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NASA NTRS2012

An Empirical Temperature Variance Source Model in Heated Jets

An acoustic analogy approach is implemented that models the sources of jet noise in heated jets. The equivalent sources of turbulent mixing noise are recognized as the differences between the fluctuating and Favre-averaged Reynolds stresses and enthalpy fluxes. While in a conventional acoustic analogy only Reynolds stress components are scrutinized for their noise generation properties, it is now accepted that a comprehensive source model should include the additional entropy source term. Following Goldstein s generalized acoustic analogy, the set of Euler equations are divided into two sets of equations that govern a non-radiating base flow plus its residual components. When the base flow is considered as a locally parallel mean flow, the residual equations may be rearranged to form an inhomogeneous third-order wave equation. A general solution is written subsequently using a Green s function method while all non-linear terms are treated as the equivalent sources of aerodynamic sound and are modeled accordingly. In a previous study, a specialized Reynolds-averaged Navier-Stokes (RANS) solver was implemented to compute the variance of thermal fluctuations that determine the enthalpy flux source strength. The main objective here is to present an empirical model capable of providing a reasonable estimate of the stagnation temperature variance in a jet. Such a model is parameterized as a function of the mean stagnation temperature gradient in the jet, and is evaluated using commonly available RANS solvers. The ensuing thermal source distribution is compared with measurements as well as computational result from a dedicated RANS solver that employs an enthalpy variance and dissipation rate model. Turbulent mixing noise predictions are presented for a wide range of jet temperature ratios from 1.0 to 3.20.

Khavaran, Abbas↗
NASA NTRS1990

Climate Fluctuations and Climate Sensitivity

Some evidence is presented that the main part of the atmospheric climate system is such that small forcings in the heat balance lead to linear responses in the surface temperature field. By examining first a noise forced energy-balance climate model and then comparing it with a long run of a highly symmetrical general circulation model, one finds a remarkable connection between spatial autocorrelation statistics and the thermal influence function for a point heat source. These findings are brought together to indicate that this particular climatological field may be largely governed by linear processes.

North, Gerald R.↗
NASA NTRS2005

Optimal Estimation of Clock Values and Trends from Finite Data

We show how to solve two problems of optimal linear estimation from a finite set of phase data. Clock noise is modeled as a stochastic process with stationary dth increments. The covariance properties of such a process are contained in the generalized autocovariance function (GACV). We set up two principles for optimal estimation: with the help of the GACV, these principles lead to a set of linear equations for the regression coefficients and some auxiliary parameters. The mean square errors of the estimators are easily calculated. The method can be used to check the results of other methods and to find good suboptimal estimators based on a small subset of the available data.

stationary increments↗
NASA NTRS1992

Transfer of contrast sensitivity in linear visual networks

Contrast sensitivity is a useful measure of the ability of an observer to distinguish contrast signals from noise. Although usually applied to human observers, contrast sensitivity can also be defined operationally for individual visual neurons. In a model linear neuron consisting of a filter and noise source, this operational measure is a function of filter gain, noise power spectrum, signal duration, and a performance criterion. This definition allows one to relate the sensitivities of linear neurons at different levels in the visual pathway. Mathematical formulas describing these relationships are derived, and the general model is applied to the specific problem of relating the sensitivities of parvocellular LGN neurons and cortical simple cells in the primate.

Watson, Andrew B.↗
NASA NTRS1993

Calculation of AGARD Wing 445.6 Flutter Using Navier-Stokes Aerodynamics

The flutter characteristics of the first AGARD standard aeroelastic configuration for dynamic response, Wing 445.6, are studied using an unsteady Navier-Stokes algorithm in order to investigate a previously noted discrepancy between Euler flutter characteristics and the experimental data. The algorithm, which is a three-dimensional, implicit, upwind Euler/Navier-Stokes code (CFL3D Version 2.1), was previously modified for the time-marching, aeroelastic analysis of wings using the unsteady Euler equations. These modifications include the incorporation of a deforming mesh algorithm and the addition of the structural equations of motion for their simultaneous time integration with the governing flow equations. In this paper, the aeroelastic method is extended and evaluated for applications that use the Navier- Stokes aerodynamics. The paper presents a brief description of the aeroelastic method and presents unsteady calculations which verify this method for Navier-Stokes calculations. A linear stability analysis and a time-marching aeroelastic analysis are used to determine the flutter characteristics of the isolated 45 deg. swept-back wing. Effects of fluid viscosity, structural damping, and number of modes in the structural model are investigated. For the linear stability analysis, the unsteady generalized aerodynamic forces of the wing are computed for a range of reduced frequencies using the pulse transfer-function approach. The flutter characteristics of the wing are determined using these unsteady generalized aerodynamic forces in a traditional V-g analysis. This stability analysis is used to determine the flutter characteristics of the wing at free-stream Mach numbers of 0.96 and 1.141 using the generalized aerodynamic forces generated by solving the Euler equations and the Navier-Stokes equations. Time-marching aeroelastic calculations are performed at a free-stream Mach number of 1.141 using the Euler and Navier-Stokes equations to compare with the linear V-g flutter analysis method. The V-g analysis, which is used in conjunction with the time-marching analysis, indicates that the fluid viscosity has a significant effect on the supersonic flutter boundary for this wing while the structural damping and number of modes in the structural model have a lesser effect.

Lee-Rausch, Elizabeth M.↗
NASA NTRS1994

Towards enhancing and delaying disturbances in free shear flows

The family of shear flows comprising the jet, wake, and the mixing layer are subjected to perturbations in an inviscid incompressible fluid. By modeling the basic mean flows as parallel with piecewise linear variations for the velocities, complete and general solutions to the linearized equations of motion can be obtained in closed form as functions of all space variables and time when posed as an initial value problem. The results show that there is a continuous as well as the discrete spectrum that is more familiar in stability theory and therefore there can be both algebraic and exponential growth of disturbances in time. These bases make it feasible to consider control of such flows. To this end, the possibility of enhancing the disturbances in the mixing layer and delaying the onset in the jet and wake is investigated. It is found that growth of perturbations can be delayed to a considerable degree for the jet and the wake but, by comparison, cannot be enhanced in the mixing layer. By using moving coordinates, a method for demonstrating the predominant early and long time behavior of disturbances in these flows is given for continuous velocity profiles. It is shown that the early time transients are always algebraic whereas the asymptotic limit is that of an exponential normal mode. Numerical treatment of the new governing equations confirm the conclusions reached by use of the piecewise linear basic models. Although not pursued here, feedback mechanisms designed for control of the flow could be devised using the results of this work.

Criminale, W. O.↗
NASA NTRS1993

The analytical representation of viscoelastic material properties using optimization techniques

This report presents a technique to model viscoelastic material properties with a function of the form of the Prony series. Generally, the method employed to determine the function constants requires assuming values for the exponential constants of the function and then resolving the remaining constants through linear least-squares techniques. The technique presented here allows all the constants to be analytically determined through optimization techniques. This technique is employed in a computer program named PRONY and makes use of commercially available optimization tool developed by VMA Engineering, Inc. The PRONY program was utilized to compare the technique against previously determined models for solid rocket motor TP-H1148 propellant and V747-75 Viton fluoroelastomer. In both cases, the optimization technique generated functions that modeled the test data with at least an order of magnitude better correlation. This technique has demonstrated the capability to use small or large data sets and to use data sets that have uniformly or nonuniformly spaced data pairs. The reduction of experimental data to accurate mathematical models is a vital part of most scientific and engineering research. This technique of regression through optimization can be applied to other mathematical models that are difficult to fit to experimental data through traditional regression techniques.

Hill, S. A.↗
NASA NTRS2003

Stochastic Mixing Model with Power Law Decay of Variance

Here we present a simple stochastic mixing model based on the law of large numbers (LLN). The reason why the LLN is involved in our formulation of the mixing problem is that the random conserved scalar c = c(t,x(t)) appears to behave as a sample mean. It converges to the mean value mu, while the variance sigma(sup 2)(sub c) (t) decays approximately as t(exp -1). Since the variance of the scalar decays faster than a sample mean (typically is greater than unity), we will introduce some non-linear modifications into the corresponding pdf-equation. The main idea is to develop a robust model which is independent from restrictive assumptions about the shape of the pdf. The remainder of this paper is organized as follows. In Section 2 we derive the integral equation from a stochastic difference equation describing the evolution of the pdf of a passive scalar in time. The stochastic difference equation introduces an exchange rate gamma(sub n) which we model in a first step as a deterministic function. In a second step, we generalize gamma(sub n) as a stochastic variable taking fluctuations in the inhomogeneous environment into account. In Section 3 we solve the non-linear integral equation numerically and analyze the influence of the different parameters on the decay rate. The paper finishes with a conclusion.

Fedotov, S.↗
NASA NTRS1992

Transition operators in electromagnetic-wave diffraction theory - General theory

A formal theory is developed for the scattering of time-harmonic electromagnetic waves from impenetrable immobile obstacles with given linear, homogeneous, and generally nonlocal boundary conditions of Leontovich (impedance) type for the wave of the obstacle's surface. The theory is modeled on the complete Green's function and the transition (T) operator in time-independent formal scattering theory of nonrelativistic quantum mechanics. An expression for the differential scattering cross section for plane electromagnetic waves is derived in terms of certain matrix elements of the T operator for the obstacle.

Hahne, G. E.↗
NASA NTRS1989

A methodology for formulating a minimal uncertainty model for robust control system design and analysis

In the design and analysis of robust control systems for uncertain plants, the technique of formulating what is termed an M-delta model has become widely accepted and applied in the robust control literature. The M represents the transfer function matrix M(s) of the nominal system, and delta represents an uncertainty matrix acting on M(s). The uncertainty can arise from various sources, such as structured uncertainty from parameter variations or multiple unstructured uncertainties from unmodeled dynamics and other neglected phenomena. In general, delta is a block diagonal matrix, and for real parameter variations the diagonal elements are real. As stated in the literature, this structure can always be formed for any linear interconnection of inputs, outputs, transfer functions, parameter variations, and perturbations. However, very little of the literature addresses methods for obtaining this structure, and none of this literature addresses a general methodology for obtaining a minimal M-delta model for a wide class of uncertainty. Since have a delta matrix of minimum order would improve the efficiency of structured singular value (or multivariable stability margin) computations, a method of obtaining a minimal M-delta model would be useful. A generalized method of obtaining a minimal M-delta structure for systems with real parameter variations is given.

Belcastro, Christine M.↗
NASA NTRS1985

Magnetospheric impulse response for many levels of geomagnetic activity

The temporal relationship between the solar wind and magnetospheric activity has been studied using 34 intervals of high time resolution IMP 8 solar wind data and the corresponding AL auroral activity index. The median values of the AL index for each interval were utilized to rank the intervals according to geomagnetic activity level. The linear prediction filtering technique was then applied to model magnetospheric response as measured by the AL index to the solar wind input function VB(s). The linear prediction filtering routine produces a filter of time-lagged response coefficients which estimates the most general linear relationship between the chosen input and output parameters of the magnetospheric system. It is found that the filters are composed of two response pulses speaking at time lags of 20 and 60 min. The amplitude of the 60-min pulse is the larger for moderate activity levels, while the 20-min pulse is the larger for strong activity levels. A possible interpretation is that the 20-min pulse represents magnetospheric activity driven directly by solar wind coupling and that the 60-min pulse represents magnetospheric activity driven by the release of energy previously stored in the magnetotail. If this interpretation is correct, the linear filtering results suggest that both the driven and the unloading models of magnetospheric response are important facets of a more comprehensive response model.

Bargatze, L. F.↗
NASA NTRS2005

Constraining Oceanic Sources and Sinks of CO2 by Inverse Modeling: A First Step Toward Assimilation of In Situ and Remote Data

The primary goal of this collaborative project, lead by Nicholas Gruber at UCLA, is to better quantify the air-sea fluxes of pre-industrial and anthropogenic carbon dioxide CO2 for the global ocean with a newly developed inverse method. The method involves using ocean general circulation models (OGCMs) to characterize the subsurface distribution of tracers injected for different regions of the ocean surface. By linearly combining a series of these basis (or Greens) functions, one should be able to recreate any arbitrary ocean tracer field. In our case, we are using the global database of ocean dissolved inorganic carbon (DIC) from the WOCE/JGOFS global CO2 survey from the 1990s. The observed DIC field has been partitioned into pre-industrial and anthropogenic components using the empirical C* technique. We then solve for an optimal combination of the regional basis functions that best match the two sets observations in a least-squares sense with singular value decomposition. This in turn provides solutions for the regional air-sea CO2 fluxes (pre-industrial and anthropogenic) that are independent of more traditional estimates derived from surface water disequilibria in the partial pressure of CO2 and wind speed gas exchange parameterizations. We are apply the method to a suite of nine different OGCMs to test the robustness of the derived surface fluxes fields to differences in ocean circulation. Together with a collegue Keith Lindsay at NCAR, S. Doney's role in this project was to create the appropriate steady-state and temporally evolving basis functions from the NCAR CSM-1 ocean circulation model. Because of a slow start across the project in defining a common set of experimental protocols, we requested and were given a one year, no cost extension. Both the steady-state and temporally evolving basis functions were delivered to the UCLA group for further analysis. Additional information is included in the original extended abstract.

Doney, Scott↗
NASA NTRS2015

Analysis of JPSS J1 VIIRS Polarization Sensitivity Using the NIST T-SIRCUS

The polarization sensitivity of the Joint Polar Satellite System (JPSS) J1 Visible Infrared Imaging Radiometer Suite (VIIRS) measured pre-launch using a broadband source was observed to be larger than expected for many reflective bands. Ray trace modeling predicted that the observed polarization sensitivity was the result of larger diattenuation at the edges of the focal plane filter spectral bandpass. Additional ground measurements were performed using a monochromatic source (the NIST T-SIRCUS) to input linearly polarized light at a number of wavelengths across the bandpass of two VIIRS spectral bands and two scan angles. This work describes the data processing, analysis, and results derived from the T-SIRCUS measurements, comparing them with broadband measurements. Results have shown that the observed degree of linear polarization, when weighted by the sensor's spectral response function, is generally larger on the edges and smaller in the center of the spectral bandpass, as predicted. However, phase angle changes in the center of the bandpass differ between model and measurement. Integration of the monochromatic polarization sensitivity over wavelength produced results consistent with the broadband source measurements, for all cases considered.

reflective bands↗
NASA NTRS2013

Towards a Comprehensive Model of Jet Noise Using an Acoustic Analogy and Steady RANS Solutions

An acoustic analogy is developed to predict the noise from jet flows. It contains two source models that independently predict the noise from turbulence and shock wave shear layer interactions. The acoustic analogy is based on the Euler equations and separates the sources from propagation. Propagation effects are taken into account by calculating the vector Green's function of the linearized Euler equations. The sources are modeled following the work of Tam and Auriault, Morris and Boluriaan, and Morris and Miller. A statistical model of the two-point cross-correlation of the velocity fluctuations is used to describe the turbulence. The acoustic analogy attempts to take into account the correct scaling of the sources for a wide range of nozzle pressure and temperature ratios. It does not make assumptions regarding fine- or large-scale turbulent noise sources, self- or shear-noise, or convective amplification. The acoustic analogy is partially informed by three-dimensional steady Reynolds-Averaged Navier-Stokes solutions that include the nozzle geometry. The predictions are compared with experiments of jets operating subsonically through supersonically and at unheated and heated temperatures. Predictions generally capture the scaling of both mixing noise and BBSAN for the conditions examined, but some discrepancies remain that are due to the accuracy of the steady RANS turbulence model closure, the equivalent sources, and the use of a simplified vector Green's function solver of the linearized Euler equations.

Miller, Steven A. E.↗
NASA NTRS1972

Digital controller for high pressure rocket engine.

Description of a general approach for the design of an adaptive digital control system for liquid bipropellant rocket engines. The technique employs linearized transfer functions derived from perturbations of an engine simulation. The linear models serve as a basis on which to develop candidate closed-loop control laws quickly and economically.

Thompson, Z.↗
NASA NTRS2012

Calculating Soil Wetness, Evapotranspiration and Carbon Cycle Processes Over Large Grid Areas Using a New Scaling Technique

Soil wetness typically shows great spatial variability over the length scales of general circulation model (GCM) grid areas (approx 100 km ), and the functions relating evapotranspiration and photosynthetic rate to local-scale (approx 1 m) soil wetness are highly non-linear. Soil respiration is also highly dependent on very small-scale variations in soil wetness. We therefore expect significant inaccuracies whenever we insert a single grid area-average soil wetness value into a function to calculate any of these rates for the grid area. For the particular case of evapotranspiration., this method - use of a grid-averaged soil wetness value - can also provoke severe oscillations in the evapotranspiration rate and soil wetness under some conditions. A method is presented whereby the probability distribution timction(pdf) for soil wetness within a grid area is represented by binning. and numerical integration of the binned pdf is performed to provide a spatially-integrated wetness stress term for the whole grid area, which then permits calculation of grid area fluxes in a single operation. The method is very accurate when 10 or more bins are used, can deal realistically with spatially variable precipitation, conserves moisture exactly and allows for precise modification of the soil wetness pdf after every time step. The method could also be applied to other ecological problems where small-scale processes must be area-integrated, or upscaled, to estimate fluxes over large areas, for example in treatments of the terrestrial carbon budget or trace gas generation.

Sellers, Piers↗
NASA NTRS1992

Linear analysis of opto-mechanical systems

A general framework is presented for the matrix-form, linear optical model analysis of controlled optomechanical systems; the models are conjoined with linear models of structures and controls to compute system performance as a function of optics, structures, and control parameters. Covariance analysis, optimization, and estimation/simulation are used. Attention is given to a tolerancing example for the Hubble Space Telescope's Wide Field and Planetary Camera, which involves the creation of a linear model of residual pupil shear.

Redding, David C.↗
NASA NTRS1991

On the formulation of a minimal uncertainty model for robust control with structured uncertainty

In the design and analysis of robust control systems for uncertain plants, representing the system transfer matrix in the form of what has come to be termed an M-delta model has become widely accepted and applied in the robust control literature. The M represents a transfer function matrix M(s) of the nominal closed loop system, and the delta represents an uncertainty matrix acting on M(s). The nominal closed loop system M(s) results from closing the feedback control system, K(s), around a nominal plant interconnection structure P(s). The uncertainty can arise from various sources, such as structured uncertainty from parameter variations or multiple unsaturated uncertainties from unmodeled dynamics and other neglected phenomena. In general, delta is a block diagonal matrix, but for real parameter variations delta is a diagonal matrix of real elements. Conceptually, the M-delta structure can always be formed for any linear interconnection of inputs, outputs, transfer functions, parameter variations, and perturbations. However, very little of the currently available literature addresses computational methods for obtaining this structure, and none of this literature addresses a general methodology for obtaining a minimal M-delta model for a wide class of uncertainty, where the term minimal refers to the dimension of the delta matrix. Since having a minimally dimensioned delta matrix would improve the efficiency of structured singular value (or multivariable stability margin) computations, a method of obtaining a minimal M-delta would be useful. Hence, a method of obtaining the interconnection system P(s) is required. A generalized procedure for obtaining a minimal P-delta structure for systems with real parameter variations is presented. Using this model, the minimal M-delta model can then be easily obtained by closing the feedback loop. The procedure involves representing the system in a cascade-form state-space realization, determining the minimal uncertainty matrix, delta, and constructing the state-space representation of P(s). Three examples are presented to illustrate the procedure.

Belcastro, Christine M.↗