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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

Choice of implicit and explicit operators for the upwind differencing method

The flux-vector and flux-difference splittings of Steger-Warming, Van Leer and Roe are tested in all possible combinations in the implicit and explicit operators that can be distinguished in implicit relaxation methods for the steady Euler and Navier-Stokes equations. The tests include one-dimensional inviscid nozzle flow, and two-dimensional inviscid and viscous shock reflection. Roe's splitting, as anticipated, is found to uniformly yield the most accurate results. On the other hand, an approximate Roe splitting of the implicit operator (the complete Roe splitting is too complicated for practical use) proves to be the least robust with regard to convergence to the steady state. In this respect, the Steger-Warming splitting is the most robust: it leads to convergence when combined with any of the splittings in the explicit operator, although not necessarily in the most efficient way.

Liou, Meng-Sing↗
NASA NTRS1986

Determination of water vapor profiles and total ozone burden from HIRS2/MSU sounding data

Algorithms for determining total ozone content and humidity from HIRS2/MSU data are examined. The methods are based on the ability to accurately model the response of a given channel to changes in a given atmospheric component. The steps of the iterative relaxation method for determining atmospheric water vapor and ozone content are described. Examples of retrieved fields of total ozone and precipitable water are presented.

Reuter, D.↗
NASA NTRS1999

Dynamic Nucleation of Supercooled Melts and Measurement of the Surface Tension and Viscosity

We investigate the phenomenon of acoustic pressure-induced nucleation by using a novel approach involving the large amplitude resonant radial oscillations and collapse of a single bubble intentionally injected into a supercooled liquid. Using a combination of previously developed and proven techniques, the bubble is suspended in a fluid host by an ultrasonic field which supplies both the levitation capability as well as the forcing of the radial oscillations. We observe the effects of an increase in pressure (due to bubble collapse) in a region no larger than 100 microns within the supercooled melt to rigorously probe the hypothesis of pressure-induced nucleation of the solid phase. The use of single bubbles operating in narrow temporal and spatial scales will allow the direct and unambiguous correlation between the origin and location of the generation of the disturbance and the location and timing of the nucleation event. In a companion research effort, we are developing novel techniques for the non-contact measurements of the surface tension and viscosity of highly viscous supercooled liquids. Currently used non-invasive methods of surface tension measurement for the case of undercooled liquids generally rely of the quantitative determination of the resonance frequencies of drop shape oscillations, of the dynamics of surface capillary waves, or of the velocity of streaming flows. These methods become quickly ineffective when the liquid viscosity rises to a significant value. An alternate and accurate method which would be applicable to liquids of significant viscosity is therefore needed. We plan to develop such a capability by measuring the equilibrium shape of levitated undercooled melt droplets as they undergo solid-body rotation. The experimental measurement of the characteristic point of transition (bifurcation point) between axisymmetric and two-lobed shapes will be used to calculate the surface tension of the liquid. Such an approach has already been validated through the experimental verification of numerical modeling results. The experimental approach involves levitation, melting, and solidification of undercooled droplets using a hybrid ultrasonic-electrostatic technique in both a gaseous as well as a vacuum environment. A shape relaxation method will be investigated in order to derive a reliable method to measure the viscosity of undercooled melts. The analysis of the monotonic relaxation to equilibrium shape of a drastically deformed and super-critically damped free drop has been used to derive interfacial tension of immiscible liquid combinations where one of the component has high viscosity. A standard approach uses the initial elongation of a droplet through shear flows, but an equivalent method could involve the initial deformation of a drop levitated in a gas by ultrasonic radiation pressure, electric stresses, or even solid body rotation. The dynamic behavior of the free drop relaxing back to equilibrium shape will be modeled, and its characteristic time dependence should provide a quantitative means to evaluate the liquid viscosity.

Trinh, E. H.↗
NASA NTRS1959

Numerical Solution of the Flow of a Perfect Gas Over A Circular Cylinder at Infinite Mach Number

A solution for the two-dimensional flow of an inviscid perfect gas over a circular cylinder at infinite Mach number is obtained by numerical methods of analysis. Nonisentropic conditions of curved shock waves and vorticity are included in the solution. The analysis is divided into two distinct regions, the subsonic region which is analyzed by the relaxation method of Southwell and the supersonic region which was treated by the method of characteristics. Both these methods of analysis are inapplicable on the sonic line which is therefore considered separately. The shapes of the sonic line and the shock wave are obtained by iteration techniques. The striking result of the solution is the strong curvature of the sonic line and of the other lines of constant Mach number. Because of this the influence of the supersonic flow on the sonic line is negligible. On comparison with Newtonian flow methods, it is found that the approximate methods show a larger variation of surface pressure than is given by the present solution.

Hamaker, Frank M.↗
NASA NTRS1993

Multigrid solution of the Navier-Stokes equations on highly stretched grids with defect correction

Relaxation-based multigrid solvers for the steady incompressible Navier-Stokes equations are examined to determine their computational speed and robustness. Four relaxation methods with a common discretization have been used as smoothers in a single tailored multigrid procedure. The equations are discretized on a staggered grid with first order upwind used for convection in the relaxation process on all grids and defect correction to second order central on the fine grid introduced once per multigrid cycle. A fixed W(1,1) cycle with full weighting of residuals is used in the FAS multigrid process. The resulting solvers have been applied to three 2D flow problems, over a range of Reynolds numbers, on both uniform and highly stretched grids. In all cases the L(sub 2) norm of the velocity changes is reduced to 10(exp -6) in a few 10's of fine grid sweeps. The results from this study are used to draw conclusions on the strengths and weaknesses of the individual relaxation schemes as well as those of the overall multigrid procedure when used as a solver on highly stretched grids.

Sockol, Peter M.↗
NASA NTRS1990

An implicit finite element method for high speed flows

A fast algorithm is presented for constructing continuous lines, consisting of element sides, on general unstructured two-dimensional triangular meshes. The lines must pass through each node of the mesh once and only once. The discussion focuses on the use of these lines in a relaxation method for the solution of the equation system arising from an implicit algorithm for the solution of two-dimensional Euler and Navier-Stokes equations on general unstructured grids. It is also shown that the method can be used for solving three-dimensional Navier-Stokes equations on a grid composed of both structured and unstructured regions.

Hassan, O.↗
NASA NTRS1976

Numerical computation of transonic flows with shock waves

Some recent developments in numerical methods for calculating solutions to the transonic potential flow equation are reviewed, including (1) the construction of the stable coordinate independent difference schemes; (2) the use of conservation form to insure proper shock jump conditions; (3) analysis of the relaxation method by the time dependent analogy; (4) accelerated iterative schemes.

Jameson, A.↗
NASA NTRS2015

A New Formulation of the Filter-Error Method for Aerodynamic Parameter Estimation in Turbulence

A new formulation of the filter-error method for estimating aerodynamic parameters in nonlinear aircraft dynamic models during turbulence was developed and demonstrated. The approach uses an estimate of the measurement noise covariance to identify the model parameters, their uncertainties, and the process noise covariance, in a relaxation method analogous to the output-error method. Prior information on the model parameters and uncertainties can be supplied, and a post-estimation correction to the uncertainty was included to account for colored residuals not considered in the theory. No tuning parameters, needing adjustment by the analyst, are used in the estimation. The method was demonstrated in simulation using the NASA Generic Transport Model, then applied to the subscale T-2 jet-engine transport aircraft flight. Modeling results in different levels of turbulence were compared with results from time-domain output error and frequency- domain equation error methods to demonstrate the effectiveness of the approach.

Grauer, Jared A.↗
NASA NTRS2000

Color M-mode Doppler flow propagation velocity is a preload insensitive index of left ventricular relaxation: animal and human validation

OBJECTIVES: To determine the effect of preload in color M-mode Doppler flow propagation velocity (v(p)). BACKGROUND: The interpretation of Doppler filling patterns is limited by confounding effects of left ventricular (LV) relaxation and preload. Color M-mode v(p) has been proposed as a new index of LV relaxation. METHODS: We studied four dogs before and during inferior caval (IVC) occlusion at five different inotropic stages and 14 patients before and during partial cardiopulmonary bypass. Left ventricular (LV) end-diastolic volumes (LV-EDV), the time constant of isovolumic relaxation (tau), left atrial (LA) pre-A and LV end-diastolic pressures (LV-EDP) were measured. Peak velocity during early filling (E) and v(p) were extracted by digital analysis of color M-mode Doppler images. RESULTS: In both animals and humans, LV-EDV and LV-EDP decreased significantly from baseline to IVC occlusion (both p < 0.001). Peak early filling (E) velocity decreased in animals from 56 +/- 21 to 42 +/- 17 cm/s (p < 0.001) without change in v(p) (from 35 +/- 15 to 35 +/- 16, p = 0.99). Results were similar in humans (from 69 +/- 15 to 53 +/- 22 cm/s, p < 0.001, and 37 +/- 12 to 34 +/- 16, p = 0.30). In both species, there was a strong correlation between LV relaxation (tau) and v(p) (r = 0.78, p < 0.001, r = 0.86, p < 0.001). CONCLUSIONS: Our results indicate that color M-mode Doppler v(p) is not affected by preload alterations and confirms that LV relaxation is its main physiologic determinant in both animals during varying lusitropic conditions and in humans with heart disease.

Non-NASA Center↗
NASA NTRS1985

Acoustic emission monitoring crack propagation in single crystal silicon

The feasibility of acoustic emission (AE) monitoring of cracking and crack propagation in Si semiconductor materials was evaluated experimentally. A double torsion load relaxation method was employed wherein the propagation velocity and the AE levels in precracked (but not notched) boron-doped wafers were recorded simultaneously. A numerical model for the critical stress intensity factor (KIC) was used to relate the crack growth velocity, the instantaneous load and the load relaxation rate. All specimens were monitored with acoustic transducers at six points and examined with SEM after failure. The AE levels reached a peak amplitude of 70 dB at a KIC of 0.997 MNm to the -3/2 for cracking in the 111 plane. No AE was detected before the load reached the KIC, indicating that no subcritical crack growth occurs in Si. The results support the use of AE for monitoring crack propagation in crystal Si.

Chen, C. P.↗
NASA NTRS1984

Conservative streamtube solution of steady-state Euler equations

This paper presents a new method for solving the steady state Euler equations. The method is similar to streamline curvature methods but has a conserative finite volume formulation which ensures correct shock capturing. Either wall position or wall pressure may be prescribed as boundary conditions, permitting both direct and inverse calculations. In supersonic applications the solution is obtained by space-marching while in subsonic and transonic applications iterative relaxation methods are used. Numerical results are given for: (1) supersonic diffuser with oblique shocks (direct calculation); (2) supersonic jet entering still reservoir (inverse calculation); (3) subsonic bump in a channel with 25 percent blockage (direct and inverse); (4) subsonic high-work turbine cascade (direct); and (5) transonic bump in a channel with 12 percent blockage (direct calculation).

Drela, M.↗
NASA NTRS1944

The numerical solution of compressible fluid flow problems

Numerical methods have been developed for obtaining the steady, adiabatic flow field of a frictionless, perfect gas about arbitrary two-dimensional bodies. The solutions include the subsonic velocity regions, the supersonic velocity regions, and the transition compression shocks, if required. Furthermore, the rotational motion and entropy changes following shocks are taken into account. Extensive use is made of the relaxation method. In this report the details of the methods of solution are emphasized so as to permit others to solve similar problems. Solutions already obtained are mentioned only by way of illustrating the possibilities of the methods described. The methods can be applied directly to wind tunnel and free air tests of arbitrary airfoil shapes at subsonic, sonic, and supersonic speeds.

Emmons, Howard W↗
NASA NTRS1978

Preliminary study of the use of the STAR-100 computer for transonic flow calculations

A description is presented for a new explicit algorithm for solving the transonic small-disturbance potential equation on the STAR-100 computer. The STAR computer has a 'pipeline' type of processor which is very efficient in doing arithmetic operations on long vectors. Unfortunately, the successive line over-relaxation method, which represents the best method for solving the considered equation, is not suitable for vector-arithmetic procedures. The described algorithm, however, can be vectorized to make an employment of the STAR-100 possible. It is found that a use of the new algorithm for solving the equation on the STAR-100 computer can almost halve the computer time required for this type of computation when compared to successive line over-relaxation on the CYBER 175 computer.

Keller, J. D.↗
NASA NTRS1993

Euler solutions for blunt bodies using triangular meshes - Artificial viscosity forms and numerical boundary conditions

A finite volume method is used to calculate compressible inviscid flows over blunt bodies using, in general, unstructured grids. Artificial viscosity forms are derived based on a simplified least squares procedure. The extra second order terms are consistent with the governing equations, hence a systematic treatment of the numerical boundary conditions can be easily implemented. A special treatment of blunt bodies may be required. The discrete equations are linearized and the resulting system is solved by a relaxation method. Preliminary results indicate that the effect of the numerical dissipation is minimal. For subsonic flows over smooth bodies, the solution is practically vorticity-free and the total pressure loss is of the same order as the truncation error. Finally, some extensions of the present method are briefly discussed.

Winterstein, R.↗
NASA NTRS2011

Three-Dimensional Modeling of the Solar Wind: From the Coronal Base to the Outer Heliosphere

We have developed a global fully three-dimensional magnetohydrodynamic solar wind model for the region that extends from the coronal base to 100 AU. The simulation domain consists of tree spherical shell subdomains with computational boundaries between them placed at 20 solar radii and 0.3 AU. The location of the first boundary ensures that the flow at the boundary is both supersonic and super-Alfvenic. A steady-state solution in the innermost (coronal) region is obtained by the time-relaxation method. The solution uses a tilted dipole model or solar magnetograms as the boundary condition at the coronal base and includes a flux of Alfven waves in the WKB approximation which provide additional acceleration for the coronal outflow in the open field regions. The intermediate region solution is constructed by the integration of steady-state equations along radius using a marching scheme. The outer region solution (0.3-100 AU) is obtained again by the time relaxation and takes into account turbulence transport and heating as well as heating, flow deceleration, and other effects due to the interstellar pickup protons treated as a separate fluid. We use the model to simulate the global steady-state structure of the solar wind from the coronal base to the heliospheric boundary and compare the results with Ulysses and Voyager observations.

Usmanov, A. V↗
NASA NTRS1949

Two-dimensional compressible flow in turbomachines with conic flow surfaces

A general method of analysis is developed for two-dimensional, steady, compressible flow in stators or rotors of radial and mixed flow turbomachines with conic flow surfaces (surfaces of right circular cones generated by center line of flow passage in the axial-radial plane). The variables taken into account are: (1) tip speed of the rotor, (2) flow rate, (3) blade shape, (4) variation in passage height with radius, (5) number of blades, and (6) cone angle of the flow surface. Relaxation methods are used to solve the nonlinear differential equation for the stream function. Two numerical examples are presented; one for compressible and the other for incompressible flow in a centrifugal compressor with thin, straight blades. The results of these examples are given by plots of the streamlines, constant velocity-ratio lines, and constant pressure-ratio line.

Stanitz, John D↗
NASA NTRS1987

A numerical method for the solution of three dimensional, incompressible, viscous flows over slender bodies

A marching iterative method for the solution of the three dimensional, incompressibhle, steady and parabolized Navier-Stokes equations is described. The equations are written in primitive variables and discretized in general axisymmetric orthogonal coordinate systems. The coupled set of finite-difference equations are solved without any splitting or factorization errors. Moreover, the continuity equation and the two crossflow momentum equations are exactly satisfied at every step of the iterative process. The solution scheme is equivalent to the solution of one Poisson equation by the Successive Plane Over Relaxation method and has good convergence properties. Other existing solution methods resemble a Jacobi-type iterative scheme and therefore are less efficient. Numerical experiments include the laminar, incompressible flow over prolate spheroids at incidence.

Rosenfeld, Moshe↗
NASA NTRS1976

Numerical solution of periodic transonic flow through a fan stage

A numerical method of solution of the inviscid, compressible, two-dimensional unsteady flow on a blade-to-blade stream surface through a stage (rotor and stator), or a single blade row, of an axial flow compressor or fan is described. A cyclic procedure has been developed for representation of adjacent blade-to-blade passages, which asymptotically achieves the correct phase between all passages of a stage. A shock-capturing finite-difference method is employed in the interior of the passage, and a method-of-characteristics technique is used at the boundaries. The blade slipstreams form two of the passage boundaries, and are treated as moving contact surfaces capable of supporting jumps in entropy and tangential velocity. The Kutta condition is imposed by requiring the slipstreams to originate at the trailing edges, which are assumed to be sharp. Results are presented for several transonic fan rotors, and compared with available experimental data consisting of holographic observations of shock structure and pressure contour maps. A subcritical stator solution is also compared with results from a relaxation method. Finally, a periodic solution for a stage consisting of 44 rotor blades and 46 stator blades is discussed.

Erdos, J. I.↗