Experimental investigation of instabilities in flow through a long square channel rotating about the transverse axis

The results of an experimental investigation of bifurcation phenomena in a laminar flow through a rotating square channel approximately 50 channel widths long are presented. A comparison with known results of the numerical modeling of bifurcations of developed steady-state flow is carried out. A map of the steady and unsteady flow regimes is plotted. The effect of artificially generated input perturbations on the conditions of onset of longitudinally oriented vortex structures in the neighborhood of the elevated-pressure side of channels of lesser length is investigated.St. Petersburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 87–93, March–April, 1996.     

Flow of a shear-thinning liquid in a cylindrical container with a rotating end wall

The flow patterns produced by rotating one end wall of a circular cylinder completely filled with a strongly shear-thinning viscoelastic liquid have been investigated using the laser-induced fluorescence flow visualization technique. An intense toroidal vortex is produced in the vicinity of the rotating end wall with outward spiraling flow over the end wall itself. This vortex drives a second countercirculating vortex of low intensity in the region of the stationary end wall. Under some circumstances an axial jet of fluid is observed moving away from the rotating end wall. This jet showed evidence of instability, whereas all flows were otherwise completely steady. The double-vortex structure is different from those recently observed in either a Newtonian or slightly shear-thinning liquid or in the low Reynolds number flow of an elastic liquid. There are, however, similarities with older work for a viscoelastic liquid at relatively high Reynolds numbers. The observations highlight the suitability of the cylinder/rotating end wall configuration as a sensitive test case for computational work.     

Rarefied gas flow into a vacuum from a plane long channel closed at one end

The time-dependent problem of rarefied gas flow into a vacuum from a plane long channel closed at one end is solved on the basis of the kinetic S-model. The effect of diffuse molecular reflection from the channel walls on the flow velocity and the process of channel cavity vacuumization is studied as a function of the channel length and the extent of gas rarefaction under the condition that the wall temperature is maintained to be constant. The kinetic equation is solved numerically using a conservative finite-difference method of the second order of accuracy in spatial coordinates. The possibility of simplification of the problem for long times by means of reduction to the diffusion process is considered.     

Fluid flow through heterogeneous porous media in a rotating square channel

An analytical three-dimensional solution to the fluid flow problem through heterogeneous porous media in a rotating square channel is presented. The permeability of the fluid saturated porous domain varies in the vertical direction, thus affecting the imposed main flow in the channel. As a result of Coriolis acceleration, secondary circulation in a plane perpendicular to the main flow direction is created. A particular example of a monotonic distribution of the permeability function is analyzed leading to a single vortex secondary circulation. Nevertheless, multiple vortex secondary flow solutions are possible depending on the particular variation of the permeability in the vertical direction. No secondary motion is expected for isothermal flows in homogeneous porous media.     

通道中并列旋转圆柱的LB-DF/FD模拟

通过结合格子Boltzmann方法(LBM)和DF(Direct Forcing)/FD(Fictitious Domain)思想,建立了一种新的LB-DF/FD方法。采用两套网格系统,欧拉网格用于流体,拉格朗日网格用于固体,有效地避免了计算中重新生成网格的步骤,同时在处理流固问题方面优于LBM方法。通过模拟通道中单圆柱旋转的流场,验证了该方法的正确性;并利用该方法模拟了低雷诺数下通道中并列旋转圆柱周围的流场,分析了圆柱距离壁面间距gw和雷诺数Re对流场结构的影响。研究结果表明:gw显著影响了流场的结构及圆柱的受力;而Re对圆柱升力及Stokes单元数目的影响较大。     

Flow through a diverging channel: instability and bifurcation

The flow of a viscous fluid along a diverging channel is important practically. The mechanics of the flow also poses many theoretical problems. Some of these problems were considered before the foundation of the Japan Society of Fluid Mechanics, so it is perhaps surprising that their solutions are still so poorly understood. Nonetheless, a revival of interest in the last 20 years has led to progress in our understanding of the early stages of transition to turbulence in a two-dimensional channel. The present paper is a review of this progress in the theory of instabilities and bifurcations as the flux driven steadily along the channel is increased.     

Flow division at a channel crossing with subcritical or supercritical flow

The passage of an extreme storm over an urban area can lead to the flooding of the streets if the rainfall intensity exceeds the design value and/or the drainage system is not functional. The study of flow distribution in street networks thus is important for the design of flood protection measures. The flow distribution is affected by the junction flow characteristics, inflow discharges and downstream water depths. To reduce the degree of empiricism, a 3D Reynolds‐averaged Navier–Stokes equations model has been implemented in this study to investigate the flow phenomena in a cross junction. The Spalart–Allmaras model is used for turbulence closure. The numerical model utilizes the split‐operator approach, in which the advection, diffusion and pressure propagations are solved separately. The numerical model predicts accurately the flow distribution in a channel crossing under different subcritical flow conditions, for which experimental data are available. Recirculation zones exist at both the downstream channels and the associated contraction coefficient varies linearly with the ratio of the discharges at the two inlets. Secondary currents are apparent for the flow with strong asymmetric outlet conditions. Under supercritical inflow conditions, the model reproduces the hydraulic jump and hydraulic drop phenomena and predicts accurately the relationship between the input power ratio and the outflow discharge ratio of the street crossing. Copyright © 2009 John Wiley & Sons, Ltd.     

Flow of magnetizable fluid through long pipes

International Applied Mechanics -     

Hydromagnetic flow in a rotating channel

The steady flow in a parallel plate channel rotating with an angular velocity Ω and subjected to a constant transverse magnetic field is analysed. An exact solution of the governing equations is obtained. The solution in the dimensionless form contains two parameters: the Hartmann number, M ², and K ² which is the reciprocal of the Ekman number. The effects of these parameters on the velocity and magnetic field distributions are studied. For large values of the parameters, there arise thin boundary layers on the walls of the channel.     

Flow past a rotating cylinder translating at different gap heights along a wall

The flow past a rotating circular cylinder translating parallel to a wall at different heights is investigated for Reynolds numbers up to 400 for three discrete rotation rates. In particular, the various wake transitions that occur as a function of gap height are quantified for the three cases examined: non-rotation, and forward and reverse rotations. At low gap heights, only a single steady three-dimensional mode is found to become unstable on the steady base flow. As the gap height is increased, several new three-dimensional modes are observed, of which one attains large amplitudes in the near wake and another preferentially in the far wake. At still larger gap heights, the transition sequence resembles that observed in a rotating cylinder wake, for which the wake first undergoes transition to a periodic state, prior to the onset of three-dimensional flow. Parameter space maps showing the neutral stability curves and regions of instability for each mode are presented for each rotation rate, together with a discussion of the spatio-temporal characteristics and spatial distributions of the new modes. Finally, the force coefficients for the steady and periodic two-dimensional base flows are presented.     

Flow structure on a rotating plate

The flow structure on a rotating plate of low aspect ratio is characterized well after the onset of motion, such that transient effects are not significant, and only centripetal and Coriolis accelerations are present. Patterns of vorticity, velocity contours, and streamline topology are determined via quantitative imaging, in order to characterize the leading-edge vortex in relation to the overall flow structure. A stable leading-edge vortex is maintained over effective angles of attack from 30° to 75°, and at each angle of attack, its sectional structure at midspan is relatively insensitive to Reynolds number over the range from 3,600 to 14,500. The streamline topology, vorticity distribution, and circulation of the leading-edge vortex are determined as a function of angle of attack, and related to the velocity field oriented toward, and extending along, the leeward surface of the plate. The structure of the leading-edge vortex is classified into basic regimes along the span of the plate. Images of these regimes are complemented by patterns on crossflow planes, which indicate the influence of root and tip swirl, and spanwise flow along the leeward surface of the plate. Comparison with the equivalent of the purely translating plate, which does not induce the foregoing flow structure, further clarifies the effects of rotation.     

Fluid flow in a rotating cylindrical container with a rotating disk at the fluid surface

Fluid flow in a rotating cylindrical container of radius R_w and height H with a co-axially rotating disk of radius R_d at the fluid surface is numerically investigated. The container and the disk rotate with angular velocities Ω_w and Ω_d, respectively. We solve the axisymmetric Navier-Stokes equations using a finite-volume method. The effects of the relative directions and magnitudes of the disk and container rotations are studied. The calculations are carried out with various ratios of Ω_w and Ω_d for H/R_w = 2 and R_d/R_w = 0.7. Streamlines and velocity vectors in the meridional plane and azimuthal velocities are obtained. The flow fields in the meridional plane are discussed with relation to azimuthal velocities in the interior of the container. The numerical results are also compared with experimental data.     

Unusual hydrodynamic structures in a rotating channel

Visualizing the flow in the meridional plane of a rotating circular pipe has revealed two interesting three-dimensional hydrodynamic effects. The first is the unsteady process that follows the sudden stopping of the rotation, including the appearance on the inner surface of periodic localized inhomogeneities. These grow differently in the axial and radial directions with the eventual formation of mushroom-like structures; this process can be qualitatively explained in terms of the theory of unsteady Görtler vortices [1]. The second effect is the establishment of an unusual extended stable periodic structure as the rotating channel, initially open at one end, is closed off by a fixed plate, leaving a small gap between the plate and the end of the pipe for air to flow into the pipe from the outside. This periodic structure consists of volumes with a closed circulating flow alternating with open volumes hydrodynamically communicating with each other and the end of the pipe through wall flow zones. Simple relations are proposed for some of the characteristics of the periodic structure detected.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 35–40, March–April, 1993.In conclusion, the authors wish to express their gratitude to Dr. Yu. G. Gurevich for his assistance and helpful discussion of the results obtained in Sec. 2.