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A second-order unstructured-grid code, developed and used primarily for steady aerodynamic simulations, is applied to the synthetic jet in a cross flow. The code, FUN3D, is a vertex-centered finite-volume method originally developed by Anderson[1, 2], and is currently supported by members of the Fast Adaptive Aerospace Tools team at NASA Langley. Used primarily for design[3] and analysis[4] of steady aerodynamic configurations, FUN3D incorporates a discrete adjoint capability, and supports parallel computations using MPI. A detailed description of the FUN3D code can be found in the references given above. The code is under continuous development and contains a variety of flux splitting algorithms for the inviscid terms, two methods for computing gradients, several turbulence models, and several solution methodologies; all in varying states of development. Only the most robust and reliable components, based on experiences with steady aerodynamic simulations, were employed in this work. As applied in this work, FUN3D solves the Reynolds averaged Navier-Stokes equations using the one equation turbulence model of Spalart and Allmaras[5]. The spatial discretization is formed on unstructured meshes using a vertex-centered approach. The inviscid terms are evaluated by a flux-difference splitting formulation using least-squares reconstruction and Roe-type approximate Riemann fluxes. Green-Gauss gradient evaluations are used for viscous and turbulence modeling terms. The discrete spatial operator is combined with a backward time operator which is then solved iteratively using point or line Gauss-Seidel and local time stepping in a pseudo time. For steady flows, the physical time step is set to infinity and the pseudo time step is ramped up with the iteration count. A second-order backward in time operator is used for time accurate flows with 20 to 50 steps in the pseudo time applied at each physical time step. For this effort, FUN3D was modified to support spatially varying boundary and initial conditions, and unsteady boundary conditions. Also, a specialized in/out flow boundary condition was implemented to model the action of the diaphragm. This boundary condition is described below in more detail. The grids were generated using the internally developed codes GridEX[6] for meshing the surfaces and inviscid regions of the domain, and for CAD access; and MesherX[7] for meshing the viscous regions. Grid spacing in on the surfaces and in the inviscid regions are indirectly controlled by specifying sources. The viscous layers are generated using an advancing layer technique. MeshersX allows the user to control the spatial variation of the first step off the surface, growth rates, and the termination criterion by providing small problem dependent subroutines.

We investigate p-multigrid as a solution method for several different discontinuous Galerkin (DG) formulations of the Poisson equation. Different combinations of relaxation schemes and basis sets have been combined with the DG formulations to find the best performing combination. The damping factors of the schemes have been determined using Fourier analysis for both one and two-dimensional problems. One important finding is that when using DG formulations, the standard approach of forming the coarse p matrices separately for each level of multigrid is often unstable. To ensure stability the coarse p matrices must be constructed from the fine grid matrices using algebraic multigrid techniques. Of the relaxation schemes, we find that the combination of Jacobi relaxation with the spectral element basis is fairly effective. The results using this combination are p sensitive in both one and two dimensions, but reasonable convergence rates can still be achieved for moderate values of p and isotropic meshes. A competitive alternative is a block Gauss-Seidel relaxation. This actually out performs a more expensive line relaxation when the mesh is isotropic. When the mesh becomes highly anisotropic, the implicit line method and the Gauss-Seidel implicit line method are the only effective schemes. Adding the Gauss-Seidel terms to the implicit line method gives a significant improvement over the line relaxation method.

This paper describes numerical experiments with P-multigrid to corroborate analysis, validate the present implementation, and to examine issues that arise in the implementations of the various combinations of relaxation schemes, discretizations and P-multigrid methods. The two approaches to implement P-multigrid presented here are equivalent for most high-order discretization methods such as spectral element, SUPG, and discontinuous Galerkin applied to advection; however it is discovered that the approach that mimics the common geometric multigrid implementation is less robust, and frequently unstable when applied to discontinuous Galerkin discretizations of di usion. Gauss-Seidel relaxation converges 40% faster than block Jacobi, as predicted by analysis; however, the implementation of Gauss-Seidel is considerably more expensive that one would expect because gradients in most neighboring elements must be updated. A compromise quasi Gauss-Seidel relaxation method that evaluates the gradient in each element twice per iteration converges at rates similar to those predicted for true Gauss-Seidel.

A collaborative approach to software development is described. The approach employs the agile development techniques: project retrospectives, Scrum status meetings, and elements of Extreme Programming to efficiently develop a cohesive and extensible software suite. The software product under development is a fluid dynamics simulator for performing aerodynamic and aerothermodynamic analysis and design. The functionality of the software product is achieved both through the merging, with substantial rewrite, of separate legacy codes and the authorship of new routines. Examples of rapid implementation of new functionality demonstrate the benefits obtained with this agile software development process. The appendix contains a discussion of coding issues encountered while porting legacy Fortran 77 code to Fortran 95, software design principles, and a Fortran 95 coding standard.

The explicit stability constraint of the discontinuous Galerkin method applied to the diffusion operator decreases dramatically as the order of the method is increased. Block Jacobi and block Gauss-Seidel preconditioner operators are examined for their effectiveness at accelerating convergence. A Fourier analysis for methods of order 2 through 6 reveals that both preconditioner operators bound the eigenvalues of the discrete spatial operator. Additionally, in one dimension, the eigenvalues are grouped into two or three regions that are invariant with order of the method. Local relaxation methods are constructed that rapidly damp high frequencies for arbitrarily large time step.

The application of the quadrature-free form of the discontinuous Galerkin method to two problems from Category 1 of the Second Computational Aeroacoustics Workshop on Benchmark problems is presented. The method and boundary conditions relevant to this work are described followed by two test problems, both of which involve the scattering of an acoustic wave off a cylinder. The numerical test performed to evaluate mesh-resolution requirements and boundary-condition effectiveness are also described.

The formulation and the implementation of boundary conditions within the context of the quadrature-free form of the discontinuous Galerkin method are presented for several types of boundary conditions for the Euler equations. An important feature of the discontinuous Galerkin method is that the interior point algorithm is well behaved in the neighborhood of the boundary and requires no modifications. This feature leads to a simple and accurate treatment for wall boundary conditions and simple inflow and outflow boundary conditions. Curved walls are accurately treated with only minor changes to the implementation described in earlier work. The 'perfectly matched layer' approach to nonreflecting boundary conditions is easily applied to the discontinuous Galerkin. The compactness of the discontinuous Galerkin method makes it better suited for buffer-zone-type methods than high-order finite-difference methods. Results are presented for wall, characteristic inflow and outflow, and nonreflecting boundary conditions.

The compact form of the discontinuous Galerkin method allows for a detailed local analysis of the method in the neighborhood of the shock for a non-linear model problem. Insight gained from the analysis leads to new flux formulas that are stable and that preserve the compactness of the method. Although developed for a model equation, the flux formulas are applicable to systems such as the Euler equations. This article presents the analysis for methods with a degree up to 5. The analysis is accompanied by supporting numerical experiments using Burgers' equation and the Euler equations.

A discontinuous Galerkin formulation that avoids the use of discrete quadrature formulas is described and applied to linear and nonlinear test problems in one and two space dimensions. This approach requires less computational time and storage than conventional implementations but preserves the compactness and robustness inherent to the discontinuous Galerkin method. Test problems include both linear and nonlinear one-dimensional scalar advection of botH smooth and discontinuous initial value problems, two-dimensional scalar advection of smooth initial value problems discretized by using unstructured grids with varying degrees of smoothness and regularity, and two-dimensional linear Euler solutions on unstructured grids.

A different approach to nonreflective boundary conditions for the Euler equations is presented. This work is motivated by a need for inflow and outflow boundary conditions that do not limit the useful accuracy of high-order accurate methods. The primary interest is in the propagation and convection of continuous acoustic and convective waves. This new approach employs the exact solution to finite waves to relate interior values and ambient conditions to boundary values. The method is first presented in one dimension and then generalized to multidimensions. Grid refinement studies are used to demonstrate high-order convergence for both one-dimensional and two-dimensional flows.

The finite-volume and finite-difference implementations of high-order accurate essentially non-oscillatory shock-capturing schemes are discussed and compared. Results obtained with fourth-order accurate algorithms based on both formulations are examined for accuracy, sensitivity to grid irregularities, resolution of waves that are oblique to the mesh, and computational efficiency. Some algorithm modifications that may be required for a given application are suggested. Conclusions that pertain to the relative merits of both formulations are drawn, and some circumstances for which each might be useful are noted.

The finite-volume approach is presently used to obtain a 2D, high-order accurate and basically nonoscillatory shock-capture method whose high-order spatial accuracy is obtained by means of a piecewise polynomial approximation of the solution from cell averages. Attention is given to a high-order spatial operator that is able to both retain high-order accuracy in smooth regions and avoid the oscillations that are associated with interpolations across steep gradients. The operator is extended to hyperbolic systems of equations and curvilinear meshes.

The finite-volume and finite-difference implementations of high-order accurate essentially nonoscillatory shock-capturing schemes are discussed and compared. Results obtained with fourth-order accurate algorithms based on both formulations are examined for accuracy, sensitivity to grid irregularities, resolution of waves that are oblique to the mesh, and computational efficiency. Some algorithm modifications that may be required for a given application are suggested. Conclusions that pertain to the relative merits of both formulations are drawn, and some circumstances for which each might be useful are noted.

A different approach to nonreflective boundary conditions for the Euler equations is presented. This work is motivated by a need for in and outflow boundary conditions that do not limit the useful accuracy of high-order accurate methods. The primary interest is in the propagation and convection of continuous acoustic and convective waves. This new approach employs the exact solution to finite waves to relate interior values and ambient conditions to boundary values. The method is first presented in one dimension and then generalized to multidimensions. Grid refinement studies are used to demonstrate high-order convergence for both one-dimensional and two-dimensional flows.

A multi-block multigrid method for the solution of the three-dimensional Euler and Navier-Stokes equations is presented. The basic flow solver is a cell-vertex method which employs central-difference spatial approximations and Runge-Kutta time stepping. The use of local time stepping, implicit residual smoothing, multigrid techniques, and variable-coefficient numerical smoothing results in an efficient and robust scheme. The multi-block strategy places the block loop within the Runge-Kutta loop such that accuracy and convergence are not affected by block boundaries. This has been verified by comparing the results of one- and two-block calculations in which the two-block grid is generated by splitting the one-block grid. Results are presented for both Euler and Navier-Stokes computations of wings and wing-fuselage combinations.

The adaptive stencil concepts of ENO (Essentially Non-Oscillatory) methods are applied to the laminar Navier-Stokes equations to yield a high-order, time-accurate algorithm with a shock-capturing capability. The method targets problems in the areas of nonlinear acoustics, compressible transition, and turbulence which, due to the presence of shocks or complex geometries, are not easily solved by spectral methods. The present approach has been implemented and tested for the full three-dimensional Navier-Stokes equations in a transformed curvilinear coordinate system. Validation results are presented for a variety of problems which verify the method's accuracy properties and shock capturing capabilities, as well as demonstrate its use as a direct simulation tool.

A finite-volume method for solving the compressible laminar Navier-Stokes equation in two dimensions is assessed for use in the simulation of transitional flows. The method is second-order-accurate, uses alternating-direction-implicit time integration, and a total-variation-diminishing smoothing operator in the inviscid flux terms. The test problem was a free shear layer with a forced periodicity in x at a specified wavelength and with the parallel mean flow specified as a hyperbolic-tangent profile. A grid refinement investigation verified this method to be second-order-accurate with less than 4 percent error in the growth rate of isolated modes on a 32 by 64 grid. The interaction between modes of similar amplitude was small, less than 1 percent. However, in cases where there was a dominant mode, numerical phase error pumped energy into all other modes. This error results in nonphysical growth rate for modes whose energy content is several orders of magnitude below the dominant mode. In the case when the dominant mode saturates, the pumping action stops and the growth rate of the next largest growing mode regains physical significance.

The Microgravity and Materials Processing Facility (MMPF) of the Space Station is examined. The MMPF is designed to accommodate individual experiments and associated hardware and is to be housed in the Manufacturing and Technology Laboratory Module. The objectives of the microgravity and materials processing study and the user, experiment/equipment, MMPF system requirements, and programmatics and planning development tasks of the study are described. Consideration is given to the acceleration environment, on-orbit sample preparation and analysis, mission-time-line analyses, and payload complement trades. Diagrams of the MMPF are presented.

Space-based materials processing R&D is examined. It is proposed that the Space Station's Microgravity and Materials Processing Facility will be utilized by academic, government, and commercial customers. Users requirements for materials processing in space are discussed. Consideration is given to the time allocation of the facility, charges to users, and the property rights of the users.

Commerce Lab is conceived as an adjunct to the National Space Transportation System (NSTS) by providing a focal point for commercial missions which could utilize existing NSTS carrier and resource capabilities for on-orbit experimentation in the microgravity sciences. In this context, the Commerce Lab program provides mission planning for private sector involvement in the space program, in general, and the commercial exploitation of the microgravity environment for materials processing research and development. It is expected that Commerce Lab will provide a logical transition between currently planned NSTS missions and future microgravity science and commercial R&D missions centered around the Space Station. The present study identifies candidate Commerce Lab flight experiments and their development status and projects a mission traffic model that can be used in commercial mission planning.

The possible applications of technology of materials processing in low gravity is discussed. A special office established by NASA to familiarize commercial organizations with materials processing in low gravity is described. This office provides information on present research and will, if requested, hold a seminar to present the technological and business aspects of joint investigations and joint endeavors to interested organizations. Arrangements can be made for visits to laboratories where ground based research is in progress.

Previously cited in issue 06, p. 796, Accession no. A82-17786

A new stream function formulation is developed for the solution of Euler's equations in the transonic flow region. The stream function and the density are the dependent variables in this method, while the governing equations for adiabatic flow are the momentum equations which are solved in the strong conservation law form. The application of this method does not require a knowledge of the vorticity. The algorithm is combined with the automatic grid solver (GRAPE) of Steger and Sorenson (1979) in order to study arbitrary geometries. Results of the application of this method are presented for the NACA 0012 airfoil at various Mach numbers and angles of attack, and cylinders. In addition, detailed comparisons are made with other solutions of the Euler equations.

An implicit finite difference method with implicit boundary conditions is employed to solve the steady Euler's equations for flows past arbitrary geometries. The resulting code is used to investigate in a systematic way various aspects of flow past airfoils at transonic speeds such as, method of solution, boundary conditions, grid stretching and generation, shock and sonic point operators, the Kutta condition, and smoothing. Results obtained are in good agreement with results of other codes. Moreover, it appears that the method of solution employed is such that Kutta's condition need not be invoked. This statement appears to be valid for other existing schemes employed in the solution of Euler's equations.

The Skylab vehicle from its first conception until its flight underwent several iterations. In a similar manner, the scientific experiments changed in both their physical appearance and operational mode because of the evolution of Skylab. In some cases the scientific requirements changed operational requirements of Skylab. The interactions between Skylab and the scientific experiments objectives as well as individual experiment problems are the subject of this paper. The authors use examples from the experiment S-183 (Ultraviolet Panorama) as well as examples from sophisticated groups of experiments such as the Apollo Telescope Mount (ATM). Examples of the positive aspects of the operation are indicated as well as problems, their solution, and the decision-making process. Various phases of the program are discussed and important aspects emphasized. Some general conclusions and recommendations are presented which, hopefully, will aid potential experimenters on Shuttle payloads.

An overview is presented of an investigation which was conducted to determine the actual effects of the Skylab environment on flight films. Examples of the flight film performance data are provided. Attention is given to the Skylab film, the environmental parameters, a major events profile of the Skylab mission, and a film environmental effects analysis. Representative Skylab film environmental response data are shown in a graph.

A proposal is made for inclusion of a very wide field camera onboard Spacelab. Its scientific program is outlined: detection and photometry, spectrography, and star and starlike object photography. The optics, receptor, and mechanical structure are described. Scientific and technical constraints are discussed, and a development plan is detailed. The dust contamination of Spacelab using the camera was also studied.

Rhesus monkey active bone marrow distribution and volume studied by radioactive tracing techniques

Subject classification bibliography for thermal contact resistance

Heat and mass transfer, thermodynamics, fluid mechanics, and energy conversion studies for space flight applications

Interface thermal contact conductance between metals in vacuum studied for data on heat transfer mechanism

Bibliography of contact heat transfer measurements and theories, and thermal metallic contact conductance

Thermal contact conductance tests in vacuum as function of pressure, and elastic deformation data plotted as function of applied loading