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All sourcesNASA NTRSDOE OSTI
NASA NTRS2011

Uncertainty Assessments of 2D and Axisymmetric Hypersonic Shock Wave - Turbulent Boundary Layer Interaction Simulations at Compression Corners

This paper is one of a series of five papers in a special session organized by the NASA Fundamental Aeronautics Program that addresses uncertainty assessments for CFD simulations in hypersonic flow. Simulations of a shock emanating from a compression corner and interacting with a fully developed turbulent boundary layer are evaluated herein. Mission relevant conditions at Mach 7 and Mach 14 are defined for a pre-compression ramp of a scramjet powered vehicle. Three compression angles are defined, the smallest to avoid separation losses and the largest to force a separated flow engaging more complicated flow physics. The Baldwin-Lomax and the Cebeci-Smith algebraic models, the one-equation Spalart-Allmaras model with the Catrix-Aupoix compressibility modification and two-equation models including Menter SST, Wilcox k-omega 98, and Wilcox k-omega 06 turbulence models are evaluated. Each model is fully defined herein to preclude any ambiguity regarding model implementation. Comparisons are made to existing experimental data and Van Driest theory to provide preliminary assessment of model form uncertainty. A set of coarse grained uncertainty metrics are defined to capture essential differences among turbulence models. Except for the inability of algebraic models to converge for some separated flows there is no clearly superior model as judged by these metrics. A preliminary metric for the numerical component of uncertainty in shock-turbulent-boundary-layer interactions at compression corners sufficiently steep to cause separation is defined as 55%. This value is a median of differences with experimental data averaged for peak pressure and heating and for extent of separation captured in new, grid-converged solutions presented here. This value is consistent with existing results in a literature review of hypersonic shock-turbulent-boundary-layer interactions by Roy and Blottner and with more recent computations of MacLean.

Gnoffo, Peter A.↗
NASA NTRSDate not supplied

Simulation and Modeling of Hypersonic Turbulent Boundary Layers Subject to Favorable Pressure Gradients due to Streamline Curvature

Direct numerical simulations (DNS) of favorable-pressure-gradient turbulent boundary layers are presented for a nominal freestream Mach number of 5, with the objective of assessing the limitations of the currently available Reynolds-averaged Navier-Stokes (RANS) models.The wall geometry and flow conditions of the DNS are representative of the experimental data for a Mach 4.9 turbulent boundary layer that was tested on a two-dimensional planar convexwall model in the high-speed blow-down wind tunnel located at the National Aerothermochemistry Laboratory at Texas A&M University. The favorable pressure gradient is induced bythe streamwise surface curvature. The DNS results will be compared with experimental measurements and RANS computations for the same flow conditions and wall geometry. The DNS datasets will also be analyzed to provide an improved physical understanding of hypersonic boundary-layer turbulence subject to mechanical nonequilibrium, including the validity of Morkovin’s hypothesis and the various available compressibility transformations, as well as to obtain turbulence statistics that are relevant to RANS modeling, including the distribution ofeddy viscosity, the budgets of turbulent kinetic energy and Reynolds stresses, and the velocity-temperature correlations. The RANS predictions will be obtained by using both the commonly used one- and two-equation models that assume a constant turbulent Prandtl number and an algebraic, variable Prandtl number model for the turbulent energy flux.

turbulent boundary layers↗
NASA NTRS1995

Rapid Numerical Simulation of Viscous Axisymmetric Flow Fields

A two-dimensional Navier-Stokes code has been developed for rapid numerical simulation of axisymmetric flow fields, including flow fields with an azimuthal velocity component. The azimuthal-invariant Navier-Stokes equations in a cylindrical coordinate system are mapped to a general body-fitted coordinate system, with the streamwise viscous terms then neglected by applying the thin-layer approximation. Turbulence effects are modeled using an algebraic model, typically the Baldwin-Lomax turbulence model, although a modified Cebeci-Smith model can also be used. The equations are discretized using central finite differences and solved using a multistage Runge-Kutta algorithm with a spatially varying time step and implicit residual smoothing. Results are presented for calculations of supersonic flow over a waisted body-of-revolution, transonic flow through a normal shock wave in a straight circular duct of constant cross sectional area, swirling supersonic (inviscid) flow through a strong shock in a straight radial duct, and swirling subsonic flow in an annular-to-circular diffuser duct. Comparisons between computed and experimental results are in fair to good agreement, demonstrating that the viscous code can be a useful tool for practical engineering design and analysis work.

Tweedt, Daniel L.↗
NASA NTRS1993

Proteus three-dimensional Navier-Stokes computer code, version 1.0. Volume 3: Programmer's reference

A computer code called Proteus 3D was developed to solve the three-dimensional, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. The Programmer's Reference contains detailed information useful when modifying the program. The program structure, the Fortran variables stored in common blocks, and the details of each subprogram are described.

Towne, Charles E.↗
NASA NTRS1996

[Formian 2 and a Formian Function for Processing Polyhedric Configurations]

The work began in October 1994 with the following objectives: (1) to produce an improved version of the programming language Formian; and (2) to create a means for computer aided handling of polyhedric configurations including the geodesic forms of all kinds. A new version of Formian, referred to as Formian 2, is being implemented to operate in the Windows 95 environment. It is an ideal tool for configuration management in a convenient and user-friendly manner. The second objective was achieved by creating a standard Formian function that allows convenient handling of all types of polyhedric configurations. In particular, the focus of attention is on polyhedric configurations that are of importance in architectural and structural engineering fields. The natural medium for processing of polyhedric configurations is a programming language that incorporates the concepts of 'formex algebra'. Formian is such a programming language in which the processing of polyhedric configurations can be carried out using the standard elements of the language. A description of this function is included in a chapter for a book entitled 'Beyond the Cube: the Architecture of space Frames and Polyhedra'. A copy of this chapter is appended.

Nooshin, H.↗
NASA NTRS1993

Proteus two-dimensional Navier-Stokes computer code, version 2.0. Volume 1: Analysis description

A computer code called Proteus 2D was developed to solve the two-dimensional planar or axisymmetric, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body-fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. This is the Analysis Description, and presents the equations and solution procedure. The governing equations, the turbulence model, the linearization of the equations and boundary conditions, the time and space differencing formulas, the ADI solution procedure, and the artificial viscosity models are described in detail.

Towne, Charles E.↗
NASA NTRS1993

Proteus two-dimensional Navier-Stokes computer code, version 2.0. Volume 3: Programmer's reference

A computer code called Proteus 2D was developed to solve the two-dimensional planar or axisymmetric, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body-fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. The Programmer's Reference contains detailed information useful when modifying the program. The program structure, the Fortran variables stored in common blocks, and the details of each subprogram are described.

Towne, Charles E.↗
NASA NTRS1993

Proteus three-dimensional Navier-Stokes computer code, version 1.0. Volume 1: Analysis description

A computer code called Proteus 3D has been developed to solve the three dimensional, Reynolds averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort has been to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation have been emphasized. The governing equations are solved in generalized non-orthogonal body-fitted coordinates by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. This is the Analysis Description, and presents the equations and solution procedure. It describes in detail the governing equations, the turbulence model, the linearization of the equations and boundary conditions, the time and space differencing formulas, the ADI solution procedure, and the artificial viscosity models.

Towne, Charles E.↗
NASA NTRS2008

A Study of Visualization for Mathematics Education

Graphical representations such as figures, illustrations, and diagrams play a critical role in mathematics and they are equally important in mathematics education. However, graphical representations in mathematics textbooks are static, Le. they are used to illustrate only a specific example or a limited set. of examples. By using computer software to visualize mathematical principles, virtually there is no limit to the number of specific cases and examples that can be demonstrated. However, we have not seen widespread adoption of visualization software in mathematics education. There are currently a number of software packages that provide visualization of mathematics for research and also software packages specifically developed for mathematics education. We conducted a survey of mathematics visualization software packages, summarized their features and user bases, and analyzed their limitations. In this survey, we focused on evaluating the software packages for their use with mathematical subjects adopted by institutions of secondary education in the United States (middle schools and high schools), including algebra, geometry, trigonometry, and calculus. We found that cost, complexity, and lack of flexibility are the major factors that hinder the widespread use of mathematics visualization software in education.

Daugherty, Sarah C.↗
NASA NTRS1981

Numerical models for Halley dust environments

The algebra, parameter values, and results of a reference model for the dust environment of Comet P/Halley are presented. The model employs simplified treatments of the icy conglomerate nucleus and of the hydrodynamic outflow of gas and dust. The model includes a gas production rate derived from observations of Halley's visual magnitude in 1910, gas and dust flux nonuniformly distributed over the nuclear surface, a dust distribution function consistent with large particle inferences from comet antitails, dust density variable with mass, and an approximation to the distribution of particles near the dust envelope. Many parameter values are derived by analogy with the results for other comets. The features are incorporated in a computer program which calculates the concentration, flux, and fluence of dust particles as functions of time, position and particle mass.

Divine, N.↗
NASA NTRS1988

A numerical method for computing unsteady 2-D boundary layer flows

A numerical method for computing unsteady two-dimensional boundary layers in incompressible laminar and turbulent flows is described and applied to a single airfoil changing its incidence angle in time. The solution procedure adopts a first order panel method with a simple wake model to solve for the inviscid part of the flow, and an implicit finite difference method for the viscous part of the flow. Both procedures integrate in time in a step-by-step fashion, in the course of which each step involves the solution of the elliptic Laplace equation and the solution of the parabolic boundary layer equations. The Reynolds shear stress term of the boundary layer equations is modeled by an algebraic eddy viscosity closure. The location of transition is predicted by an empirical data correlation originating from Michel. Since transition and turbulence modeling are key factors in the prediction of viscous flows, their accuracy will be of dominant influence to the overall results.

Krainer, Andreas↗
NASA NTRS1990

Parallel processors and nonlinear structural dynamics algorithms and software

Techniques are discussed for the implementation and improvement of vectorization and concurrency in nonlinear explicit structural finite element codes. In explicit integration methods, the computation of the element internal force vector consumes the bulk of the computer time. The program can be efficiently vectorized by subdividing the elements into blocks and executing all computations in vector mode. The structuring of elements into blocks also provides a convenient way to implement concurrency by creating tasks which can be assigned to available processors for evaluation. The techniques were implemented in a 3-D nonlinear program with one-point quadrature shell elements. Concurrency and vectorization were first implemented in a single time step version of the program. Techniques were developed to minimize processor idle time and to select the optimal vector length. A comparison of run times between the program executed in scalar, serial mode and the fully vectorized code executed concurrently using eight processors shows speed-ups of over 25. Conjugate gradient methods for solving nonlinear algebraic equations are also readily adapted to a parallel environment. A new technique for improving convergence properties of conjugate gradients in nonlinear problems is developed in conjunction with other techniques such as diagonal scaling. A significant reduction in the number of iterations required for convergence is shown for a statically loaded rigid bar suspended by three equally spaced springs.

Belytschko, Ted↗
NASA NTRS2011

Improve Data Mining and Knowledge Discovery Through the Use of MatLab

Data mining is widely used to mine business, engineering, and scientific data. Data mining uses pattern based queries, searches, or other analyses of one or more electronic databases/datasets in order to discover or locate a predictive pattern or anomaly indicative of system failure, criminal or terrorist activity, etc. There are various algorithms, techniques and methods used to mine data; including neural networks, genetic algorithms, decision trees, nearest neighbor method, rule induction association analysis, slice and dice, segmentation, and clustering. These algorithms, techniques and methods used to detect patterns in a dataset, have been used in the development of numerous open source and commercially available products and technology for data mining. Data mining is best realized when latent information in a large quantity of data stored is discovered. No one technique solves all data mining problems; challenges are to select algorithms or methods appropriate to strengthen data/text mining and trending within given datasets. In recent years, throughout industry, academia and government agencies, thousands of data systems have been designed and tailored to serve specific engineering and business needs. Many of these systems use databases with relational algebra and structured query language to categorize and retrieve data. In these systems, data analyses are limited and require prior explicit knowledge of metadata and database relations; lacking exploratory data mining and discoveries of latent information. This presentation introduces MatLab(R) (MATrix LABoratory), an engineering and scientific data analyses tool to perform data mining. MatLab was originally intended to perform purely numerical calculations (a glorified calculator). Now, in addition to having hundreds of mathematical functions, it is a programming language with hundreds built in standard functions and numerous available toolboxes. MatLab's ease of data processing, visualization and its enormous availability of built in functionalities and toolboxes make it suitable to perform numerical computations and simulations as well as a data mining tool. Engineers and scientists can take advantage of the readily available functions/toolboxes to gain wider insight in their perspective data mining experiments.

Shaykhian, Gholam Ali↗
NASA NTRS2011

Improve Data Mining and Knowledge Discovery through the use of MatLab

Data mining is widely used to mine business, engineering, and scientific data. Data mining uses pattern based queries, searches, or other analyses of one or more electronic databases/datasets in order to discover or locate a predictive pattern or anomaly indicative of system failure, criminal or terrorist activity, etc. There are various algorithms, techniques and methods used to mine data; including neural networks, genetic algorithms, decision trees, nearest neighbor method, rule induction association analysis, slice and dice, segmentation, and clustering. These algorithms, techniques and methods used to detect patterns in a dataset, have been used in the development of numerous open source and commercially available products and technology for data mining. Data mining is best realized when latent information in a large quantity of data stored is discovered. No one technique solves all data mining problems; challenges are to select algorithms or methods appropriate to strengthen data/text mining and trending within given datasets. In recent years, throughout industry, academia and government agencies, thousands of data systems have been designed and tailored to serve specific engineering and business needs. Many of these systems use databases with relational algebra and structured query language to categorize and retrieve data. In these systems, data analyses are limited and require prior explicit knowledge of metadata and database relations; lacking exploratory data mining and discoveries of latent information. This presentation introduces MatLab(TradeMark)(MATrix LABoratory), an engineering and scientific data analyses tool to perform data mining. MatLab was originally intended to perform purely numerical calculations (a glorified calculator). Now, in addition to having hundreds of mathematical functions, it is a programming language with hundreds built in standard functions and numerous available toolboxes. MatLab's ease of data processing, visualization and its enormous availability of built in functionalities and toolboxes make it suitable to perform numerical computations and simulations as well as a data mining tool. Engineers and scientists can take advantage of the readily available functions/toolboxes to gain wider insight in their perspective data mining experiments.

Shaykahian, Gholan Ali↗
NASA NTRSDate not supplied

Dude Where's My Stars: A Novel Topologically Justified Approach to Star Tracking

In this paper, we consider two novel approaches to celestial navigation for spacecraft. Determining attitude without any prior knowledge using star tracking is known to be a difficult task, particularly given the computational complexity and the many potential sources of misinformation. We consider localization by optimizing matching parameters without explicit star identification in a computationally tractable manner. This is achieved using the mathematical tools of topological data analysis (TDA) and cellular sheaves to study the geometry and distribution of cataloged stars. A framework is gained that enhances the statistical approach to noise handling and false star detection, and heterogeneous sensor fusion. Finally, we discuss confidence bounds and minimum information requirements for successful operation.

Sheaf theory↗
NASA NTRSDate not supplied

Efficient and Singularity-Aware Inverse Kinematics for 6-DOF and 7-DOF Revolute Manipulators

Inverse kinematics (IK) for 6-DOF and 7-DOF revolute robot manipulators may be decomposed into canonical subproblems which find the angles on circles where they intersect with other geometric objects. We present new algebraic solutions and geometric interpretations for six subproblems. We demonstrate significant performance improvements over existing IK methods. 7-DOF manipulators have one redundant DOF to parameterize, so we introduce the general SEW angle, which generalizes the conventional SEW angle but with an arbitrary reference direction function. One special choice, the stereographic SEW angle, has a singularity when the wrist is on a half-line instead of a full line.

Computational Geometry↗
NASA NTRS2013

Scheduling Operations for Massive Heterogeneous Clusters

High-performance computing (HPC) programming has become increasingly difficult with the advent of hybrid supercomputers consisting of multicore CPUs and accelerator boards such as the GPU. Manual tuning of software to achieve high performance on this type of machine has been performed by programmers. This is needlessly difficult and prone to being invalidated by new hardware, new software, or changes in the underlying code. A system was developed for task-based representation of programs, which when coupled with a scheduler and runtime system, allows for many benefits, including higher performance and utilization of computational resources, easier programming and porting, and adaptations of code during runtime. The system consists of a method of representing computer algorithms as a series of data-dependent tasks. The series forms a graph, which can be scheduled for execution on many nodes of a supercomputer efficiently by a computer algorithm. The schedule is executed by a dispatch component, which is tailored to understand all of the hardware types that may be available within the system. The scheduler is informed by a cluster mapping tool, which generates a topology of available resources and their strengths and communication costs. Software is decoupled from its hardware, which aids in porting to future architectures. A computer algorithm schedules all operations, which for systems of high complexity (i.e., most NASA codes), cannot be performed optimally by a human. The system aids in reducing repetitive code, such as communication code, and aids in the reduction of redundant code across projects. It adds new features to code automatically, such as recovering from a lost node or the ability to modify the code while running. In this project, the innovators at the time of this reporting intend to develop two distinct technologies that build upon each other and both of which serve as building blocks for more efficient HPC usage. First is the scheduling and dynamic execution framework, and the second is scalable linear algebra libraries that are built directly on the former.

Humphrey, John↗
NASA NTRS1994

Prediction of Film Cooling on Gas Turbine Airfoils

A three-dimensional Navier-Stokes analysis tool has been developed in order to study the effect of film cooling on the flow and heat transfer characteristics of actual turbine airfoils. An existing code (Arnone et al., 1991) has been modified for the purpose. The code is an explicit, multigrid, cell-centered, finite volume code with an algebraic turbulence model. Eigenvalue scaled artificial dissipation and variable-coefficient implicit residual smoothing are used with a full-multigrid technique. Moreover, Mayle's transition criterion (Mayle, 1991) is used. The effects of film cooling have been incorporated into the code in the form of appropriate boundary conditions at the hole locations on the airfoil surface. Each hole exit is represented by several control volumes, thus providing an ability to study the effect of hole shape on the film-cooling characteristics. Comparison is fair with near mid-span experimental data for four and nine rows of cooling holes, five on the shower head, and two rows each on the pressure and suction surfaces. The computations, however, show a strong spanwise variation of the heat transfer coefficient on the airfoil surface, specially with shower-head cooling.

Garg, Vijay K.↗