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NASA NTRS1994

A wall interference assessment/correction system

A Wall Signature method originally developed by Hackett has been selected to be adapted for the Ames 12-ft Wind Tunnel WIAC system in the project. This method uses limited measurements of the static pressure at the wall, in conjunction with the solid wall boundary condition, to determine the strength and distribution of singularities representing the test article. The singularities are used in turn for estimating wall interference at the model location. The development and implementation of a working prototype will be completed, delivered and documented with a software manual. The WIAC code will be validated by conducting numerically simulated experiments rather than actual wind tunnel experiments. The simulations will be used to generate both free-air and confined wind-tunnel flow fields for each of the test articles over a range of test configurations. Specifically, the pressure signature at the test section wall will be computed for the tunnel case to provide the simulated 'measured' data. These data will serve as the input for the WIAC method--Wall Signature method. The performance of the WIAC method then may be evaluated by comparing the corrected parameters with those for the free-air simulation. The following two additional tasks are included: (1) On-line wall interference calculation: The developed wall signature method (modified Hackett's method) for Ames 12-ft Tunnel will be the pre-computed coefficients which facilitate the on-line calculation of wall interference, and (2) Support system effects estimation: The effects on the wall pressure measurements due to the presence of the model support systems will be evaluated.

Lo, C. F.↗
NASA NTRS1994

Accelerated panel methods using the fast multipole method

Panel methods are commonly used in computational fluid dynamics for the solution of potential flow problems. The methods are a numerical technique based on the surface distribution of singularity elements. The solution is the process of finding the strength of the singularity elements distributed over the body's surface. This process involves the solution of the matrix problem Pq = p' for a set of unknowns q. The Fast Multipole Method is used to directly compute q without using matrix solvers. The algorithm works in O(N) time for N points, a great improvement over standard matrix solvers. In panel methods, the surface of a body is divided into a series of quadrilateral panels. The methods involve the computation of the influence of all other panels on each individual panel. The influence is based on the surface distribution, though this can be approximated by the area for distant panels. An alternative approximation, though with arbitrary accuracy, is to develop a multipole expansion about the center of the panel to describe the effect of a given panel on distant points in space. The expansion is based on the moments of the panel, thus allow the use of various surface distributions without changing the basic algorithm, just the computation of the various moments. The expansions are then manipulated in a tree walk to develop Taylor series expansions about a point in space which describe the effect of all distant panels on any point within a volume of convergence. The effect of near panels then needs to be computed directly, but the effect of all distant panels can be computed by simply evaluating the resulting expansion. The Fast Multipole Method has been applied to panel methods for the solution of source and doublet distributions. A major feature of the algorithm is that the algorithm does not change to derive the potential and velocity for sources and doublets. The same expansions can be used for both sources and doublets. Since the velocity is related to the potential, and the doublet potential is related to the z-component of the source velocity, all values can be derived from the same expansion by taking a series of partial derivatives. This requires more expansion terms to be kept since terms are lost in the process of taking partial derivatives. Thus to maintain accuracy for the doublet computation, more terms are required than if just evaluating for sources. The resulting Fast Multipole code should then parallelize better than classical panel methods due to the locality of data dependencies found in the Fast Multipole Method. Theoretically the parallelized code should execute in O(log N) time with O(N) processors, though this is not practical. Ongoing work includes implementing the parallel accelerated panel method, including methods to improve the load balancing of the problem by taking advantage of the known geometry of panels, and to encorporate sensitivity analysis into the algorithm.

Leathrum, James F., Jr.↗
NASA NTRS1995

Optimal guidance law development for an advanced launch system

The objective of this research effort was to develop a real-time guidance approach for launch vehicles ascent to orbit injection. Various analytical approaches combined with a variety of model order and model complexity reduction have been investigated. Singular perturbation methods were first attempted and found to be unsatisfactory. The second approach based on regular perturbation analysis was subsequently investigated. It also fails because the aerodynamic effects (ignored in the zero order solution) are too large to be treated as perturbations. Therefore, the study demonstrates that perturbation methods alone (both regular and singular perturbations) are inadequate for use in developing a guidance algorithm for the atmospheric flight phase of a launch vehicle. During a second phase of the research effort, a hybrid analytic/numerical approach was developed and evaluated. The approach combines the numerical methods of collocation and the analytical method of regular perturbations. The concept of choosing intelligent interpolating functions is also introduced. Regular perturbation analysis allows the use of a crude representation for the collocation solution, and intelligent interpolating functions further reduce the number of elements without sacrificing the approximation accuracy. As a result, the combined method forms a powerful tool for solving real-time optimal control problems. Details of the approach are illustrated in a fourth order nonlinear example. The hybrid approach is then applied to the launch vehicle problem. The collocation solution is derived from a bilinear tangent steering law, and results in a guidance solution for the entire flight regime that includes both atmospheric and exoatmospheric flight phases.

Calise, Anthony J.↗
NASA NTRS1994

Mode properties of low-frequency waves: Kinetic theory versus Hall-MHD

In fluid theory, the ordering of low-frequency modes in a homogeneous plasma is based on the phase velocity, since modes do not intersect each other in dispersion diagrams as a function of wavenumber or other parameters. In linear kinetic theory, modes cross each other. Thus a consistent and useful classification should be based on the physical properties of the modes instead. This paper attempts such a classification by documeting the dispersion and general mode properties of the low-frequency waves (omega much less than (OMEGA(sub ci) OMEGA(sub ce) (exp 1/2)), where OMEGA(sub ci), OMEGA(sub ce) are the cyclotron frequencies of the ions and electrons, respectively) in kinetic theory, and by comparing them to the results of two-fluid theory. Kinetic theory gives a seperate Alfven/ion-cyclotron (A/IC) wave with phase speed Omega/k approximately = v(sub A) cos theta for omega much less than OMEGA(sub ci), where v(sub A) is the Alfven velocity and theta the angle of propagation between wave vector k and background magnetic field B(sub o). For a given wavenumber, the magnetosonic mode is a double-valued solution with a singular point in theta, beta parameter space, where beta is the ratio of thermal pressure to magnetic pressure. It is shown that a branch cut starting at the singular point theta approximately 30 deg, beta approximately 3 and leading to larger beta gives a practical and consitent seperation of this double-valued magnetosonic solution. Selection of this branch cut results in a moderately damped fast/magnetos onic and a heavily damped slow/sound wave. A comprehensive review of the polarization, compressibility and other mode properties is given and shown to be consistent with the selected branch cut. At small wavenumbers, the kinetic mode properties typically start to deviate significantly from their fluid counterparts at beta approximately 0.5. At larger beta, there is no longer a consistent correspondence between the fluid and kinetic modes. Kinetic theory also dictates the use of different mode properties to distinguish between them in observational data. For example, the phase between the density and magnetic field perturbation may become useless at high beta, whereas the direction of the magnetic field perturbations with respect to k and B(sub o) remains a useful characteristic. Two quantities based on this characteristic are suggested and are shown to be useful also to distinguish between the mirror mode and A/IC waves in a plasma with temperature anisotropy.

Krauss-Varban, D.↗
NASA NTRS1994

Multifractal characterizations of nonstationarity and intermittency in geophysical fields: Observed, retrieved, or simulated

Geophysical data rarely show any smoothness at any scale, and this often makes comparison with theoretical model output difficult. However, highly fluctuating signals and fractal structures are typical of open dissipative systems with nonlinear dynamics, the focus of most geophysical research. High levels of variability are excited over a large range of scales by the combined actions of external forcing and internal instability. At very small scales we expect geophysical fields to be smooth, but these are rarely resolved with available instrumentation or simulation tools; nondifferentiable and even discontinuous models are therefore in order. We need methods of statistically analyzing geophysical data, whether measured in situ, remotely sensed or even generated by a computer model, that are adapted to these characteristics. An important preliminary task is to define statistically stationary features in generally nonstationary signals. We first discuss a simple criterion for stationarity in finite data streams that exhibit power law energy spectra and then, guided by developments in turbulence studies, we advocate the use of two ways of analyzing the scale dependence of statistical information: singular measures and qth order structure functions. In nonstationary situations, the approach based on singular measures seeks power law behavior in integrals over all possible scales of a nonnegative stationary field derived from the data, leading to a characterization of the intermittency in this (gradient-related) field. In contrast, the approach based on structure functions uses the signal itself, seeking power laws for the statistical moments of absolute increments over arbitrarily large scales, leading to a characterization of the prevailing nonstationarity in both quantitative and qualitative terms. We explain graphically, step by step, both multifractal statistics which are largely complementary to each other. The geometrical manifestations of nonstationarity and intermittency, 'roughness' and 'sparseness', respectively, are illustrated and the associated analytical (differentiability and continuity) properties are discussed. As an example, the two techniques are applied to a series of recent measurements of liquid water distributions inside marine stratocumulus decks; these are found to be multifractal over scales ranging from approximately 60 m to approximately 60 km. Finally, we define the 'mean multifractal plane' and show it to be a simple yet comprehensive tool with many applications including data intercomparison, (dynamical or stochastic) model and retrieval validations.

Davis, Anthony↗
NASA NTRS1993

On the electric field model for an open magnetosphere

We have developed a new canonical separator line type magnetospheric magnetic field and electric field model for use in magnetospheric calculations, we determine the magnetic and electric field by controlling the reconnection rate at the subsolar magnetopause. The model is applicable only for purely southward interplanetary magnetic field (IMF). We have obtained a more realistic magnetotail configuration by applying a stretch transformation to an axially symmetric field solution. We also discuss the Stern singularity in which there is an electric field singlarity in the canonical separate line models for B(sub y) not = to 0 by using a new technique that solves for the electric field along a field line directly instead of determining it by a potential mapping. The singularity not only causes an infinite electric field on the polar cap, but also causes the boundary conditions at plus infinity and minus infinity in the solar wind to contradict each other. This means that the canonical separator line models do not represent the open magnetosphere well, except for the case of purely southward IMF.

Wang, Zhi↗
NASA NTRS1993

Optimal open-loop and feedback control using single gimbal control moment gyroscopes

Methods for control of spacecraft maneuvers through the use of single gimbal control moment gyroscopes are developed. The development employs an integrated model of the spacecraft dynamics with the control moment gyroscope dynamics. Smooth and continuous open-loop control profiles are obtained which minimize a weighted function of maneuver time, magnitude of control effort, and proximity to singular gimbal configurations. Closed-loop state feedback control laws are derived by invoking Lyapunov stability theory. The schemes are presented for implementing the commanded state feedback: gimbal rate control and gimbal acceleration control. The appropriate handling of singular gimbal configurations is also discussed.

Hoelscher, Brian R.↗
NASA NTRS1993

A new technique for deconvolution of data from instruments that make integral measurements, e.g. RIMS on DE-1

A general method for deconvolving an unknown function from integral measurements is described and applied to data from the instrument Retarding Ion Mass Spectrometer (RIMS) aboard the spacecraft Dynamics Explorer 1 (DE-1). The principal features of the method are: (1) it uses objective criteria based upon fundamental statistical principles, i.e. Bayesian statistics; (2) it provides for insertion of prior knowledge in a non-prejudicial, explicit manner through the choice of breakpoints that determine the bicubic spline expansion functions; (3) it prevents random fluctuations from controlling the fit to the data through the use of singular value decomposition and the elimination of small singular values; and (4) it guards agianst the introduction of spurious features into the result by including a penalty function and using the principle of generalized cross validation. Illustrative examples from RIMS data for H(+) and O(+) show that the method provides enhanced accuracy and detail in deconvolving the ion phase space density.

Perez, J. D.↗
NASA NTRS1994

Asymptotic behavior of solutions of the renormalization group K-epsilon turbulence model

Presently, the only efficient way to calculate turbulent flows in complex geometries of engineering interest is to use Reynolds-average Navier-Stokes (RANS) equations. As compared to the original Navier-Stokes problem, these RANS equations posses much more complicated nonlinear structure and may exhibit far more complex nonlinear behavior. In certain cases, the asymptotic behavior of such models can be studied analytically which, aside from being an interesting fundamental problem, is important for better understanding of the internal structure of the models as well as to improve their performances. The renormalization group (RNG) K-epsilon turbulence model, derived directly from the incompresible Navier-Stokes equations, is analyzed. It has already been used to calculate a variety of turbulent and transitional flows in complex geometries. For large values of the RNG viscosity parameter, the model may exhibit singular behavior. In the form of the RNG K-epsilon model that avoids the use of explicit wall functions, a = 1, so the RNG viscosity parameter must be smaller than 23.62 to avoid singularities.

Yakhot, A.↗
NASA NTRS1994

Effect of radiance-to-reflectance transformation and atmosphere removal on maximum likelihood classification accuracy of high-dimensional remote sensing data

Many analysis algorithms for high-dimensional remote sensing data require that the remotely sensed radiance spectra be transformed to approximate reflectance to allow comparison with a library of laboratory reflectance spectra. In maximum likelihood classification, however, the remotely sensed spectra are compared to training samples, thus a transformation to reflectance may or may not be helpful. The effect of several radiance-to-reflectance transformations on maximum likelihood classification accuracy is investigated in this paper. We show that the empirical line approach, LOWTRAN7, flat-field correction, single spectrum method, and internal average reflectance are all non-singular affine transformations, and that non-singular affine transformations have no effect on discriminant analysis feature extraction and maximum likelihood classification accuracy. (An affine transformation is a linear transformation with an optional offset.) Since the Atmosphere Removal Program (ATREM) and the log residue method are not affine transformations, experiments with Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) data were conducted to determine the effect of these transformations on maximum likelihood classification accuracy. The average classification accuracy of the data transformed by ATREM and the log residue method was slightly less than the accuracy of the original radiance data. Since the radiance-to-reflectance transformations allow direct comparison of remotely sensed spectra with laboratory reflectance spectra, they can be quite useful in labeling the training samples required by maximum likelihood classification, but these transformations have only a slight effect or no effect at all on discriminant analysis and maximum likelihood classification accuracy.

Hoffbeck, Joseph P.↗
NASA NTRS1995

Protostellar Collapse with a Shock

We reexamine both numerically and analytically the collapse of the singular isothermal sphere in the context of low-mass star formation. We consider the case where the onset of collapse is initiated by some arbitrary process which is accompanied by a central output of either heat or kinetic energy. We find two classes of numerical solutions describing this manner of collapse. The first approaches in time the expansion wave solution of Shu, while the second class is characterized by an ever-decreasing central accretion rate and the presence of an outwardly propagating weak shock. The collapse solution which represents the dividing case between these two classes is determined analytically by a similarity analysis. This solution shares with the expansion wave solution the properties that the gas remains stationary with an r(exp -2) density profile at large radius and that, at small radius, the gas free-falls onto a nascent core at a constant rate which depends only on the isothermal sound speed. This accretion rate is a factor of approx. 0.1 that predicted by the expansion wave solution. This reduction is due in part to the presence of a weak shock which propagates outward at 1.26 times the sound speed. Gas in the postshock region first moves out subsonically but is then decelerated and begins to collapse. The existence of two classes of numerical collapse solutions is explained in terms of the instability to radial perturbations of the analytic solution. Collapse occurring in the manner described by some of our solutions would eventually unbind a finite-sized core. However, this does not constitute a violation of the instability properties of the singular isothermal sphere which is unstable both to collapse and to expansion. To emphasize this, we consider a purely expanding solution for isothermal spheres. This solution is found to be self-similar and results in a uniform density core in the central regions of the gas. Our solutions may be relevant to the 'luminosity' problem of protostellar cores since the predicted central accretion rates are significantly reduced relative to that of the expansion wave solution. Furthermore, our calculations indicate that star-forming cloud cores are not very tightly bound and that modest disturbances can easily result in both termination of infall and dispersal of unaccreted material.

Tsai, John C.↗
NASA NTRS1997

Steady-State and Transient Boundary Element Methods for Coupled Heat Conduction

Boundary element algorithms for the solution of steady-state and transient heat conduction are presented. The algorithms are designed for efficient coupling with computational fluid dynamic discretizations and feature piecewise linear elements with offset nodal points. The steady-state algorithm employs the fundamental solution approach; the integration kernels are computed analytically based on linear shape functions, linear elements, and variably offset nodal points. The analytic expressions for both singular and nonsingular integrands are presented. The transient algorithm employs the transient fundamental solution; the temporal integration is performed analytically and the nonsingular spatial integration is performed numerically using Gaussian quadrature. A series solution to the integration is derived for the instance of a singular integrand. The boundary-only character of the algorithm is maintained by integrating the influence coefficients from initial time. Numerical results are compared to analytical solutions to verify the current boundary element algorithms. The steady-state and transient algorithms are numerically shown to be second-order accurate in space and time, respectively.

Kontinos, Dean A.↗
NASA NTRS1997

Global-Local Finite Element Analysis for Thermo-Mechanical Stresses in Bonded Joints

An analysis of adhesively bonded joints using conventional finite elements does not capture the singular behavior of the stress field in regions where two or three dissimilar materials form a junction with or without free edges. However, these regions are characteristic of the bonded joints and are prone to failure initiation. This study presents a method to capture the singular stress field arising from the geometric and material discontinuities in bonded composites. It is achieved by coupling the local (conventional) elements with global (special) elements whose interpolation functions are constructed from the asymptotic solution.

Shkarayev, S.↗
NASA NTRS1995

Protostellar Collapse with a Shock

We reexamine both numerically and analytically the collapse of the singular isothermal sphere in the context of low-mass star formation. We consider the case where the onset of collapse is initiated by some arbitrary process which is accompanied by a central output of either heat or kinetic energy. We find two classes of numerical solutions describing this manner of collapse. The first approaches in time the expansion wave solution of Shu, while the second class is characterized by an ever-decreasing central accretion rate and the presence of an outwardly propagating weak shock. The collapse solution which represents the dividing case between these two classes is determined analytically by a similarity analysis. This solution shares with the expansion wave solution the properties that the gas remains stationary with an r(sup -2) density profile at large radius and that, at small radius, the gas free-falls onto a nascent core at a constant rate which depends only on the isothermal sound speed. This accretion rate is a factor of approx. 0.1 that predicted by the expansion wave solution. This reduction is due in part to the presence of a weak shock which propagates outward at 1.26 times the sound speed. Gas in the postshock region first moves out subsonically but is then decelerated and begins to collapse. The existence of two classes of numerical collapse solutions is explained in terms of the instability to radial perturbations of the analytic solution. Collapse occurring in the manner described by some of our solutions would eventually unbind a finite-sized core. However, this does not constitute a violation of the instability properties of the singular isothermal sphere which is unstable both to collapse and to expansion. To emphasize this, we consider a purely expanding solution for isothermal spheres. This solution is found to be self-similar and results in a uniform density core in the central regions of the gas. Our solutions may be relevant to the 'luminosity' problem of protostellar cores since the predicted central accretion rates are significantly reduced relative to that of the expansion wave solution. Furthermore, our calculations indicate that star-forming cloud cores are not very tightly bound and that modest disturbances can easily result in both termination of infall and dispersal of unaccreted material.

Tsai, John C.↗
NASA NTRS1995

Experimental Study of Saddle Point of Attachment in Laminar Juncture Flow

An experimental study of laminar horseshoe vortex flows upstream of a cylinder/flat plate juncture has been conducted to verify the existence of saddle-point-of-attachment topologies. In the classical depiction of this flowfield, a saddle point of separation exists on the flat plate upstream of the cylinder, and the boundary layer separates from the surface. Recent computations have indicated that the topology may actually involve a saddle point of attachment on the surface and additional singular points in the flow. Laser light sheet flow visualizations have been performed on the symmetry plane and crossflow planes to identify the saddle-point-of-attachment flowfields. The visualizations reveal that saddle-point-of-attachment topologies occur over a range of Reynolds numbers in both single and multiple vortex regimes. An analysis of the flow topologies is presented that describes the existence and evolution of the singular points in the flowfield.

Coon, Michael D.↗
NASA NTRS1998

The Real-Time Wall Interference Correction System of the NASA Ames 12-Foot Pressure Wind Tunnel

An improved version of the Wall Signature Method was developed to compute wall interference effects in three-dimensional subsonic wind tunnel testing of aircraft models in real-time. The method may be applied to a full-span or a semispan model. A simplified singularity representation of the aircraft model is used. Fuselage, support system, propulsion simulator, and separation wake volume blockage effects are represented by point sources and sinks. Lifting effects are represented by semi-infinite line doublets. The singularity representation of the test article is combined with the measurement of wind tunnel test reference conditions, wall pressure, lift force, thrust force, pitching moment, rolling moment, and pre-computed solutions of the subsonic potential equation to determine first order wall interference corrections. Second order wall interference corrections for pitching and rolling moment coefficient are also determined. A new procedure is presented that estimates a rolling moment coefficient correction for wings with non-symmetric lift distribution. Experimental data obtained during the calibration of the Ames Bipod model support system and during tests of two semispan models mounted on an image plane in the NASA Ames 12 ft. Pressure Wind Tunnel are used to demonstrate the application of the wall interference correction method.

Ulbrich, Norbert↗
NASA NTRS1998

Microwave Imaging on Metal Objects

This final report for the project discusses the attempts to model, using different methods, microwave image reconstruction. Maximum Entropy Method was not successful. Attempts to use Singular Value Decomposition (SVD) got some good results after initial failure. SVD is based upon a theory of linear algebra, to the effect that any M X N Matrix A whose number of rows M is greater than or equal to its number of columns, N can be written as the product of an M X N column-orthogonal matrix U, an N X N diagonal Matrix, W, with m positive or zero elements (the singular values) and the transposition of an N X N orthogonal matrix V. In microwave imaging, the scattered fields can be expressed by the induced current distribution. The SVD method required more contiguous computer memory than was available. Work was also done on the Conjugate Gradient Method (CGM), which didn't work well when tried earlier. It was found that separation of the imaginary part and the real part during calculation may work. This work was considered incomplete as of the end of the grant period.

Tolliver, C. L.↗
NASA NTRS2000

Ground Vibration Test Planning and Pre-Test Analysis for the X-33 Vehicle

This paper describes the results of the modal test planning and the pre-test analysis for the X-33 vehicle. The pre-test analysis included the selection of the target modes, selection of the sensor and shaker locations and the development of an accurate Test Analysis Model (TAM). For target mode selection, four techniques were considered, one based on the Modal Cost technique, one based on Balanced Singular Value technique, a technique known as the Root Sum Squared (RSS) method, and a Modal Kinetic Energy (MKE) approach. For selecting sensor locations, four techniques were also considered; one based on the Weighted Average Kinetic Energy (WAKE), one based on Guyan Reduction (GR), one emphasizing engineering judgment, and one based on an optimum sensor selection technique using Genetic Algorithm (GA) search technique combined with a criteria based on Hankel Singular Values (HSV's). For selecting shaker locations, four techniques were also considered; one based on the Weighted Average Driving Point Residue (WADPR), one based on engineering judgment and accessibility considerations, a frequency response method, and an optimum shaker location selection based on a GA search technique combined with a criteria based on HSV's. To evaluate the effectiveness of the proposed sensor and shaker locations for exciting the target modes, extensive numerical simulations were performed. Multivariate Mode Indicator Function (MMIF) was used to evaluate the effectiveness of each sensor & shaker set with respect to modal parameter identification. Several TAM reduction techniques were considered including, Guyan, IRS, Modal, and Hybrid. Based on a pre-test cross-orthogonality checks using various reduction techniques, a Hybrid TAM reduction technique was selected and was used for all three vehicle fuel level configurations.

Bedrossian, Herand↗