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NASA NTRS1994

Wall pressure fluctuations in the reattachment region of a supersonic free shear layer

The primary aim of this research program was to investigate the mechanisms which cause the unsteady wall-pressure fluctuations in shock wave turbulent shear layer interactions. The secondary aim was to find means to reduce the magnitude of the fluctuating pressure loads by controlling the unsteady shock motion. The particular flow under study is the unsteady shock wave interaction formed in the reattachment zone of a separated supersonic flow. Similar flows are encountered in many practical situations, and they are associated with high levels of fluctuating wall pressure. The free shear layer is formed by the flow over a backward facing step, using an existing model, with the base pressure on the step adjusted so that there is no pressure discontinuity at the lip. The shear layer therefore develops in a zero pressure gradient. The primary advantage of this flow configuration is that the reattachment process can be studied in the absence of a separation shock. The mean flow data, and some preliminary hot-wire measurements of the mass-flux fluctuations were made by Baca and Settles, Baca, Williams and Bogdonoff, who showed that the shear layer became self-similar at about 17 delta(sub 0) downstream of the lip, and that it grew at a rate typical of the observed Mach number difference (about 1/3rd the incompressible growth rate). The turbulence measurements were later extended by Hayakawa, Smits and Bogdonoff under NASA Headquarters support.

Smits, Alexander J.↗
NASA NTRS1994

An analysis of supersonic flows with low-Reynolds number compressible two-equation turbulence models using LU finite volume implicit numerical techniques

A generalized flow solver using an implicit Lower-upper (LU) diagonal decomposition based numerical technique has been coupled with three low-Reynolds number kappa-epsilon models for analysis of problems with engineering applications. The feasibility of using the LU technique to obtain efficient solutions to supersonic problems using the kappa-epsilon model has been demonstrated. The flow solver is then used to explore limitations and convergence characteristics of several popular two equation turbulence models. Several changes to the LU solver have been made to improve the efficiency of turbulent flow predictions. In general, the low-Reynolds number kappa-epsilon models are easier to implement than the models with wall-functions, but require much finer near-wall grid to accurately resolve the physics. The three kappa-epsilon models use different approaches to characterize the near wall regions of the flow. Therefore, the limitations imposed by the near wall characteristics have been carefully resolved. The convergence characteristics of a particular model using a given numerical technique are also an important, but most often overlooked, aspect of turbulence model predictions. It is found that some convergence characteristics could be sacrificed for more accurate near-wall prediction. However, even this gain in accuracy is not sufficient to model the effects of an external pressure gradient imposed by a shock-wave/ boundary-layer interaction. Additional work on turbulence models, especially for compressibility, is required since the solutions obtained with base line turbulence are in only reasonable agreement with the experimental data for the viscous interaction problems.

Lee, J.↗
NASA NTRS1993

Numerical simulation of thermally induced near-surface flows over Martian terrain

Numerical simulations of the Martian near-surface wind regime using a mesoscale atmospheric model have shown that the thermally induced near-surface winds are analogous to terrestrial circulations. In particular, katabatic wind displays a striking similarity to flow observed over Antarctica. Introduction of solar radiation strongly perturbs the slope flows; anabatic conditions develop in middle to high latitudes during the daytime hours due to the solar heating of the sloping terrain. There appears to be a rapid transition from the katabatic to the anabatic flow regimes, emphasizing the primary importance of radiative exchanges at the surface in specifying the horizontal pressure gradient force.

Parish, T. R.↗
NASA NTRS1992

Departure solutions of the unsteady thin-layer and full Navier-Stokes equations solved using streamline curvature based iteration techniques

The development of a thorough understanding of the mechanisms for vortex eruptions from viscous layers, which are believed to be associated with phenomena such as dynamic stall onset and transition, is crucial if accurate models of such phenomena are to be formulated. The development of such models may, in turn, allow for the possibility that such effects could be accounted for during the design of various aerodynamic devices such as wings, helicopter rotors, and turbomachinery blading and thus lead to designs which are stall free or stall resistant and which have better stall-recovery properties. The present investigation is being conducted as part of an effort to develop analytical and numerical tools which can be used to help improve our understanding of the vortex-eruption mechanism at high Reynolds numbers. The addition of the normal-momentum equation to the classical unsteady boundary-layer equations is crucial according to recent asymptotic analyses of the vortex-eruption problem and is a key feature of the analyses being developed by the present authors. The purpose of this paper is as follows: to describe departure solution behavior observed when using unsteady, streamline-curvature based solution procedures in which nontrivial transverse pressure gradient effects are included; and to show that special treatment of the time-derivative of the normal velocity is needed to eliminate the ill-posed solution behavior, which is observed when small spatial and temporal step sizes are used.

Barnett, M.↗
NASA NTRS1994

Vortex tubes in turbulent flows: Identification, representation, reconstruction

In many cases the structure of a fluid flow is well-characterized by its vortices, especially for the purpose of visualization. In this paper we present a new algorithm for identifying vortices in complex flows. The algorithm produces a skeleton line along the center of a vortex by using a two-step predictor-corrector scheme. The vorticity vector field serves as the predictor and the pressure gradient (in the perpendicular plane) serves as the corrector. We describe an economical description of the vortex tube's cross-section: a 5-term truncated Fourier series is generally sufficient, and it compresses the representation of the flow by a factor of 4000 or more. We reconstruct the vortex tubes as generalized cylinders, providing a polygonal mesh suitable for display on a graphics workstation. We show how the reconstructed geometry of vortex tubes can be enhanced to help visualize helical motion in a static image.

Banks, David C.↗
NASA NTRS1993

Contributions of the low-latitude boundary layer to the finite width magnetotail convection model

The finite tail width model of magnetotail plasma sheet convection has been extended in order to characterize the steady-state convection process. The model assumes uniform plasma sources and accounts for both the duskward gradient/curvature drift and the earthward E x B drift of ions in a 2D magnetic geometry. A secondary source of plasma originating in the dawnside low-latitude boundary layer (LLBL) is added. Model results show that the LLBL may be a significant source of near-tail central plasma sheet plasma during periods of weak convection; a cross-tail pressure gradient from dawn to dusk is predicted in the near magnetotail.

Spence, Harlan E.↗
NASA NTRS1994

Computation and modeling of aero-thermal fields in turbine cascades and strongly curved ducts

Advanced turbulence models are crucial for accurate prediction of rocket engine flows, due to existence of very large extra strain rates, such as strong streamline curvature. Numerical simulation of the turbulent flow in a strongly curved turn-around duct (TAD) has been carried out with a Reynolds stress model (RSM), an algebraic Reynolds stress model (ARSM) and a kappa-epsilon model. the RSM model and the ARSM model are found to capture the turbulence damping due to the convex curvature, but underpredict the turbulence enhancement caused by the concave curvature. To capture the concave curvature effects, it is necessary to modify the epsilon-equation. The modification of episilon-equation suggested by Launder, et.al, provides the correct trend, but over-corrects the curvature effects. A comparative study of two modes of transition in gas turbine, the by-pass transition and the separation-induced transition, has been carried out with several low-Reynolds-number (LRN) kappa-epsilon models. Effects of blade surface pressure gradient, freestream turbulence and Reynolds number on the blade boundary layer development, and particularly the inception of transition are examined in detail. The present study indicates that the turbine blade transition, in the presence of high freestream turbulence, is predicted well with LRN kappa-epsilon models employed.

Luo, J.↗
NASA NTRS1994

A New K-epsilon Eddy Viscosity Model for High Reynolds Number Turbulent Flows: Model Development and Validation

A new k-epsilon eddy viscosity model, which consists of a new model dissipation rate equation and a new realizable eddy viscosity formulation, is proposed. The new model dissipation rate equation is based on the dynamic equation of the mean-square vorticity fluctuation at large turbulent Reynolds number. The new eddy viscosity formulation is based on the realizability constraints: the positivity of normal Reynolds stresses and Schwarz' inequality for turbulent shear stresses. We find that the present model with a set of unified model coefficients can perform well for a variety of flows. The flows that are examined include: (1) rotating homogeneous shear flows; (2) boundary-free shear flows including a mixing layer, planar and round jets; (3) a channel flow, and flat plate boundary layers with and without a pressure gradient; and (4) backward facing step separated flows. The model predictions are compared with available experimental data. The results from the standard k-epsilon eddy viscosity model are also included for comparison. It is shown that the present model is a significant improvement over the standard k-epsilon eddy viscosity model.

Shih, T.-H.↗
NASA NTRS1994

Computation of turbulent boundary layers employing the defect wall-function method

In order to decrease overall computational time requirements of spatially-marching parabolized Navier-Stokes finite-difference computer code when applied to turbulent fluid flow, a wall-function methodology, originally proposed by R. Barnwell, was implemented. This numerical effort increases computational speed and calculates reasonably accurate wall shear stress spatial distributions and boundary-layer profiles. Since the wall shear stress is analytically determined from the wall-function model, the computational grid near the wall is not required to spatially resolve the laminar-viscous sublayer. Consequently, a substantially increased computational integration step size is achieved resulting in a considerable decrease in net computational time. This wall-function technique is demonstrated for adiabatic flat plate test cases from Mach 2 to Mach 8. These test cases are analytically verified employing: (1) Eckert reference method solutions, (2) experimental turbulent boundary-layer data of Mabey, and (3) finite-difference computational code solutions with fully resolved laminar-viscous sublayers. Additionally, results have been obtained for two pressure-gradient cases: (1) an adiabatic expansion corner and (2) an adiabatic compression corner.

Brown, Douglas L.↗
NASA NTRS1994

Stability of separating subsonic boundary layers

The primary and subharmonic instabilities of separating compressible subsonic two-dimensional boundary layers in the presence of a two-dimensional roughness element on a flat plate are investigated. The roughness elements considered are humps and forward- and backward-facing steps. The use of cooling and suction to control these instabilities is studied. The similarities and differences between the instability characteristics of separating boundary layers and those of the boundary layer over a flat plate with a zero pressure gradient are pointed out and discussed. The theoretical results agree qualitatively and quantitatively with the experimental data of Dovgal and Kozlov. Cooling and suction decrease the growth rates of primary and subharmonic waves in the attached-flow regions but increase them in the separated-flow regions.

Masad, Jamal A.↗
NASA NTRS1994

A spectrally accurate boundary-layer code for infinite swept wings

This report documents the development, validation, and application of a spectrally accurate boundary-layer code, WINGBL2, which has been designed specifically for use in stability analyses of swept-wing configurations. Currently, we consider only the quasi-three-dimensional case of an infinitely long wing of constant cross section. The effects of streamwise curvature, streamwise pressure gradient, and wall suction and/or blowing are taken into account in the governing equations and boundary conditions. The boundary-layer equations are formulated both for the attachment-line flow and for the evolving boundary layer. The boundary-layer equations are solved by marching in the direction perpendicular to the leading edge, for which high-order (up to fifth) backward differencing techniques are used. In the wall-normal direction, a spectral collocation method, based upon Chebyshev polynomial approximations, is exploited. The accuracy, efficiency, and user-friendliness of WINGBL2 make it well suited for applications to linear stability theory, parabolized stability equation methodology, direct numerical simulation, and large-eddy simulation. The method is validated against existing schemes for three test cases, including incompressible swept Hiemenz flow and Mach 2.4 flow over an airfoil swept at 70 deg to the free stream.

Pruett, C. David↗
NASA NTRS1993

An augmented Young-Laplace model of an evaporating meniscus in a micro-channel with high heat flux

High flux evaporations from a steady meniscus formed in a 2 micron channel is modeled using the augmented Young-Laplace equation. The heat flux is found to be a function of the long range van der Waals dispersion force which represents interfacial conditions between heptane and various substrates. Heat fluxes of (1.3-1.6) x 10(exp 6) W/m(exp 2) based on the width of the channel are obtained for heptane completely wetting the substrate at 100 C. Small channels are used to obtain these large fluxes. Even though the real contact angle is 0 deg, the apparent contact angle is found to vary between 24.8 deg and 25.6 deg. The apparent contact angle, which represents viscous losses near the contact line, has a large effect on the heat flow rate because of its effect on capillary suction and the area of the meniscus. The interfacial heat flux is modeled using kinetic theory for the evaporation rate. The superheated state depends on the temperature and the pressure of the liquid phase. The liquid pressure differs from the pressure of the vapor phase due to capillarity and long range van der Waals dispersion forces which are relevant in the ultra think film formed at the leading edge of the meniscus. Important pressure gradients in the thin film cause a substantial apparent contact angle for a complete wetting system. The temperature of the liquid is related to the evaporation rate and to the substrate temperature through the steady heat conduction equation. Conduction in the liquid phase is calculated using finite element analysis except in the vicinity of the thin film. A lubrication theory solution for the thin film is combined with the finite element analysis by the method of matched asymptotic expansions.

Wayner, P. C., Jr.↗
NASA NTRS1994

Simulations of bypass transition for spatially evolving disturbances

The spatial evolution of disturbances in plane Poiseuille flow and zero pressure gradient boundary layer flow is considered. For disturbances governed by the linearized equations, potential for significant transient growth of the amplitude is demonstrated. The maximum amplification occurs for disturbances with zero or near zero frequencies. Spatial numerical simulations of the transition scenario involving a pair of oblique waves has been conducted for both flows. A fully spectral solver using a simple but efficient fringe region technique allowed the flows to be computed with high resolution into the fully turbulent domain. A modal decomposition of the simulation results indicates that non-linear excitation of the transient growth is responsible for the rapid emergence of low-frequency structures. Physically, this corresponds to streaky flow structures, as seen from the results of a numerical amplitude expansion. Thus, this spatial transition scenario has been found to be similar to the corresponding temporal one. In the boundary layer simulations the streaks are seen to break down from what appears to be a secondary instability.

Lundbladh, A.↗
NASA NTRS1993

A Generalized Eulerian-Lagrangian Analysis, with Application to Liquid Flows with Vapor Bubbles

Under a NASA MSFC SBIR Phase 2 effort an analysis has been developed for liquid flows with vapor bubbles such as those in liquid rocket engine components. The analysis is based on a combined Eulerian-Lagrangian technique, in which Eulerian conservation equations are solved for the liquid phase, while Lagrangian equations of motion are integrated in computational coordinates for the vapor phase. The novel aspect of the Lagrangian analysis developed under this effort is that it combines features of the so-called particle distribution approach with those of the so-called particle trajectory approach and can, in fact, be considered as a generalization of both of those traditional methods. The result of this generalization is a reduction in CPU time and memory requirements. Particle time step (stability) limitations have been eliminated by semi-implicit integration of the particle equations of motion (and, for certain applications, the particle temperature equation), although practical limitations remain in effect for reasons of accuracy. The analysis has been applied to the simulation of cavitating flow through a single-bladed section of a labyrinth seal. Models for the simulation of bubble formation and growth have been included, as well as models for bubble drag and heat transfer. The results indicate that bubble formation is more or less 'explosive'. for a given flow field, the number density of bubble nucleation sites is very sensitive to the vapor properties and the surface tension. The bubble motion, on the other hand, is much less sensitive to the properties, but is affected strongly by the local pressure gradients in the flow field. In situations where either the material properties or the flow field are not known with sufficient accuracy, parametric studies can be carried out rapidly to assess the effect of the important variables. Future work will include application of the analysis to cavitation in inducer flow fields.

Dejong, Frederik J.↗
NASA NTRS1995

Apparatus for consolidating a pre-impregnated, filament-reinforced polymeric prepreg material

An apparatus and method were developed for providing a uniform, consolidated, unidirectional, continuous, fiber-reinforced polymeric material. The apparatus comprises a supply means, a forming means, a shaping means, and a take-up means. The forming means further comprises a pre-melting chamber and a stationary bar assembly. The shaping means is a loaded cooled nip-roller apparatus. Forming takes place by heating a polymeric prepreg material to a temperature where the polymer becomes viscous and applying pressure gradients at separate locations along the prepreg material. Upon exiting the forming means, the polymeric prepreg material is malleable, consolidated, and flattened. Shaping takes place by passing the malleable, consolidated, flattened prepreg material through a shaped, matched groove in a loaded, cooled nip-roller apparatus to provide the final solid product.

Sandusky, Donald A.↗
NASA NTRS1995

On the nonlinear stability of the unsteady, viscous flow of an incompressible fluid in a curved pipe

The stability of the flow of an incompressible, viscous fluid through a pipe of circular cross-section curved about a central axis is investigated in a weakly nonlinear regime. A sinusoidal pressure gradient with zero mean is imposed, acting along the pipe. A WKBJ perturbation solution is constructed, taking into account the need for an inner solution in the vicinity of the outer bend, which is obtained by identifying the saddle point of the Taylor number in the complex plane of the cross-sectional angle co-ordinate. The equation governing the nonlinear evolution of the leading order vortex amplitude is thus determined. The stability analysis of this flow to periodic disturbances leads to a partial differential system dependent on three variables, and since the differential operators in this system are periodic in time, Floquet theory may be applied to reduce this system to a coupled infinite system of ordinary differential equations, together with homogeneous uncoupled boundary conditions. The eigenvalues of this system are calculated numerically to predict a critical Taylor number consistent with the analysis of Papageorgiou. A discussion of how nonlinear effects alter the linear stability analysis is also given, and the nature of the instability determined.

Shortis, Trudi A.↗
NASA NTRS1995

Turbulance boundary conditions for shear flow analysis, using the DTNS flow solver

The effects of different turbulence boundary conditions were examined for two classical flows: a turbulent plane free shear layer and a flat plate turbulent boundary layer with zero pressure gradient. The flow solver used was DTNS, an incompressible Reynolds averaged Navier-Stokes solver with k-epsilon turbulence modeling, developed at the U.S. Navy David Taylor Research Center. Six different combinations of turbulence boundary conditions at the inflow boundary were investigated: In case 1, 'exact' k and epsilon profiles were used; in case 2, the 'exact' k profile was used, and epsilon was extrapolated upstream; in case 3, both k and epsilon were extrapolated; in case 4, the turbulence intensity (I) was 1 percent, and the turbulent viscosity (mu(sub t)) was equal to the laminar viscosity; in case 5, the 'exact' k profile was used and mu(sub t) was equal to the laminar viscosity; in case 6, the I was 1 percent, and epsilon was extrapolated. Comparisons were made with experimental data, direct numerical simulation results, or theoretical predictions as applicable. Results obtained with DTNS showed that turbulence boundary conditions can have significant impacts on the solutions, especially for the free shear layer.

Mizukami, M.↗
NASA NTRS1995

Control of unsteady separated flow associated with the dynamic stall of airfoils

An effort to understand and control the unsteady separated flow associated with the dynamic stall of airfoils was funded for three years through the NASA cooperative agreement program. As part of this effort a substantial data base was compiled detailing the effects various parameters have on the development of the dynamic stall flow field. Parameters studied include Mach number, pitch rate, and pitch history, as well as Reynolds number (through two different model chord lengths) and the condition of the boundary layer at the leading edge of the airfoil (through application of surface roughness). It was found for free stream Mach numbers as low as 0.4 that a region of supersonic flow forms on the leading edge of the suction surface of the airfoil at moderate angles of attack. The shocks which form in this supersonic region induce boundary-layer separation and advance the dynamic stall process. Under such conditions a supercritical airfoil profile is called for to produce a flow field having a weaker leading-edge pressure gradient and no leading-edge shocks. An airfoil having an adaptive-geometry, or dynamically deformable leading edge (DDLE), is under development as a unique active flow-control device. The DDLE, formed of carbon-fiber composite and fiberglass, can be flexed between a NACA 0012 profile and a supercritical profile in a controllable fashion while the airfoil is executing an angle-of-attack pitch-up maneuver. The dynamic stall data were recorded using point diffraction interferometry (PDI), a noninvasive measurement technique. A new high-speed cinematography system was developed for recording interferometric images. The system is capable of phase-locking with the pitching airfoil motion for real-time documentation of the development of the dynamic stall flow field. Computer-aided image analysis algorithms were developed for fast and accurate reduction of the images, improving interpretation of the results.

Wilder, M. C.↗