Mean Recirculation Length Research Articles

Gap ratio effects on the coherent structures surrounding a near-wall square cylinder

Turbulent flow around a square cylinder offset at different heights from an upstream rough wall are investigated using time-resolved particle image velocimetry. The Reynolds number based on the freestream velocity and cylinder height was 12750 and the incoming turbulent boundary layer thickness was 7.2 times the cylinder height. The examined gaps beneath the cylinder were 0.0, 0.3, 0.5, 1.0, 2.0, 4.0, and 8.0 times the cylinder height. The results show that the mean recirculation length remains relatively constant for cases with a gap size greater than or equal to 1.0 times the cylinder height. Flow acceleration through the gap under the cylinder is strongest with a gap size of 2.0 times cylinder height. Downstream of the cylinder, the vertical velocity fluctuations contribute strongly to the production of turbulent kinetic energy by interacting with mean wall-normal velocity gradient in the vertical direction. The dominant frequency embedded in the incoming turbulent boundary layer persists in the wake of the cylinder when the gap size is less than 1.0 cylinder height. Kelvin-Helmholtz vortices originating from the top leading edge of cylinder occur at Strouhal numbers of 2.77-3.11 for the cases with gap ratio ranging from 0.3-8.0 cylinder heights, while spectral migration towards lower frequencies is observed for cases with gap sizes equal to 0.3 and 0.5 cylinder heights. The spatial trajectory of top Kelvin-Helmholtz vortices extends further away from the cylinder as the gap size increases. Spectral proper orthogonal decomposition analysis shows that the von Kármán vortex shedding structures possess the highest spectral energy for all offset cases despite regular vortex shedding being disrupted when the gap size is 0.3 times the cylinder height.

Interaction between a stationary sphere and turbulent flow in a boundary layer

We investigate the interaction of a stationary sphere with turbulent flows in a spatially developing boundary layer over a flat plate by means of fully resolved direct numerical simulations. The diameter of the sphere D is much larger than the Kolmogorov length scale. The sphere Reynolds number ReD is changed by varying the sphere diameter, while the gap ratio is held constant with G/D=0.1, where G is the distance between the bottom of the sphere and the flat plate. The simulation results indicate that there exist complex interactions between the small-scale vortex in the wake of the sphere and the large-scale coherent structures inside the turbulent boundary layer. The jet-like flow through the gap is deflected away from the wall, and the level of deflection increases with ReD. As a result, asymmetrical flow structures are observed in the recirculation zone. In addition, the mean recirculation length is found to decrease with the increase in ReD. Concerning the turbulence modulation, statistics show that the skin-friction drag and boundary layer thickness are decreased in the recirculation region with respect to the undisturbed flow, whereas the displacement thickness is increased due to the presence of reverse flow. These effects become more pronounced as ReD increases. The budget of the turbulent kinetic energy in the sphere wake is also examined. It is revealed that the turbulent production and viscous dissipation rate are significantly enhanced under the effect of the sphere with size of the same order of magnitude as the local boundary layer thickness.

Experimental investigation of flow past a confined bluff body: Effects of body shape, blockage ratio and Reynolds number

This paper presents a Particle Image Velocimetry (PIV) study of the two-dimensional flow past a bluff body confined in a channel. Three typical shapes of bluff body with the same height, namely, circular cylinder (CC), flat plate (FP), and square cylinder (SC), but with varying blockage ratio (β = 0.25, 0.3, 0.4 and 0.5) and Reynolds number (Re = 3200, 4600 and 5400) are investigated. It is shown that for each body shape, vortex shedding patterns are relatively insensitive to Reynolds number (most notably for the case of FP), but strongly depend on the blockage ratio. As β increases, the mean recirculation length of the wake is initially constant and then displays a sharp increase at about β ≥ 0.4–0.5, which corresponds to the flow transition from periodic vortex shedding state to steady state. The strength of vortex shedding generally decreases with the increase in β except for CC at β = 0.25–0.3. On the other hand, the vortex shedding frequency expressed in terms of dimensionless Strouhal number (St) increases monotonically with blockage ratio until vortex shedding is suppressed. The critical blockage ratio for the cessation of vortex shedding, βCri, follows the order of βCri_FP<βCri_SC<βCri_CC.

Flow around a 5:1 rectangular cylinder: Effects of upstream-edge rounding

A sensitivity analysis of highly-resolved large-eddy simulations of the flow around a 5:1 rectangular cylinder to the introduction of a small rounding of the upstream edges is presented. Different values of the edge radius of curvature are considered, in a range such that they might reasonably be ascribed to manufacturing tolerances. A stochastic approach is adopted in order to build response curves of the quantities of interest as a function of the radius of curvature. The considered computational set-up, characterized by a fine numerical resolution and a low subgrid-scale (SGS) dissipation, predicts for the body having perfectly sharp edges a short mean recirculation length on the cylinder side, in disagreement with experimental data. On the other hand, even for the smallest considered radius of curvature, the length of the mean recirculation region increases significantly and, hence, the agreement with the experimental data is much improved. It is observed that the sharp edge introduces a higher level of turbulent fluctuations in the shear-layer at separation, which, if not artificially damped by numerical or SGS dissipation, grows faster and leads to a further upstream roll-up of the shear-layers and, hence, to a shorter mean recirculation region than in simulations with rounded edges.

Performance of Turbulence Models in Simulating Wind Loads on Photovoltaics Modules

The performance of five conventional turbulence models, commonly used in the wind industry, are examined in predicting the complex wake of an infinite span thin normal flat plate with large pressure gradients at Reynolds number of 1200. This body represents a large array of Photovoltaics modules, where two edges of the plate dominate the flow. This study provided a benchmark for capabilities of conventional turbulence models that are commonly used for wind forecasting in the wind energy industry. The results obtained from Reynolds Averaged Navier-Stokes (RANS) k - ε , Reynolds Normalization Group (RNG) k - ε , RANS k - ω Shear Stress Transport (SST) and Reynolds Stress Model (RSM) were compared with existing Direct Numerical Simulations (DNS). The mean flow features and unsteady wake characteristics were used as testing criteria amongst these models. All turbulence models over-predicted the mean recirculation length and under-predicted the mean drag coefficient. The major differences between numerical results in predicting the mean recirculation length, mean drag and velocity gradients, leading to deficits in turbulence kinetic energy production and diffusion, hint at major difficulties in modeling velocity gradients and thus turbulence energy transport terms, by traditional turbulence models. Unsteadiness of flow physics and nature of eddy viscosity approximations are potential reasons. This hints at the deficiencies of these models to predict complex flows with large pressure gradients, which are commonly observed in wind and solar farms. The under-prediction of wind loads on PV modules and over-estimation of the recirculation length behind them significantly affects the efficiency and operational feasibility of solar energy systems.

On simulating the flow past a normal thin flat plate

Initially, the uniform flow past a normal two-dimensional flat plate of zero-thickness was studied using Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES) at Reynolds number of 1200. An extensive review of previous numerical and experimental studies on the wake of flat plates highlights important discrepancies, which are reconciled by the present detailed sensitivity study of domain, boundary conditions and turbulence modeling specifications. It is shown that differences in important flow features, such as the mean recirculation length, drag and pressure distributions are related to the strong Re−effects for Re<1000. Detailed comparison of DNS and LES studies at Re=1200 with measurements up to Re=1.5×105 suggest that for Re>1000, the influence of the Reynolds number is small. Moreover, it is found that some important differences in the LES and DNS simulations, despite similar grid resolution, can be related to specific behavior of the Sub-Grid Scale Smagorinsky model in regions of high anisotropy and adverse pressure gradient in the recirculation zone even at high Re. Finally, it is observed that the pressure distribution on the windward surface of the plate is highly sensitive to the wake flow, which helps explain discrepancies between experimental and numerical studies in terms of an unusual sensitivity to the experimental conditions.

Effect of side-edge vortices and secondary induced flow on the wake of normal thin flat plates

The wake of a normal thin flat plate of aspect ratio 3.2 was studied in comparison to that of an infinite span (2D) plate at Reynolds number of 1200 (based on the common dimension of the two plates) using Direct Numerical Simulations. The presence of side-edge shear layers suppressed the spanwise instabilities responsible for the three distinct flow regimes in the wake of 2D plates. There was a vortex “peeling” mechanism that detached the vortices in the shear layers on the shorter sides. It increased the Strouhal number to 0.317 from 0.158 for 2D plates. It is also associated with increased entrainment of freestream fluid and a reduction in the mean recirculation length by 40% to 1.6h. Moreover, the peeling mechanism led to formation of interlocked vortex loops outside the base region. The maximum turbulence kinetic energy along the wake centreline for the 3D case was 76% lower than for the 2D flow. Vortex detachment was constrained to the plate sharp corners in contrast to the most common example of thin flat bodies (circular flat disks). This difference lead to a relatively higher vortex shedding frequency for flat plates. The side-edge vortices are associated with a secondary induced flow behind the plate, which formed two interlocked vortex loops and resulted in formation of separating vortex streets in the wake (wake split). Two opposing in-wash flows (in the chordwise direction) were observed accompanied by a similar system of out-wash flows (normal to the plate chord), which increased the freestream fluid entrainment. The in-wash flow contracted the wake in the plane of the chord. The out-wash flow expanded the wake in the spanwise direction and resulted in two counter-rotating vortex streets.

Connection between base drag, separating boundary layer characteristics and wake mean recirculation length of an axisymmetric blunt-based body

The variation of the base drag of an axisymmetric bluff body caused by modifications of the boundary-layer separating at the sharp-edged contour of its base is analysed through different numerical simulations, and the results are compared with those of a previous experimental investigation. Variational MultiScale Large-Eddy Simulations (VMS-LES) are first carried out on the same nominal geometry and at the same Reynolds number of the experiments. Subsequently, Direct Numerical Simulations (DNS) are performed at Reynolds numbers that are roughly two orders of magnitude lower, in order to investigate on the sensitivity of the main findings to the Reynolds number. The results of experiments, VMS-LES and DNS simulations show that an increase of the base pressure – and thus a decrease of the base drag – may be obtained by increasing the boundary layer thickness before separation, which causes a proportional increase of the length of the mean recirculation region behind the body. In spite of the different setups, Reynolds numbers and turbulence levels in the experiments and numerical simulations, in all cases the base pressure is found to be directly proportional to the length of the mean recirculation region, which is thus a key index of the base drag value. In turn, the recirculation length seems to be connected with the location of the incipient instability of the detaching shear layers, which can be moved downstream by an increase of the thickness of the separating boundary layer and upstream by an increase of the turbulence level.

Large-eddy simulation applied to study the influence of upstream conditions on the time-dependant and averaged characteristics of a backward-facing step flow

The unsteady backward-facing step flow is investigated using large-eddy simulation. Two different inlet conditions are tested to study the sensitivity of the separated flow to a modification of the upstream boundary layer. The first inlet condition consists of a mean turbulent profile perturbed by a white noise. The second relies upon a more realistic condition, in which fully turbulent inflow data are derived from an auxiliary simulation of a quasi-temporal boundary layer. The temporal pressure spectra in different locations downstream of the step exhibit four different characteristic frequencies in both cases. Pressure and velocity statistics, supplemented by visualizations, demonstrate how the flow in the shear layer is strongly influenced by the upstream conditions. The turbulent boundary layer triggers a rapid destabilization of the mixing layer, resulting in a shortening of the mean recirculation length. The temporal spectra reveal that the precursor simulation leads to an increase of the characteristic frequencies associated with the Kelvin–Helmholtz vortices and to the flapping of the shear layer. Streaks and quasi-longitudinal vortices created in the turbulent boundary layer induce high- and low-longitudinal velocity modulations upstream of the step edge. The spanwise modulation of the velocity seems to be responsible for the wavy destabilization of the Kelvin–Helmholtz vortices. The dependency of the mean flow and of the characteristic frequencies of pressure fluctuations to the incoming boundary layer clearly demonstrates the importance of defining as realistic boundary conditions as possible for the simulation of 3D separated flows.

The manipulated transitional backward-facing step flow: an experimental and direct numerical simulation investigation

Results from a joint experimental and direct numerical simulation (DNS) investigation are presented for the flow over a backward-facing step manipulated by low-amplitude time-periodic (harmonic) blowing/suction excitation through a narrow slot at the edge of the step. For a Reynolds number of Re h =3000 (based on step height, h, and inflow velocity, U o ) and for laminar inflow, a 33% reduction of the mean recirculation length (in comparison to the non-manipulated reference case) could be obtained with a forcing amplitude of the order of one per cent of U o . Based on the momentum thickness, θ, of the incoming laminar boundary layer (at the edge of the step), the corresponding optimum Strouhal number is St θ = f opt θ/ U o =0.012. From the experimental data it can be concluded that, in our flow case, the optimum frequency, f opt=50 Hz , was the most amplified frequency in the transition-to-turbulence process of the separated laminar shear layer. Detailed comparison of the experimental data with data from the numerical simulation shows that DNS and experimental data agree up to second-order statistics. The joint experimental and numerical investigations exhibit a complementary nature in the sense that, on the one hand, the main advantage of the experiment was the relative ease with which a wide range of forcing parameters could be tested and, on the other hand, DNS could provide spatio-temporal details of the flow which could not be so easily obtained in the experiment.