Square Cylinders In Tandem Arrangement Research Articles

Splitter plate-based flow control study for two square cylinders in tandem arrangement

A numerical study is performed to investigate the effectiveness of a splitter plate (SP) for the unsteady wake-regime control of two-dimensional tandem square cylinders (TSC) arranged with large (G/D = 6), intermediate (G/D = 4) and small (G/D = 2) gap-widths. Here, G is the center-to-center distance between the cylinders, and D is their side-length. The numerical simulations are conducted using an in-house developed FFIBLBM (flexible-forcing-immersed-boundary-lattice-Boltzmann-method) solver at Reynolds number (Re) of 100. The TSC arrangement with SP attached to either upstream or downstream cylinders is named TSC-SPU and TSC-SPD, respectively. It is found that the shear-layer characteristics, wake-regime, and flow-induced forces on TSC are highly susceptible to the G/D ratio and SP length. We observed four distinct flow patterns: VS-VS (vortex shedding-vortex shedding), QS-VS (quasi-steady-vortex shedding), S-VS (steady-vortex shedding), and S–S (steady-steady) in the wakes of TSC. Among them, the S–S flow pattern is the controlled wake-regime, with steady and stabilized vortices behind both cylinders, yielding considerably lesser drag on the TSC. Precisely, at large gap-width (G/D = 6), the TSC-SPU configuration only attains the S–S flow type for which the upstream and downstream cylinder experience 11.86% and 97.73% lesser drag, respectively, than the TSC without an attached SP. However, at intermediate gap-width (G/D = 4), both TSC-SPU and TSC-SPD generate the S–S flow type. Still, the TSC-SPU is advantageous in drag reduction, where the drag of the upstream and downstream cylinders is reduced by 1.61% and 7.26%, respectively. On the other hand, the S–S flow type is established for low gap-width (G/D = 2) with TSC-SPD setup for which the drag reduction for upstream and downstream cylinders are 1.85% and 12.76%, respectively.

Impact of inlet shear on unsteady boundary layer separation from two square cylinders in tandem arrangement

Impact of inlet shear on unsteady boundary layer separation from two square cylinders in tandem arrangement

Numerical study of the effect of blockage ratio in forced convection confined flows of shear-thinning fluids

In this work, the fluid dynamics and heat transfer of time-dependent flows with shear-thinning behaviour over two confined square cylinders in tandem arrangement are studied numerically. The case studies include two- and three-dimensional flows under a wide range of power-law indices, $0.25\leq n \leq 1.0$ , and blockage ratios, $\beta =0.50$ , 0.66 and 0.80, for a fixed Reynolds number of $Re=100$ and Prandtl number of $Pr=10$ . The fluid dynamic analysis includes detailed qualitative and quantitative comparisons between the different fluids and blockage ratios, where streamlines, viscosity fields, and lift and drag coefficients are presented. Moreover, a detailed study of the route from laminar time-dependent to chaotic flows is included. It was determined that the flow exhibits a transition from laminar to chaotic by decreasing the power-law index ( $n$ ) and increasing the blockage ratio ( $\beta$ ). With respect to the thermal analysis, isotherms and Nusselt numbers are compared between the different case studies. This analysis demonstrates that the average Nusselt numbers increased in chaotic flows. The three-dimensional cases confirmed the results proposed for the two-dimensional case.

Numerical study of the flow past two wall-mounted finite-length square cylinders in tandem arrangement

Flow past two wall-mounted square cylinders in a tandem arrangement are simulated through direct numerical simulation to investigate the effects of the gap between the two cylinders on the wake. Numerical simulations are conducted for a constant Reynolds number of 500, height to width length ratio H = 4, and gap to width ratios of G = 1 to 8 with an interval of 1. The flow in the wake of the downstream cylinder is found to be significantly affected by the free shear layers from the top and sides of the upstream cylinder. At G = 1 and 2, the free-shear layer generated from the upstream cylinder reattaches the top surface of the downstream cylinder and further develops into a downwash behind the downstream cylinder. At G = 3 to 8, the downwash behind the downstream cylinder disappears because flow separation from the top upstream edge of the downstream cylinder does not occur for G = 3 to 6 and is very weak for G = 7 and 8. The disappearance of downwash in the wake of the downstream cylinder further results in very weak variation of flow along the span of the downstream cylinder. The single, reattachment, and binary wake modes at the mid-span of the cylinder occur at G = (1 and 2), (3 and 4), and (5 and above), respectively.

Effect of the gap ratio on the flow patterns of the vortex flow forming behind the two square cylinders in tandem arrangement

Effect of the gap ratio on the flow patterns of the vortex flow forming behind the two square cylinders in tandem arrangement

Two-degree-of-freedom vortex-induced vibrations of two square cylinders in tandem arrangement at low Reynolds numbers

Although flow past cylinders has a vast spectrum of applications in various fields of engineering, the existence of flow-induced vibrations (FIVs) add a need for a more precise and thorough approach when studying such flows. In this context, this work investigates the FIVs’ mechanism due to two square cylinders placed in tandem arrangement through a characteristics-based-split (CBS) finite element method. Both cylinders, with a low mass ratio (mr= 2), are free to oscillate in in-line and transverse directions. The center-to-center distance of 5D (D being the cylinder side width) is kept fixed between the cylinders. The Reynolds number (Re) is ranged from 40 to 200 with an increment of 40, and computations are carried out for the reduced velocity (Ur) ranging from 3 to 13 under each Re value. Results show that the effects of Re and Ur on the dynamic responses are qualitatively similar for both cylinders. However, effects on the downstream cylinder are stronger due to the upstream wake. For Re equal to or beyond 120, the in-line low-frequency characteristic becomes obvious at some higher values of Ur for the upstream cylinder, whereas it exists over a wide range of Ur for the downstream cylinder. For lower Re (up to 120), cylinders show steady behavior at Ur= 5. However, for higher Re, they vibrate with the maximum amplitudes (especially the in-line amplitude of the downstream cylinder), and show complex wake flow at the same Ur. Compared to higher Re, the maximum vibration amplitudes in the transverse direction of lower Re are relatively higher, while the opposite trend is observed for in-line vibration amplitudes. Several unstable trajectories are also identified other than the typical figure-eight trajectories. In context of vortex shedding, different permutation of steady state, 2S, P+S, and complex modes are observed for different values of Re. It is also noted that the vortex shedding pattern keeps changing in the far wake for higher Re.

Modification of a Square Cylinder Wake through a Secondary Upstream Cylinder

One of the inherent characteristics of a bluff body is the large drag coefficient even at a relatively low velocity. The condition is made worse when the flow separates from the body, and a time-dependent flow occurs downstream of the body; i.e. a vortex shedding phenomenon. It has been shown that suppression of the vortex shedding can significantly reduce drag coefficient of the bluff body. The present study investigates the intensity of the resulting laminar wake of a single and two square cylinders in tandem arrangement, where the intensity was measured through the lift force signals. The findings indicated that the presence of the secondary cylinder significantly altered the magnitude of lift force of the cylinder system, particularly at high Reynolds numbers under the laminar flow regime. Furthermore, the magnitude of lift force was lower when the secondary cylinder was separated from the main cylinder as compared to the case where both cylinders were attached.

Steady separated flow around a pair of identical square cylinders in tandem array at low Reynolds numbers

The steady separated flow past two identical square cylinders in tandem arrangement is studied numerically. For a Reynolds number of 40, flow features are investigated for varied centre-to-centre distance, S between cylinders. The range of normalized spacing, SD is 2–30 where D denotes edge length of cylinders. Based on separation topology, four distinct flow regimes are identified. In regime I, the cylinders are closely spaced and gap between the cylinders is occupied by a pair of eddies and no wake forms behind the upstream cylinder. In regimes I and II, the cylinders are bridged by zero streamlines enveloping the gap flow. Thus, the cylinders along with the enclosed fluid, act as a single obstacle. Regime II forms as a manifestation of the first bifurcation of flow; the twin eddies in the gap split into four vortices. In regime III, the second bifurcation of flow occurs. The gap recirculation with four eddies splits; the first pair of counterrotating eddies contribute to wake of the upstream cylinder whereas the other pair adheres as a tiny vortical structure to the front part of downstream cylinder. In regime IV, separation topology is characterized by individual cylinder wakes. Four separation topologies, one corresponding to each regime, are proposed. The maximum width of the recirculation zone/wake of the upstream cylinder always exceeds the width of its downstream counterpart signifying higher drag for the former. For most of regime I, the downstream cylinder acts as a streamlined body.

Numerical investigation of vortex induced rotation of two square cylinders in tandem arrangement

This work performs a numerical investigation on the dynamics of the system with two square cylinders arranged in tandem at Reynolds number of 100. The influence of the vortex induced rotation and the spacing ratio (center-to-center distance over square width) between two cylinders is studied. Four system setups are considered. Case 1: Two stationary square cylinders in tandem; Case 2: Only the trailing square cylinder is allowed to rotate around its axis; Case 3: Only the leading square cylinder is allowed to rotate and Case 4: Both square cylinders are allowed to rotate around their own axes respectively. It shows that both the system setup and the spacing ratio can have significant influence on the dynamics of the system. When the leading cylinder is fixed, as in Case 1 and Case 2, the spacing ratio has the dominant effect. In these two cases, it can be very effective to suppress Cdmean/Clrms (mean drag coefficient/root mean square of lift coefficient) by keeping the spacing ratio below the critical value. In contrast, allowing the leading cylinder to rotate freely as in Case 3 and Case 4, changes the baseline of the dynamics of the system. It triggers formation of vortex shedding in the gap region with a smaller critical spacing ratio, compared with cases having a fixed leading cylinder. The force fluctuations and rotational amplitude are also much larger than those in Case 1 and Case 2. More complex flow patterns and interactions can be observed in these cases as well. It can be concluded that, keeping the leading cylinder stationary is crucial to suppress force fluctuations of the system under the conditions studied in this paper (at the Reynolds number of 100, ξ=0, Uθ=10 and I=1).

Direct and integral noise computation of two square cylinders in tandem arrangement

The present paper presents a comparison between two different approaches for calculating far-field noise of two square cylinders in tandem arrangement. Experimental data show that a flow past such an arrangement results in aeolian tones as well as broadband noise. The turbulent flow past the cylinders is computed using a compressible solver for low-Mach number flows. In order to validate the direct computation of acoustic waves, the complete span including endplates is calculated. Wind tunnel measurements show two different but stable flow states past the cylinders: a quiet state, where no vortex shedding is present in the wake of the upstream cylinder, and a loud state, where separated shear layers flow into the gap between the cylinders intermittently. Different initialisations of the velocity field are used in order to capture both flow states. Mean flow quantities as well as surface pressure spectra are compared to wind tunnel measurements. Far-field noise is calculated directly using the compressible solver, as well as indirectly using a hybrid method based on a Ffowcs Williams Hawkings formulation for stationary rigid surfaces. Far-field spectra and directivity patterns are compared to wind tunnel measurements. Results of both methods show good agreement with experimental data.

Numerical investigation of wake modes for flow past three tandem cylinders using the multi-relaxation-time lattice Boltzmann method for different gap spacings

In this paper, the effect of gap spacing on the flow past three square cylinders in tandem arrangement is studied numerically using a 2-D multi-relaxation-time lattice Boltzmann method (MRT-LBM). The Reynolds number is fixed at 75 and variation of the gap spacing is from 0.5 to 17. The results are compared to some earlier published results and found to be in good agreement. Five different wake modes are observed by the increment in the gap spacing. To understand the effect of different gap spacings on the flow-induced forces; a detailed analysis of mean drag coefficient, time signal analysis of drag and lift coefficients, Strouhal number, root mean square values of drag and lift coefficients is presented in this article. In this study, it is observed that the critical gap spacing is 3, its existence and effects on the flow characteristics are also studied.

Flow around two tandem square cylinders near a plane wall

An experimental study has been conducted to investigate the flow around two identical square cylinders in tandem arrangement and placed near a plane wall at a Reynolds number of 6,300. The inter-cylinder spacing ratio was varied from S* = 0.5 to 6, and the cylinder-to-wall gap ratio from G* = 0.25 to 2. Totally, 42 cases were considered to systematically examine the effects of wall proximity and the mutual interference between the two cylinders in the normalized gap–spacing (G*–S*) plane. The flow fields were captured using digital particle image velocimetry, in conjunction with measurements of the fluid forces (drag and lift) acting on the downstream cylinder using a piezoelectric load cell. The results show that the flow is highly dependent on the combined values of G* and S*. Categories relating to G* could be broadly classified as small-gap regime (G* 1) where the wall effects become negligible. Similarly, the flow interference between the two cylinders can be divided into three basic categories as a function of S*, namely, shielding regime at S* 3. Variations of force coefficients, amplitude spectra, Strouhal numbers, and Reynolds shear stress with G* and S* are presented to characterize the different flow regimes.

Low Reynolds number flow of power-law fluids over two square cylinders in tandem

The governing partial differential equations have been solved numerically for the 2-D and steady powerlaw fluid flow over two square cylinders in tandem arrangement. Extensive numerical results spanning wide ranges of the governing parameters as Reynolds number (0.1≤Re≤40), power-law index (0.2≤n≤1) and inter-cylinder spacing (2≤L/d≤6) are presented herein; limited results for L/d=24 are also obtained to approach the single cylinder behavior. The detailed flow visualization is done by means of the streamline and vorticity contours in the vicinity of two cylinders. The global characteristics are analyzed in terms of the surface pressure distribution and pressure drag coefficient. The drag coefficient shows the classical inverse dependence on the Reynolds number irrespective of the value of the powerlaw index; the drag on the upstream cylinder is always greater than that for the downstream cylinder.

Power-Law Fluid Flow Passing Two Square Cylinders in Tandem Arrangement

Two-dimensional laminar flow of a power-law fluid passing two square cylinders in a tandem arrangement is numerically investigated in the ranges of 1< Re< 200 and 1 ≤ G ≤ 9. The fluid viscosity power-law index lies in the range 0.5 ≤ n ≤ 1.8, which covers shear-thinning, Newtonian and shear-thickening fluids. A finite volume code based on the SIMPLEC algorithm with nonstaggered grid is used. In order to discretize the convective and diffusive terms, the third order QUICK and the second-order central difference scheme are used, respectively. The influence of the power-law index, Reynolds number and gap ratio on the drag coefficient, Strouhal number and streamlines are investigated, and the results are compared with other studies in the literature to validate the methodology. The effect of the time integration scheme on accuracy and computational time is also analyzed. In the ranges of Reynolds number and power-law index studied here, vortex shedding is known to occur for square cylinders in tandem. This study represents the first systematic investigation of this phenomenon for non-Newtonian fluids in the open literature. In comparison to Newtonian fluids, it is found that the onset of leading edge separation occurs at lower Reynolds number for shear-thinning fluids and is delayed to larger values for shear-thickening fluids.

Natural convection in power-law fluids from two square cylinders in tandem arrangement at moderate Grashof numbers

In this work, free convective flow and heat transfer in power-law fluids from two heated square cylinders in tandem arrangement is studied. The governing differential equations have been solved numerically over wide ranges of Grashof number, 10 ≤ Gr ≤ 1,000, Prandtl number, 0.71 ≤ Pr ≤ 50 and power-law index, 0.4 ≤ n ≤ 1.8. In order to elucidate the extent of inter-cylinder interaction, the non-dimensional inter-cylinder spacing, L/d is varied in the range, 2 ≤ L/d ≤ 6. The results are interpreted in terms of streamline and isotherm contours in the proximity of two cylinders to gain physical insights into the nature of flow. At the next level, the distribution of the local Nusselt number along the surface of the cylinders is presented. At the minimum inter-cylinder spacing due to the intense interference, the downstream cylinder contributes much less to the overall heat transfer whereas it experiences much higher hydrodynamic drag than the upstream cylinder. Broadly, the local and average Nusselt number for both cylinders show a positive dependence on both Grashof and Prandtl numbers. Also, all else being equal, shear-thinning fluid behaviour promotes the rate of heat transfer and shear-thickening fluid behaviour impedes it. Finally, the present numerical results have been correlated by using simple forms of equations thereby enabling the estimation of Nusselt number in a new application.

Effect of Prandtl number on heat transfer from tandem square cylinders immersed in power-law fluids in the low Reynolds number regime

In this work, forced convection heat transfer from two square cylinders in tandem arrangement to power-law and Newtonian fluids has been investigated. The governing differential equations (continuity, momentum and energy balance) have been solved numerically. The results reported herein encompass wide ranges of the pertinent dimensionless parameters, namely, Prandtl number, 0.71⩽Pr⩽100, Reynolds number, 0.1⩽Re⩽40, power-law index, 0.2⩽n⩽1 and centre-to-center cylinder spacing, 2⩽L/d⩽6, albeit limited results were also obtained for L/d=24 to retrieve the limiting case of non-interacting cylinders. The range of the center-to-center gap between the two cylinders is such that it corresponds to strong to virtually no interactions between the two cylinders. Furthermore, the range of Reynolds number is such that the flow is expected to be steady. The detailed heat transfer characteristics are interpreted in terms of the isotherm patterns in the close proximity of each cylinder and the variation of the local Nusselt number on the surface of each cylinder. Finally, the surface averaged values of the Nusselt number are expressed in terms of Reynolds number, power-law index and Prandtl number for center-to-center distances L/d=2, 4 and 6. These results are also expressed in terms of the usual Colburn j-factor as a function of the Reynolds number and power-law index over the range of conditions spanned here.

Numerical Study of Particle Dispersion in the Wake of Two Tandem Square Cylinders Using Discrete Vortex Method

This study has been conducted to investigate numerically the particle dispersion in the wake of dilute particle-laden gas flows past two identical square cylinders in tandem arrangement at Reynolds number of 10,000,000. In the numerical method, the discrete vortex method is employed to calculate the gas flow fields, and the Lagrangian approach is applied to track individual solid particles. A dispersion function is defined to represent the lateral dispersion scale of particles. The wake vortex patterns and the distributions of particles with various Stokes numbers ranging from 0.01 to 10 are obtained. The numerical results reveal that: (1) the particles with St = 0.01 can distribute both in the vortex core and around the vortex periphery, whereas the particles with St = 1.0, 10 congregate mainly around the vortex periphery; (2) the particles with St = 0.01, 0.1 are trapped by the vortices into the gap between the two square cylinders, while very few particles with St = 1.0, 10 are distributed within the gap; (3) the particle's dispersion intensity along the lateral direction decreases greatly as St is increased from 0.01 to 10.

Interference effect of two equal‐sized square cylinders in tandem arrangement: With planar shear flow

AbstractNumerical simulations have been performed for flow past two equal‐sized square cylinders in tandem arrangement subjected to incoming planar shear flow. Effect of L/d ratio and the shear parameter has been studied. The range of L/d ratio (ratio of center‐to‐center distance (L) to cylinder width (d)) is varied from 2 to 7 and the non‐dimensional shear parameter (K) is varied from 0.0 to 0.4 in steps of 0.1. For all the cases the Reynolds number (Re) based on centerline velocity and cylinder width is fixed at 100. The results are compared with that of isolated square cylinder with uniform flow. Strouhal number decreases with increasing shear parameter. There are more than one shedding frequency at high shear parameters and L/d ratios. The mean drag coefficient is decreased with shear parameter and lesser than that of the single cylinder. The root mean square (RMS) value of both lift and drag coefficients is higher for the downstream cylinder for all values of shear parameter. With increasing L/d ratio, for both lift and drag, the RMS value increases and then decreases for upstream cylinder, whereas it continuously increases for the downstream cylinder. The stagnation point is moved towards the top leading edge with increasing shear. The critical L/d ratio, which is defined as the distance between two cylinders, beyond which the vortex shedding from the upstream cylinder occurs, decreases with increasing shear parameter. Copyright © 2007 John Wiley & Sons, Ltd.

Flow-Induced In-Line Oscillation of Two Square Cylinders in Tandem Arrangement

Flow-Induced In-Line Oscillation of Two Square Cylinders in Tandem Arrangement

Vortex shedding from two surface-mounted cubes in tandem

Periodic vortex shedding from two surface-mounted cubes, of height H, in tandem arrangement placed in a thin boundary layer is investigated for a spacing 2H using phase-averaged Laser Doppler Velocimetry. Tests were conducted for a Reynolds number of 22,000, based on H and the freestream velocity, and an approximately 0.07 H thick laminar boundary layer. For obstacle separations between 1.5 H and 2.5 H, the shedding frequency scales inversely with the obstacle spacing, S, such that the Strouhal number based on S is constant or geometrically locked. In this locked regime, periodic shedding is triggered by the interference between a vertical flow stream along the front face of the downstream obstacle and the vortex in the inter-obstacle cavity. This three-dimensional mechanism is not observed for two-dimensional geometries and helps explain why a locked regime cannot be observed for square cylinders in tandem arrangement. Furthermore, it is shown that the structure of the turbulent field in the cavity region differs significantly from that in the base region of a two-dimensional obstacle.