Spacing Ratio Increases Research Articles

Unsteady wake interference of unequal-height tandem cylinders mounted in a turbulent boundary layer

The unsteady wake interference of unequal-height tandem finite wall-mounted cylinders (FWMCs) fully submerged in a turbulent boundary layer (TBL) was investigated using time-resolved particle image velocimetry. The aspect ratios of the cylinders were fixed at $h/d = 5.3$ for the upstream cylinder (UC) and $H/d = 7.0$ for the downstream cylinder (DC) to achieve a height ratio of $h/H = 0.75$ , where d is the diameter of the cylinders. The Reynolds number based on the cylinder diameter was $Re = 5540$ and the submergence ratio was $\delta /H = 1.2$ , where $\delta $ is the TBL thickness. Three main flow regimes of tandem FWMCs were examined by varying the centre-to-centre spacing ( $s$ ) between the cylinders: extended-body ( $s/d = 2$ ), reattachment ( $s/d = 4$ ) and co-shedding ( $s/d = 6$ ) regimes. These test cases denoted as SR2, SR4 and SR6, respectively, were compared with a reference isolated cylinder (SC) with an aspect ratio similar to that of the DC. Spatio-temporal analysis of the flow field showed that the gap region of SR2 is characterized by a strong downwash of alternating low- and high-momentum fluid induced by the approach flow that is deflected from the unsheltered portion of the DC. In contrast, the gap region of SR4 and SR6 exhibited both downwash and upwash flow with a saddle point that moves closer to the mid-height of the UC as the spacing ratio increases. The upwash and downwash shear layers were associated with small-scale vortices with Strouhal numbers larger than that of the Kármán vortex shedding in the spanwise shear layers. The wake structure behind the DC was significantly altered compared with the SC due to sheltering effects, and the spacing ratio had a significant impact on the spatio-temporal evolution of the vortices.

Numerical simulations of the flows past two parallel square columns by MPS method

The hydrodynamic interactions between an offshore platform and surrounding water mainly occurs in way of the pile legs, and the flow past the pile legs can be simplified to the flow past the columns. This is the reason why it is of great significance to simulate the flow around multiple columns with accuracy. In this paper, based on a mesh-less method, Moving Particle Semi-implicit (MPS) method, the MLParticle-SJTU solver is used to simulate the flow past two parallel square columns. Firstly, the reliability and accuracy of the solver is verified by simulating the Poiseuille flow, in which the no-slip boundary condition is applied. Then, the flow past two parallel square columns with different spacing between the two columns is simulated when the Reynold number is 40. The influence of spacing on flow pattern, force on columns and the vortex shedding frequency is analyzed. It is found that when the spacing is relatively small, small vortices will be attached to the surface of the columns. As the spacing ratio increases, periodic shedding of vortices will occur.

Large eddy simulation of flow around two side-by-side circular cylinders at Reynolds number 3900

This paper investigates the flow dynamics around two circular cylinders in a side-by-side arrangement with different spacing ratios (T/D, T is the center-to-center cylinder spacing and D is the diameter) under a subcritical Reynolds number condition (Re = 3900). A three-dimensional (3D) numerical model was developed with Large Eddy Simulation (LES) technique. The model was well validated against published data of flow around a single cylinder at Re = 3900. Numerical simulations were conducted for flow around two side-by-side circular cylinders with T/D = 1.2, 1.5, 1.75, 2, 2.5, 3, 3.5, and 4. Based on the LES results, three wake regimes were identified: single bluff body regime (T/D = 1.2), biased flow regime (T/D = 1.5–2), and parallel vortex streets regime (T/D = 2.5–4). In the single bluff body regime with T/D = 1.2, the stable deflection of gap flow is also observed which indicates that there may exist a transition state from the single bluff body regime to the biased flow regime. In biased flow regime, the pairing and merging process of the outer vortices with the inner vortices are analyzed. The occurrence of the flip-flopping phenomenon is found to be related to the merging tendency between gap-side vortices in narrow wake region and free-flow-side vortices in wide wake region, and the relative phase of gap side vortices in transient state. In the parallel vortex streets regime, the phase relation of the vortex shedding process was analyzed. The time proportions of the in-phase mode and anti-phase mode are found to be varied with spacing ratio. As the spacing ratio increases, the wakes behind the cylinders lose their dependency on the anti-phase mode. The results of the present study were compared with the existing results at other Reynolds numbers. It is found that vortex shedding manner during the flip-over transitions is closely related to the spacing ratios and is independent of the Reynolds number.

Numerical analysis of WIV phenomenon with two in-series cylinders: WIV suppression and energy harvesting

This numerical study aims to analyze the hydrodynamic characteristics of in-series structures with two cross-sections, as well as their power characteristics under different spacing (α) and radius (φ) ratios respectively. The results show that as the spacing ratio increases, the in-series circular/square-cylinder system displays VIV, whereas the in-series square-cylinder system can effectively suppress vibration within the interval of α = 5.3 – 5.7, 6 ≤ Ur ≤ 8 when φ = 1. It is worth noting that as the radius ratio increases, the vibration of the downstream square cylinder transits from VIV to galloping. Subsequently, the short-time Fourier transform and wavelet transform are employed to perform time-frequency analysis of different cases. In terms of energy harvesting, the in-series circular-cylinder system shows its maximum power of 48.83 mW at Ur = 9 when α = 6, φ = 1. Additionally, the power of the in-series square-cylinder system at φ = 2 is higher than that in the other two cases (φ = 1 and 3), and in these three cases, the power at α = 6 is much greater than that of the case α = 8 and 4 regardless of the radius ratio. As to conversion efficiency, the case α = 6 and φ = 2 demonstrates the optimal energy harvesting performance. Thus, flexible control of the radius ratio and spacing ratio in a special range can not only suppress vibration but also enhance energy harvesting efficiency.

Investigation of large-scale coherent structures and momentum interference of twin rectangular jets

An experimental study was performed to investigate the effects of nozzle spacing between twin rectangular jets on the non-linear momentum interference and spatial evolution of large-scale flow structures. Five test cases of different spacing ratios (S/de = 1.8, 2.8, 3.7, 5.5 and 7.3) were examined. Two-point correlation, joint probability density function and swirling strength were used to characterize the large-scale structures. Turbulent/non-turbulent interface along the inner and outer shear layers were investigated. The results showed that due to the interactions in the merging region, the spatial correlation of streamwise velocity fluctuations was considerably lower along the inner shear layer than along the outer shear layer. As a result of the mixing process, the swirling strength of retrograde vortices generated along the inner shear layer was also lower than that of the prograde vortices. Along the symmetry line, longitudinal and transverse integral length scales increased linearly as the downstream distance from the jets increases. For the longitudinal length scale, the slope of the linear region was independent of the spacing ratio, while for the transverse length scale, the slope increases as the spacing ratio increases. For cases of S/de < 3.7, due to the suppression effects of the adjacent jet, the jump in the conditionally-averaged mean streamwise velocity profile around the turbulent/non-turbulent interface was lower for the inner shear layer compared to the outer shear layer.

Numerical acoustic simulation of flow around circular cylinders based on Lattice Boltzmann method and Ffowcs Williams-Hawkings acoustic equation

Based on the GPU acceleration technique, Lattice Boltzmann method (LBM) and Ffowcs Williams-Hawkings (FW-H) acoustic equation are adopted to simulate the noise generated by flow around fixed and rotating circular cylinders when Reynolds number (Re) is 200. The results show that the sound pressure level has a peak in the vertical direction and it is higher than that in the streamwise direction. The maximum sound pressure level is significantly reduced when the cylinder rotates due to the suppression of vortex shedding compared to the case of a fixed cylinder. For tandem cylinders, the maximum sound pressure level in the vertical direction increases as the spacing ratio increases, and for parallel cylinders, it decreases as the spacing ratio increases. In addition, when using graphic processing unit (GPU), the computational efficiency is improved greatly and the speed-up reaches nearly 100.

Hydrodynamics of mangrove-type root models: the effect of porosity, spacing ratio and flexibility

Mangrove trees play a prominent role in coastal tropic and subtropical regions, providing habitats for many organisms and protecting shorelines against high energy flows. In particular, the species Rhizophora mangle (red mangrove) exhibits complex cluster roots interacting with different hydrological flow conditions. To better understand the resilience of mangrove trees, we modeled the roots as a collection of cylinders with a circular pattern subject to unidirectional flow. We investigated the effect of porosity and spacing ratio between roots by varying both the diameter of the patch, D, and inset cylinders, d. In addition, we modeled hanging roots of red mangroves as cantilevered rigid cylinders on a hinge. Force and velocity measurements were performed in a water tunnel (Reynolds numbers from 2200 to 11 000). Concurrently, we performed 2D flow visualization using a flowing soap film. We found that the frequency of the vortex shedding increases as the diameter of the small cylinders decreases while the patch diameter is constant, therefore increasing the Strouhal number, . By comparing the change of Strouhal numbers with a single solid cylinder, we introduced a new length scale, the effective diameter. The effective diameter of the patch decreases as the porosity increases. In addition, we found that patch drag scales linearly with the patch diameter but decreases linearly as the spacing ratio increases. After a spacing ratio of (), the force scales linearly with the free stream velocity, and the mean velocity behind the patch is independent of the Reynolds number and the patch effect disappears. For flexible cylinders, we found that a decrease in stiffness increases both patch drag and the wake deficit behind the patch in a similar fashion as increasing the blockage of the patch. This information has the potential to help in the development of methods to design resilient bio-inspired coastline structures.

Lift forces induced by phase lag between the vortex sheddings from two tandem bluff bodies

Flow-induced forces on two tandem circular cylinders of identical diameter are numerically studied at a Reynolds number of 200. The cylinder center-to-center spacing ratio is varied from 2 to 9. We focus on fluctuating (rms) lift coefficient of the upstream cylinder, vortex dynamics in the gap between cylinders, and phase lag between vortex shedding from the two cylinders. The phase lag was a linear function of the spacing ratio as known in the literature; but it is, as proved here, indeed a nonlinear function of the spacing ratio, Strouhal number and convection velocity of vortices in the gap between the cylinders. The shedding from the two cylinders turns out to be inphase and antiphase alternately as the spacing ratio increases. We unearth that both phase lag and spacing ratio influence the fluctuating lift of the upstream cylinder. With an increase in the spacing ratio, while the influence of the spacing ratio on fluctuating lift diminishes rapidly in an overdamped manner, that of the phase lag makes the fluctuating lift variation underdamped sinusoidal. The inphase and antiphase flows correspond to a local maximum and a local minimum, respectively, in the fluctuating lift variation. An equation is deduced, showing the relationship between the fluctuating lift, spacing ratio, and phase lag. The physics behind the damped-sinusoidal variation in the fluctuating lift is discussed. The investigation directs that the streamwise separation between two tandem wings of airplanes/submarines should be taken into account or optimized. It would also be interesting to see whether fish exploits phase-lag-induced lift to enhance its forward thrust.

Time-Averaged Behavior of Gap Flow Between Two Side-by-Side Circular Cylinders

The time-averaged behavior of gap flow between two stationary side-by-side circular cylinders immersed in the subcritical Reynolds number regime and its variation with gap spacing are presented. A series of experiments and numerical simulations are performed. Results reveal that gap flow, which is the flow passing between the cylinders, can be classified broadly into pressure- and momentum-driven regimes, depending on the spacing ratio (), where is the transverse center-to-center spacing between the cylinders and is the cylinder diameter. The pressure-driven regime occurs for roughly , where the mean velocity of the gap flow increases as the spacing ratio increases. The momentum-driven regime follows with a monotonic decrease in the mean velocity as the spacing ratio increases when . Within the pressure-driven regime, subtransitions of the gap flow are further classified, based on distinct changes in the circumferential static pressure distribution, as well as the velocity profile, transverse pressure gradient, and mean velocity at the throat of the two cylinders.

Statistical analysis of stochastic blocks and its application to rock support

The orientation, trace length, spacing, and location of probabilistic discontinuities in rock masses are randomly developed. Thus, the shape, size, and location of blocks cut off by these probabilistic discontinuities are accordingly stochastic. It is difficult, or even impossible, to determine the volume and location of the blocks using the block theory proposed by Goodman and Shi (1985). Stochastic block analysis (SBA) is capable of identifying three-dimensional (3-D) stochastic blocks from a randomly developed discontinuity network (discrete fracture network). However, in practice, 3-D blocks are not identified well in simulated fracture networks and so the use of SBA is seldom encountered. In this paper, the procedures involved in stochastic block identification are first outlined. The concept and calculation of overlaying area and ratio are then introduced. Then, the stochastic block identification results are used to explore the statistical distribution of the block size and overlaying ratio. Subsequently, the laws governing development of the stochastic blocks were elucidated. The results show that the block size has a negative exponential distribution and the overlaying ratio follows a Γ distribution. The overlaying ratio increases as the trace length to spacing ratio increases. We further outline, for the first time, approaches to determine block support measures by analyzing the characteristics of the statistical distributions of the stochastic blocks. Block support issues relating to a practical underground plant were also studied. The lengths and anchor forces and spacings of the rock bolts were quantitatively determined according to the results of a statistical analysis of the stochastic blocks. Statistical analysis of stochastic blocks is of great significance in understanding the development characteristics of the stochastic blocks and in quantitatively determining block support measures.

Numerical investigation of lobe spacing ratio on performance of forced mixer nozzle

AbstractGeometric models of a lobed mixer nozzle with variation of lobe spacing ratios are created and the corresponding flow fields are simulated using a steady Reynolds Averaged Navier–Stokes (RANS) equation with a realizable k‐ϵ turbulence model and standard wall function. According to the numerical simulation results, the spacing ratio has a large influence on the shape of streamwise vortices, but a relatively small effect on the streamwise vorticity field at the lobe exit. Therefore, at the initial part of mixing, a change of spacing ratio has little effect on the thermal mixing efficiency and the total pressure recovery coefficient. In addition, the thermal mixing efficiency increases sharply at the initial part, and near the nozzle exit it approaches some constant. The development of the total pressure recovery coefficient is totally reverse to the thermal mixing efficiency. It falls rapidly at the beginning. Then the rate of descent gradually slows down, and approaches some constant. At the nozzle exit cross‐section, the thermal mixing efficiency ascends and the total pressure recovery efficiency reduces as the spacing ratio increases. Besides, the thrust coefficient has little relationship to the spacing ratio, with a variation smaller than 0.01 when the spacing ratio increases from 4.87 to 0.497. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.20363

Phase Transition and Lattice Thermal Expansion of Cs‐Deficient Pollucite, Cs1−xAl1−xSi2+xO6 (x≤0.25), Compounds

Cs‐deficient pollucite compounds with the general composition Cs1−xAl1−xSi2+xO6 and a cubic pollucite structure at room temperature (RT) were prepared by a multistep solid‐state reaction. The single phase of the products was confirmed by powder X‐ray diffraction (XRD) analysis at RT. Structural phase transition was influenced by the Cs content of compounds of the Cs1−xAl1−xSi2+xO6 series. Cs0.8Al0.8Si2.2O6 and Cs0.75Al0.75Si2.25O6 were cubic at 123 K from the XRD patterns and did not undergo structural phase transition. The lattice thermal expansion behavior of the Cs‐deficient pollucite compounds was investigated by low‐temperature and high‐temperature XRD analyses in the temperature range of 123–1173 K and was found to show a gradual decrease with decreasing Cs content of Cs1−xAl1−xSi2+xO6 series. The variation in unit cell volume with temperature for each composition showed that Cs0.8Al0.8Si2.2O6 and Cs0.75Al0.75Si2.25O6 had significantly smaller degrees of lattice thermal expansion than CsAlSi2O6 and Cs0.9Al0.9Si2.1O6. CsAlSi2O6, Cs0.9Al0.9Si2.1O6, Cs0.8Al0.8Si2.2O6, and Cs0.75Al0.75Si2.25O6 showed linear coefficients of thermal expansion of 2.7 × 10−6, 2.2 × 10−6, 1.5 × 10−6, and 1.1 × 10−6 K−1, respectively, which are attributed to not only an increase in space ratio but also a decrease in Al/Si ratio in the framework in the unit cell.

Phenomena of vortex shedding and flow interference of three cylinders in different equilateral arrangements

This paper describes how the flows around three equal circular cylinders arranged in an equilateral-triangular manner interact at different angles of incidence α and spacing ratios l/d. Some vortex-shedding-frequency data evaluated from flow visualization experiments conducted at Reynolds numbers of 2.1 × 103 and 3.5 × 103, based on the diameter of a single cylinder, using a dye -injection technique, are presented. In order to provide additional insight to the understanding of the flow structure around this particular cylinder array, some photographs indicating the typical flow patterns for various arrangements are also presented. The investigation indicates that the flows interact in a complex fashion for spacing ratios smaller than 2.29 and it also reveals that, at this range of spacing ratios and at α = 0°, bistable flow characteristic exists. Moreover, for l/d approximately smaller than 4.65 there always exists an angle at which the vortex shedding behind an upstream cylinder is suppressed by a nearest downstream cylinder. This angle is found not to remain constant but increases as the spacing ratio increases. For illustration and comparisons, some numerical results obtained from the application of the surface-vorticity method have also been presented.

Heat Transfer to Longitudinal Laminar Flow Between Cylinders

Consideration is given to the fully developed heat-transfer characteristics for longitudinal laminar flow between cylinders arranged in an equilateral triangular array. The analysis is carried out for the condition of uniform heat transfer per unit length. Solutions are obtained for the temperature distribution, and from these, Nusselt numbers are derived for a wide range of spacing-to-diameter ratios. It is found that as the spacing ratio increases, so also does the wall-to-bulk temperature difference for a fixed heat transfer per unit length. Corresponding to a uniform surface temperature around the circumference of a cylinder, the circumferential variation of the local heat flux is computed. For spacing ratios of 1.5 ∼ 2.0 and greater, uniform peripheral wall temperature and uniform peripheral heat flux are simultaneously achieved. A simplified analysis which neglects circumferential variations is also carried out, and the results are compared with those from the more exact formulation.