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NASA NTRS1994

Magnetocentrifugally driven flows from young stars and disks. 2: Formulation of the dynamical problem

We formulate the dynamical problem of a cool wind centrifugally driven from the magnetic interface of a young star and an adjoining Keplerian disk. We examine the situation for mildly accreting T Tauri stars that rotate slowly as well as rapidly accreting protostars that rotate near break-up. In both cases a wind can be driven from a small X-region just outside the stellar magnetopause, where the field lines assume an open geometry and are rooted to material that rotates at an angular speed equal both to the local Keplerian value and to the stellar angular speed. Assuming axial symmetry for the ideal magnetohydrodynamic flow, which requires us to postpone asking how the (lightly ionized) gas is loaded onto field lines, we can formally integrate all the governing equations analytically except for a partial equation that describes how streamlines spread in the meridional plane. Apart from the difficulty of dealing with PDEs of mixed type, finding the functional forms of the conserved quantities along streamlines - the ratio beta of magnetic field to mass flux, the specific energy H of the fluid in the rotating frame, and the total specific angular momentum J carried in the matter and the field - constitutes a standard difficulty in this kind of (Grad-Shafranov) formalism. Fortunately, because the ratio of the thermal speed of the mass-loss regions to the Keplerian speed of rotation of the interface constitutes a small parameter epsilon, we can attack the overall problem by the method of matched asymptotic expansions. This procedure leads to a natural and systematic technique for obtaining the relevant functional dependences of beta, H, and J. Moreover, we are able to solve analytically for the properties of the flow emergent from the small transsonic region driven by gas pressure without having to specify the detailed form of any of the conserved functions, beta, H, and J. This analytical solution provides inner boundary conditions for the numerical computation in a companion paper by Najita & Shu of the larger region where the main acceleration to terminal speeds occurs.

Shu, Frank H.↗
NASA NTRS1995

Theoretical study of hole initiated impact ionization in bulk silicon and GaAs using a wave-vector-dependent numerical transition rate formulation within an ensemble Monte Carlo calculation

In this paper, calculations of the hole initiated interband impact ionization rate in bulk silicon and GaAs are presented based on an ensemble Monte Carlo simulation with the inclusion of a wave-vector-dependent numerical transition rate formulation. The ionization transition rate is determined for each of the three valence bands, heavy, light, and split-off, using Fermi's golden rule with a two-body, screened Coulomb interaction. The dielectric function used within the calculation is assumed to be wave-vector-dependent. Calculations of the field-dependent impact ionization rate as well as the quantum yield are presented. It is found from both the quantum yield results and examination of the hole distribution function that the effective threshold energy for hole initiated impact ionization is relatively soft, similar to that predicted for the corresponding electron initiated ionization events occur more frequently than either heavy or split-offf initiated ionization events in bulk silicon over the applied electric field strengths examined here, 250-500 kV/cm. Conversely,in GaAs, the vast majority of hole initated ionization events originate from holes within the split-off band.

Oguzman, Ismail H.↗
NASA NTRS1995

Universal Formulation For Symmetries In Computed Flows

Universal formulation for high-order symmetries in boundary conditions on flows devised. Eliminates need for special procedures to incorporate symmetries and corresponding boundary conditions into computer codes solving Navier-Stokes and Euler equations of flow.

Pao, S. Paul↗
NASA NTRS1995

Supersonic wing and wing-body shape optimization using an adjoint formulation

This paper describes the implementation of optimization techniques based on control theory for wing and wing-body design of supersonic configurations. The work represents an extension of our earlier research in which control theory is used to devise a design procedure that significantly reduces the computational cost by employing an adjoint equation. In previous studies it was shown that control theory could be used to~eviseransonic design methods for airfoils and wings in which the shape and the surrounding body-fitted mesh are both generated analytically, and the control is the mapping function. The method has also been implemented for both transonic potential flows and transonic flows governed by the Euler equations using an alternative formulation which employs numerically generated grids, so that it can treat more general configurations. Here results are presented for three-dimensional design cases subject to supersonic flows governed by the Euler equation.

Reuther, James↗
NASA NTRS1966

An Analysis of the Impact of the Federal Budgetary Cycle Upon the NASA Manned Spacecraft Center Research and Development Budget Formulation Process

The subsequent dissertation represents an analysis of the impact of the Federal Budgetary Cycle upon the National Aeronautics and Space Administration (NASA) Manned Spacecraft Center (MSC) Research and Development (R&D) budget formulation process. The author's objectives may therefore be seen as the following: (1) to analyze the Federal Budgetary Cycle; (2) to analyze MSC R&D estimates and growth trends in relation to their implications on the Federal Cycle; (3) to identify relevant problems; and, (4) to-recommend solutions which display promise and feasibility. Any research involving the Federal Budgetary Cycle can well be characterized as of almost infinite scope and enormous complexity. For such reasons one must meticulously delineate all operational parameters and there-afore maintain their integrity. To do otherwise is to invite intellectual dilution and hazard a paltry effort.

Peterson, Ronald Keith↗
NASA NTRS1993

Formulation for Simultaneous Aerodynamic Analysis and Design Optimization

An efficient approach for simultaneous aerodynamic analysis and design optimization is presented. This approach does not require the performance of many flow analyses at each design optimization step, which can be an expensive procedure. Thus, this approach brings us one step closer to meeting the challenge of incorporating computational fluid dynamic codes into gradient-based optimization techniques for aerodynamic design. An adjoint-variable method is introduced to nullify the effect of the increased number of design variables in the problem formulation. The method has been successfully tested on one-dimensional nozzle flow problems, including a sample problem with a normal shock. Implementations of the above algorithm are also presented that incorporate Newton iterations to secure a high-quality flow solution at the end of the design process. Implementations with iterative flow solvers are possible and will be required for large, multidimensional flow problems.

Hou, G. W.↗
NASA NTRS1995

Ensemble Monte Carlo calculation of the hole initiated impact ionization rate in bulk GaAs and silicon using a k-dependent, numerical transition rate formulation

The hole initiated impact ionization rate in bulk silicon and GaAs is calculated using a numerical formulation of the impact ionization transition rate incorporated into an ensemble Monte Carlo simulation. The transition rate is calculated from Fermi's golden rule using a two-body screened Coulomb interaction including a wavevector dependent dielectric function. It is found that the effective threshold for hole initiated ionization is relatively soft in both materials, that the split-off band dominates the ionization process in GaAs. and that no clear dominance by any one band is observed in silicon, though the rate out of the light hole band is greatest.

Oguzman, Ismail H.↗
NASA NTRS1996

Aerodynamic Shape Optimization of Complex Aircraft Configurations via an Adjoint Formulation

This work describes the implementation of optimization techniques based on control theory for complex aircraft configurations. Here control theory is employed to derive the adjoint differential equations, the solution of which allows for a drastic reduction in computational costs over previous design methods (13, 12, 43, 38). In our earlier studies (19, 20, 22, 23, 39, 25, 40, 41, 42) it was shown that this method could be used to devise effective optimization procedures for airfoils, wings and wing-bodies subject to either analytic or arbitrary meshes. Design formulations for both potential flows and flows governed by the Euler equations have been demonstrated, showing that such methods can be devised for various governing equations (39, 25). In our most recent works (40, 42) the method was extended to treat wing-body configurations with a large number of mesh points, verifying that significant computational savings can be gained for practical design problems. In this paper the method is extended for the Euler equations to treat complete aircraft configurations via a new multiblock implementation. New elements include a multiblock-multigrid flow solver, a multiblock-multigrid adjoint solver, and a multiblock mesh perturbation scheme. Two design examples are presented in which the new method is used for the wing redesign of a transonic business jet.

Reuther, James↗
NASA NTRS1996

Development of a Vorticity-Velocity Navier-Stokes Formulation for the Study of Compressibility Effects on Dynamic Stall

The first major area of this study was to develop a vorticity-velocity formulation and numerical solution algorithms suitable for the analyses of incompressible as well as low-to- moderate-speed compressible flows. Research performed towards contributing to the determination of the appropriate vorticity and dilation creation boundary conditions suggested to temporarily set aside this approach and use a primitive-variable approach other than the pseudo-compressibility approach used. The second major area of study was initiated to comprehensively examine the INS-2D and INS-3D programs from the point of view of boundary conditions. The research carried out was documented in the form of two technical papers which are included in Appendices A and B; the boundary-condition related issues for INS-3D are briefly mentioned.

Ghia, K. N.↗
NASA NTRS2000

Multidisciplinary High-Fidelity Analysis and Optimization of Aerospace Vehicles: Formulation - Part 1

An objective of the High Performance Computing and Communication Program at the NASA Langley Research Center is to demonstrate multidisciplinary shape and sizing optimization of a complete aerospace vehicle configuration by using high-fidelity, finite element structural analysis and computational fluid dynamics aerodynamic analysis in a distributed, heterogeneous computing environment that includes high performance parallel computing. A software system has been designed and implemented to integrate a set of existing discipline analysis codes, some of them computationally intensive, into a distributed computational environment for the design of a highspeed civil transport configuration. The paper describes the engineering aspects of formulating the optimization by integrating these analysis codes and associated interface codes into the system. The discipline codes are integrated by using the Java programming language and a Common Object Request Broker Architecture (CORBA) compliant software product. A companion paper presents currently available results.

Walsh, J. L.↗
NASA NTRS2001

Factorizable Upwind Schemes: the Triangular Unstructured Grid Formulation

The upwind factorizable schemes for the equations of fluid was introduced recently. They facilitate achieving the Textbook Multigrid Efficiency (TME) and are expected also to result in the solvers of unparalleled robustness. The approach itself is very general. Therefore, it may well become a general framework for the large-scale Computational Fluid Dynamics. In this paper we outline the triangular grid formulation of the factorizable schemes. The derivation is based on the fact that the factorizable schemes can be expressed entirely using vector notation, without explicitly mentioning a particular coordinate frame. We describe the resulting discrete scheme in detail and present some computational results verifying the basic properties of the scheme/solver.

Nielsen, Eric J.↗
NASA NTRS2001

Factorizable Upwind Schemes: The Triangular Unstructured Grid Formulation

The upwind factorizable schemes for the equations of fluid were introduced recently. They facilitate achieving the Textbook Multigrid Efficiency (TME) and are expected also to result in the solvers of unparalleled robustness. The approach itself is very general. Therefore, it may well become a general framework for the large-scale, Computational Fluid Dynamics. In this paper we outline the triangular grid formulation of the factorizable schemes. The derivation is based on the fact that the factorizable schemes can be expressed entirely using vector notation. without explicitly mentioning a particular coordinate frame. We, describe the resulting discrete scheme in detail and present some computational results verifying the basic properties of the scheme/solver.

Sidilkover, David↗
NASA NTRS2000

A New Eddy Dissipation Rate Formulation for the Terminal Area PBL Prediction System(TAPPS)

The TAPPS employs the MASS model to produce mesoscale atmospheric simulations in support of the Wake Vortex project at Dallas Fort-Worth International Airport (DFW). A post-processing scheme uses the simulated three-dimensional atmospheric characteristics in the planetary boundary layer (PBL) to calculate the turbulence quantities most important to the dissipation of vortices: turbulent kinetic energy and eddy dissipation rate. TAPPS will ultimately be employed to enhance terminal area productivity by providing weather forecasts for the Aircraft Vortex Spacing System (AVOSS). The post-processing scheme utilizes experimental data and similarity theory to determine the turbulence quantities from the simulated horizontal wind field and stability characteristics of the atmosphere. Characteristic PBL quantities important to these calculations are determined based on formulations from the Blackadar PBL parameterization, which is regularly employed in the MASS model to account for PBL processes in mesoscale simulations. The TAPPS forecasts are verified against high-resolution observations of the horizontal winds at DFW. Statistical assessments of the error in the wind forecasts suggest that TAPPS captures the essential features of the horizontal winds with considerable skill. Additionally, the turbulence quantities produced by the post-processor are shown to compare favorably with corresponding tower observations.

Charney, Joseph J.↗
NASA NTRS2004

Numerical Study of Flow Past a Circular Cylinder Using RANS, Hybrid RANS/LES and PANS Formulations

Two multiscale type turbulence models are implemented in the PAB3D solver. The models are based on modifying the Reynolds Averaged Navier-Stokes (RANS) equations. The first scheme is a hybrid RANS/LES model utilizing the two-equation (k(sub epsilon)) model with a RANS/LES transition function dependent on grid spacing and the computed turbulence length scale. The second scheme is a modified version of the partially averaged Navier-Stokes (PANS) model, where the unresolved kinetic energy parameter (f(sub k)) is allowed to vary as a function of grid spacing and the turbulence length scale. Solutions from these models are compared to RANS results and experimental data for a stationary and rotating cylinder. The parameter f(sub k) varies between zero and one and has the characteristic to be equal to one in the viscous sub layer, and when the RANS turbulent viscosity becomes smaller than the LES viscosity. The formulation, usage methodology, and validation example are presented to demonstrate the enhancement of PAB3D's time-accurate and turbulence modeling capabilities. The models are compared to RANS results and experimental data for turbulent separated flows (TS) and laminar separated flows (LS) around stationary and rotating cylinders. For a stationary cylinder, the TS case is accurately simulated using the general two-equation k(sub epsilon) turbulence model (eddy-viscosity model). PAB3D accurately predicts the drag coefficient (CD), lift coefficient (CL) and the Strouhal number (St). The LS case was a challenge for the RANS computation with an eddy-viscosity turbulence model. The RANS/LES and PANS performed well and showed marked improvements over the RANS solution. The modified PANS model was the most accurate. For the rotating cylinder, the spin ratio varied from zero to one, and the PANS results were in good agreement with published experimental data. RANS/LES and PANS capture both temporal and spatial fluctuations and produce large-scale structures that do not occur in the RANS simulation. The current results show promise for the capability of PANS in simulating unsteady and complex flow phenomena.

Elmiligui, Alaa A.↗
NASA NTRS1997

An Analytical Comparison of the Acoustic Analogy and Kirchhoff Formulation for Moving Surfaces

The Lighthill acoustic analogy, as embodied in the Ffowcs Williams-Hawkings (FW-H) equation, is compared with the Kirchhoff formulation for moving surfaces. A comparison of the two governing equations reveals that the main Kirchhoff advantage (namely nonlinear flow effects are included in the surface integration) is also available to the FW-H method if the integration surface used in the FW-H equation is not assumed impenetrable. The FW-H equation is analytically superior for aeroacoustics because it is based upon the conservation laws of fluid mechanics rather than the wave equation. This means that the FW-H equation is valid even if the integration surface is in the nonlinear region. This is demonstrated numerically in the paper. The Kirchhoff approach can lead to substantial errors if the integration surface is not positioned in the linear region. These errors may be hard to identify. Finally, new metrics based on the Sobolev norm are introduced which may be used to compare input data for both quadrupole noise calculations and Kirchhoff noise predictions.

Brentner, Kenneth S.↗
NASA NTRS2004

A Variable Turbulent Schmidt Number Formulation for Scramjet Application

In high speed engines, thorough turbulent mixing of fuel and air is required to obtain high performance and high efficiency. Thus, the ability to predict turbulent mixing is crucial in obtaining accurate numerical simulation of an engine and its performance. Current state of the art in CFD simulation is to assume both turbulent Prandtl number and Schmidt numbers to be constants. However, since the mixing of fuel and air is inversely proportional to the Schmidt number, a value of 0.45 for the Schmidt number will produce twice as much diffusion as that with a value of 0.9. Because of this, current CFD tools and models have not been able to provide the needed guidance required for the efficient design of a scramjet engine. The goal of this investigation is to develop the framework needed to calculate turbulent Prandtl and Schmidt numbers as part of the solution. This requires four additional equations: two for the temperature variance and its dissipation rate and two for the concentration variance and its dissipation rate. In the current investigation emphasis will be placed on studying mixing without reactions. For such flows, variable Prandtl number does not play a major role in determining the flow. This, however, will have to be addressed when combustion is present. The approach to be used is similar to that used to develop the k-zeta model. In this approach, relevant equations are derived from the exact Navier-Stokes equations and each individual correlation is modeled. This ensures that relevant physics is incorporated into the model equations. This task has been accomplished. The final set of equations have no wall or damping functions. Moreover, they are tensorially consistent and Galilean invariant. The derivation of the model equations is rather lengthy and thus will not be incorporated into this abstract, but will be included in the final paper. As a preliminary to formulating the proposed model, the original k-zeta model with constant turbulent Prandtl and Schmidt numbers is used to model the supersonic coaxial jet mixing experiments involving He, O2 and air.

Xiao, X.↗
NASA NTRS2005

Project Integration Architecture: Formulation of Dimensionality in Semantic Parameters Outline

One of several key elements of the Project Integration Architecture (PIA) is the formulation of parameter objects which convey meaningful semantic information. The infusion of measurement dimensionality into such objects is an important part of that effort since it promises to automate the conversion of units between cooperating applications and, thereby, eliminate the mistakes that have occasionally beset other systems of information transport. This paper discusses the conceptualization of dimensionality developed as a result of that effort.

Jones, William Henry↗