Absolute and convective instabilities of two-dimensional bluff body wakes in ground effect

Local and global instabilities are investigated of wakes of general two-dimensional bluff bodies placed near and parallel to a plane boundary or ground. A spatio-temporal linear stability analysis is first applied to a four-parameter family of local wake profiles to investigate the fundamental local stability characteristics of the wake in ground effect. The analysis shows significant dependencies of the stability characteristics of the wake on the distance from the wake centreline to the ground (normalised by the wake width), and also on the velocity ratio of the near- and far-ground sides of the wake. The analysis is then compared with earlier experiments on a circular cylinder to examine, according to the transition scenario of the steep global modes, the streamwise variation of the local stability characteristics of the wake in ground effect. The comparison indicates that the near wake region of the cylinder changes from being absolutely unstable to being convectively unstable when the cylinder comes down into the near-ground range in which the von Kármán-type vortex shedding from the cylinder is suppressed, being qualitatively consistent with the transition scenario for general wake-type flows. A possible explanation is also given for the counter-intuitive relation between the thickness of the boundary layer on the ground and the critical gap distance for the cessation of the von Kármán-type vortex shedding in ground effect.     

Numerical investigation of confined wakes behind a square cylinder in a channel

The structure of confined wakes behind a square cylinder in a channel is investigated via the numerical solution of the unsteady Navier–Stokes equations. Vortex shedding behind the cylinder induces periodicity in the flow field. Details of the phenomenon are simulated through numerical flow visualization. The unsteady periodic wake can be characterized by the Strouhal number, which varies with the Reynolds number and the blockage ratio of the channel. The periodicity of the flow is, however, damped in the downstream region of a long duct. This damping may be attributed to the influence of side walls on the flow structure.     

Direct numerical simulation of turbulent wake behind a surface-mounted square cylinder

In this research, direct numerical simulation has been performed to study the turbulent wake behind a wall-mounted square cylinder with aspect ratio 4 and Reynolds number 12 000 (based on the free-stream velocity and obstacle side length) in a developing boundary layer. Owing to the relatively high Reynolds number and high aspect ratio of the cylinder tested, the wake is wide spread behind the cylinder and exhibits complex and energetic vortex motions. The lateral and tip vortex shedding patterns at different frequencies, coherent structures downstream of the obstacle, the production rate and distribution of turbulent kinetic energy, and the instantaneous pressure distribution in the wake region have been thoroughly investigated. In order to validate the numerical results, the first- and second-order flow statistics obtained from the simulations have been carefully compared against available wind-tunnel measurement data.     

Orthogonal wavelet analysis of counter gradient transport phenomena in turbulent asymmetric channel flow

In this paper four families of orthogonal wavelets are applied to analyze the turbulent counter gradient transport phenomena in fully developed asymmetric channel flows. The results show that: (1) In the instance of counter gradient transport, the principal scale of the coherent structure is responsible for the strong local counter gradient transport; (2) Counter gradient transport phenomena have a strong effect on the intermittency of turbulence; (3) Non-Gaussian part of the principal coherent structure is essential for counter gradient transport phenomena.The project supported by the National Natural Science Foundation of China (10272071, 10472063)     

Wavelet analysis of unsteady flows: Application on the determination of the Strouhal number of the transient wake behind a single cylinder

This paper presents experimental results of the accelerating and decelerating flow in the wake of a cylinder obtained by means of hot wire anemometry measurements in a wind tunnel with high blockage ratio. The analysis was done in Fourier and wavelet spaces. The Strouhal number for Reynolds numbers up to 3 × 10⁴ was studied in a transient flow and compared with the results obtained from steady flows at several velocities uniformly distributed from Re = 1.7 × 10³ to 3 × 10⁴. Results show that the wavelet analysis is a valuable tool to deal with both transient and stationary random phenomena and that is able to capture the characteristics of the transient flow as well as the Fourier analysis can do with the steady state acquisitions.     

LES and RANS for Turbulent Flow over Arrays of Wall-Mounted Obstacles

Large-eddy simulation (LES) has been applied to calculate the turbulent flow over staggered wall-mounted cubes and staggered random arrays of obstacles with area density 25%, at Reynolds numbers between 5 × 10³ and 5 10⁶, based on the free stream velocity and the obstacle height. Re = 5 × 10³ data were intensively validated against direct numerical simulation (DNS) results at the same Re and experimental data obtained in a boundary layer developing over an identical roughness and at a rather higher Re. The results collectively confirm that Reynolds number dependency is very weak, principally because the surface drag is predominantly form drag and the turbulence production process is at scales comparable to the roughness element sizes. LES is thus able to simulate turbulent flow over the urban-like obstacles at high Re with grids that would be far too coarse for adequate computation of corresponding smooth-wall flows. Comparison between LES and steady Reynolds-averaged Navier-Stokes (RANS) results are included, emphasising that the latter are inadequate, especially within the canopy region.     

End effects of nominally two-dimensional thin flat plates

Differences in the structure and dynamics of nominally two-dimensional turbulent wakes are investigated experimentally for a thin flat plate, normal to a uniform flow, with two different end conditions: with and without end plates. Both cases are characterized by Karman-like vortex shedding with broadband low frequency unsteadiness. Both wakes evidence a low frequency flapping motion in addition to the slowly drifting base flow common to cylinder wakes. For the case without end plates, an interaction between the drift motion and the vortex formation process is associated with a much stronger modulation of the quasiperiodic vortex shedding amplitude when compared to the case with end plates where a flapping motion is more strongly expressed. These dynamics underlie structural differences in the mean wake and Reynolds stress fields.     

Numerical modeling of turbulent compound channel flow using the lattice Boltzmann method

The flow of water in a straight compound channel with prismatic cross section is investigated with a relatively new tool, the lattice Boltzmann method. The large eddy simulation model is added in the lattice Boltzmann model for nonlinear shallow water equations (LABSWE^TM) so that the turbulence, caused by lateral exchange of momentum in the shear layer between the main channel and floodplain, can be taken into account and modeled efficiently. To validate the numerical model, a symmetrical compound channel with trapezoidal main channel and flat floodplain is tested. Similar to most natural watercourses, the floodplain has higher roughness values than the main channel. Different relative depths, D_r (the ratio of the depth of flow on the floodplain to that in the main channel), are considered. The Reynolds number is set at 30 000 in the main channel. The lateral distributions of the longitudinal velocity, the boundary shear stress, the Reynolds stress and the apparent shear stress across the channel are obtained after the large eddy simulation is performed. The results of numerical simulations are compared with the available experiment data, which show that the LABSWE^TM is capable of modeling the features of flow turbulence in compound channels and is sufficiently accurate for practical applications in engineering. Copyright © 2008 John Wiley & Sons, Ltd.     

Effect of streamline curvature on flow field of a turbulent plane jet in cross-flow

The effects of the streamline curvature and finite edge velocity on the flow field of a turbulent plane jet in cross-flow are studied numerically by incorporating the curvature effect in the k–ε turbulence model. The improvement in the predictions by the streamline curvature model is assessed by comparing its prediction with those by the standard k–ε model. The predictions by both the models are compared with available experimental data. It has been observed that the performance of the k–ε model with streamline curvature modification is superior to the standard k–ε model.     

Multi-resolution analysis of wavelet transform on pressure fluctuations in an L-valve

A novel diagnostic method to characterize the flow patterns in an 80 mm-i.d. L-valve had been developed by using multi-resolution analysis (MRA) of wavelet transformation on the pressure fluctuation signals which were acquired from the standpipe and the horizontal part of L-valve. Parameters including the aeration rate, aeration positions, riser gas velocity and composition of binary particle mixture (194-μm and 937-μm sand particles) were used to investigate the relationship of performance of L-valve and its pressure fluctuations. By means of MRA, the original pressure fluctuations were divided into multi-scale signals. They were macro-scale, meso-scale and micro-scale successfully described the structures of gas–solid flow in the L-valve, such as the gas bubbles/slugs, dune-ripple flow, suspension particle flow, etc.     

Propagation of a pre-existing turbulent fluid fracture

The propagation of rough and smooth wall pre-existing turbulent fluid fractures is investigated. The laminar fluid fracture is included as a special case for comparison. Lubrication theory is assumed to apply in the fracture and turbulence is introduced through the wall shear stress. The Perkins–Kern–Nordgren approximation is made in which the fluid pressure is proportional to the half-width of the fracture. The fracture half-width satisfies a non-linear diffusion equation. By using a linear combination of the Lie point symmetries of the non-linear diffusion equation a group invariant solution for the fracture length, volume and half-width is derived. The evolution of the length, half-width and mean flow velocity is analysed for a range of working conditions at the fracture entry. It is found that the mean flow velocity increases approximately linearly along the fracture.     

Multi-scale analysis of subgrid stress and energy dissipation in turbulent channel flow

In present study, the subgrid scale （SGS） stress and dissipation for multiscale formulation of large eddy simulation are analyzed using the data of turbulent channel flow at Ret = 180 obtained by direct numerical simulation. It is found that the small scale SGS stress is much smaller than the large scale SGS stress for all the stress components. The dominant contributor to large scale SGS stress is the cross stress between small scale and subgrid scale motions, while the cross stress between large scale and subgrid scale motions make major contributions to small scale SGS stress. The energy transfer from resolved large scales to subgrid scales is mainly caused by SGS Reynolds stress, while that between resolved small scales and subgrid scales are mainly due to the cross stress. The multiscale formulation of SGS models are evaluated a priori, and it is found that the small- small model is superior to other variants in terms of SGS dissipation.     

Numerical analysis of turbulent flow in a rotating U-bend with roughened walls

A numerical analysis has been performed for a developing turbulent flow in a rotating U-bend of strong curvature with rib-roughened walls using an anisotropic turbulent model. In this calculation, an algebraic Reynolds stress model is used to precisely predict Reynolds stresses, and a boundary-fitted coordinate system is introduced as a method of coordinate transformation to set the exact boundary conditions along the complicated shape of U-bend with rib-roughened walls. Calculated results for mean velocity and Reynolds stresses are compared to the experimental data in order to validate the proposed numerical method and the algebraic Reynolds stress model. Although agreement is certainly not perfect in all details, the present method can predict characteristic velocity profiles and reproduce the separated flow generated near the outer wall, which is located just downstream of the curved duct. The Reynolds stresses predicted by the proposed turbulent model agree well with the experimental data, except in regions of flow separation.     

Numerical analysis of turbulent structure in compound meandering open channel by algebraic Reynolds stress model

The turbulent flow in a compound meandering channel with a rectangular cross section is one of the most complicated turbulent flows, because the flow behaviour is influenced by several kinds of forces, including centrifugal forces, pressure‐driven forces and shear stresses generated by momentum transfer between the main channel and the flood plain. Numerical analysis has been performed for the fully developed turbulent flow in a compound meandering open‐channel flow using an algebraic Reynolds stress model. The boundary‐fitted coordinate system is introduced as a method for coordinate transformation in order to set the boundary conditions along the complicated shape of the meandering open channel. The turbulence model consists of transport equations for turbulent energy and dissipation, in conjunction with an algebraic stress model based on the Reynolds stress transport equations. With reference to the pressure–strain term, we have made use of a modified pressure–strain term. The boundary condition of the fluctuating vertical velocity is set to zero not only for the free surface, but also for computational grid points next to the free surface, because experimental results have shown that the fluctuating vertical velocity approaches zero near the free surface. In order to examine the validity of the present numerical method and the turbulent model, the calculated results are compared with experimental data measured by laser Doppler anemometer. In addition, the compound meandering open channel is clarified somewhat based on the calculated results. As a result of the analysis, the present algebraic Reynolds stress model is shown to be able to reasonably predict the turbulent flow in a compound meandering open channel. Copyright © 2005 John Wiley & Sons, Ltd.     

Numerical analysis of characteristic features of shallow and deep cavity in supersonic flow

Flow past open cavities are numerically simulated at a Mach number of 1.5, and Reynolds number, based on initial momentum thickness at the front lip of cavity, of 3333 for variable depths (D) with constant length (L). The dominant frequency of oscillation shows a sudden jump when there is a transition from shallow (L/D > 1) to deep cavity (L/D < 1). The vorticity thickness displays two different growth rates along the length of cavity: (1) initial lower spreading rate, followed by (2) higher spreading rate. The lower spreading rate of shear layer is dictated by the type of cavity (either shallow or deep), while the higher spreading rate is directly related to the amplitude of oscillations. Proper orthogonal decomposition (POD) is implemented to visualise the coherent structures based on their energy content. The first two POD spatial structures in the shallow cavity represent vortex shedding, while in the deep cavity, they comprise vortex pairing interactions as in mixing layer. The higher POD modes contain coherent structures at mixed frequencies. The behaviour of coherent structures associated with a temporal frequency is further investigated using dynamic mode decomposition (DMD). The higher DMD modes confirm the dominance of mixing layer behaviour in the deep cavity.     

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.     

Numerical analysis of turbulent flow separation in a rectangular duct with a sharp 180‐degree turn by algebraic Reynolds stress model

Turbulent flow in a rectangular duct with a sharp 180‐degree turn is difficult to predict numerically because the flow behavior is influenced by several types of forces, including centrifugal force, pressure‐driven force, and shear stress generated by anisotropic turbulence. In particular, this type of flow is characterized by a large‐scale separated flow, and it is difficult to predict the reattachment point of a separated flow. Numerical analysis has been performed for a turbulent flow in a rectangular duct with a sharp 180‐degree turn using the algebraic Reynolds stress model. A boundary‐fitted coordinate system is introduced as a method for coordinate transformation to set the boundary conditions next to complicated shapes. The calculated results are compared with the experimental data, as measured by a laser‐Doppler anemometer, in order to examine the validity of the proposed numerical method and turbulent model. In addition, the possibility of improving the wall function method in the separated flow region is examined by replacing the log‐law velocity profile for a smooth wall with that for a rough wall. The analysis results indicated that the proposed algebraic Reynolds stress model can be used to reasonably predict the turbulent flow in a rectangular duct with a sharp 180‐degree turn. In particular, the calculated reattachment point of a separated flow, which is difficult to predict in a turbulent flow, agrees well with the experimental results. In addition, the calculation results suggest that the wall function method using the log‐law velocity profile for a rough wall over a separated flow region has some potential for improving the prediction accuracy. Copyright © 2007 John Wiley & Sons, Ltd.