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NASA NTRS1992

A nonlinear relaxation/quasi-Newton algorithm for the compressible Navier-Stokes equations

A highly efficient implicit method for the computation of steady, two-dimensional compressible Navier-Stokes flowfields is presented. The discretization of the governing equations is hybrid in nature, with flux-vector splitting utilized in the streamwise direction and central differences with flux-limited artificial dissipation used for the transverse fluxes. Line Jacobi relaxation is used to provide a suitable initial guess for a new nonlinear iteration strategy based on line Gauss-Seidel sweeps. The applicability of quasi-Newton methods as convergence accelerators for this and other line relaxation algorithms is discussed, and efficient implementations of such techniques are presented. Convergence histories and comparisons with experimental data are presented for supersonic flow over a flat plate and for several high-speed compression corner interactions. Results indicate a marked improvement in computational efficiency over more conventional upwind relaxation strategies, particularly for flowfields containing large pockets of streamwise subsonic flow.

Edwards, Jack R.↗

NASA NTRS1989

Evaluation of Equilibrium Turbulence for a Hypersonic Boundary Layer at Nonadiabatic Wall Conditions

This paper presents an experimental study to characterize the naturally developing compressible turbulent boundary layer produced along a flat plate measuring 9.7 feet long in the NASA Langley 8-Foot High Temperature Tunnel and to determine the test conditions necessary to achieve equilibrium turbulence. The measurements consist of pitot pressure, static pressure, and total temperature distributions in the boundary layer. In addition, surface measurements consisting of heat transfer and pressure distributions were obtained. The tests were conducted at a nominal free-stream Mach number of 6.5, total temperatures of 2700 and 3300 R, and angles of attack of 5 and 13 degrees. The corresponding nominal boundary-layer edge Mach numbers were 6.2 and 5.0. The nominal ratios of adiabatic wall temperature to cold wall temperature were 4.4 and 5.4 and the momentum thickness Reynolds numbers at the boundary layer probe locations ranged from 400 to 7800. The results of this study indicate that momentum thickness Reynolds numbers of at least 4000 are required to obtain an equilibrium turbulent boundary layer in the Langley 8-Foot High Temperature Tunnel. This evaluation is based primarily on the behavior of shape factors inferred from the boundary-layer measurements.

Albertson, Cindy W.↗

NASA NTRS1943

Large-deflection theory for end compression of long rectangular plates rigidly clamped along two edges

The von Karman equations for flat plates are solved beyond the buckling load up to edge strains equal to eight time the buckling strain, for the extreme case of rigid clamping along the edges parallel to the load. Deflections, bending stresses, and membrane stresses are given as a function of end compressive load. The theoretical values of effective width are compared with the values derived for simple support along the edges parallel to the load. The increases in effective width due to rigid clamping drops from about 20 percent near the buckling strain to about 8 percent at an edge strain equal to eight times the buckling strain. Experimental values of effective width in the elastic range reported in NACA Technical Note No. 684 are between the theoretical curves for the extremes of simple support and rigid clamping.

Levy, Samuel↗

NASA NTRS1974

Comments on Crocco's solution and the independence principle for compressible turbulent boundary layers

The purpose of the present note is to show that on a flat plate where both the wall temperature and mean wall pressure are constant, neither of the limitations of parallel flow or of unity for the turbulent Prandtl number are required in order for the Crocco solution to apply to the turbulent boundary-layer flow. It is shown herein that this result is subject to restrictions on the magnitude of pressure fluctuations. The same analysis is generalized to show that the compressible turbulent boundary layer on an isothermal swept flat plate is independent of the spanwise flow if the molecular Prandtl number is unity.

Beckwith, I. E.↗

NASA NTRS1984

Stability of a laminar premixed supersonic free shear layer with chemical reactions

The stability of a two-dimensional compressible supersonic flow in the wake of a flat plate is discussed. The fluid is a multi-species mixture which is undergoing finite rate chemical reactions. The spatial stability of an infinitesimal disturbance in the fluid is considered. Numerical solutions of the eigenvalue stability equations for both reactive and nonreactive supersonic flows are presented and discussed. The chemical reactions have significant influence on the stability behavior. For instance, a neutral eigenvalue is observed near the freestream Mach number of 2.375 for the nonreactive case, but disappears when the reaction is turned on. For reactive flows, the eigenvalues are not very dependent on the free stream Mach number.

Menon, S.↗

NASA NTRS1986

About the coupling of turbulence closure models with averaged Navier-Stokes equations

The MacCormack implicit predictor-corrector model (1981) for numerical solution of the coupled Navier-Stokes equations for turbulent flows is extended to nonconservative multiequation turbulence models, as well as the inclusion of second-order Reynolds stress turbulence closure. A scalar effective pressure turbulent contribution to the pressure field is defined to approximate the effects of the Reynolds stress in strongly sheared flows. The Jacobian matrices of the transport equations are diagonalized to reduce the required computer memory and run time. Techniques are defined for including turbulence in the diagonalization. Application of the method is demonstrated with solutions generated for transonic nozzle flow and for the interaction between a supersonic flat plate boundary layer and a 12 deg compression-expansion ramp.

Vandromme, D.↗

NASA NTRS1949

Critical combinations of shear and direct axial stress for curved rectangular panels

A solution is presented for the problem of the buckling of curved rectangular panels subjected to combined shear and direct axial stress. Charts giving theoretical critical combinations of shear and direct axial stress are presented for panels having five different length-width ratios. Because the actual critical compressive stress of rectangular panels having substantial curvature is known to be much lower than the theoretical value, a semiempirical method of analysis of curved panels subjected to combined shear and direct axial stress is presented for use in design. (author

PLATES - STRESSES, SHEARING CURVED↗

NASA NTRS2001

Design of Fiber Optic Sensors for Measuring Hydrodynamic Parameters

The science of optical hydrodynamics involves relating the optical properties to the fluid dynamic properties of a hydrodynamic system. Fiber-optic sensors are being designed for measuring the hydrodynamic parameters of various systems. As a flowing fluid makes an encounter with a flat surface, it forms a boundary layer near this surface. The region between the boundary layer and the flat plate contains information about parameters such as viscosity, compressibility, pressure, density, and velocity. An analytical model has been developed for examining the hydrodynamic parameters near the surface of a fiber-optic sensor. An analysis of the conservation of momentum, the continuity equation and the Navier-Stokes equation for compressible flow were used to develop expressions for the velocity and the density as a function of the distance along the flow and above the surface. When examining the flow near the surface, these expressions are used to estimate the sensitivity required to perform direct optical measurements and to derive the shear force for indirect optical measurements. The derivation of this result permits the incorporation of better design parameters for other fiber-based sensors. Future work includes analyzing the optical parametric designs of fiber-optic sensors, modeling sensors to utilize the parameters for hydrodynamics and applying different mixtures of hydrodynamic flow. Finally, the fabrication of fiber-optic sensors for hydrodynamic flow applications of the type described in this presentation could enhance aerospace, submarine, and medical technology.

Lyons, Donald R.↗

NASA NTRS2005

Laminar Heating Validation of the OVERFLOW Code

OVERFLOW, a structured finite difference code, was applied to the solution of hypersonic laminar flow over several configurations assuming perfect gas chemistry. By testing OVERFLOW's capabilities over several configurations encompassing a variety of flow physics a validated laminar heating was produced. Configurations tested were a flat plate at 0 degrees incidence, a sphere, a compression ramp, and the X-38 re-entry vehicle. This variety of test cases shows the ability of the code to predict boundary layer flow, stagnation heating, laminar separation with re-attachment heating, and complex flow over a three-dimensional body. In addition, grid resolutions studies were done to give recommendations for the correct number of off-body points to be applied to generic problems and for wall-spacing values to capture heat transfer and skin friction. Numerical results show good comparison to the test data for all the configurations.

Lillard, Randolph P.↗

NASA NTRS2006

Validation of High-Speed Turbulent Boundary Layer and Shock-Boundary Layer Interaction Computations with the OVERFLOW Code

The capability of the OVERFLOW code to accurately compute high-speed turbulent boundary layers and turbulent shock-boundary layer interactions is being evaluated. Configurations being investigated include a Mach 2.87 flat plate to compare experimental velocity profiles and boundary layer growth, a Mach 6 flat plate to compare experimental surface heat transfer,a direct numerical simulation (DNS) at Mach 2.25 for turbulent quantities, and several Mach 3 compression ramps to compare computations of shock-boundary layer interactions to experimental laser doppler velocimetry (LDV) data and hot-wire data. The present paper describes outlines the study and presents preliminary results for two of the flat plate cases and two small-angle compression corner test cases.

Oliver, A. B.↗

NASA NTRS1984

Solar photochemical process engineering for production of fuels and chemicals

The engineering costs and performance of a nominal 25,000 scmd (883,000 scfd) photochemical plant to produce dihydrogen from water were studied. Two systems were considered, one based on flat-plate collector/reactors and the other on linear parabolic troughs. Engineering subsystems were specified including the collector/reactor, support hardware, field transport piping, gas compression equipment, and balance-of-plant (BOP) items. Overall plant efficiencies of 10.3 and 11.6% are estimated for the flat-plate and trough systems, respectively, based on assumed solar photochemical efficiencies of 12.9 and 14.6%. Because of the opposing effects of concentration ratio and operating temperature on efficiency, it was concluded that reactor cooling would be necessary with the trough system. Both active and passive cooling methods were considered. Capital costs and energy costs, for both concentrating and non-concentrating systems, were determined and their sensitivity to efficiency and economic parameters were analyzed. The overall plant efficiency is the single most important factor in determining the cost of the fuel.

Biddle, J. R.↗

NASA NTRS1993

Tollmien-Schlichting/vortex interactions in compressible boundary layer flows

The weakly nonlinear interaction of oblique Tollmien-Schlichting waves and longitudinal vortices in compressible, high Reynolds number, boundary-layer flow over a flat plate is considered for all ranges of the Mach number. The interaction equations comprise of equations for the vortex which is indirectly forced by the waves via a boundary condition, whereas a vortex term appears in the amplitude equation for the wave pressure. The downstream solution properties of interaction equations are found to depend on the sign of an interaction coefficient. Compressibility is found to have a significant effect on the interaction properties; principally through its impact on the waves and their governing mechanism, the triple-deck structure. It is found that, in general, the flow quantities will grow slowly with increasing downstream co-ordinate; i.e. in general, solutions do not terminate in abrupt, finite-distance 'break-ups'.

Blackaby, Nicholas D.↗

NASA NTRS1985

Solar photochemical process engineering for production of fuels and chemicals

The engineering costs and performance of a nominal 25,000 scmd (883,000 scfd) photochemical plant to produce dihydrogen from water were studied. Two systems were considered, one based on flat-plate collector/reactors and the other on linear parabolic troughs. Engineering subsystems were specified including the collector/reactor, support hardware, field transport piping, gas compression equipment, and balance-of-plant (BOP) items. Overall plant efficiencies of 10.3 and 11.6 percent are estimated for the flat-plate and trough systems, respectively, based on assumed solar photochemical efficiencies of 12.9 and 14.6 percent. Because of the opposing effects of concentration ratio and operating temperature on efficiency, it was concluded that reactor cooling would be necessary with the trough system. Both active and passive cooling methods were considered. Capital costs and energy costs, for both concentrating and non-concentrating systems, were determined and their sensitivity to efficiency and economic parameters were analyzed. The overall plant efficiency is the single most important factor in determining the cost of the fuel.

Biddle, J. R.↗

DOE OSTI2020

Single-pulse (100 ps) extended x-ray absorption fine structure capability at the Dynamic Compression Sector

Determining real-time changes in the local atomistic order is important for a mechanistic understanding of shock wave induced structural and chemical changes. However, the single event and short duration (nanosecond times) nature of shock experiments pose challenges in obtaining Extended X-ray Absorption Fine Structure (EXAFS) measurements - typically used for monitoring local order changes. Here, we report on a new single pulse (~100 ps duration) transmission geometry EXAFS capability for use in laser shock-compression experiments at the Dynamic Compression Sector (DCS), Advanced Photon Source. We used a flat plate of highly oriented pyrolytic graphite (HOPG) as the spectrometer element to energy disperse x-rays transmitted through the sample. It provided high efficiency with approximately 15% of the x-rays incident on the HOPG reaching an x-ray area detector with high quantum efficiency. This combination resulted in good signal-to-noise ratio (~10 3 ), energy resolution of ~10 eV at 10 keV, EXAFS spectra covering 100s of eV, and good pulse to pulse reproducibility of our single pulse measurements. Ambient EXAFS spectra for Cu and Au are compared to reference spectra, validating our measurement system. Comparison of single pulse EXAFS results for ambient and laser shocked Ge(100) shows large changes to the local structure of the short lived state of shocked Ge. The current DCS EXAFS capability can be used to perform single pulse measurements in laser shocked materials from approximately 9-13 keV. These EXAFS developments will be available to all users of the DCS.

47 OTHER INSTRUMENTATION↗

DOE OSTI2022

Low-Carbon District Heating: Performance Modeling of Hybrid Solar, Heat Pump, and Thermal Storage Systems for District Thermal Energy in the United States

District heating requires thermal energy in the temperature range of 40 degrees C - 120 degrees C. Typically, the thermal energy input for these systems has largely been met through fossil energy. However, the temperature range is low enough that it presents an opportunity for low-carbon technologies such as solar thermal and electrified thermal generators like heat pumps to decarbonize the heat generation. In this paper, a heat pump model was applied to estimate the performance and economics of a real-world low-carbon district heating substation. This system is comprised of a flat plate solar collector field paired with a mechanical vapor compression heat pump and hot water thermal storage, augmented by gas-fired boilers. Plant data was used to tune the model and estimate the system's benefits in terms of both standard financial metrics (IRR and payback), and environmental metrics, including avoided CO2 emissions. The model is subsequently employed to estimate the technical and economic potential of solar + heat pump + ther-mal storage hybrid systems as retrofits for district heating systems in eight US Markets.

district heating↗

NASA NTRS1993

Calculations of Supersonic and Hypersonic Flows using Compressible Wall Functions

The present paper presents a numerical procedure to calculate supersonic and hypersonic flows using the compressible law of the wall. The turbulence models under consideration include the Launder-Reece-Rodi-Gibson Reynolds-stress model and the k-epsilon model. The models coupled with the proposed wall function technique have been tested in both separated and unseparated flows. The flows include (1) an insulated flat plate flow over a range of Mach numbers, (2) a Mach 5 flat plate flow with cold wall conditions, (3) a two dimensional supersonic compression corner flow, (4) a hypersonic flow over an axisymmetric flare, and (5) a hypersonic flow over a 2-D compression corner. Results indicate that the wall function technique gives improved predictions of skin friction and heat transfer in separated flows compared with models using wall dampers. Predictions of the extent of separation are not improved over the wall damper models except with the Reynolds-stress model for the supersonic compression corner flow case.

Huang, P. G.↗

NASA NTRS1989

Recent results concerning the stability of viscoelastic shear deformable plates under compressive edge loading

Some recent results obtained by the authors are summarized concerning the stability of transversely isotropic flat panels whose materials exhibit a viscoelastic behavior and whose edges are subjected to in-plane biaxial compressive loads. Two transversely isotropic type materials, largely used in advanced technology, are considered: (1) the pyrolytic-graphite type, used in the thermal protection of aerospace vehicles, and (2) the type corresponding to unidirectional fiber-reinforced composites. In the former case, the planes of isotropy are parallel at each point to the midplane of the plate. In the latter case, they are normal to the fiber directions. The micromechanical relations developed by Aboudi (1984, 1986, 1987) are considered in conjunction with the correspondence principle of linear viscoelastic theory in order to predict the macroscopic viscoelastic properties of a material composed of uniaxial elastic fibers embedded in a linear viscoelastic matrix.

Librescu, L.↗

NASA NTRS2002

Deformation Response of Unsymmetrically Laminated Plates Subjected to Inplane Loading

This paper discusses the out-of-plane deformation behavior of unsymmetric cross-ply composite plates compressed inplane by displacing one edge of the plate a known amount. The plates are assumed to be initially flat and several boundary conditions are considered. Geometrically nonlinear behavior is assumed. The primary objectives are to study the out-of-plane behavior as a function of increasing inplane compression and to determine if bifurcation behavior and secondary buckling can occur. It is shown that, depending on the boundary conditions, both can occur, though the characteristics are different than the pre and post-buckling behavior of a companion symmetric cross-ply plate. Furthermore, while a symmetric cross-ply plate can postbuckle with either a positive or negative out-of-plane displacement, the unsymmetric cross-ply plates studied deflect out-of-plane only in one direction throughout the range of inplane compression, the direction again depending on the boundary conditions

Ochinero, Tomoya T.↗