Large eddy simulation of flow around a rectangular cylinder

A large eddy simulation (LES) of turbulent flow around a stationary rectangular cylinder at high Reynolds number of 2.2×10⁴ is conducted as the first step to prove the applicability of LES to practical engineering problems. Time-averaged and phase-averaged velocities and turbulent stresses are obtained and they are compared with the experimental data. To investigate mesh dependence on computational results of the LES, two kinds of grid resolution are used. In addition, the effect of a second-order upwind scheme QUICK for convection terms is also investigated due to its dependence on grid resolution. The drag coefficients, the base pressure coefficients and Strouhal numbers are in fairly good agreement with the experimental results, while the computational results show that the artificial dissipative and dispersive effect of QUICK is large in the vicinity of the cylinder in our computation. Thus, it is necessary to use higher-order upwind schemes to reduce the numerical errors, since it is effective in applying LES to practical engineering problems with complicated geometry.     

Steady flow past a torus with aspect ratio less than 5

Steady flow past a torus with an aspect ratio less than 5 and its axis aligned with the flow is studied numerically by solving the steady, axisymmetric Navier–Stokes equations. The wake structure behind tori exhibits diverse behaviours. The detached recirculating zone on the axis, the attached recirculating zone, and the detached recirculating zone behind the torus tube may appear individually or concurrently, depending on the aspect ratio and the Reynolds number. A wake structure map is summarized based on the observed flow behaviours. Six flow regimes with different wake behaviours are identified and the corresponding flow regime map is plotted, which include the no-recirculating-zone regime, the single-detached-recirculating-zone regime, the single-attached-recirculating-zone regime, the two-recirculating-zone regime I, the two-recirculating-zone regime II, and the three-recirculating-zone regime. Over the range of aspect ratio 1.9<AR<2.4, the detached wake initially increases but then decreases in size with Reynolds number, and eventually disappears at Reynolds numbers beyond a critical value (depending on the aspect ratio). The underlying mechanisms of the onset and disappearance of the recirculating zones are discussed in terms of vorticity accumulation and base bleed. The recirculating zone first occurs when the maximum vorticity on the surface of the torus exceeds about 5. The detached recirculating zone on the axis of the torus disappears once the flow rate through the hole of the torus is beyond a certain threshold. In addition, the present results suggest that different transition modes to non-axisymmetric flow for tori with different aspect ratios reported in the literature may result from the wake structures prior to the transition.     

Impact of aspect ratio on flow boiling of water in rectangular microchannels

In this paper we focus on the impact of varying the aspect ratio of rectangular microchannels, on the overall pressure drop involving water boiling. An integrated system comprising micro-heaters, sensors and microchannels has been realized on (1 1 0) silicon wafers, following CMOS compatible process steps. Rectangular microchannels were fabricated with varying aspect ratios (width [W] to depth [H]) but constant hydraulic diameter of 142 ± 2 μm and length of 20 mm. The invariant nature of the hydraulic diameter is confirmed through two independent means: physical measurements using profilometer and by measuring the pressure drop in single-phase fluid flow. The experimental results show that the pressure drop for two-phase flow in rectangular microchannels experiences minima at an aspect ratio of about 1.6. The minimum is possibly due to opposing trends of frictional and acceleration pressure drops, with respect to aspect ratio. In a certain heat flux and mass flux range, it is observed that the two-phase pressure drop is lower than the corresponding single-phase value. This is the first study to investigate the effect of aspect ratio in two-phase flow in microchannels, to the best of our knowledge. The results are in qualitative agreement with annular flow model predictions. These results improve the possibility of designing effective heat-sinks based on two-phase fluid flow in microchannels.     

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.     

Influence of aspect ratio on the flow above the free end of a surface-mounted finite cylinder

The flow above the free end of a surface-mounted finite-height cylinder was studied in a low-speed wind tunnel using particle image velocimetry (PIV). Velocity measurements were made in vertical and horizontal measurement planes above the free end of finite cylinders of aspect ratios AR = 9, 7, 5 and 3, at a Reynolds number of Re = 4.2 × 10⁴. The relative thickness of the boundary layer on the ground plane was δ/D = 1.7. Flow separating from the leading edge formed a prominent recirculation zone on the free-end surface. The legs of the mean arch vortex contained within the recirculation zone terminate on the free-end surface on either side of the centreline. Separated flow from the leading edge attaches onto the upper surface of the cylinder along a prominent attachment line. Local separation downstream of the leading edge is also induced by the reverse flow and arch vortex circulation within the recirculation zone. As the cylinder aspect ratio is lowered from AR = 9 to AR = 3, the thickness of the recirculation zone increases, the arch vortex centre moves downstream and higher above the free-end surface, the attachment position moves downstream, and the termination points of the arch vortex move upstream. A lowering of the aspect ratio therefore results in accentuated curvature of the arch vortex line. Changes in aspect ratio also influence the vorticity generation in the near-wake region and the shape of the attachment line.     

Slow visco-elastic flow past a cylinder in a rectangular channel

This paper is concerned with the flow of a visco-elastic liquid through a rectangular channel containing a cylindrical obstruction placed either in a symmetric or asymmetric position with respect to the centre of the channel. Numerical predictions of the flow are obtained using a well established finite element Galerkin mixed formulation. The influence of elasticity on the streamline pattern is found to be negligible, and one only observes changes due to different geometries, i.e. relative positions of cylinder and channel. However, both elasticity and a variable viscosity are found to have significant effects on the forces exerted on the cylinder.     

Interactions between a rectangular cylinder and a free-surface flow

The salient features of the interaction between a free-surface flow and a cylinder of rectangular cross-section are investigated and discussed. Laboratory-scale experiments are performed in a water channel under various flow conditions and elevations of the cylinder above the channel floor. The flow field is characterized on the basis of time-averaged and fluctuating local velocity measurements. Dynamic loadings on the cylinder are measured by two water-insulated dynamometers placed inside the cylinder structure. Starting from frequency and spectral analyses of the force signals, insights on the relationship between force dominant frequencies and the Strouhal number of the vortex shedding phenomenon are provided. Experimental results highlight the strong influence of the asymmetric configuration imposed by the two different boundary conditions (free surface and channel floor) on (i) the mean force coefficients and (ii) the vortex shedding frequencies. We provide an analysis of the nature of the dependence of average force coefficients on relevant dimensionless groups, i.e., the Reynolds number, normalized flow depth and cylinder submersion.     

Low-frequency fluctuations in the near-wake region of a trapezoidal cylinder with low aspect ratio

Base pressure signals obtained on a trapezoidal cylinder with an aspect ratio 4.7, at Reynolds numbers of the order of 10⁴, were examined after being low-pass filtered at different cut-off frequencies. For the range of the Reynolds numbers studied, the integral time scales of the low-passed fluctuations versus the cut-off frequencies chosen was found to fall on a curve. Cross-correlation between the pressure fluctuations measured at the cylinder base and the velocity fluctuations detected in the near-wake region were examined with the signal traces low-passed at different cut-off frequencies. Accordingly, an optimal cut-off frequency was defined as the one corresponding to the highest correlation obtained. The integral time scale of the low-passed fluctuations in reference to the optimal cut-off frequency was found to be about two times the vortex-shedding period. The low-frequency variations measured appeared to be insensitive to the artificial tripping to the sidewall boundary layer, and exhibited a global behavior in a near-wake region.     

Heat transfer and flow around a circular cylinder with tripping-wires

An experimental study was conducted on the heat transfer under the condition of constant heat flux and the flow around a circular cylinder with tripping-wires, which were affixed at ± 65° from the forward stagnation point on the cylinder surface. The testing fluid was air and the Reynolds number Red, based on the cylinder diameter, ranged from 1.2 × 10⁴ to 5.2×10⁴. Especially investigated are the interactions between the heat transfer and the flow in the critical flow state, in relation to the static pressure distribution along the cylinder surface and the mean and turbulent fluctuating velocities in the wake. It is found that the heat transfer from the cylinder to the cross flow is in very close connection with the width of near wake.     

Torsion problems for a cylinder with a rectangular hole and a rectangular cylinder with a crack

Using the method of singular integral equation and the crack-cutting technique, the rigorous solutions are obtained for a cylinder with a rectangular hole and a rectangular cylinder with a crack, which exactly satisfy the boundary conditions and the conditions at the corner points. After that the torsional rigidities and the stress intensity factors at the crack tip are determined. Next, for the doubly connected circular cylinder with a rectangular hole the expressions for the singular stresses around the concave corner points are derived and the generalized stress intensity factors are then defined. Since the crack-cutting technique is used in this paper, the solution of the matching rectangular cylinder is also obtained and its numerical results coincide with those in references. Thus the method proposed here is verified. The project supported by National Natural Science Foundation of China     

Numerical simulation of flow around a square cylinder in uniform-shear flow

This paper presents results obtained from a numerical simulation of a two-dimensional (2-D) incompressible linear shear flow over a square cylinder. Numerical simulations are performed, using the lattice Boltzmann method, in the ranges of 50⩽Re⩽200 and 0⩽K⩽0.5, where Re and K are the Reynolds number and the shear rate, respectively. The effect of the shear rate on the frequency of vortex shedding from the cylinder, and the lift and drag forces exerted on the cylinder are quantified together with the flow patterns around the cylinder. The present results show that vortex structure behind the cylinder is strongly dependant on both the shear rate and Reynolds number. When Re=50, a small K can disturb the steady state and cause an alternative vortex shedding with uneven intensity. In contrast, a large value of K will suppress the vortex shedding from the cylinder. When Re>50, the differences in the strength and size of vortices shed from the upper and lower sides of the cylinder become more pronounced as K increases. Vortex shedding disappears when K is larger than a critical value, which depends on Re. The flow patterns around the cylinder for different Re tend towards self-similarity with increasing K. The lift and drag forces exerted on the cylinder, in general, decrease with increasing K. Unlike a shear flow past a circular cylinder, the vortex shedding frequency past a square cylinder decreases with increasing the shear rate. A significant reduction of the drag force occurs in the range 0.15<K<0.3.     

Wake structure of a finite circular cylinder of small aspect ratio

The wake of a finite circular cylinder of small aspect ratio was studied with a seven-hole probe and thermal anemometry. The cylinder was mounted normal to a ground plane and was partially immersed in a turbulent boundary layer. The time-averaged velocity and streamwise vorticity fields showed the development of the tip vortex structures, the extent of the near-wake recirculation zone, the downwash phenomenon and base vortex structures within the boundary layer. The wake structure and power spectra were similar for cylinder aspect ratios of 5 to 9, but a distinctly different behaviour was observed for an aspect ratio of 3.     

Turbulent flow around a rotating cylinder in a quiescent fluid

 Hot-wire measurements have been carried out in the turbulent flow around a rotating circular cylinder in still air for Reynolds numbers Re=∣U _w ∣D/ν=1.5×10⁴ to 10⁵. The experimental results confirm the analysis derived by asymptotic theory for high Reynolds numbers. Two different ways of deriving the friction law from the experiments (via shear stress and via velocity distribution) resulted practically in the same law. It is shown, that in spite of the curvature of the streamlines the universal logarithmic velocity distribution is still valid near the wall. Received: 8 August 1996/Accepted: 24 April 1998     

Stokes paradox for power-law flow around a cylinder

A simple analysis for power-law fluids shows that the Stokes paradox for creeping flow around a cylinder is removed for shear-thinning (n < 1) but not for shear-thickening (n 1) fluids. An approximate drag value is found for n < 1 and is compared with computed results.