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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 469 records · Page 26
All sourcesNASA NTRSDOE OSTI
NASA NTRS2009

Stability Analysis of Roughness Array Wake in a High-Speed Boundary Layer

Computations are performed to examine the effects of both an isolated and spanwise periodic array of trip elements on a high-speed laminar boundary layer, so as to identify the potential physical mechanisms underlying an earlier transition to turbulence as a result of the trip(s). In the context of a 0.333 scale model of the Hyper-X forebody configuration, the time accurate solution for an array of ramp shaped trips asymptotes to a stationary field at large times, indicating the likely absence of a strong absolute instability in the mildly separated flow due to the trips. A prominent feature of the wake flow behind the trip array corresponds to streamwise streaks that are further amplified in passing through the compression corner. Stability analysis of the streaks using a spatial, 2D eigenvalue approach reveals the potential for a strong convective instability that might explain the earlier onset of turbulence within the array wake. The dominant modes of streak instability are primarily sustained by the spanwise gradients associated with the streaks and lead to integrated logarithmic amplification factors (N factors) approaching 7 over the first ramp of the scaled Hyper-X forebody, and substantially higher over the second ramp. Additional computations are presented to shed further light on the effects of both trip geometry and the presence of a compression corner on the evolution of the streaks.

Choudhari, Meelan↗
NASA NTRS1973

Maximally slicing a black hole.

Analytic and computer-derived solutions are presented of the problem of slicing the Schwarzschild geometry into asymptotically flat, asymptotically static, maximal spacelike hypersurfaces. The sequence of hypersurfaces advances forward in time in both halves (u greater than or equal to 0, u less than or equal to 0) of the Kruskal diagram, tending asymptotically to the hypersurface r = 3/2 M and avoiding the singularity at r = 0. Maximality is therefore a potentially useful condition to impose in obtaining computer solutions of Einstein's equations.

Estabrook, F.↗
NASA NTRS1984

Complete flowfields over low and wide angle AOTV conceptual configurations

Flowfields over two conceptual aeroassisted orbital transfer vehicles, a moderate lift-to-drag ratio biconic, and an axisymmetric zero lift aerobrake are investigated. The solution procedures employ a compressible Navier-Stokes time-asymptotic technique for blunt body flow and a Parabolized Navier-Stokes spatial marching technique for the primarily supersonic shock layer flow over low-angle bodies. Emphasis is placed on the laminar convective heating predictions and comparisons to experimental data where available. Code robustness and solution times are discussed and guidelines are given for the specification of various numerical parameters. The Parabolized Navier-Stokes technique has a high probability of solution success for the range of applications considered herein, and very good comparisons with experimental heat-transfer data have been obtained. The blunt body Navier-Stokes code is more sensitive to parameter specification for the aerobrake calculations. Still, coarse grid solutions can be obtained quickly to get a good first cut at flowfield definition. Fair to good comparisons have been obtained between experimental heating and pressure data and coarse and fine grid solutions.

Gnoffo, P. A.↗
NASA NTRS1991

Resonant Triad in Boundary-Layer Stability: Composite Solution and Comparison with Observations - Part 2

Here, numerical results are computed from an asymptotic near-resonance triad analysis. The analysis considers a resonant triad of instability waves consisting of a plane fundamental wave and a pair of symmetrical oblique subharmonic waves. The relevant scaling ensures that nonlinearity is confined to a distinct critical layer. The analysis is first used to form a composite solution that accounts for both the flow divergence and nonlinear effects. It is shown that the backreaction on the plane Tollmien Schlichting (TS) fundamental wave, although fully accounted for, is of little significance. The observed enhancement at the fundamental frequency disturbance is not in the plane TS wave, but is caused by nonlinearly generated waves at the fundamental frequency that result from nonlinear interactions in the critical layer. The saturation of the oblique waves is caused by their self-interaction. The nonlinear phase-locking phenomenon, the location of resonance with respect to the neutral stability curve, low frequency effects, detuning in the streamwise wave numbers, and nonlinear distortion of the mode shapes are discussed. Nonlinearity modifies the initially two dimensional Blasius profile into a fuller one with spanwise periodicity. The interactions at a wide range of unstable spanwise wave numbers are considered, and the existence of a preferred spanwise wave number is explained by means of the vorticity distribution in the critical layer. Besides presenting novel features of the phenomena and explaining the delicate mechanisms of the interactions, the results of the theory are in excellent agreement with experimental and numerical observations for all stages of the development and for various input parameters.

Mankbadi, Reda R.↗
NASA NTRS1977

Slender streams with gravity - Outer asymptotic expansions. I, II

The steady, three-dimensional, potential flow (neglecting surface tension) of a slender stream of fluid in the presence of gravity is considered and a description is presented of the first part of an asymptotic theory of such a flow. The theory will provide the ingredients for the construction of the solution to many flow problems involving slender streams. The flows and their boundaries are represented as asymptotic power series in the slenderness ratio of the stream. Attention is given to the formulation of the outer expansion problems, first approximations for a jet, a first approximation for pipe flow, and a first approximation for channel flow.

Geer, J.↗
NASA NTRS1982

A wave envelope finite element scheme for acoustical radiation

The aeroacoustic problem associated with the radiation of fan noise from the inlet of a turbofan aircraft engine, the dimensions of which are generally many times larger than the acoustical wavelengths of the major energy-carrying frequencies, is considered. In the present approach, a conventional finite element solution in the inner region is compatibly matched to a 'wave envelope' finite element solution in a large but finite outer region. The inclusion of a wavelike variation with the correct asymptotic decay in the shape functions for the outer region preserves the correct behavior of the solution at large distances. The method is initially presented for a simple one-dimensional model based on the solution of Webster's horn equation. Results are presented for the specific case of a uniform cylindrical section joined to a conical expansion, and also for a simple axisymmetric test case of the calculation of acoustical pressure generated by a vibrating circular piston located at the center of an infinite rigid baffle.

Astley, R. J.↗
DOE OSTI2024

Off-shell Partition Functions in 3d Gravity

We explore three-dimensional gravity with negative cosmological constant via canonical quantization. We focus on chiral gravity which is related to a single copy of PSL(2,R) Chern-Simons theory and is simpler to treat in canonical quantization. Its phase space for an initial value surface Σ is given by the appropriate moduli space of Riemann surfaces. We use geometric quantization to compute partition functions of chiral gravity on three-manifolds of the form Σ×S 1 , where Σ can have asymptotic boundaries. Most of these topologies do not admit a classical solution and are thus not amenable to a direct semiclassical path integral computation. We use an index theorem that expresses the partition function as an integral of characteristic classes over phase space. In the presence of n asymptotic boundaries, we use techniques from equivariant cohomology to localize the integral to a finite-dimensional integral over $\overline{M}$ g,n , which we evaluate in low genus cases. Higher genus partition functions quickly become complicated since they depend in an oscillatory way on Newton's constant. There is a precise sense in which one can isolate the non-oscillatory part which we call the fake partition function. We establish that there is a topological recursion that computes the fake partition functions for arbitrary Riemann surfaces Σ. As a result, there is a scaling limit in which the model reduces to JT gravity and our methods give a novel way to compute JT partition functions via equivariant localization.

Classical and Quantum Gravity↗
NASA NTRS1978

Numerical integration of nearly-Hamiltonian systems

The reported investigation is concerned with the solution of systems of differential equations which are derived from a Hamiltonian function in the extended phase space. The problem selected involves a one-dimensional perturbed harmonic oscillator. The van der Pol equation considered has an exact asymptotic value for its amplitude. Comparisons are made between a numerical solution and a known analytical solution. In addition to the van der Pol problem, known solutions regarding the restricted problem of three bodies are used as examples for perturbed Keplerian motion. The extended phase space Hamiltonian discussed by Stiefel and Scheifele (1971) is considered. A description is presented of two canonical formulations of the perturbed harmonic oscillator.

Bond, V. R.↗
NASA NTRS1987

Simplified solution for a class of fading memory filters

A fading memory filter is a least squares estimator (LSE) that applies an exponentially decaying weight to past measurements. When compared with a standard Kalman filter, its key advantages are asymptotic stability and reduced sensitivity to modeling errors. This paper derives a simple solution for a class of fading memory filters, resulting in a reduction in computational complexity. Steady state filter solutions are obtained for second- and third-order filters used in a global positioning system (GPS) receiver for high dynamic vehicles.

Statman, Joseph I.↗
NASA NTRS1972

Singular perturbations in the state regulator problem

Most of the results of singular perturbation theory have been concerned with initial value problems whereas optimal control problems are of two-point boundary value type. The portions of this theory applicable to the open loop state regulator problem are reviewed. For obtaining approximate solutions to the state regulator problem the method of matched asymptotic expansions is employed. This method has been developed in connection with certain fluid mechanics problems and is applicable to nonlinear as well as linear problems. It has been found in the past to be advantageous not to formulate this method generally but to apply it to each individual problem and this approach is adopted here. A general recipe for the method is given and its application is illustrated by using the method to obtain an approximate solution to a simple, specific state regulator problem.

Ardema, M. D.↗
NASA NTRS1982

Applications of perturbation techniques

Two perturbation techniques were applied to two singular perturbation problems in heat transfer to obtain uniformly valid solutions which can serve as benchmarks for finite difference and finite element techniques. In the first problem, the method of strained parameters coupled with the application of a solvability condition is used to obtain a uniform solution for the problem of unsteady heat conduction in a long nearly circular cylinder. In the second problem, the method of matched asymptotic expansion coupled with Van Dyke's matching principle is used to obtain a uniform solution for the problem of one dimensional conduction-convection heat transfer of a uniform fluid flow.

Kandil, O. A.↗
NASA NTRS1977

Navier-Stokes solution for the laminar and turbulent supersonic flow near the trailing edge of a flat plate

The present paper deals with problems of two-dimensional laminar and turbulent flow of a viscous incompressible fluid near the trailing edge of a thin flat plate. The complete system of Navier-Stokes equations is solved by means of MacCormack's finite-difference scheme. In the laminar case, the results are compared with the triple deck solution of Daniels (1973). The comparisons indicate that the asymptotic triple deck theory for supersonic trailing-edge flow is accurate within five percent for Reynolds numbers greater than 1000. In the turbulent case, the Prandtl-Van Driest-Clausner algebraic eddy viscosity model is used, showing that the region of upstream influence is roughly of the order of the boundary layer thickness.

Hussaini, M. Y.↗
NASA NTRS1985

Vortex-dominated flow with viscous core structure

Recent theoretical studies of vortex-dominated flows are reviewed with special emphasis on those for which the viscous core structures play an important role. The problems to be described are: The interaction and merging of two-dimensional vortices and of curved vortex filaments, the roll-up and decay of trailing far wakes, and the initiation of vortex breakdown. The analysis utilizes finite-difference solutions of the Navier-Stokes equations complemented by asymptotic expansion techniques.

Liu, C. H.↗
NASA NTRS1989

On the Lagrangian description of unsteady boundary layer separation. Part 1: General theory

Although unsteady, high-Reynolds number, laminar boundary layers have conventionally been studied in terms of Eulerian coordinates, a Lagrangian approach may have significant analytical and computational advantages. In Lagrangian coordinates the classical boundary layer equations decouple into a momentum equation for the motion parallel to the boundary, and a hyperbolic continuity equation (essentially a conserved Jacobian) for the motion normal to the boundary. The momentum equations, plus the energy equation if the flow is compressible, can be solved independently of the continuity equation. Unsteady separation occurs when the continuity equation becomes singular as a result of touching characteristics, the condition for which can be expressed in terms of the solution of the momentum equations. The solutions to the momentum and energy equations remain regular. Asymptotic structures for a number of unsteady 3-D separating flows follow and depend on the symmetry properties of the flow. In the absence of any symmetry, the singularity structure just prior to separation is found to be quasi 2-D with a displacement thickness in the form of a crescent shaped ridge. Physically the singularities can be understood in terms of the behavior of a fluid element inside the boundary layer which contracts in a direction parallel to the boundary and expands normal to it, thus forcing the fluid above it to be ejected from the boundary layer.

Vandommelen, Leon L.↗
NASA NTRS1990

On the Lagrangian description of unsteady boundary-layer separation. I - General theory

Although unsteady, high-Reynolds number, laminar boundary layers have conventionally been studied in terms of Eulerian coordinates, a Lagrangian approach may have significant analytical and computational advantages. In Lagrangian coordinates the classical boundary layer equations decouple into a momentum equation for the motion parallel to the boundary, and a hyperbolic continuity equation (essentially a conserved Jacobian) for the motion normal to the boundary. The momentum equations, plus the energy equation if the flow is compressible, can be solved independently of the continuity equation. Unsteady separation occurs when the continuity equation becomes singular as a result of touching characteristics, the condition for which can be expressed in terms of the solution of the momentum equations. The solutions to the momentum and energy equations remain regular. Asymptotic structures for a number of unsteady 3-D separating flows follow and depend on the symmetry properties of the flow. In the absence of any symmetry, the singularity structure just prior to separation is found to be quasi 2-D with a displacement thickness in the form of a crescent shaped ridge. Physically the singularities can be understood in terms of the behavior of a fluid element inside the boundary layer which contracts in a direction parallel to the boundary and expands normal to it, thus forcing the fluid above it to be ejected from the boundary layer.

Van Dommelen, Leon L.↗
NASA NTRS1991

Alfven shock trains

The Cohen-Kulsrud-Burgers equation (CKB) is used to consider the nonlinear evolution of resistive, quasi-parallel Alfven waves subject to a long-wavelength, plane-polarized, monochromatic instability. The instability saturates by nonlinear steepening, which proceeds until the periodic waveform develops an interior scale length comparable to the dissipation length; a fast or an intermediate shock then forms. The result is a periodic train of Alfven shocks of one or the other type. For propagation strictly parallel to the magnetic field, there will be two shocks per instability wavelength. Numerical integration of the time-dependent CKB equation shows that an initial, small-amplitude growing wave asymptotes to a stable, periodic stationary wave whose analytic solution specifies how the type of shock embedded in the shock train, and the amplitude and speed of the shock train, depend on the strength and phase of the instability. Waveforms observed upstream of the earth's bowshock and cometary shocks resemble those calculated here.

Malkov, M. A.↗
NASA NTRS1953

On the application of transonic similarity rules to wings of finite span

The transonic aerodynamic characteristics of wings of finite span are discussed from the point of view of a unified small perturbation theory for subsonic, transonic, and supersonic flows about thin wings. This approach avoids certain ambiguities which appear if one studies transonic flows by means of equations derived under the more restrictive assumption that the local velocities are everywhere close to sonic velocity. The relation between the two methods of analysis of transonic flow is examined, the similarity rules and known solutions of transonic flow theory are reviewed, and the asymptotic behavior of the lift, drag, and pitching-moment characteristics of wings of large and small aspect ratio is discussed. It is shown that certain methods of data presentation are advantageous for the effective display of these characteristics.

Spreiter, John R↗