The characteristics of spiral waves in an axially rotating pipe

An experimental study of the instability of a flow in an axially rotating pipe is performed by means of LDV and flow visualization technique. It is found that the axial velocity of the rotating pipe flow fluctuates like a sine wave at first, then its fluctuating pattern assumes a somewhat sawtooth wave form as a spiral wave appears, which is predicted by means of linear and nonlinear stability analysis. At a certain rotation rate, the amplitude of the velocity fluctuations amounts to 30% of the axial velocity. At the down-stream section, another fluctuating component appears in the velocity, which interferes with the initially appearing component, then the fluctuation becomes one with broad-band spectral components. There is a close analogy between this spectral evolution and that of a Taylor-Couette flow. Deformation of the velocity distribution is obtained from the velocity fluctuating pattern and its phase, and the structure of the spiral wave is considered. The strength, azimuthal wavenumber and angular velocity of the spiral wave obtained from the velocity data are confirmed by flow visualization. The change of pressure loss in the rotating pipe is compared with the case without rotation.     

Nonparallel stability of the flow in an axially rotating pipe

The linear stability of the developing flow in an axially rotating pipe is analyzed using parabolized stability equations (PSE). The results are compared with those obtained from a near-parallel stability approximation that only takes into account the axial variation of the basic flow. Though the PSE results obviously coincide with the near-parallel ones far downstream, when the flow has reached a Hagen-Poiseuille axial velocity profile with superimposed solid-body rotation, they differ significantly in the developing region. Therefore, the onset of instability strongly depends on the axial evolution of the perturbations. The PSE results are also compared with experimental data from Imao et al. [Exp. Fluids 12 (1992) 277], showing a good agreement in the frequencies and wavelengths of the unstable disturbances, that take the form of spiral waves. Finally, a simple method for detecting one of the conditions to characterize the onset of absolute instability using PSE is given.     

Vortex-speed selection within the boundary-layer flow over a rotating sphere placed in an enforced axial flow

This paper furthers existing work into the instability mechanisms within the boundary-layer flow over a rotating sphere through the study of amplification rates within the convectively-unstable region. The onset of convective instability is associated with the experimentally observed onset of spiral vortices reported in the literature. Axial flow is found to stabilize the boundary layer by both delaying the onset of convective instability at all latitudes and also by significantly reducing the spatial amplification rates. We find that the type II (streamline curvature) mode becomes increasingly amplified with respect to the type I (crossflow) mode and is therefore likely to be selected in practice for sufficiently high axial flow rates. Furthermore, in experiments where special care is taken to remove all surface roughness, we predict that vortices will rotate at around 75% of the local surface speed. This is consistent with the experimental observations of Kobayashi & Arai who note a speed of around 76% under particular experimental conditions. These predictions are entirely consistent with related work on the rotating-disk and cone boundary layers.     

Instability of hagen-poiseuille flow for axisymmetric mode

An investigation is described for instability problem of flow through a.pipe of circular cross section. As a disturbance motion, we consider an axisymmetric nonlinear mode. An associated amplitude or modulation equation has been derived for this perturbation. This equation belongs to the diffusion type. The coefficient of it can be negative with Reynolds number increasing, because of the complex interaction between molecular diffusion and convection. The negative diffusion, when it occurs, cause a concentration and focusing of energy within the decaying slug, acting as a role of reversing natural decays.     

Interchangeability of vortex-breakdown types

In order to investigate the connection between the bubble and the spiral form of vortex breakdown, experiments were conducted: an external disturbance in the form of an azimuthally spinning waveform was imposed in a pipe. The azimuthal wave number was varied by adjusting the phase difference among four oscillating pistons mounted circumferentially on the pipe. By imposing a disturbance of zero azimuthal wave number, a spiral was transformed into a bubble, and this occurred only for selective piston frequencies; the vortex breakdown which altered from the spiral to the bubble moved upstream, where it remained as a bubble as long as the external disturbance remained. Once the disturbance was removed, the bubble returned to a spiral. By imposing a disturbance of azimuthal wave number +1 (the first circumferential mode rotating in the same direction as the mean swirl), a bubble was transformed into a spiral for selective piston frequencies, and the spiral moved downstream. These preferred frequencies were found to be the same as the unexcited frequencies observed in the spiral in its natural state. As long as the external disturbance was imposed, the breakdown altered from the bubble to the spiral remained as a spiral; once the disturbance was removed, the spiral reverted to a bubble. By imposing a disturbance with azimuthal wave number -1 (the first circumferential mode rotating in the opposite direction to the mean swirl), no change was detected in either a bubble or a spiral. By imposing a disturbance with azimuthal wave number 2 (the second circumferential mode), for selective piston frequencies a bubble was transformed into what appears to be the so-called two-tailed type. Thus, it appears that hydrodynamic instability plays a role in interchanging vortex breakdown types, and a comparison with available stability theories is discussed.     

Nonlinear Stability Analysis of Thin Viscoelastic Film Flowing Down on the Inner Surface of a Rotating Vertical Cylinder

This paper investigates the stability of thin viscoelastic liquid film flowing down on the inner surface of a rotating vertical cylinder by means of the long wave perturbation. After proving the insufficiency of the linear model in characterization of certain flow behaviors, a generalized nonlinear kinematic model is then derived to represent the physical system. This model is solved through the following procedure. In the first step, the normal mode method is used to characterize the linear behaviors. The amplitude growth rates and the threshold conditions are characterized subsequently and summarized as the by-products of the linear solutions. In the second step, a nonlinear film flow model is solved by using the method of multiple scales to characterize flow behaviors at various states of sub-critical stability, sub-critical instability, supercritical stability, and supercritical explosion. The modeling results indicate that with the increase in the rotation speed Ω and the radius of cylinder R, the film flow system will be more stable.     

内管自转且公转时环管幂律流的受力分析

数值模拟了环管中内管偏心自转且公转时由轴向压力所驱动的幂律流体充分发展层流,分析了内管上的流体作用力。结果表明,内管偏心自转时流体作用力具有推动内管作和自转同向公转的效果。当只有外力矩驱动内管自转时,由于流体的作用,随内管线密度的不同,内管能达到的受力平衡态也不同:线密度较小时内管仅能在同心自转时达到受力平衡;线密度较大时内管能在作具有不变角速度和偏心率公转时达到受力平衡,且内管线密度越大,对应的受力平衡的公转的偏心率也越大。     

Theoretical analysis of using airflow to purge residual water in an inclined pipe

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Asymptotic solutions of the flow of a Johnson-Segalman fluid through a slowly varying pipe using double perturbation strategy

A double perturbation strategy is presented to solve the asymptotic solutions of a Johnson-Segalman (J-S) fluid through a slowly varying pipe. First, a small parameter of the slowly varying angle is taken as the small perturbation parameter, and then the second-order asymptotic solution of the flow of a Newtonian fluid through a slowly varying pipe is obtained in the first perturbation strategy. Second, the viscoelastic parameter is selected as the small perturbation parameter in the second perturbation strategy to solve the asymptotic solution of the flow of a J-S fluid through a slowly varying pipe. Finally, the parameter effects, including the axial distance, the slowly varying angle, and the Reynolds number, on the velocity distributions are analyzed. The results show that the increases in both the axial distance and the slowly varying angle make the axial velocity slow down. However, the radial velocity increases with the slowly varying angle, and decreases with the axial distance. There are two special positions in the distribution curves of the axial velocity and the radial velocity with different Reynolds numbers, and there are different trends on both sides of the special positions. The double perturbation strategy is applicable to such problems with the flow of a non-Newtonian fluid through a slowly varying pipe.     

DYNAMIC ANALYSIS OF A SPATIAL COUPLED TIMOSHENKO ROTATING SHAFT WITH LARGE DISPLACEMENTS

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Perturbation threshold and hysteresis associated with the transition to turbulence in sudden expansion pipe flow

The complex flow resulting from the laminar-turbulent transition in a sudden expansion pipe flow, with expansion ratio of 1:2, subjected to an inlet parabolic velocity profile and a vortex perturbation, is investigated by means of direct numerical simulations. It is shown that the threshold amplitude for disordered motion is described by a power law scaling, with -3 exponent, as a function of the subcritical Reynolds number. The instability originates from a region of intense shear rate, which results on the flow symmetry breakdown. Above the threshold, several unsteady states are identified using space-time diagrams of the centreline axial velocity fluctuation and their energy. In addition, the simulations show a small hysteresis transition mode due to the reestablishment of the recirculation region in the subcritical range of Reynolds numbers, which depends on: (i) The initial and final quasi-steady states, (ii) the observation time and (iii) the number of intermediate steps taken when increasing and decreasing the Reynolds number.     

Coriolis effect on thermal convection in a couple-stress fluid-saturated rotating rigid porous layer

Both linear and weakly nonlinear stability analyses are performed to study thermal convection in a rotating couple-stress fluid-saturated rigid porous layer. In the case of linear stability analysis, conditions for the occurrence of possible bifurcations are obtained. It is shown that Hopf bifurcation is possible due to Coriolis force, and it occurs at a lower value of the Rayleigh number at which the simple bifurcation occurs. In contrast to the nonrotating case, it is found that the couple-stress parameter plays a dual role in deciding the stability characteristics of the system, depending on the strength of rotation. Nonlinear stability analysis is carried out by constructing a set of coupled nonlinear ordinary differential equations using truncated representation of Fourier series. Sub-critical finite amplitude steady motions occur depending on the choice of physical parameters but at higher rotation rates oscillatory convection is found to be the preferred mode of instability. Besides, the stability of steady bifurcating equilibrium solution is discussed using modified perturbation theory. Heat transfer is calculated in terms of Nusselt number. Also, the transient behavior of the Nusselt number is investigated by solving the nonlinear differential equations numerically using the Runge–Kutta–Gill method. It is noted that increase in the value of Taylor number and the couple-stress parameter is to dampen the oscillations of Nusselt number and thereby to decrease the heat transfer.     

Nonlinear dynamics of a pipe conveying pulsating fluid with parametric and internal resonances

In this paper, the nonlinear planar vibration of a pipe conveying pulsatile fluid subjected to principal parametric resonance in the presence of internal resonance is investigated. The pipe is hinged to two immovable supports at both ends and conveys fluid at a velocity with a harmonically varying component over a constant mean velocity. The geometric cubic nonlinearity in the equation of motion is due to stretching effect of the pipe. The natural frequency of the second mode is approximately three times the natural frequency of the first mode for a range of mean flow velocity, resulting in a three-to-one internal resonance. The analysis is done using the method of multiple scales (MMS) by directly attacking the governing nonlinear integral-partial-differential equations and the associated boundary conditions. The resulting set of first-order ordinary differential equations governing the modulation of amplitude and phase is analyzed numerically for principal parametric resonance of first mode. Stability, bifurcation, and response behavior of the pipe are investigated. The results show new zones of instability due to the presence of internal resonance. A wide array of dynamical behavior is observed, illustrating the influence of internal resonance.     

Aeroacoustical coupling in a ducted shallow cavity and fluid/structure effects on a steam line

A pure tone phenomenon has been observed at 460 Hz in a piping steam line. The acoustical energy has been identified to be generated in an open gate valve and to be of cavity noise type. This energy is then transmitted to the main pipe by fluid/structure coupling. The objectives here are to display the mechanism of the flow acoustic coupling in the cavity and in the duct through an aeroacoustical analysis and to understand the way of energy transfer from the fluid to the main pipe through a vibroacoustical analysis. Concerning the first objective, an experimental study by means of 2/7 scale models in air is analysed by means of numerical flow simulation. The flow acoustic phenomena are modelled by computing the Euler equations. Two different computations are carried out: in the first one, a pure Euler modelling is used, in the second one, a boundary layer obtained from experimental data is introduced in the computation in order to have a realistic flow profile upstream the cavity. The boundary layer flow profile appears to be essential to recover the experimentally observed coupling between the shear-layer instability and the acoustical transverse mode of the pipe. The numerical results confirm that the second aerodynamic mode is responsible for the oscillation. While the predicted frequency agrees about 1% with the scale model experiments, the predicted amplitude is approximately 15 dB too low. For the second objective, fluid/structure coupling in the main pipe is studied using two fully coupled methods. The first method consists in a modal analysis of the line using a fluid–structure finite element model. The second one is based on the analysis of dispersion diagrams derived from the local equations of cylindrical shells filled with fluid. The way of energy transfer in transverse acoustical waves coupled with flexion-ovalization deformations of the pipe is highlighted using both methods. The dispersion diagrams allow a fast and accurate analysis. The modal analysis using a finite-element model may complete the first one with quantitative data. The link between the fluid/acoustic and the fluid/structure analysis is then the excitation of the transverse acoustical mode of the duct.     

可降解性表面活性剂体系下水平管内气液两相螺旋流实验研究

通过气液两相螺旋流实验仪器,研究具有可降解性的天然椰子油新型添加剂对于气液两相螺旋流流型影响以及流型的转变规律,并与表面活性剂十二烷基苯磺酸钠(SDBS)进行对比研究。实验工况设定为:实验介质为空气和水,含气率10%~90%,气相折算速度0.01~4.0m/s,液相折算速度0.01~4.0m/s,表面活性剂采用从植物提取的可降解性椰子油和SDBS,起旋装置为叶轮。实验观察到天然椰子油对于螺旋轴状流、螺旋团状流、螺旋弥散流转换特性的影响与SDBS的效果相类似,该三种流型发生条件相比于以往都有所提前,且存在范围被拓宽。浓度为500ppm时椰子油体系下的主要流型为螺旋弥散流,而SDBS体系下则以螺旋团状流为主。     

Fluid flow in a helical pipe

Without simplifying the N-S equations of Germano's^[5], we study the flow in a helical circular pipe employing perturbation method. A third perturbation solution is fully presented. The first- second- and third-order effects of curvature κ and torsion τ on the secondary flow and axial velocity are discussed in detail. The first-order effect of curvature is to form two counter-rotating cells of the secondary flow and to push the maximum axial velocity to the outer bend. The two cells are pushed to the outer bend by the pure second-order effect of curvature. The combined higher-order (second-, third-) effects of curvature and torsion, are found to be an enlargement of the lower vortex of the secondary flow at expense of the upper one and a clockwise shift of the centers of the secondary vortices and the location of maximum axial velocity. When the axial pressure gradient is small enough or the torsion is sufficiently larger than the curvature, the location of the maximal axial velocity is near the inner bend. The equation of the volume flux is obtained from integrating the perturbation solutions of axial velocity. From the equation the validity range of the perturbation solutions in this paper can be obtained and the conclusion that the three terms of torsion have no effect on the volume flux can easily be drawn. When the axial pressure gradient is less than 22.67, the volume flux in a helical pipe is larger than that in a straight pipe.     

Radial variation of adiabatic and diabatic spiral vortex flow in a wide annular gap

Transitions occurring after the onset of spiral vortex flow in a wide concentric annular gap of radius ratio 0.8, formed by a stationary outer cylinder and a rotatable inner cylinder, have been studied experimentally. By isothermal heating of the annular surface, it was possible to consider diabatic as well as adiabatic conditions. At an axial Reynolds number of 500 and for a range of Taylor numbers up to 10⁷, power spectra and auto-correlograms were taken at two radial positions near to the inner and outer annular surfaces; these are compared with previous results taken at mid-gap under adiabatic conditions. Measurements of turbulence intensity across the gap were made also. Probability histograms and signal traces for diabatic flow near to the outer annular surface are presented. It has been shown that the vortex transitions affect the thermal boundary layer and, consequently, the heat transfer rates at the outer surface. A positive radial thermal gradient was seen to have little effect on the flow. The imposed axial flow was shown to be stabilising under adiabatic conditions but destabilising under diabatic conditions.     

Symmetric vortex shedding in the near wake of a circular cylinder due to streamwise perturbations

Symmetric perturbations imposed on cylinder wakes may result in a modification of the vortex shedding mode from its natural antisymmetric, or alternating, to a symmetric one where twin vortices are simultaneously shed from both sides of the cylinder. In this paper, the symmetric mode in the wake of a circular cylinder is induced by periodic perturbations imposed on the in-flow velocity. The wake field is examined by PIV and LDV for Reynolds numbers about 1200 and for a range of perturbation frequencies between three and four times the natural shedding frequency of the unperturbed wake. In this range, a strong competition between symmetric and antisymmetric vortex shedding occurs for the perturbation amplitudes employed. The results show that symmetric formation of twin vortices occurs close to the cylinder synchronized with the oscillatory component of the flow. The symmetric mode rapidly breaks down and gives rise to an antisymmetric arrangement of vortex structures further downstream. The downstream wake may or may not be phase-locked to the imposed oscillation. The number of cycles for which the symmetric vortices persist in the near wake is a probabilistic function of the perturbation frequency and amplitude. Finally, it is shown that symmetric shedding is associated with positive energy transfer from the fluid to the cylinder due to the fluctuating drag.     

Resistance of a circular pipe with pulsatory variation of the flow rate

The results of an experimental investigation of the hydraulic resistance of a circular pipe for turbulent flow with periodic flow rate fluctuations are presented. The presence of resonance phenomena in the pipe is revealed. It is established that, for hydrodynamic nonstationarity, the pipe resistance is a nonmonotonous function of the frequency of the imposed flow rate fluctuations and differs from the pipe resistance in the stationary flow regime. Under the conditions considered, to find the pipe resistance it is necessary to take into account the variation of the flow kinetic energy with respect to the phase of the imposed flow rate fluctuations due to the deformation of the velocity profile.     

Throughflow and g-jitter effects on binary fluid saturated porous medium

A non-autonomous complex Ginzburg-Landau equation (CGLE) for the finite amplitude of convection is derived, and a method is presented here to determine the amplitude of this convection with a weakly nonlinear thermal instability for an oscillatory mode under throughflow and gravity modulation. Only infinitesimal disturbances are considered. The disturbances in velocity, temperature, and solutal fields are treated by a perturbation expansion in powers of the amplitude of the applied gravity field. Throughflow can stabilize or destabilize the system for stress free and isothermal boundary conditions. The Nusselt and Sherwood numbers are obtained numerically to present the results of heat and mass transfer. It is found that throughflow and gravity modulation can be used alternately to heat and mass transfer. Further, oscillatory flow, rather than stationary flow, enhances heat and mass transfer.