Showing papers in "AIAA Journal in 1967"

Divergence in the Kalman Filter

Abstract: Under certain conditions, the orbit estimated by a Kalman filter has errors that are much greater than predicted by theory. This phenomenon is called divergence, and renders the operation of the Kalman filter unsatisfactory. This paper investigates the control of divergence in a Kalman filter used for autonomous navigation in a low earth orbit. The system studied utilizes stellar-referenced angle sightings to a sequence of known terrestrial landmarks. A Kalman filter is used to compute differential corrections to spacecraft position, spacecraft velocity, and landmark location. A variety of filter modifications for the control of divergence was investigated. These included the Schmidt-Pines analytical modification and an "empirical" modification based upon Pines' machine noise treatment. Several simplified approximations to the theoretically optimum analytical modifications were also investigated. The principal numerical results are presented in graphs of the magnitude of the error in estimated position and velocity vs time for sixteen orbits. These graphs compare actual position and velocity errors with the theoretical estimates furnished by the trace of the position and velocity covariance matrices. Numerical results indicate that a properly modified filter achieves a steady-state operating level.

Further experimental results for three- dimensional free jets.

Abstract: This paper presents a succinct exposition of further investigations into the bulk properties of three-dimensional, turbulent, incompressible jets, supplementing earlier research. Additional remarks based on recent experiments are made with regard to the axis velocity decays, the three flow regions, half-width boundaries, velocity profile similarity, approach to axisymmetry, mass entrainment, and momentum conservation and velocity irregularities in threedimensional jets.

Turbulent boundary-layer separation in front of a forward-facing step.

Abstract: A review of experiments concerned with the description of the steady flowfield produced by the separation of a turbulent boundary layer ahead of a forward-facing step is presented. The Mach number is restricted to the supersonic range and only two-dimensional flows are investigated. The dependence of the induced pressure field at the wall on Reynolds number, Mach number, and step height is considered. It is shown that the pressure rise in the separation region expressed in normalized form is independent of Mach number and Reynolds number and that the scale for the separation phenomena is the boundary-layer thickness. In addition, it was found that the plateau pressure rise is independent of Reynolds number for the turbulent regime and that the induced side force increases linearly with Mach number.

Rapid identification of linear and nonlinear systems.

Abstract: Rapid parameter identification system for linear time-invariant plant with only input and output measurable

Shock tunnel investigation of boundary-layer transition at M equals 5.5.

Abstract: The effects of nose bluntness, angle of attack, and boundary-layer cooling on boundarylayer transition on an 8° half-angle cone are presented. A small amount of bluntness was found to displace the transition location rearward. Greater amounts of bluntness produced a blunting transition reversal in that the rearward movement of transition ceased and additional blunting produced a forward displacement. The maximum rearward displacement from the cone tip was about 4.1 times that of a sharp cone. The swallowing distance was found to be an important correlation parameter. For the sharp cone, an angle of attack caused the transition location to move rearward on the windward meridian of the cone, with a 55% increase in transition distance at 10° angle of attack. On the leeward meridian, the transition location moved forward such that for 4° angle of attack, or greater, the transition distance was constant at about one-third of the value found for the zero-angle-of-attack case. For the two blunted cones tested, the transition location moved forward on both the windward and leeward meridians. A transition reversal was observed as the ratio of wall-toadiabatic temperature decreased from 0.58 to 0.25.

A square root formulation of the Kalman- Schmidt filter.

Abstract: Kalman filter alternate form extended to include multiple simultaneous correlated measurements, testing with ballistic model and using square root formulation for trajectory determination

Nonsteady burning phenomena of solid propellants - theory and experiments

Abstract: : Non-steady burning of solid propellants was investigated both theoretically and experimentally, with attention to combustion instability, transient burning during motor ignition, and extinction by depressurization. The theory is based on a one-dimensional model of the combustion zone consisting of a thin gaseous flame and a solid heat up zone. The non-steady gaseous flame behavior is deduced from experimental steady burning characteristics; the response of the solid phase is described by the time-dependent Fourier equation. Solutions were obtained for dynamic burning rate, flame temperature, and burnt gas entropy under different pressure variations; two methods were employed. First, the equations were linearized and solved by standard techniques. Then, to observe nonlinear effects, solutions were obtained by digital computer for prescribed pressure variations. One significant result is that a propellant with a large heat evolution at the surface is intrinsically unstable under dynamic conditions even though a steady-state solution exists. Another interesting result is that the gas entropy amplitude and phase depend critically on the frequency of pressure oscillation and that either near-isentropic or near-isothermal oscillations may be observable. Experiments with an oscillating combustion chamber and with a special combustor equipped for sudden pressurization tend to support the latter conclusion. (Author)

A cylindrical shell discrete element.

Abstract: The development of the stiffness and consistent mass matrices for a finite cylindrical shell element is reported. The derivation of these matrices is based upon linear behavior and thin-shell assumptions. Expressing the assumed displacement state over the middle surface of the cylindrical shell element as products of one-dimensional, first-order Hermite interpolation formulas, it is possible to insure that the displacement state for the assembled set of cylindrical elements is geometrically admissible. Mono tonic convergence of the total potential energy is therefore assured as the modeling is successively refined, since the assumed displacement pattern satisfies the admissibility requirements in the statement of the principle of minimum potential energy. A numerical example is included to demonstrate the effectiveness of this cylindrical shell discrete element.

Design of minimum mass structures with specified natural frequencies.

Abstract: A numerical procedure is developed for proportioning the members of an elastic structure so that one or more of its natural frequencies assume given values and the total structural mass is a minimum. It is assumed that the structure is required to support nonstructural masses and that the vibratory inertia loads due to structural masses must be of appreciable magnitude relative to those generated by nonstructural masses. The principal development is based on a finite element idealization and matrix formulation in which the inertia and stiffness matrices of each structural element are proportional to the mass of the element. Lagrange multipliers are employed to introduce the free vibration equations as constraint conditions.

Imperfection-sensitivity of eccentrically stiffened cylindrical shells.

Abstract: Imperfection sensitivity of eccentrically axial and ring stiffened cylinderal shells under axial compression and hydrostatic pressure

Heat and mass transfer at a general three- dimensional stagnation point.

Abstract: Simultaneous effects of heat and mass transfer on properties of stagnation point flows analyzed over full range of velocity gradients

Observations on the dynamic behavior of large flexible bodies in orbit.

Abstract: 9 Warren, W R and Diaconis, N S, "Air arc simulation of hypersonic environments," ARS Progress in Astronautics and Rocketry: Hypersonic Flow Research, edited by F R Riddell (Academic Press Inc, New York, 1962), Vol 7, pp 663-700; also General Electric Co, GE MSD TIS R62SD25 (April 1962) 10 Eschenroader, A W, Boyer, D W, and Hall, J G, "Exact solutions for non-equilibrium expansions of air with coupled chemical reactions," Cornell Aeronautical Labs, Rept AF-1413A-l, Air Force Office of Scientific Research 622 (May 1961) 11 Boison, J C and Curtiss, H A, "An experimental investigation of blunt body stagnation point velocity gradient," ARS J 29,130-135(1959) 12 Scala, S M and Baulknight, C W, "Transport and thermodynamic properties in a hypersonic laminar boundary layer, Part 2, Applications," ARS J 30, 329-336 (1960)

Ion-Neutral Propulsion in Atmospheric Media

Abstract: A basic theoretical and experimental investigation of an aerodynamic corona discharge propulsion system is presented. A one-dimensional, constant-area analytical model with multiple point, space-charge-limited emission of negative ions is considered. Explicit relations expressing performance are derived for this system. Experimental results verify the validity of the theoretical expressions and indicate that the energy conversion efficiency leading to propulsion is approximately 1%. The experiments further indicate that the remaining energy manifests itself in the form of heat. Ion mobility is found to be the most decisive factor in determining system performance. Results suggest that future studies should be directed toward lowering the effective ion mobility to achieve an acceptable level of propulsive power efficiency.

Study of electric arc behavior with superimposed flow.

Abstract: Symptomatic behavior and anode regimes of arc for electric arc with superimposed subsonic flow of argon

A modification of the differential approximation for radiative transfer.

Abstract: In radiation-gas dynamics problems, frequent use has been made of the differential approximation, which involves replacing the integral equation of transfer by a differential equation for the flux. This differential approximation may be inaccurate at small optical depths if external radiation sources are present. A procedure that correctly accounts for the external radiation is developed in this paper. The resulting modified differential approximation is first applied to the one-dimensional problem of a medium in radiative equilibrium between two parallel walls held at different temperatures. The calculated flux is superior to that obtained using the unmodified differential approximation, especially in the optically thin limit where the modified differential approximation gives the correct (though small) absorption of the medium. The modified differential approximation is also used to solve the two-dimensional problem of linearized flow of a radiating gas over a wall with a sinusoidal temperature distribution. With a characteristic optical depth defined with respect to the wavelength of the wall temperature variation, it is found that the modified differential approximation gives accurate values for the flow variables over the entire opacity range, yielding the correct values in the optically thin limit. On the other hand, the unmodified differential approximation yields values that become increasingly inaccurate as the characteristic optical depth becomes small.

Breakup rate and penetration of a liquid jet in a gas stream.

Abstract: An analysis of a disintegrating liquid jet penetrating a high-speed gas stream is presentedc Conditions are analyzed for which two types of waves (capillary and acceleration) will be amplified and will account for the jet disintegration. The results in the form of jet trajectories and penetration are found to be consistent with experimental data (180 cases, 8 liquids, suband supersonic flows). In each case, a parameter is determined by comparison with experiment and found to be approximately constant.

On liquid droplet combustion at high pressures.

Abstract: 2 to 5. It is found that in the upstream there is a wake or heat transfer along the x axis and this wake is larger for higher freestream temperature. On the x axis in the upstream the temperature has a significant change in a short distance near the leading edge and becomes essentially uniform beyond the station x/L = —1.9 (not shown). In the y direction the radiation has a large effect on the temperature field in the range 0 < y/L < 0.2. All of these temperature variations are larger in the case of higher freestream temperatures. In the downstream the temperature variation in the vicinity of the plate should be determined from the boundary-layer equations. Here we show the only results for the optically thick case. For the optically thin case the procedure is quite the same. For gases of finite optical depth the energy equation is a nonlinear integro-differential equation of high complexity; this method may still be applicable but needs extensive computing time.

General instability and face wrinkling of sandwich plates - Unified theory and applications.

Abstract: The governing equations and applicable boundary conditions for sandwich plates with ideally orthotropic cores (honeycomb) are presented. The equations and boundary conditions are the first to be derived variationally with both transverse shear and normal strain effects included. The variational development, based on potential energy and the use of Lagrange multipliers to introduce face-core continuity requirements, leads to the desired results. It is noted that for symmetric buckling there are two multiple-choice boundary conditions per plate edge, and for antisymmetric buckling there are five multiple-choice boundary conditions per plate edge. The theory presented lends itself to certain exact solutions of the governing equations, where boundary conditions permit, and approximate solutions via the Rayleigh-Ritz procedure for more general problems. Buckling criteria are presented in the form of design charts, including both general instability and face wrinkling, for plates with one type of simple support, and for plates with one type of clamped loaded edges and simply supported unloaded edges. The ramifications of the present work relative to existing highly restricted solutions are examined and discussed.

A study of three-dimensional, incompressible turbulent wall jets

Abstract: : The report presents an experimental investigation of the mean properties of turbulent, three-dimensional, incompressible air jets issuing into a quiescent air ambient from various rectangular orifices parallel to, and at the surface of, a flat plate. An analytical approach to estimate the shear stress distribution at the plate is also presented. The flow field of a three- dimensional wall jet is found to be characterized by three distinct regions in the axis velocity decay. From the results obtained it is concluded that for three-dimensional wall jets the maximum velocity in the flow in the near field exhibits a decay rate dependent on orifice geometry, while far downstream of the jet exit it decays at the same rate as that in a radial wall jet flow field independent of orifice geometry. Furthermore, it is shown that the growth of the mixing layer normal to the plate is apparently independent of orifice shape while the near field spanwise growth is affected by initial geometry. Irregularities in the spanwise distribution of streamwise mean velocity attest to the strong three-dimensionality in the near field of the wall jets studied. These irregularities are manifested as local excesses, or defects, in the velocity profile. Such results indicate that the characterization of the wall jet flow field generated by a finite slot as quasi-two-dimensional may be of questionable validity.

A multicomponent boundary layer chemically coupled to an ablating surface.

Abstract: Based upon an accurate approximation for binary diffusion coefficients, simplified equations are presented for a multicomponent boundary layer with unequal diffusion coefficients for all species. Correlation equations are then presented for representing the multicomponent boundary layer in terms of convective transfer coefficients. These equations are based upon analogy between the form of the present species conservation equation and that for the case of equal diffusion coefficients. The form chosen for the correlation equations is such that they should be valid for a wide range of boundary conditions. These equations are then chemically coupled to an ablating surface, allowing arbitrary chemical composition of the ablation material and boundary-layer-edge gas. Results of some numerical calculations are presented which demonstrate transient response of charring materials in rocket nozzle environments with and without the assumption of equal diffusion coefficients.

A method for deriving structural influence coefficients from ground vibration tests.

Abstract: A method is presented for finding the structural influence coefficients of an arbitrarily restrained system from the experimental results of an effectively free-free ground vibration test. A theoretical example is presented to illustrate the general procedure and to demonstrate the manner of convergence of the method. A discussion of nonorthogonality of measured modes is given, and a practical application is made to a delta wing specimen for which influence coefficients, modes, and frequencies have been measured, and the degree of correlation is discussed. Finally, a method for finding a complex influence coefficient matrix that includes structural damping is suggested for use in oscillatory aeroelastic analyses. Nomenclature

Comparing theory and experiment for the supersonic flutter of circular cylindrical shells.

Abstract: The flutter boundaries obtained from recent experiments on the supersonic flutter of circular cylindrical shells are compared with various theoretical predictions. Following Voss, a modal analysis of Donnell's equations is used in conjunction with piston theory and the potential solution of Leonard and Hedgepeth. It was found that the pressurized cylindrical shells fluttered at a lower level of freestream energy than predicted by either theory. Of the two results, that using piston theory appears to correspond more closely to the experiment. The influence of the viscous boundary layer is discussed in the light of recent investigations, and it is concluded that for the thicknesses of boundary layer present in the experiments this influence is not overly important. A nonlinear analysis is presented for calculating amplitudes of flutter based on a two-mode, piston-theory approximation. The shallow-shell equations of Marguerre are solved by Galerkin's method, and a limit-cycle solution is obtained by the method of Krylov and Bogoliubov.

Minimum mass bar for axial vibration at specified natural frequency.

Abstract: Minimum mass bar design for axial vibration of beam with load distribution at specified natural frequency