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NASA NTRS1985

A comparison of observed and forecast energetics over North America

The observed kinetic energy balance is calculated over North America and compared with that computed from forecast fields for the 13-15 January 1979 cyclone. The FGGE upper-air rawinsonde network serves as the observational database while the forecast energetics are derived from a numerical integration with the GLAS fourth-order general circulation model initialized at 00 GMT 13 January. Maps of the observed and predicted kinetic energy and eddy conversion are in good qualitative agreement, although the model eddy conversion tends to be 2 to 3 times stronger than the observed values. Both the forecast and observations exhibit the lower and upper tropospheric maxima in vertical profiles of kinetic energy generation and dissipation typically found in cyclonic disturbances. An interesting time lag is noted in the observational analysis with the maximum observed kinetic energy occurring 12 h later than the maximum eddy conversion over the same region.

Baker, W. E.↗

NASA NTRS1985

A fully implicit scheme for the barotropic primitive equations

An efficient implicit finite-difference method is developed and tested for a global barotropic model. The scheme requires, at each time step, the solution of only one-dimensional block-tridiagonal linear systems. This additional computation is offset by the use of a time step chosen independently of the mesh spacing. The method is second-order accurate in time and fourth-order accurate in space. Present experience indicates that this implicit method is practical for numerical simulation on fine meshes.

Cohn, S. E.↗

NASA NTRS1985

New analytical results for AOTV guidance

Minimum energy-loss turns of an Aero-assisted, Orbital Transfer Vehicle (AOTV) performing the atmospheric portion of an orbital-plane-change maneuver are developed using the heading angle as the independent variable. Because the heading angle is monotonic, several difficulties previously encountered using the flight path angle, which is not monotonic, as the independent variable are eliminated. In addition, the solution of the optimal control problem reduces to the solution of a fourth-order polynomial which can be accomplished analytically.

Hull, D. G.↗

NASA NTRS1985

Higher-order derivative correlations and the alignment of small-scale structures in isotropic numerical turbulence

The classical approach to the investigation of small-scale intermittency in turbulence is based on the higher-order derivative correlations such as skewness and flatness factors. In the study of the small scales, numerial simulations can provide more detail than experiments. In the present paper, a variety of velocity- and scalar-derivative correlations are calculated over a range of Reynolds numbers. Particular attention is given to third- and fourth-order correlations, taking into account also some fifth- and sixth-order correlations to allow comparisons with the phenomenological models. The governing equations are the incompresssible Navier-Stokes equation for the velocity and transport equation for a passive scalar. Two numerical codes are used for the simulations presented. Attention is given to details regarding the numerical method used, forcing, simulation parameters, spectra and skewnesses, and graphics.

Kerr, R. M.↗

NASA NTRS1985

A method to stabilize linear systems using eigenvalue gradient information

Formal optimization methods and eigenvalue gradient information are used to develop a stabilizing control law for a closed loop linear system that is initially unstable. The method was originally formulated by using direct, constrained optimization methods with the constraints being the real parts of the eigenvalues. However, because of problems in trying to achieve stabilizing control laws, the problem was reformulated to be solved differently. The method described uses the Davidon-Fletcher-Powell minimization technique to solve an indirect, constrained minimization problem in which the performance index is the Kreisselmeier-Steinhauser function of the real parts of all the eigenvalues. The method is applied successfully to solve two different problems: the determination of a fourth-order control law stabilizes a single-input single-output active flutter suppression system and the determination of a second-order control law for a multi-input multi-output lateral-directional flight control system. Various sets of design variables and initial starting points were chosen to show the robustness of the method.

Wieseman, C. D.↗

NASA NTRS1986

A shock capturing technique for hypersonic, chemically relaxing flows

A fully coupled, shock capturing technique is presented for chemically reacting flows at high Mach numbers. The technique makes use of a total variation diminishing (TVD) dissipation operator which results in sharp, crisp shocks. The eigenvalues and eigenvectors of the fully coupled system, which includes species conversion equations in addition to the gas dynamics equations, are analytically derived for a general reacting gas. Species production terms for a model dissociating gas are introduced and are included in the algorithm. The convective terms are solved using a first-order TVD scheme while the source terms are solved using a fourth-order Runge-Kutta scheme to enhance stability. Results from one-dimensional numerical experiments are shown for a two species and a three species gas.

Eberhardt, S.↗

NASA NTRS1986

A diagonal algorithm for the method of pseudocompressibility

The method of pseudocompressibility has been shown to be an efficient method for obtaining a steady-state solution to the incompressible Navier-Stokes equations. Recent improvements to this method include the use of a diagonal scheme for the inversion of the equations at each iteration. The necessary transformations have been derived for the pseudocompressibility equations in generalized coordinates. The diagonal algorithm reduces the computing time necessary to obtain a steady-state solution by a factor of nearly three. Implicit viscous terms are maintained in the equations, and it has become possible to use fourth-order implicit dissipation. The steady-state solution is unchanged by the approximations resulting from the diagonalization of the equations. Computed results for flow over a two-dimensional backward-facing step and a three-dimensional cylinder mounted normal to a flat plate are presented for both the old and new algorithms. The accuracy and computing efficiency of these algorithms are compared.

Rogers, S. E.↗

NASA NTRS1986

Influence of numerical dissipation in computing supersonic vortex-dominated flows

Steady supersonic vortex-dominated flows are solved using the unsteady Euler equations for conical and three-dimensional flows around sharp- and round-edged delta wings. The computational method is a finite-volume scheme which uses a four-stage Runge-Kutta time stepping with explicit second- and fourth-order dissipation terms. The grid is generated by a modified Joukowski transformation. The steady flow solution is obtained through time-stepping with initial conditions corresponding to the freestream conditions, and the bow shock is captured as a part of the solution. The scheme is applied to flat-plate and elliptic-section wings with a leading edge sweep of 70 deg at an angle of attack of 10 deg and a freestream Mach number of 2.0. Three grid sizes of 29 x 39, 65 x 65 and 100 x 100 have been used. The results for sharp-edged wings show that they are consistent with all grid sizes and variation of the artificial viscosity coefficients. The results for round-edged wings show that separated and attached flow solutions can be obtained by varying the artificial viscosity coefficients. They also show that the solutions are independent of the way time stepping is done. Local time-stepping and global minimum time-steeping produce same solutions.

Kandil, O. A.↗

NASA NTRS1986

Turbulent two-phase flow in annular seals

Steady, turbulent two-phase fluid flow in a rotating annular seal with no eccentricity is analyzed. The fluid is assumed to be a homogeneous mixture of liquid and vapor in thermodynamic equilibrum. Further, the flow is assumed to be adiabatic, but the effects due to heat generation by viscous dissipation are accounted for fully. Solution of the model governing differential equations is accomplished by use of a fourth-order Runge-Kutta numerical integration scheme. The calculation of mass leakage rates under choked and unchoked conditions are discussed and the phenomenon of all-liquid choked flow is explained. Several numerical examples are presented supposing cyrogenic oxygen as the sealed fluid.

Beatty, P. A.↗

NASA NTRS1986

Finite-volume and integral-equation techniques for transonic and supersonic vortex-dominated flows

Two computational techniques are developed to calculate the compressible vortex-dominated flows. The first technique is a finite-volume Euler Solver which uses four-Stage Runge-Kutta time stepping with second- and fourth-order dissipation terms. The technique is applied to supersonic conical and three-dimensional flows about sharp- and round-edged delta wings. Attached and separated-flow solutions have been obtained depending on the values of damping coefficients. The second technique is an integral-equation solver of the full potential equation which uses a volume-integral term in addition to the classical surface-integral terms. The technique is applied to transonic three-dimensional flows about sharp-edged delta wings. A hybrid technique which combines the finite-volume and the integral-equation solvers is also presented.

Kandil, O. A.↗

NASA NTRS1986

The effect of a small initial curvature on the free vibration of clamped, rectangular plates

An analytical method of obtaining the natural frequencies and mode shapes of clamped, rectangular plates having a small initial curvature is presented. Specifically, the singular perturbation technique is used to reduce the fourth-order plate vibration problem to the simpler membrane problem with modified boundary conditions that account for the bending effects. The eigenfrequencies for plates with inverse aspect ratios varying between 0.1 and 1.0 and for the dimensionless normal prestress between 0.1 and 1.0 have been presented for values of epsilon, the normalized bending rigidity, ranging between 0.0010 and 0.2500. It is established that a small initial curvature has no effect on the frequency of vibration of the plate. However, its effect is manifested in the eigenmodes.

Adeniji-Fashola, A. A.↗

NASA NTRS1987

Quantitative analysis of the reconstruction performance of interpolants

The analysis presented provides a quantitative measure of the reconstruction or interpolation performance of linear, shift-invariant interpolants. The performance criterion is the mean square error of the difference between the sampled and reconstructed functions. The analysis is applicable to reconstruction algorithms used in image processing and to many types of splines used in numerical analysis and computer graphics. When formulated in the frequency domain, the mean square error clearly separates the contribution of the interpolation method from the contribution of the sampled data. The equations provide a rational basis for selecting an optimal interpolant; that is, one which minimizes the mean square error. The analysis has been applied to a selection of frequently used data splines and reconstruction algorithms: parametric cubic and quintic Hermite splines, exponential and nu splines (including the special case of the cubic spline), parametric cubic convolution, Keys' fourth-order cubic, and a cubic with a discontinuous first derivative. The emphasis in this paper is on the image-dependent case in which no a priori knowledge of the frequency spectrum of the sampled function is assumed.

Lansing, Donald L.↗

NASA NTRS1985

The influence of tropical wind data on the analysis and forecasts of the GLAS GCM for the Global Weather Experiment

Several densities of tropical divergent wind data were included in a fourth-order GCM to examine the effects on the accuracy of the model predictions. The experiments covered assimilation of all available tropical wind data, no tropical wind data between 20 deg N and 20 deg S, only westerly tropical wind data and only easterly tropical wind data. The predictions were all made for the 200 mb upper troposphere. Elimination of tropical data produced excessively strong upper tropospheric westerlies which in turn amplified the globally integrated rotational flow kinetic energy by around 10 percent and doubled the global divergent flow kinetic energy. Retaining only easterly wind data, ameliorated most of the error. Inclusion of all the tropical wind data however, did not lead to overall positive effects, as the data were linked to tropical wave energetics and ageostrophic winds which were already assimilated in the model.

Paegle, J.↗

NASA NTRS1985

A study of GLAS and UCLA model forecasts of explosive maritime cyclogenesis

The explosive development of a maritime cyclone was examined with a numeric model of a cyclone which occurred during the FGGE Special Observing Period One in January 1979. The storm exhibited a Petterssen type-system frontal wave development. The model used was a nine-level, fourth-order coarse-mesh GLAS model initialized with FGGE level II-B data. Two versions of 72 hr synoptic-scale predictions were performed for the storm: with and without the input of meteorological satellite data. Attention was focused on the heat, mass and vorticity budgets of the storm, starting 24 hr before storm onset. The inclusion of satellite data, due to the poor quality of remotely sensed wind fields, degraded the performance of the model.

Peak, J. E.↗

NASA NTRS1987

Wave phenomena in a high Reynolds number compressible boundary layer

The behavior of spatially unstable waves in a high Reynolds number compressible laminar boundary layer is investigated by solution of the laminar two-dimensional compressible Navier-Stokes equations (solved to fourth-order accuracy) over a flat plate with a fluctuating disturbance generated at the inflow. A significant nonlinear distortion is produced, in qualitative agreement with experimental data. It is shown that increasing compressibility can significantly stabilize the flow over a flat plate, and that the mechanism of phase cancellation is a viable mechanism for the control of growing disturbances.

Bayliss, A.↗

NASA NTRS1987

Study of instability and active control of boundary layers using Navier-Stokes equations

Spatial stability of a three-dimensional growing boundary layer is studied using Navier-Stokes equations. The finite difference method used is an explicit, predictor-corrector type which is fourth-order accurate in space and second-order in time. Active control of two-dimensional disturbances is simulated by localized surface heating. The computations show features of the flow relevant to early stages of transition such as lifting of vorticity away from the wall and localized regions of intense shear. Active control with single heating strip is only marginally effective, but may be improved by multiple strips.

Parikh, Paresh↗

NASA NTRS1987

Numerical experiments related to the summer 1980 U.S. heat wave

The NASA Goddard Laboratory for Atmospheres fourth-order GCM was used in a series of medium-range numerical forecast experiments in order to improve understanding of the severe summer 1980 heat wave over the U.S. The results show that the derived soil moisture anomalies in the summer of 1980 contributed positively to the model's simulation of the heat wave maintenance, and suggest that once a region of reduced soil moisture is established, it tends to persist and maintain warmer and drier conditions. The lower soil moisture values resulted in reduced evaporation, higher ground temperatures, increased sensible heat flux from ground to air, higher surface air temperature, lower sea-level pressure, and higher 500-mb height. The effects of North Pacific sea-surface-temperature anomalies were mostly opposite to those of the soil-moisture anomalies: enhanced northerly flow of cooler drier air, increased evaporation, lower ground and air temperature, higher sea level pressure, and lower 500 mb heights over the Great Plains.

Wolfson, N.↗

NASA NTRS1987

Numerical methods for one-dimensional reaction-diffusion equations arising in combustion theory

A review of numerical methods for one-dimensional reaction-diffusion equations arising in combustion theory is presented. The methods reviewed include explicit, implicit, quasi-linearization, time linearization, operator-splitting, random walk and finite-element techniques and methods of lines. Adaptive and nonadaptive procedures are also reviewed. These techniques are applied first to solve two model problems which have exact traveling wave solutions with which the numerical results can be compared. This comparison is performed in terms of both the wave profile and computed wave speed. It is shown that the computed wave speed is not a good indicator of the accuracy of a particular method. A fourth-order time-linearized, Hermitian compact operator technique is found to be the most accurate method for a variety of time and space sizes.

Ramos, J. I.↗