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NASA NTRS1987

Ultra-high-energy cosmic rays in a galactic wind and its termination shock

Results are reported from numerical modeling of the acceleration and transport of ultra-high-energy cosmic rays in a galactic wind and its termination shock. A two-dimensional (azimuthally symmetric) wind and spiral magnetic field, with a spherical termination shock, where the velocity drops suddenly, is assumed. The time-dependent cosmic-ray transport equation, including all major transport effects is solved using an implicit finite-difference scheme. Particles are injected as the shock of low energy, and the subsequent evolution of the distribution function is followed. Iron nuclei are readily accelerated at the shock to energies up to 100 billion GeV, and protons to 10 billion GeV. A major effect aiding the acceleration of these particles is the spiral of the magnetic field carried out by the wind, caused by the rotation of the Galaxy, with the result that the shock is nearly normal over most of its area. Increasing the magnetic field or rotation rate increases the maximum energy attainable. Anisotropies and energy densities of the particles are also discussed. It is concluded that the process is consistent with observations of ultra-high-energy cosmic rays.

Jokipii, J. R.↗

NASA NTRS1987

Wall jet analysis for circulation control aerodynamics. Part 1: Fundamental CFD and turbulence modeling concepts

An overview of parabolic and PNS (Parabolized Navier-Stokes) methodology developed to treat highly curved sub and supersonic wall jets is presented. The fundamental data base to which these models were applied is discussed in detail. The analysis of strong curvature effects was found to require a semi-elliptic extension of the parabolic modeling to account for turbulent contributions to the normal pressure variations, as well as an extension to the turbulence models utilized, to account for the highly enhanced mixing rates observed in situations with large convex curvature. A noniterative, pressure split procedure is shown to extend parabolic models to account for such normal pressure variations in an efficient manner, requiring minimal additional run time over a standard parabolic approach. A new PNS methodology is presented to solve this problem which extends parabolic methodology via the addition of a characteristic base wave solver. Applications of this approach to analyze the interaction of wave and turbulence processes in wall jets is presented.

Dash, S. M.↗

NASA NTRS1988

Numerical analysis of three-dimensional viscous internal flows

A 3-D Navier-Stokes code has been developed for analysis of turbomachinery blade rows and other internal flows. The Navier-Stokes equations are written in a Cartesian coordinate system rotating about the x-axis, and then mapped to a general body-fitted coordinate system. Streamwise viscous terms are neglected using the thin-layer assumption, and turbulence effects are modeled using the Baldwin-Lomax turbulence model. The equations are discretized using finite differences on stacked C-type grids and are solved using a multistage Runge-Kutta algorithm with a spatially-varying time step and implicit residual smoothing. Calculations have been made of a horseshoe vortex formed in front of a flat plate with a round leading edge standing in a turbulent endwall boundary layer. Comparisons are made with experimental data taken by Eckerle and Langston for a circular cylinder under similar conditions. Computer and measured results are compared in terms of endwall flow visualization pictures and total pressure loss contours and vector plots on the symmetry plane. Calculated details of the primary vortex show excellent agreement with the experimental data. The calculations also show a small secondary vortex not seen experimentally.

Chima, Rodrick V.↗

NASA NTRS1988

A space station onboard scheduling assistant

One of the goals for the Space Station is to achieve greater autonomy, and have less reliance on ground commanding than previous space missions. This means that the crew will have to take an active role in scheduling and rescheduling their activities onboard, perhaps working from preliminary schedules generated on the ground. Scheduling is a time intensive task, whether performed manually or automatically, so the best approach to solving onboard scheduling problems may involve crew members working with an interactive software scheduling package. A project is described which investigates a system that uses knowledge based techniques for the rescheduling of experiments within the Materials Technology Laboratory of the Space Station. Particular attention is paid to: (1) methods for rapid response rescheduling to accommodate unplanned changes in resource availability, (2) the nature of the interface to the crew, (3) the representation of the many types of data within the knowledge base, and (4) the possibility of applying rule-based and constraint-based reasoning methods to onboard activity scheduling.

Brindle, A. F.↗

NASA NTRS1988

Computational simulation of turbulent flow in Space Shuttle Main Engine turnaround ducts

Two axisymmetric 180-deg turnaround ducts are used in the Space Shuttle Main Engine (SSME) to connnect the preburners with the main thrust chamber. The prediction of the flow field and heat transfer within the turnaround ducts is important to minimize the pressure drops, size of recirculation and stagnation zones, local overheating, etc. This paper presents the computational approach and selected results for the turbulent flow in the turnaround ducts of the fuel and oxidizer sides of the SSME. The time-averaged, Navier-Stokes equations for the viscous, compressible, turbulent flow are solved in body-fitted-coordinates by using a finite-volume approach. Two turbulence models, viz: the k-epsilon model and a multiple scale turbulence model, are used to examine the sensitivity of calculated flows. Both models produce almost identical solutions for the fuelside turnaround duct (which has no recirculation region). However, for the oxidizer-side duct which has a large recirculation region, the two models show quite different results.

Przekwas, Andrzej J.↗

NASA NTRS1988

Numerical analysis of three-dimensional viscous internal flows

Chima, Rodrick V.↗

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

System identification in the microcomputer environment

An implementation of an algorithm for system identification, the eigenvalue realization algorithm (ERA), on a microcomputer is reported. Test results are presented to show that accurate structural identification can be performed in a microcomputer environment. It is also shown that the memory limits (640 K) of small machines are generally adequate for solving large scale problems (e.g., Hankel matrices with 15,000 elements), with run times being on the order of several minutes.

Garcia, Ephrahim↗

NASA NTRS1989

Thermal-structural finite element analysis using linear flux formulation

A linear flux approach is developed for a finite element thermal-structural analysis of steady-state thermal and structural problems. The element fluxes are assumed to vary linearly in the same form as the element unknown variables, and the finite element matrices are evaluated in closed form. Since numerical integration is avoided, significant computational time saving is achieved. Solution accuracy and computational speed improvements are demonstrated by solving several two-and three-dimensional thermal-structural examples.

Pandey, Ajay K.↗

NASA NTRS1989

A Transient Response Method for Linear Coupled Substructures

A method is presented for determining the transient response of a discrete coordinate model of a linear structural system composed of substructures. The method is applicable to systems consisting of any number of substructures, both determinate and indeterminate interface boundaries, and any topological arrangement of the substructures. The method is simple to implement from a computational point of view because the equations of motion of each of the substructures are solved independently, and the interface boundary compatibility conditions are enforced at each integration time step by a matrix multiplication. The method is demonstrated for a structural system consisting of two beam segments and acted upon by a time dependent force. The numerical results from the demonstration problem validates the accuracy of the method. The application of this method to structural systems with changing interface boundary conditions between substructures is discussed.

Admire, J. R.↗

NASA NTRS1989

Dynamics of flare-driven chromospheric condensations

A general model of chromospheric condensation dynamics is developed under the assumption of sudden impulsive-phase flare energy release. The basic equation of motion for the downward-moving condensation is derived from the momentum equation and from general features seen in numerical simulations. This equation is solved for a number of different cases. The 'lifetime' of condensation and the time for the velocity to drop to half its peak value are computed. The peak downflow speed is examined as a function of the flare energy flux, and comparisons are made between downflow speeds predicted by both thick-target 'explosive evaporation' and evaporation driven conductively.

Fisher, George H.↗

NASA NTRS1989

The computation of thermo-chemical nonequilibrium hypersonic flows

Several conceptual designs for vehicles that would fly in the atmosphere at hypersonic speeds have been developed recently. For the proposed flight conditions the air in the shock layer that envelops the body is at a sufficiently high temperature to cause chemical reaction, vibrational excitation, and ionization. However, these processes occur at finite rates which, when coupled with large convection speeds, cause the gas to be removed from thermo-chemical equilibrium. This non-ideal behavior affects the aerothermal loading on the vehicle and has ramifications in its design. A numerical method to solve the equations that describe these types of flows in 2-D was developed. The state of the gas is represented with seven chemical species, a separate vibrational temperature for each diatomic species, an electron translational temperature, and a mass-average translational-rotational temperature for the heavy particles. The equations for this gas model are solved numerically in a fully coupled fashion using an implicit finite volume time-marching technique. Gauss-Seidel line-relaxation is used to reduce the cost of the solution and flux-dependent differencing is employed to maintain stability. The numerical method was tested against several experiments. The calculated bow shock wave detachment on a sphere and two cones was compared to those measured in ground testing facilities. The computed peak electron number density on a sphere-cone was compared to that measured in a flight test. In each case the results from the numerical method were in excellent agreement with experiment. The technique was used to predict the aerothermal loads on an Aeroassisted Orbital Transfer Vehicle including radiative heating. These results indicate that the current physical model of high temperature air is appropriate and that the numerical algorithm is capable of treating this class of flows.

Candler, Graham↗

NASA NTRS1990

Thermal-structural finite element analysis using linear flux formulation

A linear flux approach is developed for a finite element thermal-structural analysis of steady state thermal and structural problems. The element fluxes are assumed to vary linearly in the same form as the element unknown variables, and the finite element matrices are evaluated in closed form. Since numerical integration is avoided, significant computational time saving is achieved. Solution accuracy and computational speed improvements are demonstrated by solving several two and three dimensional thermal-structural examples.

Pandey, Ajay K.↗

NASA NTRS1990

Modulational stability of rotating-disk flow

The problem of modulational primary stability of rotating-disk boundary layer flow for stationary modes was studied by using the method of multiple scales. The system of equations for infinitesimal disturbances is solved by linear stability theory to determine the modulated solution which represents the time and azimuthal variations of the wave pattern. The solution for the amplitude of the most critical disturbance indicates that the disturbance spreads out as the flow time increases and grows exponentially at the center.

Riahi, Daniel N.↗

NASA NTRS1991

Multigrid for hypersonic viscous two- and three-dimensional flows

The use of a multigrid method with central differencing to solve the Navier-Stokes equations for hypersonic flows is considered. The time-dependent form of the equations is integrated with an explicit Runge-Kutta scheme accelerated by local time stepping and implicit residual smoothing. Variable coefficients are developed for the implicit process that remove the diffusion limit on the time step, producing significant improvement in convergence. A numerical dissipation formulation that provides good shock-capturing capability for hypersonic flows is presented. This formulation is shown to be a crucial aspect of the multigrid method. Solutions are given for two-dimensional viscous flow over a NACA 0012 airfoil and three-dimensional viscous flow over a blunt biconic.

Turkel, E.↗

NASA NTRS1992

Large eddy simulation of compressible turbulent channel flows

The development of turbulence within rocket propulsion chamber flows remains a difficult problem to predict. Within solid propellant rockets, the flow can exhibit multiple regions of transition to turbulence, and is susceptible to various modes of aero-acoustic interaction. The objective is to formulate, develop, and validate, a large eddy simulation (LES) method for compressible channel flows. The LES method separates the resolvable scale motions from the unresolvable scales by applying a spatial filter to the compressible Navier-Stokes equations. The equations are solved numerically using a modified four-step Runge-Kutta procedure in time and second or fourth order finite differences in space. The current simulations have validated the algorithm in the incompressible limit and have demonstrated the ability of the method to simulate high subsonic Mach number flows.

Beddini, Robert A.↗

NASA NTRS1991

Calculating satellite umbra/penumbra entry and exit positions and times

The problem of calculating earth satellite entry/exit positions and times through the earth's umbra and penumbra for elliptical satellite orbits is solved in closed form; i.e., without iteration, by reducing the problem to that of finding the roots of a quartic polynomial in a cartesian coordinate. Typical results from an algorithm constructed from the method are shown.

Mullins, Larry D.↗

NASA NTRS1992

Aerodynamic design and optimization in one shot

This paper describes an efficient numerical approach for the design and optimization of aerodynamic bodies. As in classical optimal control methods, the present approach introduces a cost function and a costate variable (Lagrange multiplier) in order to achieve a minimum. High efficiency is achieved by using a multigrid technique to solve for all the unknowns simultaneously, but restricting work on a design variable only to grids on which their changes produce nonsmooth perturbations. Thus, the effort required to evaluate design variables that have nonlocal effects on the solution is confined to the coarse grids. However, if a variable has a nonsmooth local effect on the solution in some neighborhood, it is relaxed in that neighborhood on finer grids. The cost of solving the optimal control problem is shown to be approximately two to three times the cost of the equivalent analysis problem. Examples are presented to illustrate the application of the method to aerodynamic design and constraint optimization.

Ta'asan, Shlomo↗