On the impacts of coarse-scale models of realistic roughness on a forward-facing step turbulent flow

The present work explores the impacts of the coarse-scale models of realistic roughness on the turbulent boundary layers over forward-facing steps. The surface topographies of different scale resolutions were obtained from a novel multi-resolution analysis using discrete wavelet transform. PIV measurements are performed in the streamwise–wall-normal (x–y) planes at two different spanwise positions in turbulent boundary layers at Re_h = 3450 and δ/h = 8, where h is the mean step height and δ is the incoming boundary layer thickness. It was observed that large-scale but low-amplitude roughness scales had small effects on the forward-facing step turbulent flow. For the higher-resolution model of the roughness, the turbulence characteristics within 2h downstream of the steps are observed to be distinct from those over the original realistic rough step at a measurement position where the roughness profile possesses a positive slope immediately after the step’s front. On the other hand, much smaller differences exist in the flow characteristics at the other measurement position whose roughness profile possesses a negative slope following the step’s front.     

Experimental study of parallel and inclined turbulent wall jets

An experimental study of the flow field in a two-dimensional wall jet has been conducted. All measurements were carried out using hot-wire anemometry. The experimental facility has a rectangular slot nozzle of high aspect ratio l/b = 100 (where l and b are the length and height slot, respectively). Mean velocities and Reynolds stresses were determined with three nozzle Reynolds numbers (Re = 1 × 10⁴, 2 × 10⁴ and 3 × 10⁴) and four different inclination angles between the wall and the flow velocity at the nozzle (β = 0°, 10°, 20° and 30°). Results indicate that all wall jets are self-preserving in the developed region. Normal to the wall two regions can be identified: one similar to a plane free jet and the other similar to a boundary layer. Downstream the interaction between these two regions creates a mixed or third region. The logarithmic region increases with the distance from the nozzle and with the Reynolds number. For the inclined wall jet, the spreading rate expressed in terms of jet half-width or maximum velocity decay with respect to the streamwise distance, asymptotes to a linear law. The streamwise locations where the jet becomes self-similar are farther from the exit than in parallel wall jet. The slope of both half-width and maximum velocity decay in the developed region are affected by both wall jet inclination angle and nozzle exit Reynolds number.     

Turbulence modulation in a particle-laden flow over a hemisphere-roughened wall

Turbulence modulation by the inertia particles in a spatially developing turbulent boundary layer flow over a hemisphere-roughened wall was investigated using the direct numerical simulation method. The Eulerian and Lagrangian approaches were used for the gas- and particle-phases, respectively. An immersed boundary method was employed to resolve the hemispherical roughness element. The hemispheres were staggered in the downstream direction and arranged periodically in the streamwise and spanwise directions with spacing of p_x/d= 4 and p_z/d= 2 (where p_x and p_z are the streamwise and spanwise spacing of the hemispheres, and d is the diameter). The effects of particles on the turbulent coherent structures, turbulent statistics and quadrant events were analyzed. The results show that the addition of particles significantly damps the vortices structures and increases the length scales of streak structures. Compared with the particle-laden flow over the smooth wall, the existence of the wall roughness decreases the mean streamwise velocity in the near wall region, and makes the peaks of Reynolds stresses profiles shift up. In addition, the existence of particles also increases the percentage contributions to Reynolds shear stress from the Q4 events, however, decreases the percentage contributions from other quadrant events.     

The flow field around a micropillar confined in a microchannel

The flow field over a low aspect ratio (AR) circular pillar (L/D = 1.5) in a microchannel was studied experimentally. Microparticle image velocimetry (μPIV) was employed to quantify flow parameters such as flow field, spanwise vorticity, and turbulent kinetic energy (TKE) in the microchannel. Flow regimes of cylinder-diameter-based Reynolds number at 100 ⩽ Re_D ⩽ 700 (i.e., steady, transition from quasi-steady to unsteady, and unsteady flow) were elucidated at the microscale. In addition, active flow control (AFC), via a steady control jet (issued from the pillar itself in the downstream direction), was implemented to induce favorable disturbances to the flow in order to alter the flow field, promote turbulence, and increase mixing. Together with passive flow control (i.e., a circular pillar), turbulent kinetic energy was significantly increased in a controllable manner throughout the flow field.     

An experimental study of circular sand–water wall jets

Laboratory experiments were carried out to study the effects of sand particles on circular sand–water wall jets. Mean and turbulence characteristics of sand particles in the sand–water wall jets were measured for different sand concentrations c_o ranging from 0.5% to 2.5%. Effects of sand particle size on the centerline sand velocity of the jets were evaluated for sand size ranging from 0.21 mm to 0.54 mm. Interesting results with the range of measurements are presented in this paper. It was found that the centerline sand velocity of the wall jets with larger particle size were 15% higher than the jets with smaller particle size. Concentration profiles in the vertical direction showed a peak value at x/d = 5 (where x is the longitudinal distance from the nozzle and d is the nozzle diameter) and the sand concentration decreased linearly for x/d > 5. Experimental results showed that the turbulence level enhanced from the nozzle to x/d = 10. For sand–water wall jets with a higher concentration (c_o = 1.5–2.5%), the turbulence intensity became smaller than the corresponding single-phase wall jets by 34% due to turbulent modulation. A modified logarithmic formulation was introduced to model the longitudinal turbulent intensity at the centerline and along the axis of the jet.     

Turbulent boundary layers over sparsely-spaced rod-roughened walls

Direct numerical simulations (DNSs) of spatially developing turbulent boundary layers (TBLs) over sparsely-spaced two-dimensional (2D) rod-roughened walls were performed. The rod elements were periodically arranged along the streamwise direction with pitches of p_x/k = 8, 16, 32, 64 and 128, where p_x is the streamwise spacing of the rods, and k is the roughness height. The Reynolds number based on the momentum thickness was varied from Re_θ = 300–1400, and the height of the roughness element was k = 1.5θ_in, where θ_in is the momentum thickness at the inlet. The characteristics of the TBLs, such as the friction velocity, mean velocity, and Reynolds stresses over the rod-roughened walls, were examined by varying the spacing of the roughness features (8 ⩽ p_x/k ⩽ 128). The outer-layer similarity between the rough and smooth walls was established for the sparsely-distributed rough walls (p_x/k ⩾ 32) based on the profiles of the Reynolds stresses, whereas those are not for p_x/k = 8 and 16. Inspection of the interaction between outer-layer large-scale motions and near-wall small-scale motions using two-point amplitude modulation (AM) covariance showed that modulation effect of large-scale motions on near-wall small-scale motions was strongly disturbed over the rough wall for p_x/k = 8 and 16. For p_x/k ⩾ 32, the flow that passed through the upstream roughness element transitioned to a smooth wall flow between the consecutive rods. The strong influence of the surface roughness in the outer layer for p_x/k = 8 and 16 was attributed to large-scale erupting motions by the surface roughness, creating both upward shift of the near-wall turbulent energy and active energy production in the outer layer with little influence on the near-wall region.     

Air flow aerodynamic on a wall-mounted hemisphere for various turbulent boundary layers

Air flow field around a surface-mounted hemisphere of a fixed height for two different turbulent boundary layers (thin and thick) are investigated experimentally and numerically. Flow measurements are performed in a wind tunnel using hot-wire anemometer and streamwise component of velocity fluctuation are calculated using a special developed program of the hardware system. Mean surface pressure coefficients and velocity field for the same hemisphere are determined by the numerical simulation. Turbulent flow field and intensity are measured for two types of boundary layers and compared at various sections in both streamwise and spanwise directions. Numerical scheme based on finite volume and SIMPLE algorithm is used to treat pressure and velocity coupling. Studies are performed for Reynolds number, Re_H = 32,000. Based on the numerical simulation using RNG k–ε turbulence model, flow pathlines, separation region and recirculation area are determined for the two types of turbulent boundary layer flows and complex flow field and recirculation regions are identified and presented graphically.     

Hybrid RANS/LES computations of plane impinging jets with DES and PANS models

The qualities of a DES (Detached Eddy Simulation) and a PANS (Partially-Averaged Navier–Stokes) hybrid RANS/LES model, both based on the k–ω RANS turbulence model of Wilcox (2008, “Formulation of the k–ω turbulence model revisited” AIAA J., 46: 2823–2838), are analysed for simulation of plane impinging jets at a high nozzle-plate distance (H/B = 10, Re = 13,500; H is nozzle-plate distance, B is slot width; Reynolds number based on slot width and maximum velocity at nozzle exit) and a low nozzle-plate distance (H/B = 4, Re = 20,000). The mean velocity field, fluctuating velocity components, Reynolds stresses and skin friction at the impingement plate are compared with experimental data and LES (Large Eddy Simulation) results. The k–ω DES model is a double substitution type, following Davidson and Peng (2003, “Hybrid LES–RANS modelling: a one-equation SGS model combined with a k–ω model for predicting recirculating flows” Int. J. Numer. Meth. Fluids, 43: 1003–1018). This means that the turbulent length scale is replaced by the grid size in the destruction term of the k-equation and in the eddy viscosity formula. The k–ω PANS model is derived following Girimaji (2006, “Partially-Averaged Navier–Stokes model for turbulence: a Reynolds-Averaged Navier–Stokes to Direct Numerical Simulation bridging method” J. Appl. Mech., 73: 413–421). The turbulent length scale in the PANS model is constructed from the total turbulent kinetic energy and the sub-filter dissipation rate. Both hybrid models change between RANS (Reynolds-Averaged Navier–Stokes) and LES based on the cube root of the cell volume. The hybrid techniques, in contrast to RANS, are able to reproduce the turbulent flow dynamics in the shear layers of the impacting jet. The change from RANS to LES is much slower however for the PANS model than for the DES model on fine enough grids. This delays the break-up process of the vortices generated in the shear layers with as a consequence that the DES model produces better results than the PANS model.     

Particle image velocimetry investigation on mixing enhancement of non-circular sharp edge nozzles

An experimental study using Particle Image Velocimetry (PIV) on free jets issuing from different orifice plate (OP) nozzles is reported. Mean velocity, turbulence intensity and higher order profiles relevant for large and small scale mixing are considered in the near field and interaction zone (0 < X/D < 20). This is done to determine mixing enhancement due to rectangular, squared, elliptic and triangular nozzles in comparison to circular nozzle results in two orthogonal planes. The effect of Reynolds number on the differences among the nozzle shapes is also considered by performing measurements just after laminar–turbulent transition (Re = 8000) and in the fully turbulent regime (Re = 35,000). The results at low Reynolds number show two classes of jets, i.e. at one side, those closer to axial-symmetric conditions, as circular, square and triangular jets, whereas on the other side those with elongated nozzles as rectangular and elliptic. The reason for the different behavior of the latter is connected to the phenomenon of axis-switching which allows a rearrangement of turbulence over the different velocity components and directions. However, for the highest Reynolds number investigated, all nozzles show similar behavior especially in the jet far field (X/D > 10), thus suggesting a significant Reynolds number dependence of the results.     

LES of turbulent jet in cross-flow: Part 1 – A numerical validation study

The paper presents results of a LES based numerical simulation of the turbulent jet-in-cross-flow (JICF) flowfield, with Reynolds number based on cross-flow velocity and jet diameter Re = 2400 and jet-to-cross-flow velocity ratio of R = 3.3. The JICF flow case has been investigated in great detail, involving conduction of two independent precursor simulations, prior to the main JICF simulation, as the considered case has turbulent inflow conditions on both jet and cross-stream side. The LES results are directly compared to pointwise Laser Doppler Anemometry (LDA) measurements, showing a very good agreement on the level of various statistical quantities in all flow regions but the immediate jet-to-cross-flow exhaustion zone. Several LES computations involving grids of up to 15 million grid points have been conducted, showing no improvement in the agreement between numerical results and measurements, possibly indicating a LDA measurement problem in this particular region.     

Flow evolution of a turbulent submerged two-dimensional rectangular free jet of air. Average Particle Image Velocimetry (PIV) visualizations and measurements

The paper presents average flow visualizations and measurements, obtained with the Particle Image Velocimetry (PIV) technique, of a submerged rectangular free jet of air in the range of Reynolds numbers from Re = 35,300 to Re = 2200, where the Reynolds number is defined according to the hydraulic diameter of a rectangular slot of height H. According to the literature, just after the exit of the jet there is a zone of flow, called zone of flow establishment, containing the region of mixing fluid, at the border with the stagnant fluid, and the potential core, where velocity on the centerline maintains a value almost equal to the exit one. After this zone is present the zone of established flow or fully developed region. The goal of the paper is to show, with average PIV visualizations and measurements, that, before the zone of flow establishment is present a region of flow, never mentioned by the literature and called undisturbed region of flow, with a length, L_U, which decreases with the increase of the Reynolds number. The main characteristics of the undisturbed region is the fact that the velocity profile maintains almost equal to the exit one, and can also be identified by a constant height of the average PIV visualizations, with length, L_CH, or by a constant turbulence on the centerline, with length L_CT. The average PIV velocity and turbulence measurements are compared to those performed with the Hot Film Anemometry (HFA) technique. The average PIV visualizations show that the region of constant height has a length L_CH which increases from L_CH = H at Re = 35,300 to L_CH = 4–5H at Re = 2200. The PIV measurements on the centerline of the jet show that turbulence remains constant at the level of the exit for a length, L_CT, which increases from L_CT = H at Re = 35,300 to L_CT = 4–5H at Re = 2200. The PIV measurements show that velocity remains constant at the exit level for a length, L_U, which increases from L_U = H at Re = 35,300 to L_U = 6H at Re = 2200 and is called undisturbed region of flow. In turbulent flow the length L_U is almost equal to the lengths of the regions of constant height, L_CH, and constant turbulence, L_CT. In laminar flow, Re = 2200, the length of the undisturbed region of flow, L_U, is greater than the lengths of the regions of constant height and turbulence, L_CT = L_CH = 4–5H. The average PIV and HFA velocity measurements confirm that the length of potential core, L_P, increases from L_P = 4–5H at Re = 35,300 to L_P = 7–8H at Re = 2200, and are compared to the previous experimental and theoretical results of the literature in the zone of mixing fluid and in the fully developed region with a good agreement.     

Large-eddy simulations of chevron jet flows with noise predictions

Hybrid large-eddy type simulations for chevron nozzle jet flows are performed at Mach 0.9 and Re = 1.03 × 10⁶. Without using any subgrid scale model (SGS), the numerical approach applied in the present study is essentially implicit large-eddy simulation (ILES). However, a Reynolds-averaged Navier–Stokes (RANS) solution is patched into the near wall region. This makes the overall solution strategy hybrid RANS–ILES. The disparate turbulence length scales, implied by these different modeling approaches, are matched using a Hamilton–Jacobi equation. The complex geometry features of the chevron nozzles are fully meshed. With numerical fidelity in mind, high quality, hexahedral multi-block meshes of 12.5 × 10⁶ cells are used. Despite the modest meshes, the novel RANS–ILES approach shows encouraging performance. Computed mean and second-order fluctuating quantities of the turbulent near field compare favorably with measurements. The radiated far-field sound is predicted using the Ffowcs Williams and Hawkings (FW–H) surface integral method. Encouraging agreement of the predicted far-field sound directivity and spectra with measurements is obtained.     

Separated flow structures around a cylindrical obstacle in a narrow channel

A detailed experimental study is performed on the separated flow structures around a low aspect-ratio circular cylinder (pin-fin) in a practical configuration of liquid cooling channel. Distinctive features of the present arrangement are the confinement of the cylinder at both ends, water flow at low Reynolds numbers (Re = 800, 1800, 2800), very high core flow turbulence and undeveloped boundary layers at the position of the obstacle. The horseshoe vortex system at the junctions between the cylinder and the confining walls and the near wake region behind the obstacle are deeply investigated by means of Particle Image Velocimetry (PIV). Upstream of the cylinder, the horseshoe vortex system turns out to be perturbed by vorticity bursts from the incoming boundary layers, leading to aperiodical vortex oscillations at Re = 800 or to break-away and secondary vorticity eruptions at the higher Reynolds numbers. The flow structures in the near wake show a complex three-dimensional behaviour associated with a peculiar mechanism of spanwise mass transport. High levels of free-stream turbulence trigger an early instabilization of the shear layers and strong Bloor–Gerrard vortices are observed even at Re = 800. Coalescence of these vortices and intense spanwise flow inhibit the alternate primary vortex shedding for time periods whose length and frequency increase as the Reynolds number is reduced. The inhibition of alternate vortex shedding for long time periods is finally related to the very large wake characteristic lengths and to the low velocity fluctuations observed especially at the lowest Reynolds number.     

The effect of incidence angle on the mean wake of surface-mounted finite-height square prisms

The mean wake of a surface-mounted finite-height square prism was studied experimentally in a low-speed wind tunnel to explore the combined effects of incidence angle (α) and aspect ratio (AR). Measurements of the mean wake velocity field were made with a seven-hole pressure probe for finite square prisms of AR = 9, 7, 5 and 3, at a Reynolds number of Re = 3.7 × 10⁴, for incidence angles from α = 0° to 45°. The relative thickness of the boundary layer on the ground plane, compared to the prism width, was δ/D = 1.5. As the incidence angle increases from α = 0° to 15°, the mean recirculation zone shortens and the mean wake shifts in the direction opposite to that of the mean lift force. The downwash is also deflected to this side of the wake and the mean streamwise vortex structures in the upper part of the wake become strongly asymmetric. The shortest mean recirculation zone, and the greatest asymmetry in the mean wake, is found at the critical incidence angle of α_critical ≈ 15°. As the incidence angle increases from α = 15° to 45°, the mean recirculation zone lengthens and the mean streamwise vortex structures regain their symmetry. These vortices also elongate in the wall-normal direction and become contiguous with the horseshoe vortex trailing arms. The mean wake of the prism of AR = 3 has some differences, such as an absence of induced streamwise vorticity near the ground plane, which support its classification as lying below the critical aspect ratio for the present flow conditions.     

Effects of the jet-to-crossflow momentum ratio on a sonic jet into a supersonic crossflow

Numerical investigation of a transverse sonic jet injected into a supersonic crossflow was carried out using large-eddy simulation for a free-stream Mach number M = 1.6 and a Reynolds number Re = 1.38 × 10⁵ based on the jet diameter. Effects of the jet-to-crossflow momentum ratio on various fundamental mechanisms dictating the intricate flow phenomena, including flow structures, turbulent characters and frequency behaviors, have been studied. The complex flow structures and the relevant flow features are discussed to exhibit the evolution of shock structures, vortical structures and jet shear layers. The strength of the bow shock increases and the sizes of the barrel shock and Mach disk also increase with increasing momentum ratio. Turbulent characters are clarified to be closely related to the flow structures. The jet penetration increases with the increase of the momentum ratio. Moreover, the dominant frequencies of the flow structures are obtained using spectral analysis. The results obtained in this letter provide physical insight in understanding the mechanisms relevant to this complex flow.     

Effect of side ratio on fluid flow and heat transfer from rectangular cylinders using the PANS method

A computational study of heat transfer from rectangular cylinders is carried out. Rectangular cylinders are distinguished based on the ratio of the length of streamwise face to the height of the cross-stream face (side ratio, R). The simulations were performed to understand the heat transfer in a flow field comprising separation, reattachment, vortex shedding and stagnation. The Partially-Averaged Navier–Stokes (PANS) modeling approach is used to solve the turbulent flow physics associated and the wall resolve approach is used for the near wall treatment because of the flow separation involved. The simulations were performed using a finite volume based opensource software, OpenFOAM, at Reynolds number (Re) = 22,000 for rectangular cylinder at constant temperature kept in an air stream. Two critical side ratios were obtained, R = 0.62 and 3.0. At R = 0.62, the maximum value of the drag coefficient (C_d) = 2.681 was observed which gradually reduced by 54% at R = 4.0. The base pressure coefficient and global Nusselt number also attained the maximum value at R = 0.62 and from R = 2.5 to 3.0 a sharp discontinuous increase by 140% in the Strouhal number was observed. At R = 0.62, it was observed that the separated flow reattaches at the trailing edge after rolling over the side face and therefore increases the overall Nusselt number. The phase averaging was also performed to analyze the unsteady behavior of heat transfer.     

Structure of the turbulent boundary layer over a rod-roughened wall

Turbulent coherent structures near a rod-roughened wall are scrutinized by analyzing instantaneous flow fields obtained from direct numerical simulations (DNSs) of a turbulent boundary layer (TBL). The roughness elements used are periodically arranged two-dimensional spanwise rods, and the roughness height is k/δ = 0.05 where δ is the boundary layer thickness. The Reynolds number based on the momentum thickness is varied in the range Re_θ = 300–1400. The effect of surface roughness is examined by comparing the characteristics of the TBLs over smooth and rough walls. Although introduction of roughness elements onto the smooth wall affects the Reynolds stresses throughout the entire boundary layer when scaled by the friction velocity, the roughness has little effect on the vorticity fluctuations in the outer layer. Pressure-strain tensors of the transport equation for the Reynolds stresses and quadrant analysis disclose that the redistribution of turbulent kinetic energy of the rough wall is similar to that of the smooth wall, and that the roughness has little effect on the relative contributions of ejection and sweep motions in the outer layer. To elucidate the modifications of the near-wall vortical structure induced by surface roughness, we used two-point correlations, joint weighted probability density function, and linear stochastic estimation. Finally, we demonstrate the existence of coherent structures in the instantaneous flow field over the rod-roughened surface.     

Computational and experimental characterization of a liquid jet plunging into a quiescent pool at shallow inclination

A circular water jet (Re = 1.6 × 10⁵; We = 8.8 × 10³) plunging at shallow angles (θ ≈ 12.5°) into a quiescent pool is investigated computationally and experimentally. A surprising finding from the work is that cavities, of the order of jet diameter, are formed periodically in the impact location, even though the impinging flow is smooth and completely devoid of such a periodicity. Computational prediction of these frequencies was compared with experimental findings, yielding excellent agreement. The region in the vicinity of the impact is characterized by strong churning due to splashing and formation of air cavities. Measured velocity profiles indicate a concentration of momentum beneath the free surface slightly beyond the impact location (X/D_j ≈ 14), with a subsequent shift towards the free surface further downstream of this point (X/D_j ≈ 30). This shift is due primarily to the action of buoyancy on the cavity/bubble population. Comparisons of the mean velocity profile between simulations and experiments are performed, yielding good agreement, with the exception of the relatively small churning flow region. Further downstream (X/D_j ≳ 40), the flow develops mostly due to diffusion and the location of peak velocity coincides with the free surface. In this region, the free surface acts as an adiabatic boundary and restricts momentum diffusion, causing the peak velocity to occur at the free surface.     

Flow structures around an equilateral triangle arrangement of three spheres

This paper represents the results of an experimental study on the flow structure around a single sphere and three spheres in an equilateral-triangular arrangement. Flow field measurements were performed using a Particle Image Velocimetry (PIV) technique and dye visualization in an open water channel for a Reynolds number of Re = 5 × 10³ based on the sphere diameter. The distributions and flow features at the critical locations of the contours of the velocity fluctuations, the patterns of sectional streamlines, the vorticity contours, the turbulent kinetic energy, the Reynolds stress correlations and shedding frequency are discussed. The gap ratios (G/D) of the three spheres were varied in the range of 1.0 ⩽ G/D ⩽ 2.5 where G was the distance between the sphere centers, and D was the sphere diameter which was taken as 30 mm. Due to the interference of the shedding shear layers and the wakes, more complex features of the flow patterns can be found in the wake region of the two downstream spheres behind the leading sphere. For G/D = 1.25, a jet-like flow around the leading sphere through the gap between the two downstream spheres occurred, which significantly enhanced the wake region. It was observed that a continuous flow development involving shearing phenomena and the interactions of shedding vortices caused a high rate of fluctuations over the whole flow field although most of the time-averaged flow patterns were almost symmetric about the two downstream spheres.     

LES of turbulent flow in a concentric annulus with rotating outer wall

Fully-developed turbulent flow in a concentric annulus, r₁/r₂ = 0.5, Re_h = 12,500, with the outer wall rotating at a range of rotation rates N = U_θ,wall/U_b from 0.5 up to 4 is studied by large-eddy simulations. The focus is on the effects of moderate to very high rotation rates on the mean flow, turbulence statistics and eddy structure. For N up to ∼2, an increase in the rotation rate dampens progressively the turbulence near the rotating outer wall, while affecting only mildly the inner-wall region. At higher rotation rates this trend is reversed: for N = 2.8 close to the inner wall turbulence is dramatically reduced while the outer wall region remains turbulent with discernible helical vortices as the dominant turbulent structure. The turbulence parameters and eddy structures differ significantly for N = 2 and 2.8. This switch is attributed to the centrifuged turbulence (generated near the inner wall) prevailing over the axial inertial force as well as over the counteracting laminarizing effects of the rotating outer wall. At still higher rotation, N = 4, the flow gets laminarized but with distinct spiralling vortices akin to the Taylor–Couette rolls found between the two counter-rotating cylinders without axial flow, which is the limiting case when N approaches to infinity. The ratio of the centrifugal to axial inertial forces, Ta/Re² ∝ N² (where Ta is the Taylor number) is considered as a possible criterion for defining the conditions for the above regime change.