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At least 937 records · Page 52

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NASA NTRS1988

An explicit Runge-Kutta method for unsteady rotor/stator interaction

A quasi-three-dimensional rotor/stator analysis has been developed for blade-to-blade flows in turbomachinery. The analysis solves the unsteady Euler or thin-layer Navier-Stokes equations in a body-fitted coordinate system. It accounts for the effects of rotation, radius change, and stream-surface thickness. The Baldwin-Lomax eddy-viscosity model is used for turbulent flows. The equations are integrated in time using a four-stage Runge-Kutta scheme with a constant timestep. Results are shown for the first stage of the Space Shuttle Main Engine high pressure fuel turbopump. Euler and Navier-Stokes results are compared on the scaled single- and multi-passage machine. The method is relatively fast and the quasi-three-dimensional formulation is applicable to a wide range of turbomachinery geometries.

Jorgenson, Philip C. E.↗

NASA NTRS1987

A numerical method for the solution of three dimensional, incompressible, viscous flows over slender bodies

A marching iterative method for the solution of the three dimensional, incompressibhle, steady and parabolized Navier-Stokes equations is described. The equations are written in primitive variables and discretized in general axisymmetric orthogonal coordinate systems. The coupled set of finite-difference equations are solved without any splitting or factorization errors. Moreover, the continuity equation and the two crossflow momentum equations are exactly satisfied at every step of the iterative process. The solution scheme is equivalent to the solution of one Poisson equation by the Successive Plane Over Relaxation method and has good convergence properties. Other existing solution methods resemble a Jacobi-type iterative scheme and therefore are less efficient. Numerical experiments include the laminar, incompressible flow over prolate spheroids at incidence.

Rosenfeld, Moshe↗

NASA NTRS1988

Dual periodicity of the Jovian magnetosphere

Using data from the 1979 Voyager flybys of Jupiter and two sets of ground-based observations of the Io torus, this paper presents an extensive analysis concerning the nature of the second magnetospheric periodicity of the Jupiter's magnetic field, along with a definition of a new Jovian matching coordinate system (referred to as system IV). It is shown that available independent data sets covering a time interval of 4 years, which either drift or show no particular organization in system III, fit mutually consistent patterns in system IV. Provisional values are derived for a transformation between systems III and IV. It is emphasized that system IV needs to be tested against additional data before its durability is assured.

Sandel, B. R.↗

NASA NTRS1989

Algorithm For Hypersonic Flow In Chemical Equilibrium

Implicit, finite-difference, shock-capturing algorithm calculates inviscid, hypersonic flows in chemical equilibrium. Implicit formulation chosen because overcomes limitation on mathematical stability encountered in explicit formulations. For dynamical portion of problem, Euler equations written in conservation-law form in Cartesian coordinate system for two-dimensional or axisymmetric flow. For chemical portion of problem, equilibrium state of gas at each point in computational grid determined by minimizing local Gibbs free energy, subject to local conservation of molecules, atoms, ions, and total enthalpy. Major advantage: resulting algorithm naturally stable and captures strong shocks without help of artificial-dissipation terms to damp out spurious numerical oscillations.

Palmer, Grant↗

NASA NTRS1988

A transonic interactive boundary-layer theory for laminar and turbulent flow over swept wings

A 3-D laminar and turbulent boundary-layer method is developed for compressible flow over swept wings. The governing equations and curvature terms are derived in detail for a nonorthogonal, curvilinear coordinate system. Reynolds shear-stress terms are modeled by the Cebeci-Smith eddy-viscosity formulation. The governing equations are descretized using the second-order accurate, predictor-corrector finite-difference technique of Matsuno, which has the advantage that the crossflow difference formulas are formed independent of the sign of the crossflow velocity component. The method is coupled with a full potential wing/body inviscid code (FLO-30) and the inviscid-viscous interaction is performed by updating the original wing surface with the viscous displacement surface calculated by the boundary-layer code. The number of these global iterations ranged from five to twelve depending on Mach number, sweep angle, and angle of attack. Several test cases are computed by this method and the results are compared with another inviscid-viscous interaction method (TAWFIVE) and with experimental data.

Woodson, Shawn H.↗

NASA NTRS1988

Three-dimensional multigrid algorithms for the flux-split Euler equations

The Full Approximation Scheme (FAS) multigrid method is applied to several implicit flux-split algorithms for solving the three-dimensional Euler equations in a body fitted coordinate system. Each of the splitting algorithms uses a variation of approximate factorization and is implemented in a finite volume formulation. The algorithms are all vectorizable with little or no scalar computation required. The flux vectors are split into upwind components using both the splittings of Steger-Warming and Van Leer. The stability and smoothing rate of each of the schemes are examined using a Fourier analysis of the complete system of equations. Results are presented for three-dimensional subsonic, transonic, and supersonic flows which demonstrate substantially improved convergence rates with the multigrid algorithm. The influence of using both a V-cycle and a W-cycle on the convergence is examined.

Anderson, W. Kyle↗

NASA NTRS1988

The evolution of AAOE observed constituents with the polar vortex

One of the difficulties in determining constituent trends from the ER-2 flight data is the large amount of day to day variability generated by the motion of the polar vortex. To reduce this variability, the observations have been transformed into the conservative (Lagrangian) reference frames consisting of the coordinate pairs, potential temperature (PT) and potential vorticity (PV), or PT and N2O. The requirement of only two independent coordinates rests on the assumption that constituent distributions and their chemical processes are nearly zonal in that coordinate system. Flight data is used everywhere for these transformation except for potential vorticity. Potential vorticity is determined from level flight segments, and NMC PV values during flight dives and takeoffs are combined with flight data in a smooth fashion.

Schoeberl, Mark R.↗

NASA NTRS1989

Numerical simulation and comparison of symmetrical/supercritical airfoils for the near tip region of a helicopter in forward flight

Aerodynamic loads on a multi-bladed helicopter rotor in forward flight at transonic tip conditions are calculated. The unsteady, three-dimensional, time-accurate compressible Reynolds-averaged thin layer Navier-Stokes equations are solved in a rotating coordinate system on a body-conformed, curvilinear grid of C-H topology. Detailed boundary layer and global numerical comparisons of NACA-0012 symmetrical and CAST7-158 supercritical airfoils are made under identical forward flight conditions. The rotor wake effects are modeled by applying a correction to the geometric angle of attack of the blade. This correction is obtained by computing the local induced downwash velocity with a free wake analysis program. The calculations are performed on the Numerical Aerodynamic Simulation Cray 2 and the VPS32 (a derivative of a Cyber 205 at the Langley Research Center) for a model helicopter rotor in forward flight.

Badavi, F. F.↗

NASA NTRS1988

An expert system for restructurable control

Work in progrss on an expert system which restructures and tunes control systems online in real-time is presented. The expert system coordinates the different methods involved in redesigning and implementing the control strategies due to plant changes.

Litt, Jonathan↗

NASA NTRS1989

Inverse wing design in transonic flow including viscous interaction

Several inverse methods were compared and initial results indicate that differences in results are primarily due to coordinate systems and fuselage representations and not to design procedures. Further, results from a direct-inverse method that includes 3-D wing boundary layer effects, wake curvature, and wake displacement are represented. These results show that boundary layer displacements must be included in the design process for accurate results.

Carlson, Leland A.↗

NASA NTRS1989

A 3-dimensional finite-difference method for calculating the dynamic coefficients of seals

A method to calculate the dynamic coefficients of seals with arbitrary geometry is presented. The Navier-Stokes equations are used in conjunction with the k-e turbulence model to describe the turbulent flow. These equations are solved by a full 3-dimensional finite-difference procedure instead of the normally used perturbation analysis. The time dependence of the equations is introduced by working with a coordinate system rotating with the precession frequency of the shaft. The results of this theory are compared with coefficients calculated by a perturbation analysis and with experimental results.

Dietzen, F. J.↗

NASA NTRS1989

Parallel processors and nonlinear structural dynamics algorithms and software

A nonlinear structural dynamics finite element program was developed to run on a shared memory multiprocessor with pipeline processors. The program, WHAMS, was used as a framework for this work. The program employs explicit time integration and has the capability to handle both the nonlinear material behavior and large displacement response of 3-D structures. The elasto-plastic material model uses an isotropic strain hardening law which is input as a piecewise linear function. Geometric nonlinearities are handled by a corotational formulation in which a coordinate system is embedded at the integration point of each element. Currently, the program has an element library consisting of a beam element based on Euler-Bernoulli theory and trianglar and quadrilateral plate element based on Mindlin theory.

Belytschko, Ted↗

NASA NTRS1989

Free-molecule-flow force and moment coefficients of the aeroassist flight experiment vehicle

Calculated results for the aerodynamic coefficients over the range of + or - 90 deg in both pitch and yaw attitude angles for the Aeroassist Flight Experiment (AFE) vehicle in free molecule flow are presented. The AFE body is described by a large number of small flat plate surface elements whose orientations are established in a wind axes coordinate system through the pitch and yaw attitude angles. Lift force, drag force, and three components of aerodynamic moment about a specified point are computed for each element. The elemental forces and moments are integrated over the entire body, and total force and moment coefficients are computed. The coefficients are calculated for the two limiting gas-surface molecular collision conditions, namely, specular and diffuse, which assume zero and full thermal accommodation of the incoming gas molecules with the surface, respectively. The individual contribution of the shear stress and pressure terms are calculated and also presented.

Blanchard, Robert C.↗

NASA NTRS1988

A conservative approach for flow field calculations on multiple grids

In the computation of flow fields about complex configurations, it is very difficult to construct body-fitted coordinate systems. An alternative approach is to use several grids at once, each of which is generated independently. This procedure is called the multiple grids or zonal grids approach and its applications are investigated in this study. The method follows the conservative approach and provides conservation of fluxes at grid interfaces. The Euler equations are solved numerically on such grids for various configurations. The numerical scheme used is the finite-volume technique with a three-state Runge-Kutta time integration. The code is vectorized and programmed to run on the CDC VPS-32 computer. Some steady state solutions of the Euler equations are presented and discussed.

Kathong, Monchai↗

NASA NTRS1988

A multidimensional model for aerosols - Description of computational analogs

The numerical algorithms used to simulate the advection, diffusion, sedimentation, coagulation, and condensational growth of atmospheric aerosols are described. The model can be used in one, two, or three spatial dimensions. The continuity equation in a generalized horizontal and vertical coordinate system is developed, which allows the model to be quickly adapted to a wide variety of dynamical models of global or regional scale. Algorithms are developed to treat the various physical processes, and the results of simulations are presented, which show the strengths and weaknesses of these algorithms. Although the emphasis is on the modeling of aerosols, the work is also applicable to the simulations of the transport of gases.

Toon, O. B.↗

NASA NTRS1988

The long term stability of VLBI earth orientation measurements

Tectonic motions will, in general, change the orientation as well as the length of baselines used in Very Long Baseline Interferometry (VLBI), and will thus cause slow divergences between earth orientation results obtained with different VLBI networks, as well as between VLBI results and those obtained by satellite laser ranging and lunar laser ranging. Such drifts (on the order of a milliarcsecond/year) are inherently interesting as well as being significant in combinations of orientation results from different sources. The geodetic study of tectonic motions is also closely connected to research into the nature and causes of systematic errors in data from the modern techniques of space geodesy. Both a special coordinate system found to be of use in the analysis of VLBI data and tectonic motion estimates for a VLBI baseline stretching from California to Australia are described.

Eubanks, T. M.↗

NASA NTRS1988

Dynamic inflow for practical applications

A derivation is presented which gives both the nonlinear dynamic inflow model and the perturbation dynamic inflow model in a general coordinate system. The perturbation model includes perturbations in hub motions, in skew angle, and in yaw angle. The governing equations may be switched to their dimensional forms prior to application.

Peters, David A.↗

NASA NTRS1989

An interactive three-dimensional boundary-layer method for transonic flow over swept wings

A three-dimensional laminar/turbulent boundary-layer method is developed for transonic flow over swept wings. The governing equations and curvature terms are written for a nonorthogonal body-oriented curvilinear coordinate system. The viscous method is coupled to the full-potential inviscid code, FLO-30, through a displacement-surface interaction. Typically, for transonic Mach numbers and moderate sweep angles, between 5 and 12 viscous updates are required for convergence. The method is applied to a variety of wing planforms, and the results are also compared to those obtained with the three-dimensional integral inviscid-viscous interaction method TAWFIVE (Streett and Melson, 1983).

Woodson, Shawn H.↗