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NASA NTRS1993

Fuel optimal reorientation of axisymmetric spin-stabilized satellites

The fuel optimal spin axis reorientation problem for large and small maneuver times is solved using a new numerical technique. The approach, which employs the adaptive grid bisection search, is shown to be useful in determining the fuel optimal impulsive control strategy, particularly when rapid maneuvers are desired. For large enough maneuver times, the method produces the two-impulse reorientation maneuver. For even larger maneuver times, the existence of multiple optimal pulsing schemes is demonstrated.

Redmond, Jim↗

NASA NTRS1991

Computation of thermochemical nonequilibrium flows around a simple and a double ellipse

The nonequilibrium viscous reactive flows over a simple and a double ellipse at a 30 degree angle of attack were computed. The geometry and the free stream conditions are given by INRIA/GAMNI/SMAI workshop test cases 6.2-2 and 6.2-4. The governing Navier-Stokes equations coupled with thermochemical nonequilibrium processes are solved numerically using a fully coupled, implicit, finite volume technique with a dynamically adaptive grid. The nonequilibrium gas model and the numerical method used in the calculations are briefly described.

Gokcen, Tahir↗

NASA NTRS1993

CFD analysis of hypersonic, chemically reacting flow fields

Design studies are underway for a variety of hypersonic flight vehicles. The National Aero-Space Plane will provide a reusable, single-stage-to-orbit capability for routine access to low earth orbit. Flight-capable satellites will dip into the atmosphere to maneuver to new orbits, while planetary probes will decelerate at their destination by atmospheric aerobraking. To supplement limited experimental capabilities in the hypersonic regime, computational fluid dynamics (CFD) is being used to analyze the flow about these configurations. The governing equations include fluid dynamic as well as chemical species equations, which are being solved with new, robust numerical algorithms. Examples of CFD applications to hypersonic vehicles suggest an important role this technology will play in the development of future aerospace systems. The computational resources needed to obtain solutions are large, but solution adaptive grids, convergence acceleration, and parallel processing may make run times manageable.

Edwards, T. A.↗

NASA NTRS1993

The block adaptive multigrid method applied to the solution of the Euler equations

In the present study, a scheme capable of solving very fast and robust complex nonlinear systems of equations is presented. The Block Adaptive Multigrid (BAM) solution method offers multigrid acceleration and adaptive grid refinement based on the prediction of the solution error. The proposed solution method was used with an implicit upwind Euler solver for the solution of complex transonic flows around airfoils. Very fast results were obtained (18-fold acceleration of the solution) using one fourth of the volumes of a global grid with the same solution accuracy for two test cases.

Pantelelis, Nikos↗

NASA NTRS1993

Techniques and resources for storm-scale numerical weather prediction

The topics discussed include the following: multiscale application of the 5th-generation PSU/NCAR mesoscale model, the coupling of nonhydrostatic atmospheric and hydrostatic ocean models for air-sea interaction studies; a numerical simulation of cloud formation over complex topography; adaptive grid simulations of convection; an unstructured grid, nonhydrostatic meso/cloud scale model; efficient mesoscale modeling for multiple scales using variable resolution; initialization of cloud-scale models with Doppler radar data; and making effective use of future computing architectures, networks, and visualization software.

Droegemeier, Kelvin↗

NASA NTRS1994

Incremental triangulation by way of edge swapping and local optimization

This document is intended to serve as an installation, usage, and basic theory guide for the two dimensional triangulation software 'HARLEY' written for the Silicon Graphics IRIS workstation. This code consists of an incremental triangulation algorithm based on point insertion and local edge swapping. Using this basic strategy, several types of triangulations can be produced depending on user selected options. For example, local edge swapping criteria can be chosen which minimizes the maximum interior angle (a MinMax triangulation) or which maximizes the minimum interior angle (a MaxMin or Delaunay triangulation). It should be noted that the MinMax triangulation is generally only locally optical (not globally optimal) in this measure. The MaxMin triangulation, however, is both locally and globally optical. In addition, Steiner triangulations can be constructed by inserting new sites at triangle circumcenters followed by edge swapping based on the MaxMin criteria. Incremental insertion of sites also provides flexibility in choosing cell refinement criteria. A dynamic heap structure has been implemented in the code so that once a refinement measure is specified (i.e., maximum aspect ratio or some measure of a solution gradient for the solution adaptive grid generation) the cell with the largest value of this measure is continually removed from the top of the heap and refined. The heap refinement strategy allows the user to specify either the number of cells desired or refine the mesh until all cell refinement measures satisfy a user specified tolerance level. Since the dynamic heap structure is constantly updated, the algorithm always refines the particular cell in the mesh with the largest refinement criteria value. The code allows the user to: triangulate a cloud of prespecified points (sites), triangulate a set of prespecified interior points constrained by prespecified boundary curve(s), Steiner triangulate the interior/exterior of prespecified boundary curve(s), refine existing triangulations based on solution error measures, and partition meshes based on the Cuthill-McKee, spectral, and coordinate bisection strategies.

Wiltberger, N. Lyn↗

NASA NTRS1994

Project JOVE

The goal of this project is to investigate new areas of research pertaining to free surface-interface fluids mechanics and/or microgravity which have potential commercial applications. This paper presents an introduction to ferrohydrodynamics (FHD), and discusses some applications. Also, computational methods for solving free surface flow problems are presented in detail. Both have diverse applications in industry and in microgravity fluids applications. Three different modeling schemes for FHD flows are addressed and the governing equations, including Maxwell's equations, are introduced. In the area of computational modeling of free surface flows, both Eulerian and Lagrangian schemes are discussed. The state of the art in computational methods applied to free surface flows is elucidated. In particular, adaptive grids and re-zoning methods are discussed. Additional research results are addressed and copies of the publications produced under the JOVE Project are included.

Lyell, M. J.↗

NASA NTRS1994

Computational Fluid Dynamic Modeling of Rocket Based Combined Cycle Engine Flowfields

Computational Fluid Dynamic techniques are used to study the flowfield of a fixed geometry Rocket Based Combined Cycle engine operating in rocket ejector mode. Heat addition resulting from the combustion of injected fuel causes the subsonic engine flow to choke and go supersonic in the slightly divergent combustor-mixer section. Reacting flow computations are undertaken to predict the characteristics of solutions where the heat addition is determined by the flowfield. Here, adaptive gridding is used to improve resolution in the shear layers. Results show that the sonic speed is reached in the unheated portions of the flow first, while the heated portions become supersonic later. Comparison with results from another code show reasonable agreement. The coupled solutions show that the character of the combustion-based thermal choking phenomenon can be controlled reasonably well such that there is opportunity to optimize the length and expansion ratio of the combustor-mixer.

Daines, Russell L.↗

NASA NTRS1992

Computational fluid dynamics study of the variable-pitch split-blade fan concept

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

Kepler, C. E.↗

NASA NTRS1995

A perspective on unstructured grid flow solvers

This survey paper assesses the status of compressible Euler and Navier-Stokes solvers on unstructured grids. Different spatial and temporal discretization options for steady and unsteady flows are discussed. The integration of these components into an overall framework to solve practical problems is addressed. Issues such as grid adaptation, higher order methods, hybrid discretizations and parallel computing are briefly discussed. Finally, some outstanding issues and future research directions are presented.

Venkatakrishnan, V.↗

NASA NTRS1995

Extensional flow convecting a reactant undergoing a first order homogeneous reaction and diffusional mass transfer from a sphere at low to intermediate Peclet and Damkohler numbers

Forced convective diffusion-reaction is considered for viscous axisymmetric extensional convecting velocity in the neighborhood of a sphere. For Peclet numbers in the range 0.1 less than or equal to Pe less than or equal to 500 and for Damkohler numbers increasing with increasing Pe but in the overall range 0.02 less than or equal to Da less than or equal to 10, average and local Sherwood numbers have been computed. By introducing the eigenfunction expansion c(r, Theta) = Sum of c(n)(r)P(n)(cos Theta) into the forced convective diffusion equation for the concentration of a chemical species undergoing a first order homogeneous reaction and by using properties of the Legendre functions Pn(cos Theta), the variable coefficient PDE can be reduced to a system of N + 1 second order ODEs for the radial functions c(sub n)(r), n = 0, 1, 2,..., N. The adaptive grid algorithm of Pereyra and Lentini can be used to solve the corresponding 2(N + 1) first order differential equations as a two-point boundary value problem on 1 less than or equal to r less than or equal to r(sub infinity). Convergence of the expansion for a specific value of N can thus be established and provides 'spectral' behavior as well as the full concentration field c(r, Theta).

Shah, N. Y.↗

NASA NTRS1995

CAE for thermal management of aerospace electronic boards using the BETAsoft program

Aerospace electronic boards require special attention to thermal management due to constraints such as their need to be light, small, and maintain high power densities. Also, cooling is mainly through conductive and radiative modes with minor or negligible convective cooling. Due to these particular requirements, thermal design has become an integrated part of the electronic design process in order to avoid expensive repeat prototyping and to ensure high reliability. To achieve high speed simulations, the BETAsoft code uses semi-empirical formulations and an advanced finite difference scheme that incorporates local adaptive grids. Detailed conduction, convection and radiation heat transfer is considered. Various benchmark verifications of the software simulation compared to infrared images typically prove to be within 10% of each other. The thermal analysis of a sample avionic card in a natural convection environment is shown. Then, the individual effects of attaching metal screws to the casing, increasing radiative emissivities of the casing, increasing the conductance of the wedge lock, adding an aluminum core to the board, adding metal strips in board layers, inserting conduction pads under components, and adding heat sinks to components are demonstrated.

Bobish, Kimberly↗

NASA NTRS1996

Numerical Modeling of Spray Combustion with an Unstructured-Grid Method

The present unstructured-grid method follows strictly the basic finite volume forms of the conservation laws of the governing equations for the entire flow domain. High-order spatially accurate formulation has been employed for the numerical solutions of the Navier-Stokes equations. A two-equation k-epsilon turbulence model is also incorporated in the unstructured-grid solver. The convergence of the resulted linear algebraic equation is accelerated with preconditioned Conjugate Gradient method. A statistical spray combustion model has been incorporated into the present unstructured-grid solver. In this model, spray is represented by discrete particles, rather than by continuous distributions. A finite number of computational particles are used to predict a sample of total population of particles. Particle trajectories are integrated using their momentum and motion equations and particles exchange mass, momentum and energy with the gas within the computational cell in which they are located. The interaction calculations are performed simultaneously and eliminate global iteration for the two-phase momentum exchange. A transient spray flame in a high pressure combustion chamber is predicted and then the solution of liquid-fuel combusting flow with a rotating cup atomizer is presented and compared with the experimental data. The major conclusion of this investigation is that the unstructured-grid method can be employed to study very complicated flow fields of turbulent spray combustion. Grid adaptation can be easily achieved in any flow domain such as droplet evaporation and combustion zone. Future applications of the present model can be found in the full three-dimensional study of flow fields of gas turbine and liquid propulsion engine combustion chambers with multi-injectors.

Shang, H. M.↗

NASA NTRS1997

Dynamics of Numerics & Spurious Behaviors in CFD Computations

The global nonlinear behavior of finite discretizations for constant time steps and fixed or adaptive grid spacings is studied using tools from dynamical systems theory. Detailed analysis of commonly used temporal and spatial discretizations for simple model problems is presented. The role of dynamics in the understanding of long time behavior of numerical integration and the nonlinear stability, convergence, and reliability of using time-marching approaches for obtaining steady-state numerical solutions in computational fluid dynamics (CFD) is explored. The study is complemented with examples of spurious behavior observed in steady and unsteady CFD computations. The CFD examples were chosen to illustrate non-apparent spurious behavior that was difficult to detect without extensive grid and temporal refinement studies and some knowledge from dynamical systems theory. Studies revealed the various possible dangers of misinterpreting numerical simulation of realistic complex flows that are constrained by available computing power. In large scale computations where the physics of the problem under study is not well understood and numerical simulations are the only viable means of solution, extreme care must be taken in both computation and interpretation of the numerical data. The goal of this paper is to explore the important role that dynamical systems theory can play in the understanding of the global nonlinear behavior of numerical algorithms and to aid the identification of the sources of numerical uncertainties in CFD.

Yee, Helen C.↗

NASA NTRS1998

Barriers to Achieving Textbook Multigrid Efficiency (TME) in CFD

As a guide to attaining this optimal performance for general CFD problems, the table below lists every foreseen kind of computational difficulty for achieving that goal, together with the possible ways for resolving that difficulty, their current state of development, and references. Included in the table are staggered and nonstaggered, conservative and nonconservative discretizations of viscous and inviscid, incompressible and compressible flows at various Mach numbers, as well as a simple (algebraic) turbulence model and comments on chemically reacting flows. The listing of associated computational barriers involves: non-alignment of streamlines or sonic characteristics with the grids; recirculating flows; stagnation points; discretization and relaxation on and near shocks and boundaries; far-field artificial boundary conditions; small-scale singularities (meaning important features, such as the complete airplane, which are not visible on some of the coarse grids); large grid aspect ratios; boundary layer resolution; and grid adaption.

Brandt, Achi↗

NASA NTRS1997

Instability Mechanisms of Thermally-Driven Interfacial Flows in Liquid-Encapsulated Crystal Growth

During the past year, a great deal of effort was focused on the enhancement and refinement of the computational tools developed as part of our previous NASA grant. In particular, the interface mollification algorithm developed earlier was extended to incorporate the effects of surface-rheological properties in order to allow the study of thermocapillary flows in the presence of surface contamination. These tools will be used in the computational component of the proposed research in the remaining years of this grant. A detailed description of the progress made in this area is provided elsewhere. Briefly, the method developed allows for the convection and diffusion of bulk-insoluble surfactants on a moving and deforming interface. The novelty of the method is its grid independence: there is no need for front tracking, surface reconstruction, body-fitted grid generation, or metric evaluations; these are all very expensive computational tasks in three dimensions. For small local radii of curvature there is a need for local grid adaption so that the smearing thickness remains a small fraction of the radius of curvature. A special Neumann boundary condition was devised and applied so that the calculated surfactant concentration has no variations normal to the interface, and it is hence truly a surface-defined quantity. The discretized governing equations are solved subsequently using a time-split integration scheme which updates the concentration and the shape successively. Results demonstrate excellent agreement between the computed and exact solutions.

Haj-Hariri, Hossein↗

NASA NTRS1999

Computations of Boiling in Microgravity

The absence (or reduction) of gravity, can lead to major changes in boiling heat transfer. On Earth, convection has a major effect on the heat distribution ahead of an evaporation front, and buoyancy determines the motion of the growing bubbles. In microgravity, convection and buoyancy are absent or greatly reduced and the dynamics of the growing vapor bubbles can change in a fundamental way. In particular, the lack of redistribution of heat can lead to a large superheat and explosive growth of bubbles once they form. While considerable efforts have been devoted to examining boiling experimentally, including the effect of microgravity, theoretical and computational work is limited to very simple models. In this project, the growth of boiling bubbles is studied by direct numerical simulations where the flow field is fully resolved and the effects of inertia, viscosity, surface deformation, heat conduction and convection, as well as the phase change, are fully accounted for. The proposed work is based on previously funded NASA work that allowed us to develop a two-dimensional numerical method for boiling flows and to demonstrate the ability of the method to simulate film boiling. While numerical simulations of multi-fluid flows have been advanced in a major way during the last five years, or so, similar capability for flows with phase change are still in their infancy. Although the feasibility of the proposed approach has been demonstrated, it has yet to be extended and applied to fully three-dimensional simulations. Here, a fully three-dimensional, parallel, grid adaptive code will be developed. The numerical method will be used to study nucleate boiling in microgravity, with particular emphasis on two aspects of the problem: 1) Examination of the growth of bubbles at a wall nucleation site and the instabilities of rapidly growing bubbles. Particular emphasis will be put on accurately capturing the thin wall layer left behind as a bubble expands along a wall, on computing instabilities on bubble surfaces as bubbles grow, and on quantifying the effects of both these phenomena on heat transfer; and 2) Examination of the effect of shear flow on bubble growth and heat transfer.

Tryggvason, Gretar↗

NASA NTRS1995

On the Dynamics of Some Discretizations of Convection-Diffusion Equations

Numerical discretizations of differential equations which model physical processes can possess dynamics quite different from that of the equations themselves. Recently the emphasis has been on the the dynamics of numerical discretizations for Ordinary Differential Equations (ODEs). For Partial Differential Equations (PDEs) using a method of lines approach the situation is more complex. First, the spatial discretisation may introduce dynamics not present in the original equations; second, the solution of the resulting system of ODEs is open to the modified dynamics of the ODE solver used. These two effects may interact in a complex manner. In this talk we present some results of our recent work on the dynamics of discretizations of convection-diffusion equations, including those produced using Total Variation Diminishing (TVD) schemes and adaptive grid techniques. A more general overview of the area may be found on our accompanying poster presentation.

Sweby, Peter K.↗