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NASA NTRS1979

A new inversion method of remote sounding of planetary atmospheres

A new inversion method for remote sounding of planetary atmospheres is presented which appears to have several significant advantages over the conventional methods. This method is applicable to high-resolution observations where the spectral lines are fully resolved and is based on matching the calculated slopes of the spectral line profiles with slopes of the observed line shapes. The method is applied to inversion of ozone absorption lines in the earth's atmosphere, and the results are compared with those obtained by a conventional method. The proposed method is seen to provide a significant improvement in the overall accuracy of the retrieved profiles, with higher vertical resolution and higher levels which may be probed.

Abbas, M. M.↗

NASA NTRS1979

Improved Woodward's panel method for calculating edge suction forces

A new technique to improve Woodward's (1968) unified subsonic and supersonic panel method is described. The pressure prediction is improved based on a new two-dimensional theory. The method used by Lan (1977) is then used to calculate the leading-edge and side-edge suction forces by direct use of the predicted pressure distribution. The method is applicable to both subsonic and supersonic flow. It is shown that the improved Woodward panel method is capable of accurately predicting leading-edge and side-edge suction forces in subsonic and supersonic flow. Therefore, the method can be used not only to predict the vortex lift of complex planforms through the method of suction analogy, but also to calculate some lateral-directional stability derivatives.

Lan, C. E.↗

NASA NTRS1980

Newton's method: A link between continuous and discrete solutions of nonlinear problems

Newton's method for nonlinear mechanics problems replaces the governing nonlinear equations by an iterative sequence of linear equations. When the linear equations are linear differential equations, the equations are usually solved by numerical methods. The iterative sequence in Newton's method can exhibit poor convergence properties when the nonlinear problem has multiple solutions for a fixed set of parameters, unless the iterative sequences are aimed at solving for each solution separately. The theory of the linear differential operators is often a better guide for solution strategies in applying Newton's method than the theory of linear algebra associated with the numerical analogs of the differential operators. In fact, the theory for the differential operators can suggest the choice of numerical linear operators. In this paper the method of variation of parameters from the theory of linear ordinary differential equations is examined in detail in the context of Newton's method to demonstrate how it might be used as a guide for numerical solutions.

Thurston, G. A.↗

NASA NTRS1981

Improved methods for fan sound field determination

Several methods for determining acoustic mode structure in aircraft turbofan engines using wall microphone data were studied. A method for reducing data was devised and implemented which makes the definition of discrete coherent sound fields measured in the presence of engine speed fluctuation more accurate. For the analytical methods, algorithms were developed to define the dominant circumferential modes from full and partial circumferential arrays of microphones. Axial arrays were explored to define mode structure as a function of cutoff ratio, and the use of data taken at several constant speeds was also evaluated in an attempt to reduce instrumentation requirements. Sensitivities of the various methods to microphone density, array size and measurement error were evaluated and results of these studies showed these new methods to be impractical. The data reduction method used to reduce the effects of engine speed variation consisted of an electronic circuit which windowed the data so that signal enhancement could occur only when the speed was within a narrow range.

Cicon, D. E.↗

NASA NTRS1981

Improved method for calculating transonic velocities on blade-to-blade stream surfaces of a turbomachine

A method was developed to improve the accuracy of an existing computer program used to calculate transonic velocities on a blade-to-blade surface of a turbomachine. The method eliminates problems encountered in obtaining solutions with the velocity gradient equation when large gradients in velocity occur through the blade row. With the improved method, results indicate that the transonic solution can be obtained by scaling the velocities obtained at the reduced mass flow rate where all velocities are subsonic thereby eliminating the need for a solution of the velocity gradient equation. Solutions obtained with the scaling method on a two dimensional compressor cascade and an axial turbine stator show good agreement with experimental data. The results obtained for the stationary blade rows and comparison of analytical results obtained with and without the present method suggest that the method will yield an improved solution for centrifugal compressor impellers.

Wood, J. R.↗

NASA NTRS1980

Evolution of solar magnetic fields - A new approach to MHD initial-boundary value problems by the method of nearcharacteristics

A method of analysis for the MHD initial-boundary problem is presented in which the model's formulation is based on the method of nearcharacteristics developed by Werner (1968) and modified by Shin and Kot (1978). With this method, the physical causality relationship can be traced from the perturbation to the response as in the method of characteristics, while achieving the advantage of a considerable reduction in mathematical procedures. The method offers the advantage of examining not only the evolution of nonforce free fields, but also the changes of physical conditions in the atmosphere accompanying the evolution of magnetic fields. The physical validity of the method is demonstrated with examples, and their significance in interpreting observations is discussed.

Nakagawa, Y.↗

NASA NTRS1980

On time discretizations for spectral methods

New methods are introduced for the time integration of the Fourier and Chebyshev methods of solution for dynamic differential equations. These methods are unconditionally stable, even though no matrix inversions are required. Time steps are chosen by accuracy requirements alone. For the Fourier method both leapfrog and Runge-Kutta methods are considered. For the Chebyshev method only Runge-Kutta schemes are tested. Numerical calculations are presented to verify the analytic results. Applications to the shallow water equations are presented.

Gottlieb, D.↗

NASA NTRS1981

Recent advances in reduction methods for nonlinear problems

Status and some recent developments in the application of reduction methods to nonlinear structural mechanics problems are summarized. The aspects of reduction methods discussed herein include: (1) selection of basis vectors in nonlinear static and dynamic problems, (2) application of reduction methods in nonlinear static analysis of structures subjected to prescribed edge displacements, and (3) use of reduction methods in conjunction with mixed finite element models. Numerical examples are presented to demonstrate the effectiveness of reduction methods in nonlinear problems. Also, a number of research areas which have high potential for application of reduction methods are identified.

Noor, A. K.↗

NASA NTRS1981

A survey of aftbody flow prediction methods

A survey of computational methods used in the calculation of nozzle aftbody flows is presented. One class of methods reviewed are those which patch together solutions for the inviscid, boundary layer, and plume flow regions. The second class of methods reviewed are those which computationally solve the Navier Stokes equations over nozzle aftbodies with jet exhaust flow. Computed results from the methods are compared with experiment. Advantages and disadvantages of the various methods are discussed along with opportunities for further development of these methods.

Putnam, L. E.↗

NASA NTRS1981

Computational methods for internal flows with emphasis on turbomachinery

Current computational methods for analyzing flows in turbomachinery and other related internal propulsion components are presented. The methods are divided into two classes. The inviscid methods deal specifically with turbomachinery applications. Viscous methods, deal with generalized duct flows as well as flows in turbomachinery passages. Inviscid methods are categorized into the potential, stream function, and Euler aproaches. Viscous methods are treated in terms of parabolic, partially parabolic, and elliptic procedures. Various grids used in association with these procedures are also discussed.

Mcnally, W. D.↗

NASA NTRS1982

Comparison of viscous-shock-layer solutions by time-asymptotic and steady-state methods

Two flow-field codes employing the time- and space-marching numerical techniques were evaluated. Both methods were used to analyze the flow field around a massively blown Jupiter entry probe under perfect-gas conditions. In order to obtain a direct point-by-point comparison, the computations were made by using identical grids and turbulence models. For the same degree of accuracy, the space-marching scheme takes much less time as compared to the time-marching method and would appear to provide accurate results for the problems with nonequilibrium chemistry, free from the effect of local differences in time on the final solution which is inherent in time-marching methods. With the time-marching method, however, the solutions are obtainable for the realistic entry probe shapes with massive or uniform surface blowing rates; whereas, with the space-marching technique, it is difficult to obtain converged solutions for such flow conditions. The choice of the numerical method is, therefore, problem dependent. Both methods give equally good results for the cases where results are compared with experimental data.

Gupta, R. N.↗

NASA NTRS1982

Thermal radiation view factor: Methods, accuracy and computer-aided procedures

The computer aided thermal analysis programs which predicts the result of predetermined acceptable temperature range prior to stationing of these orbiting equipment in various attitudes with respect to the Sun and the Earth was examined. Complexity of the surface geometries suggests the use of numerical schemes for the determination of these viewfactors. Basic definitions and standard methods which form the basis for various digital computer methods and various numerical methods are presented. The physical model and the mathematical methods on which a number of available programs are built are summarized. The strength and the weaknesses of the methods employed, the accuracy of the calculations and the time required for computations are evaluated. The situations where accuracies are important for energy calculations are identified and methods to save computational times are proposed. Guide to best use of the available programs at several centers and the future choices for efficient use of digital computers are included in the recommendations.

Kadaba, P. V.↗

NASA NTRS1983

On a finite-difference method for solving transient viscous flow problems

A method has been developed to solve the unsteady, compressible Navier-Stokes equation with the property of consistency and the ability of minimizing the equation stiffness. It relies on innovative extensions of the state-of-the-art finite-difference techniques and is composed of: (1) the upwind scheme for split-flux and the central scheme for conventional flux terms in the inviscid and viscous regions, respectively; (2) the characteristic treatment of both inviscid and viscous boundaries; (3) an ADI procedure compatible with interior and boundary points; and (4) a scalar matrix coefficient including viscous terms. The performance of this method is assessed with four sample problems; namely, a standing shock in the Laval duct, a shock reflected from the wall, the shock-induced boundary-layer separation, and a transient internal nozzle flow. The results from the present method, an existing hybrid block method, and a well-known two-step explicit method are compared and discussed. It is concluded that this method has an optimal trade-off between the solution accuracy and computational economy, and other desirable properties for analyzing transient viscous flow problems.

Li, C. P.↗

NASA NTRS1984

Newton like: Minimal residual methods applied to transonic flow calculations

A computational technique for the solution of the full potential equation is presented. The method consists of outer and inner iterations. The outer iterate is based on a Newton like algorithm, and a preconditioned Minimal Residual method is used to seek an approximate solution of the system of linear equations arising at each inner iterate. The present iterative scheme is formulated so that the uncertainties and difficulties associated with many iterative techniques, namely the requirements of acceleration parameters and the treatment of additional boundary conditions for the intermediate variables, are eliminated. Numerical experiments based on the new method for transonic potential flows around the NACA 0012 airfoil at different Mach numbers and different angles of attack are presented, and these results are compared with those obtained by the Approximate Factorization technique. Extention to three dimensional flow calculations and application in finite element methods for fluid dynamics problems by the present method are also discussed. The Inexact Newton like method produces a smoother reduction in the residual norm, and the number of supersonic points and circulations are rapidly established as the number of iterations is increased.

Wong, Y. S.↗

NASA NTRS1983

The spaced antenna drift method

The spaced antenna drift method is a simple and relatively inexpensive method for determination of atmospheric wind velocities using radars. The technique has been extensively tested in the mesosphere at high and medium frequencies, and found to give reliable results. Recently, the method has also been applied to VHF observations of the troposphere and stratosphere, and results appear to be reliable. This paper discusses briefly the principle of the method, and investigates both its strengths and weaknesses. Some discussions concerning criticisms of the technique are also given, and it is concluded that while these criticisms may be of some concern at times, appropriate care can ensure that the method is at least as viable as any other method of remote wind measurement. At times, the technique has definite advantages.

Hocking, W. K.↗

NASA NTRS1984

Analysis and testing of a new method for drop size measurement using laser scatter interferometry

Research was conducted on a laser light scatter detection method for measuring the size and velocity of spherical particles. The method is based upon the measurement of the interference fringe pattern produced by spheres passing through the intersection of two laser beams. A theoretical analysis of the method was carried out using the geometrical optics theory. Experimental verification of the theory was obtained by using monodisperse droplet streams. Several optical configurations were tested to identify all of the parametric effects upon the size measurements. Both off-axis forward and backscatter light detection were utilized. Simulated spray environments and fuel spray nozzles were used in the evaluation of the method. The measurements of the monodisperse drops showed complete agreement with the theoretical predictions. The method was demonstrated to be independent of the beam intensity and extinction resulting from the surrounding drops. Signal processing concepts were considered and a method was selected for development.

Bachalo, W. D.↗

NASA NTRS1983

Second-order explicit finite-difference methods for transient-flow analysis

Three second-order accurate numerical methods - MacCormack's method, Lambda scheme and Gabutti scheme - are introduced to solve the quasi-linear, hyperbolic partial differential equations describing transient flows in closed conduits. The details of these methods and the treatment of boundary conditions are presented and the results computed by using these methods for a typical piping system are compared. It is shown that for the same accuracy, second-order methods require considerably lesser number of computational nodes and computer time as compared to those required by the first-order methods.

Chaudhry, M. H.↗

NASA NTRS1982

Random element method for numerical modeling of diffusional processes

The random element method is a generalization of the random vortex method that was developed for the numerical modeling of momentum transport processes as expressed in terms of the Navier-Stokes equations. The method is based on the concept that random walk, as exemplified by Brownian motion, is the stochastic manifestation of diffusional processes. The algorithm based on this method is grid-free and does not require the diffusion equation to be discritized over a mesh, it is thus devoid of numerical diffusion associated with finite difference methods. Moreover, the algorithm is self-adaptive in space and explicit in time, resulting in an improved numerical resolution of gradients as well as a simple and efficient computational procedure. The method is applied here to an assortment of problems of diffusion of momentum and energy in one-dimension as well as heat conduction in two-dimensions in order to assess its validity and accuracy. The numerical solutions obtained are found to be in good agreement with exact solution except for a statistical error introduced by using a finite number of elements, the error can be reduced by increasing the number of elements or by using ensemble averaging over a number of solutions.

Ghoniem, A. F.↗