The narrow gap stability theory of blood flow between two relatively rotating concentric cones

The boundary perturdation solutions for blood flow between tworelatively rotating concentric cones(one is stationary andthe other is rotating with constant angle velocityω)havebeen obtained.On the basis of the solutions obtained andby using theory of the narrow gap stability,the stability ofthe stratified blood flow between two relatively rotating con-centric cones with an axial flow is demonstrated.     

Flow stability between separator plates

The flow of a viscous fluid in the narrow gap between two rapidly rotating coaxial cones has been examined in [1]. A similar motion takes place between the plates of a separator in various branches of engineering for the separation of emulsions and clarification of suspensions. The laminar flow regime is necessary for normal operation of the plate separator. The present paper studies the hydrodynamic stability of the interplate flow and suggests a specific criterion which is consistent with the practice of the design and operation of separators and which has a simple physical meaning.     

Coriolis effects on the stability of pulsed flows in a Taylor–Couette geometry

Results steming from the linear stability of time-periodic flows in a Taylor–Couette geometry with cylinders oscillating in phase or out-of-phase are presented. Our analysis takes into account the gap size effects and investigates the influence of a superimposed mean angular rotation of the whole system.In case of no mean rotation, the finite gap geometry is found to affect the shape of the stability diagrams (critical Taylor number versus the frequency parameter) which consist of two distinct branches as opposed to being continuous in the narrow gap approximation. In particular, in the out-of-phase configuration a new branch for low frequencies was found, thus enabling better agreement with available experimental results.When cylinders are co-rotating and subject to rotation effects, our calculations provide the evolution of the critical Taylor number versus the rotation number for two values of the frequency. The stability curves are found to be in qualitative agreement with available experimental data revealing a maximum of instability for a rotation number of about 0.3.In the high rotation regime, enhancement of the critical Taylor number is investigated through an asymptotic analysis and the value of the rotation number at which restabilization occurs is found to depend on the frequency parameter.A restabilization of the flow also occurs when the rotation number and the gap size are of the same order, a phenomenon already pointed out in the case of steady flows and attributed to the near cancellation of Coriolis and centrifugal effects. Our investigation proves that the same mechanism still holds for time-periodic flows.     

A self-aligning parallel plate (SAPP) fixture for tribology and high shear rheometry

This paper introduces a novel self-aligning parallel plate fixture for rotational rheometers. The ring-shaped shearing surface of this fixture is held on a low friction single contact point bearing and uses hydrodynamic lubrication forces in order to maintain the parallelism of the freely tilting surfaces over a full rotation. The optimized parallelism of the plates enables to conduct tribological measurements of low frictional stress between the shearing surface materials and a fluid at normal loads down to 1.3 kPa. Limited only by the degree of non-flatness of the surfaces, the new fixture can determine boundary lubrication sliding frictions within 10 % and down to angular velocities of 400 μrad/s. In a controlled gap mode, this setup reaches a gap error of 3.4 μm which enables to reliably conduct rheological measurements down to absolute gaps of the parallel plates of 10 μm and to reach high shear rates up to $10^{5}\;{\rm s}^{-1}$ .     

同心旋转圆柱间粘弹性流的非线性动力学模型

基于小间隙假设,将速度场和应力场有杉Ｆｏｕｒｉｅｒ展开式截断近似,推导了同心旋转圆柱间Ｏｌｄｒｏｙｄ－Ｂ型流体的六维动力系统,探讨了高分子添加对滑动轴承间油膜稳定性的影响。结果表明,少量的高分子添加剂具有推迟流体层流失稳的作用。     

微粗糙平面上翻身陀螺的稳定性

本文讨论微粗糙平面上翻身陀螺绕直立的极轴永久转动的稳定性。应用关于部分变量的稳定性定理,导出在粘性和库仑两种摩擦条件下的解析形式稳定性判据。该判据用永久转动角速度的大小而不是进动角速度的大小作为判别准则,较为合理。     

Dynamic Contact Behavior of a Golf Ball during Oblique Impact: Effect of Friction between the Ball and Target

The oblique impact between a golf ball and a polymethyl methacrylate (PMMA) target with smooth transparent surfaces was studied using a high-speed video camera. Video images of the impact were recorded from the backside of the target and were used to determine the contact time, contact area, and the displacement and rotation of the ball along the target. The average tangential and angular velocities were determined as functions of the inbound ball velocity. As the inbound ball velocity increased, the contact area and average tangential and angular velocities also increased while the contact time decreased. An oiled PMMA target was used to study the effect of reduced friction between the ball and target. The results were compared with earlier data for a steel target with relatively rough surfaces. The contact area and time were unaffected by friction, but the average tangential velocity increased while the average angular velocity decreased as the friction decreased.     

Rotor oscillation and stability in complex motion

Precession vibration of a rigid disk with unequal axial moments of inertia is considered when the axis of rotation turns; the disk is located asymmetrically on a flexible axle. Periodic solutions of the equations of motion and the amplitude-frequency relations are obtained for various values of the angular velocity of the axis of rotation. The critical rotational velocities of disks with various moments of inertia are defined in terms of the gyroscopic forces. The stability of motion is analyzed for various angular velocities of the rotating axis. State Technical University of Building and Architecture, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 7, pp. 104–107, July, 1999.     

The attitudes of constant angular velocity motions

A rotation can be represented by a tensor which in turn can be parameterized by an angle of rotation and an axis of rotation. This paper presents the first systematic study of the class of rotation tensors which possess constant angular velocities. In addition to the expected rotations featuring constant axes of rotation and constant angular rates, the existence of two other types of rotation are shown. For these rotations, the time variation of the angle and axis of rotation are coupled by an integrable dynamical system. Although the temporal behavior of the axis and angle of rotation can be complex, it also demonstrated how the rotations can be considered as motions about the angular velocity vector. One of the methods used to show this result is based on an analogue to the geometry of a circular helix. The presence of the class of rotations in rigid body dynamics and twistless helical deformations of rods is also discussed.     

Application of Radau IIA algorithms to flexible multibody system with holonomic constraints

The paper designs new 2- and 3-stage Radau IIA algorithms to integrate the dynamic responses of flexible multibody system with holonomic constraints. The total translation, the incremental rotation and associated velocities are selected as unknowns to avoid the linearization of angular acceleration which makes it possible to parameterize the finite rotation by using the Wiener–Milenkovi? parameters. The new algorithms release the heavy computational burden through the simplified Newton iterations and are stabilized by the preferable h-scaling technique. Contributions of the paper include: (1) For 2-stage algorithm, the resulting block triangular equations are solved efficiently by an inner iteration scheme. (2) For 3-stage algorithm, the full-size linear system is decoupled into a real and a complex subsystems which reduces the size of the system dramatically. (3) A new scheme is designed to predict the truncation error from the associated deferred correction equations without overestimation. Finally, numerical simulations show the 2- and 3-stage Radau IIA algorithms have excellent stability and convergence properties and behavior in a computationally efficient manner.     

Flow measurements inside a heated multiple rotating cavity with axial throughflow

This paper discusses experimental results from a multiple cavity test rig representative of a high pressure compressor internal air system. Measurements of the axial, tangential and radial velocity components are presented. These were made using a two component, laser doppler anemometry (LDA) system for a range of non-dimensional parameters representative of engine conditions (Re up to 4 × 10⁶ and Re_z up to 1.8 × 10⁵). Tests were carried out for two different sizes of annular gap between the (non-rotating) drive shaft and the disc bores.

The axial and radial velocities inside the cavities are virtually zero. The size of the annular gap between disc bore and shaft has a significant effect on the radial distribution of tangential velocity. For the narrow annular gap (d_h/b = 0.092), there is an increase of non-dimensional tangential velocity V/Ωr with radial location from V/Ωr < 1 at the lower radii to solid body rotation V/Ωr = 1 further into the cavity. For the wider annular gap (d_h/b = 0.164), there is a decrease from V/Ωr > 1 at the lower radii to solid body rotation further into the cavity. An analysis of the frequency spectrum obtained from the tangential velocity measurements is consistent with a flow structure in the r– plane consisting of pairs of contra rotating vortices.     

Calculation of the self-oscillations arising as a result of the loss of stability by the spiral flow of a viscous liquid in an annular tube

The spiral flow of a viscous liquid in an annular gap (formed by concentric cylinders) due to the rotation of the inner cylinder and the axial pressure gradient is considered; the stability of the flow is discussed in relation to small but finite rotationally symmetrical perturbations.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 57–63, May–June, 1976.The author wishes to thank V. I. Yudovich for interest in this work.     

Axisymmetric flows of an incompressible fluid between movable rotating disks

Within the Karman family of exact solutions of the Navier-Stokes equations, some non-selfsimilar solutions are considered to the problem of unsteady incompressible flow between two rotating disks one of which moves along a common rotation axis. Three classes of the flow regimes are studied: (i) a flow between the non-rotating disks, (ii) a flow between the disks rotating with identical angular velocities, and (iii) a flow between the disks rotating with opposite velocities. Examples of exact rotationally symmetric solutions for the inviscid-fluid equations, satisfying the no-slip conditions, are given.     

动脉狭窄对血液流速的影响

为了定量计算动脉局部狭窄对动脉管中血液流动速度的影响，本文分别对狭窄区域内定常流和非定常流动进行了求解，得出了狭窄区域内定常流和脉动流的速度表达式。本文将均匀段的流速形经Ｆｏｕｒｉｅｒ分解成定常和脉动两部分，然后分别计算出狭窄区域内对应的定常和脉动流速，经Ｆｏｕｒｉｅｒ合成还原成流速时域波形，同时针对各种情况将不同狭窄对不同的流速波形的作了分析比较。     

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.     

Convective heat transfer from two rotating circular cylinders in tandem arrangement by using lattice Boltzmann method

The numerical investigation of the two-dimensional laminar flow past two ro- tating circular cylinders in the tandem arrangement is conducted by the lattice Boltzmann method. The numerical strategy is used for dealing with curved and moving boundaries of the second-order accuracy for velocity and temperature fields. The effects of various rotational speed ratios and gap spacing are studied with the Reynolds number of 100 and the Prandtl number of 0.71. A varied range of rotational speed ratios are investigated for four different gap spacing, i.e., 3.0, 1.5, 0.7, and 0.2. The results show that, for the first cylinder, the lift and drag coefficients for large gap spacing are similar to those for a single cylinder; for the second cylinder, the lift coefficient descends with the increase in the angular velocity for all gap spacing, while the drag coefficient ascends except for the gap spacing of 3.0. The results of the averaged periodic Nusselt number on the surface of the cylinders show that, for small distances between the cylinders and low angular velocities, conduction is a dominant mechanism of heat transfer, but for large distances and high angular velocities, convection is the main mechanism of heat transfer.     

动量矩变量描述的陀螺体永久转动的分岔特性

本文建立以动量矩分量和Ｄｅｐｒｉｔ正则变量为独立变量的陀螺体动力学方程，用以描述无力矩非对称陀螺体的姿态运动。在动量矩空间内讨论了陀螺体永久转动轴的数目和稳定性随转子转速变化的分岔特性。     

The flow of viscoplastic material between two concentric spheres

The motion of a viscoplastic medium between two concentric spheres is considered upon rotation of one sphere with constant angular velocity. This problem is solved by an heuristic iterative method. The boundary of the stagnation zones is found and its specific shape is shown. The flow characteristics versus the parameter of the medium are obtained. Voronezh State Engineering Academy, Voronezh 394017. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 1, pp. 133–139, January–February, 1999.     

Three-dimensional problems of the hydrodynamic interaction between bodies in a viscous fluid in the vicinity of their contact

The study is devoted to the hydrodynamic interaction between bodies near their contact. The stresses produced in a narrow gap between the bodies in the vicinity of their contact determine the main part of forces acting on the bodies in motion. In many cases, the velocity and pressure fields in the vicinity of the contact can be determined and the main asymptotics for the hydrodynamic interaction force in the small spacing between the surfaces can be derived. An overview of the three-dimensional problems solved using this method is presented and for certain problems new formulations are given. The reliability of the results is confirmed by the comparison with available exact particular solutions and experimental data.     

Stability of the cylindrical precession of a satellite in an elliptic orbit

We study the linear problem on the stability of rotation of a dynamically symmetric satellite about the normal to the plane of the orbit of its center of mass. The orbit is assumed to be elliptic, and the orbit eccentricity is arbitrary. We assume that the Hamiltonian contains a small parameter characterizing the deviation of the satellite central ellipsoid of inertia from the sphere. This is a resonance problem, since if the small parameter is zero, then one of the frequencies of small oscillations of the symmetry axis in a neighborhood of the unperturbed rotation of the satellite about the center of mass is exactly equal to the frequency of the satellite revolution in the orbit. We indicate a countable set of values of the angular velocity of the unperturbed rotation for which the resonance is even double. The stability and instability domains are obtained in the first approximation with respect to the small parameter.