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NASA NTRS1979

Phase change in liquid face seals. II - Isothermal and adiabatic bounds with real fluids

Analytical studies of phase change effects in parallel and tapered liquid face seals are presented. An isothermal and adiabatic model of low Reynolds number flow are considered by numerical integration of the descriptive equations for a real fluid, and its thermodynamic properties are calculated for each step, using a computer program for the steam tables or fluid thermodynamic properties. It was shown that for low leakage rate the isothermal model is more accurate and for high leakage rates the adiabatic model is more accurate; that both models yield the same conclusions regarding stability; and that the transient of collapse is described by the adiabatic model which predicts a catastrophic collapse and then either failure or explosive return to a larger film thickness value. Finally, it is shown that converging seals may become unstable and the mass leakage rate is reduced significantly below the all liquid value when boiling occurs.

Hughes, W. F.↗

NASA NTRS1980

Uncontrolled dynamics of the Skylab vehicle - Comparison of simulation, theory and flight data

When the final Skylab mission was completed in 1974, the onboard systems were used to maneuver the vehicle to a gravity gradient equilibrium attitude and were then shut down. Parked in this storage attitude, the vehicle was left undisturbed until March 1978 when contact was reestablished and the control systems were reactivated. During the intervening four years, the vehicle was subjected to subtle environmental torques which caused the vehicle to gradually progress from its initial stable state to a very dynamic condition just prior to the resumption of control. The paper deals with the dynamics of this process, including the analyses and simulations which were made to explain the motion and enable the planning of the reactivation process. The complementary roles of both numerical integration and closed-form analysis are demonstrated. Flight data obtained in the spring of 1978 are presented which support the analytical and simulation results.

Buchanan, H. J.↗

NASA NTRS1980

Flow over plates with suction through porous strips

This paper addresses the steady, incompressible, two-dimensional flow past a flat plate with suction through porous strips. Closed-form solutions for each flow quantity are developed in the context of linearized triple-deck theory using Fourier transforms. To demonstrate the validity of these closed-form solutions, we compare the wall shear stress and pressure coefficients and the streamwise velocity profiles from the linearized theory with those obtained by the numerical integration of both interacting and nonsimilar boundary-layer equations. The agreement between the linearized triple-deck and interacting boundary-layer equations is good; however, the nonsimilar boundary layers, which fail to account for upstream influence, are shown to be in poor agreement with both interacting boundary layers and the linearized triple deck. The linearized closed-form solutions will therefore be very useful in future stability calculations.

Nayfeh, A. H.↗

NASA NTRS1980

Long-time predictions in nonlinear dynamics

It is known that nonintegrable dynamical systems do not allow precise predictions concerning their behavior for arbitrary long times. The available series solutions are not uniformly convergent according to Poincare's theorem and numerical integrations lose their meaningfulness after the elapse of arbitrary long times. Two approaches are the use of existing global integrals and statistical methods. This paper presents a generalized method along the first approach. As examples long-time predictions in the classical gravitational satellite and planetary problems are treated.

Szebehely, V.↗

NASA NTRS1980

Development and implementation of Shuttle/IUS proximity operations flight design software

The High Fidelity Relative Motion Program (HFRMP), a trajectory/attitude numerical integration program, was developed and implemented on the MPAD HP-9825A desk top computer systems. A solar and a lunar ephemeris is included in the HFRMP along with models of the oblate Earth, a rotating atmosphere, the orbiter's OMS/RCS/DAP system, orbiter vents, rotor dynamics, and upper stage propulsion systems. Although designed primarily for the analysis of proximity operations, it is useful in other areas such as attitude/stability analysis, propulsive consumables estimation, and trajector perturbation studies. An unique identification was assigned to each of the various configurations of the HFRMP that were developed to test new techniques and algorithms are briefly described. These include the HFRMP Versions 03H, 03M, 03T, 03U, and 05D. Development of orbiter/upper stage separation techniques including flight design support for the TDRS-A and Galileo deployment flights and design of standard maneuver sequences is discussed. Also, the development and implementation of the Euler angle conversion program is briefly addressed.

Wilson, S. W.↗

NASA NTRS1981

The prediction of normal force and rolling moment coefficients for a spinning wing

Nonlinear airfoil section data for angles of attack from 0 to 180 deg were used in a small computer code to numerically integrate the section normal force coefficients along the span as a function of the local velocity and angle of attack resulting from the combined spinning and descending motion. A correction was developed to account for the radial pressure gradient in the separated, rotating flow region above the wing. This correction was found to be necessary in order to obtain agreement, both in form and magnitude, with rotary balance test data.

Mccormick, B. W.↗

NASA NTRS1981

Acoustic properties of turbofan inlets

The finite element codes were improved using Hermitian elements and numerical integration of element relations. The question of real variable versus complex variable formulation was resolved and an integrated civil engineering system was implemented on the Georgia Tech Cyber 70/74. Efforts are underway to restructure the program to obtain the most efficient use of array storage.

Zinn, B. T.↗

NASA NTRS1981

Investigation of electrodynamic stabilization and control of long orbiting tethers

An algorithm for using electric currents to control pendular oscillations induced by various perturbing forces on the Skyhook wire is considered. Transverse and vertical forces on the tether; tether instability modes and causes during retrieval by space shuttle; simple and spherical pendulum motion and vector damping; and current generation and control are discussed. A computer program for numerical integration of the in-plane and out-of-plane displacements of the tether vs time was developed for heuristic study. Some techniques for controlling instabilities during payload retrieval and methods for employing the tether for launching satellites from the space shuttle are considered. Derivations and analyses of a general nature used in all of the areas studied are included.

Arnold, D. A.↗

NASA NTRS1979

Calculation of the flow field in supersonic inlets using a bicharacteristics method with shock wave fitting

The results of weakly viscous flow analysis are presented. The flow field, including molecular transport, is computed with the aid of a bicharacteristic method. The bow shock wave and the internal shock wave are computed with the aid of a three-dimensional shock wave fitting procedure. Characteristic equations are presented, and numerical integration procedure is discussed. Here, an inverse marching scheme is employed in which the solution is obtained on space-like planes of constant x and on space curves defined by the intersections of the internal shock wave with the solid boundaries. The distance between solution planes is arrived at by the Courant-Friedrichs-Lewy stability criterion.

Vadyak, J.↗

NASA NTRS1981

Rapid inversion of limb radiance data using an emissivity growth approximation

The time-consuming nature of limb relaxation-type inversion algorithms is due primarily to the numerous integrations over an absorption band to obtain forward radiance values with which to compare measured values. A new method has been devised for the quick and accurate (0.5% error) calculation of single gas broadband (approximately 100 per cm) limb radiance. The method uses a precalculated data base consisting of homogeneous path emissivity vs mass path data for a wide range of temperature and pressure. A 50-km altitude range, 1-km resolution, constituent inversion employing this method requires under 1 sec of computational time when run on modern computer hardware. The method does not rely upon a priori statistical knowledge.

Gordley, L. L.↗

NASA NTRS1981

Periodic solutions about the collinear Lagrangian solution in the general problem of three bodies

The article describes the solutions near Lagrange's circular collinear configuration in the planar problem of three bodies with three finite masses. The article begins with a detailed review of the properties of Lagrange's collinear solution. Lagrange's quintic equation is derived and several expressions are given for the angular velocity of the rotating frame. The equations of motion are then linearized near the circular collinear solution, and the characteristic equation is also derived in detail. The different types of roots and their corresponding solutions are discussed. The special case of two equal outer masses receives special attention, as well as the special case of two small outer masses. Finally, the fundamental family of periodic solutions is extended by numerical integration all the way up to and past a binary collision orbit. The stability and the bifurcations of this family are briefly enumerated.

Broucke, R.↗

NASA NTRS1981

Visible light scatter measurements of the Advanced X-ray Astronomical Facility /AXAF/ mirror samples

NASA is studying the properties of mirror surfaces for X-ray telescopes, the data of which will be used to develop the telescope system for the Advanced X-ray Astronomical Facility. Visible light scatter measurements, using a computer controlled scanner, are made of various mirror samples to determine surface roughness. Total diffuse scatter is calculated using numerical integration techniques and used to estimate the rms surface roughness. The data measurements are then compared with X-ray scatter measurements of the same samples. A summary of the data generated is presented, along with graphs showing changes in scatter on samples before and after cleaning. Results show that very smooth surfaces can be polished on the common substrate materials (from 2 to 10 Angstroms), and nickel appears to give the lowest visible light scatter.

Griner, D. B.↗

NASA NTRS1980

Representation and material charging response of geoplasma environments

The sensitivity of the charging response to the representation of the measured environments and material properties are discussed. Single and double Maxwellian representations are compared with direct numerical integration of the observed spectra. The effect of anisotropic incident flux distribution is modeled. In addition, the effect of the high energy radiation upon bulk conductivity and hence differential charging is examined.

Stannard, P. R.↗

NASA NTRS1981

Modelling of polymer photodegradation for solar cell modules

A computer program developed to model and calculate by numerical integration the varying concentrations of chemical species formed during photooxidation of a polymeric material over time, using as input data a choice set of elementary reactions, corresponding rate constants and a convenient set of starting conditions is evaluated. Attempts were made to validate the proposed mechanism by experimentally monitoring the photooxidation products of small liquid alkane which are useful starting models for ethylene segments of polymers like EVA. The model system proved in appropriate for the intended purposes. Another validation model is recommended.

Somersall, A. C.↗

NASA NTRS1980

An investigation of dynamic-analysis methods for variable-geometry structures

Selected space structure configurations were reviewed in order to define dynamic analysis problems associated with variable geometry. The dynamics of a beam being constructed from a flexible base and the relocation of the completed beam by rotating the remote manipulator system about the shoulder joint were selected. Equations of motion were formulated in physical coordinates for both of these problems, and FORTRAN programs were developed to generate solutions by numerically integrating the equations. These solutions served as a standard of comparison to gauge the accuracy of approximate solution techniques that were developed and studied. Good control was achieved in both problems. Unstable control system coupling with the system flexibility did not occur. An approximate method was developed for each problem to enable the analyst to investigate variable geometry effects during a short time span using standard fixed geometry programs such as NASTRAN. The average angle and average length techniques are discussed.

Austin, F.↗

NASA NTRS1981

Computer prediction of dual reflector antenna radiation properties

A program for calculating radiation patterns for reflector antennas with either smooth analytic surfaces or with surfaces composed of a number of panels. Techniques based on the geometrical optics (GO) approach were used in tracing rays over the following regions: from a feed antenna to the first reflector surface (subreflector); from this reflector to a larger reflector surface (main reflector); and from the main reflector to a mathematical plane (aperture plane) in front of the main reflector. The equations of GO were also used to calculate the reflected field components for each ray making use of the feed radiation pattern and the parameters defining the surfaces of the two reflectors. These resulting fields form an aperture distribution which is integrated numerically to compute the radiation pattern for a specified set of angles.

Christodoulou, C.↗

NASA NTRS1981

Quasi-Langrangian models of nascent thermals

The motions in and around an isolated thermal were studied and rising motion in the core, and sinking motion on the outside were found; while the circulation resembled that of a vortex ring. In an entity cloud model, cloudy thermal is tracked, in a Lagrangian fashion, as a discrete entity; the field of motion in and around the thermal is not explicitly simulated. Field of motion cloud models, in which the equations of motion are numerically integrated on an Eulerian grid were developed. It is shown that the great potential of a hybrid cloud model can combine the simplicity of the entity models with the generality and flexibility of the field-of-motion models. A key problem to be overcome in the development of a hybrid model is the formulation of a mathematical framework within which the cloud dynamics can be represented.

Rambaldi, S.↗

NASA NTRS1982

A prescribed wake rotor inflow and flow field prediction analysis, user's manual and technical approach

A user's manual is provided which includes the technical approach for the Prescribed Wake Rotor Inflow and Flow Field Prediction Analysis. The analysis is used to provide the rotor wake induced velocities at the rotor blades for use in blade airloads and response analyses and to provide induced velocities at arbitrary field points such as at a tail surface. This analysis calculates the distribution of rotor wake induced velocities based on a prescribed wake model. Section operating conditions are prescribed from blade motion and controls determined by a separate blade response analysis. The analysis represents each blade by a segmented lifting line, and the rotor wake by discrete segmented trailing vortex filaments. Blade loading and circulation distributions are calculated based on blade element strip theory including the local induced velocity predicted by the numerical integration of the Biot-Savart Law applied to the vortex wake model.

Egolf, T. A.↗