Spanwise Aspect Ratio Research Articles

A heat transfer correlation of Poiseuille-Rayleigh-Bénard convection in the thermal entrance region of a horizontal rectangular channel

In order to understand heat transfer characteristics and obtain a heat transfer correlation of Poiseuille-Rayleigh-Bénard (P-R-B) convection in the thermal entrance region of a horizontal rectangular channel, we performed a series of the direct numerical simulations. The working fluid is water, and the spanwise aspect ratio of the rectangular channel ranges from 2 to 10. The results show that the thermal entrance length for the onset of buoyancy-driven convection extends with the decreasing Rayleigh number and the increasing Reynolds number. The average Nusselt number in the thermal entrance region increases with the increase of Rayleigh number and Reynolds number. Furthermore, a smaller aspect ratio and a shorter length of the channel contributes to enhanced heat transfer in the thermal entrance region. Based on the simulation results, the heat transfer correlation in the thermal entrance region is established, which can be used as a reference for the engineering design on P-R-B convection.

Three-dimensional numerical simulations on Poiseuille-Rayleigh-Bénard convection of air in a horizontal rectangular channel

In order to reveal the combined influences of Rayleigh (Ra) number, Reynolds (Re) number and spanwise aspect ratio (B) on the flow pattern evolution and stability, and heat transfer of Poiseuille-Rayleigh-Bénard (PRB) convection, we presented a set of three-dimensional numerical simulations on PRB convection of air in the horizontal channels using commercial software Fluent in a range of 2 ≤ B ≤ 10, 0 ≤ Re ≤ 250 and 1.7 × 103 ≤ Ra ≤ 2.5 × 104. Various flow patterns are observed, including transversal rolls, longitudinal rolls, mixed rolls and wavy flow. The results show that the number of longitudinal rolls depends on B and Ra. The critical Rayleigh numbers for appearance and destabilization of the longitudinal rolls and the transversal rolls increase with increasing Re. With increasing B, the critical Rayleigh numbers for the primary and secondary instabilities will decrease and the critical Reynolds number also decreases. The heat transfer of PRB convection is enhanced with increasing Ra and B. A heat transfer correlation of the average Nusselt number with Ra and B is established.

Evaluation of wall functions for RANS turbulence models by unsteady lid-driven cavity flow

Turbulence models do not perform well near walls because the Reynolds number in this interesting area is low. The wall functions and the advantage method can be efficiently used to model fluid flow at the near wall region. The Reynolds averaged Navier-Stokes turbulence models which had the developed wall functions in Open FOAM, the open source CFD software, were evaluated by the turbulent flow. The 3-D lid-driven cavity flow at the turbulence Reynolds number of 10,000 with various spanwise aspect ratio had been referred to validate these turbulence models. The comparison shown that the realizable k-ɛ turbulence model with the standard k and ɛ wall functions of OpenFOAM was the most powerful model to represent the velocity profile of water flow in the 3-D lid-driven cavities.

Analysis of reattachment length dynamics in cavities

Recirculation zone dynamics in a cavity located in the bottom wall of a water channel with height h = 0.3 mm and width b = 0.9 mm are investigated experimentally and numerically.A microparticle image velocimetry method and instrumentation are used for the experimental determination of flow velocity distribution and reattachment pattern with Reynolds number from ReDh = 30–2000, cavity length to depth ratios of L/h1 = 10 and 16, and channel expansion ratios of H/h = 1.3, 1.5, 2, 3, and 5. Numerical simulation using commercially available Ansys Fluent software is conducted for analysis of the influence of flow regime and cavity dimensions by changing ReDh, L/h1, and H/h in the ranges of (1–105), (8–36) and (1.25–5), respectively.The experimental and numerical simulation results show that in a laminar flow regime reattachment length increases with increasing ReDh in the same manner as in flow over a backward-facing step. Reh1 and H/h are the main scaling parameters for the reattachment length. However, the results suggest that the transition to a turbulent flow regime occurs earlier due to the small channel spanwise aspect ratio AR = b/h = 3. Reh1 ≈ 500 and Reh1 ≈ 2000 are the critical values that determine the onset of flow transition from a laminar to a turbulent regime and the onset of fully developed turbulent flow, respectively. In addition, it is found that the influence degree of channel expansion ratio depends on whether H/h > 2 or H/h < 2.

3D Numerical study of the effect of aspect ratio on mixed convection air flow in upward solar air heater

A 3D Numerical study of mixed convection air flow in upward solar air heater with large spanwise aspect ratio (A = 10 to 40) was performed using CFD commercial code Fluent 14.5 (ANSYS). The main objective of this study is to investigate the channel height's effect (aspect ratio) on flow pattern and heat transfer in upward solar air heater in the particular case of low Re and high aspect ratio. The bottom plate (absorber) was submitted to Constant Heat Flux (CHF) in the range of 200 to 1000 W/m2 and Reynolds number was varied from 50 to 1000. Our results are in concordance with most of authors conclusions about Poiseuille–Rayleigh–Benard flows. In mixed convection, increasing heat flux enhances heat transfer unlike forced convection flows. Simulation results of flow visualizations and Nusselt number calculations have shown that depending on Ri*, the velocity and temperature distributions in SAH vary greatly with the channel's height. The obtained results were different from previous studies. Indeed, our investigation of channel's height was achieved for the same heat flux but different Grashof numbers. For low channel's heights (high aspect ratio), increasing heat flux has not a significant effect but for higher channel's heights, an augmentation of heat flux enhances buoyancy effects in the flow and causes high turbulence. Also, increasing Reynolds number in low channel's heights (high A), can enhance substantially heat transfer. For higher channel's heights (low A), increasing Reynolds number decreases Ri* and thus buoyancy forces. Heat transfer is reduced and so Nusselt number. The obtained results may be very useful for engineers in designing and testing solar collectors.

Flows over surface-mounted bluff bodies with different spanwise widths submerged in a deep turbulent boundary layer

The spatio-temporal dynamics of separation bubbles induced by surface-mounted bluff bodies with different spanwise widths and submerged in a thick turbulent boundary layer is experimentally investigated. The streamwise extent of the bluff bodies is fixed at 2.36 body heights and the spanwise aspect ratio ($AR$), defined as the ratio between the width and height, is increased from 1 to 20. The thickness of the upstream turbulent boundary layer is 4.8 body heights, and the dimensionless shear and turbulence intensity evaluated at the body height are 0.23 % and 15.8 %, respectively, while the Reynolds number based on the body height and upstream free-stream velocity is 12 300. For these upstream conditions and limited streamwise extent of the bluff bodies, two distinct and strongly interacting separation bubbles are formed over and behind the bluff bodies. A time-resolved particle image velocimetry is used to simultaneously measure the velocity field within these separation bubbles. Based on the dynamics of the mean separation bubbles over and behind the bluff bodies, the flow fields are categorized into three-dimensional, transitional and two-dimensional regimes. The results indicate that the low-frequency flapping motions of the separation bubble on top of the bluff body with $\mathit{AR}=1$ are primarily influenced by the vortex shedding motion, while those with larger aspect ratios are modulated by the large-scale streamwise elongated structures embedded in the oncoming turbulent boundary layer. For $\mathit{AR}=1$ and 20, the flapping motions in the wake region are strongly influenced by those on top of the bluff bodies but with a time delay that is dependent on the $AR$. Moreover, an expansion of the separation bubble on the top surface tends to lead to an expansion and contraction of separation bubbles in the wake of $\mathit{AR}=20$ and 1, respectively. As for the transitional case of $\mathit{AR}=8$, the separation bubbles over and behind the body are in phase over a wide range of time difference. The dynamics of the shear layer in the wake region of the transitional case is remarkably more complex than the limiting two-dimensional and three-dimensional configurations.

High Reynolds number incompressible turbulent flow inside a lid-driven cavity with multiple aspect ratios

The numerical simulation of incompressible turbulent flow at Re = 11 800 (equivalent Reynolds number Rem = 10 030) inside lid-driven cavities with varying spanwise aspect ratio and depthwise aspect ratio (DAR) has been carried out using the dynamic Smagorinsky model. A better comparison of central line averaged velocities and second order turbulent properties is obtained with the existing experimental result of Prasad and Koseff [“Reynolds number and end-wall effects on a lid-driven cavity flow,” Phys. Fluids A 1, 208–218 (1989)] than with the one provided by Leriche and Gavrilakis [“Direct numerical simulation of the flow in a lid-driven cubical cavity,” Phys. Fluids 12, 1363–1376 (2000)]. It is noticed that the size of the downstream secondary vortex increases with an increase in the aspect ratio. Lower DAR cavities are found to be having the maximum turbulent kinetic energy (TKE) and turbulent production, which is further confirmed by the TKE spectra shown at the point of maximum turbulent production on the symmetrical mid-plane. The power spectra maintain a slope of −53 in the inertial subrange as proposed by Kolmogorov and show a steeper slope in the dissipating range. The time integral scale shows that in low DAR cavities, eddies are formed and undergo complete distortion more frequently. The joint probability density function confirms the anisotropy in turbulence, and the anisotropy invariant map (Lumley triangle) shows the type of turbulent anisotropy which shows whether the turbulence is either one-component or two-component near the walls.

Numerical bifurcation analysis for 3‐dimensional sudden expansion fluid dynamic problem

SummaryThis paper deals with bifurcation analysis methods based on the asymptotic‐numerical method. It is used to investigate 3‐dimensional (3D) instabilities in a sudden expansion. To do so, high‐performance computing is implemented in ELMER, ie, an open‐source multiphysical software. In this work, velocity‐pressure mixed vectors are used with asymptotic‐numerical method–based methods, remarks are made for the branch‐switching method in the case of symmetry‐breaking bifurcation, and new 3D instability results are presented for the sudden expansion ratio, ie, E=3. Critical Reynolds numbers for primary bifurcations are studied with the evolution of a geometric parameter. New values are computed, which reveal new trends that complete a previous work. Several kinds of bifurcation are depicted and tracked with the evolution of the spanwise aspect ratio. One of these relies on a fully 3D effect as it breaks both spanwise and top‐bottom symmetries. This bifurcation is found for smaller aspect ratios than expected. Furthermore, a critical Reynolds number is found for the aspect ratio, ie, Ai=1, which was not previously reported. Finally, primary and secondary bifurcations are efficiently detected and all post‐bifurcated branches are followed. This makes it possible to plot a complete bifurcation diagram for this 3D case.

Natural convection in a cubical cavity with a coaxial heated cylinder

High-resolution three-dimensional simulations were conducted to investigate the velocity and temperature fields in a cold cubical cavity due to natural convection induced by a centrally placed hot cylinder. Unsteady, incompressible Navier-Stokes equations were solved by using a spectral-element method for Rayleigh numbers ranging from 103 to 109. The effect of spanwise thermal boundary conditions, aspect ratio (radius of the cylinder to the side of the cavity), and spanwise temperature distribution of the inner cylinder on the velocity and thermal fields were investigated for each Rayleigh number. Results from two-dimensional calculations were compared with three-dimensional simulations. The 3D results indicate a complex flow structure in the vicinity of the spanwise walls. The results also show that the imposed thermal wall boundary condition impacts the flow and temperature fields strongly near the spanwise walls. The variation of the local Nusselt number on the cylinder surface and enclosure walls at various spanwise locations was also investigated. The local Nusselt number on the cylinder surface and enclosure walls at the cavity mid-plane (Z = 0) is close to 2D simulations for 103 ≤ Ra ≤ 108. Simulations also show a variation in the local Nusselt number, on both the cylinder surface and the enclosure walls, in the spanwise direction, for all Rayleigh numbers studied in this work. The results also indicate that if the enclosure walls are insulated in the spanwise direction (as opposed to a constant temperature), the peak Nusselt number on the enclosure surface occurs near the spanwise walls and is about 20% higher than the peak Nusselt number at the cavity mid-plane. The temporal characteristics of 3D flows are also different from 2D results for Ra > 108. These results suggest that 3D simulations would be more appropriate for flows with Ra > 108.

The onset of centrifugal instability in an open cavity flow

This study deals with the experimental investigation of the onset of instability in an open cavity flow, in the incompressible limit. Far below the development of self-sustained oscillations, the first instability is three-dimensional on the inner recirculating flow. We address the case of a cavity of a large span-wise aspect ratio in which the side-wall effects are negligible. We study the pattern selection at threshold as the stream-wise aspect ratio is varied and, for large aspect ratios, we report the development of a second mode, which is quasi-symmetric to the primary mode.

Self-excited oscillations of two opposing planar air jets

This paper investigates the self-excited oscillations of two co-planar air jets impinging on each other, referred to, hereafter, by opposing planar jets. The study is performed for a single jet thickness of h = 2 mm and a span-wise aspect ratio of 50. The effects of flow velocity of the jets and the distance between them are examined. The opposing planar jets are found to produce strong acoustic tones over a wide range of jet Mach number and separation distance. Phase-locked averaged particle image velocity measurements showed that the tone is generated by out-of-phase flapping oscillations of the planar jets. These oscillations are sustained by two effects. The first is the high stagnation pressure at the impingement region, which deflects the jets laterally in opposite directions away from their common centerline, while the second effect is the cross stream oscillating velocity in the entrainment regions around the jet exits, which forces the jets back towards their common centerline.

Influence of a white noise at channel inlet on the parallel and wavy convective instabilities of Poiseuille-Rayleigh-Bénard flows

The present paper concerns Poiseuille-Rayleigh-Bénard mixed convection flows in horizontal rectangular air-filled channels of large spanwise aspect ratio (W/H ≥ 10) and it focuses on the primary and secondary thermoconvective instabilities made of steady longitudinal and unsteady wavy rolls for 100 ≤ Re ≤ 200, 3000 &amp;lt; Ra &amp;lt; 15 000, Pr = 0.7, and W/H = 10. Time linear stability analysis of longitudinal rolls and 3D nonlinear numerical simulations using a specially tailored finite difference code is performed for this purpose. A bibliographical review, linear stability analysis and 3D numerical simulations allow establishing the full stability diagram for Re ≤ 300 and Ra ≤ 20 000. The linear stability analysis indicates that the critical Rayleigh number Ra≈*(Re) of the neutral curve between longitudinal and wavy rolls for W/H = 10 is increased at least by a factor of 1.5 in comparison with infinite W/H. The numerical study shows that the usual definitions of growth lengths for longitudinal rolls are inappropriate and it explains the discrepancies observed on wall Nusselt numbers in the literature between experimental and numerical results for the fully developed longitudinal rolls: Nusselt number decreasing at Ra &amp;gt; 8000 is due to spanwise oscillations of thermoconvective rolls that favor a bulk temperature homogenization. Because they are a convective instability, wavy rolls and their space and time development are studied numerically by maintaining at channel inlet, a permanent random excitation: it is designed to cover all the modes and allows detecting the wavy roll modes that are naturally amplified by the flow and those that are damped. Wavy roll patterns are characterized with respect to its three control parameters: Re, the relative distance ɛ to the critical Rayleigh number Ra≈*, and the excitation magnitude Aexc. The growth length of the wavy rolls is shown to correlate with ɛ−0.72 and Log(Aexc). The frequency, wave number, and phase velocity of the most amplified mode, the wall averaged Nusselt number and the spanwise displacements of the wavy rolls are independent of Aexc in the fully developed zone, but depend a lot on ɛ for ɛ &amp;lt; 2 and nearly stabilize for ɛ &amp;gt; 2 (i.e., Ra &amp;gt; 3Ra≈*). Correlation laws as a function of Re, ɛ, and Aexc are proposed for most of the exploited quantities. Numerical simulations performed are in a good agreement with experimental results on the wavy rolls obtained by Pabiou et al. [“Wavy secondary instability of longitudinal rolls in Rayleigh-Bénard-Poiseuille flows,” J. Fluid Mech. 542, 175 (2005)10.1017/S0022112005006154]. Finally, wavy roll characteristics are shown to be potentially interesting to better homogenize the vapor depositions in the horizontal rectangular chemical vapor deposition reactors used to make thin coatings on heated substrates from gaseous components.

Three-dimensional flow in circular cavities of large spanwise aspect ratio

AbstractExperimental data are presented for the vortex flow in a nominally two-dimensional circular cavity. The vortex is driven by a separated shear layer along an open section of the cavity circumference. It is shown that the core vortex flow is perturbed three-dimensionally. An inviscid analysis of an ideal core (solid body) vortex is given and it is shown that this flow contains a steady perturbation whose characteristics are almost exactly those identified in the experiments. Viscous effects reduce (by a few per cent) the spanwise wavelength of the perturbation and also lead, via spatial variations in Reynolds stress, to a modification of the core flow so that the radial profile of the circumferential velocity is ‘S’-shaped, rather than linear.

Experimental investigation of buoyant flows in inclined differentially heated cavities

This experimental investigation focuses on the effects of angle of inclination on buoyancy-driven flows inside tall, rectangular, differentially-heated cavities. It considers a rectangular cavity with an aspect ratio of 28.6, with its two long sides maintained at different temperatures and the two short, end-walls, thermally insulated. The spanwise aspect ratio is 6.82 and the side walls are also thermally insulated. The Rayleigh number, based on the temperature difference and spacing between the long sides, is 0.86×106 for most cases and the working fluid is air (Prandtl number 0.71). Experimental data, for the flow and the thermal fields, using laser Doppler anemomentry and thermocouple traverses respectively, are presented for the cavity inclined at 60° and 15° to the horizontal, for both stable (the hot surface being the upper surface) and unstable orientations. The 15° stable case is investigated at a higher Rayleigh number of 1.54×106 and some additional data for the 15° unstable case are also presented at this higher value of Rayleigh number. For moderate angles of inclination, the flow is two-dimensional and the effects of inclination are primarily confined to the fluctuating fields. For large angles of inclination, the flow becomes three-dimensional. In the unstable 15° angle of inclination case a set of four longitudinal vortices are formed over the entire length of the cavity, with four counter-rotating re-circulation cells within the cross-section parallel to the thermally active walls. The stable 15° angle of inclination leads to the formation of two longitudinal vortices and two re-circulation cells. At the 15° angle (stable and unstable), the enhanced mixing leads to uniform temperature in the cavity core and thus to only minor deviations from two-dimensionality in the thermal field. A modest rise in Rayleigh number, in the 15° unstable case, does not affect the mean motion, but causes an increase in the normalised turbulence intensities.

Streamlines Near a Closed Curve and Chaotic Streamlines in Steady Cavity Flows

Numerical simulations are carried out for the three-dimensional steady flow in a lid-driven rectangular cavity. We study the incompressible flow in a cavity with spanwise aspect ratio 1.0 and aspect ratios 0.4, 0.6, 1.0 and 1.4. Streamlines are obtained from the steady velocity field and Poincaré sections are plotted from the streamlines for Reynolds numbers ranging from 100 and 400. There are two types of streamlines: localized streamlines near a closed curve and chaotic streamlines. In the Poincaré sections we can find various structures of ovals of invariant tori and resonant islands by localized streamlines in the regions near the end-wall and irregularly distributed points by chaotic streamlines. The structures in the Poincaré sections are similar to those in the phase portraits of one-dimensional non-autonomous Hamiltonian system. The Reynolds number ranges where the 3:1 and 2:1 resonances occur are presented for various aspect ratios.

Characterization of flow oblique to a circular cylinder with low aspect ratio using 3-D detached eddy simulation

Large-amplitude vibrations of stay cables in cable-stayed bridges can threaten the safety and serviceability of the structures. Understanding of the excitation mechanism is necessary to mitigate such vibrations effectively and efficiently. Experimental research has investigated the mechanism of oscillation using flow oblique to a cylinder; however, since the aspect ratio of the cylinder is much lower than that of a real stay cable in bridges, the results might not reliably describe the real phenomenon. The aim of this study is (1) to provide better understanding of aspect ratio effects of a circular cylinder on aerodynamic characteristics of the cylinder oblique to flow associated with the large-amplitude cable vibrations and (2) to provide the experimentalists suggestions of a requisite aspect ratio and appropriate pressure-measuring positions of a cylinder for fully developed flow around the cylinder. To this end, the current work applied three-dimensional detached eddy simulations (DES) to flow around a yawed and inclined cylinder to investigate the importance of the aspect ratio of the cylinder when flow oblique to the cylinder develops fully along its spanwise axis. The Reynolds number is 1.4 × 10 5 based on the incoming flow velocity and the diameter of the cylinder. Three aspect ratios ( L/ D=10, 20, and 30; L: a cylinder length; D: a cylinder diameter) and two numerical conditions (slip and periodic) on spanwise boundaries were employed. Results showed that three-dimensional flow and the associated forces on a yawed and inclined cylinder are significantly influenced by the spanwise aspect ratios and spanwise boundary conditions. This study suggests that when a wind tunnel experiment investigates flow oblique to a very slender cylinder, such as attempting to model a stay cable, experimentalists should use a sufficiently high spanwise aspect ratio of the cylinder. For the case of the 30° yaw and 45° inclined cylinder, the requisite ratio would be approximately 60 or higher and appropriate pressure-measuring positions of a half to two-thirds of the cylinder length from its upper/upstream end in order to accurately model inherently three-dimensional characteristics of the flow.

Numerical Analysis on the Start-Up Flow Past a Resonant Cavity

This paper presents the results of a computational analysis on a three-dimensional unsteady flow inside a resonant cavity. The cavity was fully immersed in a channel flow, had a squared cross section, and a spanwise aspect ratio equal to 3. It was partly closed to the inflow by slits upstream and downstream. The lid was 1∕4 of the cavity length. The Reynolds number was Re=8000 based on the freestream velocity. The numerical simulations were carried out for flow times up to 380 units. Results are presented for a symmetric cavity with respect to the normal to the freestream. The analysis shows complex three-dimensional vortex structures, with Taylor–Görtler-type vortices, filament vortices, and other secondary vortices, some having a relatively short life-span. It is shown that the flow is substantially symmetric, with small spanwise instabilities. It is further shown that there is an asymptotic tendency to an unsteady flow with large wavelengths. A primary vortex establishes at the center of the cavity. Most vortex regions disappear and that they depend on the type of geometry and the state of the boundary layer at the inlet.

Eddy structures in a transitional backward-facing step flow

In the present study, flow simulation has been carried out in a backward-facing step channel defined by an expansion ratio of 2.02 and a spanwise aspect ratio of 8 to provide the physical insight into the longitudinal and spanwise flow motions and to identify the presence of Taylor–Görtler-like vortices. The Reynolds numbers have been taken as 1000 and 2000, which fall in the category of transitional flow. The present simulated results were validated against the experimental and numerical data and the comparison was found to be satisfactory. The simulated results show that the flow becomes unsteady and exhibits a three-dimensional nature with the Kelvin–Helmholtz instability oscillations and Taylor–Görtler-Like longitudinal vortices. The simulated data were analysed to give an in-depth knowledge of the complex interactions among the floor and roof eddies, and the spiralling spanwise flow motion. Destabilization of the present incompressible flow system, with the amplified Reynolds number due to the Kelvin–Helmholtz and Taylor–Görtler instabilities, is also highlighted. A movie is available with the online version of the paper.

Simulation of the Askervein flow. Part 2: Large-eddy simulations

Large-eddy simulations of the neutrally stratified flow over the Askervein Hill were performed, to improve the knowledge of the flow obtained from field measurements and numerical simulations with Reynolds averaged Navier-Stokes (RANS) methods. A Lagrangian dynamic subgrid model was used but, to avoid the underdissipative character near the ground, it was merged with a damped Smagorinsky model. Simulations of a flat boundary-layer flow with this subgrid model showed that the turbulent vertical motions and shear stress were better resolved using grids with a stream to spanwise aspect ratio Δx / Δy = 2 than with an aspect ratio Δx / Δy = 1. Regarding the flow over the Askervein Hill, it was found that large-eddy simulations provide an acceptable solution for the mean-velocity field and better predictions of the turbulent kinetic energy in the upstream side of the hill than the $$k - \varepsilon$$ model. However, as with the $$k - \varepsilon$$ model, grid convergence was not achieved in the lee side and the size of the zone with reversed flow increased with the grid refinement. Nevertheless, the existence of the intermittent separation predicted with unsteady RANS in part one of this work seems unquestionable, due to the deceleration of the flow. In our opinion, a better modelling of the decelerating boundary layer in the lee side is required to improve the results obtained using equilibrium assumptions and achieve grid convergence.

Numerical analysis of 3D vortical cavity flow

AbstractThe vortical flows of an incompressible fluid in a rectangular three‐dimensional container with a large spanwise aspect ratio driven by a moving solid lid are studied using a combined compact finite difference (CCD) scheme with high accuracy and high resolution. The study focuses on the change of the steady flow structures in the cavity with Reynolds numbers ranging from 100 to 850. The results of the flow in the cavity with a spanwise aspect ratio 6.55 show that several stable closed streamlines localized near the symmetric plane are found at Re ≥500, while a closed stable streamline is found near the side wall at Re ≤300. The change of the flow pattern present in this system affects the diffusion properties in the flow but seems to have no qualitative effect on the global flow properties which include energy dissipation in the cavity. (© 2006 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)