Effect of the Coriolis Force on Thermal Convection under Microgravity

In contrast to the generally accepted viewpoint, it is shown that the Coriolis force caused by the rotation of an orbital station about Earth and the station centroid can strongly affect natural convection during fluid-flow orbital experiments. Various aspects of this influence are investigated in detail. The focus is on the interaction of the Coriolis force and the harmonically oscillating gravity force on the intensity of two-dimensional thermal convection in a rectangular enclosure with rigid walls. It is shown that the dependence of the maximum root-mean-square velocity on the Ekman number or microacceleration frequency has a distinct resonant character. The height of the resonance peak is significantly influenced by the aspect ratio of the enclosure and by the orientation of the microacceleration vector and the angular velocity vector relative to the enclosure and each other. Special attention is given to nonlinear effects caused by the convective terms of the Navier–Stokes equations. Received 12 January 1998 and accepted 2 March 1998     

Low Mach Number Limits of Compressible Rotating Fluids

We consider the low Mach number limit for a compressible fluid rotating with a constant angular velocity in an exterior domain. The effect of Coriolis and centrifugal forces are taken into account, along with strong stratification due to the effect of gravitation. The anelastic approximation is identified as the limit problem. The main issue addressed in the paper is the interaction of the centrifugal force with acoustic waves.     

Nonisothermal steady flow of a viscoplastic liquid between two coaxial rotating cylinders

Rotational viscosimeters are widely used to determine liquid viscosity. The technique for processing the experimental data is based fundamentally on the analytic solution of the problem of isothermal flow of a viscous liquid between two rotating cylinders.If in the course of the experiment the heat released due to the internal friction leads to significant heating, then the processing of the experimental results using the equations obtained on the assumption of isothermocity of the flow may lead to large errors. The dissipative heating may be reduced by reducing the angular velocity of rotation of the cylinder; however extensive reduction of the angular velocity is not desirable, since this leads to an increase of the measurement relative error. In addition, there is the possibility of conducting the experiments with a wide variation of the angular velocities in order to identify the structural-rheological peculiarities of the liquid. In the latter case we must be able to separate the purely thermal effects from the influence of the rheological factors. All these questions are discussed in detail in [1]. The authors of [1] obtained the solution of the problem of nonisothermal flow of a Newtonian fluid between two rotating cylinders and gave a technique for processing the experimental data which takes account of the dissipative heating of the fluid. The present paper pursues the same objective for a visco-plastic fluid.An attempt to solve the problem of nonisothermal flow of a viscoplastic fluid was made by Dzhafarov in [2], where the problem was solved in two versions. In the first version it was considered that the viscosity varies hyperbolically with the temperature and the gap between the cylinders is small in comparison with the radius of the inner cylinder. As a result of the linearization of the equations of motion and heat balance, it turned out that in fact the problem of Couette flow of a viscoplastic fluid was solved rather than the original problem. In this case, naturally, such a characteristic of the flow of a viscoplastic fluid in an annular gap as the possibility of the formation of an elastic zone was not covered. In the second version the problem was solved under the assumption that the viscosity is independent of the temperature and the angular velocity is small.In the present study the problem is solved without the limitations discussed above on the angular velocity, the fluid visoosity, and the gap between the cylinders. In this case we consider two types of temperature boundary conditions: a) constant temperatures are specified on the surfaces of the cylinders, which in the general case may be different; and b) a constant temperature is given on the surface of the outer cylinder and the inner cylinder is thermally insulated.     

Effect of the deformation in the inertia forces on the inverse dynamics of planar flexible mechanical systems

The inverse dynamics problem for articulated structural systems such as robotic manipulators is the problem of the determination of the joint actuator forces and motor torques such that the system components follow specified motion trajectories. In many of the previous investigations, the open loop control law was established using an inverse dynamics procedure in which the centrifugal and Coriolis inertia forces are linearized such that these forces in the flexible model are the same as those in the rigid body model. In some other investigations, the effect of the nonlinear centrifugal and Coriolis forces is neglected in the analysis and control system design of articulated structural systems. It is the objective of this investigation to study the effect of the linearization of the centrifugal and Coriolis forces on the nonlinear dynamics of constrained flexible mechanical systems. The virtual work of the inertia forces is used to define the complete nonlinear centrifugal and Coriolis force model. This nonlinear model that depends on the rate of the finite rotation and the elastic deformation of the deformable bodies is used to obtain the solution of the inverse dynamics problem, thus defining the joint torques that produce the desired motion trajectories. The effect of the linearization of the mass matrix as well as the centrifugal and Coriolis forces on the obtained feedforward control law is examined numerically. The results presented in this investigation are obtained using a slider crank mechanism with a flexible connecting rod.     

The effect of oblateness in the perturbed restricted three-body problem

In this paper the restricted three-body problem is generalized in the sense that the effects of oblateness of the three participating bodies as well as the small perturbations in the Coriolis and centrifugal forces are considered. The existence of equilibrium points, their linear stability and the periodic orbits around these points are studied under these effects. It is found that the positions of the collinear points and y-coordinate of the triangular points are not affected by the small perturbations in the Coriolis force. While x-coordinate of the triangular points is neither affected by the small perturbations in the Coriolis force nor the oblateness of the third body. Furthermore, the critical mass value and the elements of periodic orbits around the equilibrium points such as the semi-major and the semi-minor axes, the angular frequencies and corresponding periods may change by all the parameters of oblateness as well as the small perturbations in the Coriolis and centrifugal forces. This model could be applicable to send satellite or place telescope in stable regions in space.     

Flow of a third grade fluid due to an accelerated disk

The magnetohydrodynamic (MHD) flow induced by non‐coaxial rotation of porous disk and a third grade fluid at infinity is investigated. The disk is moving with uniform acceleration and rotating with a uniform angular velocity. Numerical solution of the governing nonlinear initial and boundary value problem is obtained. The effects of physical parameters on the velocity profiles are examined in detail. The present study shows that the constant acceleration part has a greater influence than the time part of the assumed variable velocity of the disk. Copyright © 2009 John Wiley & Sons, Ltd.     

Contact problem of rubber rings with large deformation

A contact problem with friction between a rubber ring with large deformation and a linear elastic thin plate is solved by means of the substructuring technique in this paper. A study of the influence of fractional contact, of the influence of plate thickness on rubber ring’ deformation is presented.     

作大范围空间运动柔性梁的刚-柔耦合动力学

研究带中心刚体的作大范围空间运动梁的刚-柔耦合动力学问题．从精确的应变-位移关系式出发，在动力学变分方程中，考虑了横截面转动的惯性力偶和与扭转变形有关的弹性力的虚功率，用速度变分原理建立了考虑几何非线性的空间梁的刚-柔耦合动力学方程，用有限元法进行离散．通过对空间梁系统的数值仿真研究扭转变形和截面转动惯量对系统动力学性态的影响．     

Measurement of the acoustic velocity field of nonlinear standing waves using the synchronized PIV technique

The motion of gas within an air-filled rigid-walled square channel subjected to acoustic standing waves is experimentally investigated. The synchronized particle image velocimetry (PIV) technique has been used to measure the acoustic velocity fields at different phases over the excitation signal period. The acoustic velocity measurements have been conducted for two different acoustic intensities in the quasi-nonlinear range (in which the nonlinear effects can be neglected in comparison with the dissipation effects), and one acoustic intensity in the finite-amplitude nonlinear range (in which both the nonlinear term and the dissipative term play a role in the wave equation). The experimental velocity fields for the quasi-nonlinear cases are compared with the analytical results obtained from the time-harmonic solution of the wave equation. Good agreement between the experimental and analytical velocity fields proves the ability of the synchronized PIV technique to accurately measure both temporal and spatial variations of the acoustic velocity fields. The verified technique is then used to measure the acoustic velocity fields of the finite-amplitude nonlinear case at different phases.     

THE RENORMALIZATION-GROUP ANALYSIS FOR THE STATISTICAL PROPERTIES OF RAPIDLY ROTATING TURBULENCE

利用重正化群方法对强旋转湍流场统计性质予以研究, 通过重正化微扰展开, 对高波数速度分量进行逐 阶平均.计算结果显示当旋转角速度Ω → ∞时, 用以表征高波数速度分量对低波数速度分量影响的重正化黏性将趋于0, 这表明在强旋转条件下科氏力将抑制湍流速度分量之间的非线性相互作用, 从而阻碍湍流的能量级串效应, 当Ω → ∞时湍流的能量级串效应消失, 导致湍流脉动消失, 流动将层流化.理论计算结果还显示对于强旋转湍流, 时域-空域联立Fourier的湍流速度分量存在二维化趋势, 球面平均能谱函数有标度关系E(k) ∝ k^-3.     

Investigation of the effect of the Coriolis force on a thin fluid film on a rotating disk

The effect of the Coriolis force on the evolution of a thin film of Newtonian fluid on a rotating disk is investigated. The thin-film approximation is made in which inertia terms in the Navier–Stokes equation are neglected. This requires that the thickness of the thin film be less than the thickness of the Ekman boundary layer in a rotating fluid of the same kinematic viscosity. A new first-order quasi-linear partial differential equation for the thickness of the thin film, which describes viscous, centrifugal and Coriolis-force effects, is derived. It extends an equation due to Emslie et al. [J. Appl. Phys. 29, 858 (1958)] which was obtained neglecting the Coriolis force. The problem is formulated as a Cauchy initial-value problem. As time increases the surface profile flattens and, if the initial profile is sufficiently negative, it develops a breaking wave. Numerical solutions of the new equation, obtained by integrating along its characteristic curves, are compared with analytical solutions of the equation of Emslie et al. to determine the effect of the Coriolis force on the surface flattening, the wave breaking and the streamlines when inertia terms are neglected.     

A NONLINEAR FLUID–STRUCTURE INTERACTION ANALYSIS OF A NEAR-BED SUBMARINE PIPELINE IN A CURRENT

A negative lift force (attraction) can be induced on a near-bed pipeline in a horizontal current due to asymmetric flow. This negative lift force has a significant influence on the behaviour of the near-bed pipeline, causing two remarkable failure patterns. One failure pattern is due to stability loss, and the pipeline fully rests on the seabed. The other is due to the excessive stress or deformation even if the pipeline is stable in a position between the original equilibrium position and the seabed. A quantitative method to assess these two failure patterns by combining boundary element and finite element methods is proposed in this paper. This is a nonlinear fluid–structure interaction problem, and an iteration procedure is used herein to solve it. Numerical examples reveal that there exists a critical current velocity, above which the pipeline fails. The relationship between the critical velocity and the distance from the pipeline to the seabed is given.     

Bénard-Marangoni convection in a rotating fluid with and without surface deformation

This paper deals with Bénard-Marangoni convection in a thin horizontal layer heated from below and rotating uniformly about a vertical axis. The analysis is linear and its objective is to determine the critical temperature drop and the critical wavenumber at the onset of convection. The lower surface of the layer is in contact with an uniformly heated rigid plate and the upper face is deformed and subjected to a temperature-dependent surface tension. Exchange of stability and Boussinesq's approximation are taken for granted. It is shown that rotation has a stabilizing effect while surface deflection plays a stabilizing role at large angular velocity and has an opposite influence at low angular velocity. By increasing the angular velocity, one reinforces the stability, whatever the surface deformation.     

Error Analysis of a Projection Method for the Navier–Stokes Equations With Coriolis Force

In this paper a projection method for the Navier–Stokes equations with Coriolis force is considered. This time-stepping algorithm takes into account the Coriolis terms both on prediction and correction steps. We study the accuracy of its semi-discretized form and show that the velocity is weakly first-order approximation and the pressure is weakly order \frac12\frac{1}{2} approximation.     

Dynamic behaviour of an axially moving plate undergoing small cylindrical deformation submerged in axially flowing ideal fluid

The out-of-plane dynamic response of a moving plate, travelling between two rollers at a constant velocity, is studied, taking into account the mutual interaction between the vibrating plate and the surrounding, axially flowing ideal fluid. Transverse displacement of the plate (assumed cylindrical) is described by an integro-differential equation that includes a local inertia term, Coriolis and centrifugal forces, the aerodynamic reaction of the external medium, the vertical projection of membrane tension, the bending resistance, and external perturbation forces. In the two-dimensional model thus set up, the aerodynamic reaction is found analytically as a functional of the cylindrical displacement, using the techniques of complex analysis. The resulting integro-differential problem is discretized in space with the Fourier-Galerkin method, and integrated in time with the diagonalization method. Examples are computed with physical parameters corresponding to air and some paper materials. The effects of the surrounding fluid on the critical velocity and first natural frequency are investigated, for stationary air, for an air mass moving with the plate, and for some arbitrary axial fluid velocities. The obtained results are applicable for both an ideal membrane and a plate with nonzero bending rigidity.     

Effects of modal truncation and condensation methods on the Frequency Response Function of a stage reducer connected by rigid coupling to a planetary gear system

The present paper is aimed at the application of a substructure methodology, based on the Frequency Response Function (FRF) simulation technique, to analyze the vibration of a stage reducer connected by a rigid coupling to a planetary gear system. The computation of the vibration response was achieved using the FRF-based substructuring method. First of all, the two subsystems were analyzed separately and their FRF were obtained. Then the coupled model was analyzed indirectly using the substructuring technique. A comparison between the full system response and the coupled model response using the FRF substructuring was investigated to validate the coupling method. Furthermore, a parametric study of the effect of the shaft coupling stiffness on the FRF was discussed and the effects of modal truncation and condensation methods on the FRF of subsystems were analyzed.     

Localized solutions to the nonlinear wave equation for flexural motions of an elastic beam traveling in an air-filled tube

Steady-progressive-wave solutions are sought to the nonlinear wave equation derived previously [J. Fluids Struct. 16 (2002) 597] for flexural motions of an elastic beam traveling in an air-filled tube along its center axis at a subsonic speed. Fluid-structure interactions are taken into account through aerodynamic loading on the lateral surface of the beam subjected to small but finite deflection but end effects and viscous effects are neglected. Linear dispersion characteristics are first examined by exploiting the small ratio of the induced mass to the mass of the beam per unit length. Centered around the traveling speed of the beam, there exists such a narrow range of propagation velocity that the linear steady propagation is prohibited. In this range, it is revealed that some interesting nonlinear solutions exist. The periodic wavetrain is found to exist as the exact solution. Asymptotic analysis is then made by applying the method of multiple scales and the stationary nonlinear Schrödinger equation is derived for a complex amplitude. A monochromatic solution to this equation corresponds to the exact periodic solution. Imposing undisturbed boundary conditions at infinity, it is revealed that the localized solution exists as a result of balance between the linear instability and the nonlinearity. This solution is checked by solving the nonlinear equation numerically. It is further revealed that the amplitude-modulated wavetrain exists not only in the range of the velocity mentioned above but also outside of it.     

Rotation correction of wall function and velocity structure under the couple effects of buoyancy force and rotating effects at the entry section of the smooth straight channel

This paper studies the effect of rotation on the turbulent boundary-layer flow in a rotating duct with a square cross section by using hot-wire. The experiments were conducted with the Reynolds numbers, based on the duct's hydraulic diameter (D = 80 mm) equaling 19,000. The rotation numbers (Ro) studied ranged from 0 to 0.362. Hot-wire measurements of the flow field were made at four cross sections of the rotating duct. The effects of rotation on velocity profile, semi-logarithmic mean velocity profile, and wall shear stress are discussed in this paper. Results obtained show the velocity deficit about the leading surface of the rotating duct, created by the secondary flows induced by the Coriolis force, to not increase monotonically with the increase in the Rotation number. Results obtained also show the effects of rotation to penetrate into the logarithm region, and the flow near the leading surface tends to laminarize. In this study, a correction factor is developed for logarithmic law to account for the effects of rotation, which can be used in CFD studies of rotating ducts that use wall functions.