Impact of osmotic pressure on the stability of Taylor vortices

We use linear stability analysis and direct numerical simulations to investigate the coupling between centrifugal instabilities, solute transport and osmotic pressure in a Taylor–Couette configuration that models rotating dynamic filtration devices. The geometry consists of a Taylor–Couette cell with a superimposed radial throughflow of solvent across two semi-permeable cylinders. Both cylinders totally reject the solute, inducing the build-up of a concentration boundary layer. The solute retroacts on the velocity field via the osmotic pressure associated with the concentration differences across the semi-permeable cylinders. Our results show that the presence of osmotic pressure strongly alters the dynamics of the centrifugal instabilities and substantially reduces the critical conditions above which Taylor vortices are observed. It is also found that this enhancement of the hydrodynamic instabilities eventually plateaus as the osmotic pressure is further increased. We propose a mechanism to explain how osmosis and instabilities cooperate and develop an analytical criterion to bound the parameter range for which osmosis fosters the hydrodynamic instabilities.

Research of Flow Stability of Non-Newtonian Magnetorheological Fluid Flow in the Gap between Two Cylinders

This paper deals with a mathematical modeling of flow stability of Newtonian and non-Newtonian fluids in the gap between two concentric cylinders, one of which rotates. A typical feature of the flow is the formation of a vortex flow, so-called Taylor vortices. Vortex structures are affected by the speed of the rotating cylinder and the physical properties of the fluids, i.e., viscosity and density. Analogy in terms of viscosity is assumed for non-Newtonian and magnetorheological fluids. Mathematical models of laminar, transient and turbulent flow with constant viscosity and viscosity as a function of the deformation gradient were formulated and numerically solved to analyze the stability of single-phase flow. To verify them, a physical experiment was performed for Newtonian fluids using visualizations of vortex structures—Taylor vortices. Based on the agreement of selected numerical and physical results, the experience was used for numerical simulations of non-Newtonian magnetorheological fluid flow.

Experimental Investigations on the Effect of a Wavy Surface on Hydrodynamic Instabilities in a Taylor-Couette System

In this work, we propose an experimental study of the effect of surface roughness of the internal cylinder Couette-Taylor system in order to investigate the hydrodynamic instabilities of the flow. During experiments, the inner cylinder, which presents a rough surface with u cylinder corrugations, rotates at a given angular speed and the outer cylinder, which is smooth, is kept fixed. The main objective of the study is to demonstrate the effect of geometric parameters on the flow (the shape of the roughness). Experimental results have shown that the shapes of the surface irregularities have an effect on the appearance of the first instabilities, which strongly depend on the size, shape and nature of the roughness. In fact, the nature of surface roughness not only affects the friction on the wall, but also strongly influences the transport of mass and momentum in a given flow regime. The flow therefore evokes more friction when the inner (rotating) cylinder has a rough surface. This friction, which slows the speed of the fluid particles, strongly depends on the surface nature in contact with the fluid. The movement of the particles in these irregularities will therefore, be damped as a function of the shape of the roughness. In addition, the results also showed that once Couette-Taylor vortices are present, surface roughness can promote continued flow disturbance. The resulting flow then becomes less slow in the troughs of surface irregularities; thus, leads to less friction.

The preferential accumulation and the settling velocity of small heavy particles in Taylor–Couette flows

ABSTRACT In a gap between two concentric cylinders, we discover that the small heavy particle settling velocity (Vs) is greater than its associated terminal velocity (Vt) in featureless turbulence that is generated by counter-rotating inner and outer cylinders simultaneously. The peak enhancement of Vs occurs at St × (Vt/u′) ∼ 1, where u′ and St are, respectively, the r.m.s. turbulence fluctuation velocity and the Stokes number defined as the ratio between the particle response time to the Kolmogorov turbulence time. The present (Vs − Vt)/u′ data as a function of St measured by the high-speed particle imaging velocimetry are compared with previous experimental results obtained from different turbulent flow configurations in an attempt to gain further understandings of the complicated interactions between small heavy particles and featureless turbulence with negligible mean velocities. Moreover, it is found that small heavy particles are preferentially accumulated around the edges of an array of counter-rotating turbulent Taylor vortices with the inner cylinder rotation alone when a time ratio between particle response and Taylor vortices is near unity. These experimental results are interesting that may deserve to disseminate in our fluid mechanics community.

Annular Frictional Pressure Losses for Drilling Fluids

The most common viscosity models used in the drilling industry are the Bingham, the Power-Law and the Herschel-Bulkley models. In addition, it is common to refer to the low-shear yield-point. The scope of the present paper is to discuss numerical methods applicable for calculating annular frictional pressure losses. The topic of annular frictional pressure loss modelling has been treated in textbooks. None of these couple their models with the selection of viscosity data from measurements at the relevant shear rates. It is earlier shown how rotation of the inner string in an annulus can complicate the flow due to establishment of Taylor vortices. There are currently no analytical methods to handle such flow. The effect of the vortices depends strongly on the fluid’s composition in addition to the flow conditions. The practical way to handle these situations are by “fingerprinting” during circulation. In the paper examples will be presented showing how the Herschel-Bulkley fluid can be transferred to simple models for axial flow in an annulus where the inner cylinder does not rotate. It is common to use the narrow slot approximation. This method was used by Founargiotakis et al. In this paper both the modified Herschel-Bulkley model with dimensionless shear rates and the traditional model where the consistency depends on the shear rate will be presented. The dimensionless shear rate model can easily be translated back to the traditional form and vice-versa. Mathematical models will be presented. Hence a framework is given that is easier to use for digitalization and automation and in correlations including pressure, temperature and composition.

Statistics, plumes and azimuthally travelling waves in ultimate Taylor–Couette turbulent vortices

In this paper, we experimentally study the influence of large-scale Taylor rolls on the small-scale statistics and the flow organization in fully turbulent Taylor–Couette flow for Reynolds numbers up to $Re_{S}=3\times 10^{5}$. The velocity field in the gap confined by coaxial and independently rotating cylinders at a radius ratio of $\unicode[STIX]{x1D702}=0.714$ is measured using planar particle image velocimetry in horizontal planes at different cylinder heights. Flow regions with and without prominent Taylor vortices are compared. We show that the local angular momentum transport (expressed in terms of a Nusselt number) mainly takes place in the regions of the vortex in- and outflow, where the radial and azimuthal velocity components are highly correlated. The efficient momentum transfer is reflected in intermittent bursts, which becomes visible in the exponential tails of the probability density functions of the local Nusselt number. In addition, by calculating azimuthal energy co-spectra, small-scale plumes are revealed to be the underlying structure of these bursts. These flow features are very similar to the one observed in Rayleigh–Bénard convection, which emphasizes the analogies of these systems. By performing a complex proper orthogonal decomposition, we remarkably detect azimuthally travelling waves superimposed on the turbulent Taylor vortices, not only in the classical but also in the ultimate regime. This very large-scale flow pattern, which is most pronounced at the axial location of the vortex centre, is similar to the well-known wavy Taylor vortex flow, which has comparable wave speeds, but much larger azimuthal wavenumbers.

Suspension Taylor–Couette flow: co-existence of stationary and travelling waves, and the characteristics of Taylor vortices and spirals

Flow visualization and particle image velocimetry (PIV) measurements are used to unravel the pattern transition and velocity field in the Taylor–Couette flow (TCF) of neutrally buoyant non-Brownian spheres immersed in a Newtonian fluid. With increasing Reynolds number ($Re$) or the rotation rate of the inner cylinder, the bifurcation sequence in suspension TCF remains same as in its Newtonian counterpart (i.e. from the circular Couette flow (CCF) to stationary Taylor vortex flow (TVF) and then to travelling wavy Taylor vortices (WTV) with increasing $Re$) for small particle volume fractions ($\unicode[STIX]{x1D719}<0.05$). However, at $\unicode[STIX]{x1D719}\geqslant 0.05$, non-axisymmetric patterns such as (i) the spiral vortex flow (SVF) and (ii) two mixed or co-existing states of stationary (TVF, axisymmetric) and travelling (WTV or SVF, non-axisymmetric) waves, namely (iia) the ‘TVF$+$WTV’ and (iib) the ‘TVF$+$SVF’ states, are found, with the former as a primary bifurcation from CCF. While the SVF state appears both in the ramp-up and ramp-down experiments as in the work of Majji et al. (J. Fluid Mech., vol. 835, 2018, pp. 936–969), new co-existing patterns are found only during the ramp-up protocol. The secondary bifurcation TVF $\leftrightarrow$ WTV is found to be hysteretic or sub-critical for $\unicode[STIX]{x1D719}\geqslant 0.1$. In general, there is a reduction in the value of the critical Reynolds number, i.e. $Re_{c}(\unicode[STIX]{x1D719}\neq 0)<Re_{c}(\unicode[STIX]{x1D719}=0)$, for both primary and secondary transitions. The wave speeds of both travelling waves (WTV and SVF) are approximately half of the rotational velocity of the inner cylinder, with negligible dependence on $\unicode[STIX]{x1D719}$. The analysis of the radial–axial velocity field reveals that the Taylor vortices in a suspension are asymmetric and become increasingly anharmonic, with enhanced radial transport, with increasing particle loading. Instantaneous streamline patterns on the axial–radial plane confirm that the stationary Taylor vortices can indeed co-exist either with axially propagating spiral vortices or azimuthally propagating wavy Taylor vortices – their long-time stability is demonstrated. It is shown that the azimuthal velocity is considerably altered for $\unicode[STIX]{x1D719}\geqslant 0.05$, resembling shear-band type profiles, even in the CCF regime (i.e. at sub-critical Reynolds numbers) of suspension TCF; its possible role on the genesis of observed patterns as well as on the torque scaling is discussed.

Flow and heat transfer simulation with a thermal large eddy lattice Boltzmann method in an annular gap with an inner rotating cylinder

In this study, a thermal Large Eddy Lattice Boltzmann Method (LBM–LES) is applied to Taylor–Couette flow simulations, allowing detailed analysis of local heat transport over a wide range of Taylor numbers, including resolved transient Taylor vortices. The challenge in thermal management of electric motors is to control the temperature in the air gap between rotor and stator due to the gap’s small width and complex geometry, in which Taylor vortices strongly influence the heat transfer. This thin gap — here simplified by an annulus — is solved for the first time by a Thermal Lattice Boltzmann Method with a Smagorinsky sub-grid model. The influence of the rotational velocity of the inner cylinder with Taylor numbers from 36 to 511 — corresponding to a Reynolds number on the inner cylinder of up to 126[Formula: see text]000 — is numerically investigated. The simulations are validated on the basis of the global Nusselt number, where we find good agreement with a published measurement series, an empirical correlation and Finite Volume simulations using the SST turbulence model. Special attention is paid on predicting the critical Taylor number, which is reproduced almost exactly by Direct Numerical Simulations (DNS) with LBM, whereas LBM–LES slightly overestimates and the SST model further overestimates the occurrence of Taylor vortices.

Resistance force pulsations of annular flow in the Couette-Taylor system with counter-rotating cylinders

The paper presents the results of an experimental study of the Couette-Taylor flow fluctuations in a ring channel with oppositely rotating multicylinder rotors. Experiments were carried out using water-glycerine solutions as a working fluid. The rotation resistance moment and its pulsations were investigated, using the system for measuring the torque resistance of rotation of rotors, made in the form of a digital dynamometer based on a tension sensor. The investigations made it possible to establish that the classic dependence of the appearance of Taylor vortices is observed in the slit flow of a multicylinder system rotating oppositely. It was shown that in the range of Reynolds numbers Re = (100 – 500), pulsations of dissipative processes with variable frequency and amplitude up to 10% of the mean value of rotation resistance are observed.