On vortex shedding from low aspect ratio dual step cylinders

A large diameter cylinder prepared by thick wall pipe as raw material presents the shortfalls such as high cost, difficulty in procurement, the increasing amount of labour and processing cost. This work proposed a large diameter cylinder with high precision. By conducting process experiments and compared with the preparing process of existing large diameter cylinder, the preparing process of the large diameter cylinder in this work is proved to be practical and economical.

The proximity interference and the vortex dislocation are fundamental fluid dynamic features that determine a wake pattern of dual-step circular cylinders in a side-by-side arrangement. Each dual-step cylinder consists of two coaxial cylinders with different diameters. A complex wake modulation is expected due to an intrinsic interaction between the vortex shedding of the larger-diameter cylinder (LC) and the smaller-diameter cylinder (SC), and to the cross-wake interaction of side-by-side cylinders in a uniform flow. To understand the physics of fluid wake modulations, three-dimensional direct numerical simulations of the flow around a pair of dual-step circular cylinders in side-by-side arrangements are performed and investigated. Six simulation cases are presented with different combinations of diameter ratio (1.33–2.00), gap ratio (1.00–3.17), and the Reynolds number (60–200) in a laminar flow regime, providing key insights into the two distinct LC-dominated and SC-governing wake modulation characteristics. For the LC-dominated wake modulation, the wake pattern of side-by-side cylinders is determined by the predominant vortex dynamics in the LC wake. For the SC-governing wake modulation, the LC wake pattern becomes modulated and controlled by the SC wake through the connections of vortex tubes shed downstream of the two nonuniform cylinders. Owing to the proximity interference and vortex dislocation, these new evolutionary wake modulations result in distinct wake patterns, vortex structures, and associated hydrodynamic force features for the pair of side-by-side dual-step circular cylinders.

Numerical simulations of flows around a dual step cylinder with different diameter ratios at low Reynolds number

The lock-on characteristics, the detailed interactions and downstream evolutions of the wakes behind side-by-side cylinders of unequal diameter (D/d = 2), spaced by a gap ratio 0.75 (G/D = 0.75), are investigated at Reynolds number 600 by the dye flow visualization, laser Doppler anemometry (LDA) and particle image velocimeter (PIV) velocity measurements. The lock-on frequency bands are studied by LDA and PIV at Reynolds number 2,000. The D, d and G are the diameters of the large, the small cylinders and the net gap between two cylinders, respectively. Periodic excitations, in form of rotary oscillation about the cylinder center, are applied to the large cylinder with the same amplitude. It is found that while the large cylinder is excited, two lock-on frequency bands of the wake behind the large cylinder are detected. These two lock-on frequency bands correspond to the primary and the one-third sub-harmonic lock-on of the wake behind large cylinder, respectively. These two lock-on frequency bands distribute symmetrically about the fundamental and the third superharmonic of the natural shedding frequency behind a single cylinder at the same Reynolds number. The left-shifted frequency band (1.8 ≤ fe/fos ≤ 2.0) is not considered as a locked-on frequency band because the phase difference between two excitation frequencies across fe/fos = 2.0 vary significantly. While the wake behind the large cylinder is locked-on at fe/3 (or fos), the gap flow becomes unbiased and the frequency of the wake behind small cylinder remains around the natural shedding frequency. Thus, the frequency band of 3.0 ≤ fe/fos ≤ 3.22 is also not locked-on because the phase difference in the narrow wake excited at fe/fos = 2.93 and 3.07 changes significantly. Note fe and fos denote the excitation frequency and the natural shedding frequency behind a single large cylinder, respectively.

Understanding the flow characteristics of buoyancy sections in power cable and umbilical configurations is crucial for analyzing floating offshore wind turbine systems. Buoyancy sections decouple the motions from the floater and the destination point to ensure the integrity of the system. Using accurate drag coefficients in their design is essential, as they significantly impact the overall behavior of the configuration. Therefore, Computational Fluid Dynamic (CFD) analysis is performed in the present study on a single buoyancy module attached to a power cable represented by a step cylinder configuration. The Partially-Averaged Navier-Stokes (PANS) turbulence model is applied. Its accuracy is validated against experimental findings of a wall-mounted cantilever cylinder and an infinite cylinder. The numerical results reveal that the larger diameter cylinder (LDC) section reduces the drag experienced by the smaller diameter cylinder (SDC) section near the junction. The LDC has a sharp, chamfered, and filleted edge replicating the various shapes of buoyancy modules. The edge design of the LDC affects the drag forces and flow patterns. The SDC has an 8% lower drag coefficient in the fillet edge case than the sharp edge case. The drag coefficient is 3.5% lower for the LDC in the filleted edge case than the sharp edge case. The sharp edge causes a significant separation of the fluid upstream of the SDC. However, this separation is notably reduced when the LDC has a chamfered or filleted edge. Detailed drag coefficients for buoyancy section analysis of power cable configurations have been deduced from the presented results.

The present study presents a new technique for reconstructing the salient aspects of three-dimensional wake topology based on time-resolved, planar, two-component particle image velocimetry data collected in multiple orthogonal planes. The technique produces conditionally averaged flow field reconstructions based on a pattern recognition analysis of velocity fields. It is validated on the wake of a low-aspect ratio dual step cylinder geometry, consisting of a large diameter cylinder (D) with small aspect ratio (L/D) attached to the mid-span of a small diameter cylinder (d). For a dual step cylinders with D/d = 2, and L/D = 1, numerical and experimental data are considered for ReD = 150 (laminar wake) and for ReD = 2100 (turbulent wake). The results show that the proposed technique successfully reconstructs the dominant periodic wake vortex interactions and can be extended to a wide range of turbulent flows.

In this study, the effect of the aspect ratio on the aerodynamics characteristic of flexible membrane wings with different aspect ratios (AR = 1 and AR = 3) is experimentally investigated at Reynolds number of 25000. Time accurate measurements of membrane deformation using Digital Image Correlation system (DIC) is carried out while normal forces of the wing will be measured by helping a load-cell system and flow on the wing was visualized by means of smoke wire technic. The characteristics of high aspect ratio wings are shown to be affected by leading edge separation bubbles at low Reynolds number. It is concluded that the camber of membrane wing excites the separated shear layer and this situation increases the lift coefficient relatively more as compared to rigid wings. In membrane wings with low aspect ratio, unsteadiness included tip vortices and vortex shedding, and the combination of tip vortices and vortex shedding causes complex unsteady deformations of these membrane wings. The characteristic of high aspect ratio wings was shown to be affected by leading edge separation bubbles at low Reynolds numbers whereas the deformations of flexible wing with low aspect ratio affected by tip vortices and leading edge separation bubbles.

Flow past a circular cylinder with a single stepwise discontinuity in diameter was investigated numerically for the diameter ratio D/d=2 and two Reynolds numbers, ReD=150 and 300. The primary focus was on vortex shedding and vortex interactions occurring in the cylinder wake. In agreement with previous experimental findings, three distinct spanwise vortex cells were identified in the step-cylinder wake: a single vortex shedding cell in the wake of the small cylinder (the S-cell) and two vortex shedding cells in the wake of the large cylinder, one in the region downstream of the step (the N-cell) and the other away from the step (the L-cell). Due to the differences in vortex shedding frequencies, complex vortex connections occurred in two vortex interaction regions located between the adjacent cells. However, distinct differences in vortex splitting and vortex dislocations were identified in the two regions. The region at the boundary between the S-cell and the N-cell was relatively narrow and its spanwise extent did not fluctuate significantly. In this region, vortex dislocations manifested as half-loop connections between two S-cell vortices of opposite sign. In contrast, the region at the boundary between the N-cell and the L-cell exhibited transient behavior, with large scale vortex dislocations causing cyclic variation in the extent of N-cell vortices. Spectral analysis of velocity data showed that the presence of the N-cell was continuous through all simulations. For ReD=300, small scale streamwise vortices forming in the wake of the large cylinder weaken the primary spanwise vortices and vortex connections, complicating vortex dynamics in the step-cylinder wake. However, no significant Reynolds number effect on the average spanwise extent of the vortex cells and the two transition regions between neighboring cells was observed. Finally, formation of N-cell vortices was shown to be linked to downwash fluctuations near the step.

Flow around a dual step cylinder for D/d = 2 and L/D = 5 at a low Reynolds number of ReD = 200 is numerically investigated utilising the immersed boundary method. The vortex dislocation caused by two steps is investigated. It was found that a pair of streamwise vortex - the centre vortex exists at the downstream of the large cylinder. Meanwhile, due to the barrier effect of the centre vortices, a very weak L-cell exists behind the centre of the large cylinder. In a complete dislocation cycle, three positive and negative half-loop connections appear alternately. This cycle is related not only to the phase realignment of the different vortex cells, but also to the connection realignment. Moreover, the lateral velocity is always dominated by the vortex shedding frequency. While in the streamwise velocity spectra, the vortex shedding frequency gradually dissipates in the downstream, leaving lower frequencies of dislocation.

Cutout effects on the vibration of sandwich auxetic cylindrical shells with an experimental validation

An experimental investigation of fluid loading on large smooth rectangular cylinders of five different aspect ratios was carried out at the Hydrodynamics Laboratory of the University of Glasgow. The cylinders were mounted vertically as surface piercing and horizontally submerged and were subjected to regular waves. The wave force coefficients corresponding to low Keulegan-Carpenter numbers were obtained. The results show that inertia and drag coefficients are dependent of Reynolds and Keulegan-Carpenter numbers and the frequency parameter. It is found that the drag coefficient exhibits large values as KC number approaches zero and then falls sharply as KC number increases within a small range. Inertia and drag coefficients are found to be strongly affected as the cylinders aspect ratios vary. Inertia and drag coefficients are found to be higher for vertical cylinders than those of corresponding horizontal cylinders. The calculated forces using Morison equation through the use of experimentally determined inertia and drag coefficients is found to be in good agreement with the meas-ired forces at low KC numbers. INTRODUCTION With the necessity of reducing the capital cost in exploring marginal fields, new offshore structure designs are emerging with non-circular cylindrical members. An offshore platform whose members made of rectangular cross-section cylinders is considered to be economically more viable than the conventional designs with circular cylindrical sections. New generation of semi-submersible drilling rigs and tension-leg platforms whose hulls and legs are conforming to rectangular geometry in cross-section are examples of these new designs. However, the circular cylindrical geometry has always been the sentre of attention in model tests when investigating the fluid loading. While a large amount of fluid loading data for circular cylinders have been accumulated over the years, relatively little is known about the loading on rectangular cylinders. The design of marine structures requires the prediction of wave & current induced forces. The inline force applied on a body immersed in an oscillating fluid is traditionally calculated using the well-known Morison equation. Since its introduction forty years ago, the Morison equation developed by Morison, O'Brien, Johnson and schaaf1 has become widely used and several experimental results have shown that it has enough accuracy for practical applications. The Morison equation gives the in-line force acting on a cylinder as a linear sum of the drag and inertia force components. The in-line force per unit length is expressed as (mathematical equation)(available in full paper) where the hydrodynamic coefficients CD & CM must be determined experimentally. Keulegan & carpenter2 were the pioneers in using the Morison equation to compute forces on submerged horizontal circular cylinders and flat plates placed in the node of a standing wave. They successfully correlated their experimentally determined CM & CD with a period parameter (herein referred as Keulegan-Carpenter KC number) defined as UmT/D. They did not find any significant dependence of these coefficients on Reynolds number. Later Sarpkaya3,4 using his well known Ushaped water oscillation tank generated a large amount of data giving inertia CM, drag CD and lift CL coefficients for circular cylinders. He found that these coefficients were dependent not only on Keulegan Carpenter number but on Reynolds number and roughness of the cylinders as well.

Voluminous research exists on the effect of combination of low Reynolds number flow over low aspect ratio flat plate wings for usage in micro-aerial vehicles and UAVs, as they also fly under similar conditions and combination of low aspect ratio and low Reynolds number. It has been well established by many researchers (Torres and Mueller in AIAA 42(5):865–873, 2004; Okamoto and Azuma in AIAA 49(6):1135–1150, 2011; Mizoguchi and Itoh in AIAA 51(7):7–52, 2013; Shields and Mohseni in AIAA 50(1):85–99, 2012; Mizoguchi and Kajikawa in Trans Jpn Soc Aero Sp Sci 59(2):56–63, 2016; Pelletier and Mueller in J Aircr 37(5):825–832, 2000; Liu and Hsiao in J Mech 28(01):77–89, 2012; Taira and Colonius in J Fluid Mech 623:187–207, 2009) that low aspect ratio wings in low Reynolds number flow gives a higher lift coefficient and stall angle is also increased which is quite different from the high aspect ratio wing. Also, it is a well-established fact in the existing literature that linear theories cannot be applied as in case of high aspect ratio wings because of non-linear increase in lift coefficient. The reason for such increase in lift and stall angle has been attributed to wingtip vortices that become prominent in low aspect ratio wings called the vortical lift which keeps on increasing up to a certain high angle of attack till it interacts with the separation bubble. In the past, very limited work has been done to study the vortices and their contribution in enhancement of aerodynamic characteristics. In the present work, flat plate model with corrugations at an aspect ratio (AR) of 1.0 are studied and compared with flat plate wing of AR 1.0; also flow visualization in water tunnel has been carried out at Reynolds number of 102 to ascertain the flow physics involved.

This study investigates the three-dimensional (3D) wake transition of flow around rectangular cylinders with seven aspect ratios (AR = 0.25, 0.5, 1, 2, 3, 4, and 5). Direct numerical simulations were performed for Reynolds numbers up to Re = 600. Ten distinct instability modes are observed, manifesting as ordered or disordered states depending on Re and AR. Based on their similarities, these modes are classified into four categories: (i) A, (ii) B, (iii) quasi-periodic, and (iv) quasi-subharmonic. The characteristics of these modes, including their spanwise wavelength and the Reynolds number range in which they emerge, are thoroughly documented for each aspect ratio. The results indicate that increasing the aspect ratio generally raises the critical Reynolds number for the onset of secondary wake transition, with values ranging from approximately Recr = 95 for AR = 0.25 to Recr = 478.5 for AR = 5. However, an earlier onset of three-dimensionality is observed at AR = 4 compared to AR = 3, a phenomenon attributed to variations in vortex shedding dynamics. Furthermore, based on interactions between leading-edge and trailing-edge vortices, three distinct vortex-shedding patterns are identified for elongated cylinders (AR = 3–5). Notably, for the smallest aspect ratio (AR = 0.25), a transition in the base flow from a von Kármán vortex street to a two-layered vortex structure near the cylinder effectively suppresses 3D instabilities, thereby reverting the flow to a two-dimensional state. The study further explores the impact of various instability modes on hydrodynamic forces and vortex shedding frequency.

On the onset of vortex shedding from 2D confined rectangular cylinders having different aspect ratios: Application to promote mixing fluids

Vectorized numerical simulations of unsteady wake behind a low-aspect ratio (double amplitude to span ratio 0.3) sinusoidally pitching plate (Strouhal number 0.4 and 0.5) are carried out for the Reynolds number, Re = 150,300. A non-staggered finite volume based predictor-corrector type of algorithm employing 2nd-order time integration and spatial schemes is used. The first sign of instability appears on the plate promoting separation which becomes more vigorous with the increase in Reynolds number. At low Reynolds number, the separation bubble originating near the plate diffuses in the near wake region and the whole wake oscillates with the plate. Fully developed vortex shedding from the rear edge of the plate is observed at a higher Reynolds number. The shed vortices are slowly convected and eventually diffuses completely at a large downstream distance. At a higher forced frequency the wake does not alter significantly at a lower Reynolds number. However, vigorous vortex shedding leading to two layers of vortex streets from both the sides of the plate is observed at a higher Reynolds number.