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We developed a novel approach to extend the particle level set method to the simulation of as many regions as desired. The various regions can be liquids or gases of any type with differing viscosities, densities, viscoelastic properties, etc. We also proposed techniques for simulating interactions between materials, whether it be simple surface tension forces or more complex chemical reactions with one material converting to another or two materials combining to form a third. When discretizing the underlying Navier-Stokes equations for multiphase flow, an additional difficulty occurs since discretization stencils cross region boundaries naively combining non-smooth or even discontinuous data. Recently, we developed a new coding paradigm that allows one to incorporate physical jump conditions in data on the fly, which is significantly more efficient for multiple regions, especially at triple points or near boundaries with solids. This removes the need for any algorithm changes that might reduce the accuracy of the scheme, and moreover even removes the need for changes to the code itself. Besides this work we have also addressed scalability including methods on octree and Run Length Encoded (RLE) data structure, as well parallel implementation such as MPI. Other work includes work on fracture.

The papers presented at the AGARD Fluid Dynamics Panel Specialists' Meeting on 'Computational Methods for Aerodynamic Design (Inverse) and Optimization' are reviewed. Strengths and weaknesses are identified for many of the contributions as each is reviewed. The reviewer closes with some general comments. The 23 papers presented at the Meeting have been collected in AGARD CP 463 (ADA220870). Keywords: Computer aided design; Computational fluid dynamics; Inverse methods; Aerodynamic characteristics/optimization.

Implicit finite differences schemes are often the preferred numerical schemes in computational fluid dynamics, requiring less stringent stability bounds than the explicit schemes. Each iteration in an implicit scheme, however, involves global data dependencies in the form of second and higher order recurrences. Efficient parallel implementations of such iterative methods, therefore, are considerably more difficult and non-intuitive. In this paper, we consider the parallelization of the implicit schemes that are used for solving the Euler and the thin layer Navier-Stokes equations and that require inversions of large linear systems in the form of block tri-diagonal and/or block penta- diagonal matrices. We focus our attention on three-dimensional cases an present schemes that minimize the total execution time. We describe partitioning and scheduling schemes for alleviating the effects of the global data dependencies. An analysis of the communication and the computation aspects of these methods is presented. The effect of the boundary conditions on the parallel schemes is also discussed. The ARC-3D code, developed at NASA Ames, is used as an example application. Performance of the proposed methods is verified on the Victor multiprocessor system which is a message passing architecture developed at the IBM, T.J. Watson Research Center. (KR)

The objective of this project is to use computational fluid dynamics to examine the flow around three Schiebe head forms: 2 inches, 10 inches, and 20 inches in diameter. The flow around the 20-inch head form was examined experimentally in the Large Cavitation Channel by making laser Doppler velocimetry measurements. Computational analysis was used to determine the flow around all three head forms. The computational results and the experimental results were compared. The objective of the comparison was to determine if a computational model could be used to represent accurately a physical model in a test tunnel. The results showed that both viscous and inviscid flow calculations represented the experiment well. The inviscid analysis was much less costly in time and resources while still providing useful results. inviscid flow calculations seem to be the best choice for a preliminary prediction technique to support experimental investigations. This report presents a description of the experimental and computational methods used, a detailed comparison of results, and an analysis of the comparison. computational fluid dynamics, Large Cavitation Channel, Schiebe, cavitation head forms, laser Doppler velocimetry.

The objective of this project is to use computational fluid dynamics to examine the flow around three Schiebe head forms: 2 inches, 10 inches, and 20 inches in diameter. The flow around the 20-inch head form was examined experimentally in the Large Cavitation Channel by making laser Doppler velocimetry measurements. Computational analysis was used to determine the flow around all three head forms. The computational results and the experimental results were compared. The objective of the comparison was to determine if a computational model could be used to represent accurately a physical model in a test tunnel. The results showed that both viscous and inviscid flow calculations represented the experiment well. The inviscid analysis was much less costly in time and resources while still providing useful results. inviscid flow calculations seem to be the best choice for a preliminary prediction technique to support experimental investigations. This report presents a description of the experimental and computational methods used, a detailed comparison of results, and an analysis of the comparison. computational fluid dynamics, Large Cavitation Channel, Schiebe, cavitation head forms, laser Doppler velocimetry.

The Design Analysis Branch (NE-Ml) at the Kennedy Space Center has not had the ability to accurately couple Rigid Body Dynamics (RBD) and Computational Fluid Dynamics (CFD). OVERFLOW-D is a flow solver that has been developed by NASA to have the capability to analyze and simulate dynamic motions with up to six Degrees of Freedom (6-DOF). Two simulations were prepared over the course of the internship to demonstrate 6DOF motion of rigid bodies under aerodynamic loading. The geometries in the simulations were based on a conceptual Space Launch System (SLS). The first simulation that was prepared and computed was the motion of a Solid Rocket Booster (SRB) as it separates from its core stage. To reduce computational time during the development of the simulation, only half of the physical domain with respect to the symmetry plane was simulated. Then a full solution was prepared and computed. The second simulation was a model of the SLS as it departs from a launch pad under a 20 knot crosswind. This simulation was reduced to Two Dimensions (2D) to reduce both preparation and computation time. By allowing 2-DOF for translations and 1-DOF for rotation, the simulation predicted unrealistic rotation. The simulation was then constrained to only allow translations.

Spacecraft thermal protection systems are at risk of being damaged due to airflow produced from

Some recent developments in acceleration of convergence methods for vector sequences are reviewed. The methods considered are the minimal polynomial extrapolation, the reduced rank extrapolation, and the modified minimal polynomial extrapolation. The vector sequences to be accelerated are those that are obtained from the iterative solution of linear or nonlinear systems of equations. The convergence and stability properties of these methods as well as different ways of numerical implementation are discussed in detail. Based on the convergence and stability results, strategies that are useful in practical applications are suggested. Two applications to computational fluid mechanics involving the three dimensional Euler equations for ducted and external flows are considered. The numerical results demonstrate the usefulness of the methods in accelerating the convergence of the time marching techniques in the solution of steady state problems.

The aerospace plane design challenge is presented in the form of the view-graphs. The following topics are included: the CFD design technology development; CFD validation vs. measurable fluid dynamics validation; and discussion of results.

A system of computer programs was developed to model general three dimensional surfaces. Surfaces are modeled as sets of parametric bicubic patches. There are also capabilities to transform coordinates, to compute mesh/surface intersection normals, and to format input data for a transonic potential flow analysis. A graphical display of surface models and intersection normals is available. There are additional capabilities to regulate point spacing on input curves and to compute surface/surface intersection curves. Input and output data formats are described; detailed suggestions are given for user input. Instructions for execution are given, and examples are shown.

This paper describes and discusses the textbook, Fundamentals of Computational Fluid Dynamics by Lomax, Pulliam, and Zingg, which is intended for a graduate level first course in computational fluid dynamics. This textbook emphasizes fundamental concepts in developing, analyzing, and understanding numerical methods for the partial differential equations governing the physics of fluid flow. Its underlying philosophy is that the theory of linear algebra and the attendant eigenanalysis of linear systems provides a mathematical framework to describe and unify most numerical methods in common use in the field of fluid dynamics. Two linear model equations, the linear convection and diffusion equations, are used to illustrate concepts throughout. Emphasis is on the semi-discrete approach, in which the governing partial differential equations (PDE's) are reduced to systems of ordinary differential equations (ODE's) through a discretization of the spatial derivatives. The ordinary differential equations are then reduced to ordinary difference equations (O(Delta)E's) using a time-marching method. This methodology, using the progression from PDE through ODE's to O(Delta)E's, together with the use of the eigensystems of tridiagonal matrices and the theory of O(Delta)E's, gives the book its distinctiveness and provides a sound basis for a deep understanding of fundamental concepts in computational fluid dynamics.

In this paper we describe the parallelization of the multi-zone code versions of the NAS Parallel Benchmarks employing multi-level OpenMP parallelism. For our study we use the NanosCompiler, which supports nesting of OpenMP directives and provides clauses to control the grouping of threads, load balancing, and synchronization. We report the benchmark results, compare the timings with those of different hybrid parallelization paradigms and discuss OpenMP implementation issues which effect the performance of multi-level parallel applications.

Design and analysis of the inlet for a rocket based combined cycle engine is discussed. Computational fluid dynamics was used in both the design and subsequent analysis. Reynolds averaged Navier-Stokes simulations were performed using both perfect gas and real gas assumptions. An inlet design that operates over the required Mach number range from 0 to 12 was produced. Performance data for cycle analysis was post processed using a stream thrust averaging technique. A detailed performance database for cycle analysis is presented. The effect ot vehicle forebody compression on air capture is also examined.

The current compute environment that most researchers are using for the calculation of 3D unsteady Computational Fluid Dynamic (CFD) results is a super-computer class machine. The Massively Parallel Processors (MPP's) such as the 160 node IBM SP2 at NAS and clusters of workstations acting as a single MPP (like NAS's SGI Power-Challenge array and the J90 cluster) provide the required computation bandwidth for CFD calculations of transient problems. If we follow the traditional computational analysis steps for CFD (and we wish to construct an interactive visualizer) we need to be aware of the following: (1) Disk space requirements. A single snap-shot must contain at least the values (primitive variables) stored at the appropriate locations within the mesh. For most simple 3D Euler solvers that means 5 floating point words. Navier-Stokes solutions with turbulence models may contain 7 state-variables. (2) Disk speed vs. Computational speeds. The time required to read the complete solution of a saved time frame from disk is now longer than the compute time for a set number of iterations from an explicit solver. Depending, on the hardware and solver an iteration of an implicit code may also take less time than reading the solution from disk. If one examines the performance improvements in the last decade or two, it is easy to see that depending on disk performance (vs. CPU improvement) may not be the best method for enhancing interactivity. (3) Cluster and Parallel Machine I/O problems. Disk access time is much worse within current parallel machines and cluster of workstations that are acting in concert to solve a single problem. In this case we are not trying to read the volume of data, but are running the solver and the solver outputs the solution. These traditional network interfaces must be used for the file system. (4) Numerics of particle traces. Most visualization tools can work upon a single snap shot of the data but some visualization tools for transient problems require dealing with time.

This paper describes an experiment in which a large-scale scientific application development for tightly-coupled parallel machines is adapted to the distributed execution environment of the Information Power Grid (IPG). A brief overview of the IPG and a description of the computational fluid dynamics (CFD) algorithm are given. The Globus metacomputing toolkit is used as the enabling device for the geographically-distributed computation. Modifications related to latency hiding and Load balancing were required for an efficient implementation of the CFD application in the IPG environment. Performance results on a pair of SGI Origin 2000 machines indicate that real scientific applications can be effectively implemented on the IPG; however, a significant amount of continued effort is required to make such an environment useful and accessible to scientists and engineers.

This paper describes an experiment in which a large-scale scientific application development for tightly-coupled parallel machines is adapted to the distributed execution environment of the Information Power Grid (IPG). A brief overview of the IPG and a description of the computational fluid dynamics (CFD) algorithm are given. The Globus metacomputing toolkit is used as the enabling device for the geographically-distributed computation. Modifications related to latency hiding and Load balancing were required for an efficient implementation of the CFD application in the IPG environment. Performance results on a pair of SGI Origin 2000 machines indicate that real scientific applications can be effectively implemented on the IPG; however, a significant amount of continued effort is required to make such an environment useful and accessible to scientists and engineers.

This paper describes an experiment in which a large-scale scientific application development for tightly-coupled parallel machines is adapted to the distributed execution environment of the Information Power Grid (IPG). A brief overview of the IPG and a description of the computational fluid dynamics (CFD) algorithm are given. The Globus metacomputing toolkit is used as the enabling device for the geographically-distributed computation. Modifications related to latency hiding and Load balancing were required for an efficient implementation of the CFD application in the IPG environment. Performance results on a pair of SGI Origin 2000 machines indicate that real scientific applications can be effectively implemented on the IPG; however, a significant amount of continued effort is required to make such an environment useful and accessible to scientists and engineers.

Motivated by progressive climate-change influence on ice degradation in caves, in this paper we present a novel methodology to investigate the link between air dynamics and ice melting. Specifically, we use surveys available for the Leupa ice cave (LIC), located in the Canin-Kanin group in the southeastern Alps and a general purpose computational fluid dynamics model (CFD). Detailed numerical simulations are evaluated on the basis of well-established approaches that consider domain, grid, boundary-conditions, turbulence closure models, buoyancy effects, porous media properties and verification with measured data. External atmospheric conditions are the main trigger for internal circulation but morphology and thermal characteristics of ice and bedrock induce a dynamical process of heat exchange ultimately responsible for ice melting. This process is generally poorly documented in real conditions. Using CFD analyses we show that both in summer and winter, warm and cold air currents within the cave are “disturbed” by several vortices and stagnation zones which locally modify the energy balance. To account for this we introduce a macroscopic physical model based on energy balance between ice surfaces and the inner ice cave airflow to determine the heat exchanged between ice and air. Using this model, a prediction of ice thickness decay over time is obtained. In the case of LIC a reduction of initial 4 cm per year is first obtained with projection of a much faster increase. The methodology is general and easily extendable to other sites, proving to be a powerful method to estimate ice evolution in caves induced by external and internal forcing.

Geometrical, flight, computational fluid dynamics (CFD), and wind-tunnel studies for the F-16XL-1 airplane are summarized over a wide range of test conditions. Details are as follows: (1) For geometry, the upper surface of the airplane and the numerical surface description compare reasonably well. (2) For flight, CFD, and wind-tunnel surface pressures, the comparisons are generally good at low angles of attack at both subsonic and transonic speeds, however, local differences are present. In addition, the shock location at transonic speeds from wind-tunnel pressure contours is near the aileron hinge line and generally is in correlative agreement with flight results. (3) For boundary layers, flight profiles were predicted reasonably well for attached flow and underneath the primary vortex but not for the secondary vortex. Flight data indicate the presence of an interaction of the secondary vortex system and the boundary layer and the boundary-layer measurements show the secondary vortex located more outboard than predicted. (4) Predicted and measured skin friction distributions showed qualitative agreement for a two vortex system. (5) Web-based data-extraction and computational-graphical tools have proven useful in expediting the preceding comparisons. (6) Data fusion has produced insightful results for a variety of visualization-based data sets.

The Gauss--Newton with approximated tensors (GNAT) method is a nonlinear model reduction method that operates on fully discretized computational models. It achieves dimension reduction by a Petrov--Galerkin projection associated with residual minimization; it delivers computational efficency by a hyper-reduction procedure based on the `gappy POD' technique. Originally presented in Ref. [1], where it was applied to implicit nonlinear structural-dynamics models, this method is further developed here and applied to the solution of a benchmark turbulent viscous flow problem. To begin, this paper develops global state-space error bounds that justify the method's design and highlight its advantages in terms of minimizing components of these error bounds. Next, the paper introduces a `sample mesh' concept that enables a distributed, computationally efficient implementation of the GNAT method in finite-volume-based computational-fluid-dynamics (CFD) codes. The suitability of GNAT for parameterized problems is highlighted with the solution of an academic problem featuring moving discontinuities. Finally, the capability of this method to reduce by orders of magnitude the core-hours required for large-scale CFD computations, while preserving accuracy, is demonstrated with the simulation of turbulent flow over the Ahmed body. For an instance of this benchmark problem with over 17 million degrees of freedom, GNAT outperforms several other nonlinear model-reduction methods, reduces the required computational resources by more than two orders of magnitude, and delivers a solution that differs by less than 1% from its high-dimensional counterpart.

An axisymmetric single engine Computational Fluid Dynamics calculation of the Saturn V/S 1-C vehicle base region and F1 engine plume is described. There were two objectives of this work, the first was to calculate an axisymmetric approximation of the nozzle, plume and base region flow fields of S1-C/F1, relate/scale this to flight data and apply this scaling factor to a NLS/STME axisymmetric calculations from a parallel effort. The second was to assess the differences in F1 and STME plume shear layer development and concentration of combustible gases. This second piece of information was to be input/supporting data for assumptions made in NLS2 base temperature scaling methodology from which the vehicle base thermal environments were being generated. The F1 calculations started at the main combustion chamber faceplate and incorporated the turbine exhaust dump/nozzle film coolant. The plume and base region calculations were made for ten thousand feet and 57 thousand feet altitude at vehicle flight velocity and in stagnant freestream. FDNS was implemented with a 14 species, 28 reaction finite rate chemistry model plus a soot burning model for the RP-1/LOX chemistry. Nozzle and plume flow fields are shown, the plume shear layer constituents are compared to a STME plume. Conclusions are made about the validity and status of the analysis and NLS2 vehicle base thermal environment definition methodology.

An axisymmetric single engine Computational Fluid Dynamics calculation of the Saturn V/S 1-C vehicle base region and F1 engine plume is described. There were two objectives of this work, the first was to calculate an axisymmetric approximation of the nozzle, plume and base region flow fields of S1-C/F1, relate/scale this to flight data and apply this scaling factor to a NLS/STME axisymmetric calculations from a parallel effort. The second was to assess the differences in F1 and STME plume shear layer development and concentration of combustible gases. This second piece of information was to be input/supporting data for assumptions made in NLS2 base temperature scaling methodology from which the vehicle base thermal environments were being generated. The F1 calculations started at the main combustion chamber faceplate and incorporated the turbine exhaust dump/nozzle film coolant. The plume and base region calculations were made for ten thousand feet and 57 thousand feet altitude at vehicle flight velocity and in stagnant freestream. FDNS was implemented with a 14 species, 28 reaction finite rate chemistry model plus a soot burning model for the RP-1/LOX chemistry. Nozzle and plume flow fields are shown, the plume shear layer constituents are compared to a STME plume. Conclusions are made about the validity and status of the analysis and NLS2 vehicle base thermal environment definition methodology.

An axisymmetric single engine Computational Fluid Dynamics calculation of the Saturn V/S 1-C vehicle base region and F1 engine plume is described. There were two objectives of this work, the first was to calculate an axisymmetric approximation of the nozzle, plume and base region flow fields of S1-C/F1, relate/scale this to flight data and apply this scaling factor to a NLS/STME axisymmetric calculations from a parallel effort. The second was to assess the differences in F1 and STME plume shear layer development and concentration of combustible gases. This second piece of information was to be input/supporting data for assumptions made in NLS2 base temperature scaling methodology from which the vehicle base thermal environments were being generated. The F1 calculations started at the main combustion chamber faceplate and incorporated the turbine exhaust dump/nozzle film coolant. The plume and base region calculations were made for ten thousand feet and 57 thousand feet altitude at vehicle flight velocity and in stagnant freestream. FDNS was implemented with a 14 species, 28 reaction finite rate chemistry model plus a soot burning model for the RP-1/LOX chemistry. Nozzle and plume flow fields are shown, the plume shear layer constituents are compared to a STME plume. Conclusions are made about the validity and status of the analysis and NLS2 vehicle base thermal environment definition methodology.

An axisymmetric single engine Computational Fluid Dynamics calculation of the Saturn V/S 1-C vehicle base region and F1 engine plume is described. There were two objectives of this work, the first was to calculate an axisymmetric approximation of the nozzle, plume and base region flow fields of S1-C/F1, relate/scale this to flight data and apply this scaling factor to a NLS/STME axisymmetric calculations from a parallel effort. The second was to assess the differences in F1 and STME plume shear layer development and concentration of combustible gases. This second piece of information was to be input/supporting data for assumptions made in NLS2 base temperature scaling methodology from which the vehicle base thermal environments were being generated. The F1 calculations started at the main combustion chamber faceplate and incorporated the turbine exhaust dump/nozzle film coolant. The plume and base region calculations were made for ten thousand feet and 57 thousand feet altitude at vehicle flight velocity and in stagnant freestream. FDNS was implemented with a 14 species, 28 reaction finite rate chemistry model plus a soot burning model for the RP-1/LOX chemistry. Nozzle and plume flow fields are shown, the plume shear layer constituents are compared to a STME plume. Conclusions are made about the validity and status of the analysis and NLS2 vehicle base thermal environment definition methodology.

An axisymmetric single engine Computational Fluid Dynamics calculation of the Saturn V/S 1-C vehicle base region and F1 engine plume is described. There were two objectives of this work, the first was to calculate an axisymmetric approximation of the nozzle, plume and base region flow fields of S1-C/F1, relate/scale this to flight data and apply this scaling factor to a NLS/STME axisymmetric calculations from a parallel effort. The second was to assess the differences in F1 and STME plume shear layer development and concentration of combustible gases. This second piece of information was to be input/supporting data for assumptions made in NLS2 base temperature scaling methodology from which the vehicle base thermal environments were being generated. The F1 calculations started at the main combustion chamber faceplate and incorporated the turbine exhaust dump/nozzle film coolant. The plume and base region calculations were made for ten thousand feet and 57 thousand feet altitude at vehicle flight velocity and in stagnant freestream. FDNS was implemented with a 14 species, 28 reaction finite rate chemistry model plus a soot burning model for the RP-1/LOX chemistry. Nozzle and plume flow fields are shown, the plume shear layer constituents are compared to a STME plume. Conclusions are made about the validity and status of the analysis and NLS2 vehicle base thermal environment definition methodology.

A study was conducted to evaluate the accuracy of a commercial computational fluid dynamics (CFD) code (CFDRC-ACE+) for predicting incompressible air jet flows with simple geometries. Specifically, the axis- symmetric and two-dimensional heated air-jets were simulated using a standard k- epsilon turbulence model. These CFD predictions were directly compared to an extensive compilation of experimental data from archive literature. The round jet results indicated that the code over-predicted the velocity-spreading rate by 24% and the temperature spreading rate by 29%

The Australian Challenge was a set of experiments chosen as a test case to establish how well computer calculations can model the blast overpressure around a complex set of structures. This paper presents the first three dImensional calculation on the Australian Challenge using CFD codes. These codes have been developed at AMRL and the Australian Challenge represents their first test in a real world' scenario. The calculations show good agreement with the experimental results. The program can now be used with a good degree of confidence in modelling other complex scenarios, reducing the need for expensive experimentation. The safety aspects of any changes in operational procedure can be evaluated quickly and efficiently. (AN)

NASA/Marshall Space Flight Center (MSFC) has an ongoing effort to transfer to industry the technologies developed at MSFC for rocket propulsion systems. The Technology Utilization (TU) Office at MSFC promotes these efforts and accepts requests for assistance from industry. One such solicitation involves a request from North American Marine Jet, Inc. (NAMJ) for assistance in the design of a water-jet-drive system to fill a gap in NAMJ's product line. NAMJ provided MSFC with a baseline axial flow impeller design as well as the relevant working parameters (rpm, flow rate, etc.). This baseline design was analyzed using CFD, and significant deficiencies identified. Four additional analyses were performed involving MSFC changes to the geometric and operational parameters of the baseline case. Subsequently, the impeller was redesigned by NAMJ and analyzed by MSFC. This new configuration performs significantly better than the baseline design. Similar cooperative activities are planned for the design of the jet-drive inlet.

A system and method for generating fluid flow parameter data for use in aerodynamic heating analysis. Computational fluid dynamics data is generated for a number of points in an area on a surface to be analyzed. Sub-areas corresponding to areas of the surface for which an aerodynamic heating analysis is to be performed are identified. A computer system automatically determines a sub-set of the number of points corresponding to each of the number of sub-areas and determines a value for each of the number of sub-areas using the data for the sub-set of points corresponding to each of the number of sub-areas. The value is determined as an average of the data for the sub-set of points corresponding to each of the number of sub-areas. The resulting parameter values then may be used to perform an aerodynamic heating analysis.

Design of Experiments (DOE) techniques were applied to the Launch Abort System (LAS) of the NASA Crew Exploration Vehicle (CEV) parametric geometry Computational Fluid Dynamics (CFD) study to efficiently identify and rank the primary contributors to the integrated drag over the vehicles ascent trajectory. Typical approaches to these types of activities involve developing all possible combinations of geometries changing one variable at a time, analyzing them with CFD, and predicting the main effects on an aerodynamic parameter, which in this application is integrated drag. The original plan for the LAS study team was to generate and analyze more than1000 geometry configurations to study 7 geometric parameters. By utilizing DOE techniques the number of geometries was strategically reduced to 84. In addition, critical information on interaction effects among the geometric factors were identified that would not have been possible with the traditional technique. Therefore, the study was performed in less time and provided more information on the geometric main effects and interactions impacting drag generated by the LAS. This paper discusses the methods utilized to develop the experimental design, execution, and data analysis.

A computational method for the analysis of longitudinal-mode liquid rocket combustion instability has been developed based on the unsteady, quasi-one-dimensional Euler equations where the combustion process source terms were introduced through the incorporation of a two-zone, linearized representation: (1) A two-parameter collapsed combustion zone at the injector face, and (2) a two-parameter distributed combustion zone based on a Lagrangian treatment of the propellant spray. The unsteady Euler equations in inhomogeneous form retain full hyperbolicity and are integrated implicitly in time using second-order, high-resolution, characteristic-based, flux-differencing spatial discretization with Roe-averaging of the Jacobian matrix. This method was initially validated against an analytical solution for nonreacting, isentropic duct acoustics with specified admittances at the inflow and outflow boundaries. For small amplitude perturbations, numerical predictions for the amplification coefficient and oscillation period were found to compare favorably with predictions from linearized small-disturbance theory as long as the grid exceeded a critical density (100 nodes/wavelength). The numerical methodology was then exercised on a generic combustor configuration using both collapsed and distributed combustion zone models with a short nozzle admittance approximation for the outflow boundary. In these cases, the response parameters were varied to determine stability limits defining resonant coupling onset.

For long-duration in-space storage of cryogenic propellants, an axial jet mixer is one concept for controlling tank pressure and reducing thermal stratification. Extensive ground-test data from the 1960s to the present exist for tank diameters of 10 ft or less. The design of axial jet mixers for tanks on the order of 30 ft diameter, such as those planned for the Ares V Earth Departure Stage (EDS) LH2 tank, will require scaling of available experimental data from much smaller tanks, as well designing for microgravity effects. This study will assess the ability for Computational Fluid Dynamics (CFD) to handle a change of scale of this magnitude by performing simulations of existing ground-based axial jet mixing experiments at two tank sizes differing by a factor of ten. Simulations of several axial jet configurations for an Ares V scale EDS LH2 tank during low Earth orbit (LEO) coast are evaluated and selected results are also presented. Data from jet mixing experiments performed in the 1960s by General Dynamics with water at two tank sizes (1 and 10 ft diameter) are used to evaluate CFD accuracy. Jet nozzle diameters ranged from 0.032 to 0.25 in. for the 1 ft diameter tank experiments and from 0.625 to 0.875 in. for the 10 ft diameter tank experiments. Thermally stratified layers were created in both tanks prior to turning on the jet mixer. Jet mixer efficiency was determined by monitoring the temperatures on thermocouple rakes in the tanks to time when the stratified layer was mixed out. Dye was frequently injected into the stratified tank and its penetration recorded. There were no velocities or turbulence quantities available in the experimental data. A commercially available, time accurate, multi-dimensional CFD code with free surface tracking (FLOW-3D from Flow Science, Inc.) is used for the simulations presented. Comparisons are made between computed temperatures at various axial locations in the tank at different times and those observed experimentally. The affect of various modeling parameters on the agreement obtained are assessed.

Launch vehicles frequently experience a reduced stability margin through the transonic Mach number range. This reduced stability margin can be caused by the aerodynamic undamping one of the lower-frequency flexible or rigid body modes. Analysis of the behavior of a flexible vehicle is routinely performed with quasi-steady aerodynamic line loads derived from steady rigid aerodynamics. However, a quasi-steady aeroelastic stability analysis can be unconservative at the critical Mach numbers, where experiment or unsteady computational aeroelastic analysis show a reduced or even negative aerodynamic damping.Amethod of enhancing the quasi-steady aeroelastic stability analysis of a launch vehicle with unsteady aerodynamics is developed that uses unsteady computational fluid dynamics to compute the response of selected lower-frequency modes. The response is contained in a time history of the vehicle line loads. A proper orthogonal decomposition of the unsteady aerodynamic line-load response is used to reduce the scale of data volume and system identification is used to derive the aerodynamic stiffness, damping, and mass matrices. The results are compared with the damping and frequency computed from unsteady computational aeroelasticity and from a quasi-steady analysis. The results show that incorporating unsteady aerodynamics in this way brings the enhanced quasi-steady aeroelastic stability analysis into close agreement with the unsteady computational aeroelastic results.

A computational study was conducted on the use of aft-mounted fairings for passive drag reduction on a sphere at Re=866,000. The sphere dimensions and operating Reynolds number were selected to approximate the flow around a proposed aircraft laser turret for which experimental data was available. To establish the validity of the computational model, flow predictions were compared to sphere data available in the open literature. The model, exercised in both the laminar and turbulent modes, showed good agreement with the published data. Two proposed laser turret fairings were then evaluated computationally: a large fairing (beginning at 49.5 degrees past the sphere apex) and a small fairing (beginning at 58.95 degrees past the sphere apex). Existing wind tunnel models were used to generate axisymmetric computational grids that approximated the geometry of these models. The computed flow field and associated drag reduction were comparable to the experimental results obtained from the wind tunnel testing. Differences in drag from the model to the experiment were explained by the axisymmetric simplifications made in the model. Finally, a new, optimized fairing model was designed which eliminated the separation zone on the aft portion of the sphere. The optimized model predicted double the drag reduction compared to the large fairing computational model.

The evolution of numerical techniques for solving problems in Fluid Dynamics is followed, in outline, from the days when Digital Computers were first available, at the end of the Second World War, to the present time, when the Computer Aerodynamic Simulator is being assembled. In this period the range of numerical methods has been broadened five fold, while the speed and capacity of computers have increased by several orders of magnitude. Two areas close to the author's interests are selected to illustrate these changes. The first concerns the extension of the Method of Integral Relations to apply to laminar and turbulent boundary layer problems, including internal flows, separated flows and turbulent mixing flows. The second area deals with unsteady inviscid compressible flow in one or more dimensions and a discussion is given of the relative merits of Godunov and Glimm techniques. (Author)

A study was undertaken to investigate and analyze the flow field results produced by various computational solvers for a projectile of interest to the U.S. Army. Computational fluid dynamics (CFD) techniques were used to obtain numerical solutions for the flow field of a kinetic energy projectile with the original and a modified (experimental) sabot. Computed results were obtained at Mach 4.5 and a 0 deg angle of attack. Qualitative flow field features showed the pressure on the surface of the model as well as pressures in the flow field. The surface pressure data on the projectile were extracted from the solution files and compared. In all cases, the results were comparable. These results show the predictive capabilities of CFD techniques in the analysis of supersonic flow over projectiles with sabots. They also provide an insight into the software capabilities of several of the many tools available to research scientists in the field of CFD.

The goal of this project is to develop a Nano Air Vehicle (NAV) with a wing span of 7.5 cm. The computational fluid dynamics study is focused on the aerodynamic efficiency of the wings. The primary focus of the computational study is on the aerodynamic performance of the wings in order to obtain a near optimal kinematics of the wing while the NAV is in a hover mode. The secondary effort was of a more fundamental nature, in order to understand the differences between a rotating helicopter blade and a similarly designed wing undergoing a flapping motion.

A vehicle propelled by an engine with a variable geometry nozzle allows the nozzle expansion ratio to vary with altitude and flight condition, thereby optimizing engine performance. Active flow control offers a method of providing the functionality of a variable throat area system without requiring variable geometry. Throttling the mass flow rate through the nozzle throat controls the effective throat area, subsequently controlling the effective expansion ratio of the overall nozzle. This paper presents findings from the Pulsed Injection for Rocket Flow Control Technology (PIRFCT) program, which evaluated potential gains in the overall performance of a rocket using active flow control to optimize nozzle expansion ratio for an Earth to orbit mission. Lockheed Martin Aeronautics Company utilized Computational Fluid Dynamics (CFD) to simulate the rocket nozzle with active flow control. Simulations were performed with steady and pulsed flow control jets which were oriented near the geometric throat and inclined upstream against the primary flow. A low stagnation pressure, steady, tertiary injection stream when combined with a steady, high momentum secondary injector was witnessed to increase throttling performance beyond that of a secondary injector alone. Nozzle discharge coefficient was largely unaffected by changes in pulsation frequency or pulsation duty cycle. Pulsed injection approached, but did not exceed, the throttling performance of a time invariant injector when compared on a equivalent mass flux, momentum flux, and energy flux basis. Simulations incorporating a single injector and large area modulations predicted a 50% area reduction when injecting approximately 18% baseline reference mass flow at Mach 2 conditions. However, the PIRFCT program concluded that secondary injection at the nozzle throat is not a good candidate for this type of throttling/altitude compensation technology for an Earth to orbit mission.

A vehicle propelled by an engine with a variable geometry nozzle allows the nozzle expansion ratio to vary with altitude and flight condition, thereby optimizing engine performance. Active flow control offers a method of providing the functionality of a variable throat area system without requiring variable geometry. Throttling the mass flow rate through the nozzle throat controls the effective throat area, subsequently controlling the effective expansion ratio of the overall nozzle. This paper presents findings from the Pulsed Injection for Rocket Flow Control Technology (PIRFCT) program, which evaluated potential gains in the overall performance of a rocket using active flow control to optimize nozzle expansion ratio for an Earth to orbit mission. Lockheed Martin Aeronautics Company utilized Computational Fluid Dynamics (CFD) to simulate the rocket nozzle with active flow control. Simulations were performed with steady and pulsed flow control jets which were oriented near the geometric throat and inclined upstream against the primary flow. A low stagnation pressure, steady, tertiary injection stream when combined with a steady, high momentum secondary injector was witnessed to increase throttling performance beyond that of a secondary injector alone. Nozzle discharge coefficient was largely unaffected by changes in pulsation frequency or pulsation duty cycle. Pulsed injection approached, but did not exceed, the throttling performance of a time invariant injector when compared on a equivalent mass flux, momentum flux, and energy flux basis. Simulations incorporating a single injector and large area modulations predicted a 50% area reduction when injecting approximately 18% baseline reference mass flow at Mach 2 conditions. However, the PIRFCT program concluded that secondary injection at the nozzle throat is not a good candidate for this type of throttling/altitude compensation technology for an Earth to orbit mission.

Probabilistic methods have been implemented with a computational fluid dynamics simulation of fluid flow and heat transfer in a gas turbine engine. The simulation models the temperatures in the T-56 series III 1-2 spacer. Three input quantities are treated as random variables. A random sampling method is used to generate the input values from a probability density function. The implemented Monte Carlo method uses a large number of samples of the input variables to calculate results repeatedly for the output variables (i.e. the predicted temperatures). Statistics of the predicted temperatures, such as the mean and variance, are then calculated. The variation in the predicted temperature at one point in the turbine of the T56 engine is seen to be more sensitive to variability in some parameters than in others.

An algorithm is presented to simulate fluid dynamics on a three qubit type II quantum computer: a lattice of small quantum computers that communicate classical information. The algorithm presented is called a three qubit factorized quantum lattice gas algorithm. It is modeled after classical lattice gas algorithms which move virtual particles along an imaginary lattice and change the particles' momentums using collision rules when they meet at a lattice node. Instead of moving particles, the quantum algorithm presented here moves probabilities, which interact via a unitary collision operator. Probabilities are determined using ensemble measurement and are moved with classical communications channels. The lattice node spacing is defined to be a microscopic scale length. A mesoscopic governing equation for the lattice is derived for the most general three qubit collision operator which preserves particle number. In the continuum limit of the lattice, a governing macroscopic partial differential equation-the diffusion equation-is derived for a particular collision operator using a Chapman-Enskog expansion. A numerical simulation of the algorithm is carried out on a conventional desktop computer and compared to the analytic solution of the diffusion equation. The simulation agrees very well with the known solution.

The primary research objective of this contract was to investigate and develop fluid flow control procedures by utilizing a hierarchical modeling approach. This project included research on control and identification methods for vortex wakes, with the primary example being stabilization of vortices behind a flat plate. Vortex blob and finite difference methods were constructed to provide the flow dynamics. Linear time-invariant feedback controllers have been developed, as well as identification results for a class of input/output models that can be used to design more sophisticated controllers. Additionally, Java based software components that support hierarchical modeling efforts were created.

Image L88-6867 is available as an electronic file from the photo lab. See URL. -- Color graphic CAD CFD model of the National Aerospace Plane.

The research has focussed on a class of domain decomposition techniques for solution of problems in Computational Fluid Dynamics using advanced vector and parallel processors. In particular we consider finite element schemes and use the natural element schemes and use the natural element- partition of the domain to construct the decomposition algorithm. This then fits conveniently into the usual framework of finite element calculations in which the primary loop is the independent calculation and assembly of element matrix and vector contributions. By recasting the conjugate gradient method at this level, the system matrix need not be assembled and the intensive matrix-vector product step can be completely parallelized. These ideas constitute a major departure from traditional finite element schemes and we feel our efforts are a major new development that will strongly influence the technology. Parallel processing, Domain decomposition.

Computational Fluid Dynamics Principles And Applications J. Blazek

The effort has had several components since it was initiated in Oct of 1989; all of these had as their objective the assistance of Dr. Joseph Shang at WRDC in the redirection of his effort toward use of massively-parallel architectures. The major objective was to gain algorithm experience in conversion of two Air Force production CFD codes to a general format applicable to a variety of commercial message-passing architectures. Earlier, an explicit N-S 3D code from WRDC had been converted to the NCUBE. This was used as a model for parallelized production code developed at WRDC under DARPA sponsorship. This effort was completed with the conversion of a serial full 3D Navier-Stokes Beam- Warming CFD code to a 1024-node scalar NCUBE hypercube at SANDIA (Albuquerque).

This report consists of brief technical descriptions and one or more pictures of charts depicting research conducted in-house during the past year. The briefs are designed to provide enough information to clearly define the task, but are short enough to hold the reader's interest. Where applicable, a reference for more detailed information is provided. The research covers a wide spectrum of work; from grid generation to flow solvers, to post-processors; and from incompressible to hypersonic speeds.

Recent advances in achieving textbook multigrid efficiency for fluid simulations are presented. Textbook multigrid efficiency is defined as attaining the solution to the governing system of equations in a computational work which is a small multiple of the operation counts associated with discretizing the system. Strategies are reviewed to attain this efficiency by exploiting the factorizability properties inherent to a range of fluid simulations, including the compressible Navier-Stokes equations. factorizability is used to separate the elliptic and hyperbolic factors contributing to the target system; each of the factors can then be treated individually and optimally. Boundary regions and discontinuities are addressed with separate (local) treatments. New formulations and recent calculations demonstrating the attainment of textbook efficiency for aerodynamic simulations are shown.

Recent advances in achieving textbook multigrid efficiency for fluid simulations are presented. Textbook multigrid efficiency is defined as attaining the solution to the governing system of equations in a computational work which is a small multiple of the operation counts associated with discretizing the system. Strategies are reviewed to attain this efficiency by exploiting the factorizability properties inherent to a range of fluid simulations, including the compressible Navier-Stokes equations. factorizability is used to separate the elliptic and hyperbolic factors contributing to the target system; each of the factors can then be treated individually and optimally. Boundary regions and discontinuities are addressed with separate (local) treatments. New formulations and recent calculations demonstrating the attainment of textbook efficiency for aerodynamic simulations are shown.

The Air Force SEEK EAGLE Office (AFSEO), Eglin Air Force Base (AFB), FL, is the United States Air Force (USAF) authority for weapons certification efforts. AFSEO performs test and evaluation for aircraft/store compatibility certification and uses Computational Fluid Dynamics (CFD) to support this process. Determining the flow about an aircraft/store combination can be extremely difficult. Complicated geometry such as pylons, launchers, and internal weapons bays can create severe acoustic and aerothermodynamic environments, which are challenging to numerically simulate. The additional challenge of rapidly and accurately simulating the trajectory of a store separation in a high-volume simulation environment is beyond the capabilities of most CFD programs. The USAF requirement for numerous, simultaneous and quick-reaction solutions for a wide variety of stores and aircraft can only be accomplished through application of parallel high-performance computing resources that meet the significant computational and memory demands of the various cases.