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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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NASA NTRS1984

Direct simulations of chemically reacting turbulent mixing layers

The report presents the results of direct numerical simulations of chemically reacting turbulent mixing layers. The work consists of two parts: (1) the development and testing of a spectral numerical computer code that treats the diffusion reaction equations; and (2) the simulation of a series of cases of chemical reactions occurring on mixing layers. The reaction considered is a binary, irreversible reaction with no heat release. The reacting species are nonpremixed. The results of the numerical tests indicate that the high accuracy of the spectral methods observed for rigid body rotation are also obtained when diffusion, reaction, and more complex flows are considered. In the simulations, the effects of vortex rollup and smaller scale turbulence on the overall reaction rates are investigated. The simulation results are found to be in approximate agreement with similarity theory. Comparisons of simulation results with certain modeling hypotheses indicate limitations in these hypotheses. The nondimensional product thickness computed from the simulations is compared with laboratory values and is found to be in reasonable agreement, especially since there are no adjustable constants in the method.

Riley, J. J.↗
NASA NTRS1984

On the instability of a 3-dimensional attachment line boundary layer: Weakly nonlinear theory and a numerical approach

The instability of a three dimensional attachment line boundary layer is considered in the nonlinear regime. Using weakly nonlinear theory, it is found that, apart from a small interval near the (linear) critical Reynolds number, finite amplitude solutions bifurcate subcritically from the upper branch of the neutral curve. The time dependent Navier-Stokes equations for the attachment line flow have been solved using a Fourier-Chebyshev spectral method and the subcritical instability is found at wavenumbers that correspond to the upper branch. Both the theory and the numerical calculations show the existence of supercritical finite amplitude (equilibrium) states near the lower branch which explains why the observed flow exhibits a preference for the lower branch modes. The effect of blowing and suction on nonlinear stability of the attachment line boundary layer is also investigated.

Hall, P.↗
NASA NTRS1985

Analysis of spectral operators in one-dimensional domains

Results are proven concerning certain projection operators on the space of all polynomials of degree less than or equal to N with respect to a class of one-dimensional weighted Sobolev spaces. The results are useful in the theory of the approximation of partial differential equations with spectral methods.

Maday, Y.↗
NASA NTRS1985

Signal analysis techniques for incipient failure detection in turbomachinery

Signal analysis techniques for the detection and classification of incipient mechanical failures in turbomachinery were developed, implemented and evaluated. Signal analysis techniques available to describe dynamic measurement characteristics are reviewed. Time domain and spectral methods are described, and statistical classification in terms of moments is discussed. Several of these waveform analysis techniques were implemented on a computer and applied to dynamic signals. A laboratory evaluation of the methods with respect to signal detection capability is described. Plans for further technique evaluation and data base development to characterize turbopump incipient failure modes from Space Shuttle main engine (SSME) hot firing measurements are outlined.

Coffin, T.↗
NASA NTRS1984

Ageostrophic instabilities in a two fluid system with rotation

The stability of synoptic scale waves formed on a frontal surface is studied including nongeostrophic effects with the basic flow subjected to both vertical and horizontal shear. Spectral method is used to obtain the desired solutions. The stability characteristics of the developed unstable modes are presented as a function of shears of the basic flow. With the inclusion of barotropic shear the spectrum of instabilities increase. The lower speeded member of the mixed mode (gravitational-rotational) pair is influenced by the barotropic shear in the basic current and it appears at lower vertical shears. The structure of the height perturbations are utilized to distinguish the various unstable modes developed in the system together with their stability characteristics. This investigation has shown that the ageostrophic effects can be a significant factor in the development of synoptic scale waves on a frontal surface.

Ramanathan, N.↗
NASA NTRS1985

Convective motions in a spherical shell

We compute the axisymmetric convective motions that exist in a spherical shell heated from below with inner to outer radius ratio equal to 0.5. The boundaries are stress-free and gravity is directly proportional to radius. Accurate solutions at large Rayleigh numbers, O(100000), are made feasible by a spectral method that employs diagonal-mode truncation. By examining the stability of axisymmetric motions it is inferred that the preferred form of convection varies dramatically according to the value of the Rayleigh number. While axisymmetric motions with different patterns may exist for modestly nonlinear convection, only a single motion persists at sufficiently large values of the Rayleigh number. This circulation is symmetric about the equator and has two meridional cells with rising motion at the poles. Instability of this single axisymmetric motion determines that the preferred pattern of three-dimensional convection has one azimuthal wave.

Zebib, A.↗
NASA NTRS1986

The construction and use of divergence free vector expansions for incompressible fluid flow calculations

For incompressible fluids the law of mass conservation reduces to a constraint on the velocity vector, namely that it be divergence free. This constraint has long been a source of great difficulty to the numericist seeking to discretize the Navier-Stokes and Euler equations. A spectral method is discussed which overcomes this difficulty. Its efficacy is demonstrated on some simple problems. The velocity is approximated by a finite sum of divergence free vectors, each of which satisfies the same boundary conditions as the velocity. Projecting the governing equation onto the space of inviscid vector fields eliminates the pressure term and produces a set of ordinary differential equations that must be solved for the coefficents in the velocity. The pressure can then be recovered if it is needed.

Mhuiris, N. M. G.↗
NASA NTRS1986

Advances in numerical and applied mathematics

This collection of papers covers some recent developments in numerical analysis and computational fluid dynamics. Some of these studies are of a fundamental nature. They address basic issues such as intermediate boundary conditions for approximate factorization schemes, existence and uniqueness of steady states for time dependent problems, and pitfalls of implicit time stepping. The other studies deal with modern numerical methods such as total variation diminishing schemes, higher order variants of vortex and particle methods, spectral multidomain techniques, and front tracking techniques. There is also a paper on adaptive grids. The fluid dynamics papers treat the classical problems of imcompressible flows in helically coiled pipes, vortex breakdown, and transonic flows.

South, J. C., Jr.↗
NASA NTRS1986

Signal Detection Techniques for Diagnostic Monitoring of Space Shuttle Main Engine Turbomachinery

An investigation to develop, implement, and evaluate signal analysis techniques for the detection and classification of incipient mechanical failures in turbomachinery is reviewed. A brief description of the Space Shuttle Main Engine (SSME) test/measurement program is presented. Signal analysis techniques available to describe dynamic measurement characteristics are reviewed. Time domain and spectral methods are described, and statistical classification in terms of moments is discussed. Several of these waveform analysis techniques have been implemented on a computer and applied to dynamc signals. A laboratory evaluation of the methods with respect to signal detection capability is described. A unique coherence function (the hyper-coherence) was developed through the course of this investigation, which appears promising as a diagnostic tool. This technique and several other non-linear methods of signal analysis are presented and illustrated by application. Software for application of these techniques has been installed on the signal processing system at the NASA/MSFC Systems Dynamics Laboratory.

Coffin, Thomas↗
NASA NTRS1985

Simulation and modeling of homogeneous, compressed turbulence

Low Reynolds number homogeneous turbulence undergoing low Mach number isotropic and one-dimensional compression was simulated by numerically solving the Navier-Stokes equations. The numerical simulations were performed on a CYBER 205 computer using a 64 x 64 x 64 mesh. A spectral method was used for spatial differencing and the second-order Runge-Kutta method for time advancement. A variety of statistical information was extracted from the computed flow fields. These include three-dimensional energy and dissipation spectra, two-point velocity correlations, one-dimensional energy spectra, turbulent kinetic energy and its dissipation rate, integral length scales, Taylor microscales, and Kolmogorov length scale. Results from the simulated flow fields were used to test one-point closure, two-equation models. A new one-point-closure, three-equation turbulence model which accounts for the effect of compression is proposed. The new model accurately calculates four types of flows (isotropic decay, isotropic compression, one-dimensional compression, and axisymmetric expansion flows) for a wide range of strain rates.

Wu, C. T.↗
NASA NTRS1985

Turbulent disruptions from the Strauss equations

Preliminary results are reported from application of a three-dimensional spectral method model to the solution of the Strauss (1976) reduced MHD equations. The investigation was focused on describing MHD turbulence in a current-carrying bounded magnetofluid. A cylindrical geometry with a square cross-section was considered, with the walls being rigid perfect conductors with free-slip boundary conditions. A uniform magnetic field and the electric current density both point in the z-direction. Initial conditions are specified which feature small amounts of random noise expressed as Fourier modes. Linearized equations are defined for tracing the movement to equlibrium conditions or other temporal development. The model is further refined with nonlinear equations to examine the effects of the appearance of disruptions. Comparisons are drawn between solutions obtained with linear and nonlinear equations, with an eye to the associated physical realities.

Dahlburg, J. P.↗
NASA NTRS1985

Direct numerical simulation of equilibrium turbulent boundary layers

This paper describes the simulation of turbulent boundary layers by direct numerical solution of the three-dimensional, time-dependent Navier-Stokes equations, using a spectral method. The flow is incompressible, with Re sub delta = 1000. The equations are written in the self-similar coordinate system and periodic streamwise and spanwise boundary conditions are imposed. A family of nine 'equilibrium' boundary layers, from the strongly accelerated 'sink' flow to Stratford's separating boundary layer is treated. Good general agreement with experiments is observed. The effects of pressure gradients on the structures and statistics, both in the wall and wake regions are discussed.

Spalart, P. R.↗
NASA NTRS1986

On the instability of a three-dimensional attachment-line boundary layer - Weakly nonlinear theory and a numerical approach

The instability of a three-dimensional attachment-line boundary layer is considered in the nonlinear regime. Using weakly nonlinear theory, it is found that, apart from a small interval near the (linear) critical Reynolds number, finite-amplitude solutions bifurcate subcritically from the upper branch of the neutral curve. The time-dependent Navier-Stokes equations for the attachment-line flow have been solved using a Fourier-Chebyshev spectral method and the subcritical instability is found at wavenumbers that correspond to the upper branch. Both the theory and the numerical calculations show the existence of supercritical finite-amplitude (equilibrium) states near the lower branch which explains why the observed flow exhibits a preference for the lower branch modes. The effect of blowing and suction on nonlinear stability of the attachment-line boundary layer is also investigated.

Hall, P.↗
NASA NTRS1986

Wave-interactions in three-dimensional boundary layers

A Fourier-Chebyshev spectral method is used to study the nonlinear stability and disturbance wave-interactions in a two-dimensional boundary layer on a curved wall and a three-dimensional boundary layer on a rotating disk. Goertler and crossflow instability, respectively, are the dominant mechanisms in these boundary layers. For the range of parameters considered, the present computational model does not support the Goertler/TS interaction of the type proposed by Nayfeh (1981). According to his model, oblique TS waves with spanwise wavelengths twice that of the finite-amplitude Goertler vortex are excited in the boundary layer. The present nonlinear calculations show that both the Goertler and crosssflow vortices develop strong instabilities in their harmonics with half the wavelength of the primary vortices.

Malik, M. R.↗
NASA NTRS1986

Numerical study of sink-flow boundary layers

Direct numerical simulations of sink-flow boundary layers, with acceleration parameters K between 1.5 x 10 to the -6th and 3.0 x 10 to the -6th, are presented. The three-dimensional, time-dependent Navier-Stokes equations are solved numerically, using a spectral method, with about one million degrees of freedom. The flow is assumed to be statistically steady, and self-similar. A multiple-scale approximation and periodic conditions are applied to the fluctuations. The turbulence is studied using instantaneous and statistical results. Good agreement with the experiments of Jones and Launder (1972) is observed. The two effects of the favorable pressure gradient are to extend the logarithmic layer, and to alter the energy balance of the turbulence near the edge of the boundary layer. At low Reynolds number the logarithmic layer is shortened and slightly displaced, but wall-layer streaks are present even at the lowest values of R(theta) for which turbulence can be sustained. Large quiescent patches appear in the flow. Relaminarization occurs at K = 3.0 x 10 to the -6th, corresponding to a Reynolds number R(theta) of about 330.

Spalart, Philippe R.↗
NASA NTRS1987

Stability of viscous flow past a circular cylinder

A spectral method which employs trigonometric functions and Chebyshev polynomials is used to compute the steady, incompressible laminar flow past a circular cylinder. Linear stability methods are used to formulate a pair of decoupled generalized eigenvalue problems for the growth of symmetric and asymmetric (about the dividing streamline) perturbations. It is shown that, while the symmetric disturbances are stable, the asymmetric perturbations become unstable at a Reynolds number about 40 with a Strouhal number about 0.12. The critical conditions are found to depend on the size of the computational domain in a manner similar to that observed in the laboratory.

Zebib, A.↗
NASA NTRS1987

Solitary waves in the resonant phenomenon between a surface gravity wave packet and an internal gravity wave

A two-layer inviscid incompressible fluid system of intermediate depth is considered. A multiple-scales perturbation technique is applied to the basic equations and boundary conditions for a two-layer fluid system to derive a system of weakly nonlinear partial integrodifferential equations governing the resonant interaction between a surface gravity wave packet and an internal gravity wave at an intermediate depth, providing a bridge between the existing shallow and deep fluid theories. The convolution integral term in these equations accounts for the dispersion in the lower-layer fluid. An iterative fast Fourier transform scheme is developed to find solitary wave solutions to this system of equations. The overtaking collision of two pairs of solitary waves, simulated using a spectral method, is found to be inelastic. It is found that the amplitude of the solitary waves changes slightly after the collision. The phase shifts these solitary waves undergo was calculated numerically.

Sepulveda, Nicasio↗
NASA NTRS1986

Numerical simulation of boundary layers. Part 3: Turbulence and relaminarization in sink flows

Direct numerical simulations of sink-flow boundary layers, with acceleration parameters K between 1.5 and 3.0 x 10 to the -6 power, are presented. The three-dimensional, time-dependent Navier-Stokes equations are solved numerically using a spectral method, with about 10 to the -6 degrees of freedom. The flow is assumed to be statistically steady, and self-similar. A multiple-scale approximation and periodic conditions are applied to the fluctuations. The turbulence is studied using instantaneous and statistical results. Good agreement with the experiments of Jones and Launder is observed. Two effects of the favorable pressure gradient are to extend the logarithmic layer, and to alter the energy balance of the turbulence near the edge of the boundary layer. At very low Reynolds number the logarithmic layer is shortened and slightly displaced, but wall-layer streaks are present even at the lowest values of the Reynolds number for which turbulence can be sustained. Large quiescent patches appear in the flow. Relaminarization occurs at K = 3.0 x 10 to the -6 power, corresponding to a Reynolds number, based on momentum thickness, of about 330.

Spalart, Philippe R.↗