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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

Karhunen-Loeve expansion of Burgers' model of turbulence

The properties of the Karhunen-Loeve expansion of a strongly inhomogeneous random process are examined with emphasis on applications to turbulent flow fields. The ability of the KL expansion to represent functions that have both slow and rapid variations in a relatively small number of expansion terms is tested on a one-dimensional model based on the forced Burgers' equation. The rate of the convergence of the expansion is evaluated, and its dependence on the Reynolds number is determined. It is shown that the KL eigenfunctions possess wall boundary layers attached to outer structures that are independent of the Reynolds number (at high Reynolds numbers). It is also shown that the spectrum of eigenvalues is broad at large Reynolds numbers, requiring many terms to represent higher-order derivatives of the function.

Chambers, D. H.↗
NASA NTRS1989

A hybrid-perturbation-Galerkin technique which combines multiple expansions

A two-step hybrid perturbation-Galerkin method for the solution of a variety of differential equations type problems is found to give better results when multiple perturbation expansions are employed. The method assumes that there is parameter in the problem formulation and that a perturbation method can be sued to construct one or more expansions in this perturbation coefficient functions multiplied by computed amplitudes. In step one, regular and/or singular perturbation methods are used to determine the perturbation coefficient functions. The results of step one are in the form of one or more expansions each expressed as a sum of perturbation coefficient functions multiplied by a priori known gauge functions. In step two the classical Bubnov-Galerkin method uses the perturbation coefficient functions computed in step one to determine a set of amplitudes which replace and improve upon the gauge functions. The hybrid method has the potential of overcoming some of the drawbacks of the perturbation and Galerkin methods as applied separately, while combining some of their better features. The proposed method is applied, with two perturbation expansions in each case, to a variety of model ordinary differential equations problems including: a family of linear two-boundary-value problems, a nonlinear two-point boundary-value problem, a quantum mechanical eigenvalue problem and a nonlinear free oscillation problem. The results obtained from the hybrid methods are compared with approximate solutions obtained by other methods, and the applicability of the hybrid method to broader problem areas is discussed.

Geer, James F.↗
NASA NTRS1990

Solar wind proton velocity distributions - Comparison of the bi-Maxwellian based 16-moment expansion with observations

The purpose of this paper is to study the possible types of velocity distributions that can be obtained from the bi-Maxwellian based 16-moment expansion of the distribution function, assuming macroscopic parameter values characteristic of the range of solar wind conditions. While previous studies also took heat flow into account, the theoretical expansions for f and the definitions of the physical moments adopted in these studies were different from those used in this paper. The choice of the 16-moment expansion and corresponding moment definitions was motivated by the fact that this is the correct generalization of the widely-used Maxwellian-based 13-moment expansion to the case where the zeroth-order distribution is a bi-Maxwellian. It is found that most of the features characteristic of solar wind proton distributions can be reproduced with the 16-moment distribution, including the appearance of secondary peaks. It is also shown how each of the physically significant velocity moments affects the shape of the distribution function.

Demars, H. G.↗
NASA NTRS1991

Development of turbulence models for shear flows by a double expansion technique

Turbulence models are developed by supplementing the renormalization group (RNG) approach of Yakhot and Orszag with scale expansions for the Reynolds stress and production of dissipation terms. The additional expansion parameter (eta) is the ratio of the turbulent to mean strain time scale. While low-order expansions appear to provide an adequate description of the Reynolds stress, no finite truncation of the expansion for the production of dissipation term in powers of eta suffices - terms of all orders must be retained. Based on these ideas, a new two-equation model and Reynolds stress transport model are developed for turbulent shear flows. The models are tested for homogeneous shear flow and flow over a backward facing step. Comparisons between the model predictions and experimental data are excellent.

Yakhot, V.↗
NASA NTRS1990

A hybrid perturbation-Galerkin technique that combines multiple expansions

A two-step hybrid perturbation-Galerkin method for the solution of a variety of differential equations type problems is found to give better results when multiple perturbation expansions are employed. The method assumes that there is parameter in the problem formulation and that a perturbation method can be used to construct one or more expansions in this perturbation coefficient functions multiplied by computed amplitudes. In step one, regular and/or singular perturbation methods are used to determine the perturbation coefficient functions. The results of step one are in the form of one or more expansions each expressed as a sum of perturbation coefficient functions multiplied by a priori known gauge functions. In step two the classical Bubnov-Galerkin method uses the perturbation coefficient functions computed in step one to determine a set of amplitudes which replace and improve upon the gauge functions. The hybrid method has the potential of overcoming some of the drawbacks of the perturbation and Galerkin methods as applied separately, while combining some of their better features. The proposed method is applied, with two perturbation expansions in each case, to a variety of model ordinary differential equations problems including: a family of linear two-boundary-value problems, a nonlinear two-point boundary-value problem, a quantum mechanical eigenvalue problem and a nonlinear free oscillation problem. The results obtained from the hybrid methods are compared with approximate solutions obtained by other methods, and the applicability of the hybrid method to broader problem areas is discussed.

Geer, James F.↗
NASA NTRS1991

The effect on an acoustic wave as it traverses an unsteady expansion

The shift in fundamental frequency that occurs in acoustic waves is obtained for waves traversing an unsteady expansion. It is shown analytically that downstream of the unsteady expansion all frequencies approach one of an infinite number of discrete frequencies independent of the frequency upstream of the unsteady expansion. This theoretical analysis is used to accurately predict the period of noise observed in an expansion tube when operated at low enthalpies.

Paull, A.↗
NASA NTRS1991

High enthalpy, hypervelocity flows of air and argon in an expansion tube

An expansion tube with a free piston driver has been used to generate quasi-steady hypersonic flows in argon and air at flow velocities in excess of 9 km/s. Irregular test flow unsteadiness has limited the performance of previous expansion tubes, and it has been found that this can be avoided by attention to the interaction between the test gas accelerating expansion and the contact surface in the primary shock tube. Test section measurements of pitot pressure, static pressure and flat plate heat transfer are reported. An approximate analytical theory has been developed for predicting the velocities achieved in the unsteady expansion of the ionizing or dissociating test gas.

Neely, A. J↗
NASA NTRS1992

Development of turbulence models for shear flows by a double expansion technique

Turbulence models are developed by supplementing the renormalization group (RNG) approach of Yakhot and Orszag with scale expansions for the Reynolds stress and production of dissipation terms. The additional expansion parameter (eta) is the ratio of the turbulent to mean strain time scale. While low-order expansions appear to provide an adequate description of the Reynolds stress, no finite truncation of the expansion for the production of dissipation term in powers of eta suffices - terms of all orders must be retained. Based on these ideas, a new two-equation model and Reynolds stress transport model are developed for turbulent shear flows. The models are tested for homogeneous shear flow and flow over a backward facing step. Comparisons between the model predictions and experimental data are excellent.

Yakhot, V.↗
NASA NTRS1992

Comparison of the Unified Perturbation Method with the two-scale expansion

The Unified Perturbation Method (UPM) converges faster over a wider domain of surface roughness than other perturbations, such as the small perturbation method, the phase perturbation method, the Kirchhoff approximation, and the momentum transfer expansion. It can be shown that UPM intrinsically possess characteristics similar to the two-scale expansion without requiring a free parameter. This paper considers whether the UPM can be improved by applying the two-scale concept to the method. In order to do so, the unknown source current is expanded in a two-scale manner starting from the extinction theorem. Several two-scale expansions are derived and are compared with the conventional two-scale approximation. It is shown that the UPM performs best without two-scale expansions.

Kim, Yunjin↗
NASA NTRS1992

Hypersonic turbulent expansion-corner flow with shock impingement

Mean and fluctuating surface pressure data were obtained in a Mach 8, turbulent, cold flow past an expansion corner subjected to shock impingement. The expansion corner of 2.5 or 4.25 deg was located at 0.77 m (30.25 in.) from the leading edge of a shape-edged flat plate while an external shock, generated by either a 2- or 4-deg sharp wedge, impinged at the corner, or at one boundary layer thickness ahead or behind the corner. The mean pressure distribution was strongly influenced by the mutual interaction between the shock and the expansion. For example, the upstream influence decreased when the shock impinged downstream of the corner. Also, the unsteadiness of the interactions was characterized by an intermittent region and a local rms pressure peak near the upstream influence line. The peak rms pressure fluctuations increased with a larger overall interaction strength. Shock impingement downstream of the corner resulted in lower peaks and also in a shorter region of reduced fluctuation levels. These features may be exploited in inlet design by impinging the cowl shock downstream of an expansion corner instead of at the corner. In addition, a limited Pitot pressure survey showed a thinning of the boundary layer downstream of the corner.

Chung, Kung-Ming↗
NASA NTRS1995

The Superorbital Expansion Tube concept, experiment and analysis

In response to the need for ground testing facilities for super orbital re-entry research, a small scale facility has been set up at the University of Queensland to demonstrate the superorbital expansion tube concept. This unique device is a free piston driven, triple diaphragm, impulse shock facility which uses the enthalpy multiplication mechanism of the unsteady expansion process and the addition of a secondary shock driver to further heat the driver gas. The pilot facility has been operated to produce quasi-steady test flows in air with shock velocities in excess of 13 km/s and with a usable test flow duration of the order of 15 micro sec. an experimental condition produced in the facility with total enthalpy of 108 MJ/kg and a total pressure of 335 MPa is reported. A simple analytical flow model which accounts for non-ideal rupture of the light tertiary diaphragm and the resulting entropy increase in the test gas is discussed. It is shown that equilibrium calculations more accurately model the unsteady expansion process than calculations assuming frozen chemistry. This is because the high enthalpy flows produced in the facility can only be achieved if the chemical energy stored in the test flow during shock heating of the test gas is partially returned to the flow during the process of unsteady expansion. Measurements of heat transfer rates to a flat plate demonstrate the usability of test flow for aerothermodynamic testing and comparison of these rates with empirical calculations confirms the usable accuracy of the flow model.

Neely, A. J.↗
NASA NTRS1995

Numerical simulations of the flow in the HYPULSE expansion tube

Axisymmetric numerical simulations with finite-rate chemistry are presented for two operating conditions in the HYPULSE expansion tube. The operating gas for these two cases is nitrogen and the computations are compared to experimental data. One test condition is at a total enthalpy of 15.2 MJ/Kg and a relatively low static pressure of 2 kPa. This case is characterized by a laminar boundary layer and significant chemical nonequilibrium in the acceleration gas. The second test condition is at a total enthalpy of 10.2 MJ/Kg and a static pressure of 38 kPa and is characterized by a turbulent boundary layer. For both cases, the time-varying test gas pressure predicted by the simulations is in good agreement with experimental data. The computations are also found to be in good agreement with Mirels' correlations for shock tube flow. It is shown that the nonuniformity of the test gas observed in the HYPULSE expansion tube is strongly linked to the boundary layer thickness. The turbulent flow investigated has a larger boundary layer and greater test gas nonuniformity. In order to investigate possibilities of improving expansion tube flow quality by reducing the boundary layer thickness, parametric studies showing the effect of density and turbulent transition point on the test conditions are also presented. Although an increase in the expansion tube operating pressure level would reduce the boundary layer thickness, the simulations indicate that the reduction would be less than what is predicted by flat plate boundary layer correlations.

Wilson, Gregory J.↗
NASA NTRS1995

Bearing-Mounting Concept Accommodates Thermal Expansion

Pins or splines allow radial expansion without slippage. Design concept for mounting rotary bearing accommodates differential thermal expansion between bearing and any structure(s) to which bearing connected. Prevents buildup of thermal stresses by allowing thermal expansion to occur freely but accommodating expansion in such way not to introduce looseness. Pin-in-slot configuration also maintains concentricity.

Nespodzany, Robert↗
NASA NTRS1995

Boundary layer blockage in expansion tube nozzles

The results of a first order perfect gas correction for the effects of the boundary layer formation within expansion tubes with nozzles are presented. The analytical model developed to describe the boundary layer formation within the expansion tube and an expansion nozzle located at the end of the acceleration tube is based on the Karman integral equations. The results of this analytical model are compared with experimental data from an expansion diffuser. The model provides a useful tool for the preliminary design of nozzles for such facilities.

Sudnitsin, Olga↗
NASA NTRS1995

Magnetic expansion of cosmic plasmas

Plasma expansion is common in many astrophysical phenomena. The understanding of the driving mechanism has usually been focused on the gas pressure that implies conversion of thermal energy into flow kinetic energy. However, 'cool' expansions have been indicated in stellar/solar winds and other expanding processes. Magnetic expansion may be the principal driving mechanism. Magnetic energy in the potential form can be converted into kinetic energy during global expansion of magnetized plasmas.

Yang, Wei-Hong↗
NASA NTRS1999

Experimental and Computational Investigation of a Translating-Throat Single-Expansion-Ramp Nozzle

An experimental and computational study was conducted on a high-speed, single-expansion-ramp nozzle (SERN) concept designed for efficient off-design performance. The translating-throat SERN concept adjusts the axial location of the throat to provide a variable expansion ratio and allow a more optimum jet exhaust expansion at various flight conditions in an effort to maximize nozzle performance. Three design points (throat locations) were investigated to simulate the operation of this concept at subsonic-transonic, low supersonic, and high supersonic flight conditions. The experimental study was conducted in the jet exit test facility at the Langley Research Center. Internal nozzle performance was obtained at nozzle pressure ratios (NPR's) up to 13 for six nozzles with design nozzle pressure ratios near 9, 42, and 102. Two expansion-ramp surfaces, one concave and one convex, were tested for each design point. Paint-oil flow and focusing schlieren flow visualization techniques were utilized to acquire additional flow data at selected NPR'S. The Navier-Stokes code, PAB3D, was used with a two-equation k-e turbulence model for the computational study. Nozzle performance characteristics were predicted at nozzle pressure ratios of 5, 9, and 13 for the concave ramp, low Mach number nozzle and at 10, 13, and 102 for the concave ramp, high Mach number nozzle.

Deere, Karen A.↗
NASA NTRS1994

Rotational Relaxation in Nonequilibrium Freejet Expansions of Heated Nitrogen

Rotational temperatures have been measured in rarefied, nonequilibrium, heated freejet expansions of nitrogen using the electron beam fluorescence technique at the University of California at Berkeley Low Density Wind Tunnel facility. Spectroscopic measurements of the (0,0) band of the first negative system of nitrogen reveal the nonequilibrium behavior in the flowfield upstream of, and through the Mach disk, which forms as the freejet expands into a region of finite back pressure. Results compare well with previous freejet expansion data and computations regarding location of the Mach disk and terminal rotational temperature in the expansion. Measurements are also presented for shock thickness based on the rotational temperature changes in the flow. Thickening shock layers, departures of rotational temperature from equilibrium in the expansion region, and downstream rotational temperature recovery much below that of an isentropic normal shock provide indications of the rarefied, nonequilibrium flow behavior. The data are analyzed to infer constant values of the rotational-relaxation collision number from 2.2 to 6.5 for the various flow conditions. Collision numbers are also calculated in a consistent manner for data from other investigations for which is seen a qualitative increase with increasing temperature. Rotational-relaxation collision numbers are seen as not fully descriptive of the rarefied freejet flows. This may be due to the high degree of nonequilibrium in the flowfields, and/or to the use of a temperature-insensitive rotational-relaxation collision number model in the data analyses.

Gochberg, Lawrence A.↗
NASA NTRS2001

Autofrettage to Counteract Coefficient of Thermal Expansion Mismatch in Cryogenic Pressurized Pipes with Metallic Liners

Composite feedlines with metal liners have the potential to reduce weight/cost while providing the same level of permeation resistance and material compatibility of all-metal feedlines carrying cryogenic propellants in spacecraft. The major technical challenges are the large difference in Coefficient of Thermal Expansion between the liner and the composite, and the manufacturing method required to make a very thin liner with the required strength and dimensional tolerance. This study investigates the use of autofrettage (compressive preload) to counteract Coefficient of Thermal Expansion when pre-pressurization procedures cannot be used to solve this problem. Promising materials (aluminum 2219, Inconel 718, nickel, nickel alloy) and manufacturing techniques (chemical milling, electroplating) are evaluated to determine the best liner candidates. Robust, autofrettaged feedlines with a low Coefficient of Thermal Expansion liner (Inconel 718 or nickel alloy) are shown to successfully counteract mismatch at LOX temperature. A new concept, autofrettage by temperature, is introduced for high Coefficient of Thermal Expansion materials (aluminum and pure nickel) where pressure cannot be used to add compressive preload.

Wen, Ed↗