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NASA NTRS1989

Numerical simulations in combustion

This paper reviews numerical simulations in reacting flows in general and combustion phenomena in particular. It is shown that use of implicit schemes and/or adaptive mesh strategies can improve convergence, stability, and accuracy of the solution. Difficulties increase as turbulence and multidimensions are considered, particularly when finite-rate chemistry governs the given combustion problem. Particular attention is given to the areas of solid-propellant combustion dynamics, turbulent diffusion flames, and spray droplet vaporization.

Chung, T. J.↗

NASA NTRS1989

Adaptive implicit-explicit methods for flow problems

Studies on the adaptive implicit-explicit (AIE) method for large-scale problems are presented. The AIE method is based on dynamic grouping of the elements into the implicit and explicit subsets as dictated by the element level stability and accuracy considerations. The method has been applied to various flow problems including the incompressible flow and convection-diffusion problems, and it has been demonstrated that substantial savings in CPU time and memory can be achieved.

Liou, J.↗

NASA NTRS1989

A new family of stable elements for the Stokes problem based on a mixed Galerkin/least-squares finite element formulation

Adding to the classical Hellinger-Reissner formulation, a residual form of the equilibrium equation, a new Galerkin/least-squares finite element method is derived. It fits within the framework of a mixed finite element method and is stable for rather general combinations of stress and velocity interpolations, including equal-order discontinuous stress and continuous velocity interpolations which are unstable within the Galerkin approach. Error estimates are presented based on a generalization of the Babuska-Brezzi theory. Numerical results (not presented herein) have confirmed these estimates as well as the good accuracy and stability of the method.

Franca, Leopoldo P.↗

NASA NTRS1990

A multigrid solver for semi-implicit global shallow-water models

A multigrid solver is developed for the discretized two-dimensional elliptic equation on the sphere that arises from a semiimplicit time discretization of the global shallow-water equations. Different formulations of the semiimplicit scheme result in variable-coefficient Helmholtz-type equations for which no fast direct solvers are available. The efficiency of the multigrid solver is optimal, in the sense that the total operation count is proportional to the number of unknowns. Numerical experiments using initial data derived from actual 300-mb height and wind velocity fields indicate that the present model has very good accuracy and stability properties.

Barros, Saulo R. M.↗

NASA NTRS1989

Comparison between pressure gradient method and MAC method on high Re calculation

A cavity flow driven by shear and buoyancy forces is used as a test problem in the application of a nonstaggered pressure gradient (PG) method in solving the two-dimensional incompressible Navier-Stokes equations. Twelve finite differencing schemes are used to solve the cavity flow problem. The schemes consist of various combinations of grid arrangements, upwinding treatments, and conservativeness of convection terms. An artificial source term is introduced, and the solutions are compared with those obtained by the conventional marker-and-cell (MAC) method. The comparisons favor the PG method. Numerical results obtained by the twelve schemes are compared with exact solutions in order to assess the stability and accuracy of each scheme.

Tan, C.-H.↗

NASA NTRS1990

Numerical simulation of three-dimensional transonic flows

The three-dimensional flow over a projectile has been computed using an implicit, approximately factored, partially flux-split algorithm. A simple composite grid scheme has been developed in which a single grid is partitioned into a series of smaller grids for applications which require an external large memory device such as the SSD of the CRAY X-MP/48 or multi-tasking. The accuracy and stability of the composite grid scheme have been tested by numerically simulating the flow over an ellipsoid at an angle of attack and comparing the solution with a single-grid solution. The flow field over a projectile at M = 0.96 and 1.1, and 4-deg angle of attack has been computed using a fine grid and compared with experiment.

Sahu, Jubaraj↗

NASA NTRS1989

An unconditionally stable Runge-Kutta method for unsteady rotor-stator interaction

A quasi-three-dimensional analysis has been developed for unsteady rotor-stator interaction 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 stress-surface thickness. The Baldwin-Lomax eddy-viscosity model is used for turbulent flows. The equations are integrated in time using an explicit four-stage Runge-Kutta scheme with a constant time step. Implicit residual smoothing is used to increase the stability limit of the time-accurate computations. The scheme is described, and stability and accuracy analyses are given.

Chima, Rodrick V.↗

NASA NTRS1991

Nonlinear dynamic analysis of flexible multibody systems

Two approaches are developed to analyze the dynamic behavior of flexible multibody systems. In the first approach each body is modeled with a modal methodology in a local non-inertial frame of reference, whereas in the second approach, each body is modeled with a finite element methodology in the inertial frame. In both cases, the interaction among the various elastic bodies is represented by constraint equations. The two approaches were compared for accuracy and efficiency: the first approach is preferable when the nonlinearities are not too strong but it becomes cumbersome and expensive to use when many modes must be used. The second approach is more general and easier to implement but could result in high computation costs for a large system. The constraints should be enforced in a time derivative fashion for better accuracy and stability.

Bauchau, Olivier A.↗

NASA NTRS1991

Site-certification imaging sensor for the exploration of Mars

A 'time dilation' push-broom imaging CCD sensor is being considered for certification of landing and roving sites for the exploration of Mars. It will be used to certify several 10 x 10 km candidate sites and to identify rocks and holes of 1 m or larger at those sites, using an optical sensor with 0.25 m resolution. This will require a high-resolution large-aperture camera and a camera-pointing system designed for high accuracy and stability. To reduce the data rate and increase the exposure time, the imaging time will be stretched out by a factor of eight over the time required to fly directly over the imaged site. Six parallel data storage strings will be used to reduce the data acquisition rate, allowing each string to process a manageable 25 Mb/s.

Scholl, M. S.↗

NASA NTRS1991

Determination of the in-flight spectral and radiometric characteristics of the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS)

AVIRIS is a science research imaging spectrometer that measures radiance in 224 channels between 400 to 2450 nm in the electromagnetic spectrum. To determine the inflight spectral and radiometric characteristics of AVIRIS a validation and calibration experiment was performed. Five data sets were acquired over a calibration site on the homogeneous playa of Rogers Dry Lake, California, U.S. Surface reflectance, atmospheric optical depths, and atmospheric water vapor measurements were acquired concurrently with the overflights. These in situ measurements were used to constrain the LOWTRAN 7 radiative transfer code to predict the total spectral radiance incident at the AVIRIS aperture. These predicted radiances and the AVIRIS measured radiances were analyzed to validate the inflight characteristics. Inflight spectral channel positions and response functions over the AVIRIS spectral range were derived. Radiometric calibration coefficients were calculated for each channel as well as radiometric accuracy, intraflight stability, and noise equivalent delta radiance.

Green, Robert O.↗

NASA NTRS1992

Nonlinearly stable compact schemes for shock calculations

The applications of high-order, compact finite difference methods in shock calculations are discussed. The main concern is to define a local mean which will serve as a reference for introducing a local nonlinear limiting to control spurious numerical oscillations while maintaining the formal accuracy of the scheme. For scalar conservation laws, the resulting schemes can be proven total-variation stable in one space dimension and maximum-norm stable in multiple space dimensions. Numerical examples are shown to verify accuracy and stability of such schemes for problems containing shocks. These ideas can also be applied to other implicit schemes such as the continuous Galerkin finite element methods.

Cockburn, Bernardo↗

NASA NTRS1992

Development of iterative techniques for the solution of unsteady compressible viscous flows

A research effort was initiated at Georgia Tech in February 1991 on the development of efficient techniques for the computation of 2-D and 3-D unsteady compressible flow problems. It was found that in 2-D unsteady viscous flow applications, the generalized minimal residual (GMRES) scheme was able to significantly improve the accuracy and stability characteristics of an existing 2-D ADI (Alternating Direction Implicit) time marching scheme. That is, the GMRES/ADI combination allowed 10 to 20 times larger time steps compared to an ADI scheme. Because the GMRES algorithm requires 5 to 10 times the CPU work compared to the ADI scheme, the combined GMRES/ADI scheme yields a net factor of 2 savings in CPU cost. During the past year, we also experimented with GMRES/multigrid/ADI combination. The purpose of this combination was to compute the low frequency components of the change in the flow properties from one time step to the next on a coarse grid. This strategy reduces the memory requirements of the GMRES method roughly by a factor of 4-8 for steady flow problems.

Sankar, Lakshmi N.↗

NASA NTRS1992

Grid generation and its application to separated flows

A method for the computation of recirculating flows on a nonorthogonal boundary-fitted coordinate system is presented. The algebraic grid generation technique is used to generate grids in a flow field of arbitrary shape. Computations are performed by using the set of governing equations transformed for use on a generalized curvilinear coordinate system. Turbulent flow computations were made by using the k-epsilon model for most of the flow cases. Three pressure correction algorithms - SIMPLE, SIMPLEC, and PISO - were incorporated for use on a nonorthogonal grid. Comparisons were made on the basis of numerical stability and accuracy. The present method was found to be efficient for computations of recirculating flows.

Maruszewski, J. P.↗

NASA NTRS1992

A generalized gamma(s)-family of self-starting algorithms for computational structural dynamics

A generalized gamma(s)-family of self-starting single-step formulations are presented in order to provide simplified yet effective dynamic attributes to include features towards eliminating the need to involve accelerations in the computational process for structural dynamic problems. By appropriately selecting the parameters pertaining to gamma(s)(s = 1, 2, 3), both explicit and implicit formulations are obtained. The stability and accuracy characteristics of the gamma(s)-family of representations are presented to validate the robustness of the formulations for structural dynamic problems. Numerous illustrative examples are described and the results are in excellent agreement and validate the applicability of these formulations for structural dynamic computations.

Namburu, Raju R.↗

NASA NTRS1992

Far-infrared self-broadening in methylcyanide - Absorber-perturber resonance

Using tunable far-infrared spectrometers with high-frequency stability and accuracy, the self-pressure broadening and shift of CH3CN are measured. Evidence of absorber-perturber resonance effects on the collisional line shape are obtained. This tests the theoretical model and its possible improvements and also allows predictions of broadening and shift for a large class of molecules. Moreover, the resonance effect produces a theoretical temperature dependence of self-broadening that is different from what is commonly assumed.

Buffa, G.↗

NASA NTRS1991

A new finite element formulation for computational fluid dynamics. IX - Fourier analysis of space-time Galerkin/least-squares algorithms

A Fourier stability and accuracy analysis of the space-time Galerkin/least-squares method as applied to a time-dependent advective-diffusive model problem is presented. Two time discretizations are studied: a constant-in-time approximation and a linear-in-time approximation. Corresponding space-time predictor multi-corrector algorithms are also derived and studied. The behavior of the space-time algorithms is compared to algorithms based on semidiscrete formulations.

Shakib, Farzin↗

NASA NTRS1992

Portable microwave test packages for beam-waveguide antenna performance evaluations

Portable microwave test packages used to evaluate a new 34-m-diameter beam-waveguide (BWG) antenna are described. The experimental methodology involved transporting test packages to different focal points of the BWG system and making noise temperature, antenna efficiency, and holography measurements. Comparisons of data measured at the different focal points enabled determinations of performance degradations caused by various mirrors in the BWG system. It is shown that, due to remarkable stabilities and accuracies of radiometric data obtained through the use of the microwave test packages, degradations caused by the BWG system were successfully determined.

Otoshi, Tom Y.↗

NASA NTRS1993

Another Nulling Hall-Effect Current-Measuring Circuit

Lightweight, low-power circuit provides noncontact measurement of alternating or direct current of many ampheres in main conductor. Advantages of circuit over other nulling Hall-effect current-measuring circuits is stability and accuracy increased by putting both analog-to-digital and digital-to-analog converters in nulling feedback loop. Converters and rest of circuit designed for operation at sampling rate of 100 kHz, but rate changed to alter time or frequency response of circuit.

Thibodeau, Phillip E.↗