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All sourcesNASA NTRSDOE OSTI
NASA NTRS2003

Real-Gas Effects on Binary Mixing Layers

This paper presents a computational study of real-gas effects on the mean flow and temporal stability of heptane/nitrogen and oxygen/hydrogen mixing layers at supercritical pressures. These layers consist of two counterflowing free streams of different composition, temperature, and density. As in related prior studies reported in NASA Tech Briefs, the governing conservation equations were the Navier-Stokes equations of compressible flow plus equations for the conservation of total energy and of chemical- species masses. In these equations, the expressions for heat fluxes and chemical-species mass fluxes were derived from fluctuation-dissipation theory and incorporate Soret and Dufour effects. Similarity equations for the streamwise velocity, temperature, and mass fractions were derived as approximations to the governing equations. Similarity profiles showed important real-gas, non-ideal-mixture effects, particularly for temperature, in departing from the error-function profile, which is the similarity solution for incompressible flow. The temperature behavior was attributed to real-gas thermodynamics and variations in Schmidt and Prandtl numbers. Temporal linear inviscid stability analyses were performed using the similarity and error-function profiles as the mean flow. For the similarity profiles, the growth rates were found to be larger and the wavelengths of highest instability shorter, relative to those of the errorfunction profiles and to those obtained from incompressible-flow stability analysis. The range of unstable wavelengths was found to be larger for the similarity profiles than for the error-function profiles

Okong'o, Nora↗
NASA NTRS1988

Investigation of supersonic chemically reacting and radiating channel flow

The 2-D time-dependent Navier-Stokes equations are used to investigate supersonic flows undergoing finite rate chemical reaction and radiation interaction for a hydrogen-air system. The explicit multistage finite volume technique of Jameson is used to advance the governing equations in time until convergence is achieved. The chemistry source term in the species equation is treated implicitly to alleviate the stiffness associated with fast reactions. The multidimensional radiative transfer equations for a nongray model are provided for a general configuration and then reduced for a planar geometry. Both pseudo-gray and nongray models are used to represent the absorption-emission characteristics of the participating species. The supersonic inviscid and viscous, nonreacting flows are solved by employing the finite volume technique of Jameson and the unsplit finite difference scheme of MacCormack. The specified problem considered is of the flow in a channel with a 10 deg compression-expansion ramp. The calculated results are compared with those of an upwind scheme. The problem of chemically reacting and radiating flows are solved for the flow of premixed hydrogen-air through a channel with parallel boundaries, and a channel with a compression corner. Results obtained for specific conditions indicate that the radiative interaction can have a significant influence on the entire flow field.

Mani, Mortaza↗
NASA NTRS1998

Comparison of MPEG digital video with super VHS tape for diagnostic echocardiographic readings

BACKGROUND: Digital recording of echocardiographic studies is on the clinical horizon. However, full digital capture of complete echocardiographic studies in traditional video format is impractical, given current storage capacity and network bandwidth. To overcome these constraints, we evaluated the diagnostic image quality of digital video by using MPEG (Motion Picture Experts Group) compression. METHODS AND RESULTS: Fifty-eight complete, consecutive studies were recorded simultaneously with the use of MPEG-1 and sVHS videotape. Each matched MPEG and sVHS study pair was reviewed by two from a total of six readers, and findings were recorded with the use of a detailed, computerized reporting tool. Intrareader and interreader discrepancies were characterized as major or minor and analyzed in total and for specific subgroups of findings (left and right ventricular parameters, valvular insufficiency, and left ventricular regional wall motion). Intrareader discrepancies were reviewed by a consensus panel for agreement with either MPEG or sVHS findings. There was an exact concordance between MPEG and sVHS readings in 83% of findings. The majority of discrepancies were minor, with major discrepancies in only 2.7% of findings. There was no difference in the rate of consensus panel agreement with MPEG or sVHS for instances of intrareader discrepancy, either in total or for any subgroup of findings. Interreader discrepancy rates were nearly identical for both MPEG and sVHS. CONCLUSIONS: MPEG-1 digital video is equivalent to sVHS videotape for diagnostic echocardiography. MPEG increases the range of practical options for digital echocardiography and offers, for the first time, the advantages of digital recording in a familiar video format.

Non-NASA Center↗
NASA NTRS2010

Hybrid Reynolds-Averaged/Large-Eddy Simulations of a Coaxial Supersonic Free-Jet Experiment

Reynolds-averaged and hybrid Reynolds-averaged/large-eddy simulations have been applied to a supersonic coaxial jet flow experiment. The experiment was designed to study compressible mixing flow phenomenon under conditions that are representative of those encountered in scramjet combustors. The experiment utilized either helium or argon as the inner jet nozzle fluid, and the outer jet nozzle fluid consisted of laboratory air. The inner and outer nozzles were designed and operated to produce nearly pressure-matched Mach 1.8 flow conditions at the jet exit. The purpose of the computational effort was to assess the state-of-the-art for each modeling approach, and to use the hybrid Reynolds-averaged/large-eddy simulations to gather insight into the deficiencies of the Reynolds-averaged closure models. The Reynolds-averaged simulations displayed a strong sensitivity to choice of turbulent Schmidt number. The initial value chosen for this parameter resulted in an over-prediction of the mixing layer spreading rate for the helium case, but the opposite trend was observed when argon was used as the injectant. A larger turbulent Schmidt number greatly improved the comparison of the results with measurements for the helium simulations, but variations in the Schmidt number did not improve the argon comparisons. The hybrid Reynolds-averaged/large-eddy simulations also over-predicted the mixing layer spreading rate for the helium case, while under-predicting the rate of mixing when argon was used as the injectant. The primary reason conjectured for the discrepancy between the hybrid simulation results and the measurements centered around issues related to the transition from a Reynolds-averaged state to one with resolved turbulent content. Improvements to the inflow conditions were suggested as a remedy to this dilemma. Second-order turbulence statistics were also compared to their modeled Reynolds-averaged counterparts to evaluate the effectiveness of common turbulence closure assumptions.

Baurle, Robert A.↗
NASA NTRS2018

Instability and Target Design in a Z-Pinch Driven Pulsed Fission / Fusion Engine

Advanced forms of propulsion are required to drastically improve upon the limits of existing technology and enable deep space exploration. Nuclear reactors, both fission and fusion, have great potential as systems with high energy density for spacecraft propulsion. There are a variety of nuclear propulsion concepts that have been proposed over the last several decades. Some of these rely on the confinement of plasmas by both magnetic and inertial means. When discussing the plasma confinement one must consider the stability of the system. The conditions of the plasma dictate the burn rate of the nuclear fuel; therefore, the plasma must maintain a minimum set of conditions in order to achieve an adequate burn. Instabilities limit plasma confinement through growing fluctuations in density and pressure. This results in turbulent mixing and loss of confinement. Thus it is desirable to find ways of managing the impact of instabilities that arise in order for a sufficient burn of the fuel such that surplus energy can be converted into a propulsive force. Note that the same instabilities plague the confinement of plasmas for terrestrial power generation. Over the last several years there has been research relating to the development of a Pulsed Fission-Fusion Engine (PuFF) conducted by the authors and others at their respective institutions. The propulsion system concept centers on the use of a z-pinch to compress a plasma in order to induce nuclear reactions. The plasma along with the additional energy released by the fission and fusion processes is expanded with a magnetic nozzle to produce thrust. The concept, if developed, is expected to have an improvement in specific impulse of several orders of magnitude in comparison with chemical propulsion systems. The z-pinch has been explored in the past as a method to confine a plasma via magnetic confinement fusion (MCF) for power generation. It suffers; however, from instabilities that so far have prevented break even conditions.

Taylor, Brian↗
NASA NTRS1950

Investigation of Effects of Inlet-air Velocity Distortion on Performance of Turbojet Engine

To determine effect of nonuniform inlet-air velocities, a full scale, axial-flow turbojet engine was investigated in Lewis altitude wind tunnel at altitudes from 20,000 to 50,000 feet, 0.21 flight Mach number and corrected engine speeds from 77.3 percent of rated speed to rated speed. Total-pressure variations as large as 103 pounds per square foot in radial direction and 90 pounds per square foot in circumferential direction at 30,000 feet were obtained. With the distortions investigated, net thrust varied between 0.95 and 1.03 of the thrust with uniform inlet-air distribution. Similarly the ratio of specific fuel consumption varied from 1.00 to 1.04. Within the arrange of this investigation the effects of nonuniform inlet velocity were not serious for the engine investigated.

AIR INLETS↗
NASA NTRS1987

Experiments on thermoacoustic convection heat transfer in gravity and zero-gravity environments

The results of an experimental study of thermoacoustic convection (TAC) heat transfer in gravity and zero-gravity environments are presented. The experimental apparatus consisted of a cylinder containing air as the compressible fluid. The enclosed air was heated electrically at the top surface which consisted of a thin high-resistance steel foil connected to a power source. Thermocouples were used to measure the transient temperature of the air on the axis of the cylinder and the heated surface in the both zero-gravity and gravity environments. The zero-gravity tests were performed in the Zero-Gravity Drop Tower Facility of NASA-Lewis Research Center. The experimental results were corrected for the error due to radiation absorption by the thermocouples. A conduction-only numerical heat transfer model was developed to compute the transient air temperature in the cylindrical geometry. The results were compared to the experimental data to determine the significance of the thermoacoustic convection heat transfer mechanism. It is observed that the rate of heat transfer to the air measured during the experiments is consistently higher than that obtained by the conduction-only solution indicating a significant presence of the TAC heat transfer. Further experiments are planned to measure directly (1) the radiative heat transfer contribution to the rise in the air temperature, and (2) the air pressure oscillations within the cylinder that are responsible for the convective heat transfer mode.

Parang, Masood↗
NASA NTRS1993

DCT quantization matrices visually optimized for individual images

This presentation describes how a vision model incorporating contrast sensitivity, contrast masking, and light adaptation is used to design visually optimal quantization matrices for Discrete Cosine Transform image compression. The Discrete Cosine Transform (DCT) underlies several image compression standards (JPEG, MPEG, H.261). The DCT is applied to 8x8 pixel blocks, and the resulting coefficients are quantized by division and rounding. The 8x8 'quantization matrix' of divisors determines the visual quality of the reconstructed image; the design of this matrix is left to the user. Since each DCT coefficient corresponds to a particular spatial frequency in a particular image region, each quantization error consists of a local increment or decrement in a particular frequency. After adjustments for contrast sensitivity, local light adaptation, and local contrast masking, this coefficient error can be converted to a just-noticeable-difference (jnd). The jnd's for different frequencies and image blocks can be pooled to yield a global perceptual error metric. With this metric, we can compute for each image the quantization matrix that minimizes the bit-rate for a given perceptual error, or perceptual error for a given bit-rate. Implementation of this system demonstrates its advantages over existing techniques. A unique feature of this scheme is that the quantization matrix is optimized for each individual image. This is compatible with the JPEG standard, which requires transmission of the quantization matrix.

Watson, Andrew B.↗
NASA NTRS2004

Microgravity Spray Cooling Research for High Powered Laser Applications

An extremely powerful laser is being developed at Goddard Space Flight Center for use on a satellite. This laser has several potential applications. One application is to use it for upper atmosphere weather research. In this case, the laser would reflect off aerosols in the upper atmosphere and bounce back to the satellite, where the aerosol velocities could be calculated and thus the upper atmosphere weather patterns could be monitored. A second application would be for the US. Air Force, which wants to use the laser strategically as a weapon for satellite defense. The Air Force fears that in the coming years as more and more nations gain limited space capabilities that American satellites may become targets, and the laser could protect the satellites. Regardless of the ultimate application, however, a critical step along the way to putting the laser in space is finding a way to efficiently cool it. While operating the laser becomes very hot and must be cooled to prevent overheating. On earth, this is accomplished by simply running cool tap water over the laser to keep it cool. But on a satellite, this is too inefficient. This would require too much water mass to be practical. Instead, we are investigating spray cooling as a means to cool the laser in microgravity. Spray cooling requires much less volume of fluid, and thus could be suitable for use on a satellite. We have inherited a 2.2 second Drop Tower rig to conduct our research with. In our experiments, water is pressurized with a compressed air tank and sprayed through a nozzle onto our test plate. We can vary the pressure applied to the water and the temperature of the plate before an experiment trial. The whole process takes place in simulated microgravity in the 2.2 second Drop Tower, and a high speed video camera records the spray as it hits the plate. We have made much progress in the past few weeks on these experiments. The rig originally did not have the capability to heat the test plate, but I did some heat transfer calculations and picked out a heater to order for the rig. I learned QBasic programming language to change the operating code for our drops, allowing us to rapidly cycle the spray nozzle open and closed to study the effects. We have derived an equation for flow rate vs. pressure for our experiment. We have recorded several videos of drops at different pressures, some with heated test plate and some without, and have noticed substantial differences in the liquid behavior. I have also changed the computer program to write a file with temperature vs. time profiles for the test plate, and once the necessary thermocouple comes in (it was ordered last week), we will have temperature profiles to accompany the videos. Once we have these temperature profiles to go with the videos, we will be able to see how the temperature is affected by the spray at different pressures, and how the spray changes its behavior once as the plate changes from hot to cool. With quantitative temperature data, we can then mathematically model the heat transfer from the plate to the cooling spray. Finally, we can look at the differences between trials in microgravity and those in normal earth gravity.

Zivich, Chad P.↗
NASA NTRS1960

Measurements of Skin Friction of the Compressible Turbulent Boundary Layer on a Cone with Foreign Gas Injection

Measurements of average skin friction of the turbulent boundary layer have been made on a 15deg total included angle cone with foreign gas injection. Measurements of total skin-friction drag were obtained at free-stream Mach numbers of 0.3, 0.7, 3.5, and 4.7 and within a Reynolds number range from 0.9 x 10(exp 6) to 5.9 x 10(exp 6) with injection of helium, air, and Freon-12 (CCl2F2) through the porous wall. Substantial reductions in skin friction are realized with gas injection within the range of Mach numbers of this test. The relative reduction in skin friction is in accordance with theory-that is, the light gases are most effective when compared on a mass flow basis. There is a marked effect of Mach number on the reduction of average skin friction; this effect is not shown by the available theories. Limited transition location measurements indicate that the boundary layer does not fully trip with gas injection but that the transition point approaches a forward limit with increasing injection. The variation of the skin-friction coefficient, for the lower injection rates with natural transition, is dependent on the flow Reynolds number and type of injected gas; and at the high injection rates the skin friction is in fair agreement with the turbulent boundary layer results.

Pappas, Constantine C.↗
NASA NTRS2004

NASA Tech Briefs, December 2004

opics include: High-Rate Digital Receiver Board; Signal Design for Improved Ranging Among Multiple Transceivers; Automated Analysis, Classification, and Display of Waveforms; Fast-Acquisition/Weak-Signal-Tracking GPS Receiver for HEO; Format for Interchange and Display of 3D Terrain Data; Program Analyzes Radar Altimeter Data; Indoor Navigation using Direction Sensor and Beacons; Software Assists in Responding to Anomalous Conditions; Software for Autonomous Spacecraft Maneuvers; WinPlot; Software for Automated Testing of Mission-Control Displays; Nanocarpets for Trapping Microscopic Particles; Precious-Metal Salt Coatings for Detecting Hydrazines; Amplifying Electrochemical Indicators; Better End-Cap Processing for Oxidation-Resistant Polyimides; Carbon-Fiber Brush Heat Exchangers; Solar-Powered Airplane with Cameras and WLAN; A Resonator for Low-Threshold Frequency Conversion; Masked Proportional Routing; Algorithm Determines Wind Speed and Direction from Venturi-Sensor Data; Feature-Identification and Data-Compression Software; Alternative Attitude Commanding and Control for Precise Spacecraft Landing; Inspecting Friction Stir Welding using Electromagnetic Probes; and Helicity in Supercritical O2/H2 and C7H16/N2 Mixing Layers.

Source record↗
NASA NTRS1986

Upwind relaxation algorithms for Euler/Navier-Stokes equations

A description of and results from a solution algorithm for the compressible Navier-Stokes equations are presented. The main features of the algorithm are second or third order accurate upwind discretization of the convection and pressure derivatives and a relaxation scheme for the unfactored implicit backward Euler time method, implemented in a finite-volume formulation. Upwind methods were successfully used to obtain solutions to the Euler equations for flows with strong shock waves. The particular upwind method being used is based on the flux vector splitting technique developed by Van Leer and both second and third order accurate discretizations were developed. Currently, the most widely used implicit solution technique for the Navier-Stokes equations use approximate factorization (AF) methods to treat multidimensional problems. The time integration scheme being used in the present algorithm corresponds to a line Gauss-Seidel relaxation method. This method produces good convergence rates for steady-state flows, and most of the algorithm was vectorized on the NASA Langley VPS 32 computer. The Navier-Stokes algorithm was tested for several two-dimensional flow problems. Solutions for the problems gave excellent results. The presented effort is directed toward the extension of the scheme to the full three-dimensional Navier-Stokes equations.

Thomas, J. L.↗
NASA NTRS1993

Visual optimization of DCT quantization matrices for individual images

Many image compression standards (JPEG, MPEG, H.261) are based on the Discrete Cosine Transform (DCT). However, these standards do not specify the actual DCT quantization matrix. We have previously provided mathematical formulae to compute a perceptually lossless quantization matrix. Here I show how to compute a matrix that is optimized for a particular image. The method treats each DCT coefficient as an approximation to the local response of a visual 'channel'. For a given quantization matrix, the DCT quantization errors are adjusted by contrast sensitivity, light adaptation, and contrast masking, and are pooled non-linearly over the blocks of the image. This yields an 8x8 'perceptual error matrix'. A second non-linear pooling over the perceptual error matrix yields total perceptual error. With this model we may estimate the quantization matrix for a particular image that yields minimum bit rate for a given total perceptual error, or minimum perceptual error for a given bit rate. Custom matrices for a number of images show clear improvement over image-independent matrices. Custom matrices are compatible with the JPEG standard, which requires transmission of the quantization matrix.

Watson, Andrew B.↗
NASA NTRS1992

Vortex-induced disturbance field in a compressible shear layer

The disturbance field induced by a small isolated vortex in a compressible shear layer is studied using direct simulation in a convected frame. The convective Mach number, M(sub c), is varied from 0.1 to 1.25. The vorticity perturbation is rapidly sheared by the mean velocity gradient. The resulting disturbance pressure field is observed to decrease both in magnitude and extent with increasing M(sub c), becoming a narrow transverse zone for M(sub c) greater than 0.8. A similar trend is seen for the perturbation velocity magnitude and for the Reynolds shear stress. By varying the vortex size, we verified that the decrease in perturbation levels is due to the mean-flow Mach number and not the Mach number across the vortex. At high M(sub c), the vortex still communicates with the edges of the shear layer, although communication in the mean-flow direction is strongly inhibited. The growth rate of perturbation kinetic energy declines with M(sub c) primarily due to the reduction in shear stress. For M(sub c) greater than or equal to 0.6, the pressure dilatation also contributes to the decrease of growth rates. Calculation of the perturbation field induced by a vortex doublet revealed the same trends as in the single-vortex case, illustrating the insensitivity of the Mach-number effect to the specific form of initial conditions.

Papamoschou, D.↗
NASA NTRS1994

Effect of density gradients in confined supersonic shear layers, part 1

The effect of density gradients on the supersonic wall modes (acoustic modes) of a 2-D confined compressible shear layer were investigated using linear analysis. Due to the inadequacies of the hyperbolic tangent profile, the boundary layer basic profiles were used. First a test case was taken with the same parameters as in Tam and Hu's analysis with convective Mach number M(sub c) = 1.836 and density ratio of 1.398. Three generalized inflection points were found giving rise to three modes. The first two show similar properties to the Class A and B modes, and the third is an 'inner mode' which will be called a Class C mode. As the density ratio is increased, the smallest of the three neutral phase speeds tends towards the speed of the lower velocity stream, and the other two eventually coalesce and then disappear. These two effects lead to a linear resonance between the Class B modes which increases the cutoff frequency and growth rate of the lowest mode. In fact, growth rates of 2-4 times the test case were found as the density ratio was increased to 7. A similar trend is observed for the Class A modes when the density ratio is decreased from the test case, but the growth rate is not changed by much from the test case.

Peroomian, Oshin↗
NASA NTRS2021

Measurements of Rainfall Rate, Drop Size Distribution, and Variability at Middle and Higher Latitudes: Application to the Combined DPR-GMI Algorithm

The Global Precipitation Measurement mission is a major U.S.–Japan joint mission to understand the physics of the Earth’s global precipitation as a key component of its weather, climate, and hydrological systems. The core satellite carries a dual-precipitation radar and an advanced microwave imager which provide measurements to retrieve the drop size distribution (DSD) and rain rates using a Combined Radar-Radiometer Algorithm (CORRA). Our objective is to validate key assumptions and parameterizations in CORRA and enable improved estimation of precipitation products, especially in the middle-to-higher latitudes in both hemispheres. The DSD parameters and statistical relationships between DSD parameters and radar measurements are a central part of the rainfall retrieval algorithm, which is complicated by regimes where DSD measurements are abysmally sparse (over the open ocean). In view of this, we have assembled optical disdrometer datasets gathered by research vessels, ground stations, and aircrafts to simulate radar observables and validate the scattering lookup tables used in CORRA. The joint use of all DSD datasets spans a large range of drop concentrations and characteristic drop diameters. The scaling normalization of DSDs defines an intercept parameter N(W), which normalizes the concentrations, and a scaling diameter D(m), which compresses or stretches the diameter coordinate axis. A major finding of this study is that a single relationship between N(W) and D(m), on average, unifies all datasets included, from stratocumulus to heavier rainfall regimes. A comparison with the N(W)–D(m) relation used as a constraint in versions 6 and 7 of CORRA highlights the scope for improvement of rainfall retrievals for small drops (D(m) < 1 mm) and large drops (D(m) > 2 mm). The normalized specific attenuation–reflectivity relationships used in the combined algorithm are also found to match well the equivalent relationships derived using DSDs from the three datasets, suggesting that the currently assumed lookup tables are not a major source of uncertainty in the combined algorithm rainfall estimates.

Viswanathan Bringi↗
NASA NTRS2010

Z-Pinch Pulsed Plasma Propulsion Technology Development

Fusion-based propulsion can enable fast interplanetary transportation. Magneto-inertial fusion (MIF) is an approach which has been shown to potentially lead to a low cost, small reactor for fusion break even. The Z-Pinch/dense plasma focus method is an MIF concept in which a column of gas is compressed to thermonuclear conditions by an axial current (I approximates 100 MA). Recent advancements in experiments and the theoretical understanding of this concept suggest favorable scaling of fusion power output yield as I(sup 4). This document presents a conceptual design of a Z-Pinch fusion propulsion system and a vehicle for human exploration. The purpose of this study is to apply Z-Pinch fusion principles to the design of a propulsion system for an interplanetary spacecraft. This study took four steps in service of that objective; these steps are identified below. 1. Z-Pinch Modeling and Analysis: There is a wealth of literature characterizing Z-Pinch physics and existing Z-Pinch physics models. In order to be useful in engineering analysis, simplified Z-Pinch fusion thermodynamic models are required to give propulsion engineers the quantity of plasma, plasma temperature, rate of expansion, etc. The study team developed these models in this study. 2. Propulsion Modeling and Analysis: While the Z-Pinch models characterize the fusion process itself, propulsion models calculate the parameters that characterize the propulsion system (thrust, specific impulse, etc.) The study team developed a Z-Pinch propulsion model and used it to determine the best values for pulse rate, amount of propellant per pulse, and mixture ratio of the D-T and liner materials as well as the resulting thrust and specific impulse of the system. 3. Mission Analysis: Several potential missions were studied. Trajectory analysis using data from the propulsion model was used to determine the duration of the propulsion burns, the amount of propellant expended to complete each mission considered. 4. Vehicle Design: To understand the applicability of Z-Pinch propulsion to interplanetary travel, it is necessary to design a concept vehicle that uses it -- the propulsion system significantly impacts the design of the electrical, thermal control, avionics and structural subsystems of a vehicle. The study team developed a conceptual design of an interplanetary vehicle that transports crew and cargo to Mars and back and can be reused for other missions. Several aspects of this vehicle are based on a previous crewed fusion vehicle study -- the Human Outer Planet Exploration (HOPE) Magnetized Target Fusion (MTF) vehicle. Portions of the vehicle design were used outright and others were modified from the MTF design in order to maintain comparability.

Polsgrove, Tara↗
NASA NTRS2011

Turbulence Modeling for Shock Wave/Turbulent Boundary Layer Interactions

Accurate aerodynamic computational predictions are essential for the safety of space vehicles, but these computations are of limited accuracy when large pressure gradients are present in the flow. The goal of the current project is to improve the state of compressible turbulence modeling for high speed flows with shock wave / turbulent boundary layer interactions (SWTBLI). Emphasis will be placed on models that can accurately predict the separated region caused by the SWTBLI. These flows are classified as nonequilibrium boundary layers because of the very large and variable adverse pressure gradients caused by the shock waves. The lag model was designed to model these nonequilibrium flows by incorporating history effects. Standard one- and two-equation models (Spalart Allmaras and SST) and the lag model will be run and compared to a new lag model. This new model, the Reynolds stress tensor lag model (lagRST), will be assessed against multiple wind tunnel tests and correlations. The basis of the lag and lagRST models are to preserve the accuracy of the standard turbulence models in equilibrium turbulence, when the Reynolds stresses are linearly related to the mean strain rates, but create a lag between mean strain rate effects and turbulence when nonequilibrium effects become important, such as in large pressure gradients. The affect this lag has on the results for SWBLI and massively separated flows will be determined. These computations will be done with a modified version of the OVERFLOW code. This code solves the RANS equations on overset grids. It was used for this study for its ability to input very complex geometries into the flow solver, such as the Space Shuttle in the full stack configuration. The model was successfully implemented within two versions of the OVERFLOW code. Results show a substantial improvement over the baseline models for transonic separated flows. The results are mixed for the SWBLI assessed. Separation predictions are not as good as the baseline models, but the over prediction of the peak heat flux downstream of the reattachment shock that plagues many models is reduced.

Lillard, Randolph P.↗