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Two dimensional stagnation point flow of a dusty gas near an oscillating plate

Necessary improvements to a paper on the flow of a dusty gas by Datta and Mishra (1980) are presented. Particular attention is given to the importance of particle phase compressibility and the hyperbolic nature of the particle momentum conservation equation which prohibits downstream (wall) boundary conditions for the solid phase. Fundamental differences between particulate and ordinary flow boundary layers are discussed, and the correct conservation equations are written.

Fernandez De La Mora, J.↗

Divergence Free High Order Filter Methods for the Compressible MHD Equations

The generalization of a class of low-dissipative high order filter finite difference methods for long time wave propagation of shock/turbulence/combustion compressible viscous gas dynamic flows to compressible MHD equations for structured curvilinear grids has been achieved. The new scheme is shown to provide a natural and efficient way for the minimization of the divergence of the magnetic field numerical error. Standard diver- gence cleaning is not required by the present filter approach. For certain MHD test cases, divergence free preservation of the magnetic fields has been achieved.

Yea, H. C.↗

High Order Filter Methods for the Non-ideal Compressible MHD Equations

The generalization of a class of low-dissipative high order filter finite difference methods for long time wave propagation of shock/turbulence/combustion compressible viscous gas dynamic flows to compressible MHD equations for structured curvilinear grids has been achieved. The new scheme is shown to provide a natural and efficient way for the minimization of the divergence of the magnetic field numerical error. Standard divergence cleaning is not required by the present filter approach. For certain non-ideal MHD test cases, divergence free preservation of the magnetic fields has been achieved.

Yee, H. C.↗

Conference on Interactions of the Interplanetary Plasma with the Modern and Ancient Moon, George Williams College, Lake Geneva, Wis., September 30-October 4, 1974, Proceedings

The papers deal with solar-wind and magnetospheric interactions with the moon, ancient and present-day lunar surface magnetic and electric fields, the dynamics and evolution of the lunar atmosphere, the lunar record of solar radiation, and nonmeteoric transport of lunar surface materials. Topics discussed include bow-shock protons in the lunar environment, energetic ion events during the lunar night, mapping of the lunar surface magnetic field from orbital observations of mirrored electrons, geomagnetic disturbances induced by the moon, the relationship between lunar topography and limb compressions, measurements of lunar sky brightness, atmospheric supply and loss mechanisms on the moon, the nature and composition of the lunar atmosphere, molecular gas species in that atmosphere, and vacuum-UV spectroscopic measurements of the surface properties of lunar materials. Individual items are announced in this issue.

Source record↗

Bypass transition in compressible boundary layers

Transition to turbulence in aerospace applications usually occurs in a strongly disturbed environment. For instance, the effects of free-stream turbulence, roughness and obstacles in the boundary layer strongly influence transition. Proper understanding of the mechanisms leading to transition is crucial in the design of aircraft wings and gas turbine blades, because lift, drag and heat transfer strongly depend on the state of the boundary layer, laminar or turbulent. Unfortunately, most of the transition research, both theoretical and experimental, has focused on natural transition. Many practical flows, however, defy any theoretical analysis and are extremely difficult to measure. Morkovin introduced in his review paper the concept of bypass transition as those forms of transition which bypass the known mechanisms of linear and non-linear transition theories and are currently not understood by experiments. In an effort to better understand the mechanisms leading to transition in a disturbed environment, experiments are conducted studying simpler cases, viz. the effects of free stream turbulence on transition on a flat plate. It turns out that these experiments are very difficult to conduct, because generation of free stream turbulence with sufficiently high fluctuation levels and reasonable homogeneity is non trivial. For a discussion see Morkovin. Serious problems also appear due to the fact that at high Reynolds numbers the boundary layers are very thin, especially in the nose region of the plate where the transition occurs, which makes the use of very small probes necessary. The effects of free-stream turbulence on transition are the subject of this research and are especially important in a gas turbine environment, where turbulence intensities are measured between 5 and 20 percent, Wang et al. Due to the fact that the Reynolds number for turbine blades is considerably lower than for aircraft wings, generally a larger portion of the blade will be in a laminar transitional state. The effects of large free stream turbulence in compressible boundary layers at Mach numbers are examined both in the subsonic and transonic regime using direct numerical simulations. The flow is computed over a flat plate and curved surface. while many applications operate in the transonic regime. Due the nature of their numerical scheme, a non-conservation formulation of the Navier-Stokes equations, it is a non-trivial extension to compute flow fields in the transonic regime. This project aims at better understanding the effects of large free-stream turbulence in compressible boundary layers at mach number both in the subsonic and transonic regime using direct numerical simulations. The present project aims at computing the flow over a flat plate and curved surface. This research will provide data which can be used to clarify mechanisms leading to transition in an environment with high free stream turbulence. This information is useful for the development of turbulence models, which are of great importance for CFD applications, and are currently unreliable for more complex flows, such as transitional flows.

Vandervegt, J. J.↗

Spectroscopy of the Perseus Cluster

We present preliminary results of a XMM-Newton 50 ks observation of the Perseus Cluster that provides an unprecedented view of the central 0.5 Mpc region. The projected gas temperature declines smoothly by a factor of 2 from a maximum value of approx. 7 keV in the outer regions to just above 3 keV at the cluster center. Over this same range, the heavy-element abundance rises slowly from 0.4 to 0.5 solar as the radius decreases from 14 ft. to 5 ft., and then it rises to a peak of almost 0.7 solar at 1&farcm;25 before declining to 0.4 at the center. Th global east-west asymmetry of the gas temperature and surface brightness distributions, approximately aligned with the chain of bright galaxies, suggests an ongoing merger, although the modest degree of the observed asymmetry certainly excludes a major merger interpretation. The chain of galaxies probably traces the filament along which accretion started some time ago and is continuing at the present time. A cold and dense (low-entropy) cluster core like Perseus is probably well "protected" against the penetration of the gas of infalling groups and poor clusters, whereas in non-cooling core clusters such as Coma and A1367, infalling subclusters can penetrate deeply into the core region. In Perseus, gas associated with infalling groups may be stripped completely at the outskirts of the main cluster and only compression waves (shocks) may reach the central regions. We argue, and show supporting simulations, that the passage of such a wave(s) can qualitatively explain the overall horseshoe shaped appearance of the gas temperature map (the hot horseshoe surrounds the colder, low-entropy core) as well as other features of the Perseus Cluster core. These simulations also show that as compression waves traverse the cluster core, they can induce oscillatory motion of the cluster gas that can generate multiple sharp "edges" on opposite sides of the central galaxy. Gas motions induced by mergers may be a natural way to explain the high frequency of "edges" seen in clusters with cooling cores.

Jones, Christine↗

Least-squares finite element methods for compressible Euler equations

A method based on backward finite differencing in time and a least-squares finite element scheme for first-order systems of partial differential equations in space is applied to the Euler equations for gas dynamics. The scheme minimizes the L-sq-norm of the residual within each time step. The method naturally generates numerical dissipation proportional to the time step size. An implicit method employing linear elements has been implemented and proves robust. For high-order elements, computed solutions based on the L-sq method may have oscillations for calculations at similar time step sizes. To overcome this difficulty, a scheme which minimizes the weighted H1-norm of the residual is proposed and leads to a successful scheme with high-degree elements. Finally, a conservative least-squares finite element method is also developed. Numerical results for two-dimensional problems are given to demonstrate the shock resolution of the methods and compare different approaches.

Jiang, Bo-Nan↗

Predicting SLS Launch Environment using a Novel Multiphase Formulation

Powerful acoustic waves generated during ignition of launch vehicles may be dangerous to the vehicle, its payload, or the surrounding structures. The water-based Ignition Overpressure and Sound Suppression (IOP/SS) system at Kennedy Space Center’s (KSC) Launch Complex 39B (LC-39B) will be used to protect the Space Launch System (SLS) from the acoustic vibrations generated during launch. The IOP/SS system uses enormous amounts of water to dampen and attenuate these sound waves. To better understand the launch environment risks and to study the effectiveness of the IOP/SS system it is desirable to have time-accurate unsteady simulations of the vehicle ignition with water-based sound suppression. This paper presents results obtained with a novel, high-order accurate, and robust numerical method designed for simulating compressible multiphase flows. A positivity-preserving finite difference scheme is utilized which is formally high-order accurate and also provably robust. Robustness is critical due to the extreme nature of the flow which exhibits highly nonlinear shock and rarefaction waves interacting with liquid-gas interfaces with density ratios of the order of 1000:1. Furthermore, the high-order accuracy (and the high resolution property) is desirable for predicting wave phenomena like IOP waves since the signal can be resolved accurately and propagated long distances with fewer grid points. This finite-difference method was developed using NASA’s Launch, Ascent, and Vehicle Aerodynamics (LAVA) Cartesian immersed boundary framework. We present a validation case by applying our solver to the SLS Scale Model Acoustic Test (SMAT). The SLS SMAT is a well-instrumented 5% scale model test meant to represent the SLS at NASA KSC’s LC-39B pad. Scale IOP tests were performed with and without the sound suppression water and included many sensors which recorded the pressure waves produced during ignition. For this validation case we conduct two simulations, likewise with and without sound suppression water, and compare the SLS SMAT pressure sensor signals with our numerical signals at identical locations. Following this validation case we present a study of the SLS launch environment to examine engineering safety concerns about the mobile launch pad. Engineers at KSC redesigned the main flame deflector at LC-39B anticipating the increased loads from the SLS and to repair damage from prior Shuttle missions. This deflector redesign made use of surface pressure and temperature data from LAVA full-scale SLS simulations without the sound suppression system. The engineers were questioning the possibility of increased pressure loads on the underside of the mobile launcher due to the water in the flame trench. Based on the results established in our simulations of the SLS SMAT, we performed updated calculations for SLS at LC-39B with and without water systems active to assess the readiness of the launch pad for Artemis I launch. Our results show that the IOP/SS system is effective at reducing the overpressure signal and overall sound pressure levels felt by the vehicle and additionally that the pressure loads experienced by the mobile launcher (ML) during engine startup is not increased by the presence of water.

EGS↗

The Physics of Cooling Flow Clusters with Central Radio Sources

Central galaxies in rich clusters are the sites of cluster cooling flows, with large masses of gas cooling through part of the X-ray band. Many of these galaxies host powerful radio sources. These sources can displace and compress the X-ray gas leading to enhanced cooling and star formation. We observed the bright cooling flow Abell 2626 with a strangely distorted central radio source. We wished to understand the interaction of radio and X-ray thermal plasma, and to determine the dynamical nature of this cluster. One aim was to constrain the source of additional pressure in radio "holes" in the X-ray emission needed to support overlying shells of X-ray gas. We also aimed to study the problem of the lack of kT < 1-2 keV gas in cooling flows by searching for abundance inhomogeneities, heating from the radio source, and excess absorption. We also have a Chandra observation of this cluster. There were problems with the pipeline processing of this data due to a telemetry dropout. We are publishing the Chandra and XMM data together. Delays with the Chandra data have slowed up the publication. At the center of the cluster, there is a complex interaction of the odd, Z-shaped radio source, and the X-ray plasma. However, there are no clear radio bubbles. Also, the cluster SO galaxy IC 5337, which is projected 1.5 arcmin west of the cluster center, has unusual tail-like structures in both the radio and X-ray. It appears to be falling into the cluster center. There is a hot, probably shocked region of gas to the southwest, which is apparently due to the merger of a subcluster in this part of the system. There is also a merging subcluster to the northeast. The axes of these two mergers agrees with a supercluster filament structure.

Sarazin, Craig L.↗

The alpha Centauri Line of Sight: D/H Ratio, Physical Properties of Local Interstellar Gas, and Measurement of Heated Hydrogen (The 'Hydrogen Wall') Near the Heliopause

We analyze high-resolution spectra of the nearby (1.34 pc) stars alpha Cen A (G2 V) and alpha Cen B (K1 V), which were obtained with the Goddard High Resolution Spectrograph on the Hubble Space Telescope. The observations consist of echelle spectra of the Mg II 2800 A and Fe II 2599 A resonance lines and the Lyman-alpha lines of hydrogen and deuterium. The interstellar gas has a velocity (v = - 18.0 +/- 0.2 km/s) consistent with the local flow vector proposed for this line of sight by Lailement & Berlin (1992). The temperature and nonthermal velocity inferred from the Fe II, Mg II, and D I line profiles are T = 5400 +/- 500 K and xi = 1.20 +/- 0.25 km/s, respectively. However, single-component fits to the H I Lyman-alpha lines yield a Doppler parameter (b(sub HI) = 11.80 km/s) that implies a significantly warmer temperature of 8350 K, and the velocity of the H I absorption (v = - 15.8 +/- 0.2 km/s) is redshifted by about 2.2 km/s with respect to the Fe II, Mg II, and D I lines. The one-component model of the interstellar gas suggests natural logarithm N base HI = 18.03 +/- 0.01 and D/H = (5.7 +/- 0.2) x 10(exp -6) . These parameters lead to a good fit to the observed spectra, but this model does not explain the higher temperature and redshift of H I relative to the other interstellar lines. The most sensible way to resolve the discrepancy between H(I) and the other lines is to add a second absorption component to the H(I) lines. This second component is hotter (T approx. equals 30,000 K), is redshifted relative to the primary component by 2-4 km/s, and has a column density too low to be detected in the Fe(II), Mg(II), and D(I) lines. We propose that the gas responsible for this component is located near the heliopause, consisting of the heated H I gas from the interstellar medium that is compressed by the solar wind. This so-called 'hydrogen wall' is predicted by recent multifluid gasdynamical models of the interstellar gas and solar wind interaction. Our data provide the first measurements of the temperature and column density of H(I) in the hydrogen wall. After considering the effects that a corresponding hydrogen wall around alpha Cen would have on our analysis, our best estimates for the parameters of the solar hydrogen wall are natural log N(sup (2))(H(I)) = 14.74 +/- 0.24, b(sup (2))(H(I)) = 21.9 +/- 1.7 km/s (corresponding to T = 29,000 +/- 5000 K), and v(sup (2))(H(I)) greater than -16km/s. Unfortunately, the existence of this heated H(I) reduces our ability to compute the H(I) column density of the interstellar medium accurately because, with slight alterations to our assumed stellar Lyman-alpha profiles, we discovered that acceptable two-component fits also exist with natural log N(H(I))approx. 17.6. We, therefore, quote large error bars for the H I column density along the alpha Cen line of sight, natural log N(H(I)) = 17.80 +/- 0.30. For this range in N(H(I)), n(H(I)) = 0.15 /cu.cm (+/- a factor of 2) and D/H = (0.5-1.9) x 10(exp -5). This is the first direct measurement of the H(I) density in a local cloud and allows us to predict the distance from the Sun to the edge of the local cloud along various lines of sight. This range in D/H is consistent with the value D/H = 1.6 x 10(exp -5) previously derived for the Capella and Procyon lines of sight. We cannot tell whether D/H ratio varies or is constant in the local interstellar medium, but we do find that the D(I)/Mg(II) ratio for the alpha Cen line of sight is about 4 times smaller than for the Capella and Procyon lines of sight. Therefore, either D/H or the Mg depletion varies significantly over distance scales of only a few parsecs.

Linsky, Jeffrey L.↗

Charge Deposition/Neutralization and Dust Removal via Plasma Interactions

Electrically charged and chemically reactive lunar dust can cause serious problems to spacecraft, surface equipment, and astronaut health, so understanding its interaction with and transport through the lunar plasma environment is important to dust mitigation efforts. We explore the charging of granular material in the natural environment of the Moon, recreate those conditions in the laboratory under high vacuum, and examine dust transport and charge neutralization for application in future lunar missions. Phenomena such as charge deposition via electron and ion beams, photoionization through ultraviolet light exposure, neutralization of charge through impingement by an ionized compressed gas, and tribocharging during dust liberation from surfaces will be presented. Surface materials of interest such as floating/grounded conductors and orthofabric for spacesuits are the preliminary focus of this effort. An electrometer is used to characterize currents interacting with the surfaces in the case of the electron/ion/UV source exposure, an electrostatic voltmeter is used to measure the potential on the surfaces without inadvertently discharging them, and a charge plate monitor is used to verify the efficiency of discharging the surfaces via ionized gas impingement. After setup of the initial charge conditions on the surfaces, a quick burst of high-pressure gas is used to overcome adhesion forces and initially dislodge the dust from the surfaces, followed by a low flow of gas that is ionized via application of a strong electric field. The gas is released in a high vacuum environment so as the pressure drops from the initial compressed state through to the vacuum state, the mean free path reaches a point where ionization can occur before all the gas disperses into the vacuum. This ionized gas can then neutralize both the dust and the surface to ensure minimal resettling. Several parameters such as gas composition, electrode geometry, high voltage waveform shape/polarity, and pulse timing have been explored and will be presented here.

electrostatics↗

A Lyapunov based nonlinear control scheme for stabilizing a basic compression system using a close-coupled control valve

The use of a closed-loop control to allow surge-free operation of a compression system beyond its uncontrolled surge line is addressed. In contrast to previous analyses which used a linearized model, the approach described directly addresses the nonlinear nature of the compressor characteristic using a Liapunov-based control law design formulation. The proposed approach is fairly generic and should be of interest for gas turbine engines as well as other applications.

Simon, J. S.↗

Lifetime prediction of materials exposed to the natural space environment

The goal of this study is to model the lifetime of different types of seal materials based on results obtained from accelerated experiments. A semi-mechanistic approach was taken. Thermal aging data were taken from the literature whereas experiments were conducted at Auburn under this contract for selected environments. The seal materials of interest are Silicone 383, Silicone 650, Viton 835, and Viton 747. The relevant conditions include thermal, oxygen, inert gas, vacuum, and gamma radiation. Compression set data available from NASA were used to examine the thermal effect. Experiments were conducted at Auburn University and at NASA to isolate the role of thermal, oxygen, inert gas, vacuum, gamma irradiation, and proton irradiation. A simple discrete stress relaxation method was developed to determine the relaxation response of the elastomers. Dynamic mechanical thermal analysis was also used to characterize the mechanical response of the specimens. These provide a more meaningful correlation between mechanisms and degradation.

Zee, Ralph↗

Noncontacting Laser Inspection System for Dimensional Profiling of Space Application Thermal Barriers

A noncontacting, two-dimensional (2-D) laser inspection system has been designed and implemented to dimensionally profile thermal barriers being developed for space vehicle applications. In a vehicle as-installed state, thermal barriers are commonly compressed between load sensitive thermal protection system (TPS) panels to prevent hot gas ingestion through the panel interface during flight. Loads required to compress the thermal barriers are functions of their construction, as well as their dimensional characteristics relative to the gaps in which they are installed. Excessive loads during a mission could damage surrounding TPS panels and have catastrophic consequences. As such, accurate dimensional profiling of thermal barriers prior to use is important. Due to the compliant nature of the thermal barriers, traditional contact measurement techniques (e.g., calipers and micrometers) are subjective and introduce significant error and variability into collected dimensional data. Implementation of a laser inspection system significantly enhanced the method by which thermal barriers are dimensionally profiled, and improved the accuracy and repeatability of collected data. A statistical design of experiments study comparing laser inspection and manual caliper measurement techniques verified these findings.

Taylor, Shawn C.↗

Use of Generalized Fluid System Simulation Program (GFSSP) for Teaching and Performing Senior Design Projects at the Educational Institutions

This paper describes the experience of the authors in using the Generalized Fluid System Simulation Program (GFSSP) in teaching Design of Thermal Systems class at University of Alabama in Huntsville. GFSSP is a finite volume based thermo-fluid system network analysis code, developed at NASA/Marshall Space Flight Center, and is extensively used in NASA, Department of Defense, and aerospace industries for propulsion system design, analysis, and performance evaluation. The educational version of GFSSP is freely available to all US higher education institutions. The main purpose of the paper is to illustrate the utilization of this user-friendly code for the thermal systems design and fluid engineering courses and to encourage the instructors to utilize the code for the class assignments as well as senior design projects. The need for a generalized computer program for thermofluid analysis in a flow network has been felt for a long time in aerospace industries. Designers of thermofluid systems often need to know pressures, temperatures, flow rates, concentrations, and heat transfer rates at different parts of a flow circuit for steady state or transient conditions. Such applications occur in propulsion systems for tank pressurization, internal flow analysis of rocket engine turbopumps, chilldown of cryogenic tanks and transfer lines, and many other applications of gas-liquid systems involving fluid transients and conjugate heat and mass transfer. Computer resource requirements to perform time-dependent, three-dimensional Navier-Stokes computational fluid dynamic (CFD) analysis of such systems are prohibitive and therefore are not practical. Available commercial codes are generally suitable for steady state, single-phase incompressible flow. Because of the proprietary nature of such codes, it is not possible to extend their capability to satisfy the above-mentioned needs. Therefore, the Generalized Fluid System Simulation Program (GFSSP1) has been developed at NASA Marshall Space Flight Center (MSFC) as a general fluid flow system solver capable of handling phase changes, compressibility, mixture thermodynamics and transient operations. It also includes the capability to model external body forces such as gravity and centrifugal effects in a complex flow network. The objectives of GFSSP development are: a) to develop a robust and efficient numerical algorithm to solve a system of equations describing a flow network containing phase changes, mixing, and rotation; and b) to implement the algorithm in a structured, easy-to-use computer program. The analysis of thermofluid dynamics in a complex network requires resolution of the system into fluid nodes and branches, and solid nodes and conductors as shown in Figure 1. Figure 1 shows a schematic and GFSSP flow circuit of a counter-flow heat exchanger. Hot nitrogen gas is flowing through a pipe, colder nitrogen is flowing counter to the hot stream in the annulus pipe and heat transfer occurs through metal tubes. The problem considered is to calculate flowrates and temperature distributions in both streams. GFSSP has a unique data structure, as shown in Figure 2, that allows constructing all possible arrangements of a flow network with no limit on the number of elements. The elements of a flow network are boundary nodes where pressure and temperature are specified, internal nodes where pressure and temperature are calculated, and branches where flowrates are calculated. For conjugate heat transfer problems, there are three additional elements: solid node, ambient node, and conductor. The solid and fluid nodes are connected with solid-fluid conductors. GFSSP solves the conservation equations of mass and energy, and equation of state in internal nodes to calculate pressure, temperature and resident mass. The momentum conservation equation is solved in branches to calculate flowrate. It also solves for energy conservation equations to calculate temperatures of solid nodes. The equations are coupled and nonlinear; therefore, they are solved by an iterative numerical scheme. GFSSP employs a unique numerical scheme known as simultaneous adjustment with successive substitution (SASS), which is a combination of Newton-Raphson and successive substitution methods. The mass and momentum conservation equations and the equation of state are solved by the Newton-Raphson method while the conservation of energy and species are solved by the successive substitution method. GFSSP is linked with two thermodynamic property programs, GASP2 and WASP3 and GASPAK4, that provide thermodynamic and thermophysical properties of selected fluids. Both programs cover a range of pressure and temperature that allows fluid properties to be evaluated for liquid, liquid-vapor (saturation), and vapor region. GASP and WASP provide properties of 12 fluids. GASPAK includes a library of 36 fluids. GFSSP has three major parts. The first part is the graphical user interface (GUI), visual thermofluid analyzer of systems and components (VTASC). VTASC allows users to create a flow circuit by a 'point and click' paradigm. It creates the GFSSP input file after the completion of the model building process. GFSSP's GUI provides the users a platform to build and run their models. It also allows post-processing of results. The network flow circuit is first built using three basic elements: boundary node, internal node, and branch.

Majumdar, A. K.↗

Supercritical microgravity droplet vaporization

Supercritical droplet vaporization is an important issue in many combustion systems, such as liquid fueled rockets and compression-ignition (diesel) engines. In order to study the details of droplet behavior at these conditions, an experiment was designed to provide a gas phase environment which is above the critical pressure and critical temperature of a single liquid droplet. In general, the droplet begins as a cold droplet in the hot, high pressure environment. In order to eliminate disruptions to the droplet by convective motion in the gas, forced and natural convection gas motion are required to be small. Implementation of this requirement for forced convection is straightforward, while reduction of natural convection is achieved by reduction in the g-level for the experiment. The resulting experiment consists of a rig which can stably position a droplet without restraint in a high-pressure, high temperature gas field in microgravity. The microgravity field is currently achieved by dropping the device in the NASA Lewis 2.2 second drop tower. The performance of the experimental device and results to date are presented.

Hartfield, J.↗

Pressure- and buoyancy-driven thermal convection in a rectangular enclosure

Results are presented for unsteady laminar thermal convection in compressible fluids at various reduced levels of gravity in a rectangular enclosure which is heated on one side and cooled on the opposite side. The results were obtained by solving numerically the equations of conservation for a viscous, compressible, heat-conducting, ideal gas in the presence of a gravitational body force. The formulation differs from the Boussinesq simplification in that the effects of variable density are completely retained. A conservative, explicit, time-dependent, finite-difference technique was used and good agreement was found for the limited cases where direct comparison with previous investigations was possible. The solutions show that the thermally induced motion is acoustic in nature at low levels of gravity and that the unsteady-state rate of heat transfer is thereby greatly enhanced relative to pure conduction. The nonlinear variable density profile skews the streamlines towards the cooler walls but is shown to have little effect on the steady-state isotherms.

Spradley, L. W.↗

Numerical solutions of Navier-Stokes equations for a Butler wing

The flow field is simulated on the surface of a given delta wing (Butler wing) at zero incident in a uniform stream. The simulation is done by integrating a set of flow field equations. This set of equations governs the unsteady, viscous, compressible, heat conducting flow of an ideal gas. The equations are written in curvilinear coordinates so that the wing surface is represented accurately. These equations are solved by the finite difference method, and results obtained for high-speed freestream conditions are compared with theoretical and experimental results. In this study, the Navier-Stokes equations are solved numerically. These equations are unsteady, compressible, viscous, and three-dimensional without neglecting any terms. The time dependency of the governing equations allows the solution to progress naturally for an arbitrary initial initial guess to an asymptotic steady state, if one exists. The equations are transformed from physical coordinates to the computational coordinates, allowing the solution of the governing equations in a rectangular parallel-piped domain. The equations are solved by the MacCormack time-split technique which is vectorized and programmed to run on the CDC VPS 32 computer.

Abolhassani, J. S.↗