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GRAPE computer program generates two-dimensional finite-difference grids about airfoils and other shapes by use of Poisson differential equation. GRAPE can be used with any boundary shape, even one specified by tabulated points and including limited number of sharp corners. Numerically stable and computationally fast, GRAPE provides aerodynamic analyst with efficient and consistant means of grid generation.
Time-stationary solutions to the Vlasov-Poisson equation for ion holes and double layers were examined along with particle simulations which pertain to recent observations of small amplitude (e phi)/t sub e approx. 1 electric field structures on auroral field lines. Both the time-stationary analysis and the simulations suggest that double layers evolve from holes in ion phase space when their amplitude reaches (e phi)/t sub e approx. 1. Multiple small amplitude double layers which are seen in long simulation systems and are seen to propagate past spacecraft may account for the acceleration of plasma sheet electrons to produce the discrete aurora.
Synchronous time division multiplexing is analyzed. Packets of information arrive at the system as a compound Poisson process, and are transmitted only during individual periodic intervals. Packet arrivals are blocked (lost) if the system has a finite capacity and is congested. Using the theory of semiregenerative processes, the distribution of the number of packets in the system (system size) is found. This nonstationary distribution is used to determine the complete system behavior, including the delay distributions, the blocking probability, and the density of the system size at arrival instants. Numerical examples illustrate applications of the results given.
A numerical procedure is derived for the solution of the Vlasov-Poisson system of equations in two phase-space variables. Derivatives with respect to the phase-space variables are approximated by a weighted sum of the values of the distribution function at property chosen neighboring points. The resulting set of ordinary differential equations is then solved by using an appropriate time intergration scheme. The accuracy of the proposed method is tested with some simple model problems. The results for the free streaming case, linear Landau damping, and nonlinear Landau damping are investigated and compared with those of the splitting scheme. The proposed method is found to be very accurate and efficient.
Boron/aluminum can develop significant internal matrix cracking when fatigued. These matrix cracks can result in a 40 percent secant modulus loss in some laminates, even when fatigued below the fatigue limit. It is shown that the same amount of fatigue damage will develop during stress or strain-controlled tests. Stacking sequence has little influence on secant modulus loss. The secant modulus loss in unidirectional composites is small, whereas the losses are substantial in laminates containing off-axis plies. A simple analysis is presented that predicts unnotched laminate secant modulus loss due to fatigue. The analysis is based upon the elastic modulus and Poisson's ratio of the fiber and matrix, fiber volume fraction, fiber orientations, and the cyclic-hardened yield stress of the matrix material. Excellent agreement was achieved between model predictions and experimental results. With this model, designers can project the material stiffness loss for design load or strain levels and assess the feasibility of its use in stiffness-critical parts.
The tensile stress-strain behavior of a variety of graphite/epoxy laminates was examined. Longitudinal and transverse specimens from eleven different layups were monotonically loaded in tension to failure. Ultimate strength, ultimate strain, and strss-strain curves wee obtained from four replicate tests in each case. Polynominal equations were fitted by the method of least squares to the stress-strain data to determine average curves. Values of Young's modulus and Poisson's ratio, derived from polynomial coefficients, were compared with laminate analysis results. While the polynomials appeared to accurately fit the stress-strain data in most cases, the use of polynomial coefficients to calculate elastic moduli appeared to be of questionable value in cases involving sharp changes in the slope of the stress-strain data or extensive scatter.
An implicit finite-difference algorithm is developed for the numerical solution of the incompressible three dimensional Navier-Stokes equations in the non-conservative primitive-variable formulation. The flow field about an airfoil spanning a wind-tunnel is computed. The coordinate system is generated by an extension of the two dimensional body-fitted coordinate generation techniques of Thompson, as well as that of Sorenson, into three dimensions. Two dimensional grids are stacked along a spanwise coordinate defined by a simple analytical function. A Poisson pressure equation for advancing the pressure in time is arrived at by performing a divergence operation on the momentum equations. The pressure at each time-step is calculated on the assumption that continuity be unconditionally satisfied. An eddy viscosity coefficient, computed according to the algebraic turbulence formulation of Baldwin and Lomax, simulates the effects of turbulence.
Delamination of composite materials has been investigated with emphasis on the relationship between the engineering properties of the individual layers and edge effects. It is shown that interlaminar shear stresses are primarily a function of the mismatch in coefficients of mutual influence which can be as much as ten times greater than the mismatch in Poisson's ratio. The mismatch in coefficients of mutual influence has a high peak value in the 10-15 deg range for plus or minus theta laminates (where theta is the angle of fiber orientation measured from the axis of the coupon). This mismatch is reduced by a factor of two when the plus or minus theta layers are interspersed between 0 and 90 deg layers. Application of the results to composite design is illustrated by an example.
Measurements of electron density, plasma potential, and mean ion mass from the Explorer 31 satellite, and measurements of ion current, plasma potential, and ion composition from the Atmosphere Explorer C satellite were used in a comparative study with Parker's theory regarding the charged particle distribution in the near wake of an ionospheric satellite (1976). It is shown that theory and experiment agree fairly well in the angle-of-attack range between 90 and 135 deg. In the maximum rarefaction zone (between 145 and 180 deg), however, the theoretical model overestimates the measured ion depletion by several orders of magnitude. A comparison between theory and the Explorer 31 electron measurements shows that the theory again overestimates the electron depletion. These discrepancies are mainly due to the use of a steady-state theory and a single ion equation (using a mean ion mass). Improved agreement between theory and experiment can be obtained by the use of the time-dependent Vlasov-Poisson equations with separate equations for the various ion species.
The effects of stresses induced by the lamination of off-axis plies to O-deg lamina on the development of damage during the fatigue loading of the O-deg plies are discussed. The transverse normal stresses in the plane of the laminae and the laminate created by the laminating constraints when an axial force is applied to the laminate are calculated in terms of a differential Poisson ratio between the ply in question in the unconstrained and constrained states, and significant differences in the constraint environments of an unnotched specimen joined to plies of 45 and 90 deg inclination are noted which correspond to an increase in longitudinal splitting in the 90 deg case and a marked decrease in longitudinal splitting in the 45 deg case. If a notch is present, shear and crack-opening damage is found to be very effectively suppressed in 45-deg laminates, and less so in the 90-deg case. It is pointed out that whereas the 45-deg laminate represents the least damage situation, it does not have the greatest notched strength. It is concluded that an understanding and prediction of damage development in laminates requires knowledge of the stress fields caused by the lamination constraints.
An order-of magnitude analysis of the subsonic, three-dimensional, steady time-averaged Navier-Stokes equations for semibounded aerodynamic juncture geometries yields the parabolic Navier-Stokes simplification. The numerical solution of the resultant pressure Poisson equation is cast into complementary and particular parts, yielding an iterative interaction algorithm with an exterior three-dimensional potential flow solution. A parabolic transverse momentum equation set is constructed, wherein robust enforcement first-order continuity effects is accomplished using a penalty differential constraint concept within a finite element solution algorithm. A Reynolds stress constitutive equation, with low turbulence Reynolds number wall functions, is employed for closure, using parabolic forms of the two-equation turbulent kinetic energy-dissipation equation system. The algorithm is employed to predict the three-dimensional turbulent flowfield in the juncture region formed by two intersecting parabolic arcs at a free-stream Mach-number of 0.08, and Re/C = 600,000/m.
This paper presents an analytical approach for assessing the effect of pulsed RFI on the error probability of a coherent phase-shift keyed signal through a nonlinear satellite repeater. The RFI is assumed to affect the uplink channel and to consist of CW pulses with random power levels and arriving randomly in time with a Poisson distribution. A model to approximate the effect of intermodulation products is introduced and the error probability conditioned on the output of the satellite repeater is computed. The classical moment technique is then used as an efficient method of averaging the conditional error probability over the numerous random parameters associated with the uplink signal.
It is noted that, for most of the mechanisms for the strong electric fields that characterize the narrow regions in which there is acceleration and precipitation of ring current and/or plasma-sheet plasma, certain effects must be taken into account in simulations of auroral electric fields. The effects are those of auroral particle anisotropy, of mirror forces due to the inhomogeneous geomagnetic field, of auroral electron backscatter by the atmosphere, and of electron trapping by the combination of magnetic mirroring and electrostatic forces. What is more, the effects of the very strong perpendicular electric field must also be taken into account in a kinetic description of the Poisson equation in order to achieve a unified theory of the auroral electrostatic structure. Progress in these areas during the past few years is reviewed. It is shown that particle anisotropies and mirror forces can account for some basic electrostatic features of the quiet arc, while additional effects may be occurring in strong events in which the parallel potential drop is more than about 10 kV.
A 1d unmagnetized double layer simulation is presented along with analytic considerations of the Langmuir-Bohm criterion for double layer formation. It is found that this requirement of large electron drift is not reduced by trapped thermal electron and ion populations; the assumption of a nonthermal population which requires the preexistence of the double layer cannot reduce the required electron drift. It is noted that negative charge density spikes and holes in ion phase space accompany the double layer. A magnetized BGK mode solution to Poisson's equation for the potential profile perpendicular to B for cold counter-streaming electrons and ions shows how the spatial structure changes in a magnetized plasma.
Two-dimensional curvilinear coordinates are used to solve the incompressible Navier-Stokes equations, in conjunction with approximate factorization for the solution of the momentum equation and the successive overrelaxation by lines method for the solution of a Poisson equation for the pressure. The combined algorithm, although not fully explicit, is marginally stable at Reynolds numbers lower than 10,000 and time increments of 0.01. Pressure distributions calculated for attack angles of zero and 6 deg are of the same shape as the experimental curves, but are shifted to one side.
Numerical simulations of the dynamics of double layers that form in response to an applied potential drop across a plasma are carried out for plasmas of lengths much greater than previously considered. The evolution of finite-size plasmas of lengths 100, 200 and 400 Debye lengths at the low-potential end of the simulation region was followed by the solution of the Vlasov and Poisson equations. Results show that the double layer moves towards the high-potential side of the layer, at a speed directly dependent on the length of the plasma. The moving double layer is accompanied by a moving density front which is similar to an ion acoustic shock created by the expansion of a high-density plasma into a low-density plasma, as well as plasma heating and evacuation, electron and ion current interruptions and recovery. Double layer formation, motion, and accompanying phenomena are found to repeat periodically. Results are in good agreement with laboratory experiments, and may be used to explain certain phenomena observed in auroral plasmas.
A theory is presented for the steady-state potential of insulated surfaces near exposed high voltages. The term 'insulated surfaces' is used to mean either dielectric surfaces or electrically isolated metallic surfaces. The potential is bounded below by the zero of the material's I-V curve assuming total suppression of secondary electrons, and above by assuming total extraction of secondaries. Within these bounds, the material's surface potential is determined consistently with the solution to Poisson's equation external to the vehicle. The theory is compared with rocket experiments and with SCATHA satellite data. Also, an explanation is suggested for the observed 'snapover' of solar cell coverslips from near plasma ground potential to near the potential of positively biased interconnects with increasing bias voltage.
The throughput performance of a TDMA channel with finite buffer capacity for transmitting data messages is considered. Each station has limited message buffer capacity and has Poisson message arrivals. Message arrivals will be blocked if the buffers are congested. Using the embedded Markov chain model, the solution procedure for the limiting system-size probabilities is presented in a recursive fashion. Numerical examples are given to demonstrate the tradeoffs between the blocking probabilities and the buffer sizing strategy.