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At least 721 records · Page 40

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NASA NTRS1984

A numerical study of the 2- and 3-dimensional unsteady Navier-Stokes equations in velocity-vorticity variables using compact difference schemes

A compact finite-difference approximation to the unsteady Navier-Stokes equations in velocity-vorticity variables is used to numerically simulate a number of flows. These include two-dimensional laminar flow of a vortex evolving over a flat plate with an embedded cavity, the unsteady flow over an elliptic cylinder, and aspects of the transient dynamics of the flow over a rearward facing step. The methodology required to extend the two-dimensional formulation to three-dimensions is presented.

Gatski, T. B.↗

NASA NTRS1984

A numerical study of the two- and three-dimensional unsteady Navier-Stokes equations in velocity-vorticity variables using compact difference schemes

Gatski, T. B.↗

NASA NTRS1988

Stochastic simulation of charged particle transport on the massively parallel processor

Computations of cosmic-ray transport based upon finite-difference methods are afflicted by instabilities, inaccuracies, and artifacts. To avoid these problems, researchers developed a Monte Carlo formulation which is closely related not only to the finite-difference formulation, but also to the underlying physics of transport phenomena. Implementations of this approach are currently running on the Massively Parallel Processor at Goddard Space Flight Center, whose enormous computing power overcomes the poor statistical accuracy that usually limits the use of stochastic methods. These simulations have progressed to a stage where they provide a useful and realistic picture of solar energetic particle propagation in interplanetary space.

Earl, James A.↗

NASA NTRS1948

Determination of stresses in gas-turbine disks subjected to plastic flow and creep

A finite-difference method previously presented for computing elastic stresses in rotating disks is extended to include the computation of the disk stresses when plastic flow and creep are considered. A finite-difference method is employed to eliminate numerical integration and to permit nontechnical personnel to make the calculations with a minimum of engineering supervision. Illustrative examples are included to facilitate explanation of the procedure by carrying out the computations on a typical gas-turbine disk through a complete running cycle. The results of the numerical examples presented indicate that plastic flow markedly alters the elastic-stress distribution.

Millenson, M B↗

NASA NTRS1979

Application of the method of integral relations to unsteady fluid flow problems with shocks

A mixed method using both the method of integral relations and the finite difference technique is developed for the solution of unsteady flow problems. The integral relations method is based upon a chosen interpolating function dependent only on the time domain. The resulting local semidiscrete finite element equations obtained are assembled into a global form. The spatial derivatives at the nodes are replaced by finite difference operators and the discretized nonlinear algebraic system is solved by an iterative scheme. Solutions are obtained for the one-dimensional gasdynamics equation, the one-dimensional wave equation and Burger's model of turbulence. Agreement with other numerical and analytical solutions is excellent for the gasdynamics problem and satisfactory for the Burger equation in cases of small viscous effects.

Wadia, A. R.↗

NASA NTRS1984

Assessment of a 3-D boundary layer code to predict heat transfer and flow losses in a turbine

Zonal concepts are utilized to delineate regions of application of three-dimensional boundary layer (DBL) theory. The zonal approach requires three distinct analyses. A modified version of the 3-DBL code named TABLET is used to analyze the boundary layer flow. This modified code solves the finite difference form of the compressible 3-DBL equations in a nonorthogonal surface coordinate system which includes coriolis forces produced by coordinate rotation. These equations are solved using an efficient, implicit, fully coupled finite difference procedure. The nonorthogonal surface coordinate system is calculated using a general analysis based on the transfinite mapping of Gordon which is valid for any arbitrary surface. Experimental data is used to determine the boundary layer edge conditions. The boundary layer edge conditions are determined by integrating the boundary layer edge equations, which are the Euler equations at the edge of the boundary layer, using the known experimental wall pressure distribution. Starting solutions along the inflow boundaries are estimated by solving the appropriate limiting form of the 3-DBL equations.

Anderson, O. L.↗

NASA NTRS1994

Computation of helicopter rotor acoustics in forward flight

This paper presents a new method for computing acoustic signals from helicopter rotors in forward flight. The aerodynamic and acoustic solutions in the near field are computed with a finite-difference solver for the Euler equations. A nonrotating cylindrical Kirchhoff surface is then placed around the entire rotor system. This Kirchhoff surface moves subsonically with the rotor in forward flight. The finite-difference solution is interpolated onto this cylindrical surface at each time step and a Kirchhoff integration is used to carry the acoustic signal to the far field. Computed values for high-speed impulsive noise show excellent agreement with model-rotor and flight-test experimental data. Results from the new method offer high accuracy with reasonable computer resource requirements.

Strawn, Roger↗

NASA NTRS1984

The Prediction of Transonic Flows on an Advancing Rotor

The object of this investigation was to find and demonstrate a means of performing efficient finite-difference computations of rotor loading for a trimmed rotor in high-speed, forward flight. The essence of the scheme that was developed is a loose-coupled iteration procedure between a finite difference and a comprehensive integral rotor code. The coupling involves a transfer of appropriate load and inflow data on the advancing side between the two codes such that consistency maintained. Sample computations, including a limited comparison with model rotor data, are presented. The scheme converges rapidly. However, even one iteration with this scheme can provide sufficient accuracy for many purposes.

Tung, Chee↗

NASA NTRS1978

The development of a three-dimensional partially elliptic flow computer program for combustor research

A three dimensional, partially elliptic, computer program was developed. Without requiring three dimensional computer storage locations for all flow variables, the partially elliptic program is capable of predicting three dimensional combustor flow fields with large downstream effects. The program requires only slight increase of computer storage over the parabolic flow program from which it was developed. A finite difference formulation for a three dimensional, fully elliptic, turbulent, reacting, flow field was derived. Because of the negligible diffusion effects in the main flow direction in a supersonic combustor, the set of finite-difference equations can be reduced to a partially elliptic form. Only the pressure field was governed by an elliptic equation and requires three dimensional storage; all other dependent variables are governed by parabolic equations. A numerical procedure which combines a marching integration scheme with an iterative scheme for solving the elliptic pressure was adopted.

Pan, Y. S.↗

NASA NTRS1971

Numerical calculation of turbulent boundary layers including suction or injection with binary diffusion.

The modelling of turbulent transport processes with an eddy viscosity representation of the inner, wall region for cases with suction or injection is considered in detail. It is shown how the van Driest solid wall model can be logically extended for such cases. Further, a new inductive model is developed. Finite difference calculations using the new inductive model are shown to be in good agreement with experimental data over a wide range of conditions. Lastly, a new method for calculating the wall shear within a finite difference solution is developed. This procedure greatly relaxes the requirement for fine grid spacing in the vertical direction.

Schetz, J. A.↗

NASA NTRS1976

A block iterative finite element algorithm for numerical solution of the steady-state, compressible Navier-Stokes equations

An iterative method for numerically solving the time independent Navier-Stokes equations for viscous compressible flows is presented. The method is based upon partial application of the Gauss-Seidel principle in block form to the systems of nonlinear algebraic equations which arise in construction of finite element (Galerkin) models approximating solutions of fluid dynamic problems. The C deg-cubic element on triangles is employed for function approximation. Computational results for a free shear flow at Re = 1,000 indicate significant achievement of economy in iterative convergence rate over finite element and finite difference models which employ the customary time dependent equations and asymptotic time marching procedure to steady solution. Numerical results are in excellent agreement with those obtained for the same test problem employing time marching finite element and finite difference solution techniques.

Cooke, C. H.↗

NASA NTRS1975

Remote sensing applied to numerical modelling

Progress and remaining difficulties in the construction of predictive mathematical models of large bodies of water as ecosystems are reviewed. Surface temperature is at present the only variable than can be measured accurately and reliably by remote sensing techniques, but satellite infrared data are of sufficient resolution for macro-scale modeling of oceans and large lakes, and airborne radiometers are useful in meso-scale analysis (of lakes, bays, and thermal plumes). Finite-element and finite-difference techniques applied to the solution of relevant coupled time-dependent nonlinear partial differential equations are compared, and the specific problem of the Biscayne Bay and environs ecosystem is tackled in a finite-differences treatment using the rigid-lid model and a rigid-line grid system.

Sengupta, S.↗

NASA NTRS1977

A block iterative finite element algorithm for numerical solution of the steady-state, compressible Navier-Stokes equations

An iterative method for numerically solving the time independent Navier-Stokes equations for viscous compressible flows is presented. The method is based upon partial application of the Gauss-Seidel principle in block form to the systems of the nonlinear algebraic equations which arise in construction of finite element (Galerkin) models approximating solutions of fluid dynamic problems. The continuous cubic element on triangles is employed for function approximation. Computational results for a free shear flow at Re = 1000 indicate significant achievement of economy in iterative convergence rate over finite element and finite difference models which employ the customary time dependent equations and symptotic time marching procedure to steady solution. Numerical results are in excellent agreement with those obtained for the same test problem employing time marching finite element and finite difference solution techniques.

Cooke, C. H.↗

NASA NTRS1989

Interpretation of F106B and CV580 in-flight lightning data and form factor determination

Two topics of in-flight aircraft/lightning interaction are addressed. The first is the analysis of measured data from the NASA F106B Thunderstorm Research Aircraft and the CV580 research program run by the FAA and Wright-Patterson Air Force Base. The CV580 data was investigated in a mostly qualitative sense, while the F106B data was subjected to both statistical and quantitative analysis using linear triggered lightning finite difference models. The second main topic is the analysis of field mill data and the calibration of the field mill systems. The calibration of the F106B field mill system was investigated using an improved finite difference model of the aircraft having a spatial resolution of one-quarter meter. The calibration was applied to measured field mill data acquired during the 1985 thunderstorm season. The experimental determination of form factors useful for field mill calibration was also investigated both experimentally and analytically. The experimental effort involved the use of conducting scale models and an electrolytic tank. An analytic technique was developed to aid in the understanding of the experimental results.

Rudolph, T.↗

NASA NTRS1978

A procedure for analyzing transonic flow over harmonically oscillating airfoils

Finite difference procedures were successfully used to solve the steady transonic flow about airfoils and appear to provide a practical means for calculating the corresponding unsteady flow. The purpose of the paper is to describe a finite difference procedure derived from the equations for the potential flow by assuming small perturbations and harmonic motion. The velocity potential is divided into steady and unsteady parts, and the resulting unsteady equation is linearized on the basis of small amplitudes of oscillation. The steady velocity potential, which must be calculated first, is described by the classical nonlinear transonic differential equation.

Weatherill, W. H.↗

NASA NTRS1992

Dispersion-relation-preserving schemes for computational aeroacoustics

Finite difference schemes that have the same dispersion relations as the original partial differential equations are referred to as dispersion-relation-preserving (DRP) schemes. A method to construct time marching DRP schemes by optimizing the finite difference approximations of the space and time derivatives in the wave number and frequency space is presented. A sequence of numerical simulations is then performed.

Tam, Christopher K. W.↗

NASA NTRS2016

Optimization of Turbine Engine Cycle Analysis with Analytic Derivatives

A new engine cycle analysis tool, called Pycycle, was built using the OpenMDAO framework. Pycycle provides analytic derivatives allowing for an efficient use of gradient-based optimization methods on engine cycle models, without requiring the use of finite difference derivative approximation methods. To demonstrate this, a gradient-based design optimization was performed on a turbofan engine model. Results demonstrate very favorable performance compared to an optimization of an identical model using finite-difference approximated derivatives.

OpenMDAO↗

NASA NTRS1988

Shape sensitivity analysis of flutter response of a laminated wing

A method is presented for calculating the shape sensitivity of a wing aeroelastic response with respect to changes in geometric shape. Yates' modified strip method is used in conjunction with Giles' equivalent plate analysis to predict the flutter speed, frequency, and reduced frequency of the wing. Three methods are used to calculate the sensitivity of the eigenvalue. The first method is purely a finite difference calculation of the eigenvalue derivative directly from the solution of the flutter problem corresponding to the two different values of the shape parameters. The second method uses an analytic expression for the eigenvalue sensitivities of a general complex matrix, where the derivatives of the aerodynamic, mass, and stiffness matrices are computed using a finite difference approximation. The third method also uses an analytic expression for the eigenvalue sensitivities, but the aerodynamic matrix is computed analytically. All three methods are found to be in good agreement with each other. The sensitivities of the eigenvalues were used to predict the flutter speed, frequency, and reduced frequency. These approximations were found to be in good agreement with those obtained using a complete reanalysis.

Bergen, Fred D.↗