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NASA NTRS1986

Accurate solutions for transonic viscous flow over finite wings

An explicit multistage Runge-Kutta type time-stepping scheme is used for solving the three-dimensional, compressible, thin-layer Navier-Stokes equations. A finite-volume formulation is employed to facilitate treatment of complex grid topologies encountered in three-dimensional calculations. Convergence to steady state is expedited through usage of acceleration techniques. Further numerical efficiency is achieved through vectorization of the computer code. The accuracy of the overall scheme is evaluated by comparing the computed solutions with the experimental data for a finite wing under different test conditions in the transonic regime. A grid refinement study ir conducted to estimate the grid requirements for adequate resolution of salient features of such flows.

Vatsa, V. N.↗

NASA NTRS1986

Feedback between neutral winds and auroral arc electrodynamics

The feedback between neutral atmospheric winds and the electrodynamics of a stable, discrete auroral arc is analyzed. The ionospheric current continuity equation and the equation for neutral gas acceleration by ion drag are solved simultaneously, as a function of time. The results show that, in general, the electric field in the ionosphere adjusts to neutral wind acceleration so as to keep auroral field-aligned currents and electron acceleration approximately independent of time. It is thus concluded that the neutral winds that develop as a result of the electrodynamical forcing associated with an arc do not significantly affect the intensity of the arc.

Lyons, L. R.↗

NASA NTRS1987

Theoretical analysis of aircraft afterbody flow

Computational methods solving the thin shear layer formulation of the compressible, Reynolds-averaged Navier-Stokes equations are presently used to investigate the strongly interactive flow field about aircraft afterbodies. Solutions for a variety of axisymmetric afterbody and nozzle geometries are solved by means of a time-dependent implicit numerical algorithm for both subsonic and supersonic external flows, and the results obtained are compared with experimental data. A novel adaptive-grid technique is used to resolve flow regimes having large gradients, as well as to improve the accuracy and efficiency of the computational scheme.

Deiwert, George S.↗

NASA NTRS1987

Numerical tests of a modified full implicit continuous Eulerian (FICE) scheme with projected normal characteristic boundary conditions for MHD flows

A numerical method has been developed based on a modified full implicit continuous Eulerian (FICE) scheme and projected normal characteristic boundary conditions for simulating MHD flows which undergo a long process of evolution. An astrophysical flow is chosen for illustration of this procedure, and numerical tests are made to verify the computational stability and physically realistic solution. Three computational tests have been accomplished; they are tests of solving methods, characteristic boundary condition, and time steps. The tests show that the program from the modified FICE scheme with proper boundary conditions and time steps can be made numerically stable for a time long enough to obtain physically plausible solutions.

Wu, S. T.↗

NASA NTRS1989

The 3-D Euler and Navier-Stokes calculations for aircraft components

An explicit multistage Runge-Kutta type of time-stepping scheme is used for solving transonic flow past a transport type wing/fuselage configuration. Solutions for both Euler and Navier-Stokes equations are obtained for quantitative assessment of boundary layer interaction effects. The viscous solutions are obtained on both a medium resolution grid of approximately 270,000 points and a find grid of 460,000 points to assess the effects of grid density on the solution. Computed pressure distributions are compared with the experimental data.

Vatsa, Veer N.↗

NASA NTRS1988

Navier-Stokes calculations for DFVLR F5-wing in wind tunnel using Runge-Kutta time-stepping scheme

A three-dimensional Navier-Stokes code using an explicit multistage Runge-Kutta type of time-stepping scheme is used for solving the transonic flow past a finite wing mounted inside a wind tunnel. Flow past the same wing in free air was also computed to assess the effect of wind-tunnel walls on such flows. Numerical efficiency is enhanced through vectorization of the computer code. A Cyber 205 computer with 32 million words of internal memory was used for these computations.

Vatsa, V. N.↗

NASA NTRS1989

Spin-lattice relaxation and the calculation of gain, pump power, and noise temperature in ruby

The use of a quantitative analysis of the dominant source of relaxation in ruby spin systems to make predictions of key maser amplifier parameters is described. The spin-lattice Hamiltonian which describes the interaction of the electron spins with the thermal vibrations of the surrounding lattice is obtained from the literature. Taking into account the vibrational anisotropy of ruby, Fermi's rule is used to calculate the spin transition rates between the maser energy levels. The spin population rate equations are solved for the spin transition relaxation times, and a comparison with previous calculations is made. Predictions of ruby gain, inversion ratio, and noise temperature as a function of physical temperature are made for 8.4-GHz and 32-GHz maser pumping schemes. The theory predicts that ruby oriented at 90 deg will have approximately 50 percent higher gain in dB and slightly lower noise temperature than a 54.7-deg ruby at 32 GHz (assuming pump saturation). A specific calculation relating pump power to inversion ratio is given for a single channel of the 32-GHz reflected wave maser.

Lyons, J. R.↗

NASA NTRS1990

Unsteady three-dimensional marginal separation, including breakdown

A situation involving a three-dimensional marginal separation is considered, where a (steady) boundary layer flow is on the verge of separating at a point (located along a line of symmetry/centerline). At this point, a triple-deck is included, thereby permitting a small amount of interaction to occur. Unsteadiness is included within this interaction region through some external means. It is shown that the problem reduces to the solution of a nonlinear, unsteady, partial-integro system, which is solved numerically by means of time-marching together with a pseudo-spectral method spatially. A number of solutions to this system are presented which strongly suggest a breakdown of this system may occur, at a finite spatial position, at a finite time. The structure and details of this breakdown are then described.

Duck, Peter W.↗

NASA NTRS1991

On the application of ENO scheme with subcell resolution to conservation laws with stiff source terms

Two approaches are used to extend the essentially non-oscillatory (ENO) schemes to treat conservation laws with stiff source terms. One approach is the application of the Strang time-splitting method. Here the basic ENO scheme and the Harten modification using subcell resolution (SR), ENO/SR scheme, are extended this way. The other approach is a direct method and a modification of the ENO/SR. Here the technique of ENO reconstruction with subcell resolution is used to locate the discontinuity within a cell and the time evolution is then accomplished by solving the differential equation along characteristics locally and advancing in the characteristic direction. This scheme is denoted ENO/SRCD (subcell resolution - characteristic direction). All the schemes are tested on the equation of LeVeque and Yee (NASA-TM-100075, 1988) modeling reacting flow problems. Numerical results show that these schemes handle this intriguing model problem very well, especially with ENO/SRCD which produces perfect resolution at the discontinuity.

Chang, Shih-Hung↗

NASA NTRS1990

Plasma density enhancement at the Comet Halley diamagnetic cavity boundary

A one-dimensional single-fluid MHD model was used by Cravens (1989) to predict the existence of a narrow (50 km) layer of enhanced plasma density at the boundary of the Comet Halley diamagnetic cavity. The existence of such a layer was confirmed by measurements made by the Giotto ion mass spectrometer (Goldstein et al., 1989). Here, the time-dependent coupled continuity equations are solved for several species including H3O(+), H2O(+), OH(+), O(+), NH4(+), NH3(+), CH4(+), and CH3(+). For several ion species, factors affecting the magnitude of this enhancement and its relationship to the thickness of the transition layer are investigated. For example, ion species with short chemical lifetimes are shown to have smaller density enhancements than species with longer lifetimes. The cometocentric distance of the cavity boundary also strongly affects the magnitude of the density enhancement; the enhancement increases with increasing distance.

Keller, C. N.↗

NASA NTRS1991

Use of finite volume schemes for transition simulation

The use of finite-volume methods in the study of spatially and temporally evolving transitional flows over a flat plate is investigated. Schemes are developed with both central and upwind differencing. The compressible Navier-Stokes equations are solved with a Runge-Kutta time stepping scheme. Disturbances are determined using linear theory and superimposed at the inflow boundary. Time accurate integration is then used to allow temporal and spatial disturbance evolution. Characteristic-based boundary conditions are employed. The requirements of using finite-volume algorithms are studied in detail. Special emphasis is placed on difference schemes, grid resolution, and disturbance amplitudes. Moreover, comparisons are made with linear theory for small amplitude disturbances. Both subsonic and supersonic flows are considered, and it is shown that the locations of branch 1 and branch 2 of the neutral stability curve are well predicted, given sufficient resolution.

Fenno, Charles C., Jr.↗

NASA NTRS1991

Computational aspects of chemically reacting flows

An implicit, time-dependent approach is taken to solve the inviscid conservative equations in a vertex-based finite-volume formulation. The convective fluxes are estimated by a modified Riemann solver, and higher-order accuracy is obtained by means of the MUSCL. Implicit techniques are adopted to deal with the equation stiffness as a result of the clustered grid and chemical source term. The real-gas Roe matrix and the ADI and LU schemes have been tested on the sample problems: hypersonic flow over blunt configurations, such as the forebody of a double ellipse, and the near wake of a conic aerobrake. Temperature distribution and standoff distance are validated against the shock-fitting, central-differencing results. Equilibrium temperature may be recovered by artificially increasing the chemical rates at the wall. The present method satisfactorily resolves the flow structure, including the strong expansion behind the flat base. The relative merits and performance of the real-gas TVD and implicit schemes are discussed briefly.

Li, C. P.↗

NASA NTRS1992

A time-accurate implicit method for chemical non-equilibrium flows at all speeds

A new time accurate coupled solution procedure for solving the chemical non-equilibrium Navier-Stokes equations over a wide range of Mach numbers is described. The scheme is shown to be very efficient and robust for flows with velocities ranging from M less than or equal to 10(exp -10) to supersonic speeds.

Shuen, Jian-Shun↗

NASA NTRS1992

A finite element method for the thermochemical decomposition of polymeric materials. I - Theory

The governing differential equations are developed to model the thermomechanical behavior of chemically decomposing, polymeric materials. These equations account for thermal and gaseous diffusion through a poroelastic, transversely isotropic solid. The Bubnov-Galerkin finite element method is applied to the governing equations to cast the coupled set into a single matrix equation. A method for solving these equations simultaneously at each time step is discussed.

Sullivan, R. M.↗

NASA NTRS1992

A coupled solution method for predicting the thermostructural response of decomposing, expanding polymeric composites

A new solution method has recently been developed to analyze the thermal and structural response of polymeric composites during chemical decomposition (Sullivan and Salamon, 1992a). This method couples the equations of energy, mass transport and momentum and solves these equations simultaneously at each time step. In this paper, the couples solution method is applied to analyze the response of a glass phenolic composite during its chemical decomposition. The numerical solution to this particular problem was originally performed by Henderson, et al. (1985) and the actual response was measured by Henderson and Hagen (1985) and Ramamurthy (1988). In addition to further verification of the coupled solution method, the present solution offers additional insight into certain physical events which occur during chemical decomposition.

Sullivan, Roy M.↗

NASA NTRS1992

Finite-difference algorithms for the time-domain Maxwell's equations - A numerical approach to RCS analysis

The applications of two CFD-based finite-difference methods to computational electromagnetics are investigated. In the first method, the time-domain Maxwell's equations are solved using the explicit Lax-Wendroff scheme and in the second method, the second-order wave equations satisfying the Maxwell's equations are solved using the implicit Crank-Nicolson scheme. The governing equations are transformed to a generalized curvilinear coordinate system and solved on a body-conforming mesh using the scattered-field formulation. The induced surface current and the bistatic radar cross section are computed and the results are validated for several two-dimensional test cases involving perfectly-conducting scatterers submerged in transverse-magnetic plane waves.

Vinh, Hoang↗

NASA NTRS1992

A hybrid approach to near-optimal launch vehicle guidance

This paper evaluates a proposed hybrid analytical/numerical approach to launch-vehicle guidance for ascent to orbit injection. The feedback-guidance approach is based on a piecewise nearly analytic zero-order solution evaluated using a collocation method. The zero-order solution is then improved through a regular perturbation analysis, wherein the neglected dynamics are corrected in the first-order term. For real-time implementation, the guidance approach requires solving a set of small dimension nonlinear algebraic equations and performing quadrature. Assessment of performance and reliability are carried out through closed-loop simulation for a vertically launched 2-stage heavy-lift capacity vehicle to a low earth orbit. The solutions are compared with optimal solutions generated from a multiple shooting code. In the example the guidance approach delivers over 99.9 percent of optimal performance and terminal constraint accuracy.

Leung, Martin S. K.↗

NASA NTRS1993

Numerical investigation of receptivity to freestream vorticity

The receptivity to freestream vorticity of the boundary layer over a flat plate with an elliptic leading edge is studied numerically. A finite-difference scheme that is second-order accurate in both time and space is utilized to solve the incompressible Navier-Stokes system in general curvilinear coordinates with the vorticity and stream function as dependent variables. Simulations show, for the conditions considered, a linear variation in the Tollmien-Schlichting response with forcing amplitude for perturbations of freestream velocity that are either symmetrical or asymmetrical with respect to the basic state stagnation streamline.

Buter, Thomas A.↗