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NASA NTRS1984

Navier-Stokes calculations for unsteady three-dimensional vortical flows in unbounded domains

Finite-difference Navier-Stokes calculations for unsteady, three-dimensional, incompressible, viscous flows induced by initial vorticity distributions are presented and discussed in this paper. The initial vorticity distributions are assumed to be embedded in a flow field of infinite extent that is quiescent at infinity. These vorticity distributions are typical of vortex rings and other closed vortical tubes or structures. Such structures are important elements in fluid flows such as jets, atmospheric convection and the far-field wakes of aircraft; studies of their interaction may aid in an understanding of complex fluid flows. The calculations employ a method recently proposed by Ting to approximate the infinite-domain boundary value problem with a finite boundary computational domain, and this method is shown to yield accurate three-dimensional results for reasonable expenditures of computer time. Because of the efficiency of the boundary condition technique and the resulting Navier-Stokes code, a 16-bit minicomputer with virtual memory was capable of performing the calculations for the unsteady motion of two obliquely colliding vortex rings. The results of these calculations are presented in the paper.

Chamberlain, J. P.↗

NASA NTRS1982

Parametric study of minimum converter loss in an energy-storage dc-to-dc converter

Through a combination of analytical and numerical minimization procedures, a converter design that results in the minimum total converter loss (including core loss, winding loss, capacitor and energy-storage-reactor loss, and various losses in the semiconductor switches) is obtained. Because the initial phase involves analytical minimization, the computation time required by the subsequent phase of numerical minimization is considerably reduced in this combination approach. The effects of various loss parameters on the optimum values of the design variables are also examined.

Wong, R. C.↗

NASA NTRS1984

Quaternions for Galileo scan platform control

The application of quaternions for the articulation control of the Galileo scan platform is presented in this paper. The purpose of selecting quaternions is to minimize onboard computation time and program size. Attention has been focused on performing inertial pointing while the spacecraft is in a dual spin configuration. Target quaternion and relative target quaternion are introduced and used to specify the target position of the scan platform for point-to-point absolute slews and mosaic relative slews, respectively. The pointing error of the platform is represented by an error quaternion which is converted into gimbal angular errors defining the attitude change. For path control, a moving target quaternion is generated; the corresponding tracking error quaternion and the related spacecraft motion compensation capability are also addressed. A sample slew case is used to demonstrate the implementation of these concepts.

Breckenridge, W. G.↗

NASA NTRS1983

An integral solution procedure for radiative transfer in concentric cylindrical media

A complete integral formulation is developed for radiative transfer in emitting and absorbing media contained between infinitely long, concentric cylinders with black surfaces. The resulting flux equation is used to state both the gray and nongray radiative equilibrium problems that are solved numerically with controlled error. The results are compared with those from other approaches, both approximate and geometrically limiting, to check and put into perspective the present and prior work. The nongray solution is unique for concentric cylindrical media. The independent parameters of optical thickness and radius ratio are varied to study the emissive power (temperature) distribution, total heat flux, and the required computational time.

Pandey, D. K.↗

NASA NTRS1984

Closed-form recursive formula for an optimal tracker with terminal constraints

Feedback control laws are derived for a class of optimal finite time tracking problems with terminal constraints. Analytical solutions are obtained for the feedback gain and the closed-loop response trajectory. Such formulations are expressed in recursive forms so that a real-time computer implementation becomes feasible. Two examples are given to illustrate the validity and usefulness of the formulations.

Juang, J.-N.↗

NASA NTRS1984

Computation of three-dimensional viscous flows using a space-marching method

A space-marching method, developed to compute three-dimensional flows for internal geometries, has been utilized to predict viscous flows through a curved duct and over a swept wing. The Navier-Stokes equations have been posed as an initial value problem by neglecting the streamwise viscous diffusion terms and by treating the pressure gradient as a known source term. The resulting equations have been solved by a non-iterative (single pass) algorithm at each streamwise step. The results are compared with earlier computations (based on iterative methods) and the experimental data. The agreement between the present predictions, the experimental data, and the earlier predictions is good for the cases computed. The computation time is only a fraction of the iterative methods.

Murthy, K. N. S.↗

NASA NTRS1984

A statistical correlation method for the retrieval of atmospheric moisture profiles by microwave radiometry

A statistical correlation technique is applied to the retrieval of vertical moisture profiles under clear-sky conditions from down-looking radiometric measurements of atmospheric radiation at microwave wavelengths. For a given set of channels, the method selects the optimum radiometric channels for estimating water vapor at specific pressure levels between the surface and 300 mb. The water vapor mixing ratio at these pressure levels is then calculated from a linear combination of the selected channel brightness temperatures. To test its validity the algorithm was applied, in a numerical experiment, to fifty independent tropical radiosondes. The rms absolute deviation of the estimated moisture profiles from the actual profiles was comparable to that obtained using an iterative retrieval method reported earlier. The statistical method, however, requires several orders of magnitude less computer time than the iterative method; it is suitable for high speed processing of large amounts of data.

Kakar, R. K.↗

NASA NTRS1985

Simplified Worst-Case Analysis of Complex Systems

Statistical method avoids excessive computer time. Technique involves simplified Monte Carlo simulation of system with randomly chosen parameters and comparison of tolerance extremes of several of worst-case situations found. Resulting combination of tolerance extremes then used in detailed analysis - one that makes use of full complex nonlinear model capable of accurate simulations.

Pond, C. L.↗

NASA NTRS1984

Classical free-streamline flow over a polygonal obstacle

In classical Kirchhoff flow, an ideal incompressible fluid flows past an obstacle and around a motionless wake bounded by free streamlines. Since 1869 it has been known that in principle, the two-dimensional Kirchhoff flow over a polygonal obstacle can be determined by constructing a conformal map onto a polygon in the log-hodograph plane. In practice, however, this idea has rarely been put to use except for very simple obstacles, because the conformal mapping problem has been too difficult. This paper presents a practical method for computing flows over arbitrary polygonal obstacles to high accuracy in a few seconds of computer time. We achieve this high speed and flexibility by working with a modified Schwarz-Christoffel integral that maps onto the flow region directly rather than onto the log-hodograph polygon. This integral and its associated parameter problem are treated numerically by methods developed earlier by Trefethen for standard Schwarz-Christoffel maps.

Elcrat, A. R.↗

NASA NTRS1984

Comparison of uniform perturbation solutions and numerical solutions for some potential flows past slender bodies

Approximate solutions for potential flow past an axisymmetric slender body and past a thin airfoil are calculated using a uniform perturbation method and then compared with either the exact analytical solution or the solution obtained using a purely numerical method. The perturbation method is based upon a representation of the disturbance flow as the superposition of singularities distributed entirely within the body, while the numerical (panel) method is based upon a distribution of singularities on the surface of the body. It is found that the perturbation method provides very good results for small values of the slenderness ratio and for small angles of attack. Moreover, for comparable accuracy, the perturbation method is simpler to implement, requires less computer memory, and generally uses less computation time than the panel method. In particular, the uniform perturbation method yields good resolution near the regions of the leading and trailing edges where other methods fail or require special attention.

Wong, T. C.↗

NASA NTRS1982

An exploratory study of finite difference grids for transonic unsteady aerodynamics

Unsteady aerodynamic forces are calculated by the XTRAN2L finite difference program which solves the complete two dimensional unsteady transonic small perturbation equation. The unsteady forces are obtained using a pulse transfer function technique which assumes the flow field behaves in a locally linear fashion about a mean condition. Forces are calculated for a linear flat plate using the default grids from the LTRAN2-NLR, LTRAN2-HI, and XTRAN3S programs. The forces are compared to the exact theoretical values for flat plate, and grid generated boundary and internal numerical reflections are observed to cause significant errors in the unsteady airloads. Grids are presented that alleviate the reflections while reducing computational time up to fifty-three percent and program size up to twenty-eight percent. Forces are presented for a six percent thick parabolic arc airfoil which demonstrate that the transform technique may be successfully applied to nonlinear transonic flows.

Seidel, D. A.↗

NASA NTRS1985

Performance of the Dsa's Subcarrier Demodulation Digital Loop

The subcarrier demodulation digital loop is part of the baseband assembly. The subcarrier demodulator is a fourth-order Costas-type loop corresponding to a type 2 analog loop in terms of steady state response. The expected value and the variance of the error signal are determined as functions of the input SNR. A Nyquist sampling rate of the input signal is assumed. From the integro-difference equations a mixed s/z domain block diagram is obtained. From the loop's transfer function a set of gains for the loop filter is obtained. Also, a set of state equations is presented for future reference. Finally, the noise-equivalent bandwidths are calculated for normalized computation times of 0, 0.25 and 0.5. The subcarrier demodulator analyzed tracks a parabolic phase input with finite steady state error. Since at each update instant the loop gains are adjusted to compensate for the variations in SNR of the input signal, the noise-equivalent bandwidth is maintained constant.

Simon, M. K.↗

NASA NTRS1985

Trends in computational capabilities for fluid dynamics

Milestones in the development of computational aerodynamics are reviewed together with past, present, and future computer performance (speed and memory) trends. Factors influencing computer performance requirements for both steady and unsteady flow simulations are identified. Estimates of computer speed and memory that are required to calculate both inviscid and viscous, steady and unsteady flows about airfoils, wings, and simple wing body configurations are presented and compared to computer performance which is either currently available, or is expected to be available before the end of this decade. Finally, estimates of the amounts of computer time that are required to determine flutter boundaries of airfoils and wings at transonic Mach numbers are presented and discussed.

Peterson, V. L.↗

NASA NTRS1985

Theoretical studies of solar-pumped lasers

The power output of a black body solar-pumped laser as a function of time (computer graphic solutions) and under steady state conditions (analytic conditions); computer analyses of polymerization using lasers; and metallic sodium as a laser medium were studied.

Harries, W. L.↗

NASA NTRS1985

Applications of Fuzzy Set Theory to Satellite Soundings

The introduction of an appropriate fuzzy setting for satellite soundings and its application to clustering methods via unimodal fuzzy sets in the future is proposed. Methods of hard clustering analysis and fuzzy partitioned clustering were applied on simulated data with very encouraging results. The proposed clustering technique is discussed. The notion of a unimodal fuzzy set was chosen to represent the partition of a data set for two reasons: (1) it detects all the locations in the vector space where highly concentrated clusters of points exist; and (2) the notion is general enough to represent clusters that exhibit quite general distributions of points. The technique detects all of the existing unimodal fuzzy sets and realizes the maximum separation among them. It is economical in memory space and computational time requirements and also detects groups that are fairly generally distributed in the feature space.

Munteanu, M. J.↗

NASA NTRS1983

Nonlinear potential analysis techniques for supersonic-hypersonic configuration design

Approximate nonlinear inviscid theoretical techniques for predicting aerodynamic characteristics and surface pressures for relatively slender vehicles at moderate hypersonic speeds were developed. Emphasis was placed on approaches that would be responsive to preliminary configuration design level of effort. Second order small disturbance and full potential theory was utilized to meet this objective. Numerical pilot codes were developed for relatively general three dimensional geometries to evaluate the capability of the approximate equations of motion considered. Results from the computations indicate good agreement with higher order solutions and experimental results for a variety of wing, body and wing-body shapes for values of the hypersonic similarity parameter M delta approaching one. Case computational times of a minute were achieved for practical aircraft arrangements.

Clever, W. C.↗

NASA NTRS1984

An optimized cubic interpolator for image resampling

It is noted that the cubic resampling function is only one member of a family of functions, defined by the single parameter of the slope of the cubic function at its first zero crossing, whose other members are in some cases superior to the standard cubic. This superiority is especially noteworthy with respect to the extent of gray level overshoot induced by the resampling process at high contrast edges. It is shown that there is an optimum member of this 'parametric cubic convolution' family which minimizes the mean-squared radiometric error arising from interpolation. This interpolator requires no additional computation time over the conventional cubic one. These conclusions are supported and illustrated by resampling simulations with both a high resolution digitized aerial image and a Landsat Multispectral Scanner image.

Schowengerdt, R. A.↗

NASA NTRS1984

Radiative transfer in spherical atmospheres

A method for defining spherical model atmospheres in radiative/convective and hydrostatic equilibrium is presented. A finite difference form is found for the transfer equation and a matrix operator is developed as the discrete space analog (in curvilinear coordinates) of a formal integral in plane geometry. Pressure is treated as a function of temperature. Flux conservation is maintained within the energy equation, although the correct luminosity transport must be assigned for any given level of the atmosphere. A perturbed integral operator is used in a complete linearization of the transfer and constraint equations. Finally, techniques for generating stable solutions in economical computer time are discussed.

Kalkofen, W.↗