Vortex Flow Regime Research Articles

Oscillatory flow around a vertical circular cylinder placed in an open channel: coherent structures, sediment entrainment potential and drag forces

Flow and turbulent structures generated by the interaction of forced incoming oscillatory flow with a circular, vertical cylinder placed in an open channel with a horizontal bed are investigated using eddy-resolving simulations. Validation simulations performed with a Keulegan–Carpenter (KC) number of 20 and multiple-mode forcing corresponding to the laboratory experiment of Sumeret al.(J. Fluid Mech., vol. 332, 1997, pp. 41–70) show that detached eddy simulation (DES) predicts more accurately the amplification of the bed shear stress beneath the horseshoe vortex system (upstream side of the cylinder) and the maximum magnitude of the bed shear stress at the downstream (wake) side of the cylinder compared with unsteady Reynolds-averaged Navier–Stokes simulations. High-Reynolds-number DES simulations are then conducted with 1.5 ≤ KC ≤ 30.8 and one-mode sinusoidal forcing of the streamwise velocity in the approaching flow to investigate the changes in the wake vortex-flow regimes, the coherence of the horseshoe vortices and the generation of other near-bed coherent structures in the wake during the oscillatory cycle. The flow is periodic, no horseshoe vortices form and no vortices are shed in the wake forKC = 1.5. By contrast, forKC ≥ 8 horseshoe vortices are present over part of the oscillatory cycle and up to three wake vortices are shed over each half-cycle asKCis increased to 30.8. For an intermediate range ofKCnumbers, one (KC = 15.4) or two (KC = 8) of the vortices forming at the back of the cylinder during each half-cycle are washed around it when the flow reverses. The main horseshoe vortex and other horizontal near-bed vortices have a large capacity to amplify the bed shear stresses when the incoming velocity magnitude is significantly less than its peak value. Assuming the depth-averaged velocity in the incoming (undisturbed) oscillatory flow is the same in simulations conducted with differentKCnumbers, the peak values of the sediment entrainment potential measured by the mean (cycle-averaged) volumetric flux of sediment entrained from the bed over one oscillatory cycle occur for 8 ≤ KC ≤ 15.4. For allKCnumbers, the in-line force variation over the oscillatory cycle is fairly well approximated by the Morison equation. ForKC = 1.5, the in-line force is only due to inertia effects. ForKC = 30.8, the maximum and minimum values of the phase-averaged in-line force are approximatively in phase with those of the incoming flow velocity. ForKC ≥ 15, the phase-averaged in-line force coefficients vary between 0.8 and 1.1 during most of the oscillatory cycle (e.g. when the incoming flow velocity is not close to zero). This is different from cases withKC ≤ 8 where the in-line force coefficient is equal to zero twice during the oscillatory cycle as the in-line force becomes equal to zero for non-zero values of the incoming velocity. The largest cycle-to-cycle variations of the in-line force coefficient and in-line force are observed aroundKC = 8. ForKC = 8 and 15.4, the cylinder is subject to relatively large phase-averaged spanwise drag forces that are comparable to the peak phase-averaged streamwise drag forces. AsKCis increased to 30.8, the phase-averaged spanwise drag force becomes zero over the whole oscillatory cycle but the cylinder is still subject to large instantaneous spanwise forces over part of the oscillatory cycle.

Vortex Dynamics in a Hybrid Aligned Nematic Microvolume with an Orientational Defect

The aim of this theoretical paper is to investigate the physical mechanism responsible for the appearance of vortex flow in a hybrid aligned nematic (HAN) microvolume with an orientational defect, excited by a temperature gradient ∇T. This was done in the framework of the classical Ericksen-Leslie theory, supplemented by thermomechanical correction of the shear stress and Rayleigh dissipation function, as well as taking into account the entropy balance equation. We have carried out a numerical study of the system of hydrodynamic equations including director reorientation, fluid flow v, and the temperature redistribution across the HAN microvolume under the influence of ∇T, when the HAN microvolume is heated from above. Calculations show that, due to the interaction between the gradient of the director field ∇n^ and ∇T, the HAN microvolume settles down to a stationary complex vortex flow regime.

A numerical study on the drag reduction and wake regime control of the tandem circular cylinders using splitter plates

The present study focuses on the control of an unsteady vortex flow regime and flow-induced forces on the tandem circular cylinder using the splitter plate-based technique at a Reynolds number (Re) of 100. The in-house developed flexible forcing immersed boundary lattice Boltzmann method (FFIBLBM) solver is employed for these two-dimensional numerical simulations. Three distinct tandem cylinder spacing is considered: small spacing (G/D = 2.0), medium spacing (G/D = 3.5), and large spacing (G/D = 5.0), where G is the center-to-center distance between the cylinders having diameter D. For each spacing, the effectiveness of two different configurations of splitter plates are examined: splitter plate attached to the upstream cylinder (TC-SPU) only and splitter plate attached to the downstream cylinder (TC-SPD) only. The arrangement and length of the splitter plate have a significant effect on the suppression of vortex shedding and reduction of flow-induced force on the cylinders. The result shows that the TC-SPD is beneficial for small spacing, yielding a drag reduction of 0.58 % and 0.05 % for the upstream and downstream cylinders. At the same time, both the TC-SPU and TC-SPD configurations are useful for suppressing the flow unsteadiness for medium spacing. However, the drag reduction in TC-SPD is more. In this case, the drag of the upstream and downstream cylinders is reduced by 1.4 % and 247 %, respectively. At large spacing, the TC-SPU arrangement is suitable for the suppression of vortex shedding from both cylinders. The corresponding drag reduction for the upstream and downstream cylinders is 13.7 % and 89.2 %, respectively.

Observations of pumping and vortex dynamics due to a cylinder oscillating normal to a plane wall

Understanding the fluid dynamics associated with a circular cylinder oscillating normal to a plane wall is important for safe design of offshore infrastructure, such as power cables and pipeline risers. This paper investigates the fluid dynamics of an oscillating cylinder with no imposed incident current experimentally using flow visualisation and force measurements where the ratio of the cylinder Reynolds number ( $Re$ ) to Keulegan–Carpenter number ( $KC$ ) is $\beta =500$ and $KC$ varies between 2 and 12. The minimum distance between the cylinder and wall was between 12.5 % and $50\,\%$ of the diameter. Across this parameter space three primary vortex flow regimes were observed: (i) for $KC\leq 5$ , the flow field is approximately symmetric about the cylinder centreline and the velocity field between the cylinder and the wall resembled a pumping flow in phase with cylinder motion, which is well predicted by potential theory for most of the cycle; (ii) for $5< KC<8$ , the flow field is increasingly asymmetric but with frequent switching of the side associated with vortex shedding; and (iii) for $KC\geq 8$ , the flow field is consistently asymmetric due to vortex shedding. The in-line force increases when the cylinder is near the wall due to dynamic pressures associated with pumping. This increase can be estimated using potential theory superimposed onto the force time history for an isolated cylinder at the same $KC$ and $Re$ . This study complements recent numerical modelling focused on low Reynolds number conditions and provides important insights into the fluid mechanics associated with trenching beneath cable and pipeline risers.

Flow past two tandem square cylinders placed in parallel walls

In this work, pulsating and non-pulsating flow structures past two tandem square cylinders placed in parallel walls was investigated. The variation of the distance between the cylinders and the frequency of flow pulsation was also examined. The Particle Image Velocimetry (PIV) method was applied to reveal hydrodynamic characteristics such as streamlines patterns, <Ψ>, the velocity vector distribution, the vorticity field, <ω>, the normalized streamwise velocity contours, <U/Uavg>, and turbulent statistics such as streamwise velocity fluctuations, urms, cross-streamwise velocity fluctuations, vrms, and turbulent Reynolds stress, u′v′‾/U02 distributions for non-pulsating flow cases. In addition, instantaneous and phase averaged flow data over the flow field is presented in order to evaluate the influence of flow pulsation on the quantitative analyses. The experiments were performed at Re=500. According to the results, the confinement profoundly affects the flow regime past two tandem cylinders. The alteration from the reattach flow to the co-shedding vortex flow regime take place at a lower gap ratio. Moreover, flow pulsation considerably contributes to mainstream penetration into the gap between cylinders. The mechanism of the fluid interactions near the wall and mainstream is highly dependent on the ratio of L/D and pulsation frequency.

Performance Evaluation of Flutter-Based Energy Harvester Under Different Vortex Flow Regimes: An Experimental Study

Performance Evaluation of Flutter-Based Energy Harvester Under Different Vortex Flow Regimes: An Experimental Study

Numerical Investigation of the Plunging and Vortex-Flow Regimes Occurring in Drop Shafts with a Tangential Intake

Numerical Investigation of the Plunging and Vortex-Flow Regimes Occurring in Drop Shafts with a Tangential Intake

Analysis of the re-entrant jet to twin vortex flow regimes transition in ventilated cavitation

The combination of ventilated cavitation (injection of a non-condensable gas in a liquid flow) and natural cavitation (flow vaporization due to a local pressure drop) is studied with a numerical model based on a homogeneous multiphase flow approach, using two transport equations for vapor and air. Ventilated cavitation behind an axisymmetric body is simulated and the results compare well with previous experimental data for both the reentrant jet and the twin vortex flow patterns. The transition between the two regimes is found to be primarily related to a critical shift of the vortices generated behind the body, due to air injection. It is also shown that the critical value of σc⋅Fr (product of ventilated cavitation number with the Froude number) at the transition depends strongly on the shape of the body. The influence of the baseline flow without air injection (Reynolds number and natural cavitation) on the transition is also analyzed. When natural cavitation is negligible, only the twin vortex regime is obtained for a Reynolds number Re < 8 104, while for a higher Re, the ventilation air flow coefficient at transition CQt varies almost linearly with Ln (Re). In presence of additional natural cavitation, (σ < 1), a decrease of CQt is observed. This phenomenon is amplified when natural cavitation increases. This drop of CQt can be directly related to the amount of vapor generated in the flow field, as it is shown that it corresponds to the maximum positive flux of vapor behind the body.

Strong alignment of prolate ellipsoids in Taylor–Couette flow

We report on the mobility and orientation of finite-size, neutrally buoyant, prolate ellipsoids (of aspect ratio $\varLambda =4$ ) in Taylor–Couette flow, using interface-resolved numerical simulations. The set-up consists of a particle-laden flow between a rotating inner and a stationary outer cylinder. The flow regimes explored are the well-known Taylor vortex, wavy vortex and turbulent Taylor vortex flow regimes. We simulate two particle sizes $\ell /d=0.1$ and $\ell /d=0.2$ , $\ell$ denoting the particle major axis and $d$ the gap width between the cylinders. The volume fractions are $0.01\,\%$ and $0.07\,\%$ , respectively. The particles, which are initially randomly positioned, ultimately display characteristic spatial distributions which can be categorised into four modes. Modes (i) to (iii) are observed in the Taylor vortex flow regime, while mode (iv) encompasses both the wavy vortex and turbulent Taylor vortex flow regimes. Mode (i) corresponds to stable orbits away from the vortex cores. Remarkably, in a narrow $\textit {Ta}$ range, particles get trapped in the Taylor vortex cores (mode (ii)). Mode (iii) is the transition when both modes (i) and (ii) are observed. For mode (iv), particles distribute throughout the domain due to flow instabilities. All four modes show characteristic orientational statistics. The focus of the present study is on mode (ii). We find the particle clustering for this mode to be size-dependent, with two main observations. Firstly, particle agglomeration at the core is much higher for $\ell /d=0.2$ compared with $\ell /d=0.1$ . Secondly, the $\textit {Ta}$ range for which clustering is observed depends on the particle size. For this mode (ii) we observe particles to align strongly with the local cylinder tangent. The most pronounced particle alignment is observed for $\ell /d=0.2$ at around $\textit {Ta}=4.2\times 10^5$ . This observation is found to closely correspond to a minimum of axial vorticity at the Taylor vortex core ( $\textit {Ta}=6\times 10^5$ ) and we explain why.

Secondary instabilities in Taylor–Couette flow of shear-thinning fluids

The stability of the Taylor vortex flow in Newtonian and shear-thinning fluids is investigated in the case of a wide gap Taylor–Couette system. The considered radius ratio is$\eta = R_1/R_2=0.4$. The aspect ratio (length over the gap width) of experimental configuration is 32. Flow visualization and measurements of two-dimensional flow fields with particle image velocimetry are performed in a glycerol aqueous solution (Newtonian fluid) and in xanthan gum aqueous solutions (shear-thinning fluids). The experiments are accompanied by axisymmetric numerical simulations of Taylor–Couette flow in the same gap of a Newtonian and a purely viscous shear-thinning fluid described by the Carreau model. The experimentally observed critical Reynolds and wavenumbers at the onset of Taylor vortices are in very good agreement with that obtained from a linear theory assuming a purely viscous shear-thinning fluid and infinitely long cylinders. They are not affected by the viscoelasticity of the used fluids. For the Newtonian fluid, the Taylor vortex flow (TVF) regime is found to bifurcate into a wavy vortex flow with a high frequency and low amplitude of axial oscillations of the vortices at${Re} = 5.28 \, {Re}_c$. At${Re} = 6.9 \, {Re}_c$, the frequency of oscillations decreases and the amplitude increases abruptly. For the shear-thinning fluids the secondary instability conserves axisymmetry. The latter is characterized by an instability of the array of vortices leading to a continuous sequence of creation and merging of vortex pairs. Axisymmetric numerical simulations reproduce qualitatively very well the experimentally observed flow behaviour.

Flow regimes and mixing performance in T-T jet reactor

T-T jet reactor, obtained from the classical T jet reactor by duplicating two identical inlet channels below the original inlet channels, is considered to be the study object herein. The T and T-T jet reactors have been chosen for comparison since they show significantly various flow topologies and mixing performances at 50 ≤ Re ≤ 600. In this work, both the particle image velocimetry (PIV) experiment and three-dimensional numerical simulations are employed to clarify the mixing behaviors of the T-T jet reactor. The results show that the mixing performance of the T-T jet reactor is dramatically improved due to the secondary impinging, especially for the segregated flow and vortex flow regimes at low Reynolds number, and the unsteady symmetric flow regime at high Reynolds number. The impingement plane of the segregated flow and vortex flow regimes are increased due to the secondary impinging of the T-T geometry, for which the mixing effect is improved. The secondary impinging influences flow dynamics in the unsteady symmetric flow regime and has a significant impact on mixing.

High-efficiency biodiesel production using rotating tube reactor: New insight of operating parameters on hydrodynamic regime and biodiesel yield

Transesterification is a preferred reaction in biodiesel production using oil and alcohol as feedstocks. The major limitation of biodiesel production is the immiscibility of reactants resulting in the slow reaction rate. The development of an intensification reactor is the main purpose to eliminate the limitation and to increase the production capacity. The present research explored the state of the art for the hydrodynamic regime inside the rotating tube reactor (RTR) to enhance the biodiesel production rate using alkali-catalyzed transesterification based on the design specification. The influence of operating conditions in terms of methanol-to-oil molar ratio, NaOH loading, total flowrate, rotational speed using two dimensionless numbers, i.e. rotating Reynolds number (Rer) and Taylor number (Ta), as well as torque, were originally proposed to determine the optimal operating condition for biodiesel production in this RTR. This was interesting to report that the modulated wavy vortex flow is required to promote biodiesel yield in the RTR. The increment values of Rer, Ta and torque associated with the turbulent Taylor vortex flow regime allowed the high reaction temperature which can generate excessive heat raising the methanol vaporization rate, leading to reduced biodiesel yield. Therefore, the optimal operating condition of this RTR was found to be 6:1 methanol-to-oil molar ratio, total flowrate of 30 mL/min, rotational speed of 1000 rpm at room temperature giving the highest yield of 97.5% with yield efficiency of 3.75×10−3 g/J and the quality of biodiesel met the ASTM specification.

Investigation of the Reynolds number independence of cavity flow in 2D street canyons by wind tunnel experiments and numerical simulations

The Reynolds number independence (Re independence) criterion of Re > 11,000 is widely adopted to fulfill the dynamic similarity between the urban flow modeling and the down-scale measurements. However, for 2D street canyons with H/W ≥ 1.5, experiments, numerical simulations, and in-situ observations have reported different vortex-flow regimes with similar building configurations but at different scales. This study uses both wind tunnel experiments and numerical simulations to revisit the Re-independent flow regimes and Re independence criteria with an extensive Re range for idealized 2D street canyons with various aspect ratios (H/W = 1.1, 2.4, 3, 4, and 5). We introduced an optimized ratio of relative changes (RRCs) to evaluate the flow regimes’ similarity. The wind tunnel experiment confirms that the cavity flow with H/W = 1.1 meets the Re independence when reference building Re (Reref) exceeds 11,000. Simulations validated by the experiment results are conducted to investigate detailed flow regimes and the critical Re (Rec) range for each aspect ratio. The canyons with H/W = 2.4, 3, and 4 are dominated by a single asymmetric vortex when the Re independence is satisfied, while there are two vertically-stacked counter-rotating vortices in the canyon with H/W = 5. The value range of Rec increases with aspect ratio from 1.9 × 104–2.6 × 104 (H/W = 2.4) to 1.3 × 105–2.1 × 105 (H/W = 3), and 2.1 × 106–6.4 × 106 (H/W = 4 and 5). Our results indicate that the fully Re-independent flow regimes in deep canyons have fewer vortices than the literature value with down-scale experiments and simulations. The variant Rec with different aspect ratios suggests the requirement to conduct the Re-independence test for different model configurations.

Spherical agglomeration of nickel-manganese-cobalt hydroxide in turbulent Batchelor vortex flow

In this study, turbulent Batchelor vortex flow, due to its periodic fluid motion, was used to produce highly dense and spherical Ni-Mn-Co (NMC) hydroxide agglomerates (microparticles) in a rotation disk crystallizer. A high shear stress (1500 rpm) in the turbulent Batchelor vortex regime, and the presence of ammonia at a pH of 12, help form spherical shaped agglomerates with a high tap density (2.1 g/m3) from irregular shaped agglomerates. The coefficient of variation (0.38) of the agglomerates also narrowed while using this approach. When sufficient ammonia was supplied to form a complex ([M(NH3)n]2+) with all M2+, the reaction rate with OH– slowed and the agglomeration process was affected by the high shear stress in a sufficient amount of time. On the contrary, when ammonia is not present in the reaction solution, free M2+ ions rapidly react with OH– ion, resulting in irregular shaped agglomerates. The pH was related to the OH– concentration and all of the [M(NH3)n]2+ complex was consumed during the agglomeration process when the OH– concentration reached a mol ratio of 1:2 ([M(NH3)n]2+:OH–). When the ammonia feeding rate was higher than 1.2 mL/min, highly dense agglomerate was obtained. However, the [M(NH3)n]2+ complex could not be generated when the pH exceeded a value of 12, according to the mass and equilibrium calculations. In addition, the residence time was significantly shorter (30 min) in the turbulent Batchelor vortex flow regime compared to previous studies (~12 to 50 h). This study suggests that the high shear stress in the turbulent Batchelor vortex flow regime can be effectively used for making highly dense and spherical NMC hydroxide, with high tap density, in a short amount of time.

Geometry mediated friction reduction in Taylor-Couette flow

Periodic surface microtextures inspired by textures of shark denticles can alter the frictional response of a solid wall in flow. Using 3D-printed texture-covered rotors in a bespoke Taylor-Couette cell, the effect of the geometry of the textures and flow dynamics on the frictional torque measurements in Couette flow and Taylor vortex flow regimes are investigated. The changes in the torque measurements show direct dependence on the geometric features of the textures in both flow regimes, while the effect of the Reynolds number is only seen in the Taylor vortex flow.

Enzymatic starch hydrolysis performance of Taylor-Couette flow reactor with ribbed inner cylinder

In this study, a Taylor-Couette flow reactor (TCFR) was applied to starch hydrolysis accompanied with an intricate viscosity change during reaction for the purpose of process intensification. In industries, several reactors are used in starch hydrolysis, namely gelatinization, liquefaction, and saccharification. It was possible to conduct a continuous starch hydrolysis with one TCFR. In addition, a sufficient reducing sugar yield was obtained in the Taylor vortex flow regime. However, the yield decreased at a higher effective Reynolds number (Reeff) due to axial dispersion through a bypass flow generated by the wavy motion of Taylor cells. In order to immobilize Taylor vortex flow at this condition, a ribbed inner cylinder was employed which suppressed axial dispersion at the higher Reeff. As a result, a higher reducing sugar yield was successfully obtained than that by using a standard cylinder, demonstrating that the optimization of TCFR geometry has the potential for process intensification.

Vortex deformation and turbulent energy of polymer solution in a two-dimensional turbulent flow

An experimental study was performed to investigate the effects of the extensional rheological properties of polymer solutions on vortex deformation in turbulent flow and turbulent statistics. To focus on the extensional properties, a self-standing two-dimensional (2D) turbulent flow was used as an experimental setup, and the flow was observed through interference patterns and particle image velocimetry (PIV). Vortex shedding and the resulting deformation in the 2D flow were categorized into three types. The vortex flow regime was defined by the shedding frequency and relaxation time of the polymer solution. Turbulent energy was suppressed by polymer additives; however, a characteristic peak reappeared with increasing concentration. The results imply that the characteristic turbulent energy peak is influenced by the relaxation process of the extended polymers in the flow.

Effect of shear-thinning behavior on flow regimes in Taylor–Couette flows

Taylor–Couette reactors may offer an alternative treatment method for ballast water treatment or for flocculation of small size particles to be removed in water treatment processes due to created high energy dissipation and momentum transfer by Taylor vortices occurred during transitional flow regimes. In this study, the effect of shear-thinning behavior on flow structures and transition thresholds in Taylor–Couette flows for narrow and wide gaps is experimentally investigated using xanthan solutions. The experiments presented in this paper establish the existence of non-axisymmetric flow structures before the Taylor vortex flow regime and an instability threshold to the modified wavy vortex flow from Taylor vortex flow in shear-thinning fluids i.e. altering the instability mechanisms. The critical Reynolds numbers for the first and second instabilities and the structural characteristics of the flow states were identified for Newtonian and shear thinning fluids in comparison. The vortices have varying axial wavelength and also drift along the axis in shear-thinning fluids. The variation of the critical Reynolds number with the shear-thinning index has been shown through three different Reynolds number definitions. It is shown that when the Reynolds number is defined using single preferred value of radially varying viscosity, decreasing shear-thinning index may delay the appearance of Taylor vortices depending on the gap ratio. When the local Reynolds numbers defined based on the local viscosity have been taken into account, shear thinning effect has a monotonic effect on the critical Reynolds number which decreases with decreasing shear-thinning index for both narrow and wide gaps in transition to Taylor vortex flow regime.

Fragmentation of compact polymer-bridged flocs in the laminar taylor vortex flow regime: population balance and breakage function

The breakage or fragmentation kinetic function (FKF) of a given father size floc breaking to form two specific daughter size flocs cannot be measured experimentally. Indirectly it can be determined from the FKF model used to solve the dimensionless log-form population balance (PB) equation for floc fragmentation subjected to meeting three conditions: i) the computed and experimental particle size distribution function (PSDF) matched at all fragmentation time, ii) the PSDF data at zero fragmentation time was the input in the computation and iii) the duration of the experimental fragmentation be used in making the PB equation dimensionless. The fragmentation of compact polyelectrolyte-bridged silica flocs in a narrow gap concentric cylinder flow cell was investigated in the laminar Taylor vortex flow regime. The FKF data was correlated with the Taylor number. The FKF values were much smaller for large flocs as they tend to migrate to the low shear region. Cryo-SEM images of the flocs at different fragmentation times showed compact fractal structure with dimension larger than 2.

Green, fast, and scalable production of reduced graphene oxide via Taylor vortex flow

Developing a cost-effective and bulk-scale process for graphene synthesis is essential for its commercialization in a wide range of industrial applications. In this study, for the first time, we used a Couette–Taylor fluid structure with axial flow as a green, rapid, and scalable protocol to synthesize reduced graphene oxide (RGO) flakes. We have determined five different flow characteristics in the laminar, transitional, and turbulent regimes and systematically investigated the effect of flow structure on RGO production. The toroidal vortices ensure the reactants are efficiently mixed, shortening the reduction time of graphene oxide (GO) from several hours to minutes. The results showed that the degree of RGO reduction significantly increased in the Taylor vortex flow (TVF) structure, and decreased in the wavy vortex flow (WVF) regime, because of the secondary instability of the fluid structure. More importantly, the TVF regime results in the synthesis of highly exfoliated and readily water-dispersible RGO products. Finally, the resulting RGO exhibited higher electrical conductivity and mechanical strength than conventional RGO synthesized under circular Couette flow (CCF). Thus, the proposed fluid dynamic protocol may open an effective, potentially cost-competitive, and industrially accessible pathway for producing few-layered RGO flakes for various applications.