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The research interests of the staff of the Fluid Dynamics Research Branch in the general area of vortex flows are summarized. A major factor in the development of enchanced maneuverability and reduced drag by aerodynamic means is the use of effective vortex control devices. The key to control is the use of emerging computational tools for predicting viscous fluid flow in close coordination with fundamental experiments. In fact, the extremely complex flow fields resulting from numerical solutions to boundary value problems based on the Navier-Stokes equations requires an intimate relationship between computation and experiment. The field of vortex flows is important in so many practical areas that a concerted effort in this area is justified. A brief background of the research activity undertaken is presented, including a proposed classification of the research areas. The classification makes a distinction between issues related to vortex formation and structure, and work on vortex interactions and evolution. Examples of current research results are provided, along with references where available. Based upon the current status of research and planning, speculation on future research directions of the group is also given.

An additional approach is being taken to address the problem of how to decide where to truncate spherical harmonic representations of geomagnetic data. The idea is to simply evaluate some aspect of interest at successively higher levels of truncation and then to chose that value of truncation level (N) which gives the most reasonable appearance of convergence. The preliminary determination of the onset of relative numerical stability at a truncation level of N=7 in two independent studies is thought to be a potentially significant result of practical value for field modeling. It requires further substantiation and explanation before dissemination.

A computational fluid dynamics study was conducted to evaluate the feasibility of the variable-pitch split-blade supersonic fan concept. This fan configuration was conceived as a means to enable a supersonic fan to switch from the supersonic through-flow type of operation at high speeds to a conventional fan with subsonic inflow and outflow at low speeds. During this off-design, low-speed mode of operation, the fan would operate with a substantial static pressure rise across the blade row like a conventional transonic fan; the front (variable-pitch) blade would be aligned with the incoming flow, and the aft blade would remain fixed in the position set by the supersonic design conditions. Because of these geometrical features, this low speed configuration would inherently have a large amount of turning and, thereby, would have the potential for a large total pressure increase in a single stage. Such a high-turning blade configuration is prone to flow separation; it was hoped that the channeling of the flow between the blades would act like a slotted wing and help alleviate this problem. A total of 20 blade configurations representing various supersonic and transonic configurations were evaluated using a Navier Stokes CFD program called ADAPTNS because of its adaptive grid features. The flow fields generated by this computational procedure were processed by another data reduction program which calculated average flow properties and simulated fan performance. These results were employed to make quantitative comparisons and evaluations of blade performance. The supersonic split-blade configurations generated performance comparable to a single-blade supersonic, through-flow fan configuration. Simulated rotor total pressure ratios of the order of 2.5 or better were achieved for Mach 2.0 inflow conditions. The corresponding fan efficiencies were approximately 75 percent or better. The transonic split-blade configurations having large amounts of turning were able to generate large amounts of total turning and achieve simulated total pressure ratios of 3.0 or better with subsonic inflow conditions. These configurations had large losses and low fan efficiencies in the 70's percent. They had large separated regions and low velocity wakes. Additional turning and diffusion of this flow in a subsequent stator row would probably be very inefficient. The high total pressure ratios indicated by the rotor performance would be substantially reduced by the stators, and the stage efficiency would be substantially lower. Such performance leaves this dual-mode fan concept less attractive than originally postulated.

A versatile planar reacting shear layer facility is constructed at NASA-Lewis. The research objectives, as well as design, instrumentations and the operational procedures developed for the system are described. The fundamental governing equations and the type of quantitative information that are needed from experiments are described. Additionally, a review of earlier work is presented. Whenever appropriate, comparisons are made with similar systems in other facilities and the main differences are described. Finally, the nonintrusive measurement techniques (PLIF, PMS, LDV, and Schlieren photography) and the type of experiments that are planned are described.

Accomplishments to date were summarized in three parts submitted for publication. Goddard models and MAGSAT data were used heavily in the investigation which address: (1) the sensitivity of selected geomagnetic properties to truncation level of spherical harmonic expansions; (2) the pole strength of the Earth from MAGSAT, and magnetic determination of the core radius; and (3) frozen flux upper limits to the MAGSAT geomagnetic coefficients and relative multipole indices for Earth.

A brief survey is presented of several time dependent numerical methods for multi-dimensional fluid problems in use at the Los Alamos Scientific Laboratory. Emphasis is placed on the variety of problems which can be treated, as well as on the limitations of the methods used to treat them. No details are given of the specific numerical procedures. Three examples are presented. The first, the interaction of a shock with a bubble, illustrates a type of mixed Eulerian and Lagrangian method of calculation. The second example, a shock moving down a bent channel, illustrates a pure Lagrangian calculation. The third example illustrates an incompressible fluid calculation based on a pure Eulerian method. In the second two examples comparisons are made with experimental data.

The role of experiment in the development of Computational Fluid Dynamics (CFD) for aerodynamic flow field prediction is discussed. Requirements for code verification from two sources that pace the development of CFD are described for: (1) development of adequate flow modeling, and (2) establishment of confidence in the use of CFD to predict complex flows. The types of data needed and their accuracy differs in detail and scope and leads to definite wind tunnel requirements. Examples of testing to assess and develop turbulence models, and to verify code development, are used to establish future wind tunnel testing requirements. Versatility, appropriate scale and speed range, accessibility for nonintrusive instrumentation, computerized data systems, and dedicated use for verification were among the more important requirements identified.

The possible utilization of the zero gravity resource for studies in a variety of fluid dynamics and fluid-dynamic related problems was investigated. A group of experiments are discussed and described in detail; these include experiments in the areas of geophysical fluid models, fluid dynamics, mass transfer processes, electrokinetic separation of large particles, and biophysical and physiological areas.

Marshall Space Flight Center (MSFC) is the National Aeronautics and Space Administration (NASA)-designated center for the development of space launch systems. MSFC is particularly known for propulsion system development. Many engineering skills and technical disciplines are needed to accomplish this mission. This presentation will focus on the work of the Fluid Dynamics Branch (ER42). ER42 resides in the Propulsion Systems Department at MSFC. The branch is responsible for all aspects of the discipline of fluid dynamics applied to propulsion or propulsion-induced loads and environments. This work begins with design trades and parametric studies, and continues through development, risk assessment, anomaly investigation and resolution, and failure investigations. Applications include the propellant delivery system including the main propulsion system (MPS) and turbomachinery; combustion devices for liquid engines and solid rocket motors; coupled systems; and launch environments. An advantage of the branch is that it is neither analysis nor test centric, but discipline centric. Fluid dynamics assessments are made by analysis, from lumped parameter modeling through unsteady computational fluid dynamics (CFD); testing, which can be cold flow or hot fire; or a combination of analysis and testing. Integration of all discipline methods into one branch enables efficient and accurate support to the projects. To accomplish this work, the branch currently employs approximately fifty engineers divided into four teams -- Propellant Delivery CFD, Combustion Driven Flows CFD, Unsteady and Experimental Flows, and Acoustics and Stability. This discussion will highlight some of the work performed in the branch and the direction in which the branch is headed.

Marshall Space Flight Center (MSFC) is the National Aeronautics and Space Administration (NASA)-designated center for the development of space launch systems. MSFC is particularly known for propulsion system development. Many engineering skills and technical disciplines are needed to accomplish this mission. This presentation will focus on the work of the Fluid Dynamics Branch (ER42). ER42 resides in the Propulsion Systems Department at MSFC. The branch is responsible for all aspects of the discipline of fluid dynamics applied to propulsion or propulsion-induced loads and environments. This work begins with design trades and parametric studies, and continues through development, risk assessment, anomaly investigation and resolution, and failure investigations. Applications include the propellant delivery system including the main propulsion system (MPS) and turbomachinery; combustion devices for liquid engines and solid rocket motors; coupled systems; and launch environments. An advantage of the branch is that it is neither analysis nor test centric, but discipline centric. Fluid dynamics assessments are made by analysis, from lumped parameter modeling through unsteady computational fluid dynamics (CFD); testing, which can be cold flow or hot fire; or a combination of analysis and testing. Integration of all discipline methods into one branch enables efficient and accurate support to the projects. To accomplish this work, the branch currently employs approximately fifty engineers divided into four teams -- Propellant Delivery CFD, Combustion Driven Flows CFD, Unsteady and Experimental Flows, and Acoustics and Stability. This discussion will highlight some of the work performed in the branch and the direction in which the branch is headed.

Few comments are given to clarify some issues of Weyssenhoff fluid in the Einstein-Cartan gravity.

Direct photon emission in heavy-ion collisions is calculated within a relativistic micro+macro hybrid model and compared to the microscopic transport model UrQMD. In the hybrid approach, the high-density part of the collision is calculated by an ideal 3+1-dimensional hydrodynamic calculation, while the early (pre-equilibrium-) and late (rescattering-) phase are calculated with the transport model. Different scenarios of the transition from the macroscopic description to the transport model description and their effects are studied. The calculations are compared to measurements by the WA98-collaboration and predictions for the future CBM-experiment are made.

Thirty-six papers were presented and are compiled in AGARD Conference Proceedings CP-235, published in November 1978. This report consists of an evaluation of the symposium and the presentations made in the areas of: Wind Tunnel Techniques, Flight Testing Techniques, Analytical Techniques, Motion Analyses and Nonlinear Formulations, and Sensitivity and Simulator Studies. In addition, a workshop session and roundtable discussion on the presentations are discussed. Conclusions on the state of the art and recommendations for future activity complete the evaluation.

Time series measurements of shallow-water waves and fluid-mud density variations, taken simultaneously with tide elevation and suspended sediment data, indicate that wave/fluid-mud interactions in the nearshore may be largely responsible for the present-day accumulation of fine-grained sediment on the open, unprotected coast of northeastern South America. Results of field experiments conducted along the central Surinam coast show that accumulations of fluid mud, which can be found up to 1.5 m thick on western flanks of migrating shore-attached mudbanks, affect incoming swell by changing their form from sinusoidal to solitary-like and by preventing wave breaking except for occasional spilling. As long-period swell (T = 12-16 sec) propagates over shallow banks of fluid mud, the wave height to water depth ratio remains nearly constant at 0.23; the steady decrease in wave height with shoaling water depth indicates that substantial amounts of wave energy are lost to a fluid-mud bottom even though breaking does not occur. Using the concept of wave-associated currents, it has been shown, in taking angle of wave approach, average observed concentration of sediment in suspension, and net drift as given by solitary wave theory, that volume transports can be explained by waves alone. If a hypothesis of mud transport by solitary waves is accepted, then the continuous shoreward transport of suspended fluid mud, combined with the high rate of wave energy dissipation, explains in part the ability of muddy coasts to protect their shorelines.

Time series measurements of shallow-water waves and fluid-mud density variations, taken simultaneously with tide elevation and suspended sediment data, indicate that wave/fluid-mud interactions in the nearshore may be largely responsible for the present-day accumulation of fine-grained sediment on the open, unprotected coast of northeastern South America. Results of field experiments conducted along the central Surinam coast show that accumulations of fluid mud, which can be found up to 1.5 m thick on western flanks of migrating shore-attached mudbanks, affect incoming swell by changing their form from sinusoidal to solitary-like and by preventing wave breaking except for occasional spilling. As long-period swell (T = 12-16 sec) propagates over shallow banks of fluid mud, the wave height to water depth ratio remains nearly constant at 0.23; the steady decrease in wave height with shoaling water depth indicates that substantial amounts of wave energy are lost to a fluid-mud bottom even though breaking does not occur. Using the concept of wave-associated currents, it has been shown, in taking angle of wave approach, average observed concentration of sediment in suspension, and net drift as given by solitary wave theory, that volume transports can be explained by waves alone. If a hypothesis of mud transport by solitary waves is accepted, then the continuous shoreward transport of suspended fluid mud, combined with the high rate of wave energy dissipation, explains in part the ability of muddy coasts to protect their shorelines.

195 p. 22 cm

The short term purpose of this research is to present a research plan and a roadmap developed for strategic research for the Office of Biological and Physical Research and the long term purpose is to conduct necessary ground-based and space-flight low gravity experiments, complemented by analyses, resulting in a documented framework for parameter prediction of needed by designers. This paper is presented in viewgraph form.

Contents: Transonic Wing and Far Field Test Data on a High Aspect Ratio Transport Wing for Three Dimensional Computational Method Evaluation; Transonic Wing and Far Field Test Data on a Moderate Aspect Ratio Wing for Three Dimensional Computational Method Evaluation; Pressure Distributions Measured on Research Wing M100 Mounted on an Axisymmetric Body; Pressure Distribution Measured on Research Wing M86 Mounted on an Axisymmetric Body; and Pressure Distribution on a Swept Wing Aircraft in Flight.

An overview of computational fluid dynamics (CFD) activities at the Langley Research Center is given. The role of supercomputers in CFD research, algorithm development, multigrid approaches to computational fluid flows, aerodynamics computer programs, computational grid generation, turbulence research, and studies of rarefied gas flows are among the topics that are briefly surveyed.

The results of an investigation into the feasibility of using the MPP for direct and large eddy simulations of the Navier-Stokes equations is presented. A major part of this study was devoted to the implementation of two of the standard numerical algorithms for CFD. These implementations were not run on the Massively Parallel Processor (MPP) since the machine delivered to NASA Goddard does not have sufficient capacity. Instead, a detailed implementation plan was designed and from these were derived estimates of the time and space requirements of the algorithms on a suitably configured MPP. In addition, other issues related to the practical implementation of these algorithms on an MPP-like architecture were considered; namely, adaptive grid generation, zonal boundary conditions, the table lookup problem, and the software interface. Performance estimates show that the architectural components of the MPP, the Staging Memory and the Array Unit, appear to be well suited to the numerical algorithms of CFD. This combined with the prospect of building a faster and larger MMP-like machine holds the promise of achieving sustained gigaflop rates that are required for the numerical simulations in CFD.

Methods of computational fluid dynamics were applied to simulate the aerodynamics within the turbine flowpath of a turbine-based combined-cycle propulsion system during inlet mode transition at Mach 4. Inlet mode transition involved the rotation of a splitter cowl to close the turbine flowpath to allow the full operation of a parallel dual-mode ramjet/scramjet flowpath. Steady-state simulations were performed at splitter cowl positions of 0deg, -2deg, -4deg, and -5.7deg, at which the turbine flowpath was closed half way. The simulations satisfied one objective of providing a greater understanding of the flow during inlet mode transition. Comparisons of the simulation results with wind-tunnel test data addressed another objective of assessing the applicability of the simulation methods for simulating inlet mode transition. The simulations showed that inlet mode transition could occur in a stable manner and that accurate modeling of the interactions among the shock waves, boundary layers, and porous bleed regions was critical for evaluating the inlet static and total pressures, bleed flow rates, and bleed plenum pressures. The simulations compared well with some of the wind-tunnel data, but uncertainties in both the windtunnel data and simulations prevented a formal evaluation of the accuracy of the simulation methods.

The physics of double diffusion and the role that it plays in the ocean provided the central theme for the 1996 summer program in Geophysical Fluid Dynamics at the Woods Hole Oceanographic Institution. Lectures and seminars given by staff and visitors surveyed observations, laboratory experiments and theoretical models of double diffusive phenomena. Several lectures dealt with the related phenomena of thermal convection in layered media, the dynamics of binary fluids, viscoelastic convection and magnetoconvection. Research projects by the fellows included experiments with double diffusion in a slot, work on the formation and evolution of staircases, double diffusion in stars and the interaction between convection and radiation. This volume includes write-ups of the principal lectures, reports of the fellows' research projects and abstracts of some of the seminars. A list of presentations and a bibliography may be found at the back of the volume.

The overall goal of this project is study convective heat transfer and fluid-mechanics in a concavely curved turbulent boundary layer. The objective is to identify the mechanisms whereby concavity increases surface heat transfer. Progress during the past year has centered on the recently added goal of studying the combined effects of moderate levels of grid-generated turbulence and concave curvature. Overall results from the fluid-mechanics section of the project are that grid-generated turbulence increases the skin friction, but does not alter the near-wall mean velocity scaling or the near-wall levels of the velocity fluctuations. The heat transfer measurements are showing that the Stanton number is increased by the grid-generated turbulence with the combined effects of curvature and the additional turbulence producing the largest increase. Keywords: Heat transfer, Turbulent boundary layers, Adaptive grids.

Abstracts

This memorandum reviews the major developments in computational fluid dynamics. The present and future capabilities of numerical simulations are assessed to determine the demands that they will place on available computer power. The impact that these developments will have on the use of computational fluid dynamics at ARL is considered together with their implications for the provision of new computers at ARL.

Contents: Dynamics of Ideal Fluids; Compressibility and Viscosity; Von Neumann's Influence; Potential Flows; Sound Waves; Nonlinear One-Dimensional Waves; Incompressible Viscous Flows; Lagrangian Dynamical Systems; Conformal Maps and Potential Flows; Fourier Analysis Navier-Stokes Equations; Molecular Models of Matter; 'Courant' Stability Conditions and Amplication Matrices; and Two Dimensional Airfoil Theory.

The ability to predict safe and effective release of air-launched weapons carried internally in a weapon bay or externally on a pylon/rack is required by the Safety Committee before approval is given for a flight test to validate various store separation characterisitics. Because of the novel conditions attendant to test and evaluation (T and E) testing, only limited experimental and flight data are available beforehand to aid in assessing safe weapon release. Computational methods have the potential of resolving, in a timely manner, the store separation problem without these weaknesses. Two areas need to be addressed. First, an accurate computational algorithm is needed to minimize numerical uncertainty as the store is tracked in time. Second, correct physical models must be implemented to model the moving store, including grid capability to provide accurate numerical flowfield predictions for situation of weapon carriage and release from an internal weapons bay. Based on a truly multidimensional unrestricted Essentially Non-oscillatory (ENO) scheme, a new UNIVERSE (Unification of essentially Non-oscillatory Interpolation techniques with a geometrically VERSatilE) series code has been developed at the Rockwell International Science Center. The new ENO concepts are state-of-the-art interpolation schemes that work with arbitrary cell shapes. For example, hexahedral, triangular prism, and tetrahedral elements (conservation cells) can all be covered in a unified manner. This also implies that both structured and unstructured bookkeeping schemes can be employed to conveniently treat complex topologies. A new suite of fully automatic flexible-cell mesh generation methods is also being developed for integration with the new series.

Selected information is presented from an assemblage of reports and publications on heat transfer and fluid dynamics with direct applicability to oxygen systems. For each document cited, an abstract has been prepared together with key words and a listing of most important references found in the document. Additionally, an author index, a subject index, and a key word index have been provided to simplify the retrieval of specific information from this work. In each subject area - e.g., boiling heat transfer - the individual citations are listed alphabetically by first author, with review papers dually noted under the appropriate subject category and under review papers. Of the documents reviewed and evaluated for inclusion in this publication, coverage of existing information directly concerned with oxygen was given primary emphasis. However, work not specifically oxygen-designated but considered applicable to oxygen by the reviewer e.g., a two-phase friction factor correlation derived from nitrogen experiments is occasionally given where no actual oxygen data exist, as an aid to the reader. Approximately 130 abstracts are listed.

Automatic differentiation (AD) is a powerful computational method that provides for computing exact sensitivity derivatives (SD) from existing computer programs for multidisciplinary design optimization (MDO) or in sensitivity analysis. A pre-compiler AD tool for FORTRAN programs called ADIFOR has been developed. The ADIFOR tool has been easily and quickly applied by NASA Langley researchers to assess the feasibility and computational impact of AD in MDO with several different FORTRAN programs. These include a state-of-the-art three dimensional multigrid Navier-Stokes flow solver for wings or aircraft configurations in transonic turbulent flow. With ADIFOR the user specifies sets of independent and dependent variables with an existing computer code. ADIFOR then traces the dependency path throughout the code, applies the chain rule to formulate derivative expressions, and generates new code to compute the required SD matrix. The resulting codes have been verified to compute exact non-geometric and geometric SD for a variety of cases. in less time than is required to compute the SD matrix using centered divided differences.

B-spline functions are bases for piecewise polynomials that possess attractive properties for complex flow simulations : they have compact support, provide a straightforward handling of boundary conditions and grid nonuniformities, and yield numerical schemes with high resolving power, where the order of accuracy is a mere input parameter. This paper reviews the progress made on the development and application of B-spline numerical methods to computational fluid dynamics problems. Basic B-spline approximation properties is investigated, and their relationship with conventional numerical methods is reviewed. Some fundamental developments towards efficient complex geometry spline methods are covered, such as local interpolation methods, fast solution algorithms on cartesian grid, non-conformal block-structured discretization, formulation of spline bases of higher continuity over triangulation, and treatment of pressure oscillations in Navier-Stokes equations. Application of some of these techniques to the computation of viscous incompressible flows is presented.

The Scale Model Acoustic Test (SMAT) is a 5% scale test of the Space Launch System (SLS), which is currently being designed at Marshall Space Flight Center (MSFC). The purpose of this test is to characterize and understand a variety of acoustic phenomena that occur during the early portions of lift off, one being the overpressure environment that develops shortly after booster ignition. The pressure waves that propagate from the mobile launcher (ML) exhaust hole are defined as the ignition overpressure (IOP), while the portion of the pressure waves that exit the duct or trench are the duct overpressure (DOP). Distinguishing the IOP and DOP in scale model test data has been difficult in past experiences and in early SMAT results, due to the effects of scaling the geometry. The speed of sound of the air and combustion gas constituents is not scaled, and therefore the SMAT pressure waves propagate at approximately the same speed as occurs in full scale. However, the SMAT geometry is twenty times smaller, allowing the pressure waves to move down the exhaust hole, through the trench and duct, and impact the vehicle model much faster than occurs at full scale. The DOP waves impact portions of the vehicle at the same time as the IOP waves, making it difficult to distinguish the different waves and fully understand the data. To better understand the SMAT data, a computational fluid dynamics (CFD) analysis was performed with a fictitious geometry that isolates the IOP and DOP. The upper and lower portions of the domain were segregated to accomplish the isolation in such a way that the flow physics were not significantly altered. The Loci/CHEM CFD software program was used to perform this analysis.

Distributed-memory parallel computers dominate today's parallel computing arena. These machines, such as Intel Paragon, IBM SP2, and Cray Origin2OO, have successfully delivered high performance computing power for solving some of the so-called "grand-challenge" problems. Despite initial success, parallel machines have not been widely accepted in production engineering environments due to the complexity of parallel programming. On a parallel computing system, a task has to be partitioned and distributed appropriately among processors to reduce communication cost and to attain load balance. More importantly, even with careful partitioning and mapping, the performance of an algorithm may still be unsatisfactory, since conventional sequential algorithms may be serial in nature and may not be implemented efficiently on parallel machines. In many cases, new algorithms have to be introduced to increase parallel performance. In order to achieve optimal performance, in addition to partitioning and mapping, a careful performance study should be conducted for a given application to find a good algorithm-machine combination. This process, however, is usually painful and elusive. The goal of this project is to design and develop efficient parallel algorithms for highly accurate Computational Fluid Dynamics (CFD) simulations and other engineering applications. The work plan is 1) developing highly accurate parallel numerical algorithms, 2) conduct preliminary testing to verify the effectiveness and potential of these algorithms, 3) incorporate newly developed algorithms into actual simulation packages. The work plan has well achieved. Two highly accurate, efficient Poisson solvers have been developed and tested based on two different approaches: (1) Adopting a mathematical geometry which has a better capacity to describe the fluid, (2) Using compact scheme to gain high order accuracy in numerical discretization. The previously developed Parallel Diagonal Dominant (PDD) algorithm and Reduced Parallel Diagonal Dominant (RPDD) algorithm have been carefully studied on different parallel platforms for different applications, and a NASA simulation code developed by Man M. Rai and his colleagues has been parallelized and implemented based on data dependency analysis. These achievements are addressed in detail in the paper.

An electrochemical Ni-H2 battery model has been expanded to include thermal effects. A thermal energy conservation equation was derived from first principles. An electrochemical and thermal coupled model was created by the addition of this equation to an existing multiphase, electrochemical model. Charging at various rates was investigated and the results validated against experimental data. Reaction currents, pressure changes, temperature profiles, and concentration variations within the cell are predicted numerically and compared with available data and theory.

Computational fluid dynamics was used to investigate the management of inlet distortion by the introduction of discrete vorticity sources at selected locations in the inlet for the purpose of controlling secondary flow. These sources of vorticity were introduced by means of vortex generators. A series of design observations were made concerning the importance of various vortex generator design parameters in minimizing engine face circumferential distortion. The study showed that vortex strength, generator scale, and secondary flow field structure have a complicated and interrelated influence on the engine face distortion, over and above the initial geometry and arrangement of the generators. The installed vortex generator performance was found to be a function of three categories of variables: the inflow conditions, the aerodynamic characteristics associated with the inlet duct, and the design parameters related to the geometry, arrangement, and placement of the vortex generators within the outlet duct itself.

An overview of research activities at the United Technologies Research Center (UTRC) in the area of Computational Fluid Dynamics (CFD) is presented. The requirement and use of various levels of computers, including supercomputers, for the CFD activities is described. Examples of CFD directed toward applications to helicopters, turbomachinery, heat exchangers, and the National Aerospace Plane are included. Helicopter rotor codes for the prediction of rotor and fuselage flow fields and airloads were developed with emphasis on rotor wake modeling. Airflow and airload predictions and comparisons with experimental data are presented. Examples are presented of recent parabolized Navier-Stokes and full Navier-Stokes solutions for hypersonic shock-wave/boundary layer interaction, and hydrogen/air supersonic combustion. In addition, other examples of CFD efforts in turbomachinery Navier-Stokes methodology and separated flow modeling are presented. A brief discussion of the 3-tier scientific computing environment is also presented, in which the researcher has access to workstations, mid-size computers, and supercomputers.

An overview of research activities at the United Technologies Research Center (UTRC) in the area of Computational Fluid Dynamics (CFD) is presented. The requirement and use of various levels of computers, including supercomputers, for the CFD activities is described. Examples of CFD directed toward applications to helicopters, turbomachinery, heat exchangers, and the National Aerospace Plane are included. Helicopter rotor codes for the prediction of rotor and fuselage flow fields and airloads were developed with emphasis on rotor wake modeling. Airflow and airload predictions and comparisons with experimental data are presented. Examples are presented of recent parabolized Navier-Stokes and full Navier-Stokes solutions for hypersonic shock-wave/boundary layer interaction, and hydrogen/air supersonic combustion. In addition, other examples of CFD efforts in turbomachinery Navier-Stokes methodology and separated flow modeling are presented. A brief discussion of the 3-tier scientific computing environment is also presented, in which the researcher has access to workstations, mid-size computers, and supercomputers.

We present a pedagogical review of some of the methods employed in Eulerian computational fluid dynamics (CFD). Fluid mechanics is governed by the Euler equations, which are conservation laws for mass, momentum, and energy. The standard approach to Eulerian CFD is to divide space into finite volumes or cells and store the cell-averaged values of conserved hydro quantities. The integral Euler equations are then solved by computing the flux of the mass, momentum, and energy across cell boundaries. We review both first-order and second-order flux assignment schemes. All linear schemes are either dispersive or diffusive. The nonlinear, second-order accurate total variation diminishing (TVD) approach provides high resolution capturing of shocks and prevents unphysical oscillations. We review the relaxing TVD scheme, a simple and robust method to solve systems of conservation laws like the Euler equations. A 3-D relaxing TVD code is applied to the Sedov-Taylor blast wave test. The propagation of the blast wave is accurately captured and the shock front is sharply resolved. We apply a 3-D self-gravitating hydro code to simulating the formation of blue straggler stars through stellar mergers and present some numerical results. A sample 3-D relaxing TVD code is provided in the appendix.

Incompressible two-dimensional flows such as the advection (Liouville) equation and the Euler equations have a large family of conservation laws related to conservation of area. We present two Eulerian numerical methods which preserve a discrete analog of area. The first is a fully discrete model based on a rearrangement of cells; the second is more conventional, but still preserves the area within each contour of the vorticity field. Initial tests indicate that both methods suppress the formation of spurious oscillations in the field.

Let the interface between two immiscible fluids in a Hele-Shaw cell have, at t=0, a wedge shape. As a wedge is scale-free, the fluid relaxation dynamics are self-similar. We find the dynamic exponent of this self-similar flow and show that the interface shape is given by the solution of an unusual inverse problem of potential theory. We solve this inverse problem analytically for an almost flat wedge, and numerically otherwise. The wedge solution is useful for analysis of pinch-off singularities.

This is the first of two papers examining the critical collapse of spherically symmetric perfect fluids with the equation of state P = (Gamma -1)rho. Here we present the equations of motion and describe a computer code capable of simulating the extremely relativistic flows encountered in critical solutions for Gamma

We propose a scheme for investigating the quantum dynamics of interacting electron models by means of time-dependent variational principle and spin coherent states of space lattice operators. We apply such a scheme to the one-dimensional hubbard model, and solve the resulting equations in different regimes. In particular, we find that at low densities the dynamics is mapped into two coupled nonlinear Schroedinger equations, whereas near half-filling the model is described by two coupled Josephson junction arrays. Focusing then to the case in which only the phases of the spin variables are dynamically active, we examine a number of different solutions corresponding to the excitations of few macroscopic modes. Based on fixed point equation of the simpler among them, we show that the standard one-band ground state phase space is found.

We propose a scheme for investigating the quantum dynamics of interacting electron models by means of time-dependent variational principle and spin coherent states of space lattice operators. We apply such a scheme to the one-dimensional hubbard model, and solve the resulting equations in different regimes. In particular, we find that at low densities the dynamics is mapped into two coupled nonlinear Schroedinger equations, whereas near half-filling the model is described by two coupled Josephson junction arrays. Focusing then to the case in which only the phases of the spin variables are dynamically active, we examine a number of different solutions corresponding to the excitations of few macroscopic modes. Based on fixed point equation of the simpler among them, we show that the standard one-band ground state phase space is found.

This paper describes several results of parallel and distributed computing using a large scale production flow solver program. A coarse grained parallelization based on clustering of discretization grids combined with partitioning of large grids for load balancing is presented. An assessment is given of its performance on distributed and distributed-shared memory platforms using large scale scientific problems. An experiment with this solver, adapted to a Wide Area Network execution environment is presented. We also give a comparative performance assessment of computation and communication times on both the tightly and loosely-coupled machines.

The structure, formation, and dynamics of dilute, mono-dispersive ferrofluid emulsions in an external magnetic field have been investigated using dynamic light scattering techniques. In the absence of the magnetic field, the emulsion particles are randomly distributed and behave like hard spheres in Brownian motion. An applied magnetic field induces a magnetic dipole moment in each particle. Dipolar interactions between particles align them into chains where correlation functions show two decay processes. The short-time decay shows the motion of straight chains as a whole where the apparent chain length increases with the applied magnetic field and the particle volume fraction. Good scaling results are obtained showing that the apparent chain length grows with time following a power law with exponent of 0.6 and depends on the applied field, particle volume fraction, and diffusion constant of the particles. The long-time decay in the correlation function shows oscillation when the chains reach a certain length with time and stiffness with threshold field This result shows that chains not only fluctuate, but move in a periodic motion with a frequency of 364 Hz at lambda = 15. It may suggest the existence of phonons. This work is the first step in the understanding of the structure formation, especially chain coarsening mechanism, of magnetorheological (MR) fluids at higher volume fractions.

Despite significant achievements in computational fluid dynamics, there still remain many fluid flow phenomena not well understood. For example, the prediction of temperature distributions is inaccurate when temperature gradients are high, particularly in shock wave turbulent boundary layer interactions close to the wall. Complexities of fluid flow phenomena include transition to turbulence, relaminarization separated flows, transition between viscous and inviscid incompressible and compressible flows, among others, in all speed regimes. The purpose of this paper is to introduce a new approach, called the Flowfield-Dependent Mixed Explicit-Implicit (FDMEI) method, in an attempt to resolve these difficult issues in Computational Fluid Dynamics (CFD). In this process, a total of six implicitness parameters characteristic of the current flowfield are introduced. They are calculated from the current flowfield or changes of Mach numbers, Reynolds numbers, Peclet numbers, and Damkoehler numbers (if reacting) at each nodal point and time step. This implies that every nodal point or element is provided with different or unique numerical scheme according to their current flowfield situations, whether compressible, incompressible, viscous, inviscid, laminar, turbulent, reacting, or nonreacting. In this procedure, discontinuities or fluctuations of an variables between adjacent nodal points are determined accurately. If these implicitness parameters are fixed to certain numbers instead of being calculated from the flowfield information, then practically all currently available schemes of finite differences or finite elements arise as special cases. Some benchmark problems to be presented in this paper will show the validity, accuracy, and efficiency of the proposed methodology.