ALBERT

Description: Basic algorithms for unstructured mesh generation and fluid flow calculation are discussed. In particular the following are addressed: preliminaries of graphs and meshes; duality and data structures; basic graph operations important in CFD (Computational Fluid Dynamics); triangulation methods, including Varonoi diagrams and Delaunay triangulation; maximum principle analysis; finite volume schemes for scalar conservation law equations; finite volume schemes for the Euler and Navier-Stokes equations; and convergence acceleration for steady state calculations.

Description: Transient solutions were obtained for a square region of heat conducting semitransparent material cooling by thermal radiation. The region is in a vacuum environment, so energy is dissipated only by radiation from within the medium leaving through its boundaries. The effect of heat conduction during the transient is to partially equalize the internal temperature distribution. As the optical thickness of the region is increased, the temperature gradients increase near the boundaries and corners, unless heat conduction is large. The solution procedure must provide accurate temperature distributions in these regions to prevent error in the calculated radiation losses. Two-dimensional numerical Gaussian integration is used to obtain the local radiative source term. A finite difference procedure with variable space and time increments is used to solve the transient energy equation. Variable spacing was used to concentrate grid points in regions with large temperature gradients.

Description: It is shown that to satisfy the general accepted compressible law of the wall derived from the Van Driest transformation, turbulence modeling coefficients must actually be functions of density gradients. The transformed velocity profiles obtained by using standard turbulence model constants have too small a value of the effective von Karman constant kappa in the log-law region (inner layer). Thus, if the model is otherwise accurate, the wake component is overpredicted and the predicted skin friction is lower than the expected value.

Description: The multigrid method has been applied to an existing three-dimensional compressible Euler solver to accelerate the convergence of the implicit symmetric relaxation scheme. This lower-upper symmetric Gauss-Seidel implicit scheme is shown to be an effective multigrid driver in three dimensions. A grid refinement study is performed including the effects of large cell aspect ratio meshes. Performance figures of the present multigrid code on Cray computers including the new C90 are presented. A reduction of three orders of magnitude in the residual for a three-dimensional transonic inviscid flow using 920 k grid points is obtained in less than 4 min on a Cray C90.

Description: The present paper explores the use of large-eddy simulations as a tool for predicting noise from first principles. A high-order numerical scheme is used to perform large-eddy simulations of a supersonic jet flow with emphasis on capturing the time-dependent flow structure representating the sound source. The wavelike nature of this structure under random inflow disturbances is demonstrated. This wavelike structure is then enhanced by taking the inflow disturbances to be purely harmonic. Application of Lighthill's theory to calculate the far-field noise, with the sound source obtained from the calculated time-dependent near field, is demonstrated. Alternative approaches to coupling the near-field sound source to the far-field sound are discussed.

Description: The steady state solution of the system of equations consisting of the full Navier-Stokes equations and two turbulence equations has been obtained using a multigrid strategy of unstructured meshes. The flow equations and turbulence equations are solved in a loosely coupled manner. The flow equations are advanced in time using a multistage Runge-Kutta time-stepping scheme with a stability-bound local time step, while turbulence equations are advanced in a point-implicit scheme with a time step which guarantees stability and positivity. Low-Reynolds-number modifications to the original two-equation model are incorporated in a manner which results in well-behaved equations for arbitrarily small wall distances. A variety of aerodynamic flows are solved, initializing all quantities with uniform freestream values. Rapid and uniform convergence rates for the flow and turbulence equations are observed.

Description: Numerical results obtained with direct simulation Monte Carlo and Navier-Stokes methods are presented for a Mach-20 nitrogen flow about a 70-deg blunted cone. The flow conditions simuulated are those that can be obtained in existing low-density hypersonic wind tunnels. Three sets of flow conditions are considered with freestream Knudsen numbers ranging from 0.03 to 0.001. The focus is on the wake structure: how the wake structure changes as a function of rarefaction, what the afterbody levels of heating are, and to what limits the continuum models are realistic as rarefaction in the wake is progressively increased. Calculations are made with and without an afterbody sting. Results for the after body sting are emphasizes in anticipation of an experimental study for the current flow conditions and model configuration. The Navier-Stokes calculations were made with and without slip boundary conditions. Comparisons of the results obtained with the two simulation methodologies are made for both flowfield structure and surface quantities.

Description: The transformation validity question utilizing resulting data from direct numerical simulations (DNS) of supersonic, isothermal cold wall channel flow was investigated. The DNS results stood for a wide scope of parameter and were suitable for the purpose of examining the generality of Van Driest transformation. The Van Driest law of the wall can be obtained from the inner-layer similarity arguments. It was demonstrated that the Van Driest transformation cannot be incorporated to collapse the sublayer and log-layer velocity profiles simultaneously. Velocity and temperature predictions according to the preceding composite mixing-length model were presented. Despite satisfactory congruity with the DNS data, the model must be perceived as an engineering guide and not as a rigorous analysis.

Description: A Monte Carlo solution technique has been formulated to predict the radiative heat transfer in three-dimensional, inhomogeneous participating media which exhibit spectrally dependent emission and absorption and anisotropic scattering. Details of the technique and selected numerical sensitivities are discussed. The technique was applied to a problem involving a medium composed of a gas mixture of carbon dioxide and nitrogen and suspended carbon particles. A homogeneous medium was modeled to examine the effect of total pressure and carbon-particle concentration on radiative heat transfer. Variation in total pressure, over the range studied, had minimal effect on the amount of heat radiated to the enclosure walls and on the radiative-flux distribution within the medium. Increases in the carbon particle concentration produced significantly higher heat fluxes at the boundaries and altered the radiative flux distribution. The technique was then applied to an inhomogeneous medium to examine effects of specific temperature and carbon particle concentration distributions on radiative heat transfer. For the inhomogeneous conditions examined, the largest radiative flux divergence occurs near the center of the medium and the regions near some enclosure walls act as energy sinks.

Description: Numerical results obtained with direct simulation Monte Carlo and Navier-Stokes methods are presented for a Mach-20 nitrogen flow about a 70-deg blunted cone. The flow conditions simulated are those that can be obtained in existing low-density hypersonic wind tunnels. Three sets of flow conditions are considered with freestream Knudsen numbers ranging from 0.03 to 0.001. The focus is on the wake structure: how the wake structure changes as a function of rare faction, what the afterbody levels of heating are, and to what limits the continuum models are realistic as rarefunction in the wake is progressively increased. Calculations are made with and without an afterbody sting. Results for the afterbody sting are emphasized in anticipation of an experimental study for the current flow conditions and model configuration. The Navier-Stokes calculations were made with and without slip boundary conditions. Comparisons of the results obtained with the two simulation methodologies are made for both flowfield structure and surface quantities.

Description: The Simplified Shuttle Payload Thermal Analyzer program (SSPTA) was developed to aid in the evaluation of thermal design concepts of instruments to be flown in the Space Shuttle cargo bay. SSPTA consists of a collection of programs that are currently used in the thermal analysis of spacecraft and have been modified for quick, preliminary analysis of payloads. SSPTA includes a reduced math model of the Shuttle cargo bay to simplify use of the program for payload analysis. One of the prime objectives in developing SSPTA was to create a program which was easy to use. With SSPTA, the user required input is simple and the user is free from many of the concerns of computer usage such as disk space handling, tape usage, and complicated program control. Although SSPTA was designed primarily to analyze Shuttle payloads, it can easily be used to perform thermal analysis in other situations. SSPTA is comprised of a system of data files called 'bins', a master program, and a set of thermal subprograms. The bin system is a collection of disk files which contain data required by or computed by the thermal subprograms. SSPTA currently has the capability of handling 50 bins. The master program serves primarily as a manager for the bin system and its interaction with the thermal subprograms. Input to the master program consists of simple user commands which direct the data manipulation procedures, prepare the data for these procedures, and call the appropriate thermal subprograms. The subprograms of SSPTA are all based on programs which have been used extensively in the analysis of orbiting spacecraft and space hardware. Subprogram CONSHAD uses the user supplied geometric radiation model to compute black body view factors, shadow factors, and a description of the surface model. The subprogram WORKSHEET uses the surface model description, optical property data, and node assignment data to prepare input for SCRIPTF. Subprogram SCRIPTF computes the inverses of the infrared (IR) and ultraviolet (UV) radiation transfer equations; it also computes the radiation coupling between nodes in the thermal model. Subprogram ORBITAL uses the shadow tables to compute incident flux intensities on each surface in the geometric model. Subprogram ABSORB uses these flux intensities combined with the IR and UV inverses to compute the IR and UV fluxes absorbed by each surface. The radiation couplings from SCRIPTF and the absorbed fluxes from ABSORB are used by subprogram TTA to compute the temperature and power balance for each node in the thermal model. Output consists of tabulated data from each of the subprograms executed during a particular analysis. Due to the modular form of SSPTA, analyses may be run in whole or in part, and new subprograms may be added by the user. SSPTA is written in FORTRAN for use on a DEC VAX-11/780. SSPTA was originally developed in 1977 for use on IBM 370 series computers. This version is an update which was ported to the VAX in 1980.

Description: Remote Interactive Particle-tracing (RIP) is a distributed-graphics program which computes particle traces for computational fluid dynamics (CFD) solution data sets. A particle trace is a line which shows the path a massless particle in a fluid will take; it is a visual image of where the fluid is going. The program is able to compute and display particle traces at a speed of about one trace per second because it runs on two machines concurrently. The data used by the program is contained in two files. The solution file contains data on density, momentum and energy quantities of a flow field at discrete points in three-dimensional space, while the grid file contains the physical coordinates of each of the discrete points. RIP requires two computers. A local graphics workstation interfaces with the user for program control and graphics manipulation, and a remote machine interfaces with the solution data set and performs time-intensive computations. The program utilizes two machines in a distributed mode for two reasons. First, the data to be used by the program is usually generated on the supercomputer. RIP avoids having to convert and transfer the data, eliminating any memory limitations of the local machine. Second, as computing the particle traces can be computationally expensive, RIP utilizes the power of the supercomputer for this task. Although the remote site code was developed on a CRAY, it is possible to port this to any supercomputer class machine with a UNIX-like operating system. Integration of a velocity field from a starting physical location produces the particle trace. The remote machine computes the particle traces using the particle-tracing subroutines from PLOT3D/AMES, a CFD post-processing graphics program available from COSMIC (ARC-12779). These routines use a second-order predictor-corrector method to integrate the velocity field. Then the remote program sends graphics tokens to the local machine via a remote-graphics library. The local machine interprets the graphics tokens and draws the particle traces. The program is menu driven. RIP is implemented on the silicon graphics IRIS 3000 (local workstation) with an IRIX operating system and on the CRAY2 (remote station) with a UNICOS 1.0 or 2.0 operating system. The IRIS 4D can be used in place of the IRIS 3000. The program is written in C (67%) and FORTRAN 77 (43%) and has an IRIS memory requirement of 4 MB. The remote and local stations must use the same user ID. PLOT3D/AMES unformatted data sets are required for the remote machine. The program was developed in 1988.

Description: This software package includes two programs, the KPD12 and the KPD12P. Both programs utilizes the vortex-blob method to simulate flow around solid bodies, in an unbounded domain using the KPD12, with periodicity in one direction using the KPD12P. The main advantage of the vortex-blob method is the ability to handle situations involving arbitrary shapes including multiple bodies. The user just supplies points on the solid boundaries; there is no grid. The KPD12 program has worked successfully on bluff bodies, stalled wings, and multiple-element airfoils. The KPD12P program has been used successfully on high-solidity separated cascades and on cases of rotating stall in cascades of thin airfoils. However, they do not capture subtle viscous effects such as incipient separation and friction drag. The KPD12 and the KPD12P programs apply the vortex-blob method to time-dependent, high-Reynolds-number flows around solid bodies. Both programs solve the two-dimensional incompressible Navier-Stokes equations, neglecting the viscous effects away from the walls. By creating new vortices along the wall at every time step, they treat the no-penetration and no-slip boundary conditions while using an influence matrix. The code automatically controls the number of vortices. Furthermore, the code has the option of treating the boundary layers by simple integral methods to determine the separation points. The KPD12 outputs forces, moments, and pressure distributions on the bodies. The KPD12P also outputs the turning angle and loss of total pressure. The source code is in Cray FORTRAN and contains a few calls to Cray vector functions which are vectorized with the Cray compiler. However, substitutes for these vector functions are provided. The code is set up to plot the bodies, vortex positions, and streamlines using the DISSPLA graphics software. The software requires a mainframe computer with at least 589k of memory available running under COS 1.16. KPD12 was developed in 1988.

Description: The Steady State Thermal Analysis Program (STEADY) provides the thermal designer with a quick and convenient method for calculating heat loads and temperatures. STEADY can be used on small nodal networks for conceptual or preliminary thermal design and analysis. STEADY will accept up to 20 nodes of fixed or variable temperature, with constant or temperature-dependent thermal conductivities, and any set of consistent units. In a steady state thermal network, the heat balance on each variable temperature node must sum to zero. The general heat transfer equations are solved with a Newton-Raphson technique and refined by a fourth order quartic solution. Input data includes the number of nodes, number of boundary nodes, the fixed temperatures at all boundary nodes, initial temperature guesses for variable nodes, impressed heat loads, conduction and radiation coefficients, and control parameters such as convergence criteria, maximum iterations, and damping factors. The output is stored in a print file and tabulates final temperatures and heat flows for all nodes. STEADY is menu driven and allows the user to save files for future modification. STEADY is written in FORTRAN 77 (Ryan McFarland's RMFORTRAN) for interactive execution and has been implemented on the IBM PC computer series under DOS with a central memory requirement of approximately 92K of 8 bit bytes using a math coprocessor, and 103K bytes without the coprocessor. This program was developed in 1987.

Description: The Thermal Radiation Analyzer System, TRASYS, is a computer software system with generalized capability to solve the radiation related aspects of thermal analysis problems. TRASYS computes the total thermal radiation environment for a spacecraft in orbit. The software calculates internode radiation interchange data as well as incident and absorbed heat rate data originating from environmental radiant heat sources. TRASYS provides data of both types in a format directly usable by such thermal analyzer programs as SINDA/FLUINT (available from COSMIC, program number MSC-21528). One primary feature of TRASYS is that it allows users to write their own driver programs to organize and direct the preprocessor and processor library routines in solving specific thermal radiation problems. The preprocessor first reads and converts the user's geometry input data into the form used by the processor library routines. Then, the preprocessor accepts the user's driving logic, written in the TRASYS modified FORTRAN language. In many cases, the user has a choice of routines to solve a given problem. Users may also provide their own routines where desirable. In particular, the user may write output routines to provide for an interface between TRASYS and any thermal analyzer program using the R-C network concept. Input to the TRASYS program consists of Options and Edit data, Model data, and Logic Flow and Operations data. Options and Edit data provide for basic program control and user edit capability. The Model data describe the problem in terms of geometry and other properties. This information includes surface geometry data, documentation data, nodal data, block coordinate system data, form factor data, and flux data. Logic Flow and Operations data house the user's driver logic, including the sequence of subroutine calls and the subroutine library. Output from TRASYS consists of two basic types of data: internode radiation interchange data, and incident and absorbed heat rate data. The flexible structure of TRASYS allows considerable freedom in the definition and choice of solution method for a thermal radiation problem. The program's flexible structure has also allowed TRASYS to retain the same basic input structure as the authors update it in order to keep up with changing requirements. Among its other important features are the following: 1) up to 3200 node problem size capability with shadowing by intervening opaque or semi-transparent surfaces; 2) choice of diffuse, specular, or diffuse/specular radiant interchange solutions; 3) a restart capability that minimizes recomputing; 4) macroinstructions that automatically provide the executive logic for orbit generation that optimizes the use of previously completed computations; 5) a time variable geometry package that provides automatic pointing of the various parts of an articulated spacecraft and an automatic look-back feature that eliminates redundant form factor calculations; 6) capability to specify submodel names to identify sets of surfaces or components as an entity; and 7) subroutines to perform functions which save and recall the internodal and/or space form factors in subsequent steps for nodes with fixed geometry during a variable geometry run. There are two machine versions of TRASYS v27: a DEC VAX version and a Cray UNICOS version. Both versions require installation of the NASADIG library (MSC-21801 for DEC VAX or COS-10049 for CRAY), which is available from COSMIC either separately or bundled with TRASYS. The NASADIG (NASA Device Independent Graphics Library) plot package provides a pictorial representation of input geometry, orbital/orientation parameters, and heating rate output as a function of time. NASADIG supports Tektronix terminals. The CRAY version of TRASYS v27 is written in FORTRAN 77 for batch or interactive execution and has been implemented on CRAY X-MP and CRAY Y-MP series computers running UNICOS. The standard distribution medium for MSC-21959 (CRAY version without NASADIG) is a 1600 BPI 9-track magnetic tape in UNIX tar format. The standard distribution medium for COS-10040 (CRAY version with NASADIG) is a set of two 6250 BPI 9-track magnetic tapes in UNIX tar format. Alternate distribution media and formats are available upon request. The DEC VAX version of TRASYS v27 is written in FORTRAN 77 for batch execution (only the plotting driver program is interactive) and has been implemented on a DEC VAX 8650 computer under VMS. Since the source codes for MSC-21030 and COS-10026 are in VAX/VMS text library files and DEC Command Language files, COSMIC will only provide these programs in the following formats: MSC-21030, TRASYS (DEC VAX version without NASADIG) is available on a 1600 BPI 9-track magnetic tape in VAX BACKUP format (standard distribution medium) or in VAX BACKUP format on a TK50 tape cartridge; COS-10026, TRASYS (DEC VAX version with NASADIG), is available in VAX BACKUP format on a set of three 6250 BPI 9-track magnetic tapes (standard distribution medium) or a set of three TK50 tape cartridges in VAX BACKUP format. TRASYS was last updated in 1993.

Description: TDIGG is a fast and versatile program for generating two-dimensional computational grids for use with finite-difference flow-solvers. Both algebraic and elliptic grid generation systems are included. The method for grid generation by algebraic transformation is based on an interpolation algorithm and the elliptic grid generation is established by solving the partial differential equation (PDE). Non-uniform grid distributions are carried out using a hyperbolic tangent stretching function. For algebraic grid systems, interpolations in one direction (univariate) and two directions (bivariate) are considered. These interpolations are associated with linear or cubic Lagrangian/Hermite/Bezier polynomial functions. The algebraic grids can subsequently be smoothed using an elliptic solver. For elliptic grid systems, the PDE can be in the form of Laplace (zero forcing function) or Poisson. The forcing functions in the Poisson equation come from the boundary or the entire domain of the initial algebraic grids. A graphics interface procedure using the Silicon Graphics (GL) Library is included to allow users to visualize the grid variations at each iteration. This will allow users to interactively modify the grid to match their applications. TDIGG is written in FORTRAN 77 for Silicon Graphics IRIS series computers running IRIX. This package requires either MIT's X Window System, Version 11 Revision 4 or SGI (Motif) Window System. A sample executable is provided on the distribution medium. It requires 148K of RAM for execution. The standard distribution medium is a .25 inch streaming magnetic IRIX tape cartridge in UNIX tar format. This program was developed in 1992.

Description: The Systems Improved Numerical Fluids Analysis Code, SINFAC, consists of additional routines added to the April 1983 revision of SINDA, a general thermal analyzer program. The purpose of the additional routines is to allow for the modeling of active heat transfer loops. The modeler can simulate the steady-state and pseudo-transient operations of 16 different heat transfer loop components including radiators, evaporators, condensers, mechanical pumps, reservoirs and many types of valves and fittings. In addition, the program contains a property analysis routine that can be used to compute the thermodynamic properties of 20 different refrigerants. SINFAC can simulate the response to transient boundary conditions. SINFAC was first developed as a method for computing the steady-state performance of two phase systems. It was then modified using CNFRWD, SINDA's explicit time-integration scheme, to accommodate transient thermal models. However, SINFAC cannot simulate pressure drops due to time-dependent fluid acceleration, transient boil-out, or transient fill-up, except in the accumulator. SINFAC also requires the user to be familiar with SINDA. The solution procedure used by SINFAC is similar to that which an engineer would use to solve a system manually. The solution to a system requires the determination of all of the outlet conditions of each component such as the flow rate, pressure, and enthalpy. To obtain these values, the user first estimates the inlet conditions to the first component of the system, then computes the outlet conditions from the data supplied by the manufacturer of the first component. The user then estimates the temperature at the outlet of the third component and computes the corresponding flow resistance of the second component. With the flow resistance of the second component, the user computes the conditions down stream, namely the inlet conditions of the third. The computations follow for the rest of the system, back to the first component. On the first pass, the user finds that the calculated outlet conditions of the last component do not match the estimated inlet conditions of the first. The user then modifies the estimated inlet conditions of the first component in an attempt to match the calculated values. The user estimated values are called State Variables. The differences between the user estimated values and calculated values are called the Error Variables. The procedure systematically changes the State Variables until all of the Error Variables are less than the user-specified iteration limits. The solution procedure is referred to as SCX. It consists of two phases, the Systems phase and the Controller phase. The X is to imply experimental. SCX computes each next set of State Variables in two phases. In the first phase, SCX fixes the controller positions and modifies the other State Variables by the Newton-Raphson method. This first phase is the Systems phase. Once the Newton-Raphson method has solved the problem for the fixed controller positions, SCX next calculates new controller positions based on Newton's method while treating each sensor-controller pair independently but allowing all to change in one iteration. This phase is the Controller phase. SINFAC is available by license for a period of ten (10) years to approved licensees. The licenced program product includes the source code for the additional routines to SINDA, the SINDA object code, command procedures, sample data and supporting documentation. Additional documentation may be purchased at the price below. SINFAC was created for use on a DEC VAX under VMS. Source code is written in FORTRAN 77, requires 180k of memory, and should be fully transportable. The program was developed in 1988.

Description: The Thermal Radiation Analyzer System, TRASYS, is a computer software system with generalized capability to solve the radiation related aspects of thermal analysis problems. TRASYS computes the total thermal radiation environment for a spacecraft in orbit. The software calculates internode radiation interchange data as well as incident and absorbed heat rate data originating from environmental radiant heat sources. TRASYS provides data of both types in a format directly usable by such thermal analyzer programs as SINDA/FLUINT (available from COSMIC, program number MSC-21528). One primary feature of TRASYS is that it allows users to write their own driver programs to organize and direct the preprocessor and processor library routines in solving specific thermal radiation problems. The preprocessor first reads and converts the user's geometry input data into the form used by the processor library routines. Then, the preprocessor accepts the user's driving logic, written in the TRASYS modified FORTRAN language. In many cases, the user has a choice of routines to solve a given problem. Users may also provide their own routines where desirable. In particular, the user may write output routines to provide for an interface between TRASYS and any thermal analyzer program using the R-C network concept. Input to the TRASYS program consists of Options and Edit data, Model data, and Logic Flow and Operations data. Options and Edit data provide for basic program control and user edit capability. The Model data describe the problem in terms of geometry and other properties. This information includes surface geometry data, documentation data, nodal data, block coordinate system data, form factor data, and flux data. Logic Flow and Operations data house the user's driver logic, including the sequence of subroutine calls and the subroutine library. Output from TRASYS consists of two basic types of data: internode radiation interchange data, and incident and absorbed heat rate data. The flexible structure of TRASYS allows considerable freedom in the definition and choice of solution method for a thermal radiation problem. The program's flexible structure has also allowed TRASYS to retain the same basic input structure as the authors update it in order to keep up with changing requirements. Among its other important features are the following: 1) up to 3200 node problem size capability with shadowing by intervening opaque or semi-transparent surfaces; 2) choice of diffuse, specular, or diffuse/specular radiant interchange solutions; 3) a restart capability that minimizes recomputing; 4) macroinstructions that automatically provide the executive logic for orbit generation that optimizes the use of previously completed computations; 5) a time variable geometry package that provides automatic pointing of the various parts of an articulated spacecraft and an automatic look-back feature that eliminates redundant form factor calculations; 6) capability to specify submodel names to identify sets of surfaces or components as an entity; and 7) subroutines to perform functions which save and recall the internodal and/or space form factors in subsequent steps for nodes with fixed geometry during a variable geometry run. There are two machine versions of TRASYS v27: a DEC VAX version and a Cray UNICOS version. Both versions require installation of the NASADIG library (MSC-21801 for DEC VAX or COS-10049 for CRAY), which is available from COSMIC either separately or bundled with TRASYS. The NASADIG (NASA Device Independent Graphics Library) plot package provides a pictorial representation of input geometry, orbital/orientation parameters, and heating rate output as a function of time. NASADIG supports Tektronix terminals. The CRAY version of TRASYS v27 is written in FORTRAN 77 for batch or interactive execution and has been implemented on CRAY X-MP and CRAY Y-MP series computers running UNICOS. The standard distribution medium for MSC-21959 (CRAY version without NASADIG) is a 1600 BPI 9-track magnetic tape in UNIX tar format. The standard distribution medium for COS-10040 (CRAY version with NASADIG) is a set of two 6250 BPI 9-track magnetic tapes in UNIX tar format. Alternate distribution media and formats are available upon request. The DEC VAX version of TRASYS v27 is written in FORTRAN 77 for batch execution (only the plotting driver program is interactive) and has been implemented on a DEC VAX 8650 computer under VMS. Since the source codes for MSC-21030 and COS-10026 are in VAX/VMS text library files and DEC Command Language files, COSMIC will only provide these programs in the following formats: MSC-21030, TRASYS (DEC VAX version without NASADIG) is available on a 1600 BPI 9-track magnetic tape in VAX BACKUP format (standard distribution medium) or in VAX BACKUP format on a TK50 tape cartridge; COS-10026, TRASYS (DEC VAX version with NASADIG), is available in VAX BACKUP format on a set of three 6250 BPI 9-track magnetic tapes (standard distribution medium) or a set of three TK50 tape cartridges in VAX BACKUP format. TRASYS was last updated in 1993.

Description: INS3D computes steady-state solutions to the incompressible Navier-Stokes equations. The INS3D approach utilizes pseudo-compressibility combined with an approximate factorization scheme. This computational fluid dynamics (CFD) code has been verified on problems such as flow through a channel, flow over a backwardfacing step and flow over a circular cylinder. Three dimensional cases include flow over an ogive cylinder, flow through a rectangular duct, wind tunnel inlet flow, cylinder-wall juncture flow and flow through multiple posts mounted between two plates. INS3D uses a pseudo-compressibility approach in which a time derivative of pressure is added to the continuity equation, which together with the momentum equations form a set of four equations with pressure and velocity as the dependent variables. The equations' coordinates are transformed for general three dimensional applications. The equations are advanced in time by the implicit, non-iterative, approximately-factored, finite-difference scheme of Beam and Warming. The numerical stability of the scheme depends on the use of higher-order smoothing terms to damp out higher-frequency oscillations caused by second-order central differencing. The artificial compressibility introduces pressure (sound) waves of finite speed (whereas the speed of sound would be infinite in an incompressible fluid). As the solution converges, these pressure waves die out, causing the derivation of pressure with respect to time to approach zero. Thus, continuity is satisfied for the incompressible fluid in the steady state. Computational efficiency is achieved using a diagonal algorithm. A block tri-diagonal option is also available. When a steady-state solution is reached, the modified continuity equation will satisfy the divergence-free velocity field condition. INS3D is capable of handling several different types of boundaries encountered in numerical simulations, including solid-surface, inflow and outflow, and far-field boundaries. Three machine versions of INS3D are available. INS3D for the CRAY is written in CRAY FORTRAN for execution on a CRAY X-MP under COS, INS3D for the IBM is written in FORTRAN 77 for execution on an IBM 3090 under the VM or MVS operating system, and INS3D for DEC RISC-based systems is written in RISC FORTRAN for execution on a DEC workstation running RISC ULTRIX 3.1 or later. The CRAY version has a central memory requirement of 730279 words. The central memory requirement for the IBM is 150Mb. The memory requirement for the DEC RISC ULTRIX version is 3Mb of main memory. INS3D was developed in 1987. The port to the IBM was done in 1990. The port to the DECstation 3100 was done in 1991. CRAY is a registered trademark of Cray Research Inc. IBM is a registered trademark of International Business Machines. DEC, DECstation, and ULTRIX are trademarks of the Digital Equipment Corporation.

Description: SAGE, Self Adaptive Grid codE, is a flexible tool for adapting and restructuring both 2D and 3D grids. Solution-adaptive grid methods are useful tools for efficient and accurate flow predictions. In supersonic and hypersonic flows, strong gradient regions such as shocks, contact discontinuities, shear layers, etc., require careful distribution of grid points to minimize grid error and produce accurate flow-field predictions. SAGE helps the user obtain more accurate solutions by intelligently redistributing (i.e. adapting) the original grid points based on an initial or interim flow-field solution. The user then computes a new solution using the adapted grid as input to the flow solver. The adaptive-grid methodology poses the problem in an algebraic, unidirectional manner for multi-dimensional adaptations. The procedure is analogous to applying tension and torsion spring forces proportional to the local flow gradient at every grid point and finding the equilibrium position of the resulting system of grid points. The multi-dimensional problem of grid adaption is split into a series of one-dimensional problems along the computational coordinate lines. The reduced one dimensional problem then requires a tridiagonal solver to find the location of grid points along a coordinate line. Multi-directional adaption is achieved by the sequential application of the method in each coordinate direction. The tension forces direct the redistribution of points to the strong gradient region. To maintain smoothness and a measure of orthogonality of grid lines, torsional forces are introduced that relate information between the family of lines adjacent to one another. The smoothness and orthogonality constraints are direction-dependent, since they relate only the coordinate lines that are being adapted to the neighboring lines that have already been adapted. Therefore the solutions are non-unique and depend on the order and direction of adaption. Non-uniqueness of the adapted grid is acceptable since it makes possible an overall and local error reduction through grid redistribution. SAGE includes the ability to modify the adaption techniques in boundary regions, which substantially improves the flexibility of the adaptive scheme. The vectorial approach used in the analysis also provides flexibility. The user has complete choice of adaption direction and order of sequential adaptions without concern for the computational data structure. Multiple passes are available with no restraint on stepping directions; for each adaptive pass the user can choose a completely new set of adaptive parameters. This facility, combined with the capability of edge boundary control, enables the code to individually adapt multi-dimensional multiple grids. Zonal grids can be adapted while maintaining continuity along the common boundaries. For patched grids, the multiple-pass capability enables complete adaption. SAGE is written in FORTRAN 77 and is intended to be machine independent; however, it requires a FORTRAN compiler which supports NAMELIST input. It has been successfully implemented on Sun series computers, SGI IRIS's, DEC MicroVAX computers, HP series computers, the Cray YMP, and IBM PC compatibles. Source code is provided, but no sample input and output files are provided. The code reads three datafiles: one that contains the initial grid coordinates (x,y,z), one that contains corresponding flow-field variables, and one that contains the user control parameters. It is assumed that the first two datasets are formatted as defined in the plotting software package PLOT3D. Several machine versions of PLOT3D are available from COSMIC. The amount of main memory is dependent on the size of the matrix. The standard distribution medium for SAGE is a 5.25 inch 360K MS-DOS format diskette. It is also available on a .25 inch streaming magnetic tape cartridge in UNIX tar format or on a 9-track 1600 BPI ASCII CARD IMAGE format magnetic tape. SAGE was developed in 1989, first released as a 2D version in 1991 and updated to 3D in 1993.

Description: INS3D computes steady-state solutions to the incompressible Navier-Stokes equations. The INS3D approach utilizes pseudo-compressibility combined with an approximate factorization scheme. This computational fluid dynamics (CFD) code has been verified on problems such as flow through a channel, flow over a backwardfacing step and flow over a circular cylinder. Three dimensional cases include flow over an ogive cylinder, flow through a rectangular duct, wind tunnel inlet flow, cylinder-wall juncture flow and flow through multiple posts mounted between two plates. INS3D uses a pseudo-compressibility approach in which a time derivative of pressure is added to the continuity equation, which together with the momentum equations form a set of four equations with pressure and velocity as the dependent variables. The equations' coordinates are transformed for general three dimensional applications. The equations are advanced in time by the implicit, non-iterative, approximately-factored, finite-difference scheme of Beam and Warming. The numerical stability of the scheme depends on the use of higher-order smoothing terms to damp out higher-frequency oscillations caused by second-order central differencing. The artificial compressibility introduces pressure (sound) waves of finite speed (whereas the speed of sound would be infinite in an incompressible fluid). As the solution converges, these pressure waves die out, causing the derivation of pressure with respect to time to approach zero. Thus, continuity is satisfied for the incompressible fluid in the steady state. Computational efficiency is achieved using a diagonal algorithm. A block tri-diagonal option is also available. When a steady-state solution is reached, the modified continuity equation will satisfy the divergence-free velocity field condition. INS3D is capable of handling several different types of boundaries encountered in numerical simulations, including solid-surface, inflow and outflow, and far-field boundaries. Three machine versions of INS3D are available. INS3D for the CRAY is written in CRAY FORTRAN for execution on a CRAY X-MP under COS, INS3D for the IBM is written in FORTRAN 77 for execution on an IBM 3090 under the VM or MVS operating system, and INS3D for DEC RISC-based systems is written in RISC FORTRAN for execution on a DEC workstation running RISC ULTRIX 3.1 or later. The CRAY version has a central memory requirement of 730279 words. The central memory requirement for the IBM is 150Mb. The memory requirement for the DEC RISC ULTRIX version is 3Mb of main memory. INS3D was developed in 1987. The port to the IBM was done in 1990. The port to the DECstation 3100 was done in 1991. CRAY is a registered trademark of Cray Research Inc. IBM is a registered trademark of International Business Machines. DEC, DECstation, and ULTRIX are trademarks of the Digital Equipment Corporation.

Description: The ability to treat arbitrary boundary shapes is one of the most desirable characteristics of a method for generating grids, including those about airfoils. In a grid used for computing aerodynamic flow over an airfoil, or any other body shape, the surface of the body is usually treated as an inner boundary and often cannot be easily represented as an analytic function. The GRAPE computer program was developed to incorporate a method for generating two-dimensional finite-difference grids about airfoils and other shapes by the use of the Poisson differential equation. GRAPE can be used with any boundary shape, even one specified by tabulated points and including a limited number of sharp corners. The GRAPE program has been developed to be numerically stable and computationally fast. GRAPE can provide the aerodynamic analyst with an efficient and consistent means of grid generation. The GRAPE procedure generates a grid between an inner and an outer boundary by utilizing an iterative procedure to solve the Poisson differential equation subject to geometrical restraints. In this method, the inhomogeneous terms of the equation are automatically chosen such that two important effects are imposed on the grid. The first effect is control of the spacing between mesh points along mesh lines intersecting the boundaries. The second effect is control of the angles with which mesh lines intersect the boundaries. Along with the iterative solution to Poisson's equation, a technique of coarse-fine sequencing is employed to accelerate numerical convergence. GRAPE program control cards and input data are entered via the NAMELIST feature. Each variable has a default value such that user supplied data is kept to a minimum. Basic input data consists of the boundary specification, mesh point spacings on the boundaries, and mesh line angles at the boundaries. Output consists of a dataset containing the grid data and, if requested, a plot of the generated mesh. The GRAPE program is written in FORTRAN IV for batch execution and has been implemented on a CDC 6000 series computer with a central memory requirement of approximately 135K (octal) of 60 bit words. For plotted output the commercially available DISSPLA graphics software package is required. The GRAPE program was developed in 1980.

Description: The Thermal Radiation Analyzer System, TRASYS, is a computer software system with generalized capability to solve the radiation related aspects of thermal analysis problems. TRASYS computes the total thermal radiation environment for a spacecraft in orbit. The software calculates internode radiation interchange data as well as incident and absorbed heat rate data originating from environmental radiant heat sources. TRASYS provides data of both types in a format directly usable by such thermal analyzer programs as SINDA/FLUINT (available from COSMIC, program number MSC-21528). One primary feature of TRASYS is that it allows users to write their own driver programs to organize and direct the preprocessor and processor library routines in solving specific thermal radiation problems. The preprocessor first reads and converts the user's geometry input data into the form used by the processor library routines. Then, the preprocessor accepts the user's driving logic, written in the TRASYS modified FORTRAN language. In many cases, the user has a choice of routines to solve a given problem. Users may also provide their own routines where desirable. In particular, the user may write output routines to provide for an interface between TRASYS and any thermal analyzer program using the R-C network concept. Input to the TRASYS program consists of Options and Edit data, Model data, and Logic Flow and Operations data. Options and Edit data provide for basic program control and user edit capability. The Model data describe the problem in terms of geometry and other properties. This information includes surface geometry data, documentation data, nodal data, block coordinate system data, form factor data, and flux data. Logic Flow and Operations data house the user's driver logic, including the sequence of subroutine calls and the subroutine library. Output from TRASYS consists of two basic types of data: internode radiation interchange data, and incident and absorbed heat rate data. The flexible structure of TRASYS allows considerable freedom in the definition and choice of solution method for a thermal radiation problem. The program's flexible structure has also allowed TRASYS to retain the same basic input structure as the authors update it in order to keep up with changing requirements. Among its other important features are the following: 1) up to 3200 node problem size capability with shadowing by intervening opaque or semi-transparent surfaces; 2) choice of diffuse, specular, or diffuse/specular radiant interchange solutions; 3) a restart capability that minimizes recomputing; 4) macroinstructions that automatically provide the executive logic for orbit generation that optimizes the use of previously completed computations; 5) a time variable geometry package that provides automatic pointing of the various parts of an articulated spacecraft and an automatic look-back feature that eliminates redundant form factor calculations; 6) capability to specify submodel names to identify sets of surfaces or components as an entity; and 7) subroutines to perform functions which save and recall the internodal and/or space form factors in subsequent steps for nodes with fixed geometry during a variable geometry run. There are two machine versions of TRASYS v27: a DEC VAX version and a Cray UNICOS version. Both versions require installation of the NASADIG library (MSC-21801 for DEC VAX or COS-10049 for CRAY), which is available from COSMIC either separately or bundled with TRASYS. The NASADIG (NASA Device Independent Graphics Library) plot package provides a pictorial representation of input geometry, orbital/orientation parameters, and heating rate output as a function of time. NASADIG supports Tektronix terminals. The CRAY version of TRASYS v27 is written in FORTRAN 77 for batch or interactive execution and has been implemented on CRAY X-MP and CRAY Y-MP series computers running UNICOS. The standard distribution medium for MSC-21959 (CRAY version without NASADIG) is a 1600 BPI 9-track magnetic tape in UNIX tar format. The standard distribution medium for COS-10040 (CRAY version with NASADIG) is a set of two 6250 BPI 9-track magnetic tapes in UNIX tar format. Alternate distribution media and formats are available upon request. The DEC VAX version of TRASYS v27 is written in FORTRAN 77 for batch execution (only the plotting driver program is interactive) and has been implemented on a DEC VAX 8650 computer under VMS. Since the source codes for MSC-21030 and COS-10026 are in VAX/VMS text library files and DEC Command Language files, COSMIC will only provide these programs in the following formats: MSC-21030, TRASYS (DEC VAX version without NASADIG) is available on a 1600 BPI 9-track magnetic tape in VAX BACKUP format (standard distribution medium) or in VAX BACKUP format on a TK50 tape cartridge; COS-10026, TRASYS (DEC VAX version with NASADIG), is available in VAX BACKUP format on a set of three 6250 BPI 9-track magnetic tapes (standard distribution medium) or a set of three TK50 tape cartridges in VAX BACKUP format. TRASYS was last updated in 1993.

Description: INS3D computes steady-state solutions to the incompressible Navier-Stokes equations. The INS3D approach utilizes pseudo-compressibility combined with an approximate factorization scheme. This computational fluid dynamics (CFD) code has been verified on problems such as flow through a channel, flow over a backwardfacing step and flow over a circular cylinder. Three dimensional cases include flow over an ogive cylinder, flow through a rectangular duct, wind tunnel inlet flow, cylinder-wall juncture flow and flow through multiple posts mounted between two plates. INS3D uses a pseudo-compressibility approach in which a time derivative of pressure is added to the continuity equation, which together with the momentum equations form a set of four equations with pressure and velocity as the dependent variables. The equations' coordinates are transformed for general three dimensional applications. The equations are advanced in time by the implicit, non-iterative, approximately-factored, finite-difference scheme of Beam and Warming. The numerical stability of the scheme depends on the use of higher-order smoothing terms to damp out higher-frequency oscillations caused by second-order central differencing. The artificial compressibility introduces pressure (sound) waves of finite speed (whereas the speed of sound would be infinite in an incompressible fluid). As the solution converges, these pressure waves die out, causing the derivation of pressure with respect to time to approach zero. Thus, continuity is satisfied for the incompressible fluid in the steady state. Computational efficiency is achieved using a diagonal algorithm. A block tri-diagonal option is also available. When a steady-state solution is reached, the modified continuity equation will satisfy the divergence-free velocity field condition. INS3D is capable of handling several different types of boundaries encountered in numerical simulations, including solid-surface, inflow and outflow, and far-field boundaries. Three machine versions of INS3D are available. INS3D for the CRAY is written in CRAY FORTRAN for execution on a CRAY X-MP under COS, INS3D for the IBM is written in FORTRAN 77 for execution on an IBM 3090 under the VM or MVS operating system, and INS3D for DEC RISC-based systems is written in RISC FORTRAN for execution on a DEC workstation running RISC ULTRIX 3.1 or later. The CRAY version has a central memory requirement of 730279 words. The central memory requirement for the IBM is 150Mb. The memory requirement for the DEC RISC ULTRIX version is 3Mb of main memory. INS3D was developed in 1987. The port to the IBM was done in 1990. The port to the DECstation 3100 was done in 1991. CRAY is a registered trademark of Cray Research Inc. IBM is a registered trademark of International Business Machines. DEC, DECstation, and ULTRIX are trademarks of the Digital Equipment Corporation.

Description: The ability to treat arbitrary boundary shapes is one of the most desirable characteristics of a method for generating grids. 3DGRAPE is designed to make computational grids in or about almost any shape. These grids are generated by the solution of Poisson's differential equations in three dimensions. The program automatically finds its own values for inhomogeneous terms which give near-orthogonality and controlled grid cell height at boundaries. Grids generated by 3DGRAPE have been applied to both viscous and inviscid aerodynamic problems, and to problems in other fluid-dynamic areas. 3DGRAPE uses zones to solve the problem of warping one cube into the physical domain in real-world computational fluid dynamics problems. In a zonal approach, a physical domain is divided into regions, each of which maps into its own computational cube. It is believed that even the most complicated physical region can be divided into zones, and since it is possible to warp a cube into each zone, a grid generator which is oriented to zones and allows communication across zonal boundaries (where appropriate) solves the problem of topological complexity. 3DGRAPE expects to read in already-distributed x,y,z coordinates on the bodies of interest, coordinates which will remain fixed during the entire grid-generation process. The 3DGRAPE code makes no attempt to fit given body shapes and redistribute points thereon. Body-fitting is a formidable problem in itself. The user must either be working with some simple analytical body shape, upon which a simple analytical distribution can be easily effected, or must have available some sophisticated stand-alone body-fitting software. 3DGRAPE does not require the user to supply the block-to-block boundaries nor the shapes of the distribution of points. 3DGRAPE will typically supply those block-to-block boundaries simply as surfaces in the elliptic grid. Thus at block-to-block boundaries the following conditions are obtained: (1) grids lines will match up as they approach the block-to-block boundary from either side, (2) grid lines will cross the boundary with no slope discontinuity, (3) the spacing of points along the line piercing the boundary will be continuous, (4) the shape of the boundary will be consistent with the surrounding grid, and (5) the distribution of points on the boundary will be reasonable in view of the surrounding grid. 3DGRAPE offers a powerful building-block approach to complex 3-D grid generation, but is a low-level tool. Users may build each face of each block as they wish, from a wide variety of resources. 3DGRAPE uses point-successive-over-relaxation (point-SOR) to solve the Poisson equations. This method is slow, although it does vectorize nicely. Any number of sophisticated graphics programs may be used on the stored output file of 3DGRAPE though it lacks interactive graphics. Versatility was a prominent consideration in developing the code. The block structure allows a great latitude in the problems it can treat. As the acronym implies, this program should be able to handle just about any physical region into which a computational cube or cubes can be warped. 3DGRAPE was written in FORTRAN 77 and should be machine independent. It was originally developed on a Cray under COS and tested on a MicroVAX 3200 under VMS 5.1.

Description: In the present paper, direct numerical methods by which to simulate the spatially developing free shear flows in the transitional region are described and the numerical results of a spatially developing plane wake are presented. The incompressible time-dependent Navier-Stokes equations were solved using Pade finite difference approximations in the streamwise direction, a mapped pseudospectral Fourier method in the cross-stream direction, and a third-order compact Runge-Kutta scheme for time advancement. The unstable modes of the Orr-Sommerfeld equations were used to perturb the inlet of the wake. Statistical analyses were performed and some numerical results were compared with experimental measurements. When only the fundamental mode is forced, the energy spectra show amplification of the fundamental and its higher harmonics. In this case, unperturbed alternate vortices develop in the saturation region of the wake. The phase jitter around the fundamental frequency plays a critical role in generating vortices of random shape and spacing. Large- and small-scale distortions of the fundamental structure are observed. Pairing of vortices of the same sign is observed, as well as vortex coupling of vortices of the opposite sign.

Description: This book first reviews the overall aspects and background information related to thermal radiation heat transfer and incorporates new general information, advances in analytical and computational techniques, and new reference material. Coverage focuses on radiation from opaque surfaces, radiation interchange between various types of surfaces enclosing a vacuum or transparent medium, and radiation including the effects of partially transmitting media, such as combustion gases, soot, or windows. Boundary conditions and multiple layers are discussed with information on radiation in materials with nonunity refractive indices.

Description: The growth and development of a horseshoe vortex system in an incompressible, three-dimensional turbulent junction flow were investigated experimentally. A streamlined cylinder mounted with its axis normal to a flat surface was used to generate the junction vortex flow. The flow environment was characterized by a body Reynolds number of 183,000, based on the leading edge diameter of the streamlined cylinder. The study included surface flow visualizations, surface pressure measurements, and mean flow measurements of total pressure, static pressure, and velocity distributions in three planes around the base of the streamlined cylinder, and in two planes in the wake flow. Some characterizations of vortex properties based on the measured mean cross-flow velocity components are presented. The results show the presence of a single large, dominant vortex, with strong evidence of a very small corner vortex in the junction between the cylinder and the flat surface. The center of the dominant vortex drifts away from both the body and the flat surface as the flow develops along and downstream of the body. The growth and development of the core of the large, dominant vortex are documented.

Description: The nonlinear resonant-triad interaction, proposed by Raetz (1959), Craik (1971), and others for a Blasius boundary layer, is analyzed here for an adverse-pressure-gradient boundary layer. We assume that the adverse pressure gradient is in some sense weak and, therefore, that the instability growth rate is small. This ensures that there is a well-defined critical layer located somewhere within the flow and that the nonlinear interaction is effectively confined to that layer. The initial interaction is of the parametric resonance type, even when the modal amplitudes are all of the same order. This means that the oblique instability waves exhibit faster than exponential growth and that the growth rate of the two-dimensional mode remains linear. However, the interaction and the resulting growth rates become fully coupled, once oblique-mode amplitudes become sufficiently large, but the coupling terms are now quartic, rather than quadratic as in the Craik (1971) analysis. More importantly, however, new nonlinear interactions, which were not present in the Craik-type analyses, now come into play. These interactions eventually have a dominant effect on the instability wave development.

Description: This algorithm has been developed for calculating both the quantity of compressor bleed flow required to cool a turbine and the resulting decrease in efficiency due to cooling air injected into the gas stream. Because of the trend toward higher turbine inlet temperatures, it is important to accurately predict the required cooling flow. This program is intended for use with axial flow, air-breathing jet propulsion engines with a variety of airfoil cooling configurations. The algorithm results have compared extremely well with figures given by major engine manufacturers for given bulk metal temperatures and cooling configurations. The program calculates the required cooling flow and corresponding decrease in stage efficiency for each row of airfoils throughout the turbine. These values are combined with the thermodynamic efficiency of the uncooled turbine to predict the total bleed airflow required and the altered turbine efficiency. There are ten airfoil cooling configurations and the algorithm allows a different option for each row of cooled airfoils. Materials technology is incorporated and requires the date of the first year of service for the turbine stator vane and rotor blade. The user must specify pressure, temperatures, and gas flows into the turbine. This program is written in FORTRAN IV for batch execution and has been implemented on an IBM 3080 series computer with a central memory requirement of approximately 61K of 8 bit bytes. This program was developed in 1980.

Description: A fast algorithm has been developed for accurately generating boundary-conforming, three-dimensional consecutively refined computational grids applicable to arbitrary wing-body and axial turbomachinery geometries. This algorithm has been incorporated into the GRID3O computer program. The method employed in GRID3O is based on using an analytic function to generate two-dimensional grids on a number of coaxial axisymmetric surfaces positioned between the centerbody and the outer radial boundary. These grids are of the O-type and are characterized by quasi-orthogonality, geometric periodicity, and an adequate resolution throughout the flow field. Because the built-in nonorthogonal coordinate stretching and shearing cause the grid lines leaving the blade or wing trailing-edge to end at downstream infinity, use of the generated grid simplifies the numerical treatment of three-dimensional trailing vortex sheets. The GRID3O program is written in FORTRAN IV for batch execution and has been implemented on an IBM 370 series computer with a central memory requirement of approximately 450K of 8 bit bytes. The GRID3O program was developed in 1981.

Description: As turbine-engine core operating conditions become more severe, designers must develop more effective means of cooling blades and vanes. In order to design reliable, cooled turbine blades, advanced transient thermal calculation techniques are required. The TACT1 computer program was developed to perform transient and steady-state heat-transfer and coolant-flow analyses for cooled blades, given the outside hot-gas boundary condition, the coolant inlet conditions, the geometry of the blade shell, and the cooling configuration. TACT1 can analyze turbine blades, or vanes, equipped with a central coolant-plenum insert from which coolant-air impinges on the inner surface of the blade shell. Coolant-side heat-transfer coefficients are calculated with the heat transfer mode at each station being user specified as either impingement with crossflow, forced convection channel flow, or forced convection over pin fins. A limited capability to handle film cooling is also available in the program. The TACT1 program solves for the blade temperature distribution using a transient energy equation for each node. The nodal energy balances are linearized, one-dimensional, heat-conduction equations which are applied at the wall-outer-surface node, at the junction of the cladding and the metal node, and at the wall-inner-surface node. At the mid-metal node a linear, three-dimensional, heat-conduction equation is used. Similarly, the coolant pressure distribution is determined by solving the set of transfer momentum equations for the one-dimensional flow between adjacent fluid nodes. In the coolant channel, energy and momentum equations for one-dimensional compressible flow, including friction and heat transfer, are used for the elemental channel length between two coolant nodes. The TACT1 program first obtains a steady-state solution using iterative calculations to obtain convergence of stable temperatures, pressures, coolant-flow split, and overall coolant mass balance. Transient calculations are based on the steady-state solutions obtained. Input to the TACT1 program includes a geometrical description of the blade and insert, the nodal spacing to be used, and the boundary conditions describing the outside hot-gas and the coolant-inlet conditions. The program output includes the value of nodal temperatures and pressures at each iteration. The final solution output includes the temperature at each coolant node, and the coolant flow rates and Reynolds numbers. This program is written in FORTRAN IV for batch execution and has been implemented on an IBM 360 computer with a central memory requirement of approximately 480K of 8 bit bytes. The TACT1 program was developed in 1978.

Description: This is a finite-difference program for calculating the viscous compressible boundary layer flow over either planar or axisymmetric surfaces. The flow may be initially laminar and progress through a transitional zone to a fully turbulent flow, or it may remain laminar, depending on the imposed boundary conditions, laws of viscosity, and numerical solution of the momentum and energy equations. The flow may also be forced into a turbulent flow at a chosen spot by the data input. The input may contain factors of arbitrary Reynolds number, free-stream Mach number, free stream turbulence, wall heating or cooling, longitudinal wall curvature, wall suction or blowing, and wall roughness. The solution may start from an initial Falkner-Skan similarity profile, an approximate equilibrium turbulent profile, or an initial arbitrary input profile. This program has been implemented on the IBM 7094/7044 Direct Couple System. This program is written in FORTRAN IV and was developed in 1974.

Description: A computer program has been developed for the design of sharp-edged throat supersonic nozzles where losses are accounted for by correcting the ideal nozzle geometry for boundary layer displacement thickness. The ideal nozzle is designed by the method of characteristics to produce uniform parallel flow at the nozzle exit in the smallest possible distance. Boundary-layer parameters (displacement and momentum thicknesses) are calculated for the ideal nozzle, and the final nozzle geometry is obtained by adding the displacement thickness to the ideal nozzle coordinates. The boundary layer parameters are also used to calculate the aftermixing conditions downstream of the nozzle assuming the flow mixes to a uniform state. The computer program input consists essentially of the nozzle-exit Mach number, specific-heat ratio, nozzle angle, throat half-height, nozzle subsonic section coordinates and corresponding pressure ratios, total temperature and pressure, gas constant, and initial momentum or displacement thickness. The program gas properties are set up for air; for other gases, changes are required to the program. The computer program output consists of the corrected nozzle coordinates, the principal boundary-layer parameters, and the aftermixing conditions. This program has been implemented on the IBM 7094/7044 Direct Couple System.

Description: A computer program has been developed which analyzes by means of mathematical models the temperature profiles in the contents of a filled propellant tank. In designing space vehicles using cryogenic liquid propellants, it is necessary to know how heat transferred from the tank walls and heat absorbed internally affect the temperature distribution with the tank contents. The mathematical flow model is based on results from small-scale experiments. The results showed that when a subcooled fluid is subject to both nonuniform internal heating and wall heating, two distinct temperature regions are developed. In the lower region, the fluid is thoroughly mixed and maintains a uniform temperature profile. In the upper region, a stratified layer develops, and a temperature gradient is formed from the accumulation of warm fluid from the boundary layer along the tank walls; it also indicated that the temperature profiles in the stratified layer exhibited similarity. This concept was developed primarily for internal heating caused by nuclear radiation. However, the theory and computer program are applicable for any form of internal or bulk heating. This program is written in FORTRAN IV for batch execution and has been implemented on the IBM 7094. This program was developed in 1970.

Description: This program solves the two-dimensional, compressible laminar or turbulent boundary-layer equations in an arbitrary pressure gradient. Cohen and Reshotko's method is used for the laminar boundary layer, Sasman and Cresci's method for the turbulent boundary layer, and the Schlichting-Ulrich-Granville method to predict transition. Transition may also be forced at any point by the user. Separation, if it occurs, is predicted for both laminar and turbulent flow. The user may begin values for displacement thickness and momentum thickness in either laminar or turbulent flow. This program was implemented on the IBM 7094.

Description: An account is given of interface-driven motions of drops and bubbles. It is shown that even in the simplest cases, theory predicts exotic flow topologies. Attention is given to several unsolved problems that must be addressed both theoretically and experimentally.

Description: Direct numerical simulations were made to examine the local structure of the reaction zone for a moderately fast reaction between unmixed species in decaying, homogeneous turbulence and in a homogeneous turbulent shear flow. Pseudospectral techniques were used in domains of 64 exp 3 and higher wavenumbers. A finite-rate, single step reaction between non-premixed reactants was considered, and in one case temperature-dependent Arrhenius kinetics was assumed. Locally intense reaction rates that tend to persist throughout the simulations occur in locations where the reactant concentration gradients are large and are amplified by the local rate of strain. The reaction zones are more organized in the case of a uniform mean shear than in isotropic turbulence, and regions of intense reaction rate appear to be associated with vortex structures such as horseshoe vortices and fingers seen in mixing layers. Concentration gradients tend to align with the direction of the most compressive principal strain rate, more so in the isotropic case.

Description: New research on hypersonic vehicles, such as the National Aero-Space Plane (NASP), has raised concerns about the effects of shock-wave interference on various structural components of the craft. State-of-the-art aerothermal analysis software is inadequate to predict local flow and heat flux in areas of extremely high heat transfer, such as the surface impingement of an Edney-type supersonic jet. EASI revives and updates older computational methods for calculating inviscid flow field and maximum heating from shock wave interference. The program expands these methods to solve problems involving the six shock-wave interference patterns on a two-dimensional cylindrical leading edge with an equilibrium chemically reacting gas mixture (representing, for example, the scramjet cowl of the NASP). The inclusion of gas chemistry allows for a more accurate prediction of the maximum pressure and heating loads by accounting for the effects of high temperature on the air mixture. Caloric imperfections and specie dissociation of high-temperature air cause shock-wave angles, flow deflection angles, and thermodynamic properties to differ from those calculated by a calorically perfect gas model. EASI contains pressure- and temperature-dependent thermodynamic and transport properties to determine heating rates, and uses either a calorically perfect air model or an 11-specie, 7-reaction reacting air model at equilibrium with temperatures up to 15,000 K for the inviscid flowfield calculations. EASI solves the flow field and the associated maximum surface pressure and heat flux for the six common types of shock wave interference. Depending on the type of interference, the program solves for shock-wave/boundary-layer interaction, expansion-fan/boundary-layer interaction, attaching shear layer or supersonic jet impingement. Heat flux predictions require a knowledge (from experimental data or relevant calculations) of a pertinent length scale of the interaction. Output files contain flow-field information for the various shock-wave interference patterns and their associated maximum surface pressure and heat flux predictions. EASI is written in FORTRAN 77 for a DEC VAX 8500 series computer using the VAX/VMS operating system, and requires 75K of memory. The program is available on a 9-track 1600 BPI magnetic tape in DEC VAX BACKUP format. EASI was developed in 1989. DEC, VAX, and VMS are registered trademarks of the Digital Equipment Corporation.

Description: Current investigations of the hydrogen-fueled supersonic combustion ramjet engine have delineated several technological problem areas. One area, the analysis of the injection, turbulent mixing, and combusiton of hydrogen, requires the accurate calculation of the supersonic combustion flow fields. This calculation has proven difficult because of an interesting phenomena which makes possible the transition from supersonic to subsonic flow in the combustion field, due to the temperature transitions which occur in the flow field. This computer program was developed to use viscous characteristics theory to analyze supersonic combustion flow fields with imbedded subsonic regions. Intended to be used as a practical design tool for two-dimensional and axisymmetric supersonic combustor development, this program has proven useful in the analysis of such problems as determining the flow field of a single underexpanded hydrogen jet, the internal flow of a gas sampling probe, the effects of fuel-injector strut shape, and the effects of changes in combustor configuration. Both combustion and diffusive effects can significantly alter the wave pattern in a supersonic field and generate significant pressure gradients in both the axial and radial directions. The induced pressure, in turn, substantially influences the ignition delay and reaction times as well as the velocity distribution. To accurately analyze the flow fields, the effects of finite rate chemistry, mixing, and wave propagation must be properly linked to one another. The viscous characteristics theory has been used in the past to describe flows that are purely supersonic; however, the interacting pressure effects in the combustor often allow for the development of shock waves and imbedded subsonic regions. Numerical investigation of these transonic situations has required the development of a new viscous characteristics procedure which is valid within the subsonic region and can be coupled with the standard viscous characteristics procedure in the supersonic region. The basic governing equations used are the 'viscous-inviscid' equations, similar to those employed in higher-order boundary layer analyses, with finite rate chemistry terms included. In addition, the Rankine-Hugoniot and Prandtl-Meyer relations are used to compute shock and expansion conditions. The program can handle up to 20 simultaneous shock waves. Chemistry terms are computed for a 7-species 8-mechanism hydrogen-air reaction scheme. The user input consists of a physical description of the combustor and flow determination parameters. Output includes detail flow parameter values at selected points within the flow field. This computer program is written in FORTRAN IV for batch execution and has been implemented on a CDC CYBER 175 with a central memory requirement of approximately 114K (octal) of 60 bit words. The program was developed in 1978.

Description: SINDA, the Systems Improved Numerical Differencing Analyzer, is a software system for solving lumped parameter representations of physical problems governed by diffusion-type equations. SINDA was originally designed for analyzing thermal systems represented in electrical analog, lumped parameter form, although its use may be extended to include other classes of physical systems which can be modeled in this form. As a thermal analyzer, SINDA can handle such interrelated phenomena as sublimation, diffuse radiation within enclosures, transport delay effects, and sensitivity analysis. FLUINT, the FLUid INTegrator, is an advanced one-dimensional fluid analysis program that solves arbitrary fluid flow networks. The working fluids can be single phase vapor, single phase liquid, or two phase. The SINDA'85/FLUINT system permits the mutual influences of thermal and fluid problems to be analyzed. The SINDA system consists of a programming language, a preprocessor, and a subroutine library. The SINDA language is designed for working with lumped parameter representations and finite difference solution techniques. The preprocessor accepts programs written in the SINDA language and converts them into standard FORTRAN. The SINDA library consists of a large number of FORTRAN subroutines that perform a variety of commonly needed actions. The use of these subroutines can greatly reduce the programming effort required to solve many problems. A complete run of a SINDA'85/FLUINT model is a four step process. First, the user's desired model is run through the preprocessor which writes out data files for the processor to read and translates the user's program code. Second, the translated code is compiled. The third step requires linking the user's code with the processor library. Finally, the processor is executed. SINDA'85/FLUINT program features include 20,000 nodes, 100,000 conductors, 100 thermal submodels, and 10 fluid submodels. SINDA'85/FLUINT can also model two phase flow, capillary devices, user defined fluids, gravity and acceleration body forces on a fluid, and variable volumes. SINDA'85/FLUINT offers the following numerical solution techniques. The Finite difference formulation of the explicit method is the Forward-difference explicit approximation. The formulation of the implicit method is the Crank-Nicolson approximation. The program allows simulation of non-uniform heating and facilitates modeling thin-walled heat exchangers. The ability to model non-equilibrium behavior within two-phase volumes is included. Recent improvements to the program were made in modeling real evaporator-pumps and other capillary-assist evaporators. SINDA'85/FLUINT is available by license for a period of ten (10) years to approved licensees. The licensed program product includes the source code and one copy of the supporting documentation. Additional copies of the documentation may be purchased separately at any time. SINDA'85/FLUINT is written in FORTRAN 77. Version 2.3 has been implemented on Cray series computers running UNICOS, CONVEX computers running CONVEX OS, and DEC RISC computers running ULTRIX. Binaries are included with the Cray version only. The Cray version of SINDA'85/FLUINT also contains SINGE, an additional graphics program developed at Johnson Space Flight Center. Both source and executable code are provided for SINGE. Users wishing to create their own SINGE executable will also need the NASA Device Independent Graphics Library (NASADIG, previously known as SMDDIG; UNIX version, MSC-22001). The Cray and CONVEX versions of SINDA'85/FLUINT are available on 9-track 1600 BPI UNIX tar format magnetic tapes. The CONVEX version is also available on a .25 inch streaming magnetic tape cartridge in UNIX tar format. The DEC RISC ULTRIX version is available on a TK50 magnetic tape cartridge in UNIX tar format. SINDA was developed in 1971, and first had fluid capability added in 1975. SINDA'85/FLUINT version 2.3 was released in 1990.

Description: The effects of convection on diffusive-convective physical vapor transport process are examined computationally. We analyze conditions ranging from typical laboratory conditions to conditions achievable only in a low gravity environment. This corresponds to thermal Rayleigh numbers Ra(T) ranging from 1.80 to 1.92 x 10 exp 6. Our results indicate that the effect of the sublimation and condensation fluxes at the boundaries is 10 increase the threshold of instability. For typical ground based conditions time dependent oscillatory convection can occur. This results in nonuniform temperature and concentration gradients at the crystal interface. Spectral analysis of the flow field shows regions of both periodic and quasi-periodic states. Low gravity conditions can effectively reduce convective effects, thus resulting in uniform temperature and concentration gradients at the interface, a desirable condition for crystal growth.

Description: The transient response of a thermal protection material to heat applied to the surface can be calculated using the CHAP III computer program. CHAP III can be used to analyze pyrolysis gas chemical kinetics in detail and examine pyrolysis reactions-indepth. The analysis includes the deposition of solid products produced by chemical reactions in the gas phase. CHAP III uses a modelling technique which can approximate a wide range of ablation problems. The energy equation used in CHAP III incorporates pyrolysis (both solid and gas reactions), convection, conduction, storage, work, kinetic energy, and viscous dissipation. The chemically reacting components of the solid are allowed to vary as a function of position and time. CHAP III employs a finite difference method to approximate the energy equations. Input values include specific heat, thermal conductivity, thermocouple locations, enthalpy, heating rates, and a description of the chemical reactions expected. The output tabulates the temperature at locations throughout the ablator, gas flow within the solid, density of the solid, weight of pyrolysis gases, and rate of carbon deposition. A sample case is included, which analyzes an ablator material containing several pyrolysis reactions subjected to an environment typical of entry at lunar return velocity. CHAP III is written in FORTRAN IV for batch execution and has been implemented on a CDC CYBER 170 series computer operating under NOS with a central memory requirement of approximately 102K (octal) of 60 bit words. This program was developed in 1985.

Description: This program performs a one-dimensional numerical analysis of the transient thermal response of multi-layer insulative systems. The analysis can determine the temperature distribution through a system consisting of from one to four layers, one of which can be an air gap. Concentrated heat sinks at any interface can be included. The computer program based on the analysis will determine the thickness of a specified layer that will satisfy a temperature limit criterion at any point in the insulative system. The program will also automatically calculate the thickness at several points on a system and determine the total system mass. This program was developed as a tool for designing thermal protection systems for high-speed aerospace vehicles but could be adapted to many areas of industry involved in thermal insulation systems. In this package, the equations describing the transient thermal response of a system are developed. The governing differential equation for each layer and boundary condition are put in finite-difference form using a Taylor's series expansion. These equations yield an essentially tridiagonal matrix of unknown temperatures. A procedure based on Gauss' elimination method is used to solve the matrix. This program is written in FORTRAN IV for the CDC RUN compiler and has been implemented on a CDC 6000 series machine operating under SCOPE 3.0. This program requires a minimum of 44K (octal) of 60 bit words of memory.

Description: A computer program has been developed to analyze the transient response of an ablating axisymmetric body, including the effect of shape change. The governing differential equation, the boundary conditions for the analysis on which the computer program is based, and the method of solution of the resulting finite-difference equations are discussed in the documentation. Some of the features of the analysis and the associated program are (1) the ablation material is considered to be orthotropic with temperature-dependent thermal properties; (2) the thermal response of the entire body is considered simultaneously; (3) the heat transfer and pressure distribution over the body are adjusted to the new geometry as ablation occurs; (4) the governing equations and several boundary-condition options are formulated in terms of generalized orthogonal coordinates for fixed points in a moving coordinate system; (5) the finite-difference equations are solved implicitly; and (6) other instantaneous body shapes can be displayed with a user-supplied plotting routine. The physical problem to be modeled with the analysis is described by FORTRAN input variables. For example, the external body geometry is described in the W, Z coordinates; material density is given; and the stagnation cold-wall heating rate is given in a time-dependent array. Other input variables are required which control the solution, specify boundary conditions, and determine output from the program. The equations have been programmed so that either the International System of Units or the U. S. Customary Units may be used. This program is written in FORTRAN IV for batch execution and has been implemented on a CDC 6000 Series computer. This program was developed in 1972.

Description: The GTRAN program was developed to solve transient, as well as steady state, problems for gas piping systems. GTRAN capabilities allow for the analysis of a variety of system configurations and components. These include: multiple pipe junctions; valves that change position with time; fixed restrictions (orifices, manual valves, filters, etc.); relief valves; constant pressure sources; and heat transfer for insulated piping and piping subjected to free or forced convection. In addition, boundary conditions can be incorporated to simulate specific components. The governing equations of GTRAN are the one-dimensional transient gas dynamic equations. The three equations for pressure, velocity, and density are reduced to numerical equations using an implicit Crank-Nicholson finite difference technique. Input to GTRAN includes a description of the piping network, the initial conditions, and any events (e.g. valve closings) occuring during the period of analysis. Output includes pressure, velocity, and density versus time. GTRAN is written in FORTRAN 77 for batch execution and has been implemented on a DEC VAX series computer. GTRAN was developed in 1983.

Description: An upwind-biased, point-implicit relaxation algorithm for obtaining the numerical solution to the governing equations for 3D, viscous, hypersonic flows in chemical and thermal nonequilibrium is described. The algorithm is derived using a finite-volume formulation in which the inviscid components of flux across cell walls are described with a modified Roe's averaging and Harten's entropy fix with second-order corrections based on Yee's symmetric total variation diminishing scheme. Newton relaxation of the fully coupled equation set is employed on a cell-to-cell basis. Under-relaxation of the inviscid and over-relaxation of the viscous contributions to the residual are implemented. Computational work is easily partitioned among many processors in an asynchronous, dynamic mode for convergence acceleration. An overview of the physical models employed herein for thermochemical nonequilibrium is included. Several test cases and comparisons with experimental data are presented involving hypersonic flow over blunt bodies which illustrate the qualitative and quantitative capabilities of this approach.

Description: Attention is given to an empirical model for transition to turbulence in oscillatory flows in straight tubes. Designed after a correlation for transition of a boundary layer on a flat plate, the model yields the laminar flow momentum thickness Reynolds number that must be met before transition to turbulence will occur. The transition point is located by comparing this to the actual momentum thickness Reynolds number. A scheme is proposed for estimating the momentum thickness Reynolds number in terms of the position within the cycle, the maximum value of the diameter Reynolds within the cycle, Re(max), and the dimensionless frequency, Valensi number. Results from an experimental study of oscillatory flow in a tube are employed to develop the model. When the flow is determined to be turbulent, it is proposed that a fully-developed, steady flow friction coefficient be applied. When the flow is laminar, the assumption of fully developed flow cannot be made; thus, a method is suggested for estimating the friction factor.

Description: This paper presents a 2D axisymmetric combined conduction and radiation model of a multizone crystal growth furnace. The model is based on a programmable multizone furnace (PMZF) designed and built at NASA Lewis Research Center for growing high quality semiconductor crystals. A novel feature of this model is a control algorithm which automatically adjusts the power in any number of independently controlled heaters to establish the desired crystal temperatures in the furnace model. The control algorithm eliminates the need for numerous trial and error runs previously required to obtain the same results. The finite element code, FIDAP, used to develop the furnace model, was modified to directly incorporate the control algorithm. This algorithm, which presently uses PID control, and the associated heat transfer model are briefly discussed. Together, they have been used to predict the heater power distributions for a variety of furnace configurations and desired temperature profiles. Examples are included to demonstrate the effectiveness of the PID controlled model in establishing isothermal, Bridgman, and other complicated temperature profies in the sample. Finally, an example is given to show how the algorithm can be used to change the desired profile with time according to a prescribed temperature-time evolution.

Description: The cooling arrangement of the Space Shuttle Main Engine High Pressure Oxidizer Turbopump (HPOTP) incorporates two jet rings, each of which produces 19 high-velocity coolant jets. At some operating conditions, the frequency of excitation associated with the 19 jets coincides with the natural frequency of the turbine blades, contributing to fatigue cracking of blade shanks. In this paper, an alternate turbine disk cooling arrangement, applicable to disk faces of zero hub radius, is evaluated, which consists of a single coolant jet impinging at the center of the turbine disk. Results of the CFD analysis show that replacing the jet ring with a single central coolant jet in the HPOTP leads to an acceptable thermal environment at the disk rim. Based on the predictions of flow and temperature fields for operating conditions, the single central jet cooling system was recommended for implementation into the development program of the Technology Test Bed Engine at NASA Marshall Space Flight Center.

Description: The suitability of the acetate replication method for monitoring the growth of small cracks is discussed. Applications of this technique are shown for cracks growing at the notch root in semicircular-edge-notch specimens of a variety of aluminum alloys and one steel. The calculated crack growth rate versus Delta K relationship for small cracks was compared to that for large cracks obtained from middle-crack-tension specimens. The primary advantage of this techinque is that it provides an opportunity, at the completion of the test, to go backward in time towards the crack initiation event and 'zoom in' on areas of interest on the specimen surface with a resolution of about 0.1 micron. The primary disadvantage is the inability to automate the process. Also, for some materials, the replication process may alter the crack-tip chemistry or plastic zone, thereby affecting crack growth rates.

Description: A design trade study of the SP-100 heat rejection subsystem (HRSS) was made. A system code was used to evaluate the sensitivity of the HRSS mass and performance to changes. Variations in heat pipe diameter and cross-section, fin length and thickness, armor thickness, and overall configuration and materials were evaluated. The analysis indicates that the minimum system mass occurs for the case with many small diameter heat pipes, with ducting that maximizes the fraction of the heat pipe evaporator perimeter in contact with it.

Description: Results are presented for the numerical simulation of unsteady viscous incompressible flow past thick airfoils. Specifically, flow past a NACA 4424 at an angle of attack of 2.5 deg and Reynolds numbers in the range of 1700-4000 has been simulated using the spectral element method. At these conditions the flow is separatedd and an unsteady wake is formed. Application of the method of empirical eigenfunction reveals the structure of the most energetic components of the flow. These are found to occur in pairs that, through phase exchange, are responsible for the vortex shedding. A set of ordinary differential equations is obtained for the amplitudes of these eigenfunctions by a Galerkin projection of the Navier-Stokes equations. The solutions of the model system are compared with the full simulation. The work is of relevance to the transition process and observed routes to chaos in airfoil wakes.

Description: The objective of this study is to develop a reduced mechanism for ethylene oxidation. The authors are interested in a model with a minimum number of species and reactions that still models the chemistry with reasonable accuracy for the expected combustor conditions. The model will be validated by comparing the results to those calculated with a detailed kinetic model that has been validated against the experimental data.

Description: Artificial viscosity is added either implicity or explicitly in practically every numerical scheme for suppressing spurious oscillations in the solution of fluid-dynamics equations. In the present central-difference scheme, artificial viscosity is added explicitly for suppressing high-frequency oscillations and achieving good convergence properties. The amount of artificial viscosity added is controlled through the use of preselected coefficients. In the standard scheme, scalar coefficients based on the spectral radii of the Jacobian of the convective fluxes are used. However, this can add too much viscosity to the slower waves. Hence, the use of matrix-valued coefficients, which give appropriate viscosity for each wave component, is suggested. With the matrix-valued coefficients, the central-difference scheme produces more accurate solutions on a given grid, particularly in the vicinity of shocks and boundary layers, while still maintaining good convergence properties.

Description: A potential flow based three-dimensional panel method was modified to treat time-dependent conditions in which several submerged bodies can move within the fluid along different trajectories. This modification was accomplished by formulating the momentary solution in an inertial frame of reference, attached to the undisturbed stationary fluid. Consequently, the numerical interpretation of the multiple-body, solid-surface boundary condition and the viscous wake rollup was considerably simplified. The usteady capability of this code was calibrated and validated by comparing computed results with closed-form analytical results available for an airfoil, which was impulsively set into a constant speed forward motion. To demonstrate the multicomponent capability, computations were made for two wings following closely intersecting paths (i.e., simulations aimed at avoiding mid-air collisions) and for a flowfield with relative rotation (i.e., the case of a helicopter rotor rotating relative to the fuselage). Computed results for the cases were compared to experimental data, when such data was available.

Description: An approximate method for calculating heating rates on three-dimensional vehicles at angle of attack is presented. The method is based on the axisymmetric analog for three-dimensional boundary layers and uses a generalized body-fitted coordinate system. Edge conditions for the boundary-layer solution are obtained from an inviscid flowfield solution, and because of the coordinate system used, the method is applicable to any blunt body geometry for which an inviscid flowfield solution can be obtained. The method is validated by comparing with experimental heating data and with thin-layer Navier-Stokes calculations on the shuttle orbiter at both wind-tunnel and flight conditions and with thin-layer Navier-Stokes calculations on the HL-20 at wind-tunnel conditions.

Description: This paper presents the results of a study on the variation of the critical Marangoni number (Ma(sub c)) for the onset of Benard convection in a finite liquid layer bounded horizontally as well as from below. A direct-numerical-simulation procedure is devised to determine the Ma(sub c) for aspect ratios (Ar) ranging from 0.8 to 10. The results predict a strong increase of Ma(sub c) as Ar decreases to below 2. A dip of Ma(sub c) occurs between Ar = 1.45 and 1.3, which is accompanied by a pattern transition from a two-cell convection to a unicellular flow. For Ar above 4, the calculated Ma(sub c) shows little change and asymptotically approach a value of 116.15, with Biot number (Bi) equal to 1.

Description: The stability of stratified plane Couette flow in a rotating frame is investigated for a case in which the gravitational force is parallel to the rotation vector. Partial differential equations describing the behavior of disturbances in the linear regime are derived. Unstratified flow is stable as long as the angular momentum gradient is positive. If the gradient is negative, nonaxisymmetric disturbances grow as a power law in time, if the gradient is sufficiently steep. In flow which is unstable to convection, all perturbations asymptotically grow at the rate given by the Brunt-Vaisala frequency. If heat diffusion is included, all nonaxisymmetric perturbations now eventually decay as t exp -2, even if the flow is unstable to convection. If heat diffusion and viscosity are weak, nonaxisymmetric disturbances in convectively unstable flow will undergo a large transient growth before their eventual decay.

Description: We describe an approximate Riemann solver for the computation of hypervelocity flows in which there are strong shocks and viscous interactions. The scheme has three stages, the first of which computes the intermediate states assuming isentropic waves. A second stage, based on the strong shock relations, may then be invoked if the pressure jump across either wave is large. The third stage interpolates the interface state from the two initial states and the intermediate states. The solver is used as part of a finite-volume code and is demonstrated on two test cases. The first is a high Mach number flow over a sphere while the second is a flow over a flow over a slender cone with an adiabatic boundary layer. In both cases the solver performs well.

Description: The cooling requirements for an average car sized engine (spark-ignition, V-6, four-stroke, naturally aspirated, about 200 kg, about 100 kW) were looked at for Mars. Several modes of cooling were considered, including forced convection, exhaust, radiation and closed loop systems. The primary goal was to determine the effect of the thinner Martian atmosphere on the cooling system. The results show that there was only a 6-percent difference in the cooling requirements. This difference was due mostly to the thinner atmosphere during forced convection and the heat capacity of the exhaust. A method using a single pass counter-flow heat exchanger is suggested to offset this difference in cooling requirements.

Description: Space-time correlations were used to study compressibility effects on large structures in mixing layers. Two high-Reynolds number mixing layers with M(c) = 0.51 (case 1) and 0.86 (case 2) were studied. The results indicate that the structures in case 1 are similar to those in the incompressible case, but less organized. The structures in case 2 are highly three-dimensional, with a good spatial but a poor temporal orgnization. The streamwise correlations showed a decay rate four to five times greater for case 2 relative to case 1. While the spanwise correlations for case 1 showed trends similar to incompressible mixing layers, the behavior of case 2 was very different. The pressure fluctuations in the fully developed region of case 2 displayed significant rms variation in the spanwise direction with a well-defined pattern. Based on these measurements, the structures in case 2 seem to be of a horseshoe type, transversely spanning the mixing layer with the head in the low-speed side and the legs inclined in both the x-y and the x-z planes.

Description: A two-dimensional nonlinear evolution equation is studied which describes the three-dimensional spatiotemporal behavior of the air-liquid interface of a thin liquid film lying on the underside of a cooled horizontal plate. It is shown that the equation has a Liapunov functional, and this fact is exploited to demonstrate that the Marangoni effect can stabilize the destabilizing effect of gravity (the Rayleigh-Taylor instability), allowing for the existence of stable localized axisymmetric solutions for a wide range of parameter values. Various properties of these structures are discussed.

Description: A least-squares finite element method, based on the velocity-pressure-vorticity formulation, is developed for solving steady incompressible Navier-Stokes problems. This method leads to a minimization problem rather than to a saddle-point problem by the classic mixed method and can thus accommodate equal-order interpolations. This method has no parameter to tune. The associated algebraic system is symmetric, and positive definite. Numerical results for the cavity flow at Reynolds number up to 10,000 and the backward-facing step flow at Reynolds number up to 900 are presented.

Description: A subsonic and a supersonic problem are respectively treated by an upwind line-relaxation algorithm for the Navier-Stokes equations using inner iterations to accelerate steady-state solution convergence and thereby minimize CPU time. While the ability of the inner iterative procedure to mimic the quadratic convergence of the direct solver method is attested to in both test problems, some of the nonquadratic inner iterative results are noted to have been more efficient than the quadratic. In the more successful, supersonic test case, inner iteration required only about 65 percent of the line-relaxation method-entailed CPU time.

Description: Two distinct renormalization-group (RG) approaches are applied to Navier-Stokes turbulence: epsilon-RG and recursive RG. Epsilon-RG takes into account only nonlocal interactions and utilizes an infinitesimal subgrid (unresolvable scale) shell limit. Recursive RG takes into account both nonlocal and local interactions and does not require an infinitesimal subgrid shell limit to be taken. The role of local interactions and the introduction of RG-induced nonlinearities are discussed and clarified.

Description: Start-up and subsequent operation of a low-temperature heat pipe requires the liquid phase of the operating fluid to be continuously pumped back to the evaporator by the capillary action of the wick. If the pipe has been in an environment where ambient temperatures are below the freezing point of the working fluid prior to start-up, the frozen fluid in the condenser and adiabatic region scan prevent initial flow to the evaporator, causing dryout of the evaporator before all of the working fluid is in the liquid phase. This paper examines the time-dependent wall and vapor temperature profiles along the axial length of a low-temperature heat pipe during start-up from the frozen state, and freeze-out during a normal operation by applying a subfreezing temperature fluid through the condenser. In addition, the experimental transient frozen start-up wall temperature profile is compared with a two-dimensional numerical phase-change model. A successful start-up method using a pulsed power input is presented.

Description: Results from direct numerical simulations are presented to show that the weakly nonlinear results of Daudpota et al. (1988) are in error with respect to the influence of the Tollmien-Schlichting wave on the Dean vortex. The results of a new weakly nonlinear theory are then presented, and it is shown that the new results are consistent with the direct numerical simulations.

Description: Problems associated with the numerical computation of highly nonlinear equations in computational fluid dynamics are set forth and analyzed in terms of the potential ranges of spurious behaviors. A reaction-convection equation with a nonlinear source term is employed to evaluate the effects related to spatial and temporal discretizations. The discretization of the source term is described according to several methods, and the various techniques are shown to have a significant effect on the stability of the spurious solutions. Traditional linearized stability analyses cannot provide the level of confidence required for accurate fluid dynamics computations, and the incorporation of nonlinear analysis is proposed. Nonlinear analysis based on nonlinear dynamical systems complements the conventional linear approach and is valuable in the analysis of hypersonic aerodynamics and combustion phenomena.

Description: Direct numerical simulations are used to study the development of various instability modes in a spatially developing 2D wake. Five types of forcing of the inlet are investigated: fundamental mode, fundamental and one or two subharmonics, fundamental mode and random noise, and random noise only. Statistical analyses are carried out, and some numerical results are compared with experimental measurements.

Description: Using a theoretical analysis of fundamental equations and a numerical simulation of the flow field, the statistically homogeneous motion that is generated by buoyancy forces after the creation of homogeneous random fluctuations in the density of infinite fluid at an initial instant is examined. It is shown that analytical results together with numerical results provide a comprehensive description of the 'birth, life, and death' of buoyancy-generated turbulence. Results of numerical simulations yielded the mean-square density mean-square velocity fluctuations and the associated spectra as functions of time for various initial conditions, and the time required for the mean-square density fluctuation to fall to a specified small value was estimated.

Description: The present survey of important and novel CFD applications being developed and implemented by U.S. Government contractors gives attention to naval vessel flow-modeling, Army ballistic and rotary wing aerodynamics, and NASA hypersonic vehicle related applications of CFD. CFD-generated knowledge of numerical algorithms, fluid motion, and supercomputer use is being incorporated into such additional areas as computational electromagnetics and acoustics. Attention is presently given to CFD methods' development status in such fields as submarine boundary layers, hypersonic kinetic energy projectile shock structures, helicopter main rotor tip flows, and National Aerospace Plane aerothermodynamics.

Description: The applicability of a multigrid technique to block-structured, body-fitted meshes is examined focusing on three different strategies. In the first strategy data are exchanged between blocks in each stage of a five-stage Runge-Kutta time-stepping scheme which keeps a possible time lag between blocks to a minimum, but requires a large amount of I/O operations and storage. The second strategy is based on performing a complete Runge-Kutta cycle within a block before switching to the next. In the third strategy both a complete Runge-Kutta cycle and the residual evaluation for the restriction operator are done within a block, allowing a minimum of I/O and storage. The inviscid flow around a wing-body/engine-pylon configuration was computed on a mesh consisting of 11 computational blocks. It was found that both the first and the second strategies delivered converged results, but the third failed due to larger time lag between blocks.

Description: Theoretical treatment is given to the possibility of the existence of propagating confined states in the nonlinear phase equation by generalizing stationary confined states. The nonlinear phase equation is set forth for the case of propagating patterns with long wavelengths and low-frequency modulation. A large range of parameter values is shown to exist for propagating confined states which have spatially localized regions which travel on a background with unique wavelengths. The theoretical phenomena are shown to correspond to such physical systems as spirals in Taylor instabilities, traveling waves in convective systems, and slot-convection phenomena for binary fluid mixtures.

Description: An implicit finite volume lower-upper time-marching method which efficiently solves the complete Navier-Stokes and specied equations in a fully coupled fashion is the basis of the present 3D numerical program for simulating the supersonic reacting flows of H2 in air. The chemistry model incorporated has nine species and 18 reaction steps. Calculations are presented for flowfields of underexpanded hydrogen jets that are transversely injected into the supersonic airstream within scramjet combustors; the shock structure, separated flow regions around the injector, and combustion-product distributions are clearly represented.

Description: A finite-difference solution for steady natural convective flow in a concentric spherical annulus with isothermal walls has been obtained. The stream function-vorticity formulation of the equations of motion for the unsteady axisymmetric flow is used; interest lying in the final steady solution. Forward differences are used for the time derivatives and second-order central differences for the space derivatives. The alternating direction implicit method is used for solution of the discretization equations. Local one-dimensional grid adaptation is used to resolve the steep gradients in some regions of the flow at large Rayleigh numbers. The break-up into multi-cellular flow is found at high Rayleigh numbers for air and water, and at significantly low Rayleigh numbers for liquid metals. Excellent agreement with previous experimental and numerical data is obtained.

Description: The paper describes a new operatorial approach to the study of turbulence, based on the general algebraic properties of the filtered representations of a turbulence field at different levels. The main results of this analysis is the averaging invariance of the filtered Navier-Stokes eaquations in terms of the generalized central moments, and an algebraic identity that relates the turbulent stresses at different levels. The resolved turbulence is defined, the algebraic consistency rules that relate these resolved quantities to the turbulent stresses at different levels are derived, and their possible uses in subgrid modeling is discussed.

Description: The Wilcox (1988, 1991) k-omega model for eddy-viscosity turbulence does not require damping functions in the viscous sublayer, and its equations are less stiff near the wall. It has been designed to predict the requisite wake length in equilibrium, adverse pressure-gradient boundary-layer flows. When applied to free shear layers, however, a strong dependency of its results on the freestream value of omega has been noted. This feature is presently investigated via the self-similar equations for incompressible equilibrium boundary layers.

Description: The Yakhot and Orszag (1986) renormalization group (RNG) theory of turbulence has generated a number of scaling law constants in reasonable quantitative agreement with experiments. The theory itself is highly mathematical, and its assumptions and approximations are not easily appreciated. The present paper reviews the RNG theory and recasts it in more conventional terms using a distinctly different viewpoint. A new formulation based on an alternative interpretation of the origin of the random force is presented, showing that the artificially introduced epsilon in the original theory is an adjustable parameter, thus offering a plausible explanation for the remarkable record of quantitative success of the so-called epsilon-expansion procedure.

Description: The equations determining the linear growth rate omega characterizing a convectively unstable fluid with Rayleigh number R(u) bounded below by an impenetrable free boundary and above by a convectively stable fluid with Rayleigh number R(s), are solved numerically. Using the analytical Rayleigh-Benard growth rate omega (RB) as a convenient functional form, it is possible to fit the numerical values for omega if the vertical wave number k(z) = n(pi) and the Rayleigh number R(RB) are taken to be functions of R(s), R(u), and the horizontal wave number k-perpendicular rather than n = integer as in the Rayleigh-Benard case. In addition, contrary to Rayleigh-Benard convection, in which the critical Rayleigh number is fixed, it is found that R super (cr) sub u is variable in the presence of a stable layer, (i.e., it depends on R(s)).

Description: An experimental investigation carried out to determine aerodynamic and acoustic characteristics of a low area ratio rectangular jet ejector is reported. A supersonic primary jet issuing from a rectangular convergent-divergent nozzle of aspect ratio 4, into a rectangular duct of area ratio 3, was used. Improved performance was found when the ejector screech tone is most intense and appears to match the most unstable Strouhal number of the free rectangular jet. When the primary jet was operating at over and ideally expanded conditions, significant noise reduction was obtained with the ejector as compared to a corresponding free jet. Application of particle image velocimetry to high speed ejector flows was demonstrated through the measurement of instantaneous two dimensional velocity fields.

Description: Some measures of the intrinsic complexity of the near wall turbulence are reviewed. The number of modes required in an 'optimal' eigenfunction expansion is compared with the dimension obtained from the calculation of Liapunov exponents. These measures are of the same order, but they are very large. It is argued that the basic building block element of the near wall turbulence can be isolated in a small region of space (minimal flow unit). When the size of the domain is taken into account, the dimension becomes more manageable.

Description: The dissipation rate of turbulent kinetic energy in incompressible turbulence is investigated using a two-scale DIA. The dissipation rate is shown to consist of two parts; one corresponds to the dissipation rate used in the current turbulence models of eddy-viscosity type, and another comes from the viscous effect that is closely connected with mean velocity shear. This result can elucidate the physical meaning of the dissipation rate used in the current turbulence models and explain part of the discrepancy in the near-wall dissipation rates between the current turbulence models and direct numerical simulation of the Navier-Stokes equation.

Description: The author is developing a new type of turbulence model in which a new one-point quantity, the eddy structure tensor, carries information about the two-point structure of the turbulence. The model was motivated by the observation that conventional one-point turbulence models based only on the turbulent stresses do not predict the rapid changes in state that are found when anisotropic homogeneous turbulence is subjected to mean rotation, and hence are fundamentally incorrect for rotation. The model appears to give topologically correct predictions for the changes in stress state and structure state under all types of rapid distortions of homogeneous turbulence.

Description: In developing turbulence models, various model constraints were proposed in an attempt to make the model equations more general (or universal). The most recent of these are the realizability principle, the linearity principle, the rapid distortion theory, and the material indifference principle. Several issues are discussed concerning these principles and special attention is payed to the realizability principle. Realizability (defined as the requirement of non-negative energy and Schwarz' inequality between any fluctuating quantities) is the basic physical and mathematical principle that any modeled equation should obey. Hence, it is the most universal, important and also the minimal requirement for a model equation to prevent it from producing unphysical results. The principle of realizability is described in detail, the realizability conditions are derived for various turbulence models, and the model forms are proposed for the pressure correlation terms in the second moment equations. Detailed comparisons of various turbulence models with experiments and direct numerical simulations are presented. As a special case of turbulence, the two dimensional two-component turbulence modeling is also discussed.

Description: The epsilon-budget was computed from the direct simulation data (DNS) of Kim (1990) for developed channel flow at Re(tau) = 395. The relative magnitude of the terms in the epsilon-equation is shown with the aid of scaling arguments, and the parameter governing this magnitude is established. The modeling of the terms in the equation is then addressed in the context of eddy-viscosity k-epsilon models. Some existing models for the sum of all source and sink terms in the epsilon-equation are tested against DNS data, and an improved model is proposed on the basis of these data.

Description: The various flow regimes that occur in rotating isotropic turbulence and their associated turbulence structure are studied. Direct numerical simulations are conducted for moderate and rapid rotation rates and comparisons are made with the predictions of generalized Eddy Damped Quasi-Normal Markovian (EDQNM) approximations. It is shown that at high rotation rates the nonlinear transfer terms remain small and that the development of the spectrum is through pure viscous decay. This shows that the effect of rapid rotation on the turbulence kinetic energy is through the shutting off of the production term in the dissipation rate equation. At moderate and relatively rapid rates, the rotation causes a discernible anisotropy to develop in the integral length scale with a mild trend toward a two-dimensionalization of the flow. As the flow decays, the Rossby number decreases, leading again to the shutting off of the nonlinear transfer terms. For extremely rapid rotation rates, the anisotropies in the integral length scales are small and direct numerical simulation results are in good agreement with rapid distortion theory.

Description: Particle imaging velocimetry, which is rapidly becoming an essential tool for the synoptic measurement of two dimensional velocity fields, is addressed. This rapid development is carried out by a growing number of fluid mechanics experimentalists who recognize the unique capabilities of the technique to measure velocity fields in both space and time, and is supported by the concomitant development and availability of microcomputer hardware and software. Various applications of the technique to map different flow regimes are described and illustrated. Hardware implementations of the technique which utilize both conventional photography for image acquisition as well as digital 'online' methods for integrated image acquisition and processing are discussed. Recommendations to further enhance the technique and make it possible to map the three velocity components in three dimensional flow regions are given.

Description: A two-dimensional oscillating flow analysis was conducted simulating the gas flow inside Stirling engine heat exchangers. Both laminar and turbulent oscillating pipe flow were investigated numerically for Re(max) = 1920 (Va = 80), 10,800 (Va = 272), 19,300 (Va = 272), and 60,800 (Va = 126). The results are compared with experimental results of previous investigators. Predictions of the flow regime are also checked by comparing velocity amplitudes and phase difference with those from laminar theory and quasi-steady profile. A high Reynolds number k-epsilon turbulence model was used for turbulent oscillating pipe flow. Finally, the performance of the k-epsilon model was evaluated to explore the applicability of quasi-steady turbulent models to unsteady oscillating flow analysis.

Description: While current 3D CFD codes and modeling techniques have been shown capable of furnishing engineering data for complex scramjet flowfields, the usefulness of such efforts is primarily limited by solutions' CPU time requirements, and secondarily by memory requirements. Attention is presently given to the use of parallel computing capabilities for engineering CFD tools for the analysis of supersonic reacting flows, and to an illustrative incompressible CFD problem using up to 16 iPSC/2 processors with single-domain decomposition.

Description: A numerical study is conducted to simulate the shock-induced combustion in premixed H2-air mixtures. Two types of bodies, blunt (spherical projectile) and sharp (wedge), are considered in the study. A nine-species, 18-step finite-rate H2-air chemical reaction mechanism coupled with the Navier-Stokes equations is solved. The flow field over the blunt body is found to be unsteady, when the projectile velocity is same as the Chapman-Jouget velocity of the mixture. The unsteadiness is caused by the periodic instabilities originating in the stagnation zone. Numerical results show good qualitative agreement with the ballistic range shadowgraph. In addition, the frequency of oscillations, determined by using the Fourier power spectrum, is found to be in good agreement with the experiment. The flow field over the wedge is found to be stable for the conditions considered in this study. The oblique detonation wave structure is investigated and the important flow features are discussed.

Description: The motion of small, monodisperse particles in fluid was studied in a horizontal, cylindrical container rotating about its axis. One instigation for the study was the common requirement for mixed-phase, chemical or biological reactors to maintain particles in suspension for extended periods. A cylindrical, rotating reactor can allow long-term particle suspension without particle collisions and resulting agglomeration. The purpose of this study was to verify parametric effects and optimize the time of particle suspension. The theoretical and experimental results were obtained for inert, constant-diameter particles of nearly neutral buoyancy. The centrifugal buoyancy and gravitation terms were both included in the equations of motion. Laser illumination, photography and computer imaging were used to measure experimental particle concentration.

Description: An identity proposed by Germano (1992) has been widely applied to several turbulent flows to dynamically compute rather than adjust the Smagorinsky coefficient. The assumptions under which the method has been used are discussed, and some conceptual difficulties in its current implementation are examined.

Description: Simulations of simple compressible flows have been performed to enable the direct estimation of the pressure-dilatation correlation. The generally accepted belief that this correlation may be important in high-speed flows has been verified by the simulations. The pressure-dilatation correlation is theoretically investigated by considering the equation for fluctuating pressure in an arbitrary compressible flow. This leads to the isolation of a component of the pressure-dilatation that exhibits temporal oscillations on a fast time scale. Direct numerical simulations of homogeneous shear turbulence and isotropic turbulence show that this fast component has a negligible contribution to the evolution of turbulent kinetic energy. Then, an analysis for the case of homogeneous turbulence is performed to obtain a formal solution for the nonoscillatory pressure-dilatation. Simplifications lead to a model that algebraically relates the pressure-dilatation to quantities traditionally obtained in incompressible turbulence closures. The model is validated by direct comparison with the simulations.

Description: Asymptotic results obtained by Foster and Smith (1989) for inviscid instability modes of the Type-II Long's vortex is extended to account for the effects of finite Reynolds number. It is shown that the nonparallelism of the flow is more important than the viscous terms in determining the finite-Re behavior due to the radial velocity scales with Re exp -1 M. A critical layer of the three-layer structrue of the parallel-flow instability modes is considerably modified by radial velocity. It is found that for azimuthal wavenumber n greater than 1, the nonparallelism stabilizes the unstable inertial modes, leading to determination of neutral curves. For n less than -1, the nonparallel effects always destabilize the vortex to these helical modes.

Description: Transient solutions were obtained for cooling a semitransparent material by radiation and conduction. The layer is in a vacuum environment so the only means for heat dissipation is by radiation from within the medium leaving through the boundaries. Heat conduction serves only to partially equalize temperatures across the layer. As the optical thickness is increased, steep temperature gradients exist near the boundaries when conduction is relatively small. A solution procedure is required that will provide accurate temperature distributions adjacent to the boundaries, or radiative heat losses will be in error. The approach utilized numerical Gaussian integration to obtain the local radiative source term, and a finite difference procedure with variable space and time increments to solve the transient energy equation.