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Finite dimensional approximation schemes that work well for distributed parameter systems are often not suitable for the analysis and implementation of feedback control systems. The relationship between approximation schemes for distributed parameter systems and their application to optimal control problems is discussed. A numerical example is given.
A new method has been developed for two- and three-dimensional computations of viscous supersonic flows with embedded subsonic regions adjacent to solid boundaries. The approach employs a reduced form of the Navier-Stokes equations which allows solution as an initial-boundary value problem in space, using an efficient noniterative forward marching algorithm. Numerical instability associated with forward marching algorithms for flows with embedded subsonic regions is avoided by approximation of the reduced form of the Navier-Stokes equations in the subsonic regions of the boundary layers. Supersonic and subsonic portions of the flow field are simultaneously calculated by a consistently split linearized block implicit computational algorithm. The results of computations for a series of test cases relevant to internal supersonic flow is presented and compared with data. Comparison between data and computation are in general excellent thus indicating that the computational technique has great promise as a tool for calculating supersonic flow with embedded subsonic regions. Finally, a User's Manual is presented for the computer code used to perform the calculations.
A method has been developed for two- and three-dimensional computations of viscous supersonic jet flows interacting with an external flow. The approach employs a reduced form of the Navier-Stokes equations which allows solution as an initial-boundary value problem in space, using an efficient noniterative forward marching algorithm. Numerical instability associated with forward marching algorithms for flows with embedded subsonic regions is avoided by approximation of the reduced form of the Navier-Stokes equations in the subsonic regions of the boundary layers. Supersonic and subsonic portions of the flow field are simultaneously calculated by a consistently split linearized block implicit computational algorithm. The results of computations for a series of test cases associated with supersonic jet flow is presented and compared with other calculations for axisymmetric cases. Demonstration calculations indicate that the computational technique has great promise as a tool for calculating a wide range of supersonic flow problems including jet flow. Finally, a User's Manual is presented for the computer code used to perform the calculations.
A two-time scale approximation for the linear quadratic optimal output feedback regulator program is examined. Necessary conditions for optimality, as well as an algorithm for computing locally near-optimal gains are derived. If it is assumed that the slow and fast subsystem initial conditions are uniformly distributed, optimal gains for the two-time-scale problem provide a second-order approximation to optimal closed-loop performance in the unperturbed system. This is verified with a numerical example.
The dielectric properties of Maxwellian plasmas are approximated using high Pade approximants to the dispersion function and direct approximation of the distribution. Physical constraints on permissible approximations are discussed, and it is found that some previously published results can lead to predictions of qualitatively incorrect wave properties, including unphysical negative damping. Approximate dispersion functions for Maxwellian distributions are given explicitly, and some of the effects of these approximations on the resulting dispersion are discussed. The approximations discussed here are of use both in analytical work and in accelerating large-scale numerical computations.
An approximate Green's function for surface displacements in an orthotropic beam is derived as the superposition of the half-plane solution for displacements and the beam theory deflections. The Green's function is used to formulate the integral equation for the problem of smooth contact between a rigid-cylinder and a simply supported orthotropic beam. The integral equation is solved using a least-squares approximation procedure. The contact stress distribution is presented for three materials with different degrees of orthotropy. Numerical results are given for contact force-contact length and contact force-indentation relations. The effects of curvature of the deflected beam, shear deformation and length-to-thickness ratio of the beam on the contact behavior are discussed.
A two-dimensional problem of diffraction of a plane electromagnetic wave on a smooth 2 pi-periodic surface is considered. A numerical algorithm solving this problem is developed. An inverse problem of determination of the shape of 2 pi-periodic surface using the performance data of reverse scattering is considered. The inverse problem was solved by means of minimization of the residual functional with the help of the gradient descent method. The initial data were calculated with the help of the numerical method. On each step of the iterative method of minimization, the residual functional was calculated approximately with the help of the small slope method. The examples of the shape determination are considered.
Experimental data on pressure distribution and heat transfer on a turbine airfoil were obtained over a range of Reynolds numbers from 0.75 to 7.5 x 10 exp 6 and a range of turbulence intensities from 1.8 to about 15 percent. The purpose of this study was to obtain fundamental heat transfer and pressure distribution data over a wide range of high Reynolds numbers and to extend the heat transfer data base to include the range of Reynolds numbers encountered in the Space Shuttle main engine (SSME) turbopump turbines. Specifically, the study aimed to determine (1) the effect of Reynolds number on heat transfer, (2) the effect of upstream turbulence on heat transfer and pressure distribution, and (3) the relationship between heat transfer at high Reynolds numbers and the current data base. The results of this study indicated that Reynolds number and turbulence intensity have a large effect on both the transition from laminar to turbulent flow and the resulting heat transfer. For a given turbulence intensity, heat transfer for all Reynolds numbers at the leading edge can be correlated with the Frossling number developed for lower Reynolds numbers. For a given turbulence intensity, heat transfer for the airfoil surfaces downstream of the leading edge can be approximately correlated with a dimensionless parameter. Comparison of the experimental results were also made with a numerical solution from a two-dimensional Navier-Stokes code.
The behavior of an inviscid vortex layer of non-zero thickness near a wall is studied, both through direct numerical simulation of the two-dimensional vorticity equation at high Reynolds numbers, and using an approximate ordinary nonlinear integro-differential equation which is satisfied in the limit of a thin layer under long-wavelength perturbations. For appropriate initial conditions the layer rolls up and breaks into compact vortices which move along the wall at constant speed. Because of the effect of the wall, they correspond to equilibrium counter-rotating vortex dipoles. This breakup can be related to the disintegration of the initial conditions of the approximate nonlinear dispersive equation into solitary waves. The study is motivated by the formation of longitudinal vortices from vortex sheets in the wall region of a turbulent channel.
Experimental data on pressure distribution and heat transfer on a turbine airfoil were obtained over a range of Reynolds numbers from 0.75 to 7.5 million and a range of turbulence intensities from 1.8 to about 15 percent. Fundamental heat transfer and pressure distribution data are obtained over a wide range of high Reynolds numbers and to extend the heat transfer data base to include the range of Reynolds numbers encountered in the SSME turbopump turbines. The results obtained indicated that Reynolds number and turbulence intensity have a large effect on both the transition from laminar to turbulent flow and the resulting heat transfer. For a given turbulence intensity, heat transfer for all Reynolds numbers at the leading edge can be correlated with the Frossling number developed for lower Reynolds numbers. For a given turbulence intensity, heat transfer for the airfoil surfaces downstream of the leading edge can be approximately correlated with a dimensionless parameter. Comparison of the experimental results were also made with a numerical solution from a 2D Navier-Stokes code.
This report is a first attempt to devise a calculation method for representing the buckling behavior of cylindrical shells of variable curvature. The problem occurs, for instance, in dimensioning wing noses, the stability of which is decisively influenced by the variability of curvature. The calculation is made possible by simplifying the stability equations (permissible for the shell of small curvature) and by assuming that the curvature 1/R as a function of the arc lengths can be represented by a very few Fourier terms. The formulas for the special case of an ellipse-like half oval with an axis ratio 1/3 ?= e ?= 1 under compression in longitudinal direction,shear, and a combination of shear and compression were evaluated. However, the results can also be applied approximately to an unsymmetrical oval-shell segment under compression, shear, and bending so that the numerical values contained in the diagrams 10 to 12 represent directly dimensioning data for the wing nose.
Graphs and formulas are given with the aid of which all the aerodynamic coefficients required for computing the lateral dynamic stability can be determined. A number of numerical examples are given for obtaining the stability derivatives and solving the characteristic-stability equation. Approximate formulas are derived with the aid of which rapid preliminary computations may be made and the stability coefficients corrected for certain modifications of the airplane. A derivation of the lateral-dynamic-stability equations is included.
In this article, we make a few remarks on the role that attractors and inertial manifolds play in fluid mechanics problems. We then describe the role of incremental unknowns for approximating attractors and inertial manifolds when finite difference multigrid discretizations are used. The relation with direct numerical simulation and large eddy simulation is also mentioned.
Most reliability analysis techniques and tools assume that a system is used for a mission consisting of a single phase. However, multiple phases are natural in many missions. The failure rates of components, system configuration, and success criteria may vary from phase to phase. In addition, the duration of a phase may be deterministic or random. Recently, several researchers have addressed the problem of reliability analysis of such systems using a variety of methods. A new technique for phased-mission system reliability analysis based on Boolean algebraic methods is described. Our technique is computationally efficient and is applicable to a large class of systems for which the failure criterion in each phase can be expressed as a fault tree (or an equivalent representation). Our technique avoids state space explosion that commonly plague Markov chain-based analysis. A phase algebra to account for the effects of variable configurations and success criteria from phase to phase was developed. Our technique yields exact (as opposed to approximate) results. The use of our technique was demonstrated by means of an example and present numerical results to show the effects of mission phases on the system reliability.
We have monitored the evolution of the transient X-ray source GRO J0422+32 from approximately 2 weeks postdiscovery into its early decline phase at ultraviolet, optical, and radio wavelengths. Optical and ultraviolet spectra exhibit numerous, but relatively weak, high-excitation emission lines such as those arising from He II, N III, N V, and C IV superposed on an intrinsically blue continuum. High-resolution optical spectroscopy reveals line profiles which are double peaked, and in the case of the higher order Balmer lines, superposed on a broad absorption profile. The early outburst optical-ultraviolet continuum energy distribution is well represented by a two power-law fit with a break at approximately equal 4000 A. Radio observations with the Very Large Array (VLA) reveal a flat-spectrum source, slowly increasing in intensity at the earliest epochs observed, followed by an approximate power-law decay light curve with an index of -1. Light curves for each wavelength domain are presented and discussed. Notable are the multiple secondary outbursts seen in the optical more than 1 year postdiscovery, and spectral changes associated with secondary rises seen in the radio and UV. We find that the ultraviolet and optical characteristics of GRO J0422+32 as well as its radio evolution, are similar to other recent well-observed soft X-ray transients (also called X-ray novae) such as Cen X-4, A0620-00 (V616 Mon), and Nova Muscae 1991 (GS 1124-683), suggesting that GRO J0422+32 is also a member of that subclass of low-mass X-ray binaries. We present definitive astrometric determination of the source position, and place an upper limit of R approximately equals 20 from our analysis of the Palomar Observatory Sky Survey (POSS). Additionally, we derive distinct values for color excess from analysis of the optical (E(B-V) = 0.23) and ultraviolet (E(B-V) = 0.4) data, suggesting an intrinsic magnitude of 19-19.5 for the progenitor if it is mid-K dwarf. This leads to a likely range of 2.4-3.0 kpc for the source distance, which is consistent with our separate estimate of 2.4 +/- 0.4 kpc based on measurement of the NaD interstellar line profile. Adopting 2.4 kpc and E(B-V) = 0.23, the outburst absolute magnitude was M approximately equals 0.0, which is a typical value for this class of objects.
The problem of ion injection and acceleration at quasi perpendicular shocks has been the subject of some debate over the past two decades. It is widely known that these shocks efficiently accelerate particles that are well in the high-energy tail of the distribution. However, the issue of injection, or the acceleration of low-energy ions, has yet to reach a consensus. The fundamental issue is whether there is enough diffusion normal to the magnetic field for the particles to remain near the shock. Since transverse diffusion is a physical process that is not well understood in space plasmas, this is an important, and difficult issue to address. In this report, we will investigate the ion injection problem by performing test particle orbit integrations using synthesized turbulent fields. These fields are fully three-dimensional so that transverse diffusion is possible (cross-field diffusion is not possible in geometries where the electromagnetic fields are less than three dimensional). The synthesized fields are produced by superimposing a three-dimensional wave field on a background field. For completeness, we will compare the results from this model with the more well-established theories, such as the diffusive approximation and scatter-free shock drift acceleration. We will also compare these results with other numerical simulation techniques such as the well known hybrid simulation, and other test-particle calculations in which the shock fields are specified to have less than three dimensions. We will also discuss some recent relevant observations and how these compare with our results.
Experimental data on pressure distribution and heat transfer on a turbine airfoil were obtained over a range of Reynolds numbers from 0.75 to 7.0 x 10(exp 6) and a range of turbulence intensities from 1.8 to about 15%. The purpose of this study was to obtain fundamental heat transfer and pressure distribution data over a wide range of high Reynolds numbers and to extend the heat transfer data base to include the range or Reynolds numbers encountered in the Space Shuttle main engine turbopump turbines. The results of this study indicated that Reynolds number and turbulence intensity have a large effect on both the transition from laminar to turbulent flow and the resulting heat transfer. For a given turbulence intensity, heat transfer for all Reynolds numbers at the leading edge can generally be correlated with the Frossling number developed for lower Reynolds numbers. For a given turbulence intensity, heat transfer for the airfoil surfaces downstream of the leading edge can be approximately correlated with a dimensionless parameter. Comparisons of the experimental results were also made with a numerical solution from a two-dimensional Navier-Stokes code.
A research program is currently underway with the final objective of developing a fundamental understanding of the controlling mechanisms underlying the flammability diagrams of solid combustible materials and their derived fire properties. Given that there is a high possibility of an accidental fire occurring in a space-based facility, understanding the fire properties of materials that will be used in such facilities is of critical importance. With this purpose, the flammability diagrams of the materials, as those produced by the Lateral Ignition and Flame Spread Test (LIFT) apparatus and by a new forced flow device, the Forced Flow Ignition and Flame Spread Test (FIST) apparatus, will be obtained. The specific objective of the program is to apply the new flammability apparatus, which will more accurately reflect the potential ambient conditions of space-based environments, to the characterization of the materials for space applications. This paper presents a parametric study of oxidizer flow effects on the ignition curve of the flammability diagrams of PMMA. The dependence of the ignition delay time on the external radiant flux and either the sample width (LIFT) or the flow velocity (FIST) has been studied. Although preliminary, the results indicate that natural and forced convection flow changes, affect the characteristics of the ignition curves of the flammability diagrams. The major effect on the ignition time appears to be due to convective transfer variations at the fuel surface. At high radiant fluxes or high flow velocities, however, it appears that gas phase processes become increasingly important, affecting the overall ignition delay time. A numerical analysis of the solid fuel heating and pyrolysis has also been developed. The theoretical predictions approximate the experiments well for conditions in which the gas phase induction time is negligible.