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At least 325 records · Page 18

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NASA NTRS1988

A decade of computer simulations for space shuttle aerodynamics

Ten years ago computer simulations of the flow field around the Space Shuttle Orbiter were limited to inviscid calculations for the windward side of the forebody and viscous calculations for selected 2-D problems. Advances in computer hardware and numerical methods during the past ten years made it possible to calculate viscous flow over the complete orbiter configuration at angle of attack. The equations solved are the Reynolds-averaged, Navier-Stokes equation, simplified by either the thin-layer or parabolized approximation. An algebraic eddy viscosity model is used for turbulent flow. The free stream is assumed to be a perfect gas for wind tunnel conditions and a real gas in thermodynamic equilibrium for flight conditions. Four examples of recent computer simulations are presented. Flow field results include oil flow patterns on the surface and Mach number contours, isobars, and cross-flow velocity vectors in the shock layer.

Inouye, Mamoru↗

NASA NTRS1987

Calculation of strain-energy release rates with higher order and singular finite elements

A general finite element procedure for obtaining strain-energy release rates for crack growth in isotropic materials is presented. The procedure is applicable to two-dimensional finite element analyses and uses the virtual crack-closure method. The procedure was applied to nonsingular 4-noded (linear), 8-noded (parabolic), and 12-noded (cubic) elements and to quarter-point and cubic singularity elements. Simple formulas for strain-energy release rates were obtained with this procedure for both nonsingular and singularity elements. The formulas were evaluated by applying them to two mode I and two mixed mode problems. Comparisons with results from the literature for these problems showed that the formulas give accurate strain-energy release rates.

Raju, I. S.↗

NASA NTRS1988

A decade of computer simulations for Space Shuttle aerodynamics

Inouye, Mamoru↗

NASA NTRS1989

Modeling of high speed chemically reacting flow-fields

The SPARK3D and SPARK3D-PNS computer programs were developed to model 3-D supersonic, chemically reacting flow-fields. The SPARK3D code is a full Navier-Stokes solver, and is suitable for use in scramjet combustors and other regions where recirculation may be present. The SPARK3D-PNS is a parabolized Navier-Stokes solver and provides an efficient means of calculating steady-state combustor far-fields and nozzles. Each code has a generalized chemistry package, making modeling of any chemically reacting flow possible. Research activities by the Langley group range from addressing fundamental theoretical issues to simulating problems of practical importance. Algorithmic development includes work on higher order and upwind spatial difference schemes. Direct numerical simulations employ these algorithms to address the fundamental issues of flow stability and transition, and the chemical reaction of supersonic mixing layers and jets. It is believed that this work will lend greater insight into phenomenological model development for simulating supersonic chemically reacting flows in practical combustors. Currently, the SPARK3D and SPARK3D-PNS codes are used to study problems of engineering interest, including various injector designs and 3-D combustor-nozzle configurations. Examples, which demonstrate the capabilities of each code are presented.

Drummond, J. P.↗

DOE OSTI2018

On quasiconformal maps and semilinear equations in the plane

Assume that Ω is a domain in the complex plane ℂ and A(z) is a symmetric 2×2 matrix function with measurable entries, detA = 1; and such that 1/K|ξ|{sup 2} ≤ 〈A(z)ξ, ξ〉 ≤ K|ξ|{sup 2}, ξ ∈ ℝ{sup 2}, 1 ≤ K < ∞ . In particular, for semilinear elliptic equations of the form div (A(z)∇u(z)) = f(u(z)) in Ω; we prove a factorization theorem that asserts that every weak solution u to the above equation can be expressed as the composition u = To𝜔; where 𝜔 : Ω → G stands for a K−quasiconformal homeomorphism generated by the matrix function A(z); and T(w) is a weak solution of the semilinear equation ∇T(w) = J(w)f(T(w)) in G: Here, the weight J(w) is the Jacobian of the inverse mapping 𝜔{sup −1}: Similar results hold for the corresponding nonlinear parabolic and hyperbolic equations. Some applications of these results to anisotropic media are given.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1961

Theory of Electrostatic Fields in the Ionosphere at Equatorial Latitudes

The properties of the elongated electrostatic fields that are required to provide the coupling mechanism in the dynamo-motor concept of the E and F regions of the ionosphere are examined theoretically for the conditions that prevail in equatorial latitudes. The analysis is developed for an electrostatic field of arbitrary horizontal scale in a horizontally stratified partly ionized gas subject to an imposed magnetic field having the form of a parabolic arch over the equator. The anisotropic character and continuous variation with height of the conductivity are retained throughout , and numerical solutions are determined for the attenuation of the electric field with distance along the field line. The results are similar qualitatively to those found previously upon analysis of the corresponding problem for middle latitudes, but the attenuation of the electrostatic field with height is considerably greater. It develops, in particular, that the coupling between E and F regions is very small for fields having horizontal wavelengths of a few kilometers. It follows that the dynamo-motor concept could not be used to account for the presence of irregularities of this scale. On the other hand, it is found that almost all the attenuation occurs at heights near that of the E region. If an electrostatic field having a horizontal wavelength of a few kilometers could be produced at heights of, say 200 km or greater, it follows that it would be very elongated and extend with little change in amplitude from hemisphere to hemisphere. The results also indicate that effective coupling could be achieved for fields having horizontal wavelengths of the order of tens of kilometers, but the assumptions introduced to simplify the analysis may impair the quantitative reliability of the results for fields of this scale.

Briggs, Benjamin R.↗

NASA NTRS1973

Effect of shear on duct wall impedance.

The solution to the equation governing the propagation of sound in a uniform shear layer is expressed in terms of parabolic cylinder functions. This result is used to develop a closed-form solution for acoustic wall impedance which accounts for both the duct liner and the presence of a boundary layer in the duct. The effective wall impedance can then be used as the boundary condition for the much simpler problem of sound propagation in uniform flow.

Goldstein, M.↗

NASA NTRS1979

How accurate is NETTO

The historical origin and general history of vertical current total energy variometer, including its optimum airspeed selector ring are reviewed, and some later developments of it are discussed. Polars of three sailplanes of different spans are charted for straight and circling flight, then plotted to reveal their parabolic anomaly and the effect of circling flight sink rate. These effects are further analyzed for their influence on the transient compensation of NETTO variometers as well as the speed ring. Some other disturbances due to the quality of sailplane preparation and flight dynamics are listed. Conclusions are drawn about the problems to pilots from imperfect NETTO variometer compensation and its effect on the maximization of ground speed from the speed ring. A modification for improvements to the speed ring and computer is suggested.

Dupont, S.↗

NASA NTRS1986

Simple formulas for strain-energy release rates with higher order and singular finite elements

A general finite element procedure for obtaining strain-energy release rates for crack growth in isotropic materials is presented. The procedure is applicable to two-dimensional finite element analyses and uses the virtual crack-closure method. The procedure was applied to non-singular 4-noded (linear), 8-noded (parabolic), and 12-noded (cubic) elements and to quarter-point and cubic singularity elements. Simple formulas for strain-energy release rates were obtained with this procedure for both non-singular and singularity elements. The formulas were evaluated by applying them to two mode I and two mixed mode problems. Comparisons with results from the literature for these problems showed that the formulas give accurate strain-energy release rates.

Raju, I. S.↗

NASA NTRS2001

Wind Code Application to External Forebody Flowfields with Comparisons to Experimental Results

The WIND Code, a general purpose Navier-Stokes solver, has been utilized to obtain supersonic external flowfield Computational Fluid Dynamics (CFD) solutions over an axisymmetric, parabolic forebody with comparisons made to wind tunnel experimental results. Various cases have been investigated at supersonic freestream conditions ranging from Mach 2.0 to 3.5, at 0 deg and 3 deg angles-of-attack, and with either a sharp-nose or blunt-nose forebody configuration. Both a turbulent (Baldwin-Lomax algebraic turbulence model) and a laminar model have been implemented in the CFD. Obtaining the solutions involved utilizing either the parabolized- or full-Navier-Stokes analyses supplied in WIND. Comparisons have been made with static pressure measurements, with boundary-layer rake and flowfield rake pitot pressure measurements, and with temperature sensitive paint experimental results. Using WIND's parabolized Navier-Stokes capability, grid sequencing, and the Baldwin-Lomax algebraic turbulence model allowed for significant reductions in computational time while still providing good agreement with experiment. Given that CFD and experiment compare well, WIND is found to be a good computational platform for solving this type of forebody problem, and the grids developed in conjunction with it will be used in the future to investigate varying freestream conditions not tested experimentally.

Frate, F. C.↗

NASA NTRS1979

Combustor modelling for scramjet engines

A system of computer programs is being developed to analyse and predict the complex flow fields found in hydrogen-fueled scramjet combustors. Each program is designed to solve the governing equation system for the type of flow present in a particular combustor region. A two-dimensional parabolic program has been found to be valuable in the development and experimental evaluation of turbulence and chemistry models for supersonic flow, and in the development of a program to model supersonic flow downstream of the fuel injection struts by means of solutions to the three-dimensional parabolic Navier-Stokes equations and species equations. A partially elliptic code has been derived to account for local subsonic flow regions, and fully elliptic programs have been developed by the consideration of streamwise diffusion effects for the recirculating flow fields near transverse fuel injectors. The programs are currently being applied to problems of scramjet engine development.

Drummond, J. P.↗

NASA NTRS1990

Leading-edge effects on boundary-layer receptivity

Numerical calculations are presented for the incompressible flow over a parabolic cylinder. The computational domain extends from a region upstream of the body downstream to the region where the Blasius boundary-layer solution holds. A steady mean flow solution is computed and the results for the scaled surface vorticity, surface pressure and displacement thickness are compared to previous studies. The unsteady problem is then formulated as a perturbation solution starting with and evolving from the mean flow. The response to irrotational time harmonic pulsation of the free-stream is examined. Results for the initial development of the velocity profile and displacement thickness are presented. These calculations will be extended to later times to investigate the initiation of instability waves within the boundary-layer.

Gatski, Thomas B.↗

NASA NTRS1987

Multiscale turbulence effects in supersonic jets exhausting into still air

A modified version of the multiscale turbulence model of Hanjalic has been applied to the problem of supersonic jets exhausting into still air. In particular, the problem of shock-cell decay through turbulent interaction with the mixing layer has been studied for both mildly interacting and strongly resonant jet conditions. The modified Hanjalic model takes into account the nonequilibrium energy transfer between two different turbulent spectral scales. The turbulence model was incorporated into an existing shock-capturing, parabolized Navier-Stokes computational model in order to perform numerical experiments. The results show that the two-scale turbulence model provides significant improvement over one-scale models in the prediction of plume shock structure for underexpanded supersonic (Mach 2) and sonic (Mach 1) jets. For the supersonic jet, excellent agreement with experiment was obtained for the centerline shock-cell pressure decay up to 40 jet radii. For the sonic jet, the agreement with experiment was not so good, but the two-scale model still showed significant improvement over the one-scale model. It is shown that by relating some of the coefficients in the turbulent-transport equations to the relative time scale for transfer of energy between scales the two-scale model can provide predictions that bound the measured shock-cell decay rate for the sonic jet.

Abdol-Hamid, Khaled S.↗

NASA NTRS1978

Effects of pointing errors on receiver performance for parabolic dish solar concentrators

The effects of dynamic (moving) pointing errors on the performance of solar thermal receivers is investigated. Only point focusing types of solar collectors are considered. The key element in the study is the analytical derivation of the intercept factor that relates pointing errors to captured energy at the receiver. A detailed example using typical parameter values is modeled on the digital computer and demonstrates the theory and the dynamic nature of the problem.

Hughes, R. O.↗

DOE OSTI2015

Entropy–viscosity method for the single material Euler equations in Lagrangian frame

In this work, a new finite element method for solving the Euler equations in Lagrangian coordinates is proposed. The method is stabilized by adding artificial diffusion terms compatible with positivity of mass and internal energy, a minimum principle on the specific entropy, and all generalized entropy inequalities. Two options of first-order artificial diffusion are considered. One is in the spirit of the Eulerian based method (Guermond et al., 2011 [23, 22]; Zingan et al., 2013) and the other is similar to existing viscosity stabilizations in Lagrangian frame, e.g., Dobrev et al. (2012). The method is verified to be high-order for smooth solutions even with active viscosity terms. This is achieved by using high-order finite element spaces and an entropy-based viscosity stabilization that degenerates the first-order viscous terms. This stabilization automatically distinguishes smooth and singular regions. The formal accuracy and convergence properties of the proposed methods are tested on a series of benchmark problems. This is the first result extending the entropy–viscosity methodology to the Lagrangian hydrodynamics.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1989

Feasibility study of a synthesis procedure for array feeds to improve radiation performance of large distorted reflector antennas

Surface errors on parabolic reflector antennas degrade the overall performance of the antenna. The errors are in the form of roughness on the surface, distortions in the shape, or structural design details. They cause amplitude and phase errors in the aperture field which lower the gain, raise the sidelobes, and fill in the nulls. These are major problems in large space reflector antennas. Planned mobile satellite communications systems having limited signal margin need high gain from the space reflectors. Future multiple beam antenna systems requiring spatial isolation to allow frequency reuse could be rendered useless if high sidelobes are present. High sidelobes are also responsible for noise. Ways of compensating for surface errors by pattern synthesis using an array of feed antennas are examined. Pattern corrections are directed specifically toward portions of the pattern requiring improvements. The pattern synthesis does not require knowledge of the surface errors. Both the amplitude and phase of the high side lobes caused by the distortion are required.

Stutzman, W. L.↗

NASA NTRS1962

Design comparison of lunar return configurations

Parabolic manned re-entry design comparisons are made between two classes of slender and blunt configurations capable of conventional horizontal and vertical earth landings. Aerodynamic modulation using flaps and control augmentation requirements are discussed in terms of their effect upon re-entry trajectories and landing footprints. Within the environment defined by the re-entry trajectories, the convective and radiative modes of heat transfer are compared, their differences discussed, and the problems associated with the configurations for planetary return missions indicated. Thermal protection systems are discussed and the factors influencing the selection of a given system for the re-entry environment are indicated. Comparison between reflective and absorptive systems are made and the merits of each for a given flight time indicated. A thermo-structural analysis is presented which shows the trade-oft between structural operating temperature and heat protection system thickness requirements. Total heat shield and structural weights are compared for the landing footprints presented and their variation with range shown. Finally, the areas of uncertainty in the aero-thermo structural design analysis are indicated for each class of configuration studied, and the weight differences between conventional horizontal landing and vertical descent configurations are given.

Parabolic flight↗

NASA NTRS1977

Reaction diffusion in the nickel-chromium-aluminum and cobalt-chromium-aluminum systems

The effects of MCrAl coating-substrate interdiffusion on oxidation life and the general mutliphase, multicomponent diffusion problem were examined. Semi-infinite diffusion couples that had sources representing coatings and sinks representing gas turbine alloys were annealed at 1,000, 1,095, 1,150, or 1,205 C for as long as 500 hours. The source and sink aluminum and chromium contents and the base metal (cobalt or nickel) determined the parabolic diffusion rate constants of the couples and predicted finite coating lives. The beta source strength concept provided a method (1) for correlating beta recession rate constants with composition; (2) for determining reliable average total, diffusion, and constitutional activation energies; and (3) for calculating interdiffusion coefficients.

Levine, S. R.↗