Pressure signature of an axisymmetric body at angle of attack.
Incidence effect assessment upon pressure signature, considering supersonic flow about slender rotating body at angle of attack
Siegelman, D.↗
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Evanescent and inertial-like waves in rigidly rotating odd viscous liquids
Three-dimensional non-rotating odd viscous liquids give rise to Taylor columns and support axisymmetric inertial-like waves ( J. Fluid Mech ., vol. 973, 2023, A30). When an odd viscous liquid is subjected to rigid-body rotation however, there arise in addition a plethora of other phenomena that need to be clarified. In this paper, we show that three-dimensional incompressible or two-dimensional compressible odd viscous liquids, rotating rigidly with angular velocity 𝛺, give rise to both oscillatory and evanescent inertial-like waves or a combination thereof (which we call of mixed type) that can be non-axisymmetric. By evanescent, we mean that along the radial direction, typically when moving away from a solid boundary, the velocity field decreases exponentially. These waves precess in a prograde or retrograde manner with respect to the rotating frame. The oscillatory and evanescent waves resemble respectively the body and wall-modes observed in (non-odd) rotating Rayleigh–Bénard convection ( J. Fluid Mech ., vol. 248, 1993, pp. 583–604). We show that the three types of waves (wall, body or mixed) can be classified with respect to pairs of planar wavenumbers 𝜅 which are complex, real or a combination, respectively. Experimentally, by observing the precession rate of the patterns, it would be possible to determine the largely unknown values of the odd viscosity coefficients. This formulation recovers as special cases recent studies of equatorial or topological waves in two-dimensional odd viscous liquids which provided examples of the bulk–interface correspondence at frequencies 𝜔 < 2𝛺. We finally point out that the two- and three-dimensional problems are formally equivalent. Their difference then lies in the way data propagate along characteristic rays in three dimensions, which we demonstrate by classifying the resulting Poincaré–Cartan equations.
Mechanics↗
MCC level C formulation requirements. Shuttle TAEM guidance and flight control, STS-1 baseline
The TAEM guidance and body rotational dynamics models required for the MCC simulation of the TAEM mission phase are defined. This simulation begins at the end of the entry phase and terminates at TAEM autoland interface. The logic presented is the required configuration for the first shuttle orbital flight (STS-1). The TAEM guidance is simulated in detail. The rotational dynamics simulation is a simplified model that assumes that the commanded rotational rates can be achieved in the integration interval. Thus, the rotational dynamics simulation is essentially a simulation of the autopilot commanded rates and integration of these rates to determine orbiter attitude. The rotational dynamics simulation also includes a simulation of the speedbrake deflection. The body flap and elevon deflections are computed in the orbiter aerodynamic simulation.
Carman, G. L.↗
Rotating reactor studies
Undesired gravitational effects such as convection or sedimentation in a fluid can sometimes be avoided or decreased by the use of a closed chamber uniformly rotated about a horizontal axis. In a previous study, the spiral orbits of a heavy or buoyant particle in a uniformly rotating fluid were determined. The particles move in circles, and spiral in or out under the combined effects of the centrifugal force and centrifugal buoyancy. A optimization problem for the rotation rate of a cylindrical reactor rotated about its axis and containing distributed particles was formulated and solved. Related studies in several areas are addressed. A computer program based on the analysis was upgraded by correcting some minor errors, adding a sophisticated screen-and-printer graphics capability and other output options, and by improving the automation. The design, performance, and analysis of a series of experiments with monodisperse polystyrene latex microspheres in water were supported to test the theory and its limitations. The theory was amply confirmed at high rotation rates. However, at low rotation rates (1 rpm or less) the assumption of uniform solid-body rotation of the fluid became invalid, and there were increasingly strong secondary motions driven by variations in the mean fluid density due to variations in the particle concentration. In these tests the increase in the mean fluid density due to the particles was of order 0.015 percent. To a first approximation, these flows are driven by the buoyancy in a thin crescent-shaped depleted layer on the descending side of the rotating reactor. This buoyancy distribution is balanced by viscosity near the walls, and by the Coriolis force in the interior. A full analysis is beyond the scope of this study. Secondary flows are likely to be stronger for buoyant particles, which spiral in towards the neutral point near the rotation axis under the influence of their centrifugal buoyancy. This is because the depleted layer is thicker and extends all the way around the reactor.
Roberts, Glyn O.↗
Aspects of the Solar Tachocline
The splitting of the frequencies of p-mode multiplets enables information to be gained about the internal rotation of the sun. Such data have revealed a transition at the base of the convection zone from differential rotation similar to that observed at the surface to almost solid-body rotation in the radiative interior. This transition region, known as the tachocline, has been found to be relatively narrow and centered below the base of the convection zone. In this paper, the evolution of the transition region is investigated numerically. Without a large anisotropic viscosity, the depth to which it would spread in one solar age, under the assumption of a constant prescribed differential rotation at the base of the convection zone, is found to be greater than its extent as inferred from helioseismology. In the second part of the paper a highly anisotropic turbulent viscosity with a large horizontal component, as suggested by Spiegel & Zahn (1992), is assumed. In this case, a steady tachocline is formed in which the advection of angular momentum balances the Reynolds stresses. The horizontal component of turbulent viscosity required to match the thickness of the tachocline to that obtained by helioseismology, is estimated to be 5 x 1O sq cm/s The transport of helium is studied in this case and is found to yield a sound-speed increase similar to that required by helioseismology.
Elliott, J. R.↗
Stability and dynamics of rotating dielectrophoretic equilibria
Stability and dynamics of dielectrophoretic equilibria, considering circular cylindrical column of inviscid liquid with rigid body rotation
Calvert, R. T.↗
Torque Simulator for Rotating Systems
New torque brake simulates varying levels of friction in bearings of rotating body. Rolling-tail torque brake uses magnetic force to produce friction between rotating part and stationary part. Simulator electronics produce positive or negative feedback signal, depending on direction of rotation. New system allows for first time in-depth study of effects of tail-fin spin rates on pitch-, yaw-, and roll-control characteristics.
Davis, W. T.↗
New Experiments with Spinning Metallic Discs
A number of recent advanced theories related to torsion properties of the space-time matrix predict the existence of an interaction between classically spinning objects. Indeed, some experimental data suggest that spinning magnetic bodies discernibly interact with Earth's natural fields. If there are interactions between rotating bodies then nuclear spins could be used for detection. Thus, assuming a spinning body induces a hypothetical torsion field, a sensor based on the giant magnetoresistance effect would detect local changes. Experimentally, spinning a brass wheel shielded from Earth's magnetic field showed no measurable change in signals; with no shielding a Faraday disc phenomenon was observed. Unexpected experimental measurements from the non-axial Faraday disc configuration were recorded and a theoretical model was derived to explain them.
Mazuruk, Konstantin↗
Flow measurements in a model swirl combustor
Flow measurements in a model combustor composed of two confined coaxial swirling jets under noncombusting conditions are presented. Mean flow results are obtained for five different flow conditions to determine the effect of outer swirl on the recirculation zone (which is used for flame stabilization under combustion conditions). As the outer swirl magnitude is first decreased from maximum counter-swirl to zero and then increased to give co-swirl conditions, the size and the reverse flow velocity in the recirculation zone diminish. Detailed time mean and fluctuating flow measurements are obtained for a co-swirl and a counter-swirl condition with a directional pitot probe and hot-wire anenometry. For these two cases, recirculation zone occurs only with counter-swirl, near the exit of the inner jet. The recirculation zone is in the form of a one celled toroidal vortex having very low swirl velocity. Axial development of fluctuation levels, energy dissipation rates and turbulence length scales are described for the two flow conditions. Spectral analysis reveals periodic oscillations in both flows. The oscillations originate from the inner jet and up to 4 harmonics are observed. The fundamental frequencies are comparable to the rotational frequencies of the inner jets at the exit which are approximately under solid body rotation. The significance of the present results for the combustion process is discussed.
Vu, B. T.↗
Prediction of propellant behavior in spinning flow of a space motor
A model for 2-phase flow dynamics in a spinning spherical rocket motor, developed for the Ofeq satellite program, is based on the sectional approach to solution of the flow equations. An experimental model was built, to enable the motion of the aluminum/aluminum-oxide particles resulting from combustion within a solid-fuel motor to be simulated by injected paraffin droplets. The injected droplets included under-5 micrometer droplets which move with the gas stream and larger droplets, averaging 20 micrometer diameter, which simulate the motion of aluminum particles. The test chamber comprised a pair of cylindrical pyrex tubes with a sharp contraction in diameter, rotated at various speeds by a frequency-controllable motor. An optical system, based on a 5 W argon ion laser with a beam splitter and frequency shifter, mounted on a movable table, facilitated sectional measurements of the three velocity components and determination of size-velocity relationships. Preliminary results indicate that the effect of rotation on axial velocity is negligible, while its effect on tangential velocity approximates to solid-body rotation.
Gany, A.↗
Iapetus' Geophysics: Rotation Rate, Shape, and Equatorial Ridge
Iapetus has preserved evidence that constrains the modeling of its geophysical history from the time of its accretion until now. The evidence is (a) its present 79.33-day rotation or spin rate, (b) its shape that corresponds to the equilibrium figure for a hydrostatic body rotating with a period of approximately 16 h, and (c) its high, equatorial ridge, which is unique in the Solar System. This paper reports the results of an investigation into the coupling between Iapetus' thermal and orbital evolution for a wide range of conditions including the spatial distributions with time of composition, porosity, short-lived radioactive isotopes (SLRI), and temperature. The thermal model uses conductive heat transfer with temperature-dependent conductivity. Only models with a thick lithosphere and an interior viscosity in the range of about the water ice melting point can explain the observed shape. Short-lived radioactive isotopes provide the heat needed to decrease porosity in Iapetus? early history. This increases thermal conductivity and allows the development of the strong lithosphere that is required to preserve the 16-h rotational shape and the high vertical relief of the topography. Long-lived radioactive isotopes and SLRI raise internal temperatures high enough that significant tidal dissipation can start, and despin Iapetus to synchronous rotation. This occurred several hundred million years after Iapetus formed. The models also constrain the time when Iapetus formed because the successful models are critically dependent upon having just the right amount of heat added by SLRI decay in this early period. The amount of heat available from short-lived radioactivity is not a free parameter but is fixed by the time when Iapetus accreted, by the canonical concentration of Al-26, and, to a lesser extent, by the concentration of Fe-60. The needed amount of heat is available only if Iapetus accreted between 2.5 and 5.0Myr after the formation of the calcium aluminum inclusions as found in meteorites. Models with these features allow us to explain Iapetus? present synchronous rotation, its fossil 16-h shape, and the context within which the equatorial ridge arose.
geophysics↗
Protoearth mass shedding and the origin of the moon
Darwin's (1980) theory of lunar formation from the earth by means of a rotationally driven dynamic fission instability is presently considered in view of viscous shear's maintenance of solid body rotation throughout the protoearth's accretion phase. Assuming the appropriateness of a polytropic account of the protoearth, it is unlikely that dynamic fission could have occurred; instantaneous spin-up following a giant impact would instead have led to mass shedding. The dynamical phenomenon of mass shedding is here explored on the basis of numerical models for a self-gravitating, axisymmetric, polytropic and dissipative protoearth. It is concluded that mass shedding from the protoearth mantle after a giant impact and explosion could have contributed substantial matter to a lunar disk.
Boss, A. P.↗
Distributed antenna system and method
System and methods are disclosed for employing one or more radiators having non-unique phase centers mounted to a body with respect to a plurality of transmitters to determine location characteristics of the body such as the position and/or attitude of the body. The one or more radiators may consist of a single, continuous element or of two or more discrete radiation elements whose received signals are combined. In a preferred embodiment, the location characteristics are determined using carrier phase measurements whereby phase center information may be determined or estimated. A distributed antenna having a wide angle view may be mounted to a moveable body in accord with the present invention. The distributed antenna may be utilized for maintaining signal contact with multiple spaced apart transmitters, such as a GPS constellation, as the body rotates without the need for RF switches to thereby provide continuous attitude and position determination of the body.
Fink, Patrick W.↗
Torque Transmission Device at Zero Leakage
In a few critical applications, mechanical transmission of power by rotation at low speed is required without leakage at an interface. Herein we examine a device that enables torque to be transmitted across a sealed environmental barrier. The barrier represents the restraint membrane through which the torque is transmitted. The power is transferred through elastic deformation of a circular tube into an elliptical cross-section. Rotation of the principle axis of the ellipse at one end results in a commensurate rotation of an elliptical cross section at the other end of the tube. This transfer requires no rigid body rotation of the tube allowing a membrane to seal one end from the other. Both computational and experimental models of the device are presented.
Hendricks, R. C.↗
Collapse and relaxation of rotating stellar systems
The evolution of initially spherical, uniform-density, and uniform-velocity-dispersion stellar systems is investigated by means of a three-dimensional N-body computer model. Some 100,000 simulation stars are used to follow the collapse and relaxation of the system for various amounts of angular momentum in solid-body rotation. For initially low values of the angular momentum satisfying the Ostriker-Pebbles stability criterion the systems quickly relax to an axisymmetric shape and resemble elliptical galaxies in appearance. The maximum flattening for these systems is equivalent only to an E2 system. For larger values of the initial angular momentum bars develop, and the systems undergo a much more drastic evolution. The apparent rotational and random velocities of the barred systems are very sensitive to the viewing direction. An additional complication is the frequent misalignment of the apparent major axis with the direction that reflects the maximum rotation.
Hohl, F.↗
Helicity fluctuations and turbulent energy production in rotating and non-rotating pipes
Finite-difference second-order accurate direct simulation of a turbulent pipe has been used to investigate how the turbulence production and dissipation change when a solid body rotation is applied. It is shown that when the helicity increases, the dissipation is reduced. It is asserted that to have a drag reduction the external action should be such as to disrupt the symmetry of right- and left-handed helical structures. In this study the Navier-Stokes equations in rotational form permit the turbulent energy production to be split into a part related to the energy cascade from large to small scales and into a part related to the convection by large scales. The full simulation data have shown the latter is greater than the former in the wall region and that, on the contrary, these two terms balance each other in the central region. From the pdf of the former, it has been shown how the vortical structures are changed in the wall region by the background radiation and how they are related to the changes in the energy production.
Orlandi, P.↗
Full-field Deformation Measurement Techniques for a Rotating Composite Shaft
Test methods were developed to view global and local deformation in a composite tube during a test in which the tube is rotating at speeds and torques relevant to rotorcraft shafts. Digital image correlation (DIC) was used to provide quantitative displacement measurements during the tests. High speed cameras were used for the DIC measurements in order to capture images at sufficient frame rates and with sufficient resolution while the tube was rotating at speeds up to 5,000 rpm. Surface displacement data was resolved into cylindrical coordinates in order to measure rigid body rotation and global deformation of the tube. Tests were performed on both undamaged and impact damaged tubes in order to evaluate the capability to detect local deformation near an impact damaged site. Measurement of radial displacement clearly indicated a local buckling deformation near the impacted site in both dynamic and static tests. X-ray computed tomography (CT) was used to investigate variations in fiber architecture within the composite tube and to detect impact damage. No growth in the impact damage area was observed by DIC during dynamic testing or by x-ray CT in post test inspection of the composite tube.
Kohlman, Lee W.↗
Numerical Study of Rotating Turbulence with External Forcing
Direct numerical simulation at 256(exp 3) resolution have been carried out to study the response of isotropic turbulence to the concurrent effects of solid-body rotation and numerical forcing at the large scales. Because energy transfer to the smaller scales is weakened by rotation, energy input from forcing gradually builds up at the large scales, causing the overall kinetic energy to increase. At intermediate wavenumbers the energy spectrum undergoes a transition from a limited k(exp -5/3) inertial range to k(exp -2) scaling recently predicted in the literature. Although the Reynolds stress tensor remains approximately isotropic and three-components, evidence for anisotropy and quasi- two-dimensionality in length scales and spectra in different velocity components and directions is strong. The small scales are found to deviate from local isotropy, primarily as a result of anisotropic transfer to the high wavenumbers. To understand the spectral dynamics of this flow we study the detailed behavior of nonlinear triadic interactions in wavenumber space. Spectral transfer in the velocity component parallel to the axis of rotation is qualitatively similar to that in non-rotating turbulence; however the perpendicular component is characterized by a greatly suppressed energy cascade at high wavenumber and a local reverse transfer at the largest scales. The broader implications of this work are briefly addressed.
Yeung, P. K.↗