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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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1980

Damping in ring seals for compressible fluids

An analysis is presented to calculate damping in ring seals for a compressible fluid. Results show that damping in tapered ring seals (optimized for stiffness) is less than that in straight bore ring seals for the same minimum clearance. Damping in ring seals can promote fractional frequency whirl and can, thus, be detrimental. Thus, tapered seals can benefit rotor and seal stability by having lower damping as well as higher stiffness. Use of incompressible results leads to large errors.

Fleming, D. P.↗
NASA NTRS1982

A variational principle for compressible fluid mechanics: Discussion of the multi-dimensional theory

The variational principle for compressible fluid mechanics previously introduced is extended to two dimensional flow. The analysis is stable, exactly conservative, adaptable to coarse or fine grids, and very fast. Solutions for two dimensional problems are included. The excellent behavior and results lend further credence to the variational concept and its applicability to the numerical analysis of complex flow fields.

Prozan, R. J.↗
NASA NTRS1943

The flow of a compressible fluid past a curved surface

An iteration method is employed to obtain the flow of a compressible fluid past a curved surface. The first approximation which leads to the Prandtl-Glauert rule, is based on the assumption that the flow differs but little from a pure translation. The iteration process then consists in improving this first approximation in order that it will apply to a flow differing from pure translatory motion to a greater degree. The method fails when the Mach number of the undisturbed stream reaches unity but permits a transition from subsonic to supersonic conditions without the appearance of a compression shock. The limiting value at which potential flow no longer exits is indicated by the apparent divergence of the power series representing the velocity of the fluid at the surface of the solid boundary.

Kaplan, Carl↗
NASA NTRS1945

On two-dimensional flows of compressible fluids

This report is devoted to the study of two-dimensional steady motion of a compressible fluid. It is shown that the complete flow pattern around a closed obstacle cannot be obtained by the method of Chaplygin. In order to overcome this difficulty, a formula for the stream-function of a two-dimensional subsonic flow is derived. The formula involves an arbitrary function of a complex variable and yields all possible subsonic flow patterns of certain types. Conditions are given so that the flow pattern in the physical plane will represent a flow around a closed curve. The formula obtained can be employed for the approximate determination of a subsonic flow around an obstacle. The method can be extended to partially supersonic flows.

HODOGRAPHY METHOD↗
NASA NTRS2003

Convection in a Very Compressible Fluid: Comparison of Simulations With Experiments

The time profile (Delta)T(t) of the temperature difference, measured across a very compressible fluid layer of supercritical He-3 after the start of a heat flow, shows a damped oscillatory behavior before steady state convection is reached. The results for (Delta)T(t) obtained from numerical simulations and from laboratory experiments are compared over a temperature range where the compressibility varies by a factor of approx. = 40. First the steady-state convective heat current j(sup conv) as a function of the Rayleigh number R(alpha) is presented, and the agreement is found to be good. Second, the shape of the time profile and two characteristic times in the transient part of (Delta)T(t) from simulations and experiments are compared, namely: 1) t(sub osc), the oscillatory period and 2) t(sub p), the time of the first peak after starting the heat flow. These times, scaled by the diffusive time tau(sub D) versus R(alpha), are presented. The agreement is good for t(sup osc)/tau(sub D), where the results collapse on a single curve showing a powerlaw behavior. The simulation hence confirms the universal scaling behavior found experimentally. However for t(sub p)/tau(sub D), where the experimental data also collapse on a single curve, the simulation results show systematic departures from such a behavior. A possible reason for some of the disagreements, both in the time profile and in t(sub p) is discussed. In the Appendix a third characteristic time, t(sub m), between the first peak and the first oscillation minimum is plotted and a comparison between the results of experiments and simulations is made.

Meyer, H.↗
NASA NTRS1947

On the one-dimensional theory of steady compressible fluid flow in ducts with friction and heat addition

Steady, diabatic (nonadiabatic), frictional, variable-area flow of a compressible fluid is treated in differential form on the basis of the one-dimensional approximation. The basic equations are first stated in terms of pressure, temperature, density, and velocity of the fluid. Considerable simplification and unification of the equations are then achieved by choosing the square of the local Mach number as one of the variables to describe the flow. The transformed system of equations thus obtained is first examined with regard to the existence of a solution. It is shown that, in general, a solution exists whose calculation requires knowledge only of the variation with position of any three of the dependent variables of the system. The direction of change of the flow variables can be obtained directly from the transformed equations without integration. As examples of this application of the equations, the direction of change of the flow variables is determined for two special flows. In the particular case when the local Mach number m = 1, a special condition must be satisfied by the flow if a solution is to exist. This condition restricts the joint rate of variation of heating, friction, and area at m = 1. Further analysis indicates that when a solution exists at this point it is not necessarily unique. Finally it is shown that the physical phenomenon of choking, which is known to occur in certain simple flow situations, is related to restrictions imposed on the variables by the form of the transformed equations. The phenomenon of choking is thus given a more general significance in that the transformed equations apply to a more general type of flow than has hitherto been treated. (author)

HIGH-SPEED↗
NASA NTRS1947

The stability of the laminar boundary layer in a compressible fluid

Report is a continuation of a theoretical investigation of the stability of the laminar boundary layer in a compressible fluid. An approximate estimate for the minimum critical Reynolds number, or stability limit, is obtained in terms of the distribution of the kinematic viscosity and the product of the mean density and mean vorticity across the boundary layer. The extension of the results of the stability analysis to laminar boundary-layer gas flows with a pressure gradient in the direction of the free stream is discussed. (author)

Lees, Lester↗
NASA NTRS1942

On the symmetrical potential flow of compressible fluid past a circular cylinder in the tunnel in the subcritical zone

The two-dimensional symmetrical potential flow of compressible fluid past a circular cylinder placed in the center line of a straight tunnel is analyzed in second approximation according to the Jansen-Rayleigh method. The departure of the profile from the exact circular shape can be kept to the same magnitude as for the incompressible flow. The velocities in the narrowest section of the tunnel wall and at the profile edge are discussed in detail.

Lamla, Ernst↗
NASA NTRS1999

High Order Approximations for Compressible Fluid Dynamics on Unstructured and Cartesian Meshes

The development of high-order accurate numerical discretization techniques for irregular domains and meshes is often cited as one of the remaining challenges facing the field of computational fluid dynamics. In structural mechanics, the advantages of high-order finite element approximation are widely recognized. This is especially true when high-order element approximation is combined with element refinement (h-p refinement). In computational fluid dynamics, high-order discretization methods are infrequently used in the computation of compressible fluid flow. The hyperbolic nature of the governing equations and the presence of solution discontinuities makes high-order accuracy difficult to achieve. Consequently, second-order accurate methods are still predominately used in industrial applications even though evidence suggests that high-order methods may offer a way to significantly improve the resolution and accuracy for these calculations. To address this important topic, a special course was jointly organized by the Applied Vehicle Technology Panel of NATO's Research and Technology Organization (RTO), the von Karman Institute for Fluid Dynamics, and the Numerical Aerospace Simulation Division at the NASA Ames Research Center. The NATO RTO sponsored course entitled "Higher Order Discretization Methods in Computational Fluid Dynamics" was held September 14-18, 1998 at the von Karman Institute for Fluid Dynamics in Belgium and September 21-25, 1998 at the NASA Ames Research Center in the United States. During this special course, lecturers from Europe and the United States gave a series of comprehensive lectures on advanced topics related to the high-order numerical discretization of partial differential equations with primary emphasis given to computational fluid dynamics (CFD). Additional consideration was given to topics in computational physics such as the high-order discretization of the Hamilton-Jacobi, Helmholtz, and elasticity equations. This volume consists of five articles prepared by the special course lecturers. These articles should be of particular relevance to those readers with an interest in numerical discretization techniques which generalize to very high-order accuracy. The articles of Professors Abgrall and Shu consider the mathematical formulation of high-order accurate finite volume schemes utilizing essentially non-oscillatory (ENO) and weighted essentially non-oscillatory (WENO) reconstruction together with upwind flux evaluation. These formulations are particularly effective in computing numerical solutions of conservation laws containing solution discontinuities. Careful attention is given by the authors to implementational issues and techniques for improving the overall efficiency of these methods. The article of Professor Cockburn discusses the discontinuous Galerkin finite element method. This method naturally extends to high-order accuracy and has an interpretation as a finite volume method. Cockburn addresses two important issues associated with the discontinuous Galerkin method: controlling spurious extrema near solution discontinuities via "limiting" and the extension to second order advective-diffusive equations (joint work with Shu). The articles of Dr. Henderson and Professor Schwab consider the mathematical formulation and implementation of the h-p finite element methods using hierarchical basis functions and adaptive mesh refinement. These methods are particularly useful in computing high-order accurate solutions containing perturbative layers and corner singularities. Additional flexibility is obtained using a mortar FEM technique whereby nonconforming elements are interfaced together. Numerous examples are given by Henderson applying the h-p FEM method to the simulation of turbulence and turbulence transition.

Barth, Timothy↗
NASA NTRS1944

On the flow of a compressible fluid by the hodograph method I : unification and extension of present-day results

Elementary basic solutions of the equations of motion of a compressible fluid in the hodograph variables are developed and used to provide a basis for comparison, in the form of velocity correction formulas, of corresponding compressible and incompressible flows. The known approximate results of Chaplygin, Von Karman and Tsien, Temple and Yarwood, and Prandtl and Glauert are unified by means of the analysis of the present paper. Two new types of approximations, obtained from the basic solutions, are introduced; they possess certain desirable features of the other approximations and appear preferable as a basis for extrapolation into the range of high stream Mach numbers and large disturbances to the main stream. Tables and figures giving velocity and pressure-coefficient correction factors are included in order to facilitate the practical application of the results.

Garrick, I E↗
NASA NTRS1944

The flow of a compressible fluid past a circular arc profile

The Ackeret iteration process is utilized to obtain higher approximations than that of Prandtl and Glauert for the flow of a compressible fluid past a circular arc profile. The procedure is to expand the velocity potential in a power series of the camber coefficient. The first two terms of the development correspond to the Prandtl-Glauert approximation and yield the well-known correction to the circulation about the profile. The second approximation, involving the square of the camber coefficient, improves the velocity and pressure fields but yields no new results with regard to the circulation, since the circulation about the profile is an odd function of the camber coefficient. The third approximation, involving the cube of the camber coefficient, permits the use of higher values of the camber coefficient and furthermore yields an improvement to the Prandtl-Glauert rule with regard to the effect of compressibility on the circulation of the circular arc profile. Numerical examples with tables and graphs illustrate the results of the analysis.

Kaplan, Carl↗
NASA NTRS1944

On the flow of a compressible fluid by the hodograph method II : fundamental set of particular flow solutions of the Chaplygin differential equation

The differential equation of Chaplygin's jet problem is utilized to give a systematic development of particular solutions of the hodograph flow equations, which extends the treatment of Chaplygin into the supersonic range and completes the set of particular solutions. The particular solutions serve to place on a reasonable basis the use of velocity correction formulas for the comparison of incompressible and compressible flows. It is shown that the geometric-mean type of velocity correction formula introduced in part I has significance as an over-all type of approximation in the subsonic range. A brief review of general conditions limiting the potential flow of an adiabatic compressible fluid is given and application is made to the particular solutions, yielding conditions for the existence of singular loci in the supersonic range. The combining of particular solutions in accordance with prescribed boundary flow conditions is not treated in the present paper.

Garrick, I E↗
NASA NTRS1944

On the Flow of a Compressible Fluid by the Hodograph Method. II - Fundamental Set of Particular Flow Solutions of the Chaplygin Differential Equation

The differential equation of Chaplygin's jet problem is utilized to give a systematic development of particular solutions of the hodograph flow equations, which extends the treatment of Chaplygin into the supersonic range and completes the set of particular solutions. The particular solutions serve to place on a reasonable basis the use of velocity correction formulas for the comparison of incompressible and compressible flows. It is shown that the geometric-mean type of velocity correction formula introduced in part I has significance as an over-all type of approximation in the subsonic range. A brief review of general conditions limiting the potential flow of an adiabatic compressible fluid is given and application is made to the particular solutions, yielding conditions for the existence of singular loci in the supersonic range. The combining of particular solutions in accordance with prescribed boundary flow conditions is not treated in the present paper.

Garrick, I. E.↗
NASA NTRS1998

A Parallel Non-Overlapping Domain-Decomposition Algorithm for Compressible Fluid Flow Problems on Triangulated Domains

This paper considers an algebraic preconditioning algorithm for hyperbolic-elliptic fluid flow problems. The algorithm is based on a parallel non-overlapping Schur complement domain-decomposition technique for triangulated domains. In the Schur complement technique, the triangulation is first partitioned into a number of non-overlapping subdomains and interfaces. This suggests a reordering of triangulation vertices which separates subdomain and interface solution unknowns. The reordering induces a natural 2 x 2 block partitioning of the discretization matrix. Exact LU factorization of this block system yields a Schur complement matrix which couples subdomains and the interface together. The remaining sections of this paper present a family of approximate techniques for both constructing and applying the Schur complement as a domain-decomposition preconditioner. The approximate Schur complement serves as an algebraic coarse space operator, thus avoiding the known difficulties associated with the direct formation of a coarse space discretization. In developing Schur complement approximations, particular attention has been given to improving sequential and parallel efficiency of implementations without significantly degrading the quality of the preconditioner. A computer code based on these developments has been tested on the IBM SP2 using MPI message passing protocol. A number of 2-D calculations are presented for both scalar advection-diffusion equations as well as the Euler equations governing compressible fluid flow to demonstrate performance of the preconditioning algorithm.

Barth, Timothy J.↗
NASA NTRS1958

Impact on a Compressible Fluid

Upon impact of a solid body on the plane surface of a fluid, there occurs on the vetted surface of the body an abrupt pressure rise which propagates into both media with the speed of sound. Below, we assume the case where the speed of propagation of sound in the body which falls on the surface of the fluid may be regarded as infinitely large in comparison with the speed of propagation of sound in the fluid; that is, we shall assume that the falling body is absolutely rigid. IN this case, the entire relative speed of the motion which takes place at the beginning of the impact is absorbed by the fluid. The hydrodynamic pressures arising thereby are propagated from the contact surface within the fluid with the speed of sound in the form of compression and expansion waves and are gradually damped. After this, they are dispersed like impact pressures, reach ever larger regions of the fluid remote fran the body and became equal to zero; in the fluid there remain hydrodynamic pressures corresponding to the motion of the body after the impact. Neglecting the forces of viscosity and taking into account, furthermore, that the motion of the fluid begins from a state of rest, according to Thomson's theorem, we may consider the motion of an ideal compressible fluid in the process of impact to be potential. We examine the case of impact upon the surface of a ccmpressible fluid of a flat plate of infinite extent or of a body, the immersed part of the surface of which may be called approximately flat. In this report we discuss the first phase of the impact pressure on the surface of a fluid, prior to the appearance of a cavity, since at this stage the hydrodynamic pressures reach their maximum values. Observations, after the fall of the bodies on the surface of the fluid, show that the free surface of the fluid at this stage is almost completely at rest if one does not take into account the small rise in the neighborhood of the boundaries of the impact surface.

Egorov, L. T.↗