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NASA NTRS1993

A method for the modelling of porous and solid wind tunnel walls in computational fluid dynamics codes

Porous wall wind tunnels have been used for several decades and have proven effective in reducing wall interference effects in both low speed and transonic testing. They allow for testing through Mach 1, reduce blockage effects and reduce shock wave reflections in the test section. Their usefulness in developing computational fluid dynamics (CFD) codes has been limited, however, by the difficulties associated with modelling the effect of a porous wall in CFD codes. Previous approaches to modelling porous wall effects have depended either upon a simplified linear boundary condition, which has proven inadequate, or upon detailed measurements of the normal velocity near the wall, which require extensive wind tunnel time. The current work was initiated in an effort to find a simple, accurate method of modelling a porous wall boundary condition in CFD codes. The development of such a method would allow data from porous wall wind tunnels to be used more readily in validating CFD codes. This would be beneficial when transonic validations are desired, or when large models are used to achieve high Reynolds numbers in testing. A computational and experimental study was undertaken to investigate a new method of modelling solid and porous wall boundary conditions in CFD codes. The method utilized experimental measurements at the walls to develop a flow field solution based on the method of singularities. This flow field solution was then imposed as a pressure boundary condition in a CFD simulation of the internal flow field. The effectiveness of this method in describing the effect of porosity changes on the wall was investigated. Also, the effectiveness of this method when only sparse experimental measurements were available has been investigated. The current work demonstrated this approach for low speed flows and compared the results with experimental data obtained from a heavily instrumented variable porosity test section. The approach developed was simple, computationally inexpensive, and did not require extensive or intrusive measurements of the boundary conditions during the wind tunnel test. It may be applied to both solid and porous wall wind tunnel tests.

Beutner, Thomas John↗

NASA NTRS1994

Comparison of PDF and Moment Closure Methods in the Modeling of Turbulent Reacting Flows

In modeling turbulent reactive flows, Probability Density Function (PDF) methods have an advantage over the more traditional moment closure schemes in that the PDF formulation treats the chemical reaction source terms exactly, while moment closure methods are required to model the mean reaction rate. The common model used is the laminar chemistry approximation, where the effects of turbulence on the reaction are assumed negligible. For flows with low turbulence levels and fast chemistry, the difference between the two methods can be expected to be small. However for flows with finite rate chemistry and high turbulence levels, significant errors can be expected in the moment closure method. In this paper, the ability of the PDF method and the moment closure scheme to accurately model a turbulent reacting flow is tested. To accomplish this, both schemes were used to model a CO/H2/N2- air piloted diffusion flame near extinction. Identical thermochemistry, turbulence models, initial conditions and boundary conditions are employed to ensure a consistent comparison can be made. The results of the two methods are compared to experimental data as well as to each other. The comparison reveals that the PDF method provides good agreement with the experimental data, while the moment closure scheme incorrectly shows a broad, laminar-like flame structure.

Norris, Andrew T.↗

NASA NTRS1992

A finite element: Boundary integral method for electromagnetic scattering

A method that combines the finite element and boundary integral techniques for the numerical solution of electromagnetic scattering problems is presented. The finite element method is well known for requiring a low order storage and for its capability to model inhomogeneous structures. Of particular emphasis in this work is the reduction of the storage requirement by terminating the finite element mesh on a boundary in a fashion which renders the boundary integrals in convolutional form. The fast Fourier transform is then used to evaluate these integrals in a conjugate gradient solver, without a need to generate the actual matrix. This method has a marked advantage over traditional integral equation approaches with respect to the storage requirement of highly inhomogeneous structures. Rectangular, circular, and ogival mesh termination boundaries are examined for two-dimensional scattering. In the case of axially symmetric structures, the boundary integral matrix storage is reduced by exploiting matrix symmetries and solving the resulting system via the conjugate gradient method. In each case several results are presented for various scatterers aimed at validating the method and providing an assessment of its capabilities. Important in methods incorporating boundary integral equations is the issue of internal resonance. A method is implemented for their removal, and is shown to be effective in the two-dimensional and three-dimensional applications.

Collins, J. D.↗

NASA NTRS1993

A time-accurate finite volume method valid at all flow velocities

A finite volume method to solve the Navier-Stokes equations at all flow velocities (e.g., incompressible, subsonic, transonic, supersonic and hypersonic flows) is presented. The numerical method is based on a finite volume method that incorporates a pressure-staggered mesh and an incremental pressure equation for the conservation of mass. Comparison of three generally accepted time-advancing schemes, i.e., Simplified Marker-and-Cell (SMAC), Pressure-Implicit-Splitting of Operators (PISO), and Iterative-Time-Advancing (ITA) scheme, are made by solving a lid-driven polar cavity flow and self-sustained oscillatory flows over circular and square cylinders. Calculated results show that the ITA is the most stable numerically and yields the most accurate results. The SMAC is the most efficient computationally and is as stable as the ITA. It is shown that the PISO is the most weakly convergent and it exhibits an undesirable strong dependence on the time-step size. The degenerated numerical results obtained using the PISO are attributed to its second corrector step that cause the numerical results to deviate further from a divergence free velocity field. The accurate numerical results obtained using the ITA is attributed to its capability to resolve the nonlinearity of the Navier-Stokes equations. The present numerical method that incorporates the ITA is used to solve an unsteady transitional flow over an oscillating airfoil and a chemically reacting flow of hydrogen in a vitiated supersonic airstream. The turbulence fields in these flow cases are described using multiple-time-scale turbulence equations. For the unsteady transitional over an oscillating airfoil, the fluid flow is described using ensemble-averaged Navier-Stokes equations defined on the Lagrangian-Eulerian coordinates. It is shown that the numerical method successfully predicts the large dynamic stall vortex (DSV) and the trailing edge vortex (TEV) that are periodically generated by the oscillating airfoil. The calculated streaklines are in very good comparison with the experimentally obtained smoke picture. The calculated turbulent viscosity contours show that the transition from laminar to turbulent state and the relaminarization occur widely in space as well as in time. The ensemble-averaged velocity profiles are also in good agreement with the measured data and the good comparison indicates that the numerical method as well as the multipletime-scale turbulence equations successfully predict the unsteady transitional turbulence field. The chemical reactions for the hydrogen in the vitiated supersonic airstream are described using 9 chemical species and 48 reaction-steps. Consider that a fast chemistry can not be used to describe the fine details (such as the instability) of chemically reacting flows while a reduced chemical kinetics can not be used confidently due to the uncertainty contained in the reaction mechanisms. However, the use of a detailed finite rate chemistry may make it difficult to obtain a fully converged solution due to the coupling between the large number of flow, turbulence, and chemical equations. The numerical results obtained in the present study are in good agreement with the measured data. The good comparison is attributed to the numerical method that can yield strongly converged results for the reacting flow and to the use of the multiple-time-scale turbulence equations that can accurately describe the mixing of the fuel and the oxidant.

Kim, S.-W.↗

NASA NTRS1995

Pseudo-time methods for constrained optimization problems governed by PDE

In this paper we present a novel method for solving optimization problems governed by partial differential equations. Existing methods are gradient information in marching toward the minimum, where the constrained PDE is solved once (sometimes only approximately) per each optimization step. Such methods can be viewed as a marching techniques on the intersection of the state and costate hypersurfaces while improving the residuals of the design equations per each iteration. In contrast, the method presented here march on the design hypersurface and at each iteration improve the residuals of the state and costate equations. The new method is usually much less expensive per iteration step since, in most problems of practical interest, the design equation involves much less unknowns that that of either the state or costate equations. Convergence is shown using energy estimates for the evolution equations governing the iterative process. Numerical tests show that the new method allows the solution of the optimization problem in a cost of solving the analysis problems just a few times, independent of the number of design parameters. The method can be applied using single grid iterations as well as with multigrid solvers.

Taasan, Shlomo↗

NASA NTRS1995

Sensitivity analysis in multipole-accelerated panel methods for potential flow

In the design of an airframe, the effect of changing the geometry on resulting computations is necessary for design optimization. The geometry is defined in terms of a series of design variables, including design variables to define the wing planform, tail, canard, pylon, and nacelle. Design optimization in this research is based on how these design variable affect the potential flow. The potential flow is computed as a function of the geometry and location of a series of panels describing the airframe, which are in turn a function of the design variables. Multipole accelerated panel methods improve the computational complexity of the problem and thus are an attractive approach. To utilize the methods in design optimization, it was necessary to define the appropriate sensitivity derivatives. The overhead incurred from finding the sensitivity derivatives in conjunction with the original computation should be small. This research developed the background for multipole-accelerated panel methods and the framework for finding sensitivity derivatives in the methods. Potential flow panel codes are commonly used for powered-lift aerodynamic predictions for three dimensional geometries. Given an airframe which has been discretized into a series of panels to define the airframe geometry, potential is computed as a function of the influence of all panels on all other panels. This is a computationally intensive problem for which efficient solutions are desired to improve the computational time and to allow greater resolution by use of more panels. One such solution is the use of hierarchical multipole methods which entail approximations of the effects of far-field terms. Hierarchical multipole methods have become prevalent in molecular dynamics and gravitational physics, and have been introduced into the fields of capacitance calculations, computational fluid dynamics, and electromagnetics. The methods utilize multipole expansions to describe the effect of bodies (i.e. particles, astrophysical bodies, panels, etc.) within a sphere on points distant from the sphere, where the influence diminishes as a function of distance. The expansions are exact with infinite series, however, for practical computations, the series are truncated and accuracy is selected based on the number of terms retained in the expansions. A hierarchical tree structure groups bodies together based on proximity to allow definition of multipole expansions for each group. The multipole expansions are then used to compute the effect of the bodies in a group on distant bodies.

Leathrum, James F., Jr.↗

NASA NTRS1996

Improved Method for Prediction of Attainable Wing Leading-Edge Thrust

Prediction of the loss of wing leading-edge thrust and the accompanying increase in drag due to lift, when flow is not completely attached, presents a difficult but commonly encountered problem. A method (called the previous method) for the prediction of attainable leading-edge thrust and the resultant effect on airplane aerodynamic performance has been in use for more than a decade. Recently, the method has been revised to enhance its applicability to current airplane design and evaluation problems. The improved method (called the present method) provides for a greater range of airfoil shapes from very sharp to very blunt leading edges. It is also based on a wider range of Reynolds numbers than was available for the previous method. The present method, when employed in computer codes for aerodynamic analysis, generally results in improved correlation with experimental wing-body axial-force data and provides reasonable estimates of the measured drag.

Carlson, Harry W.↗

NASA NTRS1994

Three-Dimensional Navier-Stokes Method with Two-Equation Turbulence Models for Efficient Numerical Simulation of Hypersonic Flows

A new computational efficient 3-D compressible Reynolds-averaged implicit Navier-Stokes method with advanced two equation turbulence models for high speed flows is presented. All convective terms are modeled using an entropy satisfying higher-order Total Variation Diminishing (TVD) scheme based on implicit upwind flux-difference split approximations and arithmetic averaging procedure of primitive variables. This method combines the best features of data management and computational efficiency of space marching procedures with the generality and stability of time dependent Navier-Stokes procedures to solve flows with mixed supersonic and subsonic zones, including streamwise separated flows. Its robust stability derives from a combination of conservative implicit upwind flux-difference splitting with Roe's property U to provide accurate shock capturing capability that non-conservative schemes do not guarantee, alternating symmetric Gauss-Seidel 'method of planes' relaxation procedure coupled with a three-dimensional two-factor diagonal-dominant approximate factorization scheme, TVD flux limiters of higher-order flux differences satisfying realizability, and well-posed characteristic-based implicit boundary-point a'pproximations consistent with the local characteristics domain of dependence. The efficiency of the method is highly increased with Newton Raphson acceleration which allows convergence in essentially one forward sweep for supersonic flows. The method is verified by comparing with experiment and other Navier-Stokes methods. Here, results of adiabatic and cooled flat plate flows, compression corner flow, and 3-D hypersonic shock-wave/turbulent boundary layer interaction flows are presented. The robust 3-D method achieves a better computational efficiency of at least one order of magnitude over the CNS Navier-Stokes code. It provides cost-effective aerodynamic predictions in agreement with experiment, and the capability of predicting complex flow structures in complex geometries with good accuracy.

Bardina, J. E.↗

NASA NTRS1959

The Fluorescent-Oil Film Method and Other Techniques for Boundary-Layer Flow Visualization

A flow-visualization technique, known as the fluorescent-oil film method, has been developed which appears to be generally simpler and to require less experience and development of technique than previously published methods. The method is especially adapted to use in the large high-powered wind tunnels which require considerable time to reach the desired test conditions. The method consists of smearing a film of fluorescent oil over a surface and observing where the thickness is affected by the shearing action of the boundary layer. These films are detected and identified, and their relative thicknesses are determined by use of ultraviolet light. Examples are given of the use of this technique. Other methods that show promise in the study of boundary-layer conditions are described. These methods include the use of a temperature-sensitive fluorescent paint and the use of a radiometer that is sensitive to the heat radiation from a surface. Some attention is also given to methods that can be used with a spray apparatus in front of the test model.

Loving, Donald L.↗

NASA NTRS1959

A Numerical Method for Calculating the Wave Drag of a Configuration from the Second Derivative of the Area Distribution of a Series of Equivalent Bodies of Revolution

A method based on linearized and slender-body theories, which is easily adapted to electronic-machine computing equipment, is developed for calculating the zero-lift wave drag of single- and multiple-component configurations from a knowledge of the second derivative of the area distribution of a series of equivalent bodies of revolution. The accuracy and computational time required of the method to calculate zero-lift wave drag is evaluated relative to another numerical method which employs the Tchebichef form of harmonic analysis of the area distribution of a series of equivalent bodies of revolution. The results of the evaluation indicate that the total zero-lift wave drag of a multiple-component configuration can generally be calculated most accurately as the sum of the zero-lift wave drag of each component alone plus the zero-lift interference wave drag between all pairs of components. The accuracy and computational time required of both methods to calculate total zero-lift wave drag at supersonic Mach numbers is comparable for airplane-type configurations. For systems of bodies of revolution both methods yield similar results with comparable accuracy; however, the present method only requires up to 60 percent of the computing time required of the harmonic-analysis method for two bodies of revolution and less time for a larger number of bodies.

Levy, Lionel L., Jr.↗

NASA NTRS1959

Evaluation of Several Approximate Methods for Calculating the Symmetrical Bending-Moment Response of Flexible Airplanes to Isotropic Atmospheric Turbulence

Several approximate procedures for calculating the bending-moment response of flexible airplanes to continuous isotropic turbulence are presented and evaluated. The modal methods (the mode-displacement and force-summation methods) and a matrix method (segmented-wing method) are considered. These approximate procedures are applied to a simplified airplane for which an exact solution to the equation of motion can be obtained. The simplified airplane consists of a uniform beam with a concentrated fuselage mass at the center. Airplane motions are limited to vertical rigid-body translation and symmetrical wing bending deflections. Output power spectra of wing bending moments based on the exact transfer-function solutions are used as a basis for the evaluation of the approximate methods. It is shown that the force-summation and the matrix methods give satisfactory accuracy and that the mode-displacement method gives unsatisfactory accuracy.

Bennett, Floyd V.↗

NASA NTRS1999

A New Method for Nonlinear and Nonstationary Time Series Analysis and Its Application to the Earthquake and Building Response Records

A new method for analyzing nonlinear and nonstationary data has been developed. The key part of the method is the Empirical Mode Decomposition method with which any complicated data set can be decomposed into a finite and often small number of Intrinsic Mode Functions (IMF). An IMF is defined as any function having the same numbers of zero-crossing and extrema, and also having symmetric envelopes defined by the local maxima and minima respectively. The IMF also admits well-behaved Hilbert transform. This decomposition method is adaptive, and, therefore, highly efficient. Since the decomposition is based on the local characteristic time scale of the data, it is applicable to nonlinear and nonstationary processes. With the Hilbert transform, the Intrinsic Mode Functions yield instantaneous frequencies as functions of time that give sharp identifications of imbedded structures. The final presentation of the results is an energy-frequency-time distribution, designated as the Hilbert Spectrum, Example of application of this method to earthquake and building response will be given. The results indicate those low frequency components, totally missed by the Fourier analysis, are clearly identified by the new method. Comparisons with Wavelet and window Fourier analysis show the new method offers much better temporal and frequency resolutions.

Huang, Norden E.↗

NASA NTRS1999

A TRMM Rainfall Estimation Method Applicable to Land Areas

Methods developed to estimate rain rate on a footprint scale over land with the satellite-borne multispectral dual-polarization Special Sensor Microwave Imager (SSM/1) radiometer have met with limited success. Variability of surface emissivity on land and beam filling are commonly cited as the weaknesses of these methods. On the contrary, we contend a more significant reason for this lack of success is that the information content of spectral and polarization measurements of the SSM/I is limited. because of significant redundancy. As a result, the complex nature and vertical distribution C, of frozen and melting ice particles of different densities, sizes, and shapes cannot resolved satisfactorily. Extinction in the microwave region due to these complex particles can mask the extinction due to rain drops. Because of these reasons, theoretical models that attempt to retrieve rain rate do not succeed on a footprint scale. To illustrate the weakness of these models, as an example we can consider the brightness temperature measurement made by the radiometer in the 85 GHz channel (T85). Models indicate that T85 should be inversely related to the rain rate, because of scattering. However, rain rate derived from 15-minute rain gauges on land indicate that this is not true in a majority of footprints. This is also supported by the ship-borne radar observations of rain in the Tropical Oceans and Global Atmosphere Coupled Ocean-Atmosphere Response Experiment (TOGA-COARE) region over the ocean. Based on these observations. we infer that theoretical models that attempt to retrieve rain rate do not succeed on a footprint scale. We do not follow the above path of rain retrieval on a footprint scale. Instead, we depend on the limited ability of the microwave radiometer to detect the presence of rain. This capability is useful to determine the rain area in a mesoscale region. We find in a given rain event that this rain area is closely related to the mesoscale-average rain rate. Based on this observation, in this study we have developed a method to estimate the mesoscale-average rain rate over land utilizing microwave radiometer data. Because of the high degree of geographic and seasonal variability in the nature and intensity of rain, this method requires some tuning with 15-minute rain gauge data on land. After tuning the method, it can be applied to an independent set of rain events that are close in time and space. We find that the mesoscale rain rates retrieved over the period of a month on land with this method shows a correlation of about 0.85 with respect to the surface rain-gauge observations. This mesoscale-average rain rate estimation method can be useful to extend the spatial and temporal coverage of the rainfall data provided by the Precipitation Radar on board the Tropical Rainfall Measuring Mission (TRMM) satellite.

Prabhakara, C.↗

NASA NTRS1999

Methods of Viscosity Measurements in Sealed Ampoules

Viscosity of semiconductor and metallic melts is usually measured by oscillating cup method. This method utilizes the melts contained in vacuum sealed silica ampoules, thus the problems related to volatility, contamination, and high temperature and pressure can be alleviated. In a typical design, the time required for a single measurement is of the order of one hour. In order to reduce this time to a minute range, a high resolution (0.05 arc.sec) angular detection system is implemented in our design of the viscometer. Furthermore, an electromagnet generating a rotational magnetic field (RMF) is incorporated into the apparatus. This magnetic field can be used to remotely and non intrusively measure the electrical conductivity of the melt. It can also be used to induce a well controlled rotational flow in the system. The transient behavior of this flow can potentially yield the viscosity of the fluid. Based on RMF implementation, two novel viscometry methods are proposed in this work: a) the transient torque method, b) the resonance method. A unified theoretical approach to the three methods (oscillating cup, transient torque, and resonance) is presented along with the initial test results of the constructed apparatus. Advantages of each of the method are discussed.

Mazuruk, Konstantin↗

NASA NTRS2000

Fast Particle Methods for Multiscale Phenomena Simulations

We are developing particle methods oriented at improving computational modeling capabilities of multiscale physical phenomena in : (i) high Reynolds number unsteady vortical flows, (ii) particle laden and interfacial flows, (iii)molecular dynamics studies of nanoscale droplets and studies of the structure, functions, and evolution of the earliest living cell. The unifying computational approach involves particle methods implemented in parallel computer architectures. The inherent adaptivity, robustness and efficiency of particle methods makes them a multidisciplinary computational tool capable of bridging the gap of micro-scale and continuum flow simulations. Using efficient tree data structures, multipole expansion algorithms, and improved particle-grid interpolation, particle methods allow for simulations using millions of computational elements, making possible the resolution of a wide range of length and time scales of these important physical phenomena.The current challenges in these simulations are in : [i] the proper formulation of particle methods in the molecular and continuous level for the discretization of the governing equations [ii] the resolution of the wide range of time and length scales governing the phenomena under investigation. [iii] the minimization of numerical artifacts that may interfere with the physics of the systems under consideration. [iv] the parallelization of processes such as tree traversal and grid-particle interpolations We are conducting simulations using vortex methods, molecular dynamics and smooth particle hydrodynamics, exploiting their unifying concepts such as : the solution of the N-body problem in parallel computers, highly accurate particle-particle and grid-particle interpolations, parallel FFT's and the formulation of processes such as diffusion in the context of particle methods. This approach enables us to transcend among seemingly unrelated areas of research.

Koumoutsakos, P.↗

NASA NTRS2000

A New Method for Accurate Treatment of Flow Equations in Cylindrical Coordinates Using Series Expansions

The motivation of this work is the ongoing effort at the Center for Turbulence Research (CTR) to use large eddy simulation (LES) techniques to calculate the noise radiated by jet engines. The focus on engine exhaust noise reduction is motivated by the fact that a significant reduction has been achieved over the last decade on the other main sources of acoustic emissions of jet engines, such as the fan and turbomachinery noise, which gives increased priority to jet noise. To be able to propose methods to reduce the jet noise based on results of numerical simulations, one first has to be able to accurately predict the spatio-temporal distribution of the noise sources in the jet. Though a great deal of understanding of the fundamental turbulence mechanisms in high-speed jets was obtained from direct numerical simulations (DNS) at low Reynolds numbers, LES seems to be the only realistic available tool to obtain the necessary near-field information that is required to estimate the acoustic radiation of the turbulent compressible engine exhaust jets. The quality of jet-noise predictions is determined by the accuracy of the numerical method that has to capture the wide range of pressure fluctuations associated with the turbulence in the jet and with the resulting radiated noise, and by the boundary condition treatment and the quality of the mesh. Higher Reynolds numbers and coarser grids put in turn a higher burden on the robustness and accuracy of the numerical method used in this kind of jet LES simulations. As these calculations are often done in cylindrical coordinates, one of the most important requirements for the numerical method is to provide a flow solution that is not contaminated by numerical artifacts. The coordinate singularity is known to be a source of such artifacts. In the present work we use 6th order Pade schemes in the non-periodic directions to discretize the full compressible flow equations. It turns out that the quality of jet-noise predictions using these schemes is especially sensitive to the type of equation treatment at the singularity axis. The objective of this work is to develop a generally applicable numerical method for treating the singularities present at the polar axis, which is particularly suitable for highly accurate finite-differences schemes (e.g., Pade schemes) on non-staggered grids. The main idea is to reinterpret the regularity conditions developed in the context of pseudo-spectral methods. A set of exact equations at the singularity axis is derived using the appropriate series expansions for the variables in the original set of equations. The present treatment of the equations preserves the same level of accuracy as for the interior scheme. We also want to point out the wider utility of the method, proposed here in the context of compressible flow equations, as its extension for incompressible flows or for any other set of equations that are solved on a non-staggered mesh in cylindrical coordinates with finite-differences schemes of various level of accuracy is straightforward. The robustness and accuracy of the proposed technique is assessed by comparing results from simulations of laminar forced-jets and turbulent compressible jets using LES with similar calculations in which the equations are solved in Cartesian coordinates at the polar axis, or in which the singularity is removed by employing a staggered mesh in the radial direction without a mesh point at r = 0.

Constantinescu, G.S.↗

NASA NTRS2001

The CE/SE Method: a CFD Framework for the Challenges of the New Millennium

The space-time conservation element and solution element (CE/SE) method, which was originated and is continuously being developed at NASA Glenn Research Center, is a high-resolution, genuinely multidimensional and unstructured-mesh compatible numerical method for solving conservation laws. Since its inception in 1991, the CE/SE method has been used to obtain highly accurate numerical solutions for 1D, 2D and 3D flow problems involving shocks, contact discontinuities, acoustic waves, vortices, shock/acoustic waves/vortices interactions, shock/boundary layers interactions and chemical reactions. Without the aid of preconditioning or other special techniques, it has been applied to both steady and unsteady flows with speeds ranging from Mach number = 0.00288 to 10. In addition, the method has unique features that allow for (i) the use of very simple non-reflecting boundary conditions, and (ii) a unified wall boundary treatment for viscous and inviscid flows. The CE/SE method was developed with the conviction that, with a solid foundation in physics, a robust, coherent and accurate numerical framework can be built without involving overly complex mathematics. As a result, the method was constructed using a set of design principles that facilitate simplicity, robustness and accuracy. The most important among them are: (i) enforcing both local and global flux conservation in space and time, with flux evaluation at an interface being an integral part of the solution procedure and requiring no interpolation or extrapolation; (ii) unifying space and time and treating them as a single entity; and (iii) requiring that a numerical scheme be built from a nondissipative core scheme such that the numerical dissipation can be effectively controlled and, as a result, will not overwhelm the physical dissipation. Part I of the workshop will be devoted to a discussion of these principles along with a description of how the ID, 2D and 3D CE/SE schemes are constructed. In Part II, various applications of the CE/SE method, particularly those involving chemical reactions and acoustics, will be presented. The workshop will be concluded with a sketch of the future research directions.

Chang, Sin-Chung↗

NASA NTRS2001

Two Reconfigurable Flight-Control Design Methods: Robust Servomechanism and Control Allocation

Two methods for control system reconfiguration have been investigated. The first method is a robust servomechanism control approach (optimal tracking problem) that is a generalization of the classical proportional-plus-integral control to multiple input-multiple output systems. The second method is a control-allocation approach based on a quadratic programming formulation. A globally convergent fixed-point iteration algorithm has been developed to make onboard implementation of this method feasible. These methods have been applied to reconfigurable entry flight control design for the X-33 vehicle. Examples presented demonstrate simultaneous tracking of angle-of-attack and roll angle commands during failures of the fight body flap actuator. Although simulations demonstrate success of the first method in most cases, the control-allocation method appears to provide uniformly better performance in all cases.

Burken, John J.↗