Turbulent Taylor-Couette Flow Research Articles

Turbulent mixed convection in a horizontal cylindrical cavity with the off-lattice Boltzmann method

Large-eddy simulations (LES) of turbulent mixed convection in a horizontal concentric cylindrical cavity when cylinders are subjected to rotations are investigated in the present study. A characteristic-based finite-difference off-lattice Boltzmann method solver is employed to investigate whether rotation enhances heat transfer in a horizontal concentric cylindrical cavity configuration where buoyancy acts perpendicular to the cylinder axis. The study focuses on assessing heat transfer characteristics for different rotation intensities in both counter-rotating-cylinders (CRC) and outer-rotating-cylinder (ORC) configurations. The LES simulations are performed for Rayleigh number, Ra=106, and Reynolds numbers, Re=0,500,1000, and 5000 for air (Pr=0.71), employing a classical Smagorinsky sub-grid-scale (SGS) model. The numerical solver is verified using two benchmark problems, namely (i) Buoyancy-driven flow in a differentially heated air-filled cubic enclosure and (ii) turbulent Taylor-Couette flow. The CRC and ORC configurations are chosen for the three-dimensional simulations in this study, prompted by the notable improvement in heat transfer observed in their respective two-dimensional simulations. A thorough comparison between two- and three-dimensional mixed convection results reveals substantial influence from secondary flow in the axial direction. While three-dimensional CRC simulations exhibit a modest increase in heat transfer at Re=500, the ORC configuration experiences a decrease in heat transfer rate as the Reynolds number increases, contrasting with two-dimensional simulation trends. The CRC configuration enhances the axial motion of the flow with Reynolds number, and its magnitude is larger than that of the ORC configuration and natural convection. A significant difference between two-dimensional and three-dimensional mixed convection simulation results is observed because of considerable secondary flow. Furthermore, the flow and thermal characteristics of turbulent mixed convection are investigated using streamlines, isotherms, Q-criterion, Nusselt number variation along the cylinders, anisotropy analysis, turbulent kinetic energy (TKE), dissipation, contours of radial and axial components of velocity.

Flow and heat transfer characteristics of high-pressure natural gas in the gaps of high-speed motors with a high radius ratio

A motor stator-gap-rotor model is established based on the numerical heat transfer theory by using the finite volume method. The flow evolution of high-pressure natural gas in the gap with a radius ratio of 0.971 is investigated. The results demonstrate that the flow patterns of high-pressure natural gas in the motor gap can be categorized into turbulent, spiral Taylor-Couette, and turbulent Taylor-Couette flow; the flow ranges are determined based on the Ta/Re2. Then, the flow and heat transfer characteristics of the cooling medium in the gap under different flow regimes as well as the mechanism of locally enhanced heat transfer in the gap by the Taylor-Couette flow are explored. Finally, the mathematical expressions for the Nusselt number of motor gap are determined in terms of the Reynolds number, Taylor number, and Prandtl number by fitting using the Levenberg-Marquardt and global optimization methods. Using these expressions, the flow and heat transfer characteristics in the motor gap can be predicted. Overall, this study provides useful and novel insights on the design of cooling systems for high-speed motors.

Maximum drag enhancement asymptote in turbulent Taylor–Couette flow of dilute polymeric solutions

Direct numerical simulations in a wide-gap turbulent viscoelastic Taylor–Couette flow in the Reynolds number (Re) range of 1500 to 8000 reveals the existence of a maximum drag enhancement (MDE) asymptote. The statistical properties associated with the turbulent and polymer dynamics demonstrate that the turbulent drag enhances with the increase of the Weissenberg number (Wi) and eventually saturates above a critical Wi, namely, the flow reaches the MDE state. The mean velocity profile in MDE state closely follows a logarithmic-like law with an identical slope (κK=2.32) and a Re-dependent intercept. A detailed analysis of flow structures reveals that the MDE asymptote results from the creation and eventual saturation of small-scale elastic and inertio-elastic Görtler vortices in the inner- and outer-wall regions, respectively. These vortical structures arise due to competing effects of polymer-induced stresses that either suppress or promote turbulent vortices. A close examination of competing forces in the azimuthal direction shows that the ratio of polymeric to turbulent stresses reaches a large plateau, underscoring the elastic nature of the MDE state. Moreover, the energy production mechanism in the MDE state further supports: (1) the universal interplay between polymers and turbulent vortices in a broad range of curvilinear and planar turbulent flows, and (2) the fact that the elastically induced asymptotic saturation of drag modification is an inherent property of elasticity-driven and/or elasto-inertial turbulence flow states. Overall, this study provides concrete evidence for our earlier postulate that asymptotic flow states in unidirectional turbulent viscoelastic flows are of elastic nature.

Transition to the ultimate turbulent regime in a very wide gap Taylor-Couette flow (η = 0.1) with a stationary outer cylinder

The boundary layers in turbulent Taylor-Couette flow are exposed to transitions from laminar to turbulent states if the flow is sufficiently sheared. The present study examines this particular transition from the so-called “classical” to “ultimate” regime experimentally for a very wide-gap Taylor-Couette flow with a radius ratio of and shear Reynolds numbers of up to . In order to determine the transition, the angular momentum transport is measured by using torque sensors at the inner wall. This is complemented by measuring the radial and azimuthal velocities via a time-resolved Particle-Image-Velocimetry (PIV). The transition to the ultimate regime is found at . The dimensionless angular momentum flux showed an effective scaling of for and is in agreement with the scaling laws used for the ultimate regime in narrow-gap Taylor-Couette flows. In addition, a spectral analysis was performed showing the existence of highly energetic small-scale and large-scale patterns in the classical regime whereas only highly energetic large-scale patterns were observed in the ultimate regime.

Experimental investigation of turbulent counter-rotating Taylor–Couette flows for radius ratio η = 0.1

Turbulent Taylor–Couette flow between two concentric independently rotating cylinders with a radius ratio of $\eta = 0.1$ is studied experimentally. While the scope is to study the counter-rotating cases between both cylinders, the radial and azimuthal velocity components are recorded at different horizontal planes with high-speed particle image velocimetry. The parametric study considered a set of different shear Reynolds numbers in the range of $20\,000 \leq Re_s \leq 1.31 \times 10^5$ , with different rotation ratios of $-0.06 \leq \mu \leq +0.008$ . The observed flow fields had a clear dependence on the rotation ratio, where flow patterns evolved with a more pronounced axial dependence. The angular momentum transport is computed as a result of the recorded flow fields and given by a quasi-Nusselt number. The dependence of the Nusselt number on the different rotation ratios shows a maximum for the low counter-rotating case and $\mu _{max}$ is found between $-0.011 < \mu _{max} < -0.0077$ . The Nusselt number decreases for stronger counter-rotation until a minimum is reached, where it tends to increase again for higher counter-rotation rates. The space–time behaviour of the turbulent flow showed the existence of patterns propagating from the inner region towards the outer region for all studied counter-rotating cases. In addition, patterns have been found that tend to propagate from the outer region towards the inner region with a novel character at high counter-rotation cases. These patterns enhance the angular momentum transport where a second maximum in the transport mechanism has to be expected.

Evolution of Air Plastron Thickness and Slip Length over Superhydrophobic Surfaces in Taylor Couette Flows

Drag reduction (DR) using superhydrophobic surfaces (SHSs) has received intensive interest due to the emergence of SH coating technology. The air layer (plastron “δ”) trapped between the SHS and the water controls the flow slip over the SHSs. We demonstrate slippage over three fabricated SHSs in laminar and low turbulent Taylor–Couette flows. We experimentally investigate how the slip length increases with a higher Reynolds number (Re) over the tested SHSs; simultaneously, the air plastron thickness investigates using a viscous model. The mean skin friction coefficient (Cf) can be fitted to a modified semi-empirical logarithmic law expressed in the Prandtl–von Kármán coordinate. An effective slip length is estimated in the 35–41 µm range with an achieved 7–11% DR for the tested surfaces. Statistical analysis is used to develop a regression model from the experimental data. The model shows an R2 of 0.87 and good agreement with the experimental data. This shows the relation between the dimensionless slip length (b+), the dimensionless plastron thickness (δ+), and the Reynolds number, which is directly proportional. The regression model shows that b+ and Reynolds numbers have a higher impact on the δ+ than the surface wettability, which attribute to the small difference in the wetting degree between the three tested surfaces. The practical importance of the work lies in its ability to provide a deep understanding of the reduction in viscous drag in numerous industrial applications. Furthermore, this research serves as a groundwork for future studies on hydrophobic applications in internal flows.

Skin-friction drag reduction by axial oscillations of the inner cylinder in turbulent Taylor–Couette flows

Skin-friction drag reduction by axial oscillations of an inner cylinder is numerically investigated at radius ratio (η = 0.5) using direct numerical simulation. In the present study, at fixed optimal oscillating period, the effect of oscillating amplitude on skin-friction drag reduction is investigated in detail. Furthermore, the effect of Reynolds number (ranging from 1000 to 5000) is also investigated. Our results show that as we keep increasing the oscillating amplitude, the drag reduction first increases and then decreases after a critical threshold dependent on the considered Reynolds number. Crossing the threshold value leads to re-organization of flow into a patchy turbulent state with large presence of small-scale structures. With increasing oscillating amplitude, the near-wall high and low-speed streaks get skewed in the θ–z plane followed by break down of high-speed streaks. Spatial density of the vortical structure decreases till threshold amplitude while the quadrant analysis shows that the movement of high-speed fluid away from walls plays an important role in the attenuation of Reynolds shear stresses.

Experimental method for investigating the formation of flow patterns in a very wide gap Taylor-Couette flow (η = 0.1).

Abstract In this study, we investigate the turbulent Taylor-Couette (TC) flow experimentally. First, in order to show the formation of the different patterns in the flow, the flow was seeded with kalliroscope particles and by applying a vertical laser sheet we were able to capture the different patterns in the flow. For a further detailed study, the flow field was measured in horizontal planes at different cylinder heights using Particle image velocimetry (PIV). The formation of patterns appears for the counter-rotation configuration where the outer cylinder rotates in the opposing direction of the inner cylinder rotation. For low shear Reynolds numbers, stable Taylor vortices fulfilling the whole gap appear for very low counter-rotation rates. While for the same rotation rates and higher shear Reynold number, large scale patterns with shorter length scale compared to the classical Taylor vortices appears, which can be described as interlaced fingers from in and outflow. The existence of these patterns leads to enhanced angular momentum transport.

Recent developments of turbulent emulsions in Taylor-Couette flow.

Emulsions are common in many natural and industrial settings. Recently, much attention has been paid to understanding the dynamics of turbulent emulsions. This paper reviews some recent studies of emulsions in turbulent Taylor-Couette flow, mainly focusing on the statistics of the dispersed phase and the global momentum transport of the system. We first study the size distribution and the breakup mechanism of the dispersed droplets for turbulent emulsions with a low volume-fraction (dilute) of the dispersed phase. For systems with a high volume-fraction (dense) of the dispersed phase, we address the detailed response of the global transport (effective viscosity) of the turbulent emulsion and its connection to the droplet statistics. Finally, we will discuss catastrophic phase inversions, which can happen when the volume-fraction of the dispersed phase exceeds a critical value during dynamic emulsification. We end the manuscript with a summary and an outlook including some open questions for future research. This article is part of the theme issue 'Taylor-Couette and related flows on the centennial of Taylor's seminal Philosophical Transactions paper (part 1)'.

Turbulent Taylor-Couette flow of dilute polymeric solutions: a10-year retrospective.

This retrospective aims to present a coherent history of important findings in direct numerical simulations and experiments in turbulent Taylor-Couette (TC) flow of dilute polymeric solutions in the last decade. Specifically, the sequence of flow transitions due to a continuous increase of fluid elasticity from classical Newtonian, to inertially and in turn to elastically dominated, and finally to the inertialess purely elastic turbulence, is presented. In each elastically modified flow state, the drag modification, coherent flow structures, velocity and elastic stress statistics, mechanism of turbulent kinetic energy production, spectral features as well as the self-sustaining cycles of turbulence, are discussed. Finally, to provide a broader perspective, an overview of important similarities and differences between elastically induced turbulence in prototypical curvilinear and rectilinear shear flows including the curvature-free limit of TC flow, namely, the spanwise-rotating plane Couette flow, is presented. This article is part of the theme issue 'Taylor-Couette and related flows on the centennial of Taylor's seminal Philosophical Transactions paper (part 1)'.

Aspect-ratio dependence of heat and angular momentum transport in turbulent Taylor-Couette flows with axial thermal forcing

• Scaling law of transports determined in finite systems can be extrapolated to large-scale flows. • Coherent turbulent structures in form of Taylor vortices promote heat and angular transports. • Magnitudes of both heat and angular momentum transport depend on domain aspect-ratio. We report numerical studies of the effects of geometry factors, i.e. the aspect ratio Γ and radius ratio η , on the axial heat transport N u and the radial angular momentum transport N ω by turbulent Taylor-Couette flows that are subjected to a vertically destabilizing temperature gradient. For a given Reynolds number R e the magnitudes of both N u and N ω exhibit a pronounced aspect-ratio dependence. The angular momentum transport is reduced in long cylinders, since endwall effects are weakened as Γ increases. For the heat transfer in large- Γ cylinders, a significant N u -reduction appears for low- R e regime, whereas N u can be greatly enhanced in the regime of turbulent Taylor vortex (TV). The former N u -reduction is associated with the process that the thermal plumes are swept away by the Ekman vortices near the boundaries, and the fluid exchange is severely restricted between adjacent vortices in the bulk region. The latter N u -enhancement is attributed to the strengthened shears arising in large- Γ cylinders, resulting in a more turbulent boundary layer. Moreover, the pronounced inter-mixing of turbulent TVs continuously pumps the hot (cold) fluids into the bulk, intensifying the transport processes. It is found that although the constraints from the endwalls impact the global heat and angular momentum transport in the low- R e regime, they hardly affect their scaling properties in the high- R e regime with large Γ . We thus expect that the scaling relationship of N u ( R e ) and N ω ( R e ) determined with finite Γ can be extrapolated to large-scale, and even vertically unbounded industrial and geophysical flows.

Geometrical dependence of optimal bounds in Taylor–Couette flow

This paper is concerned with the optimal upper bound on mean quantities (torque, dissipation and the Nusselt number) obtained in the framework of the background method for the Taylor–Couette flow with a stationary outer cylinder. Along the way, we perform the energy stability analysis of the laminar flow, and demonstrate that below radius ratio $0.0556$ , the marginally stable perturbations are not the axisymmetric Taylor vortices but rather a fully three-dimensional flow. The main result of the paper is an analytical expression of the optimal bound as a function of the radius ratio. To obtain this bound, we begin by deriving a suboptimal analytical bound using analysis techniques. We use a definition of the background flow with two boundary layers, whose relative thicknesses are optimized to obtain the bound. In the limit of high Reynolds number, the dependence of this suboptimal bound on the radius ratio (the geometrical scaling) turns out to be the same as that of numerically computed optimal bounds in three different cases: (1) the perturbed flow only satisfies the homogeneous boundary conditions but need not be incompressible; (2) the perturbed flow is three-dimensional and incompressible; (3) the perturbed flow is two-dimensional and incompressible. We compare the geometrical scaling with the observations from the turbulent Taylor–Couette flow, and find that the analytical result indeed agrees well with the available direct numerical simulations data. In this paper, we also dismiss the applicability of the background method to certain flow problems and therefore establish the limitation of this method.

Counter-rotating Taylor-Couette flows with radial temperature gradient

In the present work, counter-rotating turbulent Taylor-Couette flows with radial temperature gradient have been studied as an extension of previously studied simple-rotating turbulent Taylor-Couette flows. The rotation axis is orthogonal to the gravity vector. Direct Numerical Simulations (DNS) have been carried out for Reynolds number ranging from 1000 to 5000 and Richardson number varying from 0 to 0.4. The effect of variation of Reynolds number and Richardson number on the flow statistics, flow dynamics, and near-wall coherent structures are studied. For neutrally buoyant cases, near-wall coherent structures exist near the inner and the outer wall, with the core being almost vortex-free. With an increase in Richardson number, more dense and finer vortical structures spread out in the core in half the circumferential domain only. This behavior is due to the spatial stable or unstable stratification in the azimuthal direction, leading to the generation of turbulence in the lower half of the domain and mitigation of turbulence in the upper half of the domain. Further, the turbulent kinetic energy (TKE) budget analysis reveals an increase in turbulence on heating the outer cylinder wall due to an increase in the production term. Heating the outer cylinder wall leads to a slight decrease in skin friction for the inner cylinder.

Mutual coherent structures for heat and angular momentum transport in turbulent Taylor-Couette flows

When subjected to a radial temperature gradient, Taylor-Couette flows undergo evolution of flow states with increasing rotations: a first transition from asymmetric vertical convection to spiral vortices, and a second transition to turbulence characterized by Taylor vortices. In the latter turbulent flow state, the radial transport of heat and angular momentum exhibits a similar power-law scaling. Our data analysis of the spatial distributions of the flux densities reveals mutual turbulent structures through which both heat and angular momentum are transported efficiently.

Computational modelling of turbulent Taylor–Couette flow for bearing chamber applications: A comparison of unsteady Reynolds-averaged Navier–Stokes models

The capability to accurately model fluid flow within rotating Taylor–Couette systems has a primary role in informing computational investigations of rotating machinery. There is considerable uncertainty regarding selection of modelling approach, including a suitable turbulence model, that can accurately resolve turbulence within such complex flows while remaining computationally feasible for industrially relevant applications. This paper presents a numerical comparison of axisymmetric and three-dimensional unsteady Reynolds-averaged Navier–Stokes (URANS) turbulence models within ANSYS Fluent. The CFD geometries are representative of ones for which there are published experimental measurements. For the Taylor–Couette study, investigation into inner cylinder start-up procedure, based on previous published findings, confirmed that the final state of the flow is highly dependent on the initial conditions and acceleration rate. Once Taylor vortices form and stabilise, they are not disrupted by small steps in inner cylinder speed, allowing computationally efficient accelerations. Investigations into applying rotational periodicity were unsuccessful, resulting in a significantly reduced core velocity. Axisymmetric predictions provided reasonable agreement with experimental data only at low rotation rates. A good prediction of the velocity flow field was obtained for three-dimensional simulations of the full 360° domain with differences of less than 5% for radial velocities. Among the URANS models, the standard k-ω model and baseline Reynolds stress model (BSL-RSM) provided the closest agreement to published experimental data. In the paper, the developed Taylor–Couette turbulence modelling methodology is extended to a bearing chamber geometry. Analysis of the secondary vortex flow field is compared both qualitatively and quantitatively to published bearing chamber experimental measurements. Overall, whilst a good agreement is still found using the standard k-ω turbulence model, discrepancies arise with the BSL-RSM. However, for this more complex bearing chamber environment compared to a Taylor–Couette flow, the shear stress transport k-ω turbulence model provided the closest agreement and is recommended for future bearing chamber modelling.

Analysis of drag reduction effects in turbulent Taylor–Couette flow controlled via axial oscillation of inner cylinder

Analysis of drag reduction effects due to axial oscillation of an inner cylinder in a turbulent Taylor–Couette (TC) flow is performed in the present study. The frictional Reynolds number on the inner cylinder is 218, and the non-dimensional oscillating period is varied from 8 to 32. By examining turbulence statistics, we uncover different impacts of the long- and short-period oscillations on the circumferential (θ) and radial (r) velocity fluctuations in large (uθl, url) and small (uθs, urs) scales. One of the most surprising findings is that the short-period oscillation increases the large-scale Reynolds shear stress ⟨uθlurl⟩ by the strong intensification of uθl exceeding the suppression of url. To understand the phenomena, the spectra of each term in the transport equations of the Reynolds normal stresses ⟨uθ′uθ′⟩ and ⟨ur′ur′⟩ are analyzed. First, it is shown that the short-period oscillation weakens the productions of uθs, urs, and url while it enhances that of uθl. In contrast, the long-period oscillation reduces the productions of uθl and url while it mainly intensifies that of urs. Second, the investigations of the pressure–strain terms indicate that the short-period oscillation mainly impedes the inter-component energy transfer originating from the small-scale background turbulence. However, the long-period oscillation benefits the small-scale inter-component energy communication while it hinders the large-scale one. In addition, the inverse energy transfer in the turbulent TC flow is confirmed by inspecting the inter-scale energy transfer terms. The hindrance of the inter-scale energy transfer by the inner-cylinder oscillation plays a non-negligible role in the reduction of the wall friction drag.

Resistance law dependence on radius ratios for turbulent Taylor-Couette flow from extended local balance model

Turbulent Couette-Taylor flow is the most interesting kind of flow for theoreticians and experimenters. There are a great number of theories and experiments for larger and larger Reynolds numbers. The picture becomes more complex if we consider the case of independently rotating cylinders. The most simple quantity is a torque, acting on the lateral surface of inner cylinder by rotating fluid. How can we deduce theoretically the torque from Navier-Stokes equation? Unfortunately we have only bounds on this variable yet. So we cause use models of turbulence to predict the torque dependence on Reynolds numbers or Taylor number and on radius ration. Here we present the results of simple calculations, based on extended local balance model. The study compares the theory with experiments.

Aspect-Ratio Dependence of Heat and Angular Momentum Transport in Turbulent Taylor-Couette Flows with Axial Thermal Forcing

Aspect-Ratio Dependence of Heat and Angular Momentum Transport in Turbulent Taylor-Couette Flows with Axial Thermal Forcing

Distribution of Nanoparticles in a Turbulent Taylor–Couette Flow Considering Particle Coagulation and Breakage

In this paper, the dynamic evolution of nanoparticles in a turbulent Taylor–Couette flow was studied by means of a numerical simulation. The initial particle size was 200 nm, and the volume concentration was 1 × 10−5. The Reynolds-averaged N–S equation for Taylor–Couette flow was solved numerically using the realizable k-ε model combined with the standard wall function. The numerical result of the velocity distribution is in good agreement with the experimental results. Additionally, the dynamic equation for the particle number distribution function was solved numerically using the Taylor series expansion moment method (TEMOM). The variation characteristics of particle number density, diameter and polydispersity in the flow were analyzed. The results show that particle breakage is obvious in the region with strong vorticity due to the large shear strength, which leads to a significant change in the particle number density, diameter and polydispersity. Furthermore, the effects of the gap width between two cylinders and the Reynolds number on the distribution of the particle number density, size and polydispersity are discussed.

Numerical study of heat flow characteristics of turbulent Taylor-Couette flow in slit wall mode

Heat transfer enhancement is by far an important component in the design of numerous industrial applications of Taylor-Couette flow including electric motors and particularly rotating machinery. To optimize the performances of these machines, superior knowledge of the fluid flow is vital to better estimate the heat transfer distribution. This study will specifically consider the effect the slit number and width possess on the distribution of turbulent Taylor-Couette flow and the resulting heat transfer correlation in the annulus of two concentric cylinders under varying conditions. A numerical simulation method is intended for the study using varying slit structure parameters of widths (2.5 ≤ w ≤ 7.5) mm and fitted with 6, 9 and 12 number of slits. The slit effect is then investigated under both isotherm and non-isotherm conditions considering the interactions between fluid flow regions in the mainstream area and the annulus. The small-scale vortex that appears in the annulus region improves the heat transferability between the fluid in the annulus and the main region as well as the heat transfer performance of the model with a gradual increase in Reynolds number.