Roll Cells Research Articles

Numerical investigation of plane Couette flow with weak spanwise rotation

Direct numerical simulation of rotating plane Couette flow (RPCF) at $Re_w=1300$ and $Ro=0.02$ was performed with different mesh resolutions and different sizes of computation domain. Our results showed that a grid resolution in wall units with $\Delta~x^+=8.51,~\Delta~z^+=4.26$, $\Delta~y^+|_{\text{min}}=0.0873$ and $\Delta~y^+|_{\text{max}}=3.89$ is fine enough to simulate the problem at the present parameters. The streamwise length $L_x$ and spanwise length $L_z$ of the computational box have different impacts on the flow statistics, where the statistics were converged if $L_x$ is longer than $8\pi~h$, while no converged results were obtained for different $L_z$. More importantly, our results with very long simulation time showed that a state transition would happen if $L_x\geq~8\pi~h$, from a state with four pairs of roll cells to a state with three pairs of roll cells with $L_z=6\pi~h$. Each state could survive for more than $1500h/U_w$, and the flow statistics were different.

Visualization of fire flood behavior under declining air flux

A conical combustion cell was built and utilized in combustion experiments at the In Situ Combustion Research Group at the University of Calgary to investigate the effect of continuous in situ air flux drop on the dynamics of the combustion process and to identify the characteristics of the process such as extinction air flux at the time the process matures. A full scale three dimensional dry combustion experiment was conducted on a formulated core representing typical Athabasca heavy oil reservoirs. The temperature profiles, the produced combustion gases and liquids as well as the unpacked core were examined. Minimum injected air flux at the termination of the experiments was calculated to be below 9.0 sm3/m2 h; gas phase combustion parameters were analyzed. It is conjectured that the formation of fuel rich condition especially in presence of water at the location of the combustion front at certain locations of the core at certain circumstances tends to prevent energy generation at the combustion front even at high air injection rates. Also, it was shown that the counter current convection/diffusion of fuel gases from the combustion front to upstream locations of the core also known as the roll cell effect adversely influences the advancement of the high temperature combustion front which in turn impacts the oil mobilization and its recovery. This study illustrates the complexity of combustion processes and signifies characteristic behavior of the process at or close to its exhaustion.

Viscoelasticity-induced pulsatile motion of 2D roll cell in laminar wall-bounded shear flow

For the clarification of the routes to elasto-inertial turbulence (EIT), it is essential to understand how viscoelasticity modulates coherent flow structures including the longitudinal vortices. We focused on a rotating plane Couette flow that provides two-dimensional (2D) roll cells for the steady laminar Newtonian-fluid case, and we investigated how the steady longitudinal vortices are modulated by viscoelasticity at different Weissenberg numbers. The viscoelasticity was found to induce an unsteady flow state where the 2D roll-cell structure was periodically enhanced and damped with a constant period, keeping the homogeneity in the streamwise direction. This pulsatile motion of the roll cell was caused by a time lag in the response of the viscoelastic force to the vortex development. Both the pulsation period and time lag were found to be scaled by the turnover time of cell rotation rather than by the relaxation time, despite the viscoelasticity-induced instability. We also discuss the counter torque on the roll cell and the net energy balance, considering their relevance to polymer drag reduction and EIT.

Viscoelastic effect on steady wavy roll cells in wall-bounded shear flow

An alternative step in understanding the flows of near wall drag-reducing turbulence can be examining the flow in a well-organized streamwise vortex with a laminar background. Herein, we studied the flow behaviors of the Giesekus viscoelastic fluid in a rotating plane Couette flow system, which is accompanied by steady roll cell structures. By fixing the Reynolds and rotation numbers at values that provide as steady wavy roll cell, i.e., an array of meandering streamwise vortices, the Weissenberg number was increased up to 2000 (where the relaxation time was normalized by the wall speed and the kinematic viscosity). We observed that, in the viscoelastic flows, the secondary flow (wall-normal and spanwise velocity fluctuations) are suppressed while the streamwise component is maintained, and the wavy roll cells are modulated into streamwise-independent straight roll cells. The kinetic energy transports among the mean shear flow, Reynolds stresses due to the roll cell, and viscoelastic stress are investigated in the non-turbulent background. We further discussed the modulation mechanism and its relevance to the drag reduction phenomenon in the viscoelastic wall turbulence.

Analysis of dry, wet and superwet in situ combustion using a novel conical cell experiment

A conical combustion cell was built and utilized in combustion experiments at the In Situ Combustion Research Group at the University of Calgary to investigate the effect of continuous in situ air flux drop on the dynamics of the combustion process and to identify the characteristics of the process most importantly the extinction air flux. Nine set of top-down (gravity stable) dry, wet and superwet combustion experiments were conducted at different injection rates in sand packs representing typical Athabasca heavy oil reservoirs. The temperature profiles, the produced combustion gases and liquids as well as the unpacked core were examined. Minimum injected air flux at the termination of the experiments was calculated; gas phase combustion parameters were analyzed. Some of the features specific to combustion experiments in conical cells were investigated.It is believed that the formation of fuel rich condition especially in presence of water at the location of the combustion front at certain locations of the core at certain circumstances tends to prevent energy generation at the combustion front even at high air injection rates. Also, it was shown that the counter current convection/diffusion of fuel gases from the combustion front to upstream locations of the core also known as the roll cell effect adversely influences the advancement of the high temperature combustion front which in turn impacts the oil mobilization and recovery.Combustion performance analysis using oil recovered/volume burned calculations for dry conical tests and oil recovered vs. volume steamed and oxygen oil ratio vs. volume burned as the crucial economical parameters of the design of wet combustion processes were calculated. This study greatly enhances the understanding of the complexity of the in situ combustion process and illustrates its characteristic behavior at or close to its exhaustion.

Development of secondary flow field under rotating condition in a straight channel with square cross-section

The developing secondary flow fields in the entrance section of a rotating straight channel were experimentally investigated using Particle Image Velocimetry (PIV). The effects of streamwise position, Reynolds number and rotation number on the development of the secondary flow fields were revealed. The results show that the absolute values of vorticity flux of the trailing side roll cells increase with increasing radius of the measured plane and rotation number. When the absolute value of vorticity flux exceeds a critical value, the merging of the trailing side roll cells appears. Moreover, when the number of the trailing side vortex pairs is even, the absolute values of vorticity flux of the leading side vortices increase along streamwise direction. Otherwise, the absolute values decrease along the streamwise direction. By the circulation analysis, this phenomenon was found to have relationship with the merging of the trailing side roll cells, and further concluded that the secondary flow field in a rotating channel has to be treated as a whole. At last, the increase of the Reynolds number was found to be able to induce the merging position moves upstream.

Marangoni Flows during Nonsolvent Induced Phase Separation.

Motivated by the much discussed, yet unexplained, presence of macrovoids in polymer membranes, we explore the impact of Marangoni flows in the process of nonsolvent induced phase separation. Such flows have been hypothesized to be important to the formation of macrovoids, but little quantitative evidence has been produced to date. Using a recently developed multifluid phase field model, we find that roll cells indicative of a solutal Marangoni instability are manifest during solvent/nonsolvent exchange across a stable interface. However, these flows are weak and subsequently do not produce morphological features that might lead to macrovoid formation. By contrast, initial conditions that lead to an immediate precipitation of the polymer film coincide with large Marangoni flows that disturb the interface. The presence of such flows suggests a new experimental and theoretical direction in the search for a macrovoid formation mechanism.

Numerical simulation of natural convection in a horizontal enclosure: Part I. On the effect of adiabatic obstacle in middle

In this study, an effect of a three-dimensional obstacle of natural convection in a horizontal enclosure was discussed. Geometry which was taken into account was horizontal enclosure with unit aspect ratio and length of π along spanwise direction. The enclosure was heated from the bottom wall, and then was cooled down from above. An obstacle was located in the middle of the enclosure to examine its effect. A three-dimensional solution was obtained using Chebyshev spectral multi-domain methodology for different Rayleigh number at which the thermal behavior was evolved from a steady state to a chaotic pattern. As the geometry was elongated in conjunction with periodic boundary conditions to allow lateral freedom for the convection cells, longitudinal geometry along spanwise direction was discretized through a Fourier series expansion with a uniform mesh configuration. An adiabatic obstacle played a different role in determining the thermal behavior: No-slip condition of the surface of the obstacle disturbed the overall plume behavior in terms of the momentum transfer, whereas the adiabatic boundary condition did not influence significantly in terms of energy transfer. At a low Rayleigh number, thermal behavior in three-dimensional enclosure showed steady invariant solution along spanwise direction which is identical to two-dimensional result. With increasing buoyant force, spanwise invariance of longitudinal roll cell was collapsed and three-dimensional mode was obtained following flow regime transition. After undergoing periodically oscillatory phase, a chaotic flow transition occurred. At a high Rayleigh number, three-dimensional thermal plume oscillates freely in elongated geometry and consequently yields higher heat transfer rate. In addition, the thermal flow field was captured by visualizing the three-dimensional vortical structure. The chaotic three-dimensional flow behavior was quantitatively examined by obtaining the turbulent statistics.

Multiple states in turbulent plane Couette flow with spanwise rotation

Turbulence is ubiquitous in nature and engineering applications. Although Kolmogorov’s (C. R. Acad. Sci. URSS, vol. 30, 1941a, pp. 301–305;Dokl. Akad. Nauk URSS, vol. 30, 1941b, pp. 538–540) theory suggested a unique turbulent state for high Reynolds numbers, multiple states were reported for several flow problems, such as Rayleigh–Bénard convection and Taylor–Couette flows. In this paper, we report that multiple states also exist for turbulent plane Couette flow with spanwise rotation through direct numerical simulations at rotation number$Ro=0.2$and Reynolds number$Re_{w}=1300$based on the angular velocity in the spanwise direction and half of the wall velocity difference. With two different initial flow fields, our results show that the flow statistics, including the mean streamwise velocity and Reynolds stresses, show different profiles. These different flow statistics are closely related to the flow structures in the domain, where one state corresponds to two pairs of roll cells, and the other shows three pairs. The present result enriches the studies on multiple states in turbulence.

Statistics and structure of spanwise rotating turbulent channel flow at moderate Reynolds numbers

A study of fully developed plane turbulent channel flow subject to spanwise system rotation through direct numerical simulations is presented. In order to study both the influence of the Reynolds number and spanwise rotation on channel flow, the Reynolds number $Re=U_{b}h/\unicode[STIX]{x1D708}$ is varied from a low 3000 to a moderate 31 600 and the rotation number $Ro=2\unicode[STIX]{x1D6FA}h/U_{b}$ is varied from 0 to 2.7, where $U_{b}$ is the mean bulk velocity, $h$ the channel half-gap, $\unicode[STIX]{x1D708}$ the viscosity and $\unicode[STIX]{x1D6FA}$ the system rotation rate. The mean streamwise velocity profile displays also at higher $Re$ a characteristic linear part with a slope near to $2\unicode[STIX]{x1D6FA}$, and a corresponding linear part in the profiles of the production and dissipation rate of turbulent kinetic energy appears. With increasing $Ro$, a distinct unstable side with large spanwise and wall-normal Reynolds stresses and a stable side with much weaker turbulence develops in the channel. The flow starts to relaminarize on the stable side of the channel and persisting turbulent–laminar patterns appear at higher $Re$. If $Ro$ is further increased, the flow on the stable side becomes laminar-like while at yet higher $Ro$ the whole flow relaminarizes, although the calm periods might be disrupted by repeating bursts of turbulence, as explained by Brethouwer (Phys. Rev. Fluids, vol. 1, 2016, 054404). The influence of the Reynolds number is considerable, in particular on the stable side of the channel where velocity fluctuations are stronger and the flow relaminarizes less quickly at higher $Re$. Visualizations and statistics show that, at $Ro=0.15$ and 0.45, large-scale structures and large counter-rotating streamwise roll cells develop on the unstable side. These become less noticeable and eventually vanish when $Ro$ rises, especially at higher $Re$. At high $Ro$, the largest energetic structures are larger at lower $Re$.

On the effect of conducting lid for natural convection in a horizontal fluid layer

In this study, effect of conducting lid attached in the horizontal fluid layer for Rayleigh-Bénard natural convection was discussed. Geometry which was taken into account was horizontal layer of fluid with conducting lid at the bottom. Conducting lid was heated from the bottom wall and the thermal energy was transferred to fluid layer through the solid/fluid interface, and then was cooled down from above. Thermal conductivity ratio varied to investigate the thermal behavior at the solid/fluid interface. Periodic boundary conditions were employed in the horizontal direction to allow lateral freedom for the convection cells. Prior to investigate thermal behavior of fluid layer with conducting lid, pure Rayleigh-Bénard natural convection without conducting body was reproduced. From two-dimensional Rayleigh-Bénard natural convection, an extension of wavelength of circulating roll cell was examined. A two-dimensional solution was obtained using Chebyshev spectral multi-domain methodology for different Rayleigh number at which the thermal behavior was evolved from steady state to chaotic pattern. Three-dimensional pure Rayleigh-Bénard natural convection was calculated from relatively low Rayleigh number such as 4×103 in order to investigate an evolution of thermal plume undergoing a representative zig-zag instability. In order to compare thermal behavior of fluid layer between with- and without conducting lid, effective Rayleigh numbers, Raeff, was introduced and 106 was applied. A solid lid at the bottom affects the flow pattern in that the flow is restricted to increase the dimensionless thermal conductivity. For three-dimensional simulation, periodic boundary condition was also applied along the span-wise direction which was discretized through a Fourier serious expansion with a uniform mesh configuration. For high effective Rayleigh number, thermal flow field was captured by visualizing the three-dimensional vortical structure. The flow behavior at the provided effective Rayleigh number showed a coherent pattern regardless of the magnitude of the thermal conductivity ratio.

The influence of interface curvature on solutal Marangoni convection in the Hele-Shaw cell

We carry out a numeric study on the impact of interfacial curvature on the Marangoni convection in a two-layer system of immiscible liquids with mass transfer of an alcohol. Assuming that there is a parabolic velocity profile and constant solute concentration across the gap, the simulations solve the Navier-Stokes equations coupled to advection-diffusion equations in both phases. Interfacial curvature imposes concentration gradients along the interface as soon as the mass transfer starts. This leads to an immediate interfacial convection which is superimposed later by the onset of the actual Marangoni roll cells. One prominent impact of interfacial curvature on the Marangoni cells is the occurrence of a locking effect, i.e., the Marangoni roll cells adapt to the shape of the interface. Whereas mass transfer is initially enhanced by the interfacial curvature compared to the planar interface, locking drastically reduces the mass transfer rate. Even for small interface curvatures significant differences are found compared with a planar setup, which might explain the accelerated growth of cells in experiments compared to that in numerical simulation, as recently observed in Koellner et al. (2015).

Three‐dimensional transient rip currents: Bathymetric excitation of low‐frequency intrinsic variability

AbstractThe ROMS‐WEC model [Uchiyama et al., 2010] based on an Eulerian wave‐averaged vortex‐force asymptotic theory of McWilliams et al. (2004) is applied to analyze 3‐D transient wave‐driven rip currents and associated intrinsic very low‐frequency (VLF) variability in the surf zone on a surveyed bathymetry under spatiotemporally uniform offshore incident waves. The 3‐D rip currents are substantially depth‐dependent due to the vertical recirculation, composed of pairs of counter‐rotating longitudinal overturning roll cells that promote surface convergence. The vortex force plays an important role in vorticity budget, preconditioning overall vorticity reduction. These rip currents are intrinsically unstable and contribute about 70% to kinetic energy (KE) as eddy kinetic energy (EKE), consistent with observations. The dominant fluctuation period fits the VLF band, at about 18 min. The current effect on waves (CEW) alters not only the mean rip structure, but also the associated turbulence as the modified cross‐shore EKE profile with considerable accentuation in the inner surf zone. Increased alongshore bathymetric variability proportionally intensifies KE and intrinsic EKE, whereas it reduces the VLF period. With a guide of a pseudo 2D model, we reveal that vortex tilting effect due to the horizontal vorticity inherent in the 3‐D rip currents promotes collapse of the 3‐D eddies through an enhanced forward kinetic energy cascade, leading to short‐lived, laterally‐stretched 3‐D eddies resulting in elongated filaments that decay more quickly than coherent, long‐lived, circular 2‐D eddies.

Thermal Instability of Convection in a Rotating Nanofluid Saturated Porous Layer Placed at a Finite Distance From the Axis of Rotation

An analytical investigation for the onset of convection in a vertical porous layer saturated by a nanofluid is presented when the porous layer is placed some finite distance from the axis of rotation. A linear stability analysis is used to determine the convection threshold in terms of the key parameters for the nanofluid. This study reconfirms that the Taylor number and gravity effects are passive, and that the most critical mode is roll cells aligned with the vertical axis of rotation. The critical Rayleigh number is presented in terms of the nanofluid parameters and offset distance for stationary convection.

Experiments in rotating plane Couette flow – momentum transport by coherent roll-cell structure and zero-absolute-vorticity state

In spanwise rotating plane Couette flow (RPCF) a secondary flow dominated by three-dimensional roll-cell structures develops. At high enough rotation rates the flow exhibits a state of zero absolute vorticity at the centre of the channel, as described by Suryadi et al. (Phys. Rev. E, vol. 89, 2014, 033003). They suggested that the zero-absolute-vorticity state is caused by the secondary flow motion of the coherent roll-cell structure induced by the Coriolis force. In the present study we focus on the momentum transport caused by the roll-cell structure of laminar RPCF in order to further understand how the zero-absolute-vorticity state is maintained by the coherent roll cells. The flow is studied through stereoscopic particle image velocimetry measurements, which allow both the Reynolds shear stress and the wall shear stress to be quantified and used as measures of the momentum transport across the channel. Various types of roll-cell structures at different system rotation rates and the momentum transport induced by them are investigated, and the processes in which the momentum is transported in the wall-normal direction are discussed based on a displaced-particle argument as well as the production of the Reynolds stresses. It is shown that the wall-normal fluid motion driven by secondary flow of the roll-cell structure induces two different effects on the mean flow which conflict each other, the momentum transport in the wall-normal direction and the Coriolis acceleration, and the zero-absolute-vorticity state is a stable state where these two effects cancel each other.

Inner–outer interactions of large-scale structures in turbulent channel flow

Direct numerical simulation data of turbulent channel flow ($Re_{{\it\tau}}=930$) are used to investigate the statistics of long motions of streamwise velocity fluctuations ($u$), and the interaction of these structures with the near-wall disturbances, which is facilitated by their associated large-scale circulations. In the log layer, the negative-$u$ structures are organized into longer streamwise extent (${>}3{\it\delta}$) in comparison to the positive-$u$ counterparts. Near the wall, the footprint of negative-$u$ structures is relatively narrow in comparison to the footprint of positive-$u$ structures. This difference is due to the opposite spanwise motions in the vicinity of the footprints, which are either congregative or dispersive depending on the circulation of the outer roll cells. Conditional sampling of the footprints shows that the spanwise velocity fluctuations ($w$) are significantly enhanced by the dispersive motions of high-speed structures. On the other hand, the near-wall congregative motions of negative-$u$ structures generate relatively weak $w$ but intense negative-$u$ regions due, in part, to the spanwise collective migration of near-wall streaks. The concentrated near-wall regions of negative-$u$ upwell during the merging of the outer long scales – an effect that is demonstrated using statistical analysis of the merging process. This leads to a reduction of the convection speed of downstream negative-$u$ structures and thus promotes the merging with upstream ones. These top-down and bottom-up interactions enhance the spatial coherence of long negative-$u$ structures in the log region.

Thermal Instability in a Rotating Vertical Porous Layer Saturated by a Nanofluid

An analytical investigation of the onset on convection in a vertical porous layer saturated by a nanofluid is presented. The Darcy model is used for the vertical porous layer and a linear stability analysis is used to determine the convection threshold in terms of the key parameters for the nanofluid. This study reveals that the Taylor number and gravity effects are passive, and that the most critical mode is roll cells aligned with the vertical axis of rotation. The critical Rayleigh number is presented in terms of the nanofluid parameters for both stationary and oscillatory convection.

Penta-decomposition of instantaneous field in spanwise-rotating turbulent plane Couette flow

Spanwise-rotating turbulent plane Couette flow (RPCF) is one of the fundamental prototypes for wall-bounded turbulent flows in rotating reference frames. In this turbulent problem, there are large-scale roll cells which are widely studied. In this paper, a penta-decomposition method is proposed to separate the instantaneous velocity and the total kinetic energy into five parts, i.e., a mean part, a streamwise part and a cross-flow part of the secondary flow, and a streamwise part and a cross-flow part of the residual field. The transport equations for the last four shares, which contribute the total turbulent kinetic energy, are derived. According to these transport equations, the mechanisms of energy transfer among different fractions of turbulent kinetic energy can be revealed clearly. Our objective is to explore the energy balance and transfer among different fractions of the turbulent kinetic energy in RPCF based on a series of direct numerical simulation databases at a Reynolds number Rew=Uwh/=1300 (here, Uw is half of the wall velocity difference, and h is the channel half-width) and rotation number Ro=2zh/Uw (z is the constant angular velocity in the spanwise direction) in a range of 0Ro0.9. The results show that the energy is transferred between the streamwise part/cross-flow part of secondary flows and the residual field through the correlation between the vorticity of secondary flows and the shear stress of residual field. The rotation term acts as a bridge to transfer the energy between the streamwise part and the cross-flow part of either the secondary flows or the residual field. Moreover, pressure-strain redistribution term also plays an important role in the energy transfer between streamwise part and cross-flow part in residual field. For the streamwise part of residual field, in certain rotate rates, the energy obtained from the streamwise part of secondary flows by the correlation between the vorticity of secondary flows and the shear stress of residual field is larger than that obtained from mean flow through mean shear, implying that the streamwise motions of secondary flows have a significant influence on the streamwise motions of residual field.

Highly-disturbed turbulent flow in a square channel with V-shaped ribs on one wall

We investigate highly-disturbed turbulent flows in a square channel with V-shaped ribs mounted on one wall. A planar particle image velocimetry (PIV) system is used to measure the fully developed turbulent flow at the channel midspan and two off-center planes. V-shaped rib configurations with three different inclinations (60°, 45° and 30°) are studied and compared to the perpendicular (90°) rib case. The highly-disturbed turbulent flow in the V-shaped rib cases are studied by investigating the statistics of first and second order moments, including the mean velocity, mean shear, mean vorticity and Reynolds stresses. Owing to the geometrical skewness of the V-shaped ribs, strong secondary flows are induced which appear in the pattern of a pair of streamwise counter-rotating roll cells and have a significant impact on the momentum transport process. Near the channel midspan of the V-shaped ribs, turbulent intensity is suppressed above the ribs but enhanced below the rib height, and turbulent vortical motions exhibit isotropic patterns due to the strong disturbances from the ribs. The coherent flow structures have been systematically analyzed based on studying two-point auto-correlation coefficient, quadrant decomposition of Reynolds stresses, swirling strength, and proper orthogonal decomposition of the turbulent flow.

Application of Reynolds stress transport turbulence closure models to flows affected by Lorentz and buoyancy forces

The effect of magnetic field strength and orientation on two types of electromagnetically influenced turbulent flows was studied numerically under the Reynolds averaged Navier–Stokes (RANS) framework. Previous work (Wilson et al., 2014) used an electromagnetically extended linear eddy-viscosity model, whilst the current paper focuses on the performance of a more advanced Reynolds stress transport type model both with and without electromagnetic modifications proposed by Kenjereš et al. (2004). First, a fully-developed 2D channel flow is considered with a magnetic field imposed in either the wall-normal or streamwise direction. Both forms of the RSM gave good agreement with the DNS data for the wall-normal magnetic field across the range of Hartmann numbers with the additional electromagnetic terms providing a small, but noticeable, difference. For the streamwise magnetic field, where electromagnetic influence is only through the turbulence, the electromagnetically extended RSM performed well at moderate Hartmann numbers but returned laminar flow at the highest Hartmann number considered, contrary to the DNS. The RSM results were, however, significantly better than the previous eddy-viscosity model predictions. The second case is that of unsteady 3D Rayleigh–Bénard convection with a magnetic field imposed in either a horizontal or vertical direction. Results revealed that a significant reorganization of the flow structures is predicted to occur. For a vertically oriented magnetic field, the plume structures increase in number and become thinner and elongated along the magnetic field lines, leading to an increase in thermal mixing within the core in agreement with Hanjalić and Kenjereš (2000). With a horizontal magnetic field, the structures become two-dimensional and a striking realignment of the roll cells’ axes with the magnetic field lines occurs. The results demonstrate the capability of the Reynolds stress transport approach in modelling MHD flows that are relevant to industry and offer potential for those wishing to control levels of turbulence, heat transfer or concentration without recourse to mechanical means.