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NASA NTRS1992

Numerical simulation of plasma transport driven by the Io torus

The Rice convection model (RCM) has been modified to a form suitable for Jupiter (RCM-J) to study plasma interchange motion in and near the Io plasma torus. The net result of the interchange is that flux tubes, heavily loaded with torus plasma, are transported outward, to be replaced by tubes containing little low-energy (less than 1 keV) plasma. The process is numerically simulated in terms of time evolution from an initial torus that is longitudinally asymmetric and with gradually decreasing density outward from Io's orbit. In the simulations, the nonlinear stage of the instability characteristically exhibits outreaching fingers of heavily-loaded flux tubes that lengthen at an accelerating rate. The principal finding is that the primary geometrical form of outward transport of torus plasma in Jupiter's magnetosphere is through long, outward-moving fingers of plasma. In the simulations, the fingers mainly form in the active sector of the Io torus (the heavier side of the asymmetric torus), and they are spaced longitudinally roughly 20 deg apart.

Yang, Y. S.↗

NASA NTRS1993

Numerical Simulation of a High Mach Number Jet Flow

The recent efforts to develop accurate numerical schemes for transition and turbulent flows are motivated, among other factors, by the need for accurate prediction of flow noise. The success of developing high speed civil transport plane (HSCT) is contingent upon our understanding and suppression of the jet exhaust noise. The radiated sound can be directly obtained by solving the full (time-dependent) compressible Navier-Stokes equations. However, this requires computational storage that is beyond currently available machines. This difficulty can be overcome by limiting the solution domain to the near field where the jet is nonlinear and then use acoustic analogy (e.g., Lighthill) to relate the far-field noise to the near-field sources. The later requires obtaining the time-dependent flow field. The other difficulty in aeroacoustics computations is that at high Reynolds numbers the turbulent flow has a large range of scales. Direct numerical simulations (DNS) cannot obtain all the scales of motion at high Reynolds number of technological interest. However, it is believed that the large scale structure is more efficient than the small-scale structure in radiating noise. Thus, one can model the small scales and calculate the acoustically active scales. The large scale structure in the noise-producing initial region of the jet can be viewed as a wavelike nature, the net radiated sound is the net cancellation after integration over space. As such, aeroacoustics computations are highly sensitive to errors in computing the sound sources. It is therefore essential to use a high-order numerical scheme to predict the flow field. The present paper presents the first step in a ongoing effort to predict jet noise. The emphasis here is in accurate prediction of the unsteady flow field. We solve the full time-dependent Navier-Stokes equations by a high order finite difference method. Time accurate spatial simulations of both plane and axisymmetric jet are presented. Jet Mach numbers of 1.5 and 2.1 are considered. Reynolds number in the simulations was about a million. Our numerical model is based on the 2-4 scheme by Gottlieb & Turkel. Bayliss et al. applied the 2-4 scheme in boundary layer computations. This scheme was also used by Ragab and Sheen to study the nonlinear development of supersonic instability waves in a mixing layer. In this study, we present two dimensional direct simulation results for both plane and axisymmetric jets. These results are compared with linear theory predictions. These computations were made for near nozzle exit region and velocity in spanwise/azimuthal direction was assumed to be zero.

Hayder, M. Ehtesham↗

NASA NTRS1962

The Restricted Three-Body-Problem as a Perturbation of Euler's Problem of Two Fixed Centers and Its Application to Lunar Trajectories

The restricted Three-Body-Problem considers the motion of an infinitesimal mass under the gravitational attraction of two finite masses, which revolve about their common center of gravity in coplanar circles. It is well known that Euler's problem of two fixed centers, consisting of the motion of an infinitesimal mass under the gravitational attraction of two finite masses fixed in space, can be solved by elliptic functions. The idea presented here is to take the solution of Euler's problem as the solution of the restricted Three-Body-Problem by allowing the initial values to be functions of time now. Differential equations for the perturbed initial values are established. These equations can be given in closed form by using the fact that the transformation to the perturbed initial values of Euler's problem is canonical. Thus, an approximation can be obtained for the solution of the restricted Three-Body-Problem. The method can also be used to represent classes of neighboring trajectories for guidance purposes.

Euler equation↗

NASA NTRS1973

Evaluation of glide paths for landing a VTOL airplane using linear regulator theory.

A method of evaluating certain characteristics of approach paths for VTOL airplanes is presented which is based on the solution of the matrix Riccati equation to obtain an optimal state variable feedback controller. The longitudinal equations of motion of the airplane are linearized about a preselected path and the resulting system of equations is treated as a linear, time-varying regulator. The controller which minimizes a quadratic cost function is applied to the linearized system to determine the airplane's ability to return to the prescribed path given a specified initial error in altitude. The procedure is applied to the XC-142A, tilt-wing, V/STOL airplane, under decelerating approach conditions with a glide path consisting of two segments, the first having a smaller angle of descent than the second.

Reid, G. F.↗

NASA NTRS1992

Transient pool boiling in microgravity

Transient nucleate pool boiling experiments using R113 are conducted for short times in microgravity and in earth gravity with different heater surface orientations and subcoolings. The heating surface is a transparent gold film sputtered on a quartz substrate, which simultaneously provides surface temperature measurements and permits viewing of the boiling process from beneath. For the microgravity experiments, which have uniform initial temperatures and no fluid motion, the temperature distribution in the R 113 at the moment of boiling inception is known. High speed cameras with views both across and through the heating surface record the boiling spread across the heater surface, which is classified into six distinct categories.

Ervin, J. S.↗

NASA NTRS1993

Unsteady, three-dimensional, Navier-Stokes simulations of multistage turbomachinery flows

Hub corner stall regions, endwall boundary layers, tip leakage flows and airfoil wakes combine to form the 3D flowfields found in axial turbomachines. Turbomachinery flow fields are also inherently unsteady because of the relative motion between rotor and stator airfoils. This relative motion causes complex time-varying aerodynamic interactions to occur between the different aerodynamic structures and the rotor and stator airfoils. It is necessary to understand the 3D unsteady aerodynamics associated with these interactions in order to design turbomachines that are both lightweight and compact as well as reliable and efficient. The current study uses a time-accurate 3D thin-layer Navier-Stokes zonal approach to investigate the unsteady aerodynamics of multistage turbines and compressors. Relative motion between rotor and stator airfoils is accounted for by the use of systems of patched and overlaid grids. Time-averaged surface pressures, surface flow visualizations, and time-averaged flow field contours have been computed for a 1 1/2-stage turbine and are in good agreement with experimental data. This favorable comparison represents an initial validation of the current method for unsteady computations of multistage turbomachinery flows.

Gundy-Burlet, Karen L.↗

NASA NTRS1967

Performance of 26 Meter Diameter Ringsail Parachute in a Simulated Martian Environment

Inflation, drag, and stability characteristics of an 85.3-foot (26-meter) nominal diameter ringsail parachute deployed at a Mach number of 1.15 and at an altitude of 132,600 feet (40.42 kilometers) were obtained from the first flight test of the Planetary Entry Parachute Program. After deployment, the parachute inflated to the reefed condition. However, the canopy was unstable and produced low drag in the reefed condition. Upon disreefing and opening to full inflation, a slight instability in the canopy mouth was observed initially. After a short time, the fluctuations diminished and a stable configuration was attained. Results indicate a loss in drag during the fluctuation period prior to stable inflation. During descent, stability characteristics of the system were such that the average pitch-yaw angle from the local vertical was less than 10 degrees. Rolling motion between the payload and parachute canopy quickly damped to small amplitude.

Whitlock, Charles H.↗

NASA NTRS2010

Comet Gas and Dust Dynamics Modeling

This software models the gas and dust dynamics of comet coma (the head region of a comet) in order to support the Microwave Instrument for Rosetta Orbiter (MIRO) project. MIRO will study the evolution of the comet 67P/Churyumov-Gerasimenko's coma system. The instrument will measure surface temperature, gas-production rates and relative abundances, and velocity and excitation temperatures of each species along with their spatial temporal variability. This software will use these measurements to improve the understanding of coma dynamics. The modeling tool solves the equation of motion of a dust particle, the energy balance equation of the dust particle, the continuity equation for the dust and gas flow, and the dust and gas mixture energy equation. By solving these equations numerically, the software calculates the temperature and velocity of gas and dust as a function of time for a given initial gas and dust production rate, and a dust characteristic parameter that measures the ability of a dust particle to adjust its velocity to the local gas velocity. The software is written in a modular manner, thereby allowing the addition of more dynamics equations as needed. All of the numerical algorithms are added in-house and no third-party libraries are used.

Von Allmen, Paul A.↗

NASA NTRS1972

Model development of supersonic trough wind with shocks.

The time-dependent one dimensional hydrodynamic equations describe the evolution of the thermal plasma flow along closed magnetic field lines outside of the plasmasphere. The convection of the supersonic polar wind onto a closed field line results in the assumed formation of collisionless plasma shocks. These shocks move earthward as the field line with its 'frozen-in' plasma remains fixed or contracts with time to smaller L coordinates. The high equatorial plasma temperature (of the order of electron volts) produced by the shock process decreases with time if the flow is isothermal, but it will increase if the contraction is under adiabatic conditions. Assuming adiabaticity a peak in the temperature forms at the equator in conjunction with a depression in the ion density. After an initial contraction, if the flux tube drifts to higher L coordinates, the direction of the shock motion can be reversed so that the supersonic region will expand along the field line toward the state characterizing the supersonic polar wind.

Grebowsky, J. M.↗

NASA NTRS1973

Variable features on Mars. II - Mariner 9 global results.

Systematic Mariner 9 monitoring of the space and time distribution of Martian bright and dark markings, the streaks and splotches, indicates a range of global correlations. The time-variable classical dark markings owe their configurations and variability to their constituent streaks and splotches, produced by windblown dust. Streaks and splotches are consistent wind direction indicators. Correlation of global streak patterns with general circulation models shows that velocities of about 50 to 90 m/sec above the boundary layer are necessary to initiate grain motion on the surface and to produce streaks and splotches. Detailed examples of changes in Syrtis Major, Lunae Palus, and Promethei Sinus are generally consistent with removal of bright sand and dust and uncovering of darker underlying material as the active agent in such changes, although dark mobile material probably also exists on Mars. The generation of streaks and the progressive albedo changes observed require only threshold velocities of about 2 m/sec for about 1 day at the grain surface.

Sagan, C.↗

NASA NTRS1977

Pre-impact conditions and cratering processes at the Flynn Creek crater, Tennessee

A description is presented of a preliminary outline for the cratering processes at Flynn Creek, Tennessee, a large, flat-floored, terrestrial impact crater with a central uplift. The initial preimpact conditions in terms of terrain, target media, and structure are defined, taking into account the possibility of impact into a shallow sea. A brief outline is provided of the generalized sequence of events from the time of entry of the impacting body into the atmosphere through the termination of late-stage cratering motions. The abbreviated sequence of cratering events is based upon a composite of recently assembled physical constraints, including new field data, experimental laboratory impact and field explosion trials, and theoretical numerical simulation studies.

Roddy, D. J.↗

NASA NTRS1986

A linear quadratic tracker for Control Moment Gyro based attitude control of the Space Station

The paper discusses a design for an attitude control system for the Space Station which produces fast response, with minimal overshoot and cross-coupling with the use of Control Moment Gyros (CMG). The rigid body equations of motion are linearized and discretized and a Linear Quadratic Regulator (LQR) design and analysis study is performed. The resulting design is then modified such that integral and differential terms are added to the state equations to enhance response characteristics. Methods for reduction of computation time through channelization are discussed as well as the reduction of initial torque requirements.

Kaidy, J. T.↗

NASA NTRS1987

Numerical investigation of V/STOL jet induced interactions

Direct numerical simulation using the full three dimensional, time dependent Navier-Stokes equations is used to investigate V/STOL jet induced interactions. The objective of this numerical simulation is to compute accurately the details of the flow field and to achieve a better understanding of the physics of the flow, including the role of initial turbulence in the jet, the influence of forward motion on hover aerodynamics, the collision zone and fountain characteristics. Preliminary results are presented.

Rizk, Magdi H.↗

NASA NTRS1992

Postexplosion hydrodynamics of SN 1987A

A comprehensive study is presented of the postexplosion hydrodynamics of the ejecta of SN 1987A encompassing the Rayleigh-Taylor instabilities at the shell interfaces and the dynamical effects of the energy input due to the radioactive decay of Ni-56 and Co-56. The dependence of the hydrodynamical behavior on progenitor structure, initial perturbations, explosion energy, and dimensionality of the numerical simulation is investigated in order to explain the observed high-velocity wings of the iron line of SN 1987A. It is shown that none of these factors leads to the required high-velocity tail of iron. When nickel is artificially premixed in the initial model, it is found that this early mixing has to affect the inner 1.5 solar mass of the ejecta to reproduce the high-velocity wings at a time of 90 d. It is argued that the high-entropy bubble associated with the delayed mechanism is responsible for this premixing by driving convective motions early in the explosion.

Herant, Marc↗

NASA NTRS1941

Velocity gained and altitude lost in recoveries from inclined flight paths

A series of charts is given showing the variation of the velocity gained and the altitude lost in dive pullouts with the initial indicated air speed and the dive angle. The effects of the maximum load factor, the drag parameter K, the initial altitude, and the type of recovery on the velocity gained and the altitude lost are also considered. The results were obtained from a step-by-step solution of the equations of motion in which mean values of the air density and the airplane drag coefficient were used. The load-factor variation with time is arbitrarily specified in various ways to simulate pull-out procedures, some of which might be encountered in flight.

Pearson, H A↗

NASA NTRS1986

Intercomparison of numerical models of flaring coronal loops

The proposed Benchmark Problem consists of an infinitesimal magnetic flux tube containing a low-beta plasma. The field strength is assumed to be so large that the plasma can move only along the flux tube, whose shape remains invariant with time (i.e., the fluid motion is essentially one-dimensional). The flux tube cross section is taken to be constant over its entire length. In planar view the flux tube has a semi-circular shape, symmetric about its midpoint s = s sub max and intersecting the chromosphere-corona interface (CCI) perpendicularly at each foot point. The arc length from the loop apex to the CCI is 10,000 km. The flux tube extends an additional 2000 km below the CCI to include the chromosphere, which initially has a uniform temperature of 8000 K. The temperature at the top of the loop was fixed initially at 2 X 1 million K. The plasma is assumed to be a perfect gas (gamma = 5/3), consisting of pure hydrogen which is considered to be fully ionized at all temperatures. For simplicity, moreover, the electron and ion temperatures are taken to be everywhere equal at all times (corresponding to an artificially enhanced electron-ion collisional coupling). While there was more-or-less unanimous agreement as to certain global properties of the system behavior (peak temperature reached, thermal-wave time scales, etc.), no two groups could claim satisfactory accord when a more detailed comparison of solutions was attempted.

Kopp, R. A.↗

NASA NTRS1970

Dynamic characteristics of a variable-mass flexible missile

The general motion of a variable mass flexible missile with internal flow and aerodynamic forces is considered. The resulting formulation comprises six ordinary differential equations for rigid body motion and three partial differential equations for elastic motion. The simultaneous differential equations are nonlinear and possess time-dependent coefficients. The differential equations are solved by a semi-analytical method leading to a set of purely ordinary differential equations which are then solved numerically. A computer program was developed for the numerical solution and results are presented for a given set of initial conditions.

Meirovitch, L.↗

NASA NTRS1974

Simulation of decelerating landing approaches on an externally blown flap STOL transport airplane

A fixed-base simulator program was conducted to define the problems and methods for solution associated with performing decelerating landing approaches on a representative STOL transport having a high wing and equipped with an external-flow jet flap in combination with four high-bypass-ratio fan-jet engines. Real-time digital simulation techniques were used. The computer was programed with equations of motion for six degrees of freedom and the aerodynamic inputs were based on measured wind-tunnel data. The pilot's task was to capture the localizer and the glide slope and to maintain them as closely as possible while decelerating from an initial airspeed of 140 knots to a final airspeed of 75 knots, while under IFR conditions.

Grantham, W. D.↗