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 613 records · Page 34

Box truss analysis and technology development. Task 1: Mesh analysis and control

An analytical tool was developed to model, analyze and predict RF performance of box truss antennas with reflective mesh surfaces. The analysis system is unique in that it integrates custom written programs for cord tied mesh surfaces, thereby drastically reducing the cost of analysis. The analysis system is capable of determining the RF performance of antennas under any type of manufacturing or operating environment by integrating together the various disciplines of design, finite element analysis, surface best fit analysis and RF analysis. The Integrated Mesh Analysis System consists of six separate programs: The Mesh Tie System Model Generator, The Loadcase Generator, The Model Optimizer, The Model Solver, The Surface Topography Solver and The RF Performance Solver. Additionally, a study using the mesh analysis system was performed to determine the effect of on orbit calibration, i.e., surface adjustment, on a typical box truss antenna.

Bachtell, E. E.↗

Finite-volume and integral-equation techniques for transonic and supersonic vortex-dominated flows

Two computational techniques are developed to calculate the compressible vortex-dominated flows. The first technique is a finite-volume Euler Solver which uses four-Stage Runge-Kutta time stepping with second- and fourth-order dissipation terms. The technique is applied to supersonic conical and three-dimensional flows about sharp- and round-edged delta wings. Attached and separated-flow solutions have been obtained depending on the values of damping coefficients. The second technique is an integral-equation solver of the full potential equation which uses a volume-integral term in addition to the classical surface-integral terms. The technique is applied to transonic three-dimensional flows about sharp-edged delta wings. A hybrid technique which combines the finite-volume and the integral-equation solvers is also presented.

Kandil, O. A.↗

Hypersonic flow analysis

While the zonal grid system of Transonic Navier-Stokes (TNS) provides excellent modeling of complex geometries, improved shock capturing, and a higher Mach number range will be required if flows about hypersonic aircraft are to be modeled accurately. A computational fluid dynamics (CFD) code, the Compressible Navier-Stokes (CNS), is under development to combine the required high Mach number capability with the existing TNS geometry capability. One of several candidate flow solvers for inclusion in the CNS is that of F3D. This upwinding flow solver promises improved shock capturing, and more accurate hypersonic solutions overall, compared to the solver currently used in TNS.

Chow, Chuen-Yen↗

Evaluation of new techniques for the calculation of internal recirculating flows

The performance of discrete methods for the prediction of fluid flows can be enhanced by improving the convergence rate of solvers and by increasing the accuracy of the discrete representation of the equations of motion. This paper evaluates the gains in solver performance that are available when various acceleration methods are applied. Various discretizations are also examined and two are recommended because of their accuracy and robustness. Insertion of the improved discretization and solver accelerator into a TEACH code, that has been widely applied to combustor flows, illustrates the substantial gains that can be achieved.

Van Doormaal, J. P.↗

Improved numerical methods for turbulent viscous recirculating flows

The performance of discrete methods for the prediction of fluid flows can be enhanced by improving the convergence rate of solvers and by increasing the accuracy of the discrete representation of the equations of motion. This report evaluates the gains in solver performance that are available when various acceleration methods are applied. Various discretizations are also examined and two are recommended because of their accuracy and robustness. Insertion of the improved discretization and solver accelerator into a TEACH mode, that has been widely applied to combustor flows, illustrates the substantial gains to be achieved.

Turan, A.↗

Euler equation computations for the flow over a hovering helicopter rotor

A numerical solution technique is developed for computing the flow field around an isolated helicopter rotor in hover. The flow is governed by the compressible Euler equations which are integrated using a finite volume approach. The Euler equations are coupled to a free wake model of the rotary wing vortical wake. This wake model is incorporated into the finite volume solver using a prescribed flow, or perturbation, technique which eliminates the numerical diffusion of vorticity due to the artificial viscosity of the scheme. The work is divided into three major parts: (1) comparisons of Euler solutions to experimental data for the flow around isolated wings show good agreement with the surface pressures, but poor agreement with the vortical wake structure; (2) the perturbation method is developed and used to compute the interaction of a streamwise vortex with a semispan wing. The rapid diffusion of the vortex when only the basic Euler solver is used is illustrated, and excellent agreement with experimental section lift coefficients is demonstrated when using the perturbation approach; and (3) the free wake solution technique is described and the coupling of the wake to the Euler solver for an isolated rotor is presented. Comparisons with experimental blade load data for several cases show good agreement, with discrepancies largely attributable to the neglect of viscous effects. The computed wake geometries agree less well with experiment, the primary difference being that too rapid a wake contraction is predicted for all the cases.

Roberts, Thomas Wesley↗

Newton solution of inviscid and viscous problems

The application of Newton iteration to inviscid and viscous airfoil calculations is examined. Spatial discretization is performed using upwind differences with split fluxes. The system of linear equations which arises as a result of linearization in time is solved directly using either a banded matrix solver or a sparse matrix solver. In the latter case, the solver is used in conjunction with the nested dissection strategy, whose implementation for airfoil calculations is discussed. The boundary conditions are also implemented in a fully implicit manner, thus yielding quadratic convergence. Complexities such as the ordering of cell nodes and the use of a far field vortex to correct freestream for a lifting airfoil are addressed. Various methods to accelerate convergence and improve computational efficiency while using Newton iteration are discussed. Results are presented for inviscid, transonic nonlifting and lifting airfoils and also for laminar viscous cases.

Venkatakrishnan, V.↗

Non-oscillatory central differencing for hyperbolic conservation laws

Many of the recently developed high resolution schemes for hyperbolic conservation laws are based on upwind differencing. The building block for these schemes is the averaging of an appropriate Godunov solver; its time consuming part involves the field-by-field decomposition which is required in order to identify the direction of the wind. Instead, the use of the more robust Lax-Friedrichs (LxF) solver is proposed. The main advantage is simplicity: no Riemann problems are solved and hence field-by-field decompositions are avoided. The main disadvantage is the excessive numerical viscosity typical to the LxF solver. This is compensated for by using high-resolution MUSCL-type interpolants. Numerical experiments show that the quality of results obtained by such convenient central differencing is comparable with those of the upwind schemes.

Nessyahu, Haim↗

Unsteady Euler airfoil solutions using unstructured dynamic meshes

Two algorithms for the solution of the time-dependent Euler equations are presented for unsteady aerodynamic analysis of oscillating airfoils. Both algorithms were developed for use on an unstructured grid made up of triangles. The first flow solver involves a Runge-Kutta time-stepping scheme with a finite-volume spatial discretization that reduces to central differencing on a rectangular mesh. The second flow solver involves a modified Euler time-integration scheme with an upwind-biased spatial discretization based on the flux-vector splitting of Van Leer. The paper presents descriptions of the Euler solvers and dynamic mesh algorithm along with results which assess the capability.

Batina, John T.↗

Implicit flux-split Euler schemes for unsteady aerodynamic analysis involving unstructured dynamic meshes

Improved algorithms for the solution of the time-dependent Euler equations are presented for unsteady aerodynamic analysis involving unstructured dynamic meshes. The improvements have been developed recently to the spatial and temporal discretizations used by unstructured grid flow solvers. The spatial discretization involves a flux-split approach which is naturally dissipative and captures shock waves sharply with at most one grid point within the shock structure. The temporal discretization involves an implicit time-integration shceme using a Gauss-Seidel relaxation procedure which is computationally efficient for either steady or unsteady flow problems. For example, very large time steps may be used for rapid convergence to steady state, and the step size for unsteady cases may be selected for temporal accuracy rather than for numerical stability. Steady and unsteady flow results are presented for the NACA 0012 airfoil to demonstrate applications of the new Euler solvers. The unsteady results were obtained for the airfoil pitching harmonically about the quarter chord. The resulting instantaneous pressure distributions and lift and moment coefficients during a cycle of motion compare well with experimental data. The paper presents a description of the Euler solvers along with results and comparisons which assess the capability.

Batina, John T.↗

Three-dimensional flux-split Euler schemes involving unstructured dynamic meshes

Improved algorithms for the solution of the three-dimensional time-dependent Euler equations are presented for aerodynamic analysis involving unstructured dynamic meshes. The improvements have been developed recently to the spatial and temporal discretizations used by unstructured grid flow solvers. The spatial discretization involves a flux-split approach which is naturally dissipative and captures shock waves sharply with at most one grid point within the shock structure. The temporal discretization involves either an explicit time-integration scheme using a multi-stage Runge-Kutta procedure or an implicit time-integration scheme using a Gauss-Seidel relaxation procedure which is computationally efficient for either steady or unsteady flow problems. With the implicit Gauss-Seidel procedure, very large time steps may be used for rapid convergence to steady state, and the step size for unsteady cases may be selected for temporal accuracy rather than for numerical stability. Steady flow results are presented for both the NACA 0012 airfoil and the ONERA M6 wing to demonstrate applications of the new Euler solvers. The paper presents a description of the Euler solvers along with results and comparisons which assess the capability.

Batina, John T.↗

Non-oscillatory central differencing for hyperbolic conservation laws

Many of the recently developed high resolution schemes for hyperbolic conservation laws are based on upwind differencing. The building block for these schemes is the averaging of an appropriate Godunov solver; its time consuming part involves the field-by-field decomposition which is required in order to identify the direction of the wind. Instead, the use of the more robust Lax-Friedrichs (LxF) solver is proposed. The main advantage is simplicity: no Riemann problems are solved and hence field-by-field decompositions are avoided. The main disadvantage is the excessive numerical viscosity typical to the LxF solver. This is compensated for by using high-resolution MUSCL-type interpolants. Numerical experiments show that the quality of results obtained by such convenient central differencing is comparable with those of the upwind schemes.

Nessyahu, Haim↗

Implicit flux-split Euler schemes for unsteady aerodynamic analysis involving unstructured dynamic meshes

Improved algorithm for the solution of the time-dependent Euler equations are presented for unsteady aerodynamic analysis involving unstructured dynamic meshes. The improvements were developed recently to the spatial and temporal discretizations used by unstructured grid flow solvers. The spatial discretization involves a flux-split approach which is naturally dissipative and captures shock waves sharply with at most one grid point within the shock structure. The temporal discretization involves an implicit time-integration scheme using a Gauss-Seidel relaxation procedure which is computationally efficient for either steady or unsteady flow problems. For example, very large time steps may be used for rapid convergence to steady state, and the step size for unsteady cases may be selected for temporal accuracy rather than for numerical stability. Steady and unsteady flow results are presented for the NACA 0012 airfoil to demonstrate applications of the new Euler solvers. The unsteady results were obtained for the airfoil pitching harmonically about the quarter chord. The resulting instantaneous pressure distributions and lift and moment coefficients during a cycle of motion compare well with experimental data. A description of the Euler solvers is presented along with results and comparisons which assess the capability.

Batina, John T.↗

Three-dimensional flux-split Euler schemes involving unstructured dynamic meshes

Improved algorithms for the solution of the 3-D time dependent Euler equations are presented for aerodynamic analysis involving unstructured dynamic meshes. The improvements were developed recently to the spatial and temporal discretizations used by unstructured grid flow solvers. The spatial discretization involves a flux split approach which is naturally dissipative and captures shock waves sharply with at most one grid point within the shock structure. The temporal discretization involves either an explicit time integration scheme using a multistage Runge-Kutta procedure or an implicit time integration scheme using a Gauss-Seidel relaxation procedure which is computationally efficient for either steady or unsteady flow problems. With the implicit Gauss-Seidel procedure, very large time steps may be used for rapid convergence to steady state, and the step size for unsteady cases may be selected for temporal accuracy rather than for numerical stability. Steady flow results are presented for both the NACA 0012 airfoil and the ONERA M6 wing to demonstrate applications of the new Euler solvers. A description of the Euler solvers is presented along with results and comparisons which assess the capability.

Batina, John T.↗

Knowledge repositories for multiple uses

In the life cycle of a complex physical device or part, for example, the docking bay door of the Space Station, there are many uses for knowledge about the device or part. The same piece of knowledge might serve several uses. Given the quantity and complexity of the knowledge that must be stored, it is critical to maintain the knowledge in one repository, in one form. At the same time, because of quantity and complexity of knowledge that must be used in life cycle applications such as cost estimation, re-design, and diagnosis, it is critical to automate such knowledge uses. For each specific use, a knowledge base must be available and must be in a from that promotes the efficient performance of that knowledge base. However, without a single source knowledge repository, the cost of maintaining consistent knowledge between multiple knowledge bases increases dramatically; as facts and descriptions change, they must be updated in each individual knowledge base. A use-neutral representation of a hydraulic system for the F-111 aircraft was developed. The ability to derive portions of four different knowledge bases is demonstrated from this use-neutral representation: one knowledge base is for re-design of the device using a model-based reasoning problem solver; two knowledge bases, at different levels of abstraction, are for diagnosis using a model-based reasoning solver; and one knowledge base is for diagnosis using an associational reasoning problem solver. It was shown how updates issued against the single source use-neutral knowledge repository can be propagated to the underlying knowledge bases.

Williamson, Keith↗

The design/analysis of flows through turbomachinery: A viscous/inviscid approach

The development of a design/analysis flow solver at NASA Lewis Research Center is discussed. The solver is axisymmetric and can be run inviscidly with assumed or calculated blockages, or with the viscous terms computed. The blade forces for each blade row are computed from blade-to-blade solutions, correlated data or force model, or from a full three dimensional solution. Codes currently under development can be separated into three distinct elements: the turbomachinery interactive grid generator energy distribution restart code (TIGGERC), the interactive blade element geometry generator (IBEGG), and the viscous/inviscid multi-blade-row average passage flow solver (VIADAC). Several experimental test cases were run to validate the VIADAC code. The tests, representative of typical axial turbomachinery duct axisymmetric wind tunnel body problems, were conducted on an SR7 Spinner axisymmetric body, a NASA Rotor 67 Fan test bed, and a transonic boatail body. The results show the computations to be in good agreement with test data.

Miller, D. P.↗

AFE base flow computations

Hypersonic wake flows behind the Aeroassist Flight Experiment (AFE) geometry are analyzed using two Navier-Stokes flow solvers. Many of the AFE wake features observed in ballistic-range shadowgraphs are simulated using a simple, two-dimensional semicylinder geometry at moderate angles of attack. At free-stream conditions corresponding to a Hypersonic Free Flight Facility (HFFF) AFE experiment, the three-dimensional base flow for the AFE geometry is computed using an ideal-gas, Navier-Stokes solver. The computed results agree reasonably well with the shadowgraphs taken at the HFFF. An ideal-gas and a nonequilibrium Navier-Stokes solver have been coupled and applied to the complete flow around the AFE vehicle at the free-stream conditions corresponding to a nomial trajectory point. Limitations of the coupled ideal-gas and nonequilibrium solution are discussed. The nonequilibrium base flow solution is analyzed for the wake radiation and the radiation profiles along various lines of sight are compared. Finally, the wake unsteadiness is predicted using experimental correlations and the numerical solutions. An adaptive grid code, SAGE, has been used in all the simulations to enhance the solution accuracy. The grid adaptation is found to be necessary in obtaining base flow solutions with accurate flow features.

Venkatapathy, Ethiraj↗

Accuracy of an unstructured-grid upwind-Euler algorithm for the ONERA M6 wing

Improved algorithms for the solution of the three-dimensional, time-dependent Euler equations are presented for aerodynamic analysis involving unstructured dynamic meshes. The improvements have been developed recently to the spatial and temporal discretizations used by unstructured-grid flow solvers. The spatial discretization involves a flux-split approach that is naturally dissipative and captures shock waves sharply with at most one grid point within the shock structure. The temporal discretization involves either an explicit time-integration scheme using a multistage Runge-Kutta procedure or an implicit time-integration scheme using a Gauss-Seidel relaxation procedure, which is computationally efficient for either steady or unsteady flow problems. With the implicit Gauss-Seidel procedure, very large time steps may be used for rapid convergence to steady state, and the step size for unsteady cases may be selected for temporal accuracy rather than for numerical stability. Steady flow results are presented for both the NACA 0012 airfoil and the Office National d'Etudes et de Recherches Aerospatiales M6 wing to demonstrate applications of the new Euler solvers. The paper presents a description of the Euler solvers along with results and comparisons that assess the capability.

Batina, John T.↗