Angular Velocity Ratio Research Articles

Topological flow evolutions in cylinder of a motored engine during intake and compression strokes

The evolution processes of the in-cylinder flows in the axial and diametral planes of a motored two-valve, single-cylinder, four-stroke engine during the intake and compression strokes are diagnosed by using a particle image velocimeter. A device, which is called the “inlet deflection-valve”, being capable of deflecting the inlet flow is installed upstream of the inlet port. The engine cylinder, piston, and accessories are modified to meet the requirements of laser-light sheet shooting and camera viewing when the particle image velocimetry is applied. A conditional sampling technique is employed to acquire the instantaneous velocity data at predetermined crank angles. Ensemble averages of large amounts of the instantaneous velocity maps obtained at various crank angles present clear pictures of the evolution processes of the tumble and swirl motions in the engine cylinder. Sectional streamlines and the velocity vectors show the topological flow structures. The inception, establishment, evolution, and destruction processes of the swirling and tumbling vortical structures during the intake and compression strokes are presented and discussed. Quantified strengths of the rotating motions in the axial and diametral planes are presented by dimensionless tumble-and-swirl ratios, which are defined as the ratio of the mean angular velocity of the vortices in the target plane at a certain crank angle divided by the average crank angle velocity. By using the quantified nondimensional parameters, the correlation between the in-cylinder flow motions and the engine performance is analyzed and discussed.

Rotation and Properties of Be Stars

The actual characteristic average surface angular velocity ratio of the Be phenomenon may be higher than Ω/Ωc= 0.8 ± 0.1 derived fromvsinivalues not corrected from gravity darkening effects. Late Be Stars need not only higher values of Ω/Ωc, but also larger main sequence age ratios τ/τMSthan early Be Stars to display the Be phenomenon. Galactic field Be Stars appear at any MS phase, but their frequency is higher for τ/τMS≳ 0.5. Be Stars are probably neat differential rotators, i.e. they rotate with energy ratios kinetic/|gravitational| larger than withstood by critical rigid rotators. Initial formation conditions must favor the existence of fast rotators, while only a small fraction of them could be accounted for by mass transfer in close binary systems. Bn stars could perhaps represent a pre-Be phase.

333 共・反回転する密閉円筒容器内の旋回流の数値解析

Numerical study was conducted on the axisymmetric swirling flows of viscous Boussinesq fluid in cylindrical containers with co-and counter-rotating end disks. Swirling flows are studied for the angular velocity ratio of end disks in the range of -1.0≦s≦1.0 with and without vertically stabilizing temperature differences. The side wall i* th*mally insulated. For the co-rotating end disks, the flows are well described by the classic similarity solutions when s ≅ 1.0. When s ≅ 0,the flow exhibits much studied vortex breakdowns depending on the Reynolds number and the cylinder aspect ratio. For the counter-rotating end disks, flow separation occurs on the side wall and recirculation zones are created. Under strong vertical temperature differences, layered structures appear for all values of studied in the meridional plane and conductive temperature distribution prevails Supression of azimuthal velocity component is noted at mid-height of the cylinder.

Gear-Cutting Method of Parallel Depth Hypoid Gears. 3rd Report. The Ellipse of Tooth Bearing and Some Gear-Cuttings.

The purpose of this study is to develop a gear-cutting method of hypoid gears to achieve a good tooth bearing and good performance for practical use. In the first report, the authors proposed a new cutting method of parallel depth hypoid gears which mesh with each other at one point at a constant angular velocity ratio, and precisely stated the theory for the gear-cutting method. In the second report, the theory of the trace of the point contact mark is shown precisely. 0ne of the features of this method is that the designer can control the trace of the point contact mark on the tooth surface as desired. In this report, the theory of the ellipse of tooth bearing is shown precisely. In order to confirm the validity of the method, some hypoid gears were designed and manufactured, and ellipse of tooth bearing on red lead corresponded to those of the theory.

Stability of ferrofluid flow between concentric rotating cylinders with an axial magnetic field

A linear stability analysis for the ferrofluid flow between two concentric rotating cylinders in the presence of an axial magnetic field is implemented in this study. Both of the wide-gap and small-gap cases are considered and the governing equations with respect to three-dimensional disturbances including axisymmetric and non-axisymmetric modes are derived and solved by a direct numerical procedure. A parametric study covering wide ranges of ϕ, the volume fraction of colloidal particles; ξ, the strength of axial magnetic field; μ, the ratio of angular velocity of the outer cylinder to that of the inner cylinder; and ε, the ratio of radius of the inner cylinder to that of the outer cylinder, is conducted. Results show that the stability characteristics depend heavily on these factors. It is found that the increases of ϕ and ξ, and decrease of ε tend to stabilize the basic flow for an assigned value of μ. The variations of the onset mode with these parameters are discussed in detail. An example for the practical application of present results is given to help the understanding of stability behaviour of this flow.

Analysis of Belt-Driven Mechanics Using a Creep-Rate-Dependent Friction Law

An analysis of the frictional mechanics of a steadily rotating belt drive is carried out using a physically appropriate creep-rate-dependent friction law. Unlike in belt-drive mechanics analyzed using a Coulomb friction law, the current analysis predicts no adhesion zones in the belt-pulley contact region. Regardless of this finding, for the limiting case of a creep-rate law approaching a Coulomb law, all predicted response quantities (including the extent of belt creep on each pulley) approach those predicted by the Coulomb law analysis. Depending on a slope parameter governing the creep-rate profile, one or two sliding zones exist on each pulley, which together span the belt-pulley contact region. Closed-form expressions are obtained for the tension distribution, the sliding-zone arc magnitudes, and the frictional and normal forces per unit length exerted on the belt. A sample two-pulley belt drive is analyzed further to determine its pulley angular velocity ratio and belt-span tensions. Results from this analysis are compared to a dynamic finite element solution of the same belt drive. Excellent agreement in predicted results is found. Due to the presence of arbitrarily large system rotations and a numerically friendly friction law, the analytical solution presented herein is recommended as a convenient comparison test case for validating friction-enabled dynamic finite element schemes.

The stability of the narrow-gap Taylor-Couette system with an axial flow

The stability of viscous flow between concentric rotating cylinders with an axial flow due to an axial pressure gradient is considered. The governing equations with respect to three-dimensional disturbances are derived and solved by a direct numerical procedure. Results are given for the case of small-gap approximation. Three typical cases μ=−1,0 and 0.5 are studied, where μ represents the ratio of angular velocity of the outer cylinder to that of the inner cylinder. The value of the axial Reynolds numberR is up to 100. It is found that the critical disturbance is a non-axisymmetric mode when the value ofR is sufficiently large, and the transition of the onset mode withR is demonstrated in detail. Results for the critical Taylor number, wave number, vortex incline angle, and relative wave velocity are also determined. The present stability analysis is found to be in agreement with previous experimental studies and particularly reveals the stability characteristics with the variation of μ.

Radiative transfer in the distorted and irradiated atmospheres of close binary components

We studied the transfer of line radiation in the distorted and expanding atmospheres of close binary components. We assumed that the distortion of the atmosphere is caused by self rotation and tidal force exerted by the presence of the secondary component. The distortion is measured in terms of the ratio of angular velocities at the equator and pole (X), mass ratio of the two components m 2 m1 , the ratio of centrifugal force to that of gravity at the equator of the primary (f) and ratio of the equatorial radius of the primary to the distance between the centres of gravity of the two components r e R. A seventh degree equation is obtained to describe the distorted surface in terms of the above mentioned parameters. We have used X = 1 for uniform rotation throughout and used values f =0 :1 and 0.5, m2 m1 =1 , and re R =0 :1, 0.3, and 0.5. The equation of line transfer is solved in the comoving frame of the expanding atmosphere of the primary using complete redistribution in the line. We used a linear law of velocity of expansion so that the density varies as r 3 where r is the radius of the star, satisfying the law of conservation of mass. We set va =0a ndvb = 10 mtu (mean thermal units) where va is the velocity at the surface of the primary with radius r = a(= 5 10 11 )c m andvb is the velocity at the surface of the extended atmosphere with radius r = b(= 10 12 ) cm. We also computed lines in a static atmosphere with density changing as r 1 . We have considered a primary with an eective temperature T and a point source of secondary with three dierent temperatures Tc equal to 2 10 4 K, 3 10 4 K, and 4 10 4 K. The maximum change in line fluxes is noticed when the parameters r e R and f are changed, while the changes due to m 2 m1 are minimal. The expansion of the atmosphere produces P Cygni type line proles. The incident radiation from the secondary increases the line fluxes and absorption in the centre of the line is replaced by emission.

TEMPORAL BEHAVIOR OF FLOW IN ROTATING CAVITIES

Temporal flow behaviors in a heated rotating cavity with an axial throughflow and sealed annulus are explored. Generally, for both systems, the ratio of the flow angular velocities to the system boundaries are found, even close to boundaries, not equal to unity. Both systems exhibit similar temporal velocity gradient component distributions. Most unsteadiness corresponds to regions of high tangential velocity gradients. As a result of the flow drift, these spatial gradients are converted to temporal gradients. For the present flows, computations suggest judicious coordinate system angular velocity choices may reduce demands on both convective term treatments and computer resources.

Dynamic microfiltration of yeast suspensions using rotating disks equipped with vanes

Rotating disk dynamic filtration devices are notorious for yielding very high permeate fluxes with particulate suspensions due to the very high shear they generate at the membrane. This paper investigates the gain in performance obtained by equipping the rotating disk with straight vanes of various heights using baker yeast suspensions as a test fluid. The presence of vanes raises the velocity factor k (ratio of angular velocity of inviscid fluid core between disk and membrane to disk angular velocity ω) from 0.45 for a flat or smooth disk to 0.65 for a disk with eight 2 mm high vanes, and to 0.84 for eight 6 mm vanes. This produces a large increase in wall shear stress which is proportional to ( kω) 1.8. The permeate flux was found to be approximately proportional to kω for both 2 and 6 mm vanes and to about ( kω) 0.864 for a smooth disk. But the increase in permeate flux obtained when adding vanes or increasing vane height is larger than that due to increase in k. This further increase is possibly due to increase mixing by vortices generated by the vanes which further decrease the cell layer thickness on the membrane. The electrical power necessary for driving these disks was measured and compared with the calculated mechanical power of friction forces. The mechanical efficiency was found to be the same for 2 and 6 mm vanes but less than for a smooth disk. However, due to the large permeate flux increase in presence of vanes, the specific energy per cubic meter of permeate was found to be the smallest with 6 mm vanes and highest with the smooth disk. The permeate flux increase resulting from higher mixing was shown to be responsible for the lower specific energy of the 6 mm vanes.

Young Populous Clusters in the Magellanic Clouds

This work examines a sample of young populous clusters in the Magellanic Clouds. The population of these clusters offers insight into the course of stellar evolution for high-mass stars in the 8–20 M, mass range. The clusters of the present study provide a statistically significant sample with which to confront the predictions of stellar evolutionary models. We have paid particular attention to the issue of internal mixing, the consequence of which is extension of the convective core boundary over the classical Schwarzschild limit. We present a quantitative determination of the degree of internal mixing within the convective core overshoot paradigm, which parameterizes the degree of extension to the convective core. The convective core overshoot parameter, Lc, represents the degree of extension that is required to match our observations. The basis of our determination of Lc is Hubble Space Telescope WFPC2 photometry of the clusters NGC 330 (SMC) and NGC 1818, NGC 2004, and NGC 2100 (LMC). Our photometry in visual (F555W), ultraviolet (F160BW), and narrowband Ha (F656N) enabled us to construct the highly temperature sensitive F160BW F555W color and to distinguish the Be star population among the upper main-sequence (MS) population. Infrared photometry in the J and K bands was conducted to obtain accurate temperatures and luminosities for the evolved members. Comparison of the cluster population is made against stellar evolutionary models that incorporate a variable level of core overshoot. The luminosity function of MS stars and the number of evolved stars provide joint constraints on Lc. It is found that models with no convective core overshoot are strongly disfavored by the temperature and luminosity of the MS turnoff of the cluster sample. With a binary fraction of 30% the cluster populations indicate a . L p 0.62 0.22 c This study has established a photometric survey technique for Be stars, a technique that spectroscopic follow-up shows is highly complete. Our study has highlighted the large proportion of Be stars on the upper MS of young Magellanic Cloud clusters. Be stars are characterized by rapid rotation. Our study of the Be star fraction within the cluster and field environs of the LMC and SMC has provided evidence for an evolutionary enhancement of the Be fraction toward the end of the MS. We propose that this enhancement is the consequence of an increase in the ratio of the surface angular velocity to the critical angular velocity toward the end of the MS. In order to verify this scenario and to investigate the dependence of average rotation rates on metallicity, we present the rotational velocities for a sample of B0–B2 V–III stars drawn from the clusters and the field of the LMC. Compared with an equivalent sample of Galactic stars, the LMC cluster stars show faster projected rotational velocities. We discuss this result in the light of emergent evolutionary models that incorporate the effects of rotational mixing.

Effects of Radial Temperature Gradient on the Stability of a Viscous Flow between Two Rotating Porous Cylinders with a Narrow Gap

The linear stability of viscous fluid flow between two rotating concentric porous cylinders at temperature θ 1 (of the inner cylinder) and θ 2 (of the outer cylinder) is studied in a narrow gap case. The numerical values of the critical wave number a c and the critical Taylor number T c are listed in a table for different values of μ (-0 only the inner cylinder rotating), μ (≷0, both cylinders co-rotating or counter-rotating) ratio of angular velocities Ω 2 /Ω 1 , and for different values of ±N, ±S where N is a radial temperature gradient parameter based on the temperature difference θ 2 - θ 1 >/ 0) or injection (<0) velocity. The effects of these parameters on the stability of flows are discussed.

VIBRATION ANALYSIS OF A ROTATING TIMOSHENKO BEAM

The governing equations for linear vibration of a rotating Timoshenko beam are derived by the d‘Alembert principle and the virtual work principle. In order to capture all inertia effect and coupling between extensional and flexural deformation, the consistent linearization of the fully geometrically non-linear beam theory is used. The effect of Coriolis force on the natural frequency of the rotating beam is considered. A method based on the power series solution is proposed to solve the natural frequency of the rotating Timoshenko beam. Numerical examples are studied to verify the accuracy of the proposed method and to investigate the effect of Coriolis force on the natural frequency of rotating beams with different angular velocity, hub radius and slenderness ratio.

NON-LINEAR VIBRATION OF A TORSIONAL SYSTEM DRIVEN BY A HOOKE'S JOINT

Non-linear vibration in a driveline which incorporates a Hooke's joint is presented in this paper. In particular, torsional vibration due to fluctuating angular velocity ratio across the joint is examined. Linearized equations are used for the prediction of critical speed ranges where parametric instabilities characterized by exponential build up of torsional response amplitudes occur. Predicted instabilities indicate the range of driveshaft speeds to be avoided during the design of a driveline which employs a Hooke's joint. Numerical simulations and bifurcation analysis performed on the full non-linear equations further demonstrate the existence of parametric, quasi-periodic and chaotic motion. Onset of chaotic motion was shown to be characterized by a quasi-periodic route.

Direct numerical simulations of turbulent forced convection between counter-rotating disks

Abstract A Fourier–Chebyshev collocation spectral method is used to simulate the three dimensional unsteady flow inside a cylindrical annular enclosure comprised of two counter-rotating disks and sidewalls. Each disk is taken to be isothermal, with an imposed temperature difference between them, and the sidewalls are adiabatic. Buoyancy forces are neglected. A shallow annulus with aspect ratio, h / r o =0.06, and radius ratio, r i / r o =0.13, is considered (where 2 h is the distance between the disks and r i and r o are the inner and outer disk radii, respectively). One disk is rotating at the maximum speed and the other disk is rotating in the opposite direction. Results are obtained over a range of Re including the transition from laminar flow, for cases with both disks rotating at the same speed, Γ =−1.0, with one disk rotating more slowly than the other, Γ =−0.4, and with one stationary disk, Γ =0 (where Γ is the disk angular velocity ratio). The heat transfer rates between the disks are also obtained, showing the effects of transition to turbulence. The three-dimensional nature of the flows is characterized, and mean and RMS turbulence quantities are presented.

Instability of Taylor Vortex and Nonaxisymmetric Modes in Flow Between Rotating Porous Cylinders

A numerical solution of linear differential equations governing the instability of Taylor vortex and nonaxisymmetric modes inflow between rotating porous cylinders is present. Solutions take into account the presence of a radial flow between the two rotating cylinders. The critical Reynolds number and corresponding critical axial and azimuthal wavenumber are shown for different values of radius ratio, ratio of angular velocities of the inner and outer cylinders. The results show that not only the critical Reynolds number but the oscillatory onset mode of nonaxisymmetric disturbances can be altered when a radial flow is superimposed on the circular Couette flow. The weak inward flow has a destablizing effect for wide-gap, corotating system of positive and large μ (ratio of angular velocities ω1 and ω2) and the weak outward flow has a destablizing effect for small gap, co-rotating system and all counter-rotating system. The most unstable mode of instability depends not only on the angular speed ratio of both cylinders but also the strength of radial flow.

The influence of misalignments on mesh performances of hypoid gears

A new method for tooth contact analysis in mismatched hypoid gears is applied for the investigation of the influence of misalignments of the mating members on mesh performances. By using the corresponding computer program, the influence of running offset error, pinion’s axial adjustment error, and angular position errors of the pinion axis on the shape and position of path of contact and of potential contact lines under load, on separations along these contact lines, on angular displacements of the gear member, and on the variation of the angular velocity ratio through a mesh cycle, have been determined. The results obtained have shown that the position errors of the mating members cause edge contact on the tip of the pinion or gear tooth, worsen the conjugation of the contacting tooth surfaces, and considerably increase the angular displacements of the gear member and the angular velocity ratio variation through the whole mesh cycle, that considerably worsens the mesh performances.

Fluid temperature distributions in a rotating cavity with an axial throughflow

Radial and circumferential variations of cavity air temperature are presented for a rotating cavity with an axial throughflow of cooling air. Results show that the air temperatures are influenced significantly by the cavity surface temperature distribution. Strong (around 5°C) circumferential air temperature variations are observed showing the flow to be three-dimensional. Temperature time traces are used to infer flow structure features and also the variation of the fluid to cavity angular velocity ratio with temperature. Features and trends are found to be consistent with flow visualisation evidence, Laser Doppler Anemometry data, and also computations of other workers.

Mill setting and microstructural evolution during mechanical alloying of Mg2Si

The mechanical alloying behaviour of magnesium and silicon to form the intermetallic compound Mg2Si and the optimum setting of a planetary ball mill for this task, were examined. For the ductile–brittle magnesium–silicon system it was found that the efficiency of the mill is mostly influenced by the ratio of the angular velocity of the planetary wheel to that of the system wheel and the amount of load. The examination of the kinetics inside the planetary ball mill for different mill settings showed that a ratio of angular velocities of at least 3 is necessary to compensate the reduction of efficiency due to slip. The optimum powder load for the 500 ml vial was found to be 10–20 g. The milling process starts with elemental magnesium and silicon bulk particles. During the milling, the silicon pieces are rapidly diminished and together with the constantly forming Mg2Si they act as an emery powder for the magnesium bulk pieces. Simultaneous to the diminution of the magnesium, alloying occurs.

A note on Freudenstein's theorem

In this paper analytical expressions for the extreme velocity ratio of a four-bar linkage are derived by the application of vector loop equations. Alternative forms for Freudenstein's theorems are presented. Either geometrically or analytically, the theorems can be proved concisely. For an arbitrary four-bar linkage, Freudenstein's theorem can examine the occurrence of the phases at which the angular velocity ratio of links becomes extreme, but it cannot straightforwardly determine the exact phases to happen.