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.     

An experimental study of diabatic spiral vortex flow

In spiral vortex flow, between concentric cylinders with the inner cylinder rotating and the outer stationary, the addition of a thermal gradient across the gap is a known complicating factor. The present diabatic study for narrow and wide gaps (radius ratios N=0.955 and N=0.8), with a heated outer and adiabatic inner cylinder, was undertaken to investigate this problem. The heat transfer characteristics and the modes of transition have been investigated together with the relationship between them. Using standard on-line digital computer techniques, the onset of vortex flow and its higher transitions have been shown to cause a sharp increase in Nusselt number. At higher Taylor numbers, of the order of 10⁶, a marked change in the Nusselt number occurs with the onset of the transition to periodic turbulent vortex flow. Outer wall heating is seen to affect the modes of transition. Diabatic critical Taylor numbers are much higher than those for adiabatic conditions and are found to depend on the close approach of the vortices to the outer wall     

Velocity distributions in Taylor vortex flow with imposed laminar axial flow and isothermal surface heat transfer

Fully-developed flow in a concentric annulus formed by a stationary outer cylinder, which may be heated isothermally, and a rotatable inner cylinder has been studied experimentally by means of hot-wire anemometry techniques. Velocity profiles for the axial, tangential, and radial directions of flow have been obtained for adiabatic conditions and for wide and narrow annular gaps.It has been shown that the onset of Taylor vortex flow has a pronounced effect on the velocity profiles for all three directions. However, while the profiles for the axial and tangential directions are explicable, those for the radial direction are not so, at present. Also, it was found that heat transfer through the outer annular surface had a greater effect on the radial velocity profile than on the axial or tangential, but in the narrow gap case only.     

Factors affecting the stability of viscous axial flow in annuli with a rotating inner cylinder

Hot-wire measurements are presented of the onset of instability in developed axial flow and in both developing and developed tangential flow caused by inner cylinder rotation in concentric annuli of radius ratio N of 0.909, 0.809 and 0.565 for axial-flow Reynolds numbers (Re) between 86 and 2000. Within assessed uncertainty intervals, the consistency of marginal stability measurements, at four azimuthal locations 90° apart, indicates insensitivity to small variations in gap width; the measurements also confirm the destabilisation of nearly-developed and developed tangential flow identified by Takeuchi and Jankowski¹ with the occurrence at increasing Re of three-dimensional initial disturbances of spiral-vortex form. Comparison with earlier measurements suggests that in particular annuli, destabilisation may be delayed to higher Re by high values of certain geometrical factors, including radius ratio and the resultant end-effects parameter. Stability may also be restored or improved at high Re by reversion to developing tangential flow in which the initial instability is not of spiral-vortex form and where, for given N, the critical Taylor number appears uniquely related to the dimensionless axial co-ordinate. Stability is then generally greatest at low N.     

3D numerical simulation of compressible swirling flow induced by means of tangential inlets

The objective of the present work is to predict compressible swirl flow in the nozzle of air‐jet spinning using the realizable k–ε turbulence model and discuss the effect of the nozzle pressure. The periodic change of flow patterns can be observed. The recirculation zone near the wall of the injectors upstream increases in size and moves gradually upstream, whereas the vortex breakdown in the injector downstream shifts slowly towards the nozzle outlet during the whole period. A low axial velocity in the core region moves gradually away from the centerline, and the magnitude of the center reverse flow and the area occupied by it increase with axial distance due to the vortex breakdown. From the tangential velocity profile, there is a very small free‐vortex zone. With increasing nozzle pressure, the velocity increases and the location of vortex breakdown is moved slightly downward. However, the increase in the velocity tends to decline at nozzle pressure up to a high level. Copyright © 2008 John Wiley & Sons, Ltd.     

Skewed Poiseuille-Couette flows of sPTT fluids in concentric annuli and channels

Analytical solutions have been derived for the helical flow of PTT fluids in concentric annuli, due to inner cylinder rotation, as well as for Poiseuille flow in a channel skewed by the movement of one plate in the spanwise direction, which constitutes a simpler solution for helical flow in the limit of very thin annuli. Since the constitutive equation is a non-linear differential equation, the axial and tangential/spanwise flows are coupled in a complex way. Expressions are derived for the radial variation of the axial and tangential velocities, as well as for the three shear stresses and the two normal stresses. For engineering purposes expressions are given relating the friction factor and the torque coefficient to the Reynolds number, the Taylor number, a nondimensional number quantifying elastic effects (εDe²) and the radius ratio. For axial dominated flows fRe and C_M are found to depend only on εDe² and the radius ratio, but as the strength of rotation increases both coefficients become dependent on the velocity ratio (ξ) which efficiently compacts the effects of Reynolds and Taylor numbers. Similar expressions are derived for the simpler planar case flow using adequate non-dimensional numbers.     

Numerical and experimental study of an axially induced swirling pipe flow

In-line flow segregators based on axial induction of swirling flow have important applications in chemical, process and petroleum production industries. In the later, the segregation of gas bubbles and/or water droplets dispersed into viscous oil by swirling pipe flow may be beneficial by either providing a pre-separation mechanism (bubble and/or drop coalescer) or, in the case of water-in-oil dispersions, by causing a water-lubricated flow pattern to establish in the pipe (friction reduction). Works addressing these applications are rare in the literature. In this paper, the features and capabilities of swirling pipe flow axially induced by a vane-type swirl generator were investigated both numerically and experimentally. The numerical analysis has been carried out using a commercial CFD package for axial Reynolds numbers less than 2000. Pressure drop, tangential and axial velocity components as well as swirl intensity along a 5 cm i.d. size and 3 m long pipe were computed. Single phase flow experiments have been performed using a water–glycerin solution of 54 mPa s viscosity and 1210 kg/m³ density as working fluid. The numerical predictions of the pressure drop were compared with the experimental data and agreement could be observed within the range of experimental conditions. The experiments confirmed that swirl flow leads to much higher friction factors compared with theoretical values for non-swirl (i.e. purely axial) flow. Furthermore, the addition of a conical trailing edge reduces vortex breakdown. Visualization of the two-phase swirling flow pattern was achieved by adding different amounts of air to the water–glycerin solution upstream the swirl generator.     

Flow pattern and stability of pseudoplastic axial Taylor–Couette flow

The effect of an axial flow on the stability of the Taylor–Couette flow is explored for pseudoplastic fluids. The fluid is assumed to follow the Carreau–Bird model and mixed boundary conditions are imposed while the axial flow can be independent of rotational flow. The four-dimensional low-order dynamical system, resulted from Galerkin projection of the conservation of mass and momentum equations, includes additional non-linear terms in the velocity components originated from the shear-dependent viscosity. In absence of axial flow the base flow loses its radial flow stability to the vortex structure at a lower critical Taylor number, as the pseudoplasticity effects increases. The emergence of the vortices corresponds to the onset of a supercritical bifurcation which is also seen in the flow of a linear fluid. However, unlike the Newtonian case, pseudoplastic Taylor vortices lose their stability as the Taylor number reaches a second critical number corresponding to the onset of a Hopf bifurcation. Existence of an axial flow, induced by a pressure gradient appears to further advance each critical point on the bifurcation diagram. Complete flow field together with viscosity maps are given for stability regions in the bifurcation diagram.     

An experimental investigation of pneumatic swirl flow induced by a three lobed helical pipe

This paper presents a discussion of the results and conclusions drawn from a series of experiments conducted to investigate the swirl flow that are generated by a three lobed helical pipe mounted within a laboratory scale pneumatic conveying rig. The experiments employed Laser Doppler Anemometry (LDA) to quantify the strength of the induced vortex formations and the decay rates of the observed downstream swirl flows over a range of Reynolds number in the turbulent regime. Instantaneous point velocity measurements were resolved in three directions across regular measurement grids transcribed across parallel planes located at four distances downstream of the swirl inducing pipe section. The equivalent axial, radial and tangential velocities were subsequently computed at these grids points. The degree of swirl measured across each measurement plane was expressed in terms of a defined swirl number.It was concluded that the three lobed helical pipe gave rise to a wall jet type of swirl whose rate of observed downstream decay is related to the Reynolds number of the upstream flow and the distance downstream of the swirl pipe. The decay rates for the swirl flows were found to be inversely proportional to the Reynolds number of the upstream flow. The swirl pipe was observed to create a redistribution of the downstream velocity field from axial to tangential, accompanied by a transfer of axial to angular momentum. The findings of this paper are believed to improve understanding to assist the selective use of swirl flow within lean phase particles pneumatic transport systems.     

Transition from vortex to wall driven turbulence production in the Taylor–Couette system with a rotating inner cylinder

Axisymmetrically stable turbulent Taylor vortices between two concentric cylinders are studied with respect to the transition from vortex to wall driven turbulent production. The outer cylinder is stationary and the inner cylinder rotates. A low Reynolds number turbulence model using the k‐ω formulation, facilitates an analysis of the velocity gradients in the Taylor–Couette flow. For a fixed inner radius, three radius ratios 0.734, 0.941 and 0.985 are employed to identify the Reynolds number range at which this transition occurs. At relatively low Reynolds numbers, turbulent production is shown to be dominated by the outflowing boundary of the Taylor vortex. As the Reynolds number increases, shear driven turbulence (due to the rotating cylinder) becomes the dominating factor. For relatively small gaps turbulent flow is shown to occur at Taylor numbers lower than previously reported. Copyright © 2002 John Wiley & Sons, Ltd.     

Velocity distributions in a hydrocyclone separator

 The internal three-dimensional flow field in a hydrocyclone was studied using laser velocimetry. Seven axial planes were investigated for three different inlet flow rates and three independent and different rejects rates. Results at each measurement plane showed that the measured tangential velocity profile behaves like a forced vortex at the region near the air core, and like a free vortex in the outer portion of the flow. The peak nondimensional tangential velocity decreases as the distance from the inlet region increases, however, the peak dimensional tangential velocity increases as the distance from the inlet region increases. The nondimensional peak tangential velocities are approximately equal for all of the flow rates. The magnitude of the tangential velocity increased in the inner forced vortex region as the rejects rate was increased. Backflows exist in the axial velocity profile near the inlet region, but these reversed flows disappear in the exit region. The dimensional vorticity is proportional to inlet flow rate and decreases with increasing rejects flow rates. Received: 27 February 2001/Accepted: 19 June 2001     

A non‐linear dynamical system approach to finite amplitude Taylor‐Vortex flow of shear‐thinning fluids

The effect of shear thinning on the stability of the Taylor–Couette flow is explored for a Carreau–Bird fluid in the narrow‐gap limit. The Galerkin projection method is used to derive a low‐order dynamical system from the conservation of mass and momentum equations. In comparison with the Newtonian system, the present equations include additional non‐linear coupling in the velocity components through the viscosity. It is found that the critical Taylor number, corresponding to the loss of stability of the circular Couette flow, becomes lower as the shear‐thinning effect increases. That is, shear thinning tends to precipitate the onset of Taylor vortex flow, which coincides with the onset of a supercritical bifurcation. Comparison with existing measurements of the effect of shear thinning on the critical Taylor and wave numbers show good agreement. The Taylor vortex cellular structure loses its stability in turn, as the Taylor number reaches a critical value. At this point, an inverse Hopf bifurcation emerges. In contrast to Newtonian flow, the bifurcation diagrams exhibit a turning point that sharpens with shear‐thinning effect. Copyright © 2004 John Wiley & Sons, Ltd.     

Numerical simulation of tangentially injected turbulent swirling flow in a divergent tube

This paper studies the properties of turbulent swirling decaying flow induced by tangential inlets in a divergent pipe using the realizable k–ε turbulence model and discusses the effects of the injector pressure and injection position. The results of transient solutions show that both the recirculation zone near the wall in upstream of the injectors and the vortex breakdown in downstream of the injectors increase in size during the whole period. A nearly axisymmetric conical breakdown is formed and its internal structure consists of two asymmetric spiral‐like vortices rotating in opposite directions. The stagnation point shifts slowly toward the pipe outlet over time. The maxima of the three velocity components, which are located near the wall, decrease gradually with streamwise direction. It can also be inferred that Mach number approaches 1.0 near the injector outlets. The velocities increase with the increasing injector pressure. However, its increasing trend is not significant. With the increase of the injection position, vortex breakdown moves in downstream direction and the pitch along the streamwise direction increases. Copyright © 2008 John Wiley & Sons, Ltd.     

Flow structures and force characteristics for flat plate in oscillatory flows withKc number from 2 to 40 and in combined flows

The evolution of wake structures and variation of the forces on a flat plate in harmonic oscillatory and in-line combined flows are obtained numerically by improved discrete vortex method. For the oscillatory oncoming flow cases, wyenKc number varies from 2 to 40, the vortex pattern changes from a “harmonic wave” shaped (in a range of smallKc number) to a slight inclined “harmonic wave” shaped (in a range of moderateKc numbers), then to inclined vortex clusters with an angle of 50° to the oncoming flow direction (atKc=20), at last, asKc number becomes large, the vortex pattern is like a normal Karman vortex street. The well predicted drag and inertia force coefficients are obtained, which are more close to the results of Keulegan & Carpenter's experiment as compared with previous vortex simulation by other authors. The existence of minimum point of inertia force coefficientC _m nearKc=20 is also well predicted and this phenomenon can be interpreted according to the vortex structure. For steady-oscillatory in-line combined flow cases, the vortex modes behave like a vortex street, exhibit a “longitudinal wave” structure, and a vortex cluster shape corresponding to the ratios ofU _m toU ₀ which are ofO (10⁻¹)O(1) andO(10), respectively. The effect on the prediction of forces on the flat plate from the disturbance component in a combined flow has been demonstrated qualitatively. In addition to this, the lock in phenomenon of vortex shedding has been checked. The project supported by National Natural Science Foundation of China & LNM, Institute of Mechanics, CAS     

Particle motion in a Taylor vortex

Here we present a study on the behavior of individual particles in the Taylor vortex. Two particle-fluid systems were tested: a cube with the edge length of 2 mm and the density of 0.13 g/cm³ (‘light particle’) in a working fluid of mineral oil (density of 0.86 g/cm³ and viscosity of 0.066 Pa.s); and a sphere with the diameter of 1.6 mm and the density of 2.2 g/cm³ (‘heavy particle’) in 90% glycerin/water (density of 1.23 g/cm³ and viscosity of 0.128 Pa.s). The Taylor–Couette device used for this study was featured with a short column (aspect ratio ≤ 6) and a wide gap (radius ratio ≤ 0.67). The interaction between the floating particle and Taylor vortices was investigated using a high speed camera and a particle image velocimetry (PIV) system. Moreover, computational fluid dynamics simulation was performed to calculate the liquid flow pattern and analyze the particle motion. Our results show that the particle behavior in the Taylor–Couette device is strongly dependent on the particle density and Reynolds number. With the increasing Reynolds number, four types of particle trajectories were sequentially identified from the light particle, including a circular trajectory on the surface of the inner cylinder, random shifting between the circular trajectory and oval orbit, a stable oval orbit in the annulus, and a circle along the vortex center. On the other hand, the heavy particle moves along a circular orbit and an oval orbit at low and high Reynolds numbers, respectively. Several unreported particle behaviors were also observed, such as the self-rotation of the particle when it moves along the above trajectories, the shifting axis of the oval orbit, etc. In addition, the PIV measurements show that the trapped particle can only influence the flow pattern locally around the particle. The study can help understand the particle behavior in a Taylor vortex better and therefore benefit applications of particle-laden Taylor vortex devices.     

不同参数下环形通道内湍流旋流流动的模拟

应用一种合理考虑湍流一旋流相互作用及湍流脉动各向异性的新的代数ＲｅｙｎｏｌｄＳ应力模型,对环形通道内的湍流旋流流动进行了数值模拟．研究了旋流数、进口轴向速度和内外半径比等参数对环形通道内湍流旋流流动的影响,以及由此产生的流场变化对强化环形通道内传热的作用．     

Measurements of an unsteady liquid metal flow during spin-up driven by a rotating magnetic field

A cylindrical cavity with an aspect ratio of unity is filled with liquid metal and suddenly exposed to an azimuthal body force generated by a rotating magnetic field (RMF). This experimental study is concerned with the secondary meridional flow during the time, if the fluid spins up from rest. Vertical profiles of the axial velocity have been measured by means of the ultrasound Doppler velocimetry. The flow measurements confirm the spin-up concept by Ungarish (J Fluid Mech 347:105–118, 1997) and the continuative study by Nikrityuk et al. (Phys Fluids 17:067101, 2005) who suggested the existence of two stages during the RMF-driven spin-up, in particular the so-called initial adjustment phase followed by an inertial phase which is dominated by inertial oscillations of the secondary flow. Evolving instabilities of the double-vortex structure of the secondary flow have been detected at a Taylor number of 1.24 × 10⁵ verifying the predictions of Grants and Gerbeth (J Fluid Mech 463:229–240, 2002). Perturbations in form of Taylor–Görtler vortices have been observed just above the instability threshold.     

On the development of Taylor vortices in a vertical annulus with a heated rotating inner cylinder

A numerical study has been conducted to determine the heat transfer characteristics and flow patterns which develop around a rotating, heated vertical cylinder enclosed within a stationary concentric cylinder. A tall annulus (aspect ratio of 10) with fixed, adiabatic horizontal end-plates and a radius ratio of 0·5 has been considered. Furthermore, the effect that the introduction of buoyancy forces by heating the inner cylinder has on the development of the Taylor vortex flow is examined. It is observed that the formation of the Taylor vortices is delayed until the rotational parameter σ = Gr/Re² has a value below unity for any given Reynolds number Re which is above the critical value Re_crit for the formation of Taylor vortices in an isothermal flow. Also, the Taylor cells first appear at the top of the annulus. As σ is gradually decreased below unity, bifurcations to other states are observed. The final structure of the secondary flow is noticeably distorted in the mixed-convection mode, with the size of the Taylor cells varying greatly along the height of the annulus. This distortion diminishes as σ is further decreased, until the isothermal flow pattern is nearly recovered below σ = 0·01.     

Theoretical and numerical study of Couette-Taylor flow with an axial flow using lattice Boltzmann method

In this study, the numerical models for swirling flows developed by Li et al and Zhou for lattice Boltzmann method (LBM) are chosen. These models were firstly validated using the Couette-Taylor flow between two concentric cylinders simulations. Numerical results showed the efficiency of the Zhou's model. Numerical simulation results using LBM are in good agreement for the steady and unsteady regimes compared to the literature review. In a second step, the Zhou model was then adopted to our study to determine the Couette-Taylor instabilities with an axial flow. Two protocols are tested. The first one (direct protocol) starts with an azimuthal flow without any axial flow (Re = 0). Once the regime is established, an axial flow is then superposed to the Couette-Taylor flow (with a sudden or a progressive manner). The second protocol (inverse protocol) starts with an axial flow at a given Reynolds number (Poiseuille flow). Once the regime is established, an azimuthal flow is the executed (with a sudden or a progressive manner). The effect of various parameters controlling the physical situation is also discussed. The increase of the azimuthal velocity mainly led to the emergence and development of Taylor vortices. Its influence decreases when the axial Reynolds number increases. The relevant result for this study is the change of the critical axial Reynolds number Re_c (total disappearance of instabilities) with both protocols and both manners.     

The lowest stability and bifurcation in supercritical Taylor vortices

Here, we numerically investigate the lowest stability and bifurcation boundary of supercritical Taylor vortices in flows with different wavenumbers and for various radius ratios; the radius ratios range from those corresponding to axisymmetrical Taylor vortex flow (TVF) to those corresponding to wavy vortex flow (WVF). The variation in the wavenumber of a supercritical TVF is found to affect the stability of the flow, because the wavenumber of the Taylor vortices remains constant only when the flow is quasi-static. The variation in the wavenumber is examined and found to be significant when the radius ratio is less than 0.7842. The results for TVF are compared with those for the flow during the quasi-static transition from TVF to WVF.