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Equations of motion and stability criteria for predicting stability and control characteristics of elastic aircraft
The boundary conditions are demonstrated for the quasi-one-dimensional Euler equations with the extension to two and three dimensions being straightforward. In this application an implicit finite-difference scheme is employed with the boundary conditions being applied implicitly. The boundary application uses both characteristic extrapolations and evaluations which distinguishes it from other theories. Flow fields with shocks are calculated with inflow-outflow conditions of supersonic-subsonic and subsonic-subsonic flow.
Determining the distribution of statistics by sampling was investigated. Characteristic functions, the quadratic regression problem, and the differential equations for the characteristic functions are analyzed.
This work formulates a method for the modeling of material damping characteristics in plates. The Sophie German equation of classical plate theory is modified to incorporate hysteresis effects represented by complex stiffness using the transfer function approach proposed by Golla and Hughes, (1985). However, this procedure is not limited to this representation. The governing characteristic equation is decoupled through separation of variables, yielding a solution similar to that of undamped classical plate theory, allowing solution of the steady state as well as the transient response problem.
One-dimensional elastic wave problems treated by hyperbolic partial differential equations and analyzed by method of characteristics
The prediction characteristics and capabilities of two popular two-equation low-Reynolds-number turbulence models (Jones, Launder 1972; Lam, Bremhorst 1981) have been evaluated with respect to the prediction of transition of a flat plate under the influence of free-stream turbulence. The sensitivity of the predictions to free-stream turbulence intensity, initial starting location of the calculation, and the assumed initial starting profiles for k and epsilon has been determined and presented. Although both models predict the correct qualitative characteristics of transition, they also exhibit significant quantitative deficiencies with regard to both the predicted location and the length of transition. A modification to the production term in the turbulent kinetic energy equation is proposed which is based on a simple stability criterion and correlated to the free-stream turbulence level. The modification becomes inactive in the fully turbulent regime, but is shown to improve both the qualitative and quantitative characteristics of the transition predictions.
An improved method is described for correcting the zeroth order (free stream) characteristics to obtain a uniformly valid first order solution to the exact equations of motion for a compressible fluid. The method is based on constructing first order bicharacteristic lines from the system of ordinary differential equations belonging to the exact equation for the characteristic surface. Calculated sonic boom signatures are compared with experiments conducted at Langley Research Center on a cone-cylinder at Mach numbers 2.96, 3.83, and 4.63. Theory and experiment agree well over the entire Mach number range.
Charge-state model for lead/acid batteries proposed as part of effort to make equivalent of fuel gage for battery-powered vehicles. Models based on equations that approximate observable characteristics of battery electrochemistry. Uses linear equations, easier to simulate on computer, and gives smooth transitions between charge, discharge, and recuperation.
The spherical harmonic analysis of cosmic ray neutron data from the worldwide network neutron monitor stations during the years, 1966 to 1969 was carried out. The second zonal harmonic component obtained from the analysis corresponds to the Pole-Equator anisotropy of the cosmic ray neutron intensity. Such an anisotropy makes a semiannual variation. In addition to this, it is shown that the Pole-Equator anisotropy makes a variation depending on the interplanetary magnetic field (IMF) sector polarities around the passages of the IMF sector boundary. A mechanism to interpret these results is also discussed.
The proposed paper will describe the state of the art associated with numerical solution of the full or exact velocity potential equation for solving transonic, external-aerodynamic flows. The presentation will begin with a review of the literature emphasizing research activities of the past decade. Next, the various forms of the full or exact velocity potential equation, the equation's corresponding mathematical characteristics, and the derivation assumptions will be presented and described in detail. Impact of the derivation assumptions on simulation accuracy, especially with respect to shock wave capture, will be presented and discussed relative to the more complete Euler or Navier-Stokes formulations. The technical presentation will continue with a description of recently developed full potential numerical approach characteristics. This description will include governing equation nondimensionalization, physical-to-computational-domain mapping procedures, a limited description of grid generation requirements, the spatial discretization scheme, numerical implementation of boundary conditions, and the iteration scheme. The next portion of the presentation will present and discuss numerical results for several two- and three-dimensional aerodynamic applications. Included in the results section will be a discussion and demonstration of a typical grid refinement analysis for determining spatial convergence of the numerical solution and level of solution accuracy. Computer timings for a variety of full potential applications will be compared and contrasted with similar results for the Euler equation formulation. Finally. the presentation will end with concluding remarks and recommendations for future work.
The propagation of waves in a random medium is studied in the 'quasi-optics' and the 'Markov random process' approximations. Under these assumptions, a Fokker-Planck equation satisfied by the characteristic functional of the random wave field is derived. A complete set of moment equations with different transverse coordinates and different wave numbers is then obtained from the Fokker-Planck equation of the characteristic functional. The application of those results to the pulse smearing of the pulsar signal and the frequency correlation function of the wave intensity in interstellar scintillation is briefly discussed.
The evolution of unsteady boundary layers on oscillating airfoils is investigated by solving the governing equations by the Characteristic Box scheme. The difficulties associated with computing the first profile on a given time line, and the velocity profiles with partial flow reversal are solved. A sample calculation is performed for an external velocity distribution typical of those found near the leading edge of thin airfoils. The viability of the calculation procedure is demonstrated.
The evolution of unsteady boundary layers on oscillating airfoils is investigated by solving the governing equations by the Characteristic Box scheme. The difficulties associated with computing the first profile on a given time line, and the velocity profiles with partial flow reversal are solved. A sample calculation is performed for an external velocity distribution typical of those found near the leading edge of thin airfoils. The viability of the calculation procedure is demonstrated. Previously announced in STAR as N81-28391
Characteristics of microwave circuits predicted accurately. Equations for propagation of quasitransverse electric and magnetic (TEM) waves along thin films of high-critical-temperature superconductors constitute basis of mathematical model useful in design of coplanar-waveguide, microstrip, and stripline microwave circuits. Model incorporated into older commercial software for computer-aided design of microwave circuit.
A derivation is presented of a local preconditioning matrix for multidimensional Euler equations, that reduces the spread of the characteristic speeds to the lowest attainable value. Numerical experiments with this preconditioning matrix are applied to an explicit upwind discretization of the two-dimensional Euler equations, showing that this matrix significantly increases the rate of convergence to a steady solution. It is predicted that local preconditioning will also simplify convergence-acceleration boundary procedures such as the Karni (1991) procedure for the far field and the Mazaheri and Roe (1991) procedure for a solid wall.
A theory of rotating stall, based on single parameters for blade-passage lag and external-flow lag and a given compressor characteristic yields limit cycles in velocity space. These limit cycles are governed by Lienard's equation with the characteristic playing the role of nonlinear damping function. Cyclic integrals of the solution determine stall propagation speed and the effect of rotating stall on average performance. Solution with various line-segment characteristics and various throttle settings are found and discussed. There is generally a limiting flow coefficient beyond which no solution is possible; this probably represents stall recovery. This recovery point is independent of internal compressor lag, but does depend on external lags and on the height-to-width ratio of the diagram. Tall diagrams and small external lags (inlet and diffusor) favor recovery. Suggestions for future theoretical and experimental research are discussed.
Reflection laws of high order elliptic differential equations in two independent variables with constant coefficients and unequal characteristics across analytic boundary conditions
A description is given of some properties of the characteristic exponents of the general three-body problem. The variational equations on which the analysis is based are obtained by linearizing the Lagrangian equations of motion in the neighborhood of a given known solution. Attention is given to the fundamental matrix of solutions, the characteristic equation, the three trivial solutions of the variational equations of the three-body problem, symmetric periodic orbits, and the half-period properties of symmetric periodic orbits.