Turbulent Taylor-Couette Flow Research Articles

Large eddy simulation of turbulent Taylor–Couette flow using isogeometric analysis and the residual-based variational multiscale method

We present an application of the residual-based variational multiscale turbulence modeling (RBVMS) methodology to the computation of turbulent Taylor–Couette flow at high Reynolds number. We show that the RBVMS formulation globally conserves angular momentum, a feature that is felt to be important for flows dominated by rotation, and that is not shared by standard stabilized formulations of fluid flow. Weak imposition of Dirichlet boundary conditions is employed to enhance the accuracy of the RBVMS framework in the presence of thin turbulent boundary layers near solid walls. Calculation of conservative boundary forces and torques is also presented for the case of weakly enforced boundary conditions. NURBS-based isogeometric analysis is employed for the spatial discretization, and mesh refinement is performed to assess the convergence characteristics of the proposed methodology. Numerical tests show that very accurate results are obtained on relatively coarse grids. To the best of the authors’ knowledge, this paper is the first to report large eddy simulation computations of this challenging test case.

Superstatistical fluctuations in time series: Applications to share-price dynamics and turbulence

We report a general technique to study a given experimental time series with superstatistics. Crucial for the applicability of the superstatistics concept is the existence of a parameter beta that fluctuates on a large time scale as compared to the other time scales of the complex system under consideration. The proposed method extracts the main superstatistical parameters out of a given data set and examines the validity of the superstatistical model assumptions. We test the method thoroughly with surrogate data sets. Then the applicability of the superstatistical approach is illustrated using real experimental data. We study two examples, velocity time series measured in turbulent Taylor-Couette flows and time series of log returns of the closing prices of some stock market indices.

UV Disinfection of E. coli Between Concentric Cylinders: Effects of the Boundary Layer and a Wavy Wall

UV inactivation of E. coli in a plug flow reactor between concentric cylinders was investigated. The concentration boundary layer thickness was computed for laminar, turbulent and Taylor-Couette flow in terms of the respective mass transfer Sherwood number. It is demonstrated that the concentration boundary layer is thin and that the mass transfer coefficient is large and comparable in size for both turbulent and laminar Taylor-Couette flow in contrast to laminar flow. Computation of the fluence distribution for each flow pattern indicate that turbulent and especially Taylor-Couette flow subject E. coli to an equal flux of photons corresponding to ideal plug flow. However, experiments with turbulent flow that require large axial velocities indicate that very long reactor lengths are necessary to inactivate E. coli. Finally, rotor wavy wall modifications are explored to increase the inactivation of microorganisms in Taylor-Couette flow.

Superstatistical distributions from a maximum entropy principle

We deal with a generalized statistical description of nonequilibrium complex systems based on least biased distributions given some prior information. A maximum entropy principle is introduced that allows for the determination of the distribution of the fluctuating intensive parameter beta of a superstatistical system, given certain constraints on the complex system under consideration. We apply the theory to three examples: the superstatistical quantum-mechanical harmonic oscillator, the superstatistical classical ideal gas, and velocity time series as measured in a turbulent Taylor-Couette flow.

Direct numerical simulation of turbulent Taylor–Couette flow

The direct numerical simulation (DNS) of the Taylor–Couette flow in the fully turbulent regime is described. The numerical method extends the work by Quadrio and Luchini [M. Quadrio, P. Luchini, Eur. J. Mech. B/Fluids 21 (2002) 413–427], and is based on a parallel computer code which uses mixed spatial discretization (spectral schemes in the homogeneous directions, and fourth-order, compact explicit finite-difference schemes in the radial direction). A DNS is carried out to simulate for the first time the turbulent Taylor–Couette flow in the turbulent regime. Statistical quantities are computed to complement the existing experimental information, with a view to compare it to planar, pressure-driven turbulent flow at the same value of the Reynolds number. The main source for differences in flow statistics between plane and curved-wall flows is attributed to the presence of large-scale rotating structures generated by curvature effects.

Direct numerical simulation of turbulent Taylor–Couette flow

We investigate the dynamical and statistical features of turbulent Taylor–Couette flow (for a radius ratio 0.5) through three-dimensional direct numerical simulations (DNS) at Reynolds numbers ranging from 1000 to 8000. We show that in three-dimensional space the Görtler vortices are randomly distributed in banded regions on the wall, concentrating at the outflow boundaries of Taylor vortex cells, which spread over the entirecylinder surface with increasing Reynolds number. Görtler vortices cause streaky structures that form herringbone-like patterns near the wall. For the Reynolds numbers studied here, the average axial spacing of the streaks is approximately 100 viscous wall units, and the average tilting angle ranges from 16° to 20°. Simulationresults have been compared to the experimental data in the literature, and the flow dynamics and statistics are discussed in detail.

Torque scaling in turbulent Taylor–Couette flow between independently rotating cylinders

Turbulent Taylor–Couette flow with arbitrary rotation frequencies ω1, ω2 of the two coaxial cylinders with radii r1 < r2 is analysed theoretically. The current Jω of the angular velocity ω(x,t) = uϕ(r,ϕ,z,t)/r across the cylinder gap and and the excess energy dissipation rate ϵw due to the turbulent, convective fluctuations (the ‘wind’) are derived and their dependence on the control parameters analysed. The very close correspondence of Taylor–Couette flow with thermal Rayleigh–Bénard convection is elaborated, using these basic quantities and the exact relations among them to calculate the torque as a function of the rotation frequencies and the radius ratio η = r1/r2 or the gap width d = r2 − r1 between the cylinders. A quantity σ corresponding to the Prandtl number in Rayleigh–Bénard flow can be introduced, $\sigma = ((1 + \eta)/2)/\sqrt{\etaacute;)^4$. In Taylor–Couette flow it characterizes the geometry, instead of material properties of the liquid as in Rayleigh–Bénard flow. The analogue of the Rayleigh number is the Taylor number, defined as Ta ∝ (ω1 − ω2)2 times a specific geometrical factor. The experimental data show no pure power law, but the exponent α of the torque versus the rotation frequency ω1 depends on the driving frequency ω1. An explanation for the physical origin of the ω1-dependence of the measured local power-law exponents α(ω1) is put forward. Also, the dependence of the torque on the gap width η is discussed and, in particular its strong increase for η → 1.

Turbulent mixing at a stable density interface: the variation of the buoyancy flux–gradient relation

Experiments conducted on mixing across a stable density interface in a turbulent Taylor–Couette flow show, for the first time, experimental evidence of an increase in mixing efficiency at large Richardson numbers. With increasing buoyancy gradient the buoyancy flux first passes a maximum, then decreases and at large values of the buoyancy gradient the flux increases again. Thus, the curve of buoyancy flux versus buoyancy gradient tends to be N-shaped (rather than simply bell shaped), a behaviour suggested by the model of Balmforth et al. (J. Fluid Mech. vol. 428, 1998, p. 349). The increase in mixing efficiency at large Richardson numbers is attributed to a scale separation of the eddies active in mixing at the interface; when the buoyancy gradient is large mean kinetic energy is injected at scales much smaller than the eddy size fixed by the gap width, thus decreasing the eddy turnover time. Observations show that there is no noticeable change in interface thickness when the mixing efficiency increases; it is the mixing mechanism that changes. The curves of buoyancy flux versus buoyancy gradient also show a large variability for identical experimental conditions. These variations occur at time scales one to two orders of magnitude larger than the eddy turnover time scale.

Bubbly Turbulent Drag Reduction Is a Boundary Layer Effect

In turbulent Taylor-Couette flow, the injection of bubbles reduces the overall drag. On the other hand, rough walls enhance the overall drag. In this work, we inject bubbles into turbulent Taylor-Couette flow with rough walls (with a Reynolds number up to 4 x 10(5), finding an enhancement of the dimensionless drag as compared to the case without bubbles. The dimensional drag is unchanged. As in the rough-wall case no smooth boundary layers can develop, the results demonstrate that bubbly drag reduction is a pure boundary layer effect.

Population balance modeling of aggregation and breakage in turbulent Taylor–Couette flow

An experimental and computational study of aggregation and breakage processes for fully destabilized polystyrene latex particles under turbulent-flow conditions in a Taylor–Couette apparatus is presented. To monitor the aggregation and breakage processes, an in situ optical imaging technique was used. Consequently, a computational study using a population balance model was carried out to test the various parameters in the aggregation and breakage models. Very good agreement was found between the time evolution of the cluster size distribution (CSD) calculated with the model and that obtained from experiment. In order to correctly model the left-hand side of the CSD (small clusters), it was necessary to use a highly unsymmetric fragment-distribution function for breakage. As another test of the model, measurements with different solid volume fractions were performed. Within the range of the solid volume fractions considered here, the steady-state CSD was not significantly affected. In order to correctly capture the right-hand side of the CSD (large aggregates) at the higher solid volume fraction, a modified aggregation rate prefactor was used in the population balance model.

Specific power input and local micromixing times in turbulent Taylor–Couette flow

In the present work, the distribution of the local dissipation rate of turbulent kinetic energy in Taylor–Couette flow was studied with the help of the particle image velocimetry (PIV). The experimental values of dissipation rate are strongly affected by spatial resolution of PIV measurements. Therefore, a reference value of the average specific power input is needed. Such a value was achieved from an independent torque measurement. Using these values it was possible to quantify the true local values of the dissipation rate. The distribution of mixing times in the gap could thus be calculated and was found to become more homogeneous with increasing turbulence intensity.

Computational Fluid Dynamics Analysis of Turbulent Flow Within a Mechanical Seal Chamber

Turbulent flow inside the seal chamber of a pump operating at high Reynolds number is investigated. The K−ε turbulence model posed in cylindrical coordinates was applied for this purpose. Simulations are performed using the fractional approach method. The results of the computer code are verified by using the FLUENT and by comparing to published results for turbulent Taylor Couette flow. Numerical results of four cases including two rotational speeds with four flush rates are reported. Significant difference between the laminar and the turbulence flow in the seal chamber is predicted. The behavior of the turbulent flows with very high Reynolds number was also investigated. The physical and practical implications of the results are discussed.

From time series to superstatistics

Complex nonequilibrium systems are often effectively described by a "statistics of a statistics", in short, a "superstatistics". We describe how to proceed from a given experimental time series to a superstatistical description. We argue that many experimental data fall into three different universality classes: Chi2 superstatistics (Tsallis statistics), Chi2 inverse superstatistics, and log-normal superstatistics. We discuss how to extract the two relevant well separated superstatistical time scales tau and T, the probability density of the superstatistical parameter beta, and the correlation function for beta from the experimental data. We illustrate our approach by applying it to velocity time series measured in turbulent Taylor-Couette flow, which is well described by log-normal superstatistics and exhibits clear time scale separation.

Reappearance of azimuthal waves in turbulent Taylor–Couette flow at large aspect ratio

Velocity field data were acquired for Taylor–Couette flow in the annular gap between an inner rotating cylinder and a stationary concentric outer cylinder using particle image velocimetry (PIV) in a meridional plane of the annulus. Data were acquired for several rotational Reynolds numbers with the ratio of the rotational and critical Reynolds numbers ranging from 6 to 200, corresponding to flow states ranging from laminar wavy Taylor vortex flow to turbulent Taylor vortex flow. Spatial correlations of velocity fluctuations were found to exhibit a sharp decrease as R , the ratio of Reynolds number to the critical Reynolds number, increases from 16, indicating the disappearance of azimuthal waves and the onset of turbulence, reaching a minimum at R = 18 . However, correlation lengths subsequently increase with increasing R , displaying a secondary peak from 20 ⩽ R ⩽ 38 , suggesting the reappearance of azimuthal waves. The reemergence of azimuthal waves was confirmed through other methods including analysis of the axial velocity. At still higher Reynolds numbers, correlation lengths decay once again. The magnitude and Reynolds number associated with the secondary peak in the fluctuation velocity correlations were found to be dependent on the location of the basis point used in the calculations. Specifically, correlation lengths were longest near the outer cylinder in the inflow boundary and near the inner cylinder in the outflow boundary. This was shown to be due to the spatial dependence of Reynolds stresses in turbulent Taylor–Couette flow.

CFD simulation of shear-induced aggregation and breakage in turbulent Taylor–Couette flow

An experimental and computational investigation of the effects of local fluid shear rate on the aggregation and breakage of ∼ 10 μm latex spheres suspended in an aqueous solution undergoing turbulent Taylor–Couette flow was carried out. First, computational fluid dynamics (CFD) simulations were performed and the flow field predictions were validated with data from particle image velocimetry experiments. Subsequently, the quadrature method of moments (QMOM) was implemented into the CFD code to obtain predictions for mean particle size that account for the effects of local shear rate on the aggregation and breakage. These predictions were then compared with experimental data for latex sphere aggregates (using an in situ optical imaging method). Excellent agreement between the CFD-QMOM and experimental results was observed for two Reynolds numbers in the turbulent-flow regime.

Visualization study and quantitative velocity measurements in turbulent taylor-couette flow by phantomm flow tagging: a description of the transition to turbulence

A visualization study and Quantitative velocity measurements have been performed in Taylor-Couette flow with a medium-gap (c= 0.356), over a large range of Taylor numbers (2.1x104 < Ta < 1.1x1011), with the outer cylinder fixed and the inner cylinder rotating about its axis. Quantitative velocity measurements were carried out using the PHANTOMM flow tagging technique. Two techniques were used for visualization study: the PHANTOMM technique that allowed flow structure visualization from small to moderate Taylor numbers, and the Particle Streak Imaging, PSI (the flow was seeded with neutrally buoyant polystyrene micro spheres) that permitted the flow structure visualization from moderate to high Taylor numbers. The results illustrate the expected three-dimensional features of flow and presence of Taylor cells at low Taylor numbers. Our study examined the interplay between small and large scales present in the flow as well as showed the gradual transition to turbulence with increasing Taylor numbers. Taylor cells were found for Taylor numbers less than 1.13 x 1010. At low Taylor numbers, the flow in the cells appeared to be a rotational laminar flow with a high degree of coherence. At higher Taylor numbers, the cells aspect became more irregular, and the flow inside them became turbulent. The Gortler instability developed inside Taylor cells and close to the inner cylinder wall. At the highest Taylor numbers, turbulence increased up to the point where no Taylor cells could be detected. For the flow in our study, at Ta = 1.13 x 1010, the homogenization by turbulence spread across the gap, and the flow structure sharply changed its pattern as a toroidal vortex in helical motion developed in a thin layer on the inner cylinder wall. Instantaneous velocities, average velocities, angular-momentum ratio and spectral density function were computed for all ranges of Taylor numbers in the range studied. These quantitative results show the same conclusions as the ones presented by the visualization study

Turbulent Taylor-Couette vortex flow between large radius ratio concentric cylinders

Turbulent Taylor vortices between two concentric cylinders have been studied at a very high radius ratio of 0.985, equivalent to that found in relatively small underwater thruster units (typically with gaps of 2 mm). In order to study the flow at this radius ratio, a 1.42-m diameter experimental apparatus (with a rotating inner cylinder and a stationary outer cylinder) was constructed possessing a gap of 10 mm. Consequently, air bubbles could be visualised translating in water. A method was developed for identifying Taylor vortex properties from filtered digital images of the air bubbles and summing intensities to produce bubble density distributions. Whereas individual instantaneous images can be misleading, averaged bubble density distributions make it possible to identify vortex separation sizes and the positions of vortex outflow boundaries.

Smooth and rough boundaries in turbulent Taylor-Couette flow.

We examine the torque required to drive the smooth or rough cylinders in turbulent Taylor-Couette flow. With rough inner and outer walls the scaling of the dimensionless torque G is found to be consistent with pure Kolmogorov scaling G approximately Re2. The results are interpreted within the Grossmann-Lohse theory for the relative role of the energy dissipation rates in the boundary layers and in the bulk; as the boundary layers are destroyed through the wall roughness, the torque scaling is due only to the bulk contribution. For the case of one rough and one smooth wall, we find that the smooth cylinder dominates the dissipation rate scaling, i.e., there are corrections to Kolmogorov scaling. A simple model based on an analogy to electrical circuits is advanced as a phenomenological organization of the observed relative drag functional forms. This model leads to a qualitative prediction for the mean velocity profile within the bulk of the flow.

Premixed-flame propagation in turbulent Taylor–Couette flow

Turbulent-flame speeds in methane–air mixtures were measured in a Taylor–Couette apparatus with counter-rotating cylinders, used to generate turbulence that is nearly homogeneous and isotropic over many integral length and time scales. While laminar-flame propagation is found to be influenced by the Darrieus–Landau instability and heat loss to the walls of the apparatus, turbulent-flame propagation in high-intensity turbulence is found to be uninfluenced by these effects. A decreasing sensitivity of the turbulent-flame speed to increases in turbulence intensity is found to occur beyond turbulence intensities of approximately 2.5 times the laminar-flame speed. This is possibly due to a transition to a nonflamelet combustion regime where flame propagation is influenced by both small-scale flame-structure modification and large-scale flame-front wrinkling. Results are compared with those obtained by earlier investigators using other experimental apparatuses and with theoretical predictions.

Nonlinear independent component analysis and multivariate time series analysis

We derive an information-theory-based unsupervised learning paradigm for nonlinear independent component analysis (NICA) with neural networks. We demonstrate that under the constraint of bounded and invertible output transfer functions the two main goals of unsupervised learning, redundancy reduction and maximization of the transmitted information between input and output (Infomax-principle), are equivalent. No assumptions are made concerning the kind of input and output distributions, i.e. the kind of nonlinearity of correlations. An adapted version of the general NICA network is used for the modeling of multivariate time series by unsupervised learning. Given time series of various observables of a dynamical system, our net learns their evolution in time by extracting statistical dependencies between past and present elements of the time series. Multivariate modeling is obtained by making present value of each time series statistically independent not only from their own past but also from the past of the other series. Therefore, in contrast to univariate methods, the information lying in the couplings between the observables is also used and a detection of higher-order cross correlations is possible. We apply our method to time series of the two-dimensional Hénon map and to experimental time series obtained from the measurements of axial velocities in different locations in weakly turbulent Taylor-Couette flow.