ALBERT

Description: In the present work, the high Reynolds number flow past an inclined plate with a splitter plate placed in its wake is considered numerically. A numerical conformal mapping technique is employed to transform the two-plate system into the same number of cylinders: the flow field is assumed to be two-dimensional. The vortex shedding from the inclined plate is modelled using the discrete vortex method. It is shown that the splitter plate has a profound effect on the development of the flow over a range of values of a suitably defined offset parameter and for a range of positions of the leading edge of the splitter plate. The acoustic field is also calculated and the spectrum reflects the flow results.

Description: Energy of a high harmonic standing wave tends to be distributed equally over the whole wave even in a stratified medium where the wave's peak amplitude can be much larger near the upper boundary than the lower one. This fact is generalized to the many diverse physical problems which solve second-order differential equations of Sturm-Liouville type. For any such solution y(z) whose sign fluctuates along the z-axis, quantities are found which have the same value between any two neighboring zeros of y. One of the equidistributed quantities for an oscillating fluid sphere is similar to kinetic energy but is identical only in limiting cases. The acoustic midpoint of a cavity can be a unique place where some nonlinear perturbations have extra strength. This may apply to the puzzling solar phenomenon called supergranulation.

Description: A computational code for the vorticity-potential method is developed for a three-dimensional bounded vorticity field. The evaluation of the boundary data for the vector potential in the code is improved so that the numerical solution simulates that in an unbounded domain to a high order. The time evolution of two vortex rings and that of an elliptic ring are investigated with this code. The cut-and-connect phenomena of vortex rings are successfully captured. The results are compared with those of asymptotic theory and the experiment. They also highlight the need for additional theoretical and numerical investigations.

Description: In the present grid-independent approximate Riemann solver for 2D and 3D flows that are governed by the Euler or Navier-Stokes equations, fluxes on grid faces are obtained by wave decomposition; the assumption of information-propagation in the velocity-difference directions leads to a more accurate resolution of shear and shock waves, when these are are oblique to the grid. The model, which yields significantly greater accuracy in both supersonic and subsonic first-order spatially accurate computations, describes the difference in states at each grid interface by the action of five waves.

Description: A new procedure, dubbed the Munich Method, has been proposed recently for the modeling of rocket engine performance. The author of the Munich Method claims it to be an extension and improvement of the thermodynamic procedures used to model rocket engines in the NASA-Lewis chemical equilibrium program. An examination of the Munich Method shows that it contains several flaws. If these defects are corrected then the Munich Method will produce results identical to those generated by the NASA-Lewis Code.

Description: The action of weak, streamwise vortices on a plane, incompressible, steady mixing layer is examined in the large Reynolds number limit. The outer, inviscid region is bounded by a vortex sheet to which the viscous region is confined. It is shown that the local linear analysis becomes invalid at streamwise distances O(epsilon sup -1), where (epsilon much less than 1) is the crossflow amplitude, and a new nonlinear analysis is constructed for this region. Numerical solutions of the nonlinear problem show that the vortex sheet undergoes an O(1) change in position and that the solution is ultimately terminated by a breakdown in the numerical procedure. The corresponding viscous layer shows downstream thickening, but appears to remain well behaved up to the terminal location.

Description: This paper investigates the linear stability of confined mixing layers with special emphasis on the effects of heat release and compressibility. The results show that reflection of supersonic disturbances by the walls makes the confined supersonic mixing layer more unstable than the unconfined free shear layer. Decreasing the distance between the walls makes the flow more unstable. However, subsonic disturbances are relatively unaffected by the walls. Heat release and Mach number hardly change the growth rates of supersonic disturbances. The most unstable supersonic disturbances are two-dimensional in rectangular channel flows, but three-dimensional in partially confined flows. Finally, the reactants are not strongly mixed by supersonic instabilities, which mainly disturb one side of the layer.

Description: Spectral local isotropy tests are applied to direct numerical simulation data, mainly at the centerline of a fully developed turbulent channel flow. Despite the small Reynolds number of the simulation, the high-wavenumber behavior of velocity and vorticity spectra is consistent with local isotropy. This consistency is verified by the relationship between streamwise wavenumber spectra and spanwise wavenumber spectra. The high-wavenumber behavior of the pressure spectrum is also consistent with local isotropy and compares favorably with the calculation of Batchelor (1951), which assumes isotropy and joint normality of the velocity field at two points in space. The latter assumption is validated by the shape but not the magnitude of the quadruple correlation of the streamwise velocity fluctuation at small separations. There is only partial support for local spectral isotropy away from the centerline as the magnitude of the mean strain rate increases.

Description: A previously derived analytical model for the small-scale structure of turbulence is reformulated in such a way that the energy spectrum may be computed. The model is an ensemble of two-dimensional (2D) vortices with internal spiral structure, each stretched by an axially symmetric strain flow. Stretching and differential rotation produce an energy cascade to smaller scales in which the stretching represents the effect of instabilities and the spiral structure is the source of dissipation at the end of the cascade. The energy spectrum of the resulting flow may be expressed as a time integration involving only the enstrophy spectrum of the time evolving 2D cross section flow, which may be obtained numerically. Examples are given in which a k exp -5/3 spectrum is obtained by this method. The k exp -5/3 inertial range spectrum is shown to be related to the existence of a self-similar enstrophy preserving range in the 2D enstrophy spectrum. The results are found to be insensitive to time dependence of the strain rate, including even intermittent on-or-off strains.

Description: A k-epsilon model is proposed for wall bonded turbulent flows. In this model, the eddy viscosity is characterized by a turbulent velocity scale and a turbulent time scale. The time scale is bounded from below by the Kolmogorov time scale. The dissipation equation is reformulated using this time scale and no singularity exists at the wall. The damping function used in the eddy viscosity is chosen to be a function of R(sub y) = (k(sup 1/2)y)/v instead of y(+). Hence, the model could be used for flows with separation. The model constants used are the same as in the high Reynolds number standard k-epsilon model. Thus, the proposed model will be also suitable for flows far from the wall. Turbulent channel flows at different Reynolds numbers and turbulent boundary layer flows with and without pressure gradient are calculated. Results show that the model predictions are in good agreement with direct numerical simulation and experimental data.

Description: Results are presented of an experimental and numerical study of a turbulent boundary layer with pressure gradients conducted using the recent 'fringe method' with its numerical advantages and good inflow quality. After an inflow transient good agreement is observed; the differences, of up to 13 percent, are discussed. Moderate deviations from the law of the wall are found in the velocity profiles of the simulation. They are fully correlated with the pressure gradient, are in fair quantitative agreement with the experimental results of Nagano et al. (1992), and are roughly the opposite of uncorrected mixing-length-model predictions. Large deviations from the wall scaling are observed for other quantities, notably for the turbulence dissipation rate. The a(1) structure parameter drops mildly in the upper layer with adverse pressure gradient.

Description: The paper formulates a tensorially consistent near-wall second-order closure model. Redistributive terms in the Reynolds stress equations are modeled by an elliptic relaxation equation in order to represent strongly nonhomogeneous effects produced by the presence of walls; this replaces the quasi-homogeneous algebraic models that are usually employed, and avoids the need for ad hoc damping functions. The model is solved for channel flow and boundary layers with zero and adverse pressure gradients. Good predictions of Reynolds stress components, mean flow, skin friction, and displacement thickness are obtained in various comparisons to experimental and direct numerical simulation data. The model is also applied to a boundary layer flowing along a wall with a 90-deg, constant-radius, convex bend.

Description: A computer code for solving the Reynolds-averaged full Navier-Stokes equations has been developed and applied using H- and C-type grids. The Baldwin-Lomax eddy-viscosity model is used for turbulence closure. The integration in time is based on an explicit four-stage Runge-Kutta scheme. Local time stepping, variable coefficient implicit residual smoothing, and a full multigrid method have been implemented to accelerate steady-state calculations. A grid independence analysis is presented for a transonic rotor blade. Comparisons with experimental data show that the code is an accurate viscous solver and can give very good blade-to-blade predictions for engineering applications.

Description: A numerical study was conducted to investigate how bleed through a two-dimensional slot affects shock-wave induced, boundary-layer separation on a flat plate. This study is based on the ensemble-averaged, compressible, Navier-Stokes equations closed by the Baldwin-Lomax, algebraic turbulence model. The algorithm used to obtain solutions was the implicit, partially split, two-factored scheme of Steger. This study examined the effects of the following parameters in controlling shock-wave induced flow separation: location of slot in relation to where the incident shock wave impinged on the boundary layer, size of slot in relation to the boundary-layer thickness, number of slots, spacings between slots, and strength of the incident shock wave. This study also showed the nature of the very complex flowfield about the slot or slots and how the plenum affects the bleed process. The results of this study are relevant to problems where bleed is used to control shock-wave induced, boundary-layer separation (e.g., inside jet engine inlets and wind tunnels).

Description: Turbulent flow in a 2D channel with repeated rectangular rib roughness was numerically simulated using a low Reynolds number form of the k-epsilon turbulence model. Friction factors and average Stanton numbers were calculated for various pitch to rib height ratios and bulk Reynolds numbers. Comparisons with experiment were generally adequate, with the predictions of friction superior to those for heat transfer. The effect of variable properties for channel flow was investigated, and the results showed a greater effect for friction than for heat transfer. Comparison with experiment yielded no clear conclusions. The turbulence model was also validated for a related problem, that of flow downstream of an abrupt pipe expansion.

Description: The purpose of this note is to construct a local solution that eliminates a residual velocity discontinuity in the inviscid portion of a solution obtained in a recent paper by Goldstein, Leib and Cowley (1992). This result is of importance because it shows that the solution obtained in that paper is entirely non-singular outside the viscous wall boundary layer and that any singularity in the problem will have to arise in the usual way through a breakdown in the viscous boundary layer.

Description: We use a set of equations, sometimes referred to as the 'delta-equations', to approximate the two-dimensional inviscid motion of an initially circular vortex sheet released from rest in a cross-flow. We present numerical solutions of these equations for the case with delta-square = 0 (for which the equations are exact) and for delta-square greater than 0. For small values of the smoothing parameter delta, a spectral filter must be used to eliminate spurious instabilities due to round-off error. Two singularities appear simultaneously in the vortex sheet when delta-square = 0 at a critical time t(c). After t(c), the solutions do not converge as the computational mesh is refined. With delta-square greater than 0, converged solutions were found for all values of delta-square when t is less than t(c), and for all but the two smallest values of delta-square used when t is greater than t(c). Our results show that, when delta-square is greater than 0, the vortex sheet deforms into two doubly branched spirals some time after t(c). The limiting solution as delta approaching 0 clearly exists and equals the delta = 0 solution when t is less than t(c).

Description: The evolution of three-dimensional temporally evolving plane mixing layers through as many as three pairings has been simulated numerically. All simulations were begun from a few low-wavenumber disturbances, usually derived from linear stability theory, in addition to the mean velocity. Three-dimensional perturbations were used with amplitudes ranging from infinitesimal to large enough to trigger a rapid transition to turbulence. Pairing is found to inhibit the growth of infinitesimal three-dimensional disturbances, and to trigger the transition to turbulence in highly three-dimensional flows. The mechanisms responsible for the growth of three-dimensionality and onset of transition to turbulence are described. The transition to turbulence is accompanied by the formation of thin sheets of spanwise vorticity, which undergo secondary rollups. The post-transitional simulated flow fields exhibit many properties characteristic of turbulent flows.

Description: An analytical solution was obtained by Siegel (1991, 1992) for local boundary heat fluxes by a radiating medium at uniform temperature in a 2D rectangular region. It is shown here that, after local fluxes from the medium to the walls have been evaluated, it is very easy to compute local fluxes arriving from the adjacent and opposite walls. This extends the previous analysis and provides convenient relations to include radiation from a black boundary, each side of the rectangle being at a different uniform temperature. The final expressions are helpful in performing spectral calculations that must be made for many spectral bands.

Description: Effects of helicity in three-dimensional incompressible inhomogeneous turbulence are examined with the aid of a two-scale direct-interaction approximation (DIA). The turbulent helicity gives a measure of the reflectional asymmetry in a turbulent flow and its inhomogeneity contributes to the sustainment of large-scale vorticity field in a three-dimensional mean flow. The importance of helicity effects is discussed in the context of flows in a rotating system and swirling flows in a pipe. A three-equation model with the turbulent helicity incorporated is proposed using the theoretical results. The validity of the model is confirmed quantitatively through the application to a decaying swirling flow in a pipe.

Description: A Runge-Kutta formula in time is presently used to advance schemes in which central differences are used to solve the time-dependent Euler equations; a second difference is added near shocks as an artificial viscosity to reduce the given scheme to a first-order upwind one at shocks. A matrix-valued dissipation is introduced and compared with the scalar viscosity; a connection is shown between this artificial viscosity and flux limiters. The use of various flux limiters for this central difference scheme is compared.

Description: An account is given of the significance for U.S. spacecraft development of a nuclear thermal rocket (NTR) reactor concept that has been developed in the (formerly Soviet) Commonwealth of Independent States (CIS). The CIS NTR reactor employs a hydrogen-cooled zirconium hydride moderator and ternary carbide fuels; the comparatively cool operating temperatures associated with this design promise overall robustness.

Description: An efficient method for calculating unsteady flows is presented, with emphasis on a modified version of the thin-layer Navier-Stokes equations. Fourier stability analysis is used to illustrate the effect of treating the source term implicitly instead of explicity, as well as to illustrate other algorithmic choices. A 2D circular cylinder (with a Reynolds number of 1200 and a Mach number of 0.3) is calculated. The present scheme requires only about 10 percent of the computer time required by global minimum time stepping.

Description: Flow solutions were analyzed using three visualization tools, FAST, UFAT, and Visual3. The simulation models axisymmetric unsteady flow inside a closed circular cylinder with a rotating lid. The capabilities and limitations of these visualization packages are presented. The versatility of these tools enhances scientific study and presentation of numerical results.

Description: The present time-accurate coupled-solution procedure addresses the chemical nonequilibrium Navier-Stokes equations over a wide Mach-number range uses, in conjunction with the strong conservation form of the governing equations, five unknown primitive variables. The numerical tests undertaken address steady convergent-divergent nozzle flows with air dissociation/recombination, dump combustor flows with n-pentane/air chemistry, and unsteady nonreacting cavity flows.

Description: A generalized anisotropic porous medium approach is developed for modelling the flow, heat and mass transport processes during binary mixture solidification. Transient predictions are obtained using FEM, coupled with an implicit time-marching scheme, for solidification inside a two-dimensional rectangular enclosure. A parametric study focusing attention on the effects of solutal buoyancy and thermal buoyancy is presented. It is observed that three parameters, namely the thermal Rayleigh number, the solutal Rayleigh number, and the relative density change parameter, significantly alter the flow fields in the liquid and the mushy regions. Depending upon the nature of these flow fields, the solute enrichment caused by macrosegregation may occur in the top or the bottom region of the enclosure.

Description: The constant C sub mu and the near-wall damping function f sub mu in the eddy-viscosity relation of the k-epsilon model are evaluated from direct numerical simulation (DNS) data for developed channel and boundary layer flow at two Reynolds numbers each. Various existing f sub mu model functions are compared with the DNS data, and a new function is fitted to the high-Reynolds-number channel flow data. The epsilon-budget is computed for the fully developed channel flow. The relative magnitude of the terms in the epsilon-equation is analyzed with the aid of scaling arguments, and the parameter governing this magnitude is established. Models for the sum of all source and sink terms in the epsilon-equation are tested against the DNS data, and an improved model is proposed.

Description: Knowledge of the amount of heat that is conducted, advected and radiated between an ampoule and the furnace is important for understanding vertical Bridgman crystal growth. This heat transfer depends on the temperature, emissivities and geometries of both the furnace and ampoule, as well as the choice of ambient gas inside the furnace. This paper presents a method which directly measures this heat transfer without the need to know any physical properties of the furnace, the ampoule, or the gaseous environment. Data are given for one specific furnace in which this method was used.

Description: A comparative description is presented for the least-squares FEM (LSFEM) for 2D steady-state pure convection problems. In addition to exhibiting better control of the streamline derivative than the streamline upwinding Petrov-Galerkin method, numerical convergence rates are obtained which show the LSFEM to be virtually optimal. The LSFEM is used as a framework for an iteratively reweighted LSFEM yielding nonoscillatory and nondiffusive solutions for problems with contact discontinuities; this method is shown to convect contact discontinuities without error when using triangular and bilinear elements.

Description: The directions of the triadic energy transfers assumed in a previous paper agree with the spectral closures, in a similarity range, if the exponent of the power-law energy spectrum is less than unity. The helical interactions showing a strong local energy transfer when the triad is nonlocal, sum up to a reverse cascade unless the spectrum falls off faster than a -7/3 power of the wave number. The energy cascades from each type of helical interaction are calculated for a -5/3 inertial range using the eddy damped quasinormal Markovian model. One type of interaction is responsible for 86 percent of the cascade. The contributions of the two classes of helical interactions to the subgrid-scale eddy viscosity are presented, together with the contributions from the forward and reverse cascading interactions. An application of the assumption on the triadic energy transfers to turbulence under rapid rotation gives a simple argument for the tendency toward nonlinear two-dimensionalization of the flow.

Description: A database obtained from direct numerical simulation of a turbulent channel flow is analyzed to extract the streamwise component of the propagation velocity V of velocity, vorticity, and pressure fluctuations from their space-time correlations. A surprising result is that V is approximately the same as the local mean velocity for most of the channel, except for the near-wall region. For y(+) less than 15, V is virtually constant, implying that perturbations of all flow variables propagate like waves near the wall. In this region V is 55 percent of the centerline velocity Uc for velocity and vorticity perturbations and 75 percent of U sub c for pressure perturbations. This is equal to U at y(+) = 15 for velocity and vorticity perturbations, and equal to U at y(+) = 20 for pressure perturbations, indicating that the dynamics of the nearwall turbulence is controlled by turbulence structures present near y(+) about 15-20. Scale dependence of V is also examined by analyzing the bandpass-filtered flow fields. This paper contains comprehensive documentation on the propagation velocities, which should prove useful in the evaluation of Taylor's hypothesis.

Description: Direct numerical simulation data for the lateral velocity derivative delta(u)/delta(y) at the centerline of a fully developed turbulent channel flow provide reasonable support for Wyngaard's analysis of the error involved in measuring this quantity using parallel hot wires. Numerical data in the wall region of the channel flow also provide a useful indication of how to select the separation between the wires. Justification for this choice is obtained by comparing several measured statistics of delta(u)/delta(y) with the corresponding numerical data.

Description: The nonlinear instability of the boundary layer on a heated flat plate placed in an oncoming flow is investigated. Such flows are unstable to stationary vortex instabilities and inviscid travelling wave disturbances governed by the Taylor-Goldstein equation. For small temperature differences the Taylor-Goldstein equation reduces to Rayleigh's equation. When the temperature difference between the wall and free stream is small the preferred mode of instability is a streamwise vortex. It is shown in this case that the vortex, assumed to be of small wavelength, restructures the underlying mean flow to produce a profile which can be massively unstable to inviscid travelling waves. The mean state is shown to be destabilized if the Prandtl number is less than unity.

Description: A new era is dawning in the ability to predict convection heat transfer in the turbine gas path. We feel that the technical community now has the capability to mount a major assault on this problem, which has eluded significant progress for a long time. In this paper we hope to make a case for this bold statement by reviewing the state of the art in three major and related areas, which we believe are indispensable to the understanding and accurate prediction of turbine gas path heat transfer: configuration-specific experiments, fundamental physics and model development, and code development. We begin our review with the configuration-specific experiments, whose data have provided the big picture and guided both the fundamental modeling research and the code development. Following that, we examine key modeling efforts and comment on what will be needed to incorporate them into the codes. In this region we concentrate on bypass transition, 3D endwalls, and film cooling. We then review progress and directions in the development of computer codes to predict turbine gas path heat transfer. Finally, we cite examples and make observations on the more recent efforts to do all this work in a simultaneous, interactive, and more synergistic manner. We conclude with an assessment of progress, suggestions for how to use the current state of the art, and recommendations for the future.

Description: The length scales appearing in the relations for the eddy viscosity and dissipation rate in one-equation models were evaluated from direct numerical (DNS) simulation data for developed channel and boundary-layer flow at two Reynolds numbers each. To prepare the ground for the evaluation, the distribution of the most relevant mean-flow and turbulence quantities is presented and discussed, also with respect to Reynolds-number influence and to differences between channel and boundary-layer flow. An alternative model is tested as near wall component of a two-layer model by application to developed-channel, boundary-layer and backward-facing-step flows.

Description: The solar array module plasma interactions experiment (SAMPIE) is an approved NASA flight experiment manifested for Shuttle deployment in early 1994. The SAMPIE experiment is designed to investigate the interaction of high voltage space power systems with ionospheric plasma. To study the behavior of solar cells, a number of solar cell coupons (representing design technologies of current interest) will be biased to high voltages to measure both arcing and current collection. Various theories of arc suppression will be tested by including several specially modified cell coupons. Finally, SAMPIE will include experiments to study the basic nature of arcing and current collection. This paper describes the rationale for a space flight experiment, the measurements to be made, and the significance of the expected results. A future paper will present a detailed discussion of the engineering design.

Description: Measured raw transfer interactions from which local energy transfer is argued to result are summed in a way that directly indicates the scale disparity (s) of contributions to the net energy flux across the spectrum. It is found that the dependence upon s closely follows the s exp -4/3 form predicted by classical arguments. As a result, it is concluded that direct numerical simulation measurements lend support to the classical Kolmogorov phenomenology of local interactions and local transfer in an inertial range.

Description: The present numerical study of unsteady, low Reynolds number flow past a 2D airfoil attempts to ascertain the bifurcation sequence leading from simple periodic to complex aperiodic flow with rising Reynolds number, as well as to characterize the degree of chaos present in the aperiodic flow and assess the role of numerics in the modification and control of the observed bifurcation scenario. The ARC2D Navier-Stokes code is used in an unsteady time-accurate mode for most of these computations. The system undergoes a period-doubling bifurcation to chaos as the Reynolds number is increased from 800 to 1600; its chaotic attractors are characterized by estimates of the fractal dimension and partial Liapunov exponent spectra.

Description: Direct numerical simulations of temporally evolving plane mixing layers undergoing as many as three pairings have been examined for evidence of spanwise scale change. All simulations were begun from a few low-wavenumber disturbances, usually derived from linear stability theory, in addition to the mean velocity. The amplitude of the initial three-dimensional disturbances varied from infinitesimal to large enough to trigger a rapid transition to turbulence. The time required for a change of characteristic spanwise scale with infinitesimal three-dimensional disturbances was found to be very long, requiring three or more pairings to complete a doubling of the spanwise scale. Stronger three-dimensionality can produce more rapid scale changes, but it is also likely to trigger transition to turbulence. No evidence was found for a change from an organized array of rib vortices at one spanwise scale to a similar array at a larger spanwise scale.

Description: A method is presented which allows diffusion terms to be treated implicitly in the lower-upper (LU) algorithm (which is a commonly used method for solving 'compressible' Euler and Navier-Stokes equations) so that the algorithm's good stability properties will not be impaired. The new method generalizes the concept of LU factorization from that associated with the sign of eigenvalues to that associated with backward- and forward-difference operators without regard to eigenvalues. The method is verified in a turbulent boundary layer study.

Description: We consider the effects of a small-amplitude, steady, streamwise vorticity field on the flow over an infinitely thin flat plate in an otherwise uniform stream. We show how the initially linear perturbation, ultimately leads to a small-amplitude but nonlinear cross flow far downstream from the leading edge. This motion is imposed on the boundary-layer flow and eventually causes the boundary layer to separate. The streamwise velocity profiles within the boundary layer become inflexional in localized spanwise regions just upstream of the separation point. The flow in these regions is therefore susceptible to rapidly growing inviscid instabilities.

Description: The paper presents a critical comment on the work of Henkes and Hoogendoorn. In particular, it is argued that the model of To and Humphrey (TH) (1986) has been implemented incorrectly, rendering invalid the conclusion that the TH model considerably deviates from the other models evaluated. In their response to the criticism, the authors present arguments in support of the correctness of their implementation of the TH model and of the validity of the conclusions reached in their work.

Description: The present extention of a Lagrangian approach of the Riemann solution procedure, which was originally proposed for perfect gases, to real gases, is nontrivial and requires the development of an exact real-gas Riemann solver for the Lagrangian form of the conservation laws. Calculations including complex wave interactions of various types were conducted to test the accuracy and robustness of the approach. Attention is given to the case of 2D oblique waves' capture, where a slip line is clearly in evidence; the real gas effect is demonstrated in the case of a generic engine nozzle.

Description: Implicit difference operator spectra are presently computed by applying eigensystem analysis techniques to finite-difference formulations of 2D Euler and Navier-Stokes equations, and attention is given to these iterative methods' convergence and stability characteristics by taking into account the effects of grid geometry, time-step, numerical viscosity, and boundary conditions. On the basis of the eigenvalue distributions for various flow configurations, the feasibility of applying such convergence-acceleration techniques as eigenvalue annihilation and relaxation is discussed. Spectrum-shifting is applied to NASA-Ames' ARC2D flow code, achieving a 20-33 percent efficiency.

Description: The NASA Lewis Research Center (LeRC) conducts and directs an electric propulsion research and technology program aimed at providing high-performance electric propulsion system options for a broad range of near and far-term missions. This evolutionary program emphasizes the development of propulsion systems for three classes of missions: (1) near term auxiliary propulsion applications such as North-South Stationkeeping for next generation communications satellites and orbit maintainence for orbiting platforms such as Space Station Freedom; (2) advanced solar electric propulsion and SP-100-class nuclear electric propulsion for Earth-space orbit transfer and robotic planetary missions; and (3) very high power systems to support major space missions including the Space Exploration Initiative. To cover widely disparate mission requirements, the LeRC program includes research on electrothermal, electrostatic, and electromagnetic systems. This paper provides an overview of the LeRC program with a focus on recent progress.

Description: The 'computational test-cell' will enable the incorporation of new methodologies, such as concurrent engineering and probabilistic methods, into the propulsion design process. This will provide the capability to conduct credible, interdisciplinary analyses of new propulsion concepts and designs. Probabilistic methods can be used as the basis for reliability-based design. Recently methods have been devised that provide the capability of simulating the performance of propulsion systems at several levels of resolution. These methods make it possible to quantify uncertainty and to establish confidence bounds for the calculated values. The introduction of reliability-based design methodology along with probabilistic analyses will provide a tool to reduce the design space for new systems and to reduce our dependence on hardware testing for proof-of-concept and system integration demonstrations. The resulting simulations will reduce the need for testing and identify potential operational problems early in the design process. This capability will make it possible to compute the expected performance, stability, reliability, and life of propulsion components, subsystems, and systems at design and off-design conditions, to bring life cycle cost trade-offs early into the design process and to determine optimum designs to satisfy specified mission requirements.

Description: Study of turbulent flows in rotating reference frames has long been an area of considerable scientific and engineering interest. Because of its importance, the subject of turbulence in rotating reference frames has motivated over the years a large number of theoretical, experimental, and computational studies. The bulk of these previous works has served to demonstrate that the effect of system rotation on turbulence is subtle and remains exceedingly difficult to predict. A rotating flow of particular interest in many studies, including the present work, is examination of the effect of solid-body rotation on an initially isotropic turbulent flow. One of the principal reasons for the interest in this flow is that it represents the most basic turbulent flow whose structure is altered by system rotation but without the complicating effects introduced by mean strains or flow inhomogeneities. The assumption of statistical homogeneity considerably simplifies analysis and computation. The principal objective of the present study has been to examine the asymptotic state of solid-body rotation applied to an initially isotropic, high Reynolds number turbulent flow. Of particular interest has been to determine the degree of two-dimensionalization and the existence of asymptotic self-similar states in homogeneous rotating turbulence.

Description: The objective here is to test the Dynamic Localization (DL) model in a wall-bounded channel flow for numerical stability and accuracy of results. Algebraic stress models suggest that the model for the residual subgrid-scale (SGS) Reynolds stress and scalar flux should generally have terms comprising most of the unique products of the resolved strain (S) and rotation (R) tensors with S and the resolved scalar gradient. The standard dynamic SGS model uses a simple (Smagorinsky) base model for the residual Reynolds stress, which is made proportional to S, and down-gradient base models for residual scalar fluxes; these correspond to the lowest, 'first-order' terms in algebraic stress models. Temporal scaling terms in these base models are formed from the magnitude of the resolved strain rate. While this is appropriate for simple shear flows, it may not be appropriate for more complicated flows (relevant to geophysical and astrophysical problems) that include any combination of shear, rotation, buoyancy, etc. On the other hand, the coefficient in the dynamic SGS model readily adjusts itself to different flow conditions and may adequately take account of these effects without the need for more complicated base models. Cabot (1993) has begun to test the dynamic SGS model in buoyant flows (Rayleigh-Benard and internally heated convection) with and without buoyancy terms explicitly included in the scaling terms of the base model; no great differences were found in large eddy simulation (LES) results for the different base model scalings. The second objective in this work is to test base models with additional, 'second-order' terms (e.g., S(sup 2) and RS for the residual Reynolds stress). These terms have been found to improve large-scale flow predictions by kappa-epsilon models in the presence of rotation and shear. Second-order base models will be tested here in the LES of channel flow with and without solid-body rotation and compared with results from the standard first-order base models to determine if there are significant differences or improvements in results that would warrant the added complexity of the second-order base models.

Description: The present study is a continuation of the examination by Hamilton et al. of the regeneration mechanisms of near-wall turbulence and an attempt to investigate the conjecture of Waleffe et al. The basis of this study is an extension of the 'minimal channel' approach of Jimenez and Moin that emphasizes the near-wall region and reduces the complexity of the turbulent flow by considering a plane Couette flow of near minimum Reynolds number and stream-wise and span-wise extent. Reduction of the flow Reynolds number to the minimum value which will allow turbulence to be sustained has the effect of reducing the ratio of the largest scales to the smallest scales or, equivalently, of causing the near-wall region to fill more of the area between the channel walls. A plane Couette flow was chosen for study since this type of flow has a mean shear of a single sign, and at low Reynolds numbers, the two wall regions are found to share a single set of structures.

Description: Free shear flows, like those of mixing layers, are encountered in aerodynamics, in the atmosphere, and in the ocean as well as in many industrial applications such as flow reactors or combustion chambers. It is, therefore, crucial to understand the mechanisms governing the process of transition to turbulence in order to predict and control the evolution of the flow. Delaying transition to turbulence as far downstream as possible allows a gain in energy expenditure while accelerating the transition can be of interest in processes where high mixing is desired. Various methods, including the use of polymer additives, can be effective in controlling fluid flows. The drag reduction obtained by the addition of small amounts of high polymers has been an active area of research for the last three decades. It is now widely believed that polymer additives can affect the stability of a large variety of flows and that dilute solutions of these polymers have been shown to produce drag reductions of over 80 percent in internal flows and over 60 percent in external flows under a wide range of conditions. The major thrust of this work is to study the effects of polymer additives on the stability of the incompressible mixing layer through large scale numerical simulations. In particular, we focus on the two dimensional flow and examine how the presence of viscoelasticity may affect the typical structures of the flow, namely roll-up and pairing of vortices.

Description: Although the different regimes of premixed combustion are not well defined, most of the recent developments in turbulent combustion modeling are led in the so-called flamelet regime. The goal of these models is to give a realistic expression to the mean reaction rate (w). Several methods can be used to estimate (w). Bray and coworkers (Libby & Bray 1980, Bray 1985, Bray & Libby 1986) express the instantaneous reaction rate by means of a flamelet library and a frequency which describes the local interaction between the laminar flamelets and the turbulent flowfield. In another way, the mean reaction rate can be directly connected to the flame surface density (Sigma). This quantity can be given by the transport equation of the coherent flame model initially proposed by Marble & Broadwell 1977 and developed elsewhere. The mean reaction rate, (w), can also be estimated thanks to the evolution of an arbitrary scalar field G(x, t) = G(sub O) which represents the flame sheet. G(x, t) is obtained from the G-equation proposed by Williams 1985, Kerstein et al. 1988 and Peters 1993. Another possibility proposed in a recent study by Mantel & Borghi 1991, where a transport equation for the mean dissipation rate (epsilon(sub c)) of the progress variable c is used to determine (w). In their model, Mantel & Borghi 1991 considered a medium with constant density and constant diffusivity in the determination of the transport equation for (epsilon(sub c)). A comparison of different flamelet models made by Duclos et al. 1993 shows the realistic behavior of this model even in the case of constant density. Our objective in this present report is to present preliminary results on the study of this equation in the case of variable density and variable diffusivity. Assumptions of constant pressure and a Lewis number equal to unity allow us to significantly simplify the equation. A systematic order of magnitude analysis based on adequate scale relations is performed on each term of the equation. As in the case of constant density and constant diffusivity, the effects of stretching of the scalar field by the turbulent strain field, of local curvature, and of chemical reactions are predominant. In this preliminary work, we suggest closure models for certain terms, which will be validated after comparisons with DNS data.

Description: The recent development of the dynamic subgrid-scale (SGS) model has provided a consistent method for generating localized turbulent mixing models and has opened up great possibilities for applying the large eddy simulation (LES) technique to real world problems. Given the fact that the direct numerical simulation (DNS) can not solve for engineering flow problems in the foreseeable future (Reynolds 1989), the LES is certainly an attractive alternative. It seems only natural to bring this new development in SGS modeling to bear on the reacting flows. The major stumbling block for introducing LES to reacting flow problems has been the proper modeling of the reaction source terms. Various models have been proposed, but none of them has a wide range of applicability. For example, some of the models in combustion have been based on the flamelet assumption which is only valid for relatively fast reactions. Some other models have neglected the effects of chemical reactions on the turbulent mixing time scale, which is certainly not valid for fast and non-isothermal reactions. The probability density function (PDF) method can be usefully employed to deal with the modeling of the reaction source terms. In order to fit into the framework of LES, a new PDF, the large eddy PDF (LEPDF), is introduced. This PDF provides an accurate representation for the filtered chemical source terms and can be readily calculated in the simulations. The details of this scheme are described.

Description: Application of the method of Large Eddy Simulation (LES) to a turbulent flow consists of three separate steps. First, a filtering operation is performed on the Navier-Stokes equations to remove the small spatial scales. The resulting equations that describe the space time evolution of the 'large eddies' contain the subgrid-scale (sgs) stress tensor that describes the effect of the unresolved small scales on the resolved scales. The second step is the replacement of the sgs stress tensor by some expression involving the large scales - this is the problem of 'subgrid-scale modeling'. The final step is the numerical simulation of the resulting 'closed' equations for the large scale fields on a grid small enough to resolve the smallest of the large eddies, but still much larger than the fine scale structures at the Kolmogorov length. In dividing a turbulent flow field into 'large' and 'small' eddies, one presumes that a cut-off length delta can be sensibly chosen such that all fluctuations on a scale larger than delta are 'large eddies' and the remainder constitute the 'small scale' fluctuations. Typically, delta would be a length scale characterizing the smallest structures of interest in the flow. In an inhomogeneous flow, the 'sensible choice' for delta may vary significantly over the flow domain. For example, in a wall bounded turbulent flow, most statistical averages of interest vary much more rapidly with position near the wall than far away from it. Further, there are dynamically important organized structures near the wall on a scale much smaller than the boundary layer thickness. Therefore, the minimum size of eddies that need to be resolved is smaller near the wall. In general, for the LES of inhomogeneous flows, the width of the filtering kernel delta must be considered to be a function of position. If a filtering operation with a nonuniform filter width is performed on the Navier-Stokes equations, one does not in general get the standard large eddy equations. The complication is caused by the fact that a filtering operation with a nonuniform filter width in general does not commute with the operation of differentiation. This is one of the issues that we have looked at in detail as it is basic to any attempt at applying LES to complex geometry flows. Our principal findings are summarized.

Description: An unified approach for solving both compressible and incompressible flows was investigated in this study. The difference in CFD code development between incompressible and compressible flows is due to the mathematical characteristics. However, if one can modify the continuity equation for incompressible flows by introducing pseudocompressibility, the governing equations for incompressible flows would have the same mathematical characters as compressible flows. The application of a compressible flow code to solve incompressible flows becomes feasible. Among numerical algorithms developed for compressible flows, the Centered Total Variation Diminishing (CTVD) schemes possess better mathematical properties to damp out the spurious oscillations while providing high-order accuracy for high speed flows. It leads us to believe that CTVD schemes can equally well solve incompressible flows. In this study, the governing equations for incompressible flows include the continuity equation and momentum equations. The continuity equation is modified by adding a time-derivative of the pressure term containing the artificial compressibility. The modified continuity equation together with the unsteady momentum equations forms a hyperbolic-parabolic type of time-dependent system of equations. The continuity equation is modified by adding a time-derivative of the pressure term containing the artificial compressibility. The modified continuity equation together with the unsteady momentum equations forms a hyperbolic-parabolic type of time-dependent system of equations. Thus, the CTVD schemes can be implemented. In addition, the boundary conditions including physical and numerical boundary conditions must be properly specified to obtain accurate solution. The CFD code for this research is currently in progress. Flow past a circular cylinder will be used for numerical experiments to determine the accuracy and efficiency of the code before applying this code to more specific applications.

Description: This report presents a method for doing load-flow analysis of a power system by using a decomposition approach. The power system for the Space Shuttle is used as a basis to build a model for the load-flow analysis. To test the decomposition method for doing load-flow analysis, simulations were performed on power systems of 16, 25, 34, 43, 52, 61, 70, and 79 nodes. Each of the power systems was divided into subsystems and simulated under steady-state conditions. The results from these tests have been found to be as accurate as tests performed using a standard serial simulator. The division of the power systems into different subsystems was done by assigning a processor to each area. There were 13 transputers available, therefore, up to 13 different subsystems could be simulated at the same time. This report has preliminary results for a load-flow analysis using a decomposition principal. The report shows that the decomposition algorithm for load-flow analysis is well suited for parallel processing and provides increases in the speed of execution.

Description: We describe a multigrid multiblock method for compressible turbulent flow simulations and present results obtained from calculations on a two-element airfoil. A vertex-based spatial discretization method and explicit multistage Runge-Kutta time-stepping are used. The slow convergence of a single grid method makes the multigrid method, which yields a speed factor of about 20, indispensable. The numerical predictions are in good agreement with experimental results. It is shown that the convergence of the multigrid process depends considerably on the ordering of the various loops. If the block loop is put inside the stage loop, the process converges more rapidly than if the block loop is situated outside the stage loop when a three-stage Runge-Kutta method is used. If a five-stage scheme is used, the process does not converge in the latter block ordering. Finally, the process based on the five-stage method is about 60 percent more efficient than with the three-stage method, if the block loop is inside the stage loop.

Description: Grid staggering is a well known remedy for the problem of velocity/pressure coupling in incompressible flow calculations. Numerous inconveniences occur, however, when staggered grids are implemented, particularly when a general-purpose code, capable of handling irregular three-dimensional domains, is sought. In several non-staggered grid numerical procedures proposed in the literature, the velocity/pressure coupling is achieved by either pressure or velocity (momentum) averaging. This approach is not convenient for simultaneous (block) solvers that are preferred when using multigrid methods. A new method is introduced in this paper that is based upon non-staggered grid formulation with a set of virtual cell face velocities used for pressure/velocity coupling. Instead of pressure or velocity averaging, a momentum balance at the cell face is used as a link between the momentum and mass balance constraints. The numerical stencil is limited to 9 nodes (in 2D) or 27 nodes (in 3D), both during the smoothing and inter-grid transfer, which is a convenient feature when a block point solver is applied. The results for a lid-driven cavity and a cube in a lid-driven cavity are presented and compared to staggered grid calculations using the same multigrid algorithm. The method is shown to be stable and produce a smooth (wiggle-free) pressure field.

Description: The study of a thin, incompressible Newtonian fluid layer trapped between two almost parallel, sliding surfaces has been actively pursued in the last decades. This subject includes lubrication applications such as slider bearings or the sealing of non-pressurized fluids with rubber rotary shaft seals. In the present work we analyze numerically the flow of lubricant fluid through a micro-gap of sealing devices. The first stage of this study is carried out assuming that a 'small-gap' parameter delta attains an extreme value in the Navier-Stokes equations. The precise meaning of small-gap is achieved by the particular limit delta = 0 which, within the bounds of the hypotheses, predicts transport of lubricant through the sealed area by centrifugal instabilities. Numerical results obtained with the penalty function approximation in the finite element method are presented. In particular, the influence of inflow and outflow boundary conditions, and their impact in the simulated flow, are discussed.

Description: For a number of years, NASA has relied primarily upon periodically updated versions of Rocketdyne's power balance model (PBM) to provide space shuttle main engine (SSME) steady-state performance prediction. A recent computational study indicated that PBM predictions do not satisfy fundamental energy conservation principles. More recently, SSME test results provided by the Technology Test Bed (TTB) program have indicated significant discrepancies between PBM flow and temperature predictions and TTB observations. Results of these investigations have diminished confidence in the predictions provided by PBM, and motivated the development of new computational tools for supporting SSME performance analysis. A multivariate least squares regression algorithm was developed and implemented during this effort in order to efficiently characterize TTB data. This procedure, called the 'gains model,' was used to approximate the variation of SSME performance parameters such as flow rate, pressure, temperature, speed, and assorted hardware characteristics in terms of six assumed independent influences. These six influences were engine power level, mixture ratio, fuel inlet pressure and temperature, and oxidizer inlet pressure and temperature. A BFGS optimization algorithm provided the base procedure for determining regression coefficients for both linear and full quadratic approximations of parameter variation. Statistical information relative to data deviation from regression derived relations was also computed. A new strategy for integrating test data with theoretical performance prediction was also investigated. The current integration procedure employed by PBM treats test data as pristine and adjusts hardware characteristics in a heuristic manner to achieve engine balance. Within PBM, this integration procedure is called 'data reduction.' By contrast, the new data integration procedure, termed 'reconciliation,' uses mathematical optimization techniques, and requires both measurement and balance uncertainty estimates. The reconciler attempts to select operational parameters that minimize the difference between theoretical prediction and observation. Selected values are further constrained to fall within measurement uncertainty limits and to satisfy fundamental physical relations (mass conservation, energy conservation, pressure drop relations, etc.) within uncertainty estimates for all SSME subsystems. The parameter selection problem described above is a traditional nonlinear programming problem. The reconciler employs a mixed penalty method to determine optimum values of SSME operating parameters associated with this problem formulation.

Description: The development of improved performance models for the Space Shuttle Main Engine (SSME) is an important, ongoing program at NASA MSFC. These models allow prediction of overall system performance, as well as analysis of run-time anomalies which might adversely affect engine performance or safety. Due to the complexity of the flow fields associated with the SSME, NASA has increasingly turned to Computational Fluid Dynamics (CFD) techniques as modeling tools. An important component of the SSME system is the fuel preburner, which consists of a cylindrical chamber with a plate containing 264 coaxial injector elements at one end. A fuel rich mixture of gaseous hydrogen and liquid oxygen is injected and combusted in the chamber. This process preheats the hydrogen fuel before it enters the main combustion chamber, powers the hydrogen turbo-pump, and provides a heat dump for nozzle cooling. Issues of interest include the temperature and pressure fields at the turbine inlet and the thermal compatibility between the preburner chamber and injector plate. Performance anomalies can occur due to incomplete combustion, blocked injector ports, etc. The performance model should include the capability to simulate the effects of these anomalies. The current approach to the numerical simulation of the SSME fuel preburner flow field is to use a global model based on the MSFC sponsored FNDS code. This code does not have the capabilities of modeling several aspects of the problem such as detailed modeling of the coaxial injectors. Therefore, an effort has been initiated to develop a detailed simulation of the preburner coaxial injectors and provide gas phase boundary conditions just downstream of the injector face as input to the FDNS code. This simulation should include three-dimensional geometric effects such as proximity of injectors to baffles and chamber walls and interaction between injectors. This report describes an investigation into the numerical simulation of GH2/LOX coaxial injectors. The following sections will discuss the physical aspects of injectors, the CFD code employed, and preliminary results of a simulation of a single coaxial injector for which experimental data is available. It is hoped that this work will lay the foundation for the development of a unique and useful tool to support the SSME program.

Description: As the workstation and personal computer become more popular than a centralized mainframe to perform thermal analysis, the methods for space vehicle thermal analysis will change. Already, many thermal analysis codes are now available for workstations, which were not in existence just five years ago. As these changes occur, some organizations will adopt the new codes and analysis techniques, while others will not. This might lead to misunderstandings between thermal shops in different organizations. If thermal analysts make an effort to understand the major differences between the new and old methods, a smoother transition to a more efficient and more versatile thermal analysis environment will be realized.

Description: Thermal loads on current and future aircraft are increasing and as a result are stressing the energy collection, control, and dissipation capabilities of current thermal management systems and technology. The thermal loads for hypersonic vehicles will be no exception. In fact, with their projected high heat loads and fluxes, hypersonic vehicles are a prime example of systems that will require thermal management systems (TMS) that have been optimized and integrated with the entire vehicle to the maximum extent possible during the initial design stages. This will not only be to meet operational requirements, but also to fulfill weight and performance constraints in order for the vehicle to takeoff and complete its mission successfully. To meet this challenge, the TMS can no longer be two or more entirely independent systems, nor can thermal management be an after thought in the design process, the typical pervasive approach in the past. Instead, a TMS that was integrated throughout the entire vehicle and subsequently optimized will be required. To accomplish this, a method that iteratively optimizes the TMS throughout the vehicle will not only be highly desirable, but advantageous in order to reduce the manhours normally required to conduct the necessary tradeoff studies and comparisons. A thermal management engineering computer code that is under development and being managed at Wright Laboratory, Wright-Patterson AFB, is discussed. The primary goal of the code is to aid in the development of a hypersonic vehicle TMS that has been optimized and integrated on a total vehicle basis.

Description: The multigrid properties of two data reconstruction methods used for achieving second-order spatial accuracy when solving the two-dimensional Euler equations are examined. The data reconstruction methods are used with an implicit upwind algorithm which uses linearized backward-Euler time-differencing. The solution of the resulting linear system is performed by an iterative procedure. In the present study only regular quadrilateral grids are considered, so a red-black Gauss-Seidel iteration is used. Although the Jacobian is approximated by first-order upwind extrapolation, two alternative data reconstruction techniques for the flux integral that yield higher-order spatial accuracy at steady state are examined. The first method, probably most popular for structured quadrilateral grids, is based on estimating the cell gradients using one-dimensional reconstruction along curvilinear coordinates. The second method is based on Green's theorem. Analysis and numerical results for the two dimensional Euler equations show that data reconstruction based on Green's theorem has superior multigrid properties as compared to the one-dimensional data reconstruction method.

Description: Many reacting flows in propulsion devices cannot be efficiently calculated by modern compressible flow CFD algorithms. Most low-speed reacting flow codes based on TEACH-type technologies are inefficient and lack robustness for complex flows. Tremendous progress has been made in high-speed compressible flow CFD in the past two decades; extending its application range to low-speed regimes is highly desirable. The objectives of this document is to present an efficient and robust algorithm for multi-phase chemically reacting flows at all speeds, with emphasis on low Mach number flows, and to calculate turbulent spray combustion flow in a gas turbine combustor.

Description: The Low Temperature Heat Pipe Flight Experiment (HEPP) is a fairly complicated thermal control experiment that was designed to evaluate the performance of two different low temperature ethane heat pipes and a low-temperature (182 K) phase change material. A total of 390 days of continuous operation with an axially grooved aluminum fixed conductance heat pipe and an axially grooved stainless steel heat pipe diode was demonstrated before the data acquisition system's batteries lost power. Each heat pipe had approximately 1 watt applied throughout this period. The HEPP was not able to cool below 188.6 K during the mission. As a result, the preprogrammed transport test sequence which initiates when the PCM temperature drops below 180 K was never exercised, and transport tests with both pipes and the diode reverse mode test could not be run in flight. Also, because the melt temperature of the n-heptane PCM is 182 K, its freeze/thaw behavior could not be tested. Post-flight thermal vacuum tests and thermal analyses have indicated that there was an apparent error in the original thermal analyses that led to this unfortunate result. Post-flight tests have demonstrated that the performance of both heat pipes and the PCM has not changed since being fabricated more than 14 years ago. A summary of HEPP's flight data and post-flight test results are presented.

Description: This experiment was designed to find a function of payload weight for altitude. The same rocket was launched a repeated number of times with the same engine and varying amounts of weight. After performing experimentation, it was calculated that the altitude in meters could be predicted with the equation A = (2.8(W exp 2)) - (70.6W + 310.3), with weight expressed in the unit ounces.

Description: Structural requirements, materials and, especially, processing are critical issues that will pace the introduction of new types of solid rocket motors. Designers must recognize and understand the drivers associated with each of the following considerations: (1) cost; (2) energy density; (3) long term storage with use on demand; (4) reliability; (5) safety of processing and handling; (6) operability; and (7) environmental acceptance.

Description: NASA supports a vigorous Earth-to-orbit (ETO) research and technology program as part of its Civil Space Technology Initiative. The purpose of this program is to provide an up-to-date technology base to support future space transportation needs for a new generation of lower cost, operationally efficient, long-lived and highly reliable ETO propulsion systems by enhancing the knowledge, understanding and design methodology applicable to advanced oxygen/hydrogen and oxygen/hydrocarbon ETO propulsion systems. Program areas of interest include analytical models, advanced component technology, instrumentation, and validation/verification testing. Organizationally, the program is divided between technology acquisition and technology verification as follows: (1) technology acquisition; and (2) technology verification.

Description: Lewis Research Center is developing broad-based new technologies for space chemical engines to satisfy long-term needs of ETO launch vehicles and other vehicles operating in and beyond Earth orbit. Specific objectives are focused on high performance LO2/LH2 engines providing moderate thrusts of 7,5-200 klb. This effort encompasses research related to design analysis and manufacturing processes needed to apply advanced materials to subcomponents, components, and subsystems of space-based systems and related ground-support equipment. High-performance space-based chemical engines face a number of technical challenges. Liquid hydrogen turbopump impellers are often so large that they cannot be machined from a single piece, yet high stress at the vane/shroud interface makes bonding extremely difficult. Tolerances on fillets are critical on large impellers. Advanced materials and fabricating techniques are needed to address these and other issues of interest. Turbopump bearings are needed which can provide reliable, long life operation at high speed and high load with low friction losses. Hydrostatic bearings provide good performance, but transients during pump starts and stops may be an issue because no pressurized fluid is available unless a separate bearing pressurization system is included. Durable materials and/or coatings are needed that can demonstrate low wear in the harsh LO2/LH2 environment. Advanced materials are also needed to improve the lifetime, reliability and performance of other propulsion system elements such as seals and chambers.

Description: Topics addressed are: (1) cryogenic tankage; (2) launch vehicle TPS/insulation; (3) durable passive thermal control devices and/or coatings; (4) development and characterization of processing methods to reduce anisotropy of material properties in Al-Li; (5) durable thermal protection system (TPS); (6) unpressurized Al-Li structures (interstages, thrust structures); (7) near net shape sections; (8) pressurized structures; (9) welding and joining; (10) micrometeoroid and debris hypervelocity shields; (11) state-of-the-art shell buckling structure optimizer program to serve as a rapid design tool; (12) test philosophy; (13) reduced load cycle time; (14) structural analysis methods; (15) optimization of structural criteria; and (16) develop an engineering approach to properly trade material and structural concepts selection, fabrication, facilities, and cost.

Description: The Advanced Solid Rocket Motor is a new design for the Space Shuttle Solid Rocket Booster. The new design will provide more thrust and more payload capability, as well as incorporating many design improvements in all facets of the design and manufacturing process. A 48-inch (diameter) test motor program is part of the ASRM development program. This program has multiple purposes for testing of propellent, insulation, nozzle characteristics, etc. An overview of the evolution of the 48-inch ASRM test motor ignition system which culminated with the implementation of a laser ignition system is presented. The laser system requirements, development, and operation configuration are reviewed in detail.

Description: This is a report on the continuation of experiments, which Dr. Srinivas Veeravalli and the present author started in 1991, to investigate the hypothesis of local isotropy in shear flows. This hypothesis, which states that at sufficiently high Reynolds numbers the small-scale structures of turbulent motions are independent of large-scale structures and mean deformations, has been used in theoretical studies of turbulence and computational methods like large-eddy simulation. The importance of Kolmogorov's ideas arises from the fact that they create a foundation for turbulence theory.

Description: A good knowledge of the turbulence structure, wall heat transfer, and friction in turbulent boundary layers (TBL) at high speeds is required for the design of hypersonic air breathing airplanes and reentry space vehicles. This work reports on recent progress in the modeling of high speed TBL flows. The specific research goal described here is the development of a second order closure model for zero pressure gradient TBL's for the range of Mach numbers up to hypersonic speeds with arbitrary wall cooling requirements.

Description: Separating turbulent boundary layers occur in many practical engineering applications. Nonetheless, the physics of separation/reattachment of flows is poorly understood. During the past decade, various turbulence models were proposed and their ability to successfully predict some types of flows was shown. However. prediction of separating/reattaching flows is still a formidable task for model developers. The present study is concerned with the process of separation from a smooth surface. Features of turbulent separating boundary layers that are relevant to modeling include the following: the occurrence of zero wall shear stress, which causes breakdown of the boundary layer approximation; the law of the wall not being satisfied in the mean back flow region; high turbulence levels in the separated region; a significant low-frequency motion in the separation bubble; and the turbulence structure of the separated shear layer being quite different from that of either the mixing layers or the boundary layers. These special characteristics of separating boundary layers make it difficult for simple turbulence models to correctly predict their behavior.

Description: This report describes two projects. Firstly, a Reynolds stress closure for near-wall turbulence is described. It was motivated by the simpler k-epsilon-(v-bar(exp 2)) model described in last year's annual research brief. Direct Numerical Simulation of three-dimensional channel flow shows a curious decrease of the turbulent kinetic energy. The second topic of this report is a model which reproduces this effect. That model is described and used to discuss the relevance of the three dimensional channel flow simulation to swept wing boundary layers.

Description: The objectives of this study are as follows: (1) to conduct a direct numerical simulation of turbulent backward facing step flow using inflow and outflow conditions; and (2) to provide data in the form of Reynolds stress budgets for Reynolds averaged modeling. The report presents the basic statistical data and comparisons with the concurrent experiments of Jovic and Driver and budgets of turbulent kinetic energy.

Description: Linear receptivity studies in parallel flows are aimed at understanding how external forcing couples to the natural unstable motions which a flow can support. The vibrating ribbon problem models the original Schubauer and Skramstad boundary layer experiment and represents the classic boundary layer receptivity problem. The process by which disturbances are initiated in convectively-unstable jets and shear layers has also received attention. Gaster was the first to handle the boundary layer analysis with the recognition that spatial modes, rather than temporal modes, were relevant when studying convectively-unstable flows that are driven by a time-harmonic source. The amplitude of the least stable spatial mode, far downstream of the source, is related to the source strength by a coupling coefficient. The determination of this coefficient is at the heart of this type of linear receptivity study. The first objective of the present study was to determine whether the various wave number derivative factors, appearing in the coupling coefficients for linear receptivity problems, could be reexpressed in a simpler form involving adjoint eigensolutions. Secondly, it was hoped that the general nature of this simplification could be shown; indeed, a rather elegant characterization of the receptivity properties of spatial instabilities does emerge. The analysis is quite distinct from the usual Fourier-inversion procedures, although a detailed knowledge of the spectrum of the Orr-Sommerfeld equation is still required. Since the cylinder wake analysis proved very useful in addressing control considerations, the final objective was to provide a foundation upon which boundary layer control theory may be developed.

Description: An accurate and efficient computational method is needed for three-dimensional incompressible viscous flows in engineering applications. On solving the turbulent shear flows directly or using the subgrid scale model, it is indispensable to resolve the small scale fluid motions as well as the large scale motions. From this point of view, the pseudo-spectral method is used so far as the computational method. However, the finite difference or the finite element methods are widely applied for computing the flow with practical importance since these methods are easily applied to the flows with complex geometric configurations. However, there exist several problems in applying the finite difference method to direct and large eddy simulations. Accuracy is one of most important problems. This point was already addressed by the present author on the direct simulations on the instability of the plane Poiseuille flow and also on the transition to turbulence. In order to obtain high efficiency, the multi-grid Poisson solver is combined with the higher-order, accurate finite difference method. The formulation method is also one of the most important problems in applying the finite difference method to the incompressible turbulent flows. The three-dimensional Navier-Stokes equations have been solved so far in the primitive variables formulation. One of the major difficulties of this method is the rigorous satisfaction of the equation of continuity. In general, the staggered grid is used for the satisfaction of the solenoidal condition for the velocity field at the wall boundary. However, the velocity field satisfies the equation of continuity automatically in the vorticity-vector potential formulation. From this point of view, the vorticity-vector potential method was extended to the generalized coordinate system. In the present article, we adopt the vorticity-vector potential formulation, the generalized coordinate system, and the 4th-order accurate difference method as the computational method. We present the computational method and apply the present method to computations of flows in a square cavity at large Reynolds number in order to investigate its effectiveness.

Description: The ultimate motivation of this work is to investigate the stability of two dimensional heated jets and its implications for aerodynamic sound generation from data obtained with direct numerical simulations (DNS). As pointed out in our last report, these flows undergo two types of instabilities, convective or absolute, depending on their temperature. We also described the limits of earlier experimental and theoretical studies and explained why a numerical investigation could give us new insight into the physics of these instabilities. The aeroacoustical interest of these flows was also underlined. In order to reach this goal, we first need to succeed in the DNS of heated jets. Our past efforts have been focused on this issue which encountered several difficulties. Our numerical difficulties are directly related to the physical problem we want to investigate since these absolutely or almost absolutely unstable flows are by definition very sensitive to the smallest disturbances and are very likely to reach nonlinear saturation through a numerical feedback mechanism. As a result, it is very difficult to compute a steady laminar solution using a spatial DNS. A steady state was reached only for strongly co-flowed jets, but these flows are almost equivalent to two independent mixing layers. Thus they are far from absolute instability and have much lower growth rates.

Description: When analyzing many turbulent flows, the effects of compressibility can be neglected. Even some relatively high-speed flows, such as boundary layers generated by a supersonic aircraft, produce turbulent statistics that are similar to those found for the incompressible case. There are other situations, however, in which the non-zero divergence of the turbulence leads to behavior that is fundamentally different from that found at constant density. Examples include flows created by internal combustion engines, hypersonic flight, and supersonic combustion. It is with instances such as these that this project is concerned. In particular, we are interested in the effects of compressibility on turbulence near a smooth solid constant temperature surface; our primary objective is an increased physical understanding that can be used to improve turbulence models of wall-bounded compressible flows. With this in mind, we have begun a direct numerical simulation (DNS) study of turbulence in a plane channel. Because all of the relevant spatial and temporal scales are to be resolved, the simulations require no subgrid scale parameterization. The DNS code developed by Buell to study compressible plane Couette flow was modified to solve the compressible Navier-Stokes equations in the plane channel. The channel was chosen over the Couette flow for two reasons: (1) to avoid using the very large streamwise domains needed to adequately capture the large Couette vortical structures; and (2) to make use of previous experience by considering the compressible version of a well established case and isolate finite Mach number effects by comparing to the incompressible channel.

Description: In this article, we make a few remarks on the role that attractors and inertial manifolds play in fluid mechanics problems. We then describe the role of incremental unknowns for approximating attractors and inertial manifolds when finite difference multigrid discretizations are used. The relation with direct numerical simulation and large eddy simulation is also mentioned.

Description: At the Space Photovoltaics Research and Technology (SPRAT) conference at NASA Lewis Research Center, a workshop session was held to discuss issues involved in using photovoltaic arrays ('solar cells') to convert laser power into electrical power for use as receiving elements for beamed power.

Description: A summary of the discussion at the workshop on solar electric propulsion (SEP) is presented. The purpose of ELITE SEP flight experiment is to demonstrate operation of solar array powered electric thrusters for raising spacecraft from parking orbit to higher altitudes, leading to definition of an operational SEP orbit transfer vehicles (OTV) for Air Force missions. Many of the problems or potential problems that may be associated with SEP are not well understood nor clearly identified, and system level phenomena such as interaction of thruster plume with the solar arrays cannot be simulated in a ground test. Therefore, an end-to-end system flight test is required to demonstrate solar electric propulsion.

Description: The Defense Research Agency (DRA) has been active in the photovoltaic field since the early 1960's, then as the Royal Aircraft Establishment (RAE). The early work was aimed at developing silicon cells, solar panels, and light-weight flexible arrays in support of the 'UK' and 'X' series of British scientific and technology satellites, for which the RAE was either the design authority or technical advisor. The X3 satellite - Prospero, launched in 1971 test flew 50 micron wrap-round silicon cells. The X4 satellite - Miranda, launched in 1974 test flew a deployable flexible silicon array which was developed at the DRA. During this period an extensive range of test equipment was developed which was maintained, modernized, and extended to date. Following a period of reduced activity in the late 1970's and early 1980's the current program evolved. The programs that have been undertaken since 1983 are briefly summarized. These range from various cell developments, new types of coverglasses, flight experiments, radiation testing, primary cell calibration, and environmental testing. The current photovoltaic program is mainly funded by the UK Ministry of Defence and by the Department of Trade and Industry through the British National Space Center (BNSC). The program is aimed at research and development, both internally and with industry, to meet the customer's technical objectives and requirements and to provide them with technical advice. The facilities are also being used on contract work for various national and international organizations.