Large eddy simulation of bluff body wake in planar shear flow

Large eddy simulation of planar shear flow past a square cylinder has been investigated. Dynamic Smagorinsky model has been used to model subgrid scale stress. The shear parameter, K, namely the nondimensional streamwise velocity gradient in the lateral direction, is 0.0, 0.1 and 0.2. Reynolds number based on the centerline velocity is fixed at Re=21400. The time and span‐averaged velocity components, pressure coefficient, Reynolds stresses for uniform are in good agreement with the literature. In shear flow the calculated flow structure and mean velocity components are shown to be markedly different from those of the uniform flow. With increasing shear parameter, the cylinder wake is dominated by clockwise vortices. Both the velocity components in shear flow are compared with respective components in uniform flow. Comparison of normal and shear stresses between shear and no shear case have also been presented. Copyright © 2009 John Wiley & Sons, Ltd.     

Flow and heat transfer over a backward-facing step with a cylinder mounted near its top corner

A study was made to see if it is possible to enhance the heat transfer in the downstream region of a backward-facing step, where heat transfer is normally deteriorated, by the insertion of a cylinder near the top corner of the step. Cylinder size and streamwise position of the cylinder were kept constant but the cross-stream position of the cylinder was changed in three steps. Results of the heat transfer experiment, flow visualization, and measurement of the averaged and fluctuating flow fields were reported. When the cylinder was mounted at a position, a little higher than the top surface of the step, a jet-like flow pattern emerged in the averaged velocity profile beneath the cylinder and the recirculating flow was intensified. Therefore, the velocity of recirculating flow near the wall is increased at some streamwise positions. Additionally, the velocity fluctuation was intensified not only in the shear layer between the jet-like flow and the recirculating flow regions but also in the near wall region, resulting in the effective augmentation of heat transfer in this case. Therefore, it is concluded that the mounting of a cylinder is effective in the enhancement of deteriorated heat transfer in the recirculating flow region, if its is mounted in a proper position.     

An experimental study of a turbulent shear layer at a clean and contaminated free-surface

An experimental study was performed to measure the flow properties of a vertically-orientated shear layer in the vicinity of a free-surface. The effect of surface contamination on the near surface flow field was also determined. Digital Particle Image Velocimetry was used to measure instantaneous and averaged velocity, vorticity, and Reynolds stresses. Results show that the presence of surfactants can cause directional shifts of the shear layer, as well as an overall damping of the turbulence in the vicinity of the free-surface, except in the vicinity of a Reynolds ridge where an increase in Reynolds stress was observed.     

Flow around a cylinder at the beginning of the critical region

Results of experiments with a turbulent flow around a transversely aligned circular cylinder located at identical distances from the walls of a rectangular channel are reported. Data on averaged velocity fields around the cylinder are obtained by means of particle image velocimetry (PIV). Based on these fields, the near wake behind the cylinder is studied, and the kinematic characteristics for flow regimes with and without cavitation are compared. Based on the vector fields of averaged velocity, the angles of separation of the boundary layer from the cylinder surface in the considered flow regimes are determined. The drag coefficients of the cylinder for different flow regimes are calculated. It is demonstrated that the vortex region behind the cylinder and the drag coefficient of the cylinder increase in the case with cavitation. It is also shown that vortex shedding from the cylinder may be irregular, despite the fact that this process is quasi-periodic for most of the time.     

Development of a Two-velocities Hybrid RANS-LES Model and its Application to a Trailing Edge Flow

The flow around a trailing edge is computed with a new hybrid method designed to more clearly separate the effects of total and sub-grid turbulent stress-modelling on the time-averaged and instantaneous velocity fields, and in turn, mean momentum and kinetic energy balances. These two velocity fields independently define Reynolds averaged and sub-grid-scale viscosities, and distinct stresses, at the same location. In particular, resolved eddies can emerge, or sweep in and out of the Reynolds averaged near wall layer, without being dampened by higher levels of the viscosity in this RANS dominated layer. The two-field hybrid model, first tested on channel flows, gives accurate predictions of mean velocities and stresses for different Reynolds numbers and coarse meshes. For the trailing edge flow the results of the hybrid model are close to the reference fine LES for mean velocity and turbulent content, whereas the DES-SST on the same coarse mesh gives too early separation.     

Turbulence in a three‐dimensional wall‐bounded shear flow

A new turbulent flow with distinct three‐dimensional characteristics has been designed in order to study the impact of mean‐flow skewing on the turbulent coherent vortices and Reynolds‐averaged statistics. The skewing of a unidirectional plane Couette flow was achieved by means of a spanwise pressure gradient. Direct numerical simulations of the statistically steady Couette–Poiseuille flow enabled in‐depth explorations of the turbulence field in the skewed flow. The imposition of a modest spanwise gradient turned the mean flow about 8° away from the original Couette flow direction and this turning angle remained nearly the same over the entire cross section. Nevertheless, a substantial non‐alignment between the turbulent shear stress angle and the mean velocity gradient angle was observed. The structure parameter turned out to slightly exceed that in the pure Couette flow, contrary to the observations made in some other three‐dimensional shear flows. Coherent flow structures, which are known to be associated with the Reynolds shear stress in near‐wall regions, were identified by the λ₂‐criterion. Instantaneous and ensemble‐averaged vortices resembled those found in the unidirectional Couette flow. In the skewed flow, however, the vortex structures were turned to align with the local mean‐flow direction. The conventional symmetry between Case 1 and Case 2 vortices was broken due to the mean‐flow three‐dimensionality. The turning of the coherent vortices and the accompanying symmetry‐breaking gave rise to secondary and tertiary turbulent shear stress components. By averaging the already ensemble‐averaged shear stresses associated with Case 1 and Case 2 vortices in the homogeneous directions, a direct link between the educed near‐wall structures and the Reynolds‐averaged turbulent stresses was established. These observations provide evidence in support of the hypothesis that the structural model proposed for two‐dimensional turbulent boundary layers remains valid also in flows with moderate mean three‐dimensionality. Copyright © 2009 John Wiley & Sons, Ltd.     

Stabilization of cylinder wakes in shallow water flows by means of roughness elements: an experimental study

Shallow wakes that occur in a wide range of natural flows tend to generate instabilities that develop into large, 2D coherent structures (2DCS). We present the results of an experimental study to stabilize shallow wakes by local, enhanced bottom roughness. Two successful stabilization strategies are compared to a base case of an unsteady bubble wake. First, localized bed roughness is placed in the lateral shear layers near the shoulders of the cylinder. Second, a local roughness element is placed at the end of the recirculation bubble, in the downstream region where large-scale vortices would normally shed. Dye visualization is used to assess the qualitative behavior of the wake, and two-component laser Doppler velocimetry (LDV) measurements are made to measure the Reynolds stress distributions and time-averaged velocity profiles. In both stabilization cases, a minimum patch size of the enhanced roughness elements is required for stabilization, which depends on the momentum thickness of the shear layers and the locations of enhanced Reynolds shear stresses. The main effect of the wake stabilization is a reduction in momentum exchange with the ambient flow due to damping of the large 2DCS. This reduction in eddy diffusivity results in a narrower wake and a slower decay of the centerline velocity deficit with downstream distance compared to the base case of an unsteady bubble wake.     

Orthogonal wavelet analysis of turbulent wakes behind various bluff bodies

The multi-scale structures of turbulent wakes generated by three kinds of bluff body, i.e. circular cylinder, square cylinder and compound of cylinder and square (CS) cylinders, have been experimentally investigated in this paper. Firstly, the instantaneous velocity fields and vorticity were measured by the high-speed PIV technique in a circulating water channel. The instantaneous streamlines and corresponding normalized vorticity contours are obtained at a Reynolds number of 5600. Then one- and two-dimensional wavelet multi-resolution technique was used to analyze the instantaneous velocities and vorticity measured by the high-speed PIV. The turbulence structures were separated into a number of subsets based on their central frequencies, which are linked with the turbulence scales. The instantaneous vorticity and Reynolds shear stresses of various scales were examined and compared between the three generators. It is found that the large-scale turbulent structure makes the largest contribution to the vorticity and Reynolds shear stresses for the three wake generators and exhibits a strong dependence upon the initial conditions or the wake generators. The large-scale vorticity and the sizes of vortex in the circular and square cylinders are larger than those in the CS cylinder wake. The contributions to the Reynolds shear stresses from the large-scale turbulent structures account for 90-96% to the measured maximum Reynolds shear stresses for the three wakes. However, the small-scale structures make less contribution to the vorticity and Reynolds shear stresses.     

Using digital holographic microscopy for simultaneous measurements of 3D near wall velocity and wall shear stress in a turbulent boundary layer

A digital holographic microscope is used to simultaneously measure the instantaneous 3D flow structure in the inner part of a turbulent boundary layer over a smooth wall, and the spatial distribution of wall shear stresses. The measurements are performed in a fully developed turbulent channel flow within square duct, at a moderately high Reynolds number. The sample volume size is 90 × 145 × 90 wall units, and the spatial resolution of the measurements is 3–8 wall units in streamwise and spanwise directions and one wall unit in the wall-normal direction. The paper describes the data acquisition and analysis procedures, including the particle tracking method and associated method for matching of particle pairs. The uncertainty in velocity is estimated to be better than 1 mm/s, less than 0.05% of the free stream velocity, by comparing the statistics of the normalized velocity divergence to divergence obtained by randomly adding an error of 1 mm/s to the data. Spatial distributions of wall shear stresses are approximated with the least square fit of velocity measurements in the viscous sublayer. Mean flow profiles and statistics of velocity fluctuations agree very well with expectations. Joint probability density distributions of instantaneous spanwise and streamwise wall shear stresses demonstrate the significance of near-wall coherent structures. The near wall 3D flow structures are classified into three groups, the first containing a pair of counter-rotating, quasi streamwise vortices and high streak-like shear stresses; the second group is characterized by multiple streamwise vortices and little variations in wall stress; and the third group has no buffer layer structures.     

Turbulent separated reattached flow in a two-dimensional curved-wall diffuser

A turbulent separation-reattachment flow in a two-dimensional asymmetrical curved-wall diffuser is studied by a two-dimensional laser doppler velocimeter. The turbulent boundary layer separates on the lower curved wall under strong pressure gradient and then reattaches on a parallel channel. At the inlet of the diffuser, Reynolds number based on the diffuser height is 1.2×10⁵ and the velocity is 25.2m/s. The results of experiments are presented and analyzed in new defined streamline-aligned coordinates. The experiment shows that after Transitory Detachment Reynolds shear stress is negative in the near-wall backflow region. Their characteristics are approximately the same as in simple turbulent shear layers near the maximum Reynolds shear stress. A scale is formed using the maximum Reynolds shear stresses. It is found that a Reynolds shear stress similarity exists from separation to reattachment and the Schofield-Perry velocity law exists in the forward shear flow. Both profiles are used in the experimental work that leads to the design of a new eddy-viscosity model. The length scale is taken from that developed by Schofield and Perry. The composite velocity scale is formed by the maximum Reynolds shear stress and the Schofield-Perry velocity scale as well as the edge velocity of the boundary layer. The results of these experiments are presented in this paper.     

A hybrid RANS/LES simulation of high-Reynolds-number channel flow using additional filtering at the interface

A hybrid method combining large eddy simulation (LES) with the Reynolds-averaged Navier-Stokes (RANS) equation is used to simulate a turbulent channel flow at high Reynolds number. It is known that the mean velocity profile has a mismatch between the RANS and LES regions in hybrid simulations of a channel flow. The velocity mismatch is reproduced and its dependence on the location of the RANS/LES interface and on the type of RANS model is examined in order to better understand its properties. To remove the mismatch and to obtain better velocity profiles, additional filtering is applied to the velocity components in the wall-parallel planes near the interface. The additional filtering was previously introduced to simulate a channel flow at low Reynolds number. It is shown that the filtering is effective in reducing the mismatch even at high Reynolds number. Profiles of the velocity fluctuations of runs with and without the additional filtering are examined to help understand the reason for the mismatch. Due to the additional filtering, the wall-normal velocity fluctuation increases at the bottom of the LES region. The resulting velocity field creates the grid-scale shear stress more efficiently, and an overestimate of the velocity gradient is removed. The dependence of the velocity profile on the grid point number is also investigated. It is found that the velocity gradient in the core region is underestimated in the case of a coarse grid. Attention should be paid not only to the velocity mismatch near the interface but also to the velocity profile in the core region in hybrid simulations of a channel flow at high Reynolds number. PACS47.27.Eq; 47.27.Nz; 47.60.+i     

Numerical analysis of developing turbulent flow in a 180° bend tube by an algebraic Reynolds stress model

A numerical analysis has been performed for three‐dimensional developing turbulent flow in a 180° bend tube with straight inlet and outlet section used by an algebraic Reynolds stress model. To our knowledge, numerical investigations, which show the detailed comparison between calculated results and experimental data including distributions of Reynolds stresses, are few and far between. From this point of view, an algebraic Reynolds stress model in conjunction with boundary‐fitted co‐ordinate system is applied to a 180° bend tube in order to predict the anisotropic turbulent structure precisely. Calculated results are compared with the experimental data including distributions of Reynolds stresses. As a result of this analysis, it has been found that the calculated results show a comparatively good agreement with the experimental data of the time‐averaged velocity and the secondary vectors in both the bent tube and straight outlet sections. For example, the location of the maximum streamwise velocity, which appears near the top or bottom wall in the bent tube, is predicted correctly by the present method. As for the comparison of Reynolds stresses, the present method has been found to simulate many characteristic features of streamwise normal stress and shear stresses in the bent tube qualitatively and has a tendency to under‐predict its value quantitatively. Judging from the comparison between the calculated and the experimental results, the algebraic Reynolds stress model is applicable to the developing turbulent flow in a bent tube that is known as a flow with a strong convective effect. Copyright © 2005 John Wiley & Sons, Ltd.     

A reassessment of the wall effect of non-newtonian flow of polymer solutions

An apparatus for checking slip interpretation of flow anomalies in the laminar capillary flow of macromolecular solutions is described. It consists of a two-dimensional flow channel, having a uniform width of 1.5 inch and an alternative, convergent taper that is adjustable. Dilute aqueous solutions of the polymers Carbopol, Natrosol, and Polyox are recirculated in steady laminar flow from a large reservoir. Velocities, pressures, and wall shear stresses are measured. Local velocities are obtained by the local injection of conductive tracer fluid, whose passage is sensed by sets of electrodes stationed along the flow. Wall shear stresses are measured on a small, freely displaceable, traction surface flush with the channel wall. The tests cover concentrations of Carbopol of 0.1% to 0.4%, Natrosol of 0.5% to 1%, and Polyox of 0.5% to 1%. Approximate viscosities range from about 10 to 1000 cP. Wall shear rates up to 1000 s^–1 are attained.The results are in good agreement with the established viscometric properties of the tested materials. Actual shear stresses agree with those calculated from pressure drops, and velocities exhibit no detectable anomaly near the wall. Any velocity anomaly in the experiment would have to be less than 3% of the mean flow velocity.An order of magnitude analysis, based on particulate behavior, is made in an attempt to delineate an underlying mechanism.     

Near-wake flow structure of elliptic cylinders close to a free surface: effect of cylinder aspect ratio

The flow fields behind elliptic cylinders adjacent to a free surface were investigated experimentally in a circulating water channel. A range of cylinder aspect ratios (AR=2, 3, 4) were considered, while the cross-sectional area of the elliptical cylinder was kept constant. The main objective of this study was to investigate the effect of cylinder aspect ratio and a free surface on the flow structure in the near-wake behind elliptic cylinders. For each elliptic cylinder, the flow structure was analyzed for various values of the submergence depth of the cylinder beneath the free surface. The flow fields were measured using a single-frame double-exposure PIV (Particle Image Velocimetry) system. For each experimental condition, 350 instantaneous velocity fields were obtained and ensemble-averaged to obtain the mean velocity field and spatial distribution of the mean vorticity statistics. The results show that near-wake can be classified into three typical flow patterns: formation of a Coanda flow, generation of substantial jet-like flow, and attachment of this jet flow to the free surface. The general flow structure observed behind the elliptic cylinders resembles the structure previously reported for a circular cylinder submerged near a free surface. However, the wake width and the angle of downward deflection of the shear layer developed from the lower surface of the elliptic cylinder differ from those observed for a circular cylinder. These trends are enhanced as cylinder aspect ratio is increased. In addition, the free surface distortion is also discussed in the paper.     

Forced Convection Heat Transfer from a Finite-Height Cylinder

This paper presents a large eddy simulation of forced convection heat transfer in the flow around a surface-mounted finite-height circular cylinder. The study was carried out for a cylinder with height-to-diameter ratio of 2.5, a Reynolds number based on the cylinder diameter of 44 000 and a Prandtl number of 1. Only the surface of the cylinder is heated while the bottom wall and the inflow are kept at a lower fixed temperature. The approach flow boundary layer had a thickness of about 10% of the cylinder height. Local and averaged heat transfer coefficients are presented. The heat transfer coefficient is strongly affected by the free-end of the cylinder. As a result of the flow over the top being downwashed behind the cylinder, a vortex-shedding process does not occur in the upper part, leading to a lower value of the local heat transfer coefficient in that region. In the lower region, vortex-shedding takes place leading to higher values of the local heat transfer coefficient. The circumferentially averaged heat transfer coefficient is 20 % higher near the ground than near the top of the cylinder. The spreading and dilution of the mean temperature field in the wake of the cylinder are also discussed.     

Three-dimensional particle-tracking velocimetry measurement of turbulence statistics and energy budget in a backward-facing step flow

Using a three-dimensional (3-D) particle-tracking velocimeter, detailed turbulent flow measurements were made in a plane channel with a one-sided 50% abrupt expansion, which acted as a backward-facing step. The turbulent channel flow reached a fully developed state well upstream of the step. The Reynolds number based on the upstream centerline velocity and the step height H was 5540. With the mean reattachment point located at 6.51H downstream of the step, the measurement region ranged from −2H upstream to 12H downstream of the step. Various turbulent statistics and the energy budget were calculated from numerous instantaneous vector distributions. As in previous experimental investigations, the Reynolds normal and shear stresses had maximum values upstream of the reattachment. The stress anisotropy tensor revealed a peculiar phenomenon near the reattachment wall, wherein the spanwise normal stress was the largest among the three normal stresses. The triple velocity correlations indicated large values in the separating shear layer, and hence the turbulent diffusion was a major term in the energy budget. Comparison was made between the present results and those of the direct numerical simulation (DNS) of Le et al. (1993), and it was found that the mean and fluctuating velocities, the Reynolds shear stress, and the turbulent energy budget were in excellent agreement, although there was a considerable difference in the inflow conditions.     

Momentum and heat transport in a finite-length cylinder wake

This paper reports an experimental study of turbulent momentum and heat transport in the wake of a wall-mounted finite-length square cylinder, with its length-to-width ratio L/d = 3–7. The cylinder was slightly heated so that heat produced could be considered as a passive scalar. A moveable three-wire probe (a combination of an X-wire and a cold wire) was used to measure velocity and temperature fluctuations at a Reynolds number of 7,300 based on d and the free-stream velocity. Measurements were performed at 10 and 20d downstream of the cylinder at various spanwise locations. Results indicate that L/d has a pronounced effect on Reynolds stresses, temperature variance and heat fluxes. The downwash flow from the free end of the cylinder acts to suppress spanwise vortices and, along with the upwash flow from the cylinder base, makes the finite-length cylinder wake highly three-dimensional. Reynolds stresses, especially the lateral normal stress, are significantly reduced as a result of suppressed spanwise vortices at a small L/d. The downwash flow acts to separate the two rows of spanwise vortices further apart from the wake centerline, resulting in a twin-peak distribution in temperature variance. While the downwash flow entrains high-speed fluid into the wake, responsible for a small deficit in the time-averaged streamwise velocity near the free end, it does not alter appreciably the distribution of time-averaged temperature. It has been found that the downwash flow gives rise to a counter-gradient transport of momentum about the central region of the wake near the free end of the cylinder, though such a counter-gradient transport does not occur for heat transport.     

FLOW PAST TWO CYLINDERS IN TANDEM: INSTANTANEOUS AND AVERAGED FLOW STRUCTURE

A technique of high-image-density particle image velocimetry is employed to characterize the instantaneous and averaged patterns of velocity, vorticity and Reynolds stress due to flow past two cylinders in tandem. These features of the flow patterns are characterized in the gap region as a function of the distance between the cylinders. In turn, they are related to the patterns in the near-wake of the two-cylinder system. Along the gap between the cylinders, small-scale concentrations of vorticity are formed in the separated shear layers. These concentrations buffet the surface boundary layer on the downstream cylinder, and thereby influence the eventual shedding of large-scale vortices. Within the gap, the instantaneous structure of the recirculation zones can exhibit both symmetrical and asymmetrical patterns. In the near-wake of the downstream cylinder, the form of the vortex shedding, as well as the averaged patterns of the flow structure, are substantially altered, relative to the case of a single cylinder. The width of the near-wake, as represented by averaged patterns of vorticity, is substantially narrower and the magnitudes of the peak Reynolds stress are significantly attenuated. On the other hand, if the gap region is sufficiently large such that Kármán-like vortices form between the cylinders, the near-wake of the downstream cylinder shows distinctive patterns, and both the wake width and the magnitude of the Reynolds stresses become larger, relative to those at smaller gap width.     

Direct numerical simulation of a turbulent Couette-Poiseuille flow,part 2: Large- and very-large-scale motions

A direct numerical simulation dataset of a fully developed turbulent Couette-Poiseuille flow is analyzed to investigate the spatial organization of streamwise velocity-fluctuating u-structures on large and very large scales. Instantaneous and statistical flow fields show that negative-u structures with a small scale on a stationary bottom wall grow throughout the centerline due to the continuous positive mean shear, and they penetrate to the opposite moving wall. The development of an initial vortical structure related to negative-u structures on the bottom wall into a large-scale hairpin vortex packet with new hairpin vortices, which are created upstream and close to the wall, is consistent with the auto-generation process in a Poiseuille flow (Zhou et al., J. Fluid Mech., vol. 387, 1999, pp. 353–396). Although the initial vortical structure associated with positive-u structures on the top wall also grows toward the bottom wall, the spatial development of the structure is less coherent with weak strength due to the reduced mean shear near the top wall, resulting in less turbulent energy on the top wall. The continuous growth of the structures from a wall to the opposite wall explains the enhanced wall-normal transport of the streamwise turbulent kinetic energy near the centerline. Finally, an inspection of the time-evolving instantaneous fields and conditional averaged flow fields for the streamwise growth of a very long structure near the centerline exhibits that a streamwise concatenation of adjacent large-scale u-structures creates a very-large-scale structure near the channel centerline.     

Effect of system rotating on turbulent boundary layer flow

This paper experimentally investigated the effect of rotating on the turbulent boundary layer flow using hot-wire. The experiments were completed in a rotating rig with a vertical axis and four measured positions along the streamwise direction in channel, which focuses on the flow flied in the rotating channel. The rotating effects on velocity profile, wall shear stress and semi-logarithmic mean velocity profile are discussed in this paper. The results indicated that: due to the Coriolis force induced by rotating, the phenomenon of velocity deficit happens near the leading side. The velocity deficit near the leading side, do not increase monotonically with the increase of Ro. The trend of the velocity deficit near the leading side is also affected by the normal component of pressure gradient, which is another important force in the cross-section of the rotating channel. The wall shear stress near the trailing side is larger than that on the leading side, and the semi-logarithmic mean velocity profile is also different under rotating effects. The phenomenon reveals that the effect of rotation penetrates into the logarithm region, and the flow near the leading side tends to turn into laminar under the effect of rotation. The rotation correction of logarithmic law is performed in current work, which can be used in the wall function of CFD to increase the simulating accuracy at rotating conditions.