Tangential Vorticity Research Articles

Experiments on the evolution process of intermittent air-entraining vortices and its influencing factors

Surface vortices are a common hydraulic phenomenon at water intakes that adversely affect safe engineering operations. The complexity of vortex motion, the diversity of influencing factors, and the limitations of research methods make the formation and development mechanisms of vortices unclear. Some analytical and experimental studies on intermittent air-entraining vortices occurring at the horizontal circular intake have been conducted to explore the mechanism of the dynamic characteristics of vortices. Based on experimental observations, the morphologies and dynamic characteristics of intermittent air-entraining vortices at different moments during the entire evolution process were studied, and the velocity field in the vortices was measured using PIV. The evolution processes of intermittent air-entraining vortices comprised inception, rapid development, stability, decay and regeneration, and the collapse and disappearance stages. The tangential velocity, kinetic energy, and vorticity increased over time, reached a maximum, and subsequently decreased. When they decrease to a certain value, they begin to increase before decreasing owing to the decay and regeneration stages. Additionally, we introduced the frequency of intermittent air-entraining vortex occurrence (P) to analyse the direct effect of the Froude number, intake submergence, and rear wall on the occurrence of air-entraining vortices. Based on the analysis of the test results, the effect of intake submergence on P was more significant than that of the intake Froude number in terms of flow conditions. By considering the effects of the flow conditions and rear wall, a method for predicting the possibility of the occurrence of intermittent air-entraining vortices was proposed.

Opposite effects of flame-generated potential and solenoidal velocity fluctuations on flame surface area in moderately intense turbulence

To explore the influence of dilatational and rotational motions on iso-scalar surface area within a premixed turbulent flame, three-dimensional compressible direct numerical simulation data obtained by Dave et al. (2018) from a lean, complex-chemistry, hydrogen-air flame propagating in intense small-scale turbulence (a ratio of laminar flame thickness to Kolmogorov length scale is about 20) in a box are analyzed using Helmholtz–Hodge decomposition of velocity field into solenoidal and potential components. The obtained results indicate that the flame surface area is created by potential velocity fluctuations generated due to combustion-induced thermal expansion, whereas the rotational motion acts to smooth wrinkles of iso-scalar surfaces within local preheat and reaction zones and, consequently, to reduce the flame surface area. The latter finding challenges the classical concept of flame-generated turbulence and is attributed to flame-generated solenoidal velocity fluctuations. Specifically, the incoming tangential (to the flame) vorticity is suppressed by baroclinic torque, which also generates vorticity in another tangential direction, with the latter (flame-generated) solenoidal velocity fluctuations working to smooth the flame surface. Thus, even under conditions of moderately intense turbulence, flame surface area can primarily be created by potential velocity perturbations caused by combustion-induced thermal expansion.

Dual-stage radial–tangential vortex tilting reverses radial vorticity and contributes to leading-edge vortex stability on revolving wings

The physics of leading-edge vortex (LEV) stability on flapping wings and autorotating seeds is still underexplored due to its complex dependency on Reynolds number ( $\textit {Re}$ ), aspect ratio (AR) and Rossby number (Ro). Our previous study observed an interesting dual-stage vortex tilting between radial and tangential components in a stable LEV. Here, the establishment of this novel mechanism, i.e. dual-stage radial–tangential vortex tilting (DS-VT $_{r-t}$ ), is investigated and explained in detail using numerical methods. The contributions of other tangential vorticity transport terms are also considered. It is shown that the stable LEV region coincides mostly with a constant ratio of tangential and radial vorticity components. The DS-VT $_{r-t}$ mechanism functions as a negative feedback loop for radial vorticity, thereby contributing to the LEV stability at $\textit {Re} > 500$ . Specifically, this mechanism involves a dual-stage vortex tilting starting from negative radial component to positive tangential component, and then back to positive radial component, thereby leading to a $180^{\circ }$ reversal of radial vorticity. The radial Coriolis acceleration can also assist the DS-VT $_{r-t}$ by enhancing the tangential vorticity component and the reduction of radial vorticity inside the LEV via the second stage of DS-VT $_{r-t}$ . The effects of $\textit {Re}$ , AR and Ro on the constant radial–tangential vorticity ratio and DS-VT $_{r-t}$ are then analysed. The coupled effects of AR and Ro are separated into rotational effects and those of tip and root vortices. Our results establish an evident relationship among the LEV stability, the constant radial–tangential vorticity ratio, and the DS-VT $_{r-t}$ , thereby deepening the understanding in the vorticity transport of LEV formation and stability.

Unsteady characteristics of tip leakage vortex structure and dynamics in an axial flow pump

The aim of this work is to investigate the unsteady characteristics of tip leakage vortex (TLV) structure in an axial flow pump experimentally and numerically. Experiments were carried out to study the performance of an axial flow pump under cavitating cavitation. The numerical simulation was conducted by employing the Large Eddy Simulation turbulence and Zwart cavitation models, and the results show a good agreement with the experimental ones. The evolution mechanisms and influencing factors of the transient TLV morphology was revealed, and the correlation between pressure difference and leakage velocity were investigated in a systematic way. The TLV evolution appears periodic development, coinciding with the variation of leakage velocity driven by the pressure difference. The cylindrical coordinate system is more suitable for analyzing the TLV dynamics, due to the impeller rotation. The vorticity in the tip region is dominated by tangential vorticity ωθ and axial vorticity ωz. The transport terms of ωθ and ωz present a great relationship with TLV and TLV-induced cavitation. Relative vortex stretching dominants the vorticity generation in the tip region, and relative vortex dilation and Coriolis force are also important sources. In contrast, baroclinic torque has the least influence on the vorticity in the flow passage.

Impact of a jet orifice on the hydrodynamics and the oil droplet size distribution

Experiments were performed to understand the impact of the orifice on droplet size in the shear breakup region. Oil jet was released vertically from two orifice types: a pipe and a converging nozzle. The roll-up vortices were observed clearly near the edge of the jet with nozzle orifice while elongated oil ligaments in the jet direction were mostly observed near the edge of the jet with pipe orifice. The size of the droplets shed from the near field shear layer increased along the jet direction for both orifice types. At different distances from the orifice, the characteristic shed droplet size (d50) was up to 40% larger with pipe orifice. Multiphase, large-eddy simulations (LES) with two orifice types were conducted to interpret the droplet size distribution (DSD) observed in the experiments. A thicker boundary layer that was initially formed inside the pipe dominated the near field of the jet with the pipe. The turbulent kinetic energy dissipation rate (ε) was higher with pipe orifice and the peak values of ε were found closer to the jet centerline with the pipe where oil holdup is larger. The viscous shear stress with the nozzle was higher than that of the pipe orifice within the initial two diameters from the orifice and slightly lower or higher at the following distances studied. The Reynolds shear stress was significantly larger with the nozzle at different distances from the orifice. The tangential vorticity within one diameter from the orifice was also dramatically higher with the nozzle. The key parameter in the shed droplet size of a liquid jet in liquid was found to be the shear layer thickness at the orifice, similar to prior works of a liquid jet in gas. A thicker shear layer at the pipe orifice induced a larger droplet size. The increase in the instabilities and shear layer thickness in the jet direction increased the droplet size in the jet direction.

Effects of Reynolds number on leading-edge vortex formation dynamics and stability in revolving wings

The mechanisms of leading-edge vortex (LEV) formation and its stable attachment to revolving wings depend highly on Reynolds number ( $\textit {Re}$ ). In this study, using numerical methods, we examined the $\textit {Re}$ dependence of LEV formation dynamics and stability on revolving wings with $\textit {Re}$ ranging from 10 to 5000. Our results show that the duration of the LEV formation period and its steady-state intensity both reduce significantly as $\textit {Re}$ decreases from 1000 to 10. Moreover, the primary mechanisms contributing to LEV stability can vary at different $\textit {Re}$ levels. At $\textit {Re} <200$ , the LEV stability is mainly driven by viscous diffusion. At $200<\textit {Re} <1000$ , the LEV is maintained by two distinct vortex-tilting-based mechanisms, i.e. the planetary vorticity tilting and the radial–tangential vorticity balance. At $\textit {Re}>1000$ , the radial–tangential vorticity balance becomes the primary contributor to LEV stability, in addition to secondary contributions from tip-ward vorticity convection, vortex compression and planetary vorticity tilting. It is further shown that the regions of tip-ward vorticity convection and tip-ward pressure gradient almost overlap at high $\textit {Re}$ . In addition, the contribution of planetary vorticity tilting in LEV stability is $\textit {Re}$ -independent. This work provides novel insights into the various mechanisms, in particular those of vortex tilting, in driving the LEV formation and stability on low- $\textit {Re}$ revolving wings.

Vorticity transport in laminar steady rotating plumes

A steady laminar rotating thermal plume was investigated by the numerical solution of the 3D momentum and energy equations. The flow originated from a low momentum hot jet (Richardson number Ri = 173 and Grashof number Gr = 5000) issued from a small inlet in the bottom wall of a cylindrical domain with a permeable lateral surface that is rotating (Ekman number Ek = 12). Second order accurate calculations of the structure and dynamics of the buoyant vortex were investigated, with specific emphasis on the evolution of the vorticity distributions and their effects on the ensuing vortex. Budgets of the vorticity transport equations were investigated to analyze the genesis of the developed axial vorticity, explaining how the whirling flow was generated. Nonslip and slip bottom boundary conditions allowed the investigation of the impact of the boundary layer on the axial vorticity generation. The results showed that there is a conversion of radial vorticity into axial vorticity. The radial vorticity was found to be generated not only in the boundary layer but also by tilting of the tangential vorticity, which results from buoyancy. Additionally, the boundary layer was found to have a strong impact on the generation of axial vorticity, but not to be necessary to generate the whirl. In fact, a stronger whirl was originated without the effect of the boundary layer, since the axial vorticity was generated closer to the inlet, where additional stretching is provided by the acceleration of the flow.

Leading-edge vortex formation and transient lift generation on a revolving wing at low Reynolds number

Both the transient formation and the stable attachment of leading-edge vortex (LEV) contribute to the high lift generation of an insect wing when it revolves at high angles of attack. In this study, we examined the LEV formation and the transient lift generation on a revolving wing with Reynolds number at 1500 and aspect ratio at 3, using combined computational and experimental methods. The wing started from stationary with a constant angular acceleration within a prescribed chord length of travel at its radius of gyration (i.e. λa), ranging from 0.25 to 2, and then revolved at a constant velocity. Our results showed that the rate of LEV development saturated when λa<1, resulting in a minimum chord length of travel of 2.5 to arrive at a steady LEV. This minimum travel distance agreed well with the prediction based on the vortex formation criterion proposed in other vortex generators. On the other hand, the instantaneous lift generation was strongly dependent on the instantaneous wing velocity and acceleration and therefore exhibited no saturation as λa decreases, which is seen in the LEV formation. The lift generation was attributed to the evolution of tangential vorticity according to the vortex impulse theory. Finally, the instantaneous volume-averaged LEV circulation at different angles of attack scaled well with the instantaneous velocity normal to the leading edge.

Dynamic Stall of a Vertical-Axis Wind Turbine and Its Control Using Plasma Actuation

In this paper, a dynamic stall control scheme for vertical-axis wind turbine (VAWT) based on pulsed dielectric-barrier-discharge (DBD) plasma actuation is proposed using computational fluid dynamics (CFD). The trend of the wind turbine power coefficient with the tip speed ratio is verified, and the numerical simulation can describe the typical dynamic stall process of the H-type VAWT. The tangential force coefficient and vorticity contours of the blade are compared, and the regular pattern of the VAWT dynamic stall under different tip speed ratios is obtained. Based on the understanding the dynamic stall phenomenon in flow field, the effect of the azimuth of the plasma actuation on the VAWT power is studied. The results show that the azimuth interval of the dynamic stall is approximately 60° or 80° by the different tip speed ratio. The pulsed plasma actuation can suppress dynamic stall. The actuation is optimally applied for the azimuthal position of 60° to 120°.

A semi-empirical model for streamwise vortex intensification

Vortex intensification plays an important role in a wide range of flows of engineering interest. One scenario of interest is when a streamwise vortex passes through the contracting streamtube of an aircraft intake. There is, however, limited experimental data of flows of this type to reveal the dominant flow physics and to guide the development of vortex models. To this end, the evolution of wing-tip vortices inside a range of streamtube contractions has been measured using stereoscopic particle image velocimetry. A semi-empirical model has been applied to provide new insight on the role of vorticity diffusion during the intensification process. The analysis demonstrates that for mild flow contractions, vorticity diffusion has a negligible influence due to the low rates of diffusion in the vortex flow prior to intensification and the short convective times associated with the streamtube contraction. As the contraction levels increase, there is a substantial increase in the rates of diffusion which is driven by the greater levels of vorticity in the vortex core. A new semi-empirical relationship, as a function of the local streamtube contraction levels and vortex Reynolds number, has been developed. The model comprises a simple correction to vortex filament theory and provides a significant improvement in the estimation of vortex characteristics in contracting flows. For the range of contractions investigated, errors in the estimation of vortex core radius, peak tangential velocity and vorticity are reduced by an order of magnitude. The model can be applied to estimate the change in vortex characteristics for a range of flows with intense axial strain, such as contracting intake streamtubes and swirling flows in turbomachinery.

A treatment for contaminated interfaces and its application to study the hydrodynamics of a spherical bubble contaminated by surfactants

A numerical model for the contaminated interface is discussed, and then it is applied to investigate detailedly the interfacial surfactant concentration, the interfacial properties and the wake flow of a contaminated spherical bubble. For the present model, the surfactant molecules adsorbed on the bubble surface are assumed to be distributed over the concentration boundary layer adjacent to the bubble. The thickness of concentration boundary layer is obtained through the revised value from a theoretical formula. Then, the interfacial surfactant concentration is evaluated by coupling the transport equations of interfacial and bulk surfactant concentrations with the Navier-Stokes equations. The connection between the tangential stress and the interfacial surfactant concentration is set through the Marangoni stress and the state equation. The current results show that the present numerical model is reliable. The convention from the main flow, the Marangoni effect and the wake vortex determine the distribution of interfacial surfactant concentration on the bubble surface. The gradient of interfacial surfactant concentration along the bubble surface further affects the interfacial properties which react on the surrounding flow as feedbacks. The gradient of interfacial surfactant concentration at the front edge of the “contaminated” interface (FECI) is closely related to the location of FECI to the strongest convection position in the bulk around the bubble. The peak point on the curves of tangential stress and interfacial vorticity corresponds to the inflection point on the curve of interfacial surfactant concentration. The vortex size is affected by the positive pressure gradient at the bubble rear in bulk and the abrupt change of interfacial vorticity at FECI.

A Deeper Analysis of Center-Finding Techniques for Tropical Cyclones in Mesoscale Models. Part I: Low-Wavenumber Analysis

AbstractA deeper analysis of possible errors and inconsistencies in the analysis of vortex asymmetries owing to the placement of centers of tropical cyclones (TCs) in mesoscale models is presented. Previous works have established that components of the 2D and 3D structure of these TCs—primarily radial wind and vertical tilt—can vary greatly depending on how the center of a model TC is defined. This work will seek to expand the previous research on this topic, but only for the 2D structure. To be specific, this work will present how low-wavenumber azimuthal Fourier analyses can vary with center displacement using idealized, parametric TC-like vortices. It is shown that the errors associated with aliasing the mean are sensitive primarily to the difference between the peak of vorticity inside the radius of maximum winds and the average vorticity inside the core. Tangential wind and vorticity aliasing occur primarily in the core; radial wind aliasing spans the whole of the vortex. It is also shown that, when adding low-wavenumber asymmetries, the aliasing is dependent on the placement of the center relative to the location of the asymmetries on the vortex. It is also shown that the primary concern for 2D analysis when calculating the center of a TC is correctly resolving azimuthal wavenumber 0 tangential wind, because errors here will alias onto all higher wavenumbers, the specific structures of which are dependent on the structure of the mean vortex itself.

Influence of a Reverse Delta-Type Add-On Device on Wake Vortex Alleviation

Particle image velocimetry was used in a low-speed wind tunnel to investigate the effect of interactions of vortices produced by a wingtip of a half-span wing (NACA 23012 in landing configuration) and a slender reverse delta-type add-on device placed near the tip on the upper surface of the half-span wing. This work investigates the characteristics of the vortex interactions generated downstream in planes perpendicular to the freestream direction and their dependence on angles of attack at a chord-based Reynolds number of . It was found that the add-on device significantly reduced the tangential velocity, vorticity, and circulation magnitude by up to 82.9, 92.6, and 42.8%, respectively, and increased the resultant vortex core radius by a factor of 6.57. A six-component force balance was used to obtain the aerodynamic performance of the half-span wing model with a reverse delta-type add-on device. It was found that the reverse delta-type add-on device marginally affected the aerodynamic performance of the half-span high-lift configuration wing model.

Superposition of vortex cylinders for steady and unsteady simulation of rotors of finite tip‐speed ratio

AbstractJoukowski introduced in 1912 a helical vortex model to represent the vorticity of a rotor and its wake. For an infinite number of blades but finite tip‐speed ratio, the model consists of a vortex cylinder of longitudinal and tangential vorticity, a root vortex and a bound vortex disk. A superposition of cylinders is used in this paper to model rotors of radially varying circulation. The relations required to form a consistent system of cylinders are derived. The model contains a term which is not accounted for in the standard blade element momentum (BEM) algorithm. This term is identified as the contribution from the pressure drop due to the wake rotation. The BEM algorithm can be corrected to account for this effect. Unlike previous work on the topic, the contribution is derived for a radially varying circulation. A high‐thrust correction is also presented to extend the model. The optimal power coefficient obtained with this model for the constant circulation rotor is assessed and compared with that of existing solutions. Results from prescribed thrust distributions are compared with that of actuator disk simulations. Steady simulations are performed to compare with the BEM algorithm. The model is also applied to compute the velocity field in the entire domain and perform unsteady simulations. Results for an unsteady simulation corresponding to a pitch change of the rotor is used to compare the model with measurements and a BEM code with a dynamic inflow model. Copyright © 2015 John Wiley &amp; Sons, Ltd.

Three-dimensional vortex wake structure of flapping wings in hovering flight

Flapping wings continuously create and send vortices into their wake, while imparting downward momentum into the surrounding fluid. However, experimental studies concerning the details of the three-dimensional vorticity distribution and evolution in the far wake are limited. In this study, the three-dimensional vortex wake structure in both the near and far field of a dynamically scaled flapping wing was investigated experimentally, using volumetric three-component velocimetry. A single wing, with shape and kinematics similar to those of a fruitfly, was examined. The overall result of the wing action is to create an integrated vortex structure consisting of a tip vortex (TV), trailing-edge shear layer (TESL) and leading-edge vortex. The TESL rolls up into a root vortex (RV) as it is shed from the wing, and together with the TV, contracts radially and stretches tangentially in the downstream wake. The downwash is distributed in an arc-shaped region enclosed by the stretched tangential vorticity of the TVs and the RVs. A closed vortex ring structure is not observed in the current study owing to the lack of well-established starting and stopping vortex structures that smoothly connect the TV and RV. An evaluation of the vorticity transport equation shows that both the TV and the RV undergo vortex stretching while convecting downwards: a three-dimensional phenomenon in rotating flows. It also confirms that convection and secondary tilting and stretching effects dominate the evolution of vorticity.

An Investigation of Composite Dropsonde Profiles for Developing and Nondeveloping Tropical Waves during the 2010 PREDICT Field Campaign

AbstractComposite dropsonde profiles are analyzed for developing and nondeveloping tropical waves in an attempt to improve the understanding of tropical cyclogenesis. These tropical waves were sampled by 25 reconnaissance missions during the 2010 Pre-Depression Investigation of Cloud-Systems in the Tropics (PREDICT) field campaign. Comparisons are made between mean profiles of temperature, mixing ratio, relative humidity, radial and tangential winds, relative vorticity, and virtual convective available potential energy (CAPE) for genesis and nongenesis cases. Genesis soundings are further analyzed in temporal progression to investigate whether significant changes in the thermodynamic or wind fields occur during the transition from tropical wave to tropical cyclone.Significant results include the development of positive temperature anomalies from 500 to 200 hPa 2 days prior to genesis in developing waves. This is not observed in the nongenesis mean. Progressive mesoscale moistening of the column is observed within 150 km of the center of circulation prior to genesis. The genesis composite is found to be significantly moister than the nongenesis composite at the middle levels, while comparatively drier at low levels, suggesting that dry air is more detrimental to genesis when located at the middle levels. Time-varying tangential wind profiles reveal an initial delay in intensification, followed by an increase in organization 24 h pregenesis. The vertical evolution of relative vorticity, in addition to a warm-over-cold thermal structure, is more consistent with a top-down than a bottom-up genesis mechanism. Last, CAPE values are much greater for nongenesis than genesis profiles, indicating that greater instability does not necessarily favor genesis.

Structure and formation of dust devil–like vortices in the atmospheric boundary layer: A high-resolution numerical study

[1] The development of dust devil–like vortices in the atmospheric convective boundary layer (CBL) is studied using large-eddy simulation (LES). Special focus is placed on the analysis of the spatial structure of the vortices, the vorticity-generating mechanisms, and how the vortices depend on the larger-scale coherent near-surface flow pattern of the CBL. Vortex centers are automatically detected during the simulation, and a tracking method is developed, which allows us to determine the temporally averaged structures of selected vortices. Also, various vorticity budget terms are calculated. A reference study with high resolution (2 m) and large model domain (2000 × 2000 × 500 grid points) is carried out to account for the dependency of vortex generation on the larger-scale CBL flow pattern, i.e., the near-surface hexagonal cells. Vortices predominantly appear within the vertices of the cells. Their vorticity is maintained by a combination of divergence and twisting effects. Flow visualizations by tracers show that the vortices have an inverted cone-like shape, similar to observed dust devils. Simulated vortex characteristics like tangential velocity or vorticity are at the lower limit of observed values. Strength and number of vortices heavily depend on the background wind. A small background wind enhances vortices, but for a mean wind speed of 4.4 m s−1, vortex generation is significantly reduced, mainly because the near-surface flow changes from a cellular to a more band-like pattern. A new mechanism is suggested, which relates the initial vortex generation to the cellular flow pattern.

A New Parametric Model of Vortex Tangential-Wind Profiles: Development, Testing, and Verification

Abstract A new parametric model of vortex tangential-wind profiles is presented that is primarily designed to depict realistic-looking tangential wind profiles such as those in intense atmospheric vortices arising in dust devils, waterspouts, tornadoes, mesocyclones, and tropical cyclones. The profile employs five key parameters: maximum tangential wind, radius of maximum tangential wind, and three power-law exponents that shape different portions of the velocity profile. In particular, a new parameter is included controlling the broadly or sharply peaked profile in the annular zone of tangential velocity maximum. Different combinations of varying the model parameters are considered to investigate and understand their effects on the physical behaviors of tangential wind and corresponding vertical vorticity profiles. Additionally, the parametric tangential velocity and vorticity profiles are favorably compared to those of an idealized Rankine model and also those of a theoretical stagnant core vortex model in which no tangential velocity exists within a core boundary and a potential flow occurs outside the core. Furthermore, the parametric profiles are evaluated against and compared to those of two other idealized vortex models (Burgers–Rott and Sullivan). The comparative profiles indicate very good agreements with low root-mean-square errors of a few tenths of a meter per second and high correlation coefficients of nearly one. Thus, the veracity of the parametric model is demonstrated.

Evolution of NACA23012 Wake Vortices Structure Using PIV

The formation and development of a wing-tip vortex in a near and extended near field were studied experimentally. A swept-back tapered wing with a NACA23012 cross-section was used as a vortex generator. Particle image velocimetry (PIV) as a whole field velocity measurement technique was used in a low-speed wind tunnel to measure and characterize the wing-tip vortex. Wake structures at successive downstream planes crosswise to the axis of the wake vortices were evaluated in internal and external core radius, maximum tangential velocities, vorticity, and circulation distributions. The effect of angle of attack on vortex parameters was examined at one downstream location. Internal core radius and circulation distributions were nearly constant along the downstream direction. A direct dependence of the circulation and tangential velocity distribution on the angle of attack was evident. The centers of the wing-tip vortices scatter in a circle of radius nearly equal to 1% of the mean wing chord. Meandering ampli...

Using vorticity to define conditions at multiple open boundaries for simulating flow in a simplified vortex settling basin

AbstractIn this paper a method is developed to define multiple open boundary (OB) conditions in a simplified vortex settling basin (VSB). In this method, the normal component of the momentum equation is solved at the OBs, and tangential components of vorticity are calculated by solving vorticity transport equations only at the OBs. Then the tangential vorticity components are used to construct Neumann boundary conditions for tangential velocity components. Pressure is set to its ambient value, and the divergence‐free condition is satisfied at these boundaries by employing the divergence as the Neumann condition for the normal‐direction momentum equation. The 3‐D incompressible Navier–Stokes equations in a primitive‐variable form are solved using the SIMPLE algorithm. Grid‐function convergence tests are utilized to verify the numerical results. The complicated laminar flow structure in the VSB is investigated, and preliminary assessment of two popular turbulence models, k–ε and k–ω, is conducted. Copyright © 2006 John Wiley &amp; Sons, Ltd.