Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “solvers”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 829 records · Page 46

Numerical prediction of transition of the F-16 wing at supersonic speeds

A parametric study is being conducted as an effort to numerically predict the extent of natural laminar flow (NLF) on finite swept wings at supersonic speeds. This study is one aspect of a High Speed Research Program (HSRP) to gain an understanding of the technical requirements for high-speed aircraft flight. The parameters that are being addressed in this study are Reynolds number, angle of attack, and leading-edge wing sweep. These parameters were analyzed through the use of an advanced Computational Fluid Dynamics (CFD) flow solver, specifically the ARC 3-D Compressible Navier-Stokes (CNS) flow solver. From the CNS code, pressure coefficients (Cp) are obtained for the various cases. These Cp's are then used to compute the boundary-layer profiles through the use of the 'Kaups and Cebeci' compressible 2-D boundary layer code. Finally, the boundary-layer parameters are processed into a 3-D compressible boundary layer stability code (COSAL) to predict transition. The parametric study then consisted of four geometries which addressed the effects of sweep, and three angles of attack from zero to ten degrees to yield a total of 12 cases. The above process was substantially automated through a procedure that was developed by the work conducted under this study. This automation procedure then yields a 3-D graphical measure of the extent of laminar flow by predicting the transition location of laminar to turbulent flow.

Cummings, Russell M.↗

A semi-Lagrangian approach to the shallow water equation

We present a formulation of the shallow water equations that emphasizes the conservation of potential vorticity. A locally conservative semi-Lagrangian time-stepping scheme is developed, which leads to a system of three coupled PDE's to be solved at each time level. We describe a smoothing analysis of these equations, on which an effective multigrid solver is constructed. Some results from applying this solver to the static version of these equations are presented.

Bates, J. R.↗

A comparative study of computational solutions to flow over a backward-facing step

A comparative study was conducted for computational fluid dynamic solutions to flow over a backward-facing step. This flow is a benchmark problem, with a simple geometry, but involves complicated flow physics such as free shear layers, reattaching flow, recirculation, and high turbulence intensities. Three Reynolds-averaged Navier-Stokes flow solvers with k-epsilon turbulence models were used, each using a different solution algorithm: finite difference, finite element, and hybrid finite element - finite difference. Comparisons were made with existing experimental data. Results showed that velocity profiles and reattachment lengths were predicted reasonably well by all three methods, while the skin friction coefficients were more difficult to predict accurately. It was noted that, in general, selecting an appropriate solver for each problem to be considered is important.

Mizukami, M.↗

FAS multigrid calculations of three dimensional flow using non-staggered grids

Grid staggering is a well known remedy for the problem of velocity/pressure coupling in incompressible flow calculations. Numerous inconveniences occur, however, when staggered grids are implemented, particularly when a general-purpose code, capable of handling irregular three-dimensional domains, is sought. In several non-staggered grid numerical procedures proposed in the literature, the velocity/pressure coupling is achieved by either pressure or velocity (momentum) averaging. This approach is not convenient for simultaneous (block) solvers that are preferred when using multigrid methods. A new method is introduced in this paper that is based upon non-staggered grid formulation with a set of virtual cell face velocities used for pressure/velocity coupling. Instead of pressure or velocity averaging, a momentum balance at the cell face is used as a link between the momentum and mass balance constraints. The numerical stencil is limited to 9 nodes (in 2D) or 27 nodes (in 3D), both during the smoothing and inter-grid transfer, which is a convenient feature when a block point solver is applied. The results for a lid-driven cavity and a cube in a lid-driven cavity are presented and compared to staggered grid calculations using the same multigrid algorithm. The method is shown to be stable and produce a smooth (wiggle-free) pressure field.

Matovic, D.↗

An object-oriented approach for parallel self adaptive mesh refinement on block structured grids

Self-adaptive mesh refinement dynamically matches the computational demands of a solver for partial differential equations to the activity in the application's domain. In this paper we present two C++ class libraries, P++ and AMR++, which significantly simplify the development of sophisticated adaptive mesh refinement codes on (massively) parallel distributed memory architectures. The development is based on our previous research in this area. The C++ class libraries provide abstractions to separate the issues of developing parallel adaptive mesh refinement applications into those of parallelism, abstracted by P++, and adaptive mesh refinement, abstracted by AMR++. P++ is a parallel array class library to permit efficient development of architecture independent codes for structured grid applications, and AMR++ provides support for self-adaptive mesh refinement on block-structured grids of rectangular non-overlapping blocks. Using these libraries, the application programmers' work is greatly simplified to primarily specifying the serial single grid application and obtaining the parallel and self-adaptive mesh refinement code with minimal effort. Initial results for simple singular perturbation problems solved by self-adaptive multilevel techniques (FAC, AFAC), being implemented on the basis of prototypes of the P++/AMR++ environment, are presented. Singular perturbation problems frequently arise in large applications, e.g. in the area of computational fluid dynamics. They usually have solutions with layers which require adaptive mesh refinement and fast basic solvers in order to be resolved efficiently.

Lemke, Max↗

Two-dimensional CFD modeling of wave rotor flow dynamics

A two-dimensional Navier-Stokes solver developed for detailed study of wave rotor flow dynamics is described. The CFD model is helping characterize important loss mechanisms within the wave rotor. The wave rotor stationary ports and the moving rotor passages are resolved on multiple computational grid blocks. The finite-volume form of the thin-layer Navier-Stokes equations with laminar viscosity are integrated in time using a four-stage Runge-Kutta scheme. Roe's approximate Riemann solution scheme or the computationally less expensive advection upstream splitting method (AUSM) flux-splitting scheme is used to effect upwind-differencing of the inviscid flux terms, using cell interface primitive variables set by MUSCL-type interpolation. The diffusion terms are central-differenced. The solver is validated using a steady shock/laminar boundary layer interaction problem and an unsteady, inviscid wave rotor passage gradual opening problem. A model inlet port/passage charging problem is simulated and key features of the unsteady wave rotor flow field are identified. Lastly, the medium pressure inlet port and high pressure outlet port portion of the NASA Lewis Research Center experimental divider cycle is simulated and computed results are compared with experimental measurements. The model accurately predicts the wave timing within the rotor passages and the distribution of flow variables in the stationary inlet port region.

Welch, Gerard E.↗

Computational strategies for three-dimensional flow simulations on distributed computer systems

An increasing amount of research activity in computational fluid dynamics has been devoted to the development of efficient algorithms for parallel computing systems. The increasing performance to price ratio of engineering workstations has led to research to development procedures for implementing a parallel computing system composed of distributed workstations. This thesis proposal outlines an ongoing research program to develop efficient strategies for performing three-dimensional flow analysis on distributed computing systems. The PVM parallel programming interface was used to modify an existing three-dimensional flow solver, the TEAM code developed by Lockheed for the Air Force, to function as a parallel flow solver on clusters of workstations. Steady flow solutions were generated for three different wing and body geometries to validate the code and evaluate code performance. The proposed research will extend the parallel code development to determine the most efficient strategies for unsteady flow simulations.

Weed, Richard Allen↗

Code validation for the simulation of supersonic viscous flow about the F-16XL

The viewgraphs and discussion on code validation for the simulation of supersonic viscous flow about the F-16XL are provided. Because of the large potential gains related to laminar flow on the swept wings of supersonic aircraft, interest in the applications of laminar flow control (LFC) techniques in the supersonic regime has increased. A supersonic laminar flow control (SLFC) technology program is currently underway within NASA. The objective of this program is to develop the data base and design methods that are critical to the development of laminar flow control technology for application to supersonic transport aircraft design. Towards this end, the program integrates computational investigations underway at NASA Ames-Moffett and NASA Langley with flight-test investigations being conducted on the F-16XL at the NASA Ames-Dryden Research Facility in cooperation with Rockwell International. The computational goal at NASA Ames-Moffett is to integrate a thin-layer Reynolds averaged Navier-Stokes flow solver with a stability analysis code. The flow solver would provide boundary layer profiles to the stability analysis code which in turn would predict transition on the F-16XL wing. To utilize the stability analysis codes, reliable boundary layer data is necessary at off-design cases. Previously, much of the prediction of boundary layer transition has been accomplished through the coupling of boundary layer codes with stability theory. However, boundary layer codes may have difficulties at high Reynolds numbers, of the order of 100 million, and with the current complex geometry in question. Therefore, a reliable code which solves the thin-layer Reynolds averaged Navier-Stokes equations is needed. Two objectives are discussed, the first in greater depth. The first objective is method verification, via comparisons of computations with experiment, of the reliability and robustness of the code. To successfully implement LFC techniques to the F-16XL wing, the flow about the leading edge must be maintained as laminar flow. Therefore, the second objective is to focus on a series of numerical simulations with different values of angle of attack, alpha, and Reynolds numbers. The purpose of the simulations is to study their effects on the two main factors which precipitate transition to turbulence at leading edges of highly swept wings (e.g., 'spanwise contamination' and 'crossflow instability').

Flores, Jolen↗

Combined LAURA-UPS solution procedure for chemically-reacting flows

A new procedure seeks to combine the thin-layer Navier-Stokes solver LAURA with the parabolized Navier-Stokes solver UPS for the aerothermodynamic solution of chemically-reacting air flowfields. The interface protocol is presented and the method is applied to two slender, blunted shapes. Both axisymmetric and three dimensional solutions are included with surface pressure and heat transfer comparisons between the present method and previously published results. The case of Mach 25 flow over an axisymmetric six degree sphere-cone with a noncatalytic wall is considered to 100 nose radii. A stability bound on the marching step size was observed with this case and is attributed to chemistry effects resulting from the noncatalytic wall boundary condition. A second case with Mach 28 flow over a sphere-cone-cylinder-flare configuration is computed at both two and five degree angles of attack with a fully-catalytic wall. Surface pressures are seen to be within five percent with the present method compared to the baseline LAURA solution and heat transfers are within 10 percent. The effect of grid resolution is investigated and the nonequilibrium results are compared with a perfect gas solution, showing that while the surface pressure is relatively unchanged by the inclusion of reacting chemistry the nonequilibrium heating is 25 percent higher. The procedure demonstrates significant, order of magnitude reductions in solution time and required memory for the three dimensional case over an all thin-layer Navier-Stokes solution.

Wood, William A.↗

Overset grid applications on distributed memory MIMD computers

Analysis of modern aerospace vehicles requires the computation of flowfields about complex three dimensional geometries composed of regions with varying spatial resolution requirements. Overset grid methods allow the use of proven structured grid flow solvers to address the twin issues of geometrical complexity and the resolution variation by decomposing the complex physical domain into a collection of overlapping subdomains. This flexibility is accompanied by the need for irregular intergrid boundary communication among the overlapping component grids. This study investigates a strategy for implementing such a static overset grid implicit flow solver on distributed memory, MIMD computers; i.e., the 128 node Intel iPSC/860 and the 208 node Intel Paragon. Performance data for two composite grid configurations characteristic of those encountered in present day aerodynamic analysis are also presented.

Chawla, Kalpana↗

The development and application of the self-adaptive grid code, SAGE

The multidimensional self-adaptive grid code, SAGE, has proven to be a flexible and useful tool in the solution of complex flow problems. Both 2- and 3-D examples given in this report show the code to be reliable and to substantially improve flowfield solutions. Since the adaptive procedure is a marching scheme the code is extremely fast and uses insignificant CPU time compared to the corresponding flow solver. The SAGE program is also machine and flow solver independent. Significant effort was made to simplify user interaction, though some parameters still need to be chosen with care. It is also difficult to tell when the adaption process has provided its best possible solution. This is particularly true if no experimental data are available or if there is a lack of theoretical understanding of the flow. Another difficulty occurs if local features are important but missing in the original grid; the adaption to this solution will not result in any improvement, and only grid refinement can result in an improved solution. These are complex issues that need to be explored within the context of each specific problem.

Davies, Carol B.↗

Hybrid structured/unstructured grid computations for the F/A-18 at high angle of attack

At high angles of attack, vortical flows play a crucial role in the maintenance of lift for fighter aircraft. However, under certain conditions, the vortical flow can have an adverse effect on the aircraft. On the F/A-18 the LEX vortex can impinge on the tail; at high angles of attack the unsteady flow from vortex bursting can cause structural fatigue on the vertical tails. At high angles of attack, the flow field can be quite complex, and a computational analysis challenging. A full configuration analysis with viscous structured grids can be computationally expensive and the task of generating the requisite grids can be quite difficult. To mitigate these difficulties and provide a medium-fidelity analysis tool, a hybrid structured/unstructured approach was adopted for this work. In this analysis, the formation and roll-up of the LEX vortex is computed with a structured Navier-Stokes solver, and the resulting vortex propagated downstream with an unstructured Euler solver.

Robert T Biedron↗

An application of a two-equation model of turbulence to three-dimensional chemically reacting flows

A numerical study of three dimensional chemically reacting and non-reacting flowfields is conducted using a two-equation model of turbulence. A generalized flow solver using an implicit Lower-Upper (LU) diagonal decomposition numerical technique and finite-rate chemistry has been coupled with a low-Reynolds number two-equation model of turbulence. This flow solver is then used to study chemically reacting turbulent supersonic flows inside combustors with synergetic fuel injectors. The reacting and non-reacting turbulent combustor solutions obtained are compared with zero-equation turbulence model solutions and with available experimental data. The hydrogen-air chemistry is modeled using a nine-species/eighteen reaction model. A low-Reynolds number k-epsilon model was used to model the effect of turbulence because, in general, the low-Reynolds number k-epsilon models are easier to implement numerically and are far more general than algebraic models. However, low-Reynolds number k-epsilon models require a much finer near-wall grid resolution than high-Reynolds number models to resolve accurately the near-wall physics. This is especially true in complex flowfields, where the stiff nature of the near-wall turbulence must be resolved. Therefore, the limitations imposed by the near-wall characteristics and compressible model corrections need to be evaluated further. The gradient-diffusion hypothesis is used to model the effects of turbulence on the mass diffusion process. The influence of this low-Reynolds number turbulence model on the reacting flowfield predictions was studied parametrically.

Lee, J.↗

Enhancements to the KATE model-based reasoning system

KATE (Knowledge-based Autonomous Test Engineer) is a model-based software system developed in the Artificial Intelligence Laboratory at the Kennedy Space Center for monitoring, fault detection, and control of launch vehicles and ground support systems. This report describes two software efforts which enhance the functionality and usability of KATE. The first addition, a flow solver, adds to KATE a tool for modeling the flow of liquid in a pipe system. The second addition adds support for editing KATE knowledge base files to the Emacs editor. The body of this report discusses design and implementation issues having to do with these two tools. It will be useful to anyone maintaining or extending either the flow solver or the editor enhancements.

Thomas, Stan J.↗

A three-dimensional structured/unstructured hybrid Navier-Stokes method for turbine blade rows

A three-dimensional viscous structured/unstructured hybrid scheme has been developed for numerical computation of high Reynolds number turbomachinery flows. The procedure allows an efficient structured solver to be employed in the densely clustered, high aspect-ratio grid around the viscous regions near solid surfaces, while employing an unstructured solver elsewhere in the flow domain to add flexibility in mesh generation. Test results for an inviscid flow over an external transonic wing and a Navier-Stokes flow for an internal annular cascade are presented.

Tsung, F.-L.↗

Collection Efficiency and Ice Accretion Calculations for a Sphere, a Swept MS(1)-317 Wing, a Swept NACA-0012 Wing Tip, an Axisymmetric Inlet, and a Boeing 737-300

Collection efficiency and ice accretion calculations have been made for a sphere, a swept MS(1)-317 wing, a swept NACA-0012 wing tip, an axisymmetric inlet, and a Boeing 737-300 inlet using the NPARC flow solver and the NASA Lewis LEWICE3D grid based ice accretion code. Euler flow solutions for the geometries were generated using the NPARC flow solver. The LEWICE3D grid based ice accretion program was used to calculate the impingement efficiencies and ice shapes. Ice shapes specifying rime and mixed icing conditions were generated for a 30 minute hold condition. All calculations were performed on an SGI Model Power Challenge Computer. The results have been compared to experimental flow and impingement data. In general, the calculated flow and collection efficiencies compared well with experiment, and the ice shapes looked reasonable and appeared representative of the rime and mixed icing conditions for which they were calculated.

Bidwell, Colin S.↗

Accelerated panel methods using the fast multipole method

Panel methods are commonly used in computational fluid dynamics for the solution of potential flow problems. The methods are a numerical technique based on the surface distribution of singularity elements. The solution is the process of finding the strength of the singularity elements distributed over the body's surface. This process involves the solution of the matrix problem Pq = p' for a set of unknowns q. The Fast Multipole Method is used to directly compute q without using matrix solvers. The algorithm works in O(N) time for N points, a great improvement over standard matrix solvers. In panel methods, the surface of a body is divided into a series of quadrilateral panels. The methods involve the computation of the influence of all other panels on each individual panel. The influence is based on the surface distribution, though this can be approximated by the area for distant panels. An alternative approximation, though with arbitrary accuracy, is to develop a multipole expansion about the center of the panel to describe the effect of a given panel on distant points in space. The expansion is based on the moments of the panel, thus allow the use of various surface distributions without changing the basic algorithm, just the computation of the various moments. The expansions are then manipulated in a tree walk to develop Taylor series expansions about a point in space which describe the effect of all distant panels on any point within a volume of convergence. The effect of near panels then needs to be computed directly, but the effect of all distant panels can be computed by simply evaluating the resulting expansion. The Fast Multipole Method has been applied to panel methods for the solution of source and doublet distributions. A major feature of the algorithm is that the algorithm does not change to derive the potential and velocity for sources and doublets. The same expansions can be used for both sources and doublets. Since the velocity is related to the potential, and the doublet potential is related to the z-component of the source velocity, all values can be derived from the same expansion by taking a series of partial derivatives. This requires more expansion terms to be kept since terms are lost in the process of taking partial derivatives. Thus to maintain accuracy for the doublet computation, more terms are required than if just evaluating for sources. The resulting Fast Multipole code should then parallelize better than classical panel methods due to the locality of data dependencies found in the Fast Multipole Method. Theoretically the parallelized code should execute in O(log N) time with O(N) processors, though this is not practical. Ongoing work includes implementing the parallel accelerated panel method, including methods to improve the load balancing of the problem by taking advantage of the known geometry of panels, and to encorporate sensitivity analysis into the algorithm.

Leathrum, James F., Jr.↗

Aerodynamic optimization studies on advanced architecture computers

The approach to carrying out multi-discipline aerospace design studies in the future, especially in massively parallel computing environments, comprises of choosing (1) suitable solvers to compute solutions to equations characterizing a discipline, and (2) efficient optimization methods. In addition, for aerodynamic optimization problems, (3) smart methodologies must be selected to modify the surface shape. In this research effort, a 'direct' optimization method is implemented on the Cray C-90 to improve aerodynamic design. It is coupled with an existing implicit Navier-Stokes solver, OVERFLOW, to compute flow solutions. The optimization method is chosen such that it can accomodate multi-discipline optimization in future computations. In the work , however, only single discipline aerodynamic optimization will be included.

Chawla, Kalpana↗