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NASA NTRS1992

Convective instability in differentially rotating disks

A normal mode analysis for nonaxisymmetric perturbations in a thin, differentially rotating disk with a vertical structure that is isothermal and convectively unstable is performed. The vertical gravity is assumed to be external and constant. The perturbation scale is assumed to be much shorter than the radius of the disk but comparable to or less than the thickness. The initial value problem is formulated in shearing coordinates. Dispersion relations are obtained for the three limiting cases of zero shear, axisymmetric perturbations, and small radial wavelengths. The full effects of shear are studied by integrating numerically the initial value problem. Nonaxisymmetric local Fourier modes are found to have a radial wavenumber that increases linearly with time in proportion to the shear times the azimuthal wavenumber. While Coriolis forces exert stabilizing effects on the convective modes, reducing their growth rate and the range of unstable wavelengths, shear has destablizing effects inasmuch as it reduces the epicyclic frequency at a given angular velocity. In a Keplerian disk, perturbations with azimuthal wavelengths about 2 times smaller than vertical wavelengths grow exponentially.

Ryu, Dongsu↗

NASA NTRS1992

Linear stability of compressible Taylor-Couette flow

A temporal stability analysis of compressible Taylor-Couette flow is presented. The viscous flow studied in this paper is contained between two concentric cylinders of infinite length, which are rotating with different angular velocities and are kept at different surface temperatures. The effects of differential rotation and temperature difference on the stability of Taylor-Couette flow are contrasted for a range of Mach numbers ranging from incompressible to Mach 3.0. The relative motion of the cylinders dramatically affects the characteristics of the Couette flow at the onset of instability. The flow is stabilized or destabilized depending upon the temperature ratio and speeds of the two cylinders. Independent of Mach number and temperature ratio, increasing Reynolds number generally promotes a destabilizing effect, indicating the inviscid nature of the Taylor-Couette flow.

Kao, Kai-Hsiung↗

NASA NTRS1992

Video Guidance Sensor for automated capture

The paper describes a video-based sensor, the Video Guidance Sensor, which has been developed for use in automated docking systems or for automated capture with robotic systems. The sensor itself consists of several basic components: IR diode illuminators, a solid-state camera, a frame grabber, and a microprocessor. The target consists of three circular retroreflectors evenly spaced in a line with the middle reflector mounted on a short pole. Each retroreflector has a narrow bandpass optical filter in front of it. From this sensor and target configuration, the positions and attitudes of the target relative to the sensor can be determined. The position information can be differenced to with respect to time in order to obtain the relative positional and angular velocities. That information is sufficient to perform automated docking, berthing, or capture. The paper gives details of the sensor's make-up, including accuracies, noise characteristics, and operating ranges.

Howard, R. T.↗

NASA NTRS1992

Is the Oort A-value a universal growth rate limit for accretion disk shear instabilities?

A weak-field local MHD instability that is of importance to accretion disks is examined. The maximum growth rate of the instability is found to be not only independent of the magnetic field strength but independent of field geometry as well. In particular, all Keplerian disks are unstable in the presence of any weak poloidal field, with the ratio of the maximum growth rate to disk angular velocity given by 3/4. The maximum growth rate of any weak field configuration that is not purely toroidal is given by the local Oort A-value of the disk. The behavior is studied by using a form of the dynamical Hill equations. It is conjectured that the Oort A-value is an upper bound to the growth rate of any instability feeding upon the free energy of differential rotation.

Balbus, Steven A.↗

NASA NTRS1992

A deterministic method for estimating attitude from magnetometer data only

A new deterministic algorithm which estimates spacecraft attitude utilizing magnetometer data only is presented. This algorithm exploits the dynamic equations of motion to propagate attitude and thus requires knowledge of both internal and external torques, except in the special case of a spacecraft rotating with constant angular velocity. Preliminary results obtained for the uncontrolled Relay Mirror Experiment satellite utilizing real telemetry data are reported.

Natanson, G. A.↗

NASA NTRS1993

Calibrating Airplane Instrumentation To Measure Winds

Elaborate combination of techniques used to calibrate wind-measuring instrumentation aboard F104 airplane. Obtains wind profiles more rapidly. Airplane equipped with standard NACA research nose boom, including pressure probes and flow vanes yielding data on static and total pressures, angle of attack, and angle of sideslip. Has ring-laser-gyroscope inertial reference unit, giving linear and angular velocities, linear acceleration, and orientation of airplane. Body-mounted total-temperature sensor also used. Improved method of calibration devised to determine whether winds aloft at and shortly after time of measurement allow safe launch of Space Shuttle. Proves beneficial in other safety- or research-oriented applications in which wind velocities over range of altitudes must be determined in nearly real time.

Haering, Edward A., Jr.↗

NASA NTRS1992

Two-dimensional viscous accretion disk models. I - On meridional circulations in radiative regions

It has been suggested that thin Keplerian disks, like rotating stars, cannot attain hydrostatic and thermal equilibrium simultaneously if the angular velocity is a function of radius only. To address the problem of vertical structure and stability of thin accretion disks, we performed 2D axisymmetric calculations by solving the set of fully nonlinear hydrodynamic equations, including radiation transport. The results indicate that the variation of the rotational velocity with height is too small to sustain hydrostatic equilibrium. Instead, the variation of the radial (inflow) velocity with height suffices to establish a stationary state. In particular, we find that for low values of the viscosity parameter alpha, there is mass outflow in the central parts of the disk close to the equatorial plane, and inflow only near the surface. Only for modestly high values of alpha, the flow throughout the disk is directed inward. Thus, the flow within the disk is the result of viscous radial inflow plus a circulatory flow directed outward in the midplane and inward near the surface.

Kley, W.↗

NASA NTRS1993

Time-variant analysis of rotorcraft systems dynamics - An exploitation of vector processors

In this paper a generalized algorithmic procedure is presented for handling constraints in mechanical transmissions. The latter are treated as multibody systems of interconnected rigid/flexible bodies. The constraint Jacobian matrices are generated automatically and suitably updated in time, depending on the geometrical and kinematical constraint conditions describing the interconnection between shafts or gears. The type of constraints are classified based on the interconnection of the bodies by assuming that one or more points of contact exist between them. The effects due to elastic deformation of the flexible bodies are included by allowing each body element to undergo small deformations. The procedure is based on recursively formulated Kane's dynamical equations of motion and the finite element method, including the concept of geometrical stiffening effects. The method is implemented on an IBM-3090-600j vector processor with pipe-lining capabilities. A significant increase in the speed of execution is achieved by vectorizing the developed code in computationally intensive areas. An example consisting of two meshing disks rotating at high angular velocity is presented. Applications are intended for the study of the dynamic behavior of helicopter transmissions.

Amirouche, F. M. L.↗

NASA NTRS1993

The problem of exact interior solutions for rotating rigid bodies in general relativity

The (3 + 1) dyadic formalism for timelike congruences is applied to derive interior solutions for stationary, axisymmetric, rigidly rotating bodies. In this approach the mathematics is formulated in terms of three-space-covariant, first-order, vector-dyadic, differential equations for a and Omega, the acceleration and angular velocity three-vectors of the rigid body; for T, the stress dyadic of the matter; and for A and B, the 'electric' and 'magnetic' Weyl curvature dyadics which describe the gravitational field. It is shown how an appropriate ansatz for the forms of these dyadics can be used to discover exact rotating interior solutions such as the perfect fluid solution first published in 1968. By incorporating anisotropic stresses, a generalization is found of that previous solution and, in addition, a very simple new solution that can only exist in toroidal configurations.

Wahlquist, H. D.↗

NASA NTRS1993

The structure and stability of transonic accretion disks surrounding black holes

Stationary transonic alpha-viscosity models of accretion disks surrounding nonrotating black holes have been investigated. The viscosity is modified such that it vanishes in the supersonic region to ensure its effect does not violate the causality condition. In contrast to previous studies, the viscous stress is taken to be explicitly proportional to the angular velocity gradient and is not assumed to depend solely on the local pressure in the disk. The numerical results reveal that the structure of the innermost regions of the disk are more sensitive to the modified form of the viscosity than to the form of the viscous stress. The critical sonic point is located inside the innermost stable circular orbit of a test particle at 3 Schwarzschild radii. In these solutions, the transition from subsonic to supersonic flow results from pressure effects and not viscous effects. The linear stability of these disks has been examined in the local approximation. It is found that radiative energy transport and viscous stresses in the radial direction can have important effects. As a result, it is shown that the growth rate of the inertial-acoustic mode reaches a maximum at a critical wavelength.

Chen, Xingming↗

NASA NTRS1990

Error analysis for reducing noisy wide-gap concentric cylinder rheometric data for nonlinear fluids - Theory and applications

This work discusses the propagation of errors for the recovery of the shear rate from wide-gap concentric cylinder viscometric measurements of non-Newtonian fluids. A least-square regression of stress on angular velocity data to a system of arbitrary functions is used to propagate the errors for the series solution to the viscometric flow developed by Krieger and Elrod (1953) and Pawlowski (1953) ('power-law' approximation) and for the first term of the series developed by Krieger (1968). A numerical experiment shows that, for measurements affected by significant errors, the first term of the Krieger-Elrod-Pawlowski series ('infinite radius' approximation) and the power-law approximation may recover the shear rate with equal accuracy as the full Krieger-Elrod-Pawlowski solution. An experiment on a clay slurry indicates that the clay has a larger yield stress at rest than during shearing, and that, for the range of shear rates investigated, a four-parameter constitutive equation approximates reasonably well its rheology. The error analysis presented is useful for studying the rheology of fluids such as particle suspensions, slurries, foams, and magma.

Borgia, Andrea↗

NASA NTRS1925

Note on the air forces on a wing caused by pitching.

The following contains information on the air forces on a wing produced by it's pitching at a finite rate of angular velocity. The condition of smooth flow at the region of the trailing edge is maintained. The wing then experiences the same lift as if moving with the momentary velocity of the rear edge.

Munk, Max M↗

NASA NTRS1933

The Effects of Slots and Flaps on Lateral Control of a Low-wing Monoplane as Determined in Flight

This paper presents the results of flight tests made to determine the effect of slots and flaps on the lateral control of a low-wing monoplane. Maximum angular accelerations in roll and yaw produced by sudden application of the ailerons and maximum accelerations in yaw produced by sudden application of the rudder during gliding flight were recorded for the following wing arrangements: (a) no auxiliary device; (b) full-span slots; (c) plain flaps; (d) flaps and full-span slots; (e) wing-tip slots. Rolling- and yawing-moment coefficients were derived from the accelerations. The full span slots and the flaps each had about the same influence on the aileron rolling moments. At values of the lift coefficient obtainable with the plain wing, the effect of these devices was negligible. At the higher lift coefficients obtainable with these devices, the rolling-moment coefficients increased slightly but, despite this increase, the aileron effectiveness progressively decreased with increasing lift coefficient, owing to the corresponding reduction in air speed. In the range covered by the tests, the effectiveness of the controls was appreciably reduced by the wing-tip slots. The adverse yawing moment of the ailerons experienced at the large lift coefficients obtained with the flaps was appreciably less than at similar lift coefficients obtained with either full-span or wing-tip slots. The yawing moments produced by the rudder were only slightly affected by the use of the auxiliary devices. The airplane was found to be laterally unstable with all combinations tested. Because of the angular velocities acquired in the time taken to deflect the ailerons the rolling moments recorded in flight were only about two thirds the values that would have been obtained with the wing restrained as in wind-tunnel tests.

WING SLOTS↗

NASA NTRS1939

Pressure-distribution Measurements on a Tapered Wing with a Full-span Split Flap in Curved Flight

Pressure-distribution tests were made on the 32-foot whirling arm of the Daniel Guggenheim Airship Institute of a tapered wing to determine the rolling and yawing moments due to an angular velocity in yaw. The model was tested at 0 degree and 5 degrees pitch, -1 degree and 5 degree yaw, and with a full-span flap deflected 60 degrees. The results are given in the form of span load distributions and in calculated moment coefficients. The rolling-moment coefficients are in fairly close agreement with those derived by means of a simple approximate theory even for high deflection of the full-span flap.

Troller, TH↗

NASA NTRS1939

Pressure-distribution measurements on a tapered wing with a partial-span split flap in curved flight

Pressure-distribution tests were made on the 32-foot whirling arm of the Daniel Guggenheim Airship Institute of a tapered wing to determine the rolling and the yawing moments due to an angular velocity in yaw. The model was tested at 0 degree and 5 degree pitch; 0 degree, 5 degree, and 10 degree yaw; and with split flaps covering 25, 50, 75, and 100 percent of the wing span and deflected 60 degrees. The results are given in the form of load distributions and as calculated moment coefficients. The experimental values of rolling- and yawing- moment coefficients were in fairly close agreement with theory.

Troller, TH↗

NASA NTRS1939

Pressure-distribution measurements on a rectangular wing with a partial-span split flap in curved flight

Pressure-distribution tests were made on the 32-foot whirling arm of the Daniel Guggenheim Airship Institute of a rectangular wing of NACA 23012 section to determine the rolling and the yawing moment due to angular velocity in yaw. The model was tested at 0 and 5 degree pitch; 0, +/- 5, and +/- 10 degrees yaw; and with no flap and with split flaps 25, 50 and 75 percent of the wing span and deflected 60 degrees. The results are given in the form of span load distributions and as calculated moment coefficients. The experimental values of rolling- and yawing-moment coefficients were in fairly close agreement with theory.

Rokus, Frank G↗

NASA NTRS1952

Generalization of Boundary-Layer Momentum-Integral Equations to Three-Dimensional Flows Including Those of Rotating System

The Navier-Stokes equations of motion and the equation of continuity are transformed so as to apply to an orthogonal curvilinear coordinate system rotating with a uniform angular velocity about an arbitrary axis in space. A usual simplification of these equations as consistent with the accepted boundary-layer theory and an integration of these equations through the boundary layer result in boundary-layer momentum-integral equations for three-dimensional flows that are applicable to either rotating or nonrotating fluid boundaries. These equations are simplified and an approximate solution in closed integral form is obtained for a generalized boundary-layer momentum-loss thickness and flow deflection at the wall in the turbulent case. A numerical evaluation of this solution carried out for data obtained in a curving nonrotating duct shows a fair quantitative agreement with the measures values. The form in which the equations are presented is readily adaptable to cases of steady, three-dimensional, incompressible boundary-layer flow like that over curved ducts or yawed wings; and it also may be used to describe the boundary-layer flow over various rotating surfaces, thus applying to turbomachinery, propellers, and helicopter blades.

Mager, Arthur↗

NASA NTRS1923

Controllability and Maneuverability of Airplanes

This investigation was conducted for the purpose of studying the behavior of the JN4H airplane in free flight under the action of its controls and from this to arrive at satisfactory definitions and coefficients for controllability and maneuverability. The method consisted in recording the angular velocity about the three axes, together with the air speed, control positions, and acceleration. (author)

Norton, F H↗