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NASA NTRS1982

Time resolved density measurements in premixed turbulent flames

Premixed, turbulent flames are important in connection with investigations of fundamental, turbulent-reacting-flow processes and the study of practical combustion devices, such as spark ignition engines and premixed, prevaporized gas turbine combustors which burn premixed reactants. The considered investigation is concerned with the application of laser induced Rayleigh scattering to measure the gas density in premixed, methane-air flames. A description is provided of the results of density and velocity measurements in an open, lean, premixed methane-air flame stabilized in grid turbulence of low Reynolds number. It is found that where applicable, Rayleigh scattering can be used to good advantage to measure molecular number density. Mean and rms density results show that the mean flame thickens with axial distance but that the maximum in rms does not change appreciably.

Dandekar, K. V.↗

NASA NTRS1990

Stable boundary conditions for Cartesian grid calculations

The inviscid Euler equations in complicated geometries are solved using a Cartesian grid. This requires solid wall boundary conditions in the irregular grid cells near the boundary. Since these cells may be orders of magnitude smaller than the regular grid cells, stability is a primary concern. An approach to this problem is presented and its use is illustrated.

Berger, M. J.↗

NASA NTRS1990

Stable boundary conditions for Cartesian grid calculations

Berger, M. J.↗

NASA NTRS1994

Stability and error estimation for Component Adaptive Grid methods

Component adaptive grid (CAG) methods for solving hyperbolic partial differential equations (PDE's) are discussed in this paper. Applying recent stability results for a class of numerical methods on uniform grids. The convergence of these methods for linear problems on component adaptive grids is established here. Furthermore, the computational error can be estimated on CAG's using the stability results. Using these estimates, the error can be controlled on CAG's. Thus, the solution can be computed efficiently on CAG's within a given error tolerance. Computational results for time dependent linear problems in one and two space dimensions are presented.

Oliger, Joseph↗

NASA NTRS2012

Numerical Dissipation and Wrong Propagation Speed of Discontinuities for Stiff Source Terms

In compressible turbulent combustion/nonequilibrium flows, the constructions of numerical schemes for (a) stable and accurate simulation of turbulence with strong shocks, and (b) obtaining correct propagation speed of discontinuities for stiff reacting terms on coarse grids share one important ingredient - minimization of numerical dissipation while maintaining numerical stability. Here coarse grids means standard mesh density requirement for accurate simulation of typical non-reacting flows. This dual requirement to achieve both numerical stability and accuracy with zero or minimal use of numerical dissipation is most often conflicting for existing schemes that were designed for non-reacting flows. The goal of this paper is to relate numerical dissipations that are inherited in a selected set of high order shock-capturing schemes with the onset of wrong propagation speed of discontinuities as a function of stiffness of the source term and the grid spacing.

Yee, H. C.↗

NASA NTRS2011

Numerical Dissipation and Wrong Propagation Speed of Discontinuities for Stiff Source Terms

In compressible turbulent combustion/nonequilibrium flows, the constructions of numerical schemes for (a) stable and accurate simulation of turbulence with strong shocks, and (b) obtaining correct propagation speed of discontinuities for stiff reacting terms on coarse grids share one important ingredient - minimization of numerical dissipation while maintaining numerical stability. Here coarse grids means standard mesh density requirement for accurate simulation of typical non-reacting flows. This dual requirement to achieve both numerical stability and accuracy with zero or minimal use of numerical dissipation is most often conflicting for existing schemes that were designed for non-reacting flows. The goal of this paper is to relate numerical dissipations that are inherited in a selected set of high order shock-capturing schemes with the onset of wrong propagation speed of discontinuities for two representative stiff detonation wave problems.

Yee, H. C.↗

NASA NTRS1999

Unstructured Grid Euler Method Assessment for Longitudinal and Lateral/Directional Stability Analysis of the HSR Reference H Configuration at Transonic Speeds

Transonic Euler computations, based on unstructured grid methodology, are performed for a proposed High Speed Civil Transport (HSCT) configuration, designated as the Reference H configuration within the High Speed Research (HSR) Program. The predicted results are correlated with appropriate experimental wind-tunnel data for the baseline configuration with and without control surface deflections for a range of angle of attack at M(sub infinity) = 0.95. Good correlations between the predictions and measured data have been obtained for the longitudinal aerodynamic characteristics of the baseline configuration. The incremental effects in the longitudinal aerodynamic characteristics due to horizontal rail deflections as well as wing leading-edge and trailing-edge flap deflections have also been predicted reasonably well. Computational results and correlations with data are also presented for the lateral and directional stability characteristics for a range of angle of attack at a constant sideslip angle as well as a range of sideslip angles at a constant angle of attack. In addition, the results are presented to assess the computational method performance and convergence characteristics.

Ghaffari, Farhad↗

NASA NTRS1990

Counterrotating prop-fan simulations which feature a relative-motion multiblock grid decomposition enabling arbitrary time-steps

Improvements are presented of a computer algorithm developed for the time-accurate flow analysis of rotating machines. The flow model is a finite volume method utilizing a high-resolution approximate Riemann solver for interface flux definitions. The numerical scheme is a block LU implicit iterative-refinement method which possesses apparent unconditional stability. Multiblock composite gridding is used to orderly partition the field into a specified arrangement of blocks exhibiting varying degrees of similarity. Block-block relative motion is achieved using local grid distortion to reduce grid skewness and accommodate arbitrary time step selection. A general high-order numerical scheme is applied to satisfy the geometric conservation law. An even-blade-count counterrotating unducted fan configuration is chosen for a computational study comparing solutions resulting from altering parameters such as time step size and iteration count. The solutions are compared with measured data.

Janus, J. Mark↗

NASA NTRS2010

An Improved Neutron Transport Algorithm for HZETRN

Long term human presence in space requires the inclusion of radiation constraints in mission planning and the design of shielding materials, structures, and vehicles. In this paper, the numerical error associated with energy discretization in HZETRN is addressed. An inadequate numerical integration scheme in the transport algorithm is shown to produce large errors in the low energy portion of the neutron and light ion fluence spectra. It is further shown that the errors result from the narrow energy domain of the neutron elastic cross section spectral distributions, and that an extremely fine energy grid is required to resolve the problem under the current formulation. Two numerical methods are developed to provide adequate resolution in the energy domain and more accurately resolve the neutron elastic interactions. Convergence testing is completed by running the code for various environments and shielding materials with various energy grids to ensure stability of the newly implemented method.

Slaba, Tony C.↗

NASA NTRS1985

Advanced ion thruster research

A series of experiments conducted on a ring cusp magnetic field ion thruster; in which the anode, cathode and discharge chamber backplate were moved relative to the magnetic cusp; are described. Optimum locations for the anode, cathode and backplate which yield the lowest energy cost per plasma ion and highest extracted ion fraction are identified. The results are discussed in terms of simple physical models. The results of preliminary experiments into the operation of hollow cathodes on nitrogen and xenon over a large pressure range (0.1 to 100 Torr) are presented. They show that the cathode discharge transfers from the cathode insert to the exterior edge of the orifice plate as the interelectrode pressure is increased. Experimental evidence showing that a new ion extractor grid concept can be used to stabilize the plasma sheath at the screen grid is presented. This concept, identified by the term constrained sheath optics, is shown to hold ion beamlet divergence and impingement characteristics to stable values as the beamlet current and the net and total accelerating voltages are changed. The current status of a study of beamlet vectoring induced by displacing the accelerator and/or decelerator grids of a three grid ion extraction system relative to the screen grid is discussed.

Wilbur, P. J.↗

NASA NTRS1993

The effect of grid aspect ratio on convergence

Vector stability theory and computational experiments are used to examine the effects of high aspect ratio grids on algorithm convergence. Emphasis is placed on identifying the degree of convergence deterioration that ADI schemes experience as grid aspect ratio increases and on deriving methods for circumventing this problem. Approximately factored implicit schemes are found to experience convergence deterioration because of nonoptimum local time stepping procedures and the increased need for viscous preconditioning. An enhanced algorithm is devised on the basis of improved selection of the local time step, appropriate definition of viscous preconditioning matrix, and proper implementation of boundary conditions. The novel algorithm provides uniformly efficient convergence at all aspect ratios for both Euler and Navier-Stokes computations for a variety of test problems.

Buelow, P. E. O.↗

NASA NTRS1991

Stability of compressible Taylor-Couette flow

Compressible stability equations are solved using the spectral collocation method in an attempt to study the effects of temperature difference and compressibility on the stability of Taylor-Couette flow. It is found that the Chebyshev collocation spectral method yields highly accurate results using fewer grid points for solving stability problems. Comparisons are made between the result obtained by assuming small Mach number with a uniform temperature distribution and that based on fully incompressible analysis.

Kao, Kai-Hsiung↗

NASA NTRS1987

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 multitasking. The accuracy and stability of the composite grid scheme has been tested by numerically simulating the flow over an ellipsoid at angle of attack and comparing the solution with a single grid solution. The flowfield over a projectile at M = 0.96 and 4 deg angle-of-attack has been computed using a fine grid, and compared with experiment.

Sahu, Jubaraj↗

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 NTRS2013

Stability, Transient Response, Control, and Safety of a High-Power Electric Grid for Turboelectric Propulsion of Aircraft

This document contains the deliverables for the NASA Research and Technology for Aerospace Propulsion Systems (RTAPS) regarding the stability, transient response, control, and safety study for a high power cryogenic turboelectric distributed propulsion (TeDP) system. The objective of this research effort is to enumerate, characterize, and evaluate the critical issues facing the development of the N3-X concept aircraft. This includes the proposal of electrical grid architecture concepts and an evaluation of any needs for energy storage.

Armstrong, Michael↗

NASA NTRS1974

Multi-off-grid methods in multi-step integration of ordinary differential equations

Description of methods of solving first- and second-order systems of differential equations in which all derivatives are evaluated at off-grid locations in order to circumvent the Dahlquist stability limitation on the order of on-grid methods. The proposed multi-off-grid methods require off-grid state predictors for the evaluation of the n derivatives at each step. Progressing forward in time, the off-grid states are predicted using a linear combination of back on-grid state values and off-grid derivative evaluations. A comparison is made between the proposed multi-off-grid methods and the corresponding Adams and Cowell on-grid integration techniques in integrating systems of ordinary differential equations, showing a significant reduction in the error at larger step sizes in the case of the multi-off-grid integrator.

Beaudet, P. R.↗

NASA NTRS1978

Numerical spatial marching techniques for estimating duct attenuation and source pressure profiles

A numerical method was developed that could predict the pressure distribution of a ducted source from far field pressure inputs. Using an initial value formulation, the two-dimensional homogeneous Helmholtz wave equation (no steady flow) was solved using explicit marching techniques. The Von Neumann method was used to develop relationships which describe how sound frequency and grid spacing effect numerical stability. At the present time, stability considerations limit the approach to high frequency sound. Sample calculations for both hard and soft wall ducts compare favorably to known boundary value solutions. In addition, assuming that reflections in the duct are small, this initial value approach was successfully used to determine the attenuation of a straight soft wall duct. Compared to conventional finite difference or finite element boundary value approaches, the numerical marching technique is orders of magnitude shorter in computation time and required computer storage and can be easily employed in problems involving high frequency sound.

Baumeister, K. J.↗

NASA NTRS1978

Numerical spatial marching techniques for estimating duct attenuation and source pressure profiles

A numerical method is developed that could predict the pressure distribution of a ducted source from far-field pressure inputs. Using an initial value formulation, the two-dimensional homogeneous Helmholtz wave equation (no steady flow) is solved using explicit marching techniques. The Von Neumann method is used to develop relationships which describe how sound frequency and grid spacing effect numerical stability. At the present time, stability considerations limit the approach to high frequency sound. Sample calculations for both hard and soft wall ducts compare favorably to known boundary value solutions. In addition, assuming that reflections in the duct are small, this initial value approach is successfully used to determine the attenuation of a straight soft wall duct. Compared to conventional finite difference or finite element boundary value approaches, the numerical marching technique is orders of magnitude shorter in computation time and required computer storage and can be easily employed in problems involving high frequency sound.

Baumeister, K. J.↗