ALBERT

Description: We study the onset of a pure Marangoni convection in a liquid layer with two deformable interfaces in the no-gravity environment. Both oscillatory and stationary instabilities are considered for a wide range of parameters. It is shown that only stationary instability is possible when surface tension at the colder interface is lower than that at the hotter one. Oscillatory instability tends to disappear and to be replaced by the stationary instability with increase of the Prandtl number and decrease of surface tension at the colder interface.

Description: A consistent solution of the radiative transfer equation characterizing photon transport in a semi-infinite medium of refractive index greater than or equal to one is obtained following the method of Sobolev. Fresnel specular reflection, Snell's law and isotropic scattering are assumed. An algorithm is developed and its accuracy is demonstrated. A numerical Laplace transform inversion leads to an efficient evaluation for the interior flux and source function distributions.

Description: Results are reported of the Surface Tension Driven Convection Experiment (STDCE) aboard USML-1 Spacelab. Steady and transient thermocapillary flows were investigated in a 10 cm dia. circular container filled with 10 Cs silicone oil. The velocity and temperature fields were studied in detail under various conditions. It is shown in this paper how the Marangoni number affects the velocity field. A numerical analysis of the flows was also conducted and its results were compared to the experimental data. Good agreement is shown.

Description: Potential flows may be utilized to represent motions produced in pulsating bulbs. While the initial bulb shape may be arbitrary, sequential shapes are related by affine transformations. Two components appear in the distribution of pressure, one dependent on the instantaneous velocity and the other on the acceleration. For flows with stationary streamlines the inertial impedance is that of a simple mass, and is proportional to the first moment of the actual mass of fluid contained within the bulb. Examples treated are: (1) Expanding and collapsing circular cylinders, and (2) elliptical cylinders in which the perimeter is held constant. The thickness of the pulsatile laminar boundary layer is found to be approximately on millimeter for conditions in the vicinity of the heart. Conditions for separation and turbulence differ from those in steady flow.

Description: The results of a parametric study on the entrance flow region in a gas core nuclear reactor are presented. The physical system is modeled as laminar confined, coaxial flow with heat generation in the inner fluid. The governing equations include the boundary layer approximations and the assumptions of only radial radiative transport of energy represented as an energy diffusion term. The Von Mises transformation and a zeta transformation are used to transform the equations into nonlinear nonhomogeneous convective-diffusion equations. A unique combination of forward and backward difference equations which yields accurate results at moderate computational times, is used in the numerical method. Results show that the rapidly accelerating, heat generating inner stream actually shrinks in radius as it expands axially.

Description: The transient response of an elastic cylindrical shell immersed in an acoustic media that is engulfed by a plane wave is determined numerically. The method applies to the USA-STAGS code which utilizes the finite element method for the structural analysis and the doubly asymptotic approximation for the fluid-structure interaction. The calculations are compared to an exact analysis for two separate loading cases: a plane step wave and an exponentially decaying plane wave.

Description: The inherent tolerance for nuclear radiation makes fluidic devices candidates for nuclear rocket control systems. Also, they are being considered for supersonic jet engine inlet control because of their high temperature and vibration tolerance. Three new control components being considered for these applications are described. A fluidic circuit to control a pneumatic stepping motor for nuclear rocket control drum actuation is discussed. An all-fluidic sensor being developed for determining the position of the normal shock in the inlet of a supersonic jet engine is outlined. A new vortex valve configuration is developed to prevent supersonic jet engine inlet unstarts by regulating bypass flow.

Description: Calculation procedures for compressible turbulent boundary layers were based upon techniques, modeling constants, etc., developed originally for the low speed case. Significant differences and new or altered physics which occur in the compressible case were considered, as compared with the low speed situation. Possible pitfalls and sources of inaccuracy in the calculations were indicated.

Description: In the absence of gravity, stirring in a liquid is suppressed because of density differences caused by thermal or compositional gradients. However, other mechanisms resulting in natural convection in a microgravity environment exist. One of the most important mechanisms for liquid metals is surface tension driven convection, which becomes predominant in the low gravity environment. In this case, surface tension differences caused by compositional or temperature gradients have been demonstrated to cause stirring in liquids during experiments performed onboard Skylab. Compositional gradients were created by adding a soap solution to a large water globule, which caused vigorous fluid motion for some moments after the addition.

Description: This numerical prediction summary indicates the wide variety of such procedures which are available. Most procedures have detailed user manuals, and in many cases the codes are available. Many of the special effects treated by various methods (such as nonequilibrium or equilibrium chemistry, transition, roughness etc.) are indicated.

Description: From comparisons of high speed data with low speed closure procedures using variable mean density, there does not appear to be any appreciable influence of compressibility upon turbulent shear stress modeling in compressible turbulent boundary layers, even for extreme cases such as Mach 14 to 20 with a change in density across the layer of up to a factor of 100. Other evidence of apparent lack of compressibility caused new physics which may alter the shear stress for the compressible boundary layer cases including: (1) fluctuation Mach number was generally less than 1; (2) the shear stress distribution through the boundary layer was not a function of Mach number for zero pressure gradient flows; (3) the Morkovin hypothesis was valid up to Mach 5 (based on fluctuation data); (4) profile N power was not a function of Mach number, at least up to Mach 10; and (5) the nondimensional burst period was approximately the same as that for low speed.

Description: Basic differential equations governing compressible turbulent boundary layer flow are reviewed, including conservation of mass and energy, momentum equations derived from Navier-Stokes equations, and equations of state. Closure procedures were broken down into: (1) simple or zeroth-order methods, (2) first-order or mean field closure methods, and (3) second-order or mean turbulence field methods.

Description: Three demonstrations of scientific concepts concerning liquids were performed during the Apollo-Soyuz Test Project mission. Chemical foaming, spreading of liquids, and capillary wicking were the subjects of each demonstration photographed in space. The results clearly illustrated the basic principles, and films suitable for educational uses are now available from the first author.

Description: Experiences derived from the development, integration, and flight of NASA spacecraft and sounding rockets are presented. They include the International Heat Pipe Experiment, OAO 3, and ATS-6. Typical flight data are presented to show the performance.

Description: A theory is proposed for analyzing the inviscid interpretation of two streams in the case when the difference in total pressure between the streams is relatively small. A stream is considered which discharges from a nozzle or reservoir into a partially moving and partially stationary environment in such a way that the flows leave the solid boundaries in a tangential direction where the two streams first interact. The problem is solved by expanding in a small parameter related to the difference in total pressure between the streams, the zeroth-order solution is obtained by classical methods, and a technique similar to that employed in thin-airfoil theory is used to transfer the first-order boundary conditions to the zeroth-order boundary. A procedure is developed to transform the problem into one that can be solved by standard techniques of the theory of sectionally analytic functions. Solutions are obtained for flows with and without free streamlines, and the general theory is applied to several specific flow configurations.

Description: An approach is presented for applying the net radiation method developed by Siegel and Howell (1972) and Sparrow and Cess (1966) to systems involving opaque and partially transmitting walls. The results obtained from the basic equations for various values of plate emissivities and temperatures are presented in graphs. Attention is given to the window temperature relative to the temperature of the hot wall and the heat transferred relative to that transferred without the window.

Description: A Green's function formulation is used to derive basic reciprocity relations for planar radiative transfer in a general medium with internal illumination. Reciprocity (or functional symmetry) allows an explicit and generalized development of the equivalence between source and probability functions. Assuming similar symmetry in three-dimensional space, a general relationship is derived between planar-source intensity and point-source total directional energy. These quantities are expressed in terms of standard (universal) functions associated with the planar medium, while all results are derived from the differential equation of radiative transfer.

Description: Radiation from an array of longitudinal fins of triangular profile is analyzed, including fin-to-fin and fin-to-base interactions. The effect of base cylinder radiation and the fin-base radiative interaction is found to be significant for fin width/tube radius ratios less than 8. Results presented may be used to optimize the design of a fin array with respect to weight.

Description: An explicit representation for the unsteady motion on a transversely sheared mean flow is obtained which corresponds to the gustline motion on a uniform mean flow. The important features of this motion are discussed. It is shown that its velocity, pressure and vorticity are all induced by a certain disturbance field that is a linear combination of the vorticity and particle-displacement fields and is everywhere frozen in the mean flow. The general ideas are illustrated by considering the scattering of a gust by a half-plane embedded in a shear flow.

Description: The two-dimensional leveling problem (Degani, Gutfinger, 1976) is extended to three dimensions in the case where the flow Re number is very low and attention is paid to the free surface boundary condition with surface tension effects included. The no-slip boundary condition on the wall is observed. The numerical solution falls back on the Marker and Cell (MAC) method (Harlow and Welch, 1965) with the computation region divided into a finite number of stationary rectangular cells (or boxes in the 3-D case) and fluid flow traverses the cells (or boxes).

Description: The proposed approach to the derivation of the Navier-Stokes equation is thought to be more plausible and easier to understand than other derivations that can be found in works on fluid mechanics. The tensor character of the stress is central to the derivation. In particular, a linear relation between stress and strain rate is assumed only for the shear, rather than for the full stress tensor as is done in most other derivations. An assumption for the shear is naturally simpler and easier to verify experimentally. The use of tensor analysis is shown to greatly simplify the derivation.

Description: A critical analysis is given of the applicability of six-beam models to radiative transfer in particulate materials. The method of introducing transverse scattering in these models is shown to cause fundamental difficulties in the case of physically plausible phase functions; in particular, the effective absorptivity is abnormally large and thus results in incorrect reflectances and transmittances. Six-beam calculations for several media are compared with accurate solutions, with Chu-Churchill two-beam results, and with a simple modification to the Eddington approximation, the last being generally superior over a wide range of conditions.

Description: The stability of the parallel flow of water between concentric cylinders at different temperatures is investigated for infinitesimal velocity and pressure disturbances. Primary interest is in the effect of heat transfer and the radius ratio a/b on the critical point of the neutral stability curve. The results indicate a strong dependence of the critical eigenvalues on both the heat transfer and the radius ratio. The critical Reynolds number of the nonisothermal flow appears to approach a finite value as the inner radius approaches zero (pipe flow) by showing an inflection point on the curve of critical Reynolds number vs a/b.

Description: Solutions for uniformly-sheared turbulence, in which the interaction of the turbulence with the mean shear dominates the turbulent self-interaction, are compared with experiment. An anisotropic spectral tensor, which appears general enough to represent the initial experimental turbulence, is used for the initial condition in the calculations. The evolution of one-point turbulence components and microscales, as well as two-point velocity correlations, are considered. In most cases the agreement with experiment is good. The theory correctly predicts the presence of a negative region for two-point longitudinal-velocity correlations only for point separations in the direction normal to the flow and the mean gradient.

Description: An experiment was conducted to determine the varying effects of six different probe-tip and support-shaft configurations on pitot tube displacement. The study was stimulated by discrepancies between supersonic wind-tunnel tests conducted by Wilson and Young (1949) and Allen (1972). Wilson (1973) had concluded that these discrepancies were caused by differences in probe geometry. It is shown that in fact, no major differences in profiles of streamwise velocity over streamwise velocity at boundary-layer edge vs normal coordinate over boundary-layer total thickness result from geometry. The true cause of the discrepancies, however, remains to be discovered.

Description: Two charts are proposed for calculating the flow coefficient and the area correction factor used in the equation for the flow rate through a sharp-edged orifice. The proposed charts account for variations in the discharge coefficient of sharp-edged orifices and can be used with any pressure ratio for both subcritical and supercritical flow conditions. They can also be used for any gas by using the appropriate gas constant and ratio of specific heats. The application of the charts is illustrated by examples.

Description: Two-dimensional temperature and heat-flux distributions are calculated for an absorbing-emitting gray medium at radiative equilibrium in a rectangular enclosure. The bounding walls are gray and diffuse with arbitrary surface-temperature distributions, and heat generation may take place inside the medium. As a first approximation, the problem is solved for optically thick systems (differential approximation). These results are subsequently improved by the introduction of a number of geometrical parameters to yield good accuracy for all optical thicknesses. As examples, two cases are discussed in detail: (1) uniform heat generation in a black enclosure, and (2) an enclosure with one gray surface at constant temperature. Comparison with some numerical solutions generated by Hottel's /Hottel and Cohen (1958) and Einstein (1963)/ zonal method shows excellent agreement.

Description: The steady state laminar motion of a viscous, incompressible and binary fluid is studied for a rotating flow in a cylindrical geometry. The mathematical model employed is a cold flow simulation of the fluid mechanics of the light-bulb concept of the gaseous core nuclear engine. A numerical treatment is developed for the rotating flow which includes a description of the nuclear fuel addition. The problem is formulated with the complete Navier-Stokes equations in order to show the interaction between the fuel addition, the main flow, and the boundary layer flow in an accurate manner. The results presented show holdup of the nuclear fuel for the case of steady fuel addition.

Description: Eleven tests were carried out in DLR's high enthalpy tunnel in Goettingen (HEG), Germany, for reservoir conditions ranging from 10 to 23 MJ/kg and a free stream Mach number of approximately 10. A blunted cone model with a cylindrical afterbody (sting) was investigated. To obtain information on the influence of defined parameters on the body back flow, especially of the reacting gas, the heat transfer rate along the body contour was measured with fast response surface thermocouples on the forebody and sensitive thin film heat transfer gauges on the base and sting of the model. Flow visualization with a holographic interferometry system was provided. Tests are described, and a preliminary interpretation of the observed flow effects are given.

Description: Get Away Special (GAS) payload G-093, also called VORTEX (VOrtex Ring Transit EXperiment), is an investigation of the propagation of a vortex ring through a liquid-gas interface in microgravity. This process results in the formation of one or more liquid droplets similar to earth based liquid atomization systems. In the absence of gravity, surface tension effects dominate the drop formation process. The Shuttle's microgravity environment allows the study of the same fluid atomization processes as using a larger drop size than is possible on Earth. This enables detailed experimental studies of the complex flow processes encountered in liquid atomization systems. With VORTEX, deformations in both the vortex ring and the fluid surface will be measured closely for the first time in a parameters range that accurately resembles liquid atomization. The experimental apparatus will record images of the interactions for analysis after the payload has been returned to earth. The current design of the VORTEX payload consists of a fluid test cell with a vortex ring generator, digital imaging system, laser illumination system, computer based controller, batteries for payload power, and an array of housekeeping and payload monitoring sensors. It is a self-contained experiment and will be flown on board the Space Shuttle in a 5 cubic feet GAS canister. The VORTEX Project is entirely run by students at the University of Michigan but is overseen by a faculty advisor acting as the payload customer and the contact person with NASA. This paper summarizes both the technical and programmatic aspects of the VORTEX Project.

Description: This paper focuses on the flight results of the Cryogenic Two-Phase Flight Experiment (CRYOTP), which was a Hitchhiker based experiment that flew on the space shuttle Columbia in March of 1994 (STS-62). CRYOTP tested two new technologies for advanced cryogenic thermal control; the Space Heat Pipe (SHP), which was a constant conductance cryogenic heat pipe, and the Brilliant Eyes Thermal Storage Unit (BETSU), which was a cryogenic phase-change thermal storage device. These two devices were tested independently during the mission. Analysis of the flight data indicated that the SHP was unable to start in either of two attempts, for reasons related to the fluid charge, parasitic heat leaks, and cryocooler capacity. The BETSU test article was successfully operated with more than 250 hours of on-orbit testing including several cooldown cycles and 56 freeze/thaw cycles. Some degradation was observed with the five tactical cryocoolers used as thermal sinks, and one of the cryocoolers failed completely after 331 hours of operation. Post-flight analysis indicated that this problem was most likely due to failure of an electrical controller internal to the unit.

Description: The Capillary Pumped Loop Flight Experiment (CAPL) employs a passive two-phase thermal control system that uses the latent heat of vaporization of ammonia to transfer heat over long distances. CAPL was designed as a prototype of the Earth Observing System (EOS) instrument thermal control systems. The purpose of the mission was to provide validation of the system performance in micro-gravity, prior to implementation on EOS. CAPL was flown on STS-60 in February, 1994, with some unexpected results related to gravitational effects on two-phase systems. Flight test results and post flight investigations will be addressed, along with a brief description of the experiment design.

Description: This paper presents an overview of the Cryogenic Test Bed (CTB) experiments including experiment results, integration techniques used, and lessons learned during integration, test and flight phases of the Cryogenic Heat Pipe Flight Experiment (STS-53) and the Cryogenic Two Phase Flight Experiment (OAST-2, STS-62). We will also discuss the Cryogenic Flexible Diode Heat Pipe (CRYOFD) experiment which will fly in the 1996/97 time frame and the fourth flight of the CTB which will fly in the 1997/98 time frame. The two missions tested two oxygen axially grooved heat pipes, a nitrogen fibrous wick heat pipe and a 2-methylpentane phase change material thermal storage unit. Techniques were found for solving problems with vibration from the cryo-collers transmitted through the compressors and the cold heads, and mounting the heat pipe without introducing parasitic heat leaks. A thermally conductive interface material was selected that would meet the requirements and perform over the temperature range of 55 to 300 K. Problems are discussed with the bi-metallic thermostats used for heater circuit protection and the S-Glass suspension straps originally used to secure the BETSU PCM in the CRYOTP mission. Flight results will be compared to 1-g test results and differences will be discussed.

Description: With the recent focus on the needs of design and applications CFD, research groups have begun to address the traditional bottlenecks of grid generation and surface modeling. Now, a host of emerging technologies promise to shortcut or dramatically simplify the simulation process. This paper discusses the current status of these emerging technologies. It will argue that some tools are already available which can have positive impact on portions of the design cycle. However, in most cases, these tools need to be integrated into specific engineering systems and process cycles to be used effectively. The rapidly maturing status of unstructured and Cartesian approaches for inviscid simulations makes suggests the possibility of highly automated Euler-boundary layer simulations with application to loads estimation and even preliminary design. Similarly, technology is available to link block structured mesh generation algorithms with topology libraries to avoid tedious re-meshing of topologically similar configurations. Work in algorithmic based auto-blocking suggests that domain decomposition and point placement operations in multi-block mesh generation may be properly posed as problems in Computational Geometry, and following this approach may lead to robust algorithmic processes for automatic mesh generation.

Description: The last decade has witnessed a vigorous and sustained research effort on unstructured methods for computational fluid dynamics. Unstructured mesh generators and flow solvers have evolved to the point where they are now in use for design purposes throughout the aerospace industry. In this paper we survey the various mesh types, structured as well as unstructured, and examine their relative strengths and weaknesses. We argue that unstructured methodology does offer the best prospect for the next generation of computational fluid dynamics algorithms.

Description: A Cartesian, cell-based approach for adaptively-refined solutions of the Euler and Navier-Stokes equations in two dimensions is developed and tested. Grids about geometrically complicated bodies are generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, N-sided 'cut' cells are created using polygon-clipping algorithms. The grid is stored in a binary-tree data structure which provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite-volume formulation. The convective terms are upwinded: A gradient-limited, linear reconstruction of the primitive variables is performed, providing input states to an approximate Riemann solver for computing the fluxes between neighboring cells. The more robust of a series of viscous flux functions is used to provide the viscous fluxes at the cell interfaces. Adaptively-refined solutions of the Navier-Stokes equations using the Cartesian, cell-based approach are obtained and compared to theory, experiment and other accepted computational results for a series of low and moderate Reynolds number flows.

Description: Grid related issues of the Chimera overset grid method are discussed in the context of a method of solution and analysis of unsteady three-dimensional viscous flows. The state of maturity of the various pieces of support software required to use the approach is considered. Current limitations of the approach are identified.

Description: This paper presents 'A view from the trenches' on CFD grid generation from a Pratt & Whitney perspective. We anticipate that other organizations have similar views. We focus on customer expectations and the consequent requirements. We enunciate a vision for grid generation, discuss issues that developers must recognize.

Description: This paper presents a perspective on the requirements that Computational Fluid Dynamics (CFD) technology must meet for its effective use in aerospace design. General observations are made on current aerospace design practices and deficiencies are noted that must be rectified for the U.S. aerospace industry to maintain its leadership position in the global marketplace. In order to rectify deficiencies, industry is transitioning to an integrated product and process development (IPPD) environment and design processes are undergoing radical changes. The role of CFD in producing data that design teams need to support flight vehicle development is briefly discussed. An overview of the current state of the art in CFD is given to provide an assessment of strengths and weaknesses of the variety of methods currently available, or under development, to produce aerodynamic data. Effectiveness requirements are examined from a customer/supplier view point with design team as customer and CFD practitioner as supplier. Partnership between the design team and CFD team is identified as an essential requirement for effective use of CFD. Rapid turnaround, reliable accuracy, and affordability are offered as three key requirements that CFD community must address if CFD is to play its rightful role in supporting the IPPD design environment needed to produce high quality yet affordable designs.

Description: The efforts in geometry modeling and grid generation at the NASA Lewis Research Center, as applied to the computational fluid dynamic (CFD) analysis of aeropropulsion systems, are presented. The efforts are mainly characterized by a focus on the analysis of components of an aeropropulsion system, which involve turbulent viscous flow with heat transfer and chemistry. Thus, this discussion will follow that characterization and will sequence through the components of typical propulsion systems consisting of inlets, compressors, combustors, turbines, and nozzles. For each component, some applications of CFD analysis will be presented to show how CFD is used to compute the desired performance information, how geometry modeling and grid generation are performed, and what issues have developed related to geometry modeling and grid generation. The discussion will illustrate the following needs related to geometry modeling and grid generation as observed in aeropropulsion analysis: (1) accurate and efficient resolution of turbulent viscous and chemically-reacting flowfields; (2) easy-to-use interfaces with CAD data for automated grid generation about complex geometries; and (3) automated batch grid generation software for use with design and optimization software.

Description: This viewgraph presentation discusses key features of current combustion system CFD modeling capabilities at GE Aircraft Engines provided by the CONCERT code; CONCERT development history; modeling applied for designing engine combustion systems; modeling applied to improve fundamental understanding; CONCERT3D results for current production combustors; CONCERT3D model of NASA/GE E3 combustor; HYBRID CONCERT CFD/Monte-Carlo modeling approach; and future modeling directions.

Description: Adequate prediction techniques for supersonic, mixing, reacting flows are of great importance in the design and performance analysis of supersonic combustion ramjet (scramjet) engines. Analytical programs for parallel injection flow fields with chemical reaction and turbulent mixing are now available for both single and multiple-jet flows. The application of these analyses to simple flow geometries is discussed, and comparisons also are made with data on the more complex case of multiple-jet, reacting flows. A review is given of Langley investigations of parallel injection flow fields. Among these are single-jet studies of nonreacting, turbulent mixing (H2 in air and H2 in N2), and of reacting turbulent mixing (H2 in air) with both single and multiple jets. Implications of the results of the studies for scramjet fuel injector design are discussed.

Description: A procedure was developed to improve the turn-around time for computational fluid dynamics (CFD) simulations of an inlet-bleed problem involving oblique shock-wave/boundary-layer interactions on a flat plate with bleed into a plenum through one or more circular holes. This procedure is embodied in a preprocessor called AUTOMAT. With AUTOMAT, once data for the geometry and flow conditions have been specified (either interactively or via a namelist), it will automatically generate all input files needed to perform a three-dimensional Navier-Stokes simulation of the prescribed inlet-bleed problem by using the PEGASUS and OVERFLOW codes. The input files automatically generated by AUTOMAT include those for the grid system and those for the initial and boundary conditions. The grid systems automatically generated by AUTOMAT are multi-block structured grids of the overlapping type. Results obtained by using AUTOMAT are presented to illustrate its capability.

Description: The role of Computational Fluid Dynamics (CFD) at Ames Research Center has expanded to address a broad range of aeronautical problems, including wind tunnel support, flight test support, design, and analysis. Balancing the requirements of each new problem against the available resources - software, hardware, time, and expertise - is critical to the effective use of CFD. Several case studies of recent applications highlight the depth of CFD capability at Ames, the tradeoffs involved in various approaches, and lessons learned in the use of CFD as an engineering tool.

Description: When computing the flow around complex three dimensional configurations, the generation of the mesh is the most time consuming part of any calculation. With some meshing technologies this can take of the order of a man month or more. The requirement for a number of design iterations coupled with ever decreasing time allocated for design leads to the need for a significant acceleration of this process. Of the two competing approaches, block-structured and unstructured, only the unstructured approach will allow fully automatic mesh generation directly from a CAD model. Using this approach coupled with the techniques described in this paper, it is possible to reduce the mesh generation time from man months to a few hours on a workstation. The desire to closely couple a CFD code with a design or optimization algorithm requires that the changes to the geometry be performed quickly and in a smooth manner. This need for smoothness necessitates the use of Bezier polynomials in place of the more usual NURBS or cubic splines. A two dimensional Bezier polynomial based design system is described.

Description: A kinetic-theory analysis is made of the flow of a rarefied monatomic gas through a two-dimensional slot connecting two reservoirs. Numerical solutions are obtained by the moment and discrete-ordinate methods. The former method portrays the transition-regime characteristics well but has limitations in the free-molecule regime. The latter method gives accurate results in the free-molecule and slip regimes and bolsters confidence in the accuracy of the transition-regime results. The numerical solution for the mass flux through the slot agrees well with an approximate analytical solution of the moment equations for length-to-width ratios from 6 to 0.5, pressure ratios from 0.8 to 0.1, and Knudsen numbers from 5 to 0.5.

Description: A numerical program was developed to compute transient laminar flows in two dimensions including multicomponent mixing and chemical reaction. The program can compute both incompressible flows and compressible flows at all speeds, and it is applied to describe transient and steady state solutions for low subsonic, coaxial entry, tue flows. Single component, nonreacting flows comprise most of the solutions, but one steady state solution is presented for trace concentration constituents engaging in a second order reaction. Numerical stability was obtained by adding at each calculation point a correction for numerical diffusion errors caused by truncation of the Taylor series used to finite difference the conservation equations. Transient computations were made for fluids initially at rest, then subjected to step velocity inputs that were uniform across each region of the entry plane and were held constant throughout the computation period. For center tube to annulus velocity ratios of 0.5 and 2.0, the bulk fluid in the tube initially moved in plug flow, but strong radial flows developed near the injection plane which moved the fluid into the high shear region between the jets and away from the tube wall.

Description: Aspects of pool boiling are considered, taking into account nucleate boiling, the nucleate boiling mechanism, film boiling, and the transition between nucleate and film boiling. The characteristics of two-phase flow are also investigated, giving attention to two-phase flow parameters and equations, the flow pattern in two-phase flow, the pressure drop in two-phase flow, heat transfer in two-phase flow, two-phase flow dynamics, the boiling crisis in two-phase flow, the critical flow rate, the propagation of the pressure pulse and the sonic velocity in two-phase media, instrumentation for two-phase flow, and geometry and field effects on boiling and two-phase flow. Near-critical fluids are also considered.

Description: It is shown that a previously derived semiempirical equation for describing observed ablation rates of isotropic graphites cannot be applied to low-density flows containing dissociated oxygen. Experimentally determined reaction probabilities of isotropic graphites to molecular and atomic oxygen are used to calculate heat-transfer rates and stagnation-point ablation rates for typical conditions. Integrated mass losses are computed for a group of flight trajectories which start from geosynchronous orbit and enter earth's atmosphere in a skipping motion following near-elliptic decaying orbits. A comparison of the results with those obtained by the equation under question shows excellent agreement for steep trajectories, but large discrepancies for shallow trajectories. The differences are attributed to surface oxidation by atomic oxygen.

Description: When a flow is forced past an obstacle in a rapidly rotating fluid, a Taylor column forms. This is defined by a set of vertical detached shear layers circumscribing the obstacle which provide the smooth transition from an external inviscid potential flow to a stagnant core above the obstacle. For a hemispherical object, the main adjustment takes place in an external E to the 1/4 power layer and an internal E to the 2/7 power layer; here, the nonlinear flow in these layers is investigated. The problem in the E to the 1/4 power layer is identical to a problem occurring in magnetohydrodynamic flow; in addition, some features of the magnetohydrodynamic problem have been resolved. Numerical solutions are obtained for the steady nonlinear external E to the 1/4 power layer flow up to the point where unsteady flow separation from the Taylor column is imminent. The response of the internal E to the 2/7 power layer to the flow in the E to the 1/4 power layer is calculated, and the results suggest that the internal shear layer is unlikely to play any significant role in the separation process

Description: On October 4, 1974, the International Heat Pipe Experiment was launched aboard a Black Brant sounding rocket from White Sands, New Mexico. The flight provided six min of near zero gravity during which a total of ten separate heat pipe experiments was performed. The fifteen heat pipes tested represent some of the latest American and European technology. This flight provided the first reported zero gravity data on cryogenic and flat plate vapor chamber heat pipes. Additionally, valuable design and engineering data were obtained on several other heat pipe configurations. The payload and several of its experiments are discussed.

Description: Experiments in weak-shock dynamics were conducted using a 17-in. diameter shock tube. Weak shocks were generated in air by a compressed nitrogen driver gas; the incident shock waves were brought to a focus by reflecting them from concave cylindrical reflectors at the endwall of the tube. It was found that the behavior of a shock discontinuity at a focus is determined by nonlinear gasdynamic processes. Consideration is also given to nonlinear resonance phenomena, i.e., phenomena associated with oscillatory motion in ducts, with amplitude so large that weak shocks occur. Attention is given to nonlinear resonance in open and closed tubes and to thermal and relaxation effects.

Description: Drop experiments proposed for Spacelab are discussed and an acoustic chamber utilizing the torques and forces produced by acoustic waves excited within the chamber is described. Its operation and how it is being tested for experiments is discussed.

Description: The paper presents a theoretical analysis of the thermal boundary layer induced by an isothermal sphere rotating in an otherwise quiescent fluid. The boundary layer is considered to be laminar and compressible, and the effects of buoyancy and viscous dissipation on torque, heat transfer, and the position of the ideal jet (the plane of impingement of the boundary layer from the Northern and Southern Hemispheres) are taken into account.

Description: A recently developed, potentially high-performance nonarterial wick was extensively tested. This slab wick has an axially varying porosity which can be tailored to match the local stress imposed on the wick. The purpose of the tests was to establish the usefulness of the graded-porosity slab wick at cryogenic temperatures between 110 and 260 K, with methane and ethane as working fluids. For comparison, a homogeneous (i.e., uniform porosity) slab wick was also tested. The tests included: maximum heat pipe performance as a function of fluid inventory, maximum performance as a function of operating temperature, maximum performance as a function of evaporator elevation, and influence of slab wick orientation on performance. The experimental data were compared with theoretical predictions obtained with the GRADE computer program.

Description: A general fourth order differencing scheme is developed and applied to three viscous test problems to verify the accuracy and applicability of the technique. The procedure is atypical since only three nodes are necessary to obtain the desired fourth order accuracy. This is accomplished by a differencing technique which considers the function and all necessary derivatives as unknowns. The relations for these derivatives yield simple tridiagonal equations which can be easily solved. Comparisons of the fourth order results with those computed using second order methods are presented for the test problems and clearly indicate that the accuracy achieved by these fourth order computations is always significantly better than current second order procedures.

Description: The present work considers the iterative solution of a coupled set of difference equations and examines methods that carry successive approximates to a state that is invariant with further iteration and independent of the initial guess. Methods are studied with regard to their efficiency and economy of computer resources. The basic principles of classical relaxation are set forth, with attention confined to linear elliptic equations. This discussion involves the evaluation of the spectral radius that is the magnitude of the eigenvalue with largest modulus. The subject of relaxation is then related to the study of ordinary differential equations and hyperbolic partial differential equations. Problems that occur when linearly dependent eigenvectors appear in the relaxation matrix are discussed, leading to multiply connected eigenvalues in the Jordan canonical form. Finally, a brief survey of relaxation methods used in aerodynamics is given.

Description: A framework is presented for a systematic kinetic theory of turbulence originating from the Liouville equation for the Fourier coefficients of fluid variables. The real and imaginary parts of these Fourier coefficients play the role that particle coordinates (positions and momenta) play in the BBGKY theory. The basic relations of the problem are the incompressible Navier-Stokes equations in two dimensions with zero viscosity, with the probability distributions of Fourier coefficients rather than moments being the basic variables of the theory. A kinetic equation is derived and shown to possess a number of requirements that any reasonable kinetic equation must have: conservation laws, positive-definite spectral densities, and an H-theorem. The major lack in the theory is any reliable information on the relaxation predicted by the complicated linear operator H. Closure of the hierarchy is achieved by the hypothesis that the five-coefficient correlation function is negligible. Problems associated with inclusion of viscosity and external driving forces are discussed.

Description: In developing computer programs to numerically solve the Navier-Stokes equations, the purpose of the computation must be clearly kept in mind. In the Air Force, the purpose is to provide design information on non-linear aerodynamic phenomenon for aircraft that perform throughout the flight corridor. This translates into the requirement for a computer program which can solve the time averaged compressible Navier-Stokes equations (with a turbulence model) in three dimensions for generalized geometries. The intended application of the results then controls the priorities in addressing critical issues. Recurrent problem areas encountered in the study of viscous flow include: (1) grid generation for arbitrary geometry; (2) numerical difficulties; (3) turbulence models; (4) accuracy and efficiency; and (5) smearing of discontinuities.

Description: The computational requirements needed for predicting steady viscous flow over complex configurations are considered. The desired predictions must be made at reasonable expense, require a reasonable amount of storage space, and result in solutions that are sufficiently accurate. The data needed to estimate the cost of Navier-Stokes solutions is not available; therefore, experience with the solution of the three-dimensional boundary layers equations are used to illustrate the needed information and what can be expected for the Navier-Stokes solutions.

Description: All known calculation methods incorporate some sort of turbulence model to reduce the infinite hierarchy of equations, under Reynolds' averaging, to a finite set. All such models suffer from a certain ad hoc nature. A dual structure model was developed wherein the turbulence field is, somewhat arbitrarily, decomposed into large eddies which presumably are dominant contributors to the Reynolds' stress and small eddies which feed on the large eddies as these, in turn feed upon the average flow to gain their energy. These concepts have been developed into a dual approach, one extractive and the other predictive as outlined below.

Description: A critical analysis of available compliant wall data which indicated drag reduction under turbulent boundary layers is presented. Detailed structural dynamic calculations suggest that the surfaces responded in a resonant, rather than a compliant, manner. Alternate explanations are given for drag reductions observed in two classes of experiments: (1) flexible pipe flows and (2) water-backed membranes in air. Analysis indicates that the wall motion for the remaining data is typified by short wavelengths in agreement with the requirements of a possible compliant wall drag reduction mechanism recently suggested by Langley.

Description: For the problem of predicting one-dimensional heat transfer between conducting and radiating mediums by an implicit finite difference method, four different formulations were used to approximate the surface radiation boundary condition while retaining an implicit formulation for the interior temperature nodes. These formulations are an explicit boundary condition, a linearized boundary condition, an iterative boundary condition, and a semi-iterative boundary method. The results of these methods in predicting surface temperature on the space shuttle orbiter thermal protection system model under a variety of heating rates were compared. The iterative technique caused the surface temperature to be bounded at each step. While the linearized and explicit methods were generally more efficient, the iterative and semi-iterative techniques provided a realistic surface temperature response without requiring step size control techniques.

Description: Turbulent shear stress and direct turbulent total heat-flux measurements have been made across a nonadiabatic, zero pressure gradient, hypersonic boundary layer by using specially designed hot-wire probes free of strain-gauging and wire oscillation. Heat-flux measurements were in reasonably good agreement with values obtained by integrating the energy equation using measured profiles of velocity and temperature. The shear-stress values deduced from the measurements, by assuming zero correlation of velocity and pressure fluctuations, were lower than the values obtained by integrating the momentum equation. Statistical properties of the cross-correlations are similar to corresponding incompressible measurements at approximately the same momentum-thickness Reynolds number.

Description: The phase change coating technique is used to obtain peak heating measurements in shock interference flow regions with high surface shear and heating. This technique provides heat transfer coefficients which are determined by measuring the time for a point on the surface to reach the phase change temperature of the thin fusible coating. Measurements were conducted on a 5.08-cm diameter hemisphere-cylinder made of silica based epoxy at Mach 6 for free stream Reynolds numbers of 3.3 to 25.6 million per meter. A sketch of the shock interference pattern produced by a flat plate shock generator is included. Heating data obtained on a 5.08-cm diameter stainless steel hemispherical model instrumented with thermocouples is presented for the purpose of comparing the phase change technique with the thermocouple-calorimeter technique.

Description: The laminar free convection flow from a right circular cone with prescribed uniform wall flux condition is studied. The governing boundary-layer equations are analyzed by the technique of similarity transformation. Numerical solutions to the transformed equations are given for Prandtl numbers 0.72, 1, 2, 4, 6, 8, 10, and 100. Expressions for both wall temperature distribution and wall skin friction distribution at Prandtl number tending to infinity are also presented.

Description: Although the goals and techniques of computational aerodynamics and computational fluid dynamics differ, advancement in the physical and mathematical aspects of the latter are required for progress in aerodynamic computation. The most attractive approach is the use of hybrid methods where both the equations treated and the solution algorithms reflect the local character of the flow. A working general turbulence model that is only peripherally related to the availability of large fast computers would provide a significant breakthrough in computational aerodynamics. There is no unanimity of opinion as to what may be the optimum algorithm or family of algorithms in the next decade. While it is premature to develop an optimum processor, such a machine dedicated to study the structure of solutions to the three-dimensional time-dependent Navier-Stokes equations and to the computability of turbulence would be very valuable.

Description: Although significant advances have been made in the simulation of two-dimensional compressible laminar viscous flows by numerically solving the compressible Navier-Stokes (N.S.) equations, problem areas still remain to be solved before viscous flows requiring solution of the compressible N.S. equations can be efficiently and accurately simulated for flows of aerodynamic interest. These problem areas include turbulence (three-dimensional character), complex geometry, flow unsteadiness, placement of artificial boundaries relative to solid boundaries, specification of boundary conditions, and large flow gradients near surfaces and in the vicinity of shock waves for supersonic flows.

Description: The problem of designing the wing-fuselage configuration of an advanced transonic commercial airliner and the optimization of a supercruiser fighter are sketched, pointing out the essential fluid mechanical phenomena that play an important role. Such problems suggest that for a numerical method to be useful, it must be able to treat highly three dimensional turbulent separations, flows with jet engine exhausts, and complex vehicle configurations. Weaknesses of the two principal tools of the aerodynamicist, the wind tunnel and the computer, suggest a complementing combined use of these tools, which is illustrated by the case of the transonic wing-fuselage design. The anticipated difficulties in developing an adequate turbulent transport model suggest that such an approach may have to suffice for an extended period. On a longer term, experimentation of turbulent transport in meaningful cases must be intensified to provide a data base for both modeling and theory validation purposes.

Description: The results of a first order perfect gas correction for the effects of the boundary layer formation within expansion tubes with nozzles are presented. The analytical model developed to describe the boundary layer formation within the expansion tube and an expansion nozzle located at the end of the acceleration tube is based on the Karman integral equations. The results of this analytical model are compared with experimental data from an expansion diffuser. The model provides a useful tool for the preliminary design of nozzles for such facilities.

Description: In this paper the capabilities of an automated CFD system which is currently available at NLR are demonstrated. Transonic flow around the AS28G wing/body configuration and hypersonic flow through a generic three-dimensional mixed-compression airbreathing inlet are simulated. An assessment of the level of automation of the current CFD-system is made. The problem-turnaround time lies within the order of a week for both applications.

Description: Detailed simulations of viscous flows in complicated geometries pose a significant challenge to current capabilities of Computational Fluid Dynamics (CFD). To enable routine application of CFD to this class of problems, advanced methodologies are required that employ (a) automated grid generation, (b) adaptivity, (c) accurate discretizations and efficient solvers, and (d) advanced software techniques. Each of these ingredients contributes to increased accuracy, efficiency (in terms of human effort and computer time), and/or reliability of CFD software. In the long run, methodologies employing structured grid systems will remain a viable choice for routine simulation of flows in complex geometries only if genuinely automatic grid generation techniques for structured grids can be developed and if adaptivity is employed more routinely. More research in both these areas is urgently needed.

Description: A discussion of the strengths and weaknesses of overset composite grid and solution technology is given, along with a sampling of current work in the area. Major trends are identified, and the observation is made that generalized and hybridized overset methods provide a natural framework for combining disparate mesh types and physics models. Because of this, the author concludes that overset methods will be the foundation for the general purpose computational fluid dynamics programs of the future.

Description: The status of CFD methods based on the use of block-structured grids for analyzing viscous flows over complex configurations is examined. The objective of the present study is to make a realistic assessment of the usability of such grids for routine computations typically encountered in the aerospace industry. It is recognized at the very outset that the total turnaround time, from the moment the configuration is identified until the computational results have been obtained and postprocessed, is more important than just the computational time. Pertinent examples will be cited to demonstrate the feasibility of solving flow over practical configurations of current interest on block-structured grids.

Description: This viewgraph presentation discusses turbulence modeling requirements, development philosophy, and approach; two major areas of concentration (high speed and low speed turbulence modeling); high speed turbulence modeling; compressibility effects; turbulence models adapted to USA code; M = 9.2 flat plate flow; Mach 7.05 flow over axisymmetric flare; Mach 8.6 flow over cold wall edge; low speed turbulence modeling; turbulence models being assessed; turbulence model deck structure and integration with Navier-Stokes solver; nonlinear algebraic-stress model; rotation modified k-epsilon model; and Reynolds stress model.

Description: This viewgraph presentation covers gas turbine combustor flow physics, turbulence model investigations, turbulent combustion modeling, and present status and future needs.

Description: This viewgraph presentation discusses geometry and flow configuration, effect of y+ on heat transfer computations, standard and extended k-epsilon turbulence model results with wall function, low-Re model results (the Lam-Bremhorst model without wall function), a criterion for flow reversal in a radially rotating square duct, and a summary.

Description: This viewgraph presentation demonstrates that computationally efficient k-l and k-kl turbulence models have been developed and implemented at Lockheed Fort Worth Company. Many years of experience have been gained applying two equation turbulence models to complex three-dimensional flows for design and analysis.

Description: The objective of this viewgraph presentation is to evaluate turbulence models for integrated aircraft components such as the forebody, wing, inlet, diffuser, nozzle, and afterbody. The one-equation models have replaced the algebraic models as the baseline turbulence models. The Spalart-Allmaras one-equation model consistently performs better than the Baldwin-Barth model, particularly in the log-layer and free shear layers. Also, the Sparlart-Allmaras model is not grid dependent like the Baldwin-Barth model. No general turbulence model exists for all engineering applications. The Spalart-Allmaras one-equation model and the Chien k-epsilon models are the preferred turbulence models. Although the two-equation models often better predict the flow field, they may take from two to five times the CPU time. Future directions are in further benchmarking the Menter blended k-w/k-epsilon and algorithmic improvements to reduce CPU time of the two-equation model.

Description: This viewgraph presentation summarizes some CFD experience at GE Aircraft Engines for flows in the primary gaspath of a gas turbine engine and in turbine blade cooling passages. It is concluded that application of the standard k-epsilon turbulence model with wall functions is not adequate for accurate CFD simulation of aerodynamic performance and heat transfer in the primary gas path of a gas turbine engine. New models are required in the near-wall region which include more physics than wall functions. The two-layer modeling approach appears attractive because of its computational complexity. In addition, improved CFD simulation of film cooling and turbine blade internal cooling passages will require anisotropic turbulence models. New turbulence models must be practical in order to have a significant impact on the engine design process. A coordinated turbulence modeling effort between NASA centers would be beneficial to the gas turbine industry.

Description: Program goals at the Center for Modeling of Turbulence and Transition (CMOTT), NASA Lewis Research Center, are (1) to develop reliable turbulence (including bypass transition) and combustion models for complex flows in propulsion systems and (2) to integrate developed models into deliverable CFD tools for propulsion systems in collaboration with industry. This viewgraph presentation covers the following topics: development of turbulence and combustion models; collaboration with industry and technology transfer; isotropic eddy viscosity models; algebraic Reynolds stress models; scalar turbulence models; second order closure models; multiple scale k-epsilon models; and PDF modeling of turbulent reacting flows.

Description: An assessment of two unstructured methods is presented in this paper. A tetrahedral unstructured method USM3D, developed at NASA Langley Research Center is compared to a Cartesian unstructured method, SPLITFLOW, developed at Lockheed Fort Worth Company. USM3D is an upwind finite volume solver that accepts grids generated primarily from the Vgrid grid generator. SPLITFLOW combines an unstructured grid generator with an implicit flow solver in one package. Both methods are exercised on three test cases, a wing, and a wing body, and a fully expanded nozzle. The results for the first two runs are included here and compared to the structured grid method TEAM and to available test data. On each test case, the set up procedure are described, including any difficulties that were encountered. Detailed descriptions of the solvers are not included in this paper.

Description: The past ten years have seen steady progress in surface modeling procedures, and wholesale changes in grid generation technology. Today, it seems fair to state that a satisfactory grid can be developed to model nearly any configuration of interest. The issues at present focus on operational concerns such as cost and quality. Continuing evolution of the engineering process is placing new demands on the technologies of surface modeling and grid generation. In the evolution toward a multidisciplinary analysis-bascd design environment, methods developed for Computational Fluid Dynamics are finding acceptance in many additional applications. These two trends, the normal evolution of the process and a watershed shift toward concurrent and multidisciplinary analysis, will be considered in assessing current capabilities and needed technological improvements.

Description: This viewgraph presentation discusses what models are used in this package and what their advantages and disadvantages are, how the probability density function (PDF) model is implemented and the features of the program, and what can be expected in the future from the NASA Lewis PDF code.

Description: This viewgraph presentation discusses an extension of the probability density function (PDF) method to the modeling of spray flames to evaluate the limitations and capabilities of this method in the modeling of gas-turbine combustor flows. The comparisons show that the general features of the flowfield are correctly predicted by the present solution procedure. The present solution appears to provide a better representation of the temperature field, particularly, in the reverse-velocity zone. The overpredictions in the centerline velocity could be attributed to the following reasons: (1) the use of k-epsilon turbulence model is known to be less precise in highly swirling flows and (2) the swirl number used here is reported to be estimated rather than measured.

Description: Viewgraphs are presented on computation of turbulent combustion, governing equations, closure problem, PDF modeling of turbulent reactive flows, validation cases, current projects, and collaboration with industry and technology transfer.

Description: Viewgraphs are presented on modeling turbulent reacting flows, regimes of turbulent combustion, regimes of premixed and regimes of non-premixed turbulent combustion, chemical closure models, flamelet model, conditional moment closure (CMC), NO(x) emissions from turbulent H2 jet flames, probability density function (PDF), departures from chemical equilibrium, mixing models for PDF methods, comparison of predicted and measured H2O mass fractions in turbulent nonpremixed jet flames, experimental evidence of preferential diffusion in turbulent jet flames, and computation of turbulent reacting flows.

Description: This viewgraph presentation discusses project description, turbulence models, and computational engine and results for second-order closures for compressible turbulence.

Description: This viewgraph presentation gives a profile of Advanced Scientific Computing (ASC) Ltd., applications, clients and clients' needs, ASC's directions, and how the Center for Modeling of Turbulence and Transition (CMOTT) can help.

Description: This viewgraph presentation discusses the following: STAR-CD computational features; STAR-CD turbulence models; common features of industrial complex flows; industry-specific CFD development requirements; applications and experiences of industrial complex flows, including flow in rotating disc cavities, diffusion hole film cooling, internal blade cooling, and external car aerodynamics; and conclusions on turbulence modeling needs.

Description: This viewgraph presentation provides a brief review of two-equation eddy-viscosity models (TEM's) from the perspective of applied CFD. It provides objective assessment of both well-known and newer models, compares model predictions from various TEM's with experiments, identifies sources of modeling error and gives historical perspective of their effects on model performance and assessment, and recommends directions for future research on TEM's.

Description: This viewgraph presentation discusses the following: introduction to CFD Research Corporation; experiences with two-equation models - models used, numerical difficulties, validation and applications, and strengths and weaknesses; and answers to three questions posed by the workshop organizing committee - what are your customers telling you, what are you doing in-house, and how can NASA-CMOTT (Center for Modeling of Turbulence and Transition) help.

Description: This viewgraph presentation concludes that a Monte Carlo probability density function (PDF) solution successfully couples with an existing finite volume code; PDF solution method applied to turbulent reacting flows shows good agreement with data; and PDF methods must be run on parallel machines for practical use.

Description: This viewgraph presentation discusses (1) turbulence modeling: challenges in turbulence modeling, desirable attributes of turbulence models, turbulence models in FLUENT, and examples using FLUENT; and (2) combustion modeling: turbulence-chemistry interaction and FLUENT equilibrium model. As of now, three turbulence models are provided: the conventional k-epsilon model, the renormalization group model, and the Reynolds-stress model. The renormalization group k-epsilon model has broadened the range of applicability of two-equation turbulence models. The Reynolds-stress model has proved useful for strongly anisotropic flows such as those encountered in cyclones, swirlers, and combustors. Issues remain, such as near-wall closure, with all classes of models.

Description: This viewgraph presentation discusses joint velocity-scalar PDF method; turbulent combustion modeling issues for gas turbine combustors; PDF calculations for a recirculating flow; stochastic dissipation model; joint PDF calculations for swirling flows; spray calculations; reduced kinetics/manifold methods; parallel processing; and joint PDF focus areas.

Description: An algorithm has been developed for time-dependent forced convective diffusion-reaction having convection by a recirculating flow field within the drop that is hydrodynamically coupled at the interface with a convective external flow field that at infinity becomes a uniform free-streaming flow. The concentration field inside the droplet is likewise coupled with that outside by boundary conditions at the interface. A chemical reaction can take place either inside or outside the droplet, or reactions can take place in both phases. The algorithm has been implemented, and for comparison results are shown here for the case of no reaction in either phase and for the case of an external first order reaction, both for unsteady behavior. For pure interphase mass transfer, concentration isocontours, local and average Sherwood numbers, and average droplet concentrations have been obtained as a function of the physical properties and external flow field. For mass transfer enhanced by an external reaction, in addition to the above forms of results, we present the enhancement factor, with the results now also depending upon the (dimensionless) rate of reaction.

Description: The application of spectral methods, using a Chebyshev collocation scheme, to solve hydrodynamic stability problems is demonstrated on the Benard problem. Implementation of the Chebyshev collocation formulation is described. The performance of the spectral scheme is compared with that of a 2nd order finite difference scheme. An exact solution to the Marangoni-Benard problem is used to evaluate the performance of both schemes. The error of the spectral scheme is at least seven orders of magnitude smaller than finite difference error for a grid resolution of N = 15 (number of points used). The performance of the spectral formulation far exceeded the performance of the finite difference formulation for this problem. The spectral scheme required only slightly more effort to set up than the 2nd order finite difference scheme. This suggests that the spectral scheme may actually be faster to implement than higher order finite difference schemes.

Description: 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.