SEARCH · Search NASA

Results for “Computer Algebra”

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.

SourceResearch connectionFrom yearThrough year

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

At least 289 records · Page 16

All sources NASA NTRS DOE OSTI

NASA NTRS1990

Improved Coupled Fluid/Structural Dynamical Model

Improved algorithm developed for simulation of coupled motions of fluids and structures. Minimum requirement for correct simulation of damping is forces and velocities at interface compatible in models of structure and fluid at each time step. Improved algorithm, conforms to this requirement, involves fluid-transient model, structural modal/transient model, and an algebraic impedance/coupling subalgorithm. Use of this algorithm greatly improves computational stability.

Fenwick, James R.↗

NASA NTRS1990

Finding the complete path and weight enumerators of convolutional codes

A method for obtaining the complete path enumerator T(D, L, I) of a convolutional code is described. A system of algebraic equations is solved, using a new algorithm for computing determinants, to obtain T(D, L, I) for the (7,1/2) NASA standard code. Generating functions, derived from T(D, L, I) are used to upper bound Viterbi decoder error rates. This technique is currently feasible for constraint length K less than 10 codes. A practical, fast algorithm is presented for computing the leading nonzero coefficients of the generating functions used to bound the performance of constraint length K less than 20 codes. Code profiles with about 50 nonzero coefficients are obtained with this algorithm for the experimental K = 15, rate 1/4, code in the Galileo mission and for the proposed K = 15, rate 1/6, 2-dB code.

Onyszchuk, I.↗

NASA NTRS1990

Numerical simulation of the incompressible internal flow through a tilting disk valve

A numerical simulation of the incompressible viscous flow through a prosthetic tilting disk heart valve is presented in order to demonstrate the current capability to model unsteady flows with moving boundaries. Both steady and unsteady flow calculations are performed by solving the incompressible Navier-Stokes equations in three-dimensional generalized curvilinear coordinates. In order to handle the moving boundary problems, the chimera grid embedding scheme which decomposes a complex computational domain into several simple subdomains is used. An algebraic turbulence model for internal flows is incorporated to reach the physiological values of Reynolds number. Good agreement is obtained between the numerical results and experimental measurements. It is found that the tilting disk valve causes large regions of separated flow, and regions of high shear.

Chang, I-Dee↗

NASA NTRS1991

Simulation of blood flow through an artificial heart

A numerical simulation of the incompressible viscous flow through a prosthetic tilting disk heart valve is presented in order to demonstrate the current capability to model unsteady flows with moving boundaries. Both steady state and unsteady flow calculations are done by solving the incompressible Navier-Stokes equations in 3-D generalized curvilinear coordinates. In order to handle the moving boundary problems, the chimera grid embedding scheme which decomposes a complex computational domain into several simple subdomains is used. An algebraic turbulence model for internal flows is incorporated to reach the physiological values of Reynolds number. Good agreement is obtained between the numerical results and experimental measurements. It is found that the tilting disk valve causes large regions of separated flow, and regions of high shear.

Kiris, Cetin↗

NASA NTRS1991

Three-dimensional shock wave-turbulent boundary layer interactions generated by a sharp fin at Mach 4

This paper describes a combined experimental and theoretical study of three-dimensional swept shock wave-turbulent boundary layer interactions at Mach 4 generated by a sharp fin of angles alpha equals 16 and 20 degrees. The theoretical model is the three-dimensional compressible Reynolds-averaged Navier-Stokes equations with turbulence incorporated through the algebraic eddy viscosity model of Baldwin and Lomax. Previous computations have been performed by Horstman using the Baldwin-Lomax, Cebeci-Smith and Jones Launder models. Computed results for the surface pressure, skin friction and streamline angles are compared with experiment and previous numerical results. The present results display good agreement with experimental data for surface pressure and surface flow direction. All turbulence models fail to accurately predict the peak skin friction. The computed flowfields are in agreement with many of the features of the quasi-conical flowfield model of Settles.

Knight, Doyle D.↗

NASA NTRS1992

Turbulence modelling in CFD: Present status, future prospects

Information is given in viewgraph form for turbulence modeling in computational fluid dynamics (CFD). The Eddy Viscosity Models (EVM), Algebraic Second Moment Closures (ASM), and Differential Second-Moment Closures (DSM) are considered. It is concluded that EVM's, ASM's, and DSM's will remain in use, though with a steady decline in importance of EVM's and ASM's in favor of DSM's. Improved versions of low-Re two-equation EVM's should lead to more reliable predictions of separated flows than are achievable at present. Further refinement of sub-models in second moment closures can be expected throughout this decade. There will be increasing attention given to interfacing SMC with higher order approaches such as LES, and an increased use of two-time-scale schemes providing distinct time scales for large and fairly small eddies.

Launder, Brian E.↗

NASA NTRS1992

Variable-complexity aerodynamic optimization of an HSCT wing using structural wing-weight equations

A new approach for combining conceptual and preliminary design techniques for wing optimization is presented for the high-speed civil transport (HSCT). A wing-shape parametrization procedure is developed which allows the linking of planform and airfoil design variables. Variable-complexity design strategies are used to combine conceptual and preliminary-design approaches, both to preserve interdisciplinary design influences and to reduce computational expense. In the study, conceptual-design-level algebraic equations are used to estimate aircraft weight, supersonic wave drag, friction drag and drag due to lift. The drag due to lift and wave drag are also evaluated using more detailed, preliminary-design-level techniques. The methodology is applied to the minimization of the gross weight of an HSCT that flies at Mach 3.0 with a range of 6500 miles.

Hutchison, M. G.↗

NASA NTRS1992

Numerical analysis of hypersonic turbulent film cooling flows

As a building block, numerical capabilities for predicting heat flux and turbulent flowfields of hypersonic vehicles require extensive model validations. Computational procedures for calculating turbulent flows and heat fluxes for supersonic film cooling with parallel slot injections are described in this study. Two injectant mass flow rates with matched and unmatched pressure conditions using the database of Holden et al. (1990) are considered. To avoid uncertainties associated with the boundary conditions in testing turbulence models, detailed three-dimensional flowfields of the injection nozzle were calculated. Two computational fluid dynamics codes, GASP and FDNS, with the algebraic Baldwin-Lomax and k-epsilon models with compressibility corrections were used. It was found that the B-L model which resolves near-wall viscous sublayer is very sensitive to the inlet boundary conditions at the nozzle exit face. The k-epsilon models with improved wall functions are less sensitive to the inlet boundary conditions. The testings show that compressibility corrections are necessary for the k-epsilon model to realistically predict the heat fluxes of the hypersonic film cooling problems.

Chen, Y. S.↗

NASA NTRS1993

General-Purpose Time-Accurate Adaptive-Grid Method

Adaptive-grid method provides for generation of time-accurate grids used to solve wide variety of problems numerically. Intended use in computation of compressible flows. Part of solution method including algebraic grid-movement scheme; algorithm solving, by use of explicit numerical-integration scheme, Euler equations of unsteady flow; and temporal coupling routine utilizing grid-prediction/correction method to link dynamic grid with Euler-equation-solving algorithm. Improves ability to adapt grid to multiple features of solution and involves use of coarse grid in prediction stage of temporal coupling reducing central-processing-unit cost of obtaining new grid.

Bockelie, Michael J.↗

NASA NTRS1995

Heat transfer predictions for two turbine nozzle geometries at high Reynolds and Mach numbers

Predictions of turbine vane and endwall heat transfer and pressure distributions are compared with experimental measurements for two vane geometries. The differences in geometries were due to differences in the hub profile, and both geometries were derived from the design of a high rim speed turbine (HRST). The experiments were conducted in the Isentropic Light Piston Facility (ILPF) at Pyestock at a Reynolds number of 5.3 x 10(exp 6), a Mach number of 1.2, and a wall-to-gas temperature ratio of 0.66. Predictions are given for two different steady-state three-dimensional Navier-Stokes computational analyses. C-type meshes were used, and algebraic models were employed to calculate the turbulent eddy viscosity. The effects of different turbulence modeling assumptions on the predicted results are examined. Comparisons are also given between predicted and measured total pressure distributions behind the vane. The combination of realistic engine geometries and flow conditions proved to be quite demanding in terms of the convergence of the CFD solutions. An appropriate method of grid generation, which resulted in consistently converged CFD solutions, was identified.

Boyle, R. J.↗

NASA NTRS1996

Simplified Phased-Mission System Analysis for Systems with Independent Component Repairs

Accurate analysis of reliability of system requires that it accounts for all major variations in system's operation. Most reliability analyses assume that the system configuration, success criteria, and component behavior remain the same. However, multiple phases are natural. We present a new computationally efficient technique for analysis of phased-mission systems where the operational states of a system can be described by combinations of components states (such as fault trees or assertions). Moreover, individual components may be repaired, if failed, as part of system operation but repairs are independent of the system state. For repairable systems Markov analysis techniques are used but they suffer from state space explosion. That limits the size of system that can be analyzed and it is expensive in computation. We avoid the state space explosion. The phase algebra is used to account for the effects of variable configurations, repairs, and success criteria from phase to phase. Our technique yields exact (as opposed to approximate) results. We demonstrate our technique by means of several examples and present numerical results to show the effects of phases and repairs on the system reliability/availability.

Somani, Arun K.↗

NASA NTRS1997

Sensitivity Analysis and Optimization of Aerodynamic Configurations with Blend Surfaces

A novel (geometrical) parametrization procedure using solutions to a suitably chosen fourth order partial differential equation is used to define a class of airplane configurations. Inclusive in this definition are surface grids, volume grids, and grid sensitivity. The general airplane configuration has wing, fuselage, vertical tail and horizontal tail. The design variables are incorporated into the boundary conditions, and the solution is expressed as a Fourier series. The fuselage has circular cross section, and the radius is an algebraic function of four design parameters and an independent computational variable. Volume grids are obtained through an application of the Control Point Form method. A graphic interface software is developed which dynamically changes the surface of the airplane configuration with the change in input design variable. The software is made user friendly and is targeted towards the initial conceptual development of any aerodynamic configurations. Grid sensitivity with respect to surface design parameters and aerodynamic sensitivity coefficients based on potential flow is obtained using an Automatic Differentiation precompiler software tool ADIFOR. Aerodynamic shape optimization of the complete aircraft with twenty four design variables is performed. Unstructured and structured volume grids and Euler solutions are obtained with standard software to demonstrate the feasibility of the new surface definition.

Thomas, A. M.↗

NASA NTRS2004

Rapid Airplane Parametric Input Design(RAPID)

An efficient methodology is presented for defining a class of airplane configurations. Inclusive in this definition are surface grids, volume grids, and grid sensitivity. A small set of design parameters and grid control parameters govern the process. The general airplane configuration has wing, fuselage, vertical tail, horizontal tail, and canard components. The wing, tail, and canard components are manifested by solving a fourth-order partial differential equation subject to Dirichlet and Neumann boundary conditions. The design variables are incorporated into the boundary conditions, and the solution is expressed as a Fourier series. The fuselage has circular cross section, and the radius is an algebraic function of four design parameters and an independent computational variable. Volume grids are obtained through an application of the Control Point Form method. Grid sensitivity is obtained by applying the automatic differentiation precompiler ADIFOR to software for the grid generation. The computed surface grids, volume grids, and sensitivity derivatives are suitable for a wide range of Computational Fluid Dynamics simulation and configuration optimizations.

Smith, Robert E.↗

NASA NTRS2003

Approaches to Cycle Analysis and Performance Metrics

The following notes were prepared as part of an American Institute of Aeronautics and Astronautics (AIAA) sponsored short course entitled Air Breathing Pulse Detonation Engine (PDE) Technology. The course was presented in January of 2003, and again in July of 2004 at two different AIAA meetings. It was taught by seven instructors, each of whom provided information on particular areas of PDE research. These notes cover two areas. The first is titled Approaches to Cycle Analysis and Performance Metrics. Here, the various methods of cycle analysis are introduced. These range from algebraic, thermodynamic equations, to single and multi-dimensional Computational Fluid Dynamic (CFD) solutions. Also discussed are the various means by which performance is measured, and how these are applied in a device which is fundamentally unsteady. The second topic covered is titled PDE Hybrid Applications. Here the concept of coupling a PDE to a conventional turbomachinery based engine is explored. Motivation for such a configuration is provided in the form of potential thermodynamic benefits. This is accompanied by a discussion of challenges to the technology.

Parson, Daniel E.↗

NASA NTRS1985

Three-dimensional vibration analysis of a uniform beam with offset inertial masses at the ends

Analysis of a flexible beam with displaced end-located inertial masses is presented. The resulting three-dimensional mode shape is shown to consist of two one-plane bending modes and one torsional mode. These three components of the mode shapes are shown to be linear combinations of trigonometric and hyperbolic sine and cosine functions. Boundary conditions are derived to obtain nonlinear algebraic equations through kinematic coupling of the general solutions of the three governing partial differential equations. A method of solution which takes these boundary conditions into account is also presented. A computer program has been written to obtain unique solutions to the resulting nonlinear algebraic equations. This program, which calculates natural frequencies and three-dimensional mode shapes for any number of modes, is presented and discussed.

Robertson, D. K.↗

NASA NTRS1993

Turbulence modeling of free shear layers for high-performance aircraft

The High Performance Aircraft (HPA) Grand Challenge of the High Performance Computing and Communications (HPCC) program involves the computation of the flow over a high performance aircraft. A variety of free shear layers, including mixing layers over cavities, impinging jets, blown flaps, and exhaust plumes, may be encountered in such flowfields. Since these free shear layers are usually turbulent, appropriate turbulence models must be utilized in computations in order to accurately simulate these flow features. The HPCC program is relying heavily on parallel computers. A Navier-Stokes solver (POVERFLOW) utilizing the Baldwin-Lomax algebraic turbulence model was developed and tested on a 128-node Intel iPSC/860. Algebraic turbulence models run very fast, and give good results for many flowfields. For complex flowfields such as those mentioned above, however, they are often inadequate. It was therefore deemed that a two-equation turbulence model will be required for the HPA computations. The k-epsilon two-equation turbulence model was implemented on the Intel iPSC/860. Both the Chien low-Reynolds-number model and a generalized wall-function formulation were included.

Sondak, Douglas L.↗

NASA NTRS2002

Software for Refining or Coarsening Computational Grids

A computer program performs calculations for refinement or coarsening of computational grids of the type called 'structured' (signifying that they are geometrically regular and/or are specified by relatively simple algebraic expressions). This program is designed to facilitate analysis of the numerical effects of changing structured grids utilized in computational fluid dynamics (CFD) software. Unlike prior grid-refinement and -coarsening programs, this program is not limited to doubling or halving: the user can specify any refinement or coarsening ratio, which can have a noninteger value. In addition to this ratio, the program accepts, as input, a grid file and the associated restart file, which is basically a file containing the most recent iteration of flow-field variables computed on the grid. The program then refines or coarsens the grid as specified, while maintaining the geometry and the stretching characteristics of the original grid. The program can interpolate from the input restart file to create a restart file for the refined or coarsened grid. The program provides a graphical user interface that facilitates the entry of input data for the grid-generation and restart-interpolation routines.

Daines, Russell↗

NASA NTRS2002

Software for Refining or Coarsening Computational Grids

A computer program performs calculations for refinement or coarsening of computational grids of the type called "structured" (signifying that they are geometrically regular and/or are specified by relatively simple algebraic expressions). This program is designed to facilitate analysis of the numerical effects of changing structured grids utilized in computational fluid dynamics (CFD) software. Unlike prior grid-refinement and -coarsening programs, this program is not limited to doubling or halving: the user can specify any refinement or coarsening ratio, which can have a noninteger value. In addition to this ratio, the program accepts, as input, a grid file and the associated restart file, which is basically a file containing the most recent iteration of flow-field variables computed on the grid. The program then refines or coarsens the grid as specified, while maintaining the geometry and the stretching characteristics of the original grid. The program can interpolate from the input restart file to create a restart file for the refined or coarsened grid. The program provides a graphical user interface that facilitates the entry of input data for the grid-generation and restart-interpolation routines.

Daines, Russell↗