonic regions. This allows the simple two- and three-banded matrix form of the AF scheme to be retained over the entire flow field, even in regions of supersonic flow. A numerical transformation is used to establish an arbitrary body-fitted finite-difference mesh. Airfoil pressure distributions have been computed and are in good agreement with independent results.

The Transonic Navier-Stokes wing code is extended to a 16-zone TNS wing-fuselage code and used to solve the transonic viscous flow over a modified F-16A. The computer code, called Transonic Navier-Stokes Wing/Fuselage uses a zonal approach to solve the three-dimensional Euler and Navier-Stokes equations. With the zonal implementation, clustering suitable for viscous calculations is achieved on all solid surfaces. The transonic case has flow conditions of free-stream M = 0.9, alpha = 4.12 deg, and a Reynolds number based on root chord of 4.5 million. This case required about 3,000 iterations to reduce the L2-norm of the residual by three orders, which takes about 15 hr of cpu time on the Cray X-MP/48 processor. Pressure distributions, as well as separaton patterns, compare favorably with experiment for this transonic case.

An analysis of the transonic flowfield around a three-dimensional wing is carried out using a strip method. Attention is given to the boundary layer growth in the streamwise direction. A viscous correction technique is defined for the TWING code for solving the full potential equations. A viscous ramp at the base of a shock is superimposed on the boundary layer displacement thickness generated by an integral boundary layer method. A relationship is then obtained between the effective displacement thickness and a vertical component of the surface velocity, a transpirational boundary condition. The viscous correction is found to be unnecessary in weak shock conditions but gives a better shock position and pressure distribution in a strong shock condition when compared with data from an ONERA M6 airfoil and the Hinson and Burdges (1980) Wing A.

Numerical solutions of the full potential equation in conservative form are presented. The iteration scheme used is a fully implicit approximate factorization technique called AF2 and provides a substantial improvement in convergence speed relative to standard successive line overrelaxation algorithms. The spatial differencing algorithm is centrally differenced in both subsonic and supersonic regions with an upwind evaluation of the density coefficient in supersonic regions to maintain stability. This effectively approximates “rotated differencing” and thereby greatly improves the reliability of the present algorithm. The solutions presented in this paper have been selected from the GAMM Workshop on Numerical Methods for the Computation of In-viscid Transonic Flow with Shock Waves.

A fast, fully implicit approximate factorization algorithm designed to solve the conservative, transonic, full-potential equation in either two or three dimensions is described. The algorithm uses an upwind bias of the density coefficient for stability in supersonic regions. This provides an effective upwind difference of the streamwise terms for any orientation of the velocity vector (i.e., rotated differencing), thereby greatly enhancing the reliability of the present algorithm. A numerical transformation is used to establish an arbitrary body-fitted, finite-difference mesh. Computed results for both airfoils and simplified wings demonstrate substantial improvement in convergence speed for the new algorithm relative to standard successive-line over-relaxation algorithms.

The viscous effects on transonic flow past an airfoil which contains a shallow cavity beneath a porous surface are studied numerically. The porous region occupies a small portion of the airfoil surface, and is near the shock. A thin-layer Navier-Stokes algorithm in combination with a modified Baldwin-Lomax turbulence model is used in computing the outer flow, whereas a stream-function formulation is used to model the inner flow in the cavity. The two flow regions are coupled at the porous surface through Darcy’s law. Shock structure and flow patterns have been computed to show the influence of shock/boundary-layer interactions. In agreement with experiments, numerical results show that the total drag of a porous airfoil is reduced at higher transonic speeds but is increased at lower Mach numbers.

Transonic flow fields about wing geometries are computed using an Euler/Navier-Stokes approach in which the flow field is divided into several zones. The grid zones immediately adjacent to the wing surface are suitably clustered and solved with the Navier-Stokes equations. Grid zones removed from the wing are less finely clustered and are solved with the Euler equations. Wind tunnel wall effects are easily and accurately modeled with the new grid-zoning algorithm because the wind tunnel grid is constructed as an exact subset of the corresponding free-air grid. Solutions are obtained that are in good agreement with experiment, including cases with significant wind tunnel wall effects and shock-induced separation on the upper wing surface.

A new algorithm for generating solution-adaptive grids (SAG) about airfoil configurations embedded in transonic flow is presented. The present SAG approach uses only the airfoil surface solution to recluster grid points on the airfoil surface, i.e., the reclustering problem is one dimension smaller than the flow-field calculation problem. Special controls automatically built into the elliptic grid generation procedure are then used to obtain grids with suitable interior behavior. This concept of redistributing grid points greatly simplifies the idea of solution-adaptive grids. Numerical results indicate significant improvements in accuracy for SAG grids relative to standard grids using the same number of points.

Transonic flow fields about a low-aspect-ratio advanced technology wing have been computed using a viscous/inviscid zonal approach. The flow field near the wing where viscous effects are important was solved using the 'Reynolds-Averaged Navier-Stokes Equations' in 'thin-layer' form. The Euler equations were used to determine the flow field in regions away from the wing where viscous effects are insignificant. A zonal grid using an H-H topology was generated around the wing by first solving a set of Poisson's equations for the global grid. This grid was then subdivided into separate zones of viscous or inviscid flow as suggested by the flow physics. A series of flow cases were computed and compared with corresponding sets of experimental data. All cases showed good agreement with experiment in terms of the pressure field. Also, a good correlation between computed separated surface flow and experimental oil flow was obtained.

A new, implicit approximate factorization (AF) algorithm designed to solve the conservative full-potential equation for the transonic flow past arbitrary airfoils has been developed. The new algorithm uses an upwind bias of the density coefficient to provide stability in supersonic regions. This allows the simple two- and three-banded matrix form of the AF scheme to be retained over the entire flow field, even in regions of supersonic flow. A numerical transformation is used to establish an arbitrary body-fitted finite-difference mesh. Airfoil pressure distributions have been computed and are in good agreement with independent results.