Flow interference between groups of three and four equispaced cylinders

This thesis is a study of the interference forces acting on one cylinder comprising a group of three and four cylinders when situated in a free stream flow. The spacing of the cylinders was such that the lines joining their axes formed an equilateral triangle, and a square respectively. The study is split into two parts, (a) potential flow over the groups of cylinders (b) real flow over the groups of cylinders. Bound with copies of the authors' published papers.~Bibliography: pages 132-137

Generalized thick strip modelling for vortex-induced vibration of long flexible cylinders

We propose a generalized strip modelling method that is computationally efficient for the VIV prediction of long flexible cylinders in three-dimensional incompressible flow. In order to overcome the shortcomings of conventional strip-theory-based 2D models, the fluid domain is divided into “thick” strips, which are sufficiently thick to locally resolve the small scale turbulence effects and three dimensionality of the flow around the cylinder. An attractive feature of the model is that we independently construct a three-dimensional scale resolving model for individual strips, which have local spanwise scale along the cylinder's axial direction and are only coupled through the structural model of the cylinder. Therefore, this approach is able to cover the full spectrum for fully resolved 3D modelling to 2D strip theory. The connection between these strips is achieved through the calculation of a tensioned beam equation, which is used to represent the dynamics of the flexible body. In the limit, however, a single “thick” strip would fill the full 3D domain. A parallel Fourier spectral/hp element method is employed to solve the 3D flow dynamics in the strip-domain, and then the VIV response prediction is achieved through the strip-structure interactions. Numerical tests on both laminar and turbulent flows as well as the comparison against the fully resolved DNS are presented to demonstrate the applicability of this approach

Effect of location in an array on heat transfer to a cylinder in crossflow

An experiment was conducted to measure the heat transfer from a heated cylinder in crossflow in an array of circular cylinders. All cylinders had a length-to-diameter ratio of 3.0. Both in-line and staggered array patterns were studied. The cylinders were spaced 2.67 diameters apart center-to-center in both the axial and transverse directions to the flow. The row containing the heated cylinder remained in a fixed position in the channel and the relative location of this row within the array was changed by adding up to five upstream rows. The working fluid was nitrogen gas at pressures from 100 to 600 kPa. The Reynolds number ranged based on cylinder diameter and average unobstructed channel velocity was from 5,000 to 125,000. Turbulence intensity: profiles were measured for each case at a point one half space upstream of the row containing the heated cylinder. The basis of comparison for all the heat transfer data was the single row with the heated cylinder. For the in-line cases the addition of a single row of cylinders upstream of the row containing the heated cylinder increased the heat transfer by an average of 50 percent above the base case. Adding up to five more rows caused no increase or decrease in heat transfer. Adding rows in the staggered array cases resulted in average increases in heat transfer of 21, 64, 58, 46, and 46 percent for one to five upstream rows, respectively

FR3D: Three-dimensional Flow Reconstruction and Force Estimation for Unsteady Flows Around Extruded Bluff Bodies via Conformal Mapping Aided Convolutional Autoencoders

In many practical fluid dynamics experiments, measuring variables such as velocity and pressure is possible only at a limited number of sensor locations, \textcolor{black}{for a few two-dimensional planes, or for a small 3D domain in the flow}. However, knowledge of the full fields is necessary to understand the dynamics of many flows. Deep learning reconstruction of full flow fields from sparse measurements has recently garnered significant research interest, as a way of overcoming this limitation. This task is referred to as the flow reconstruction (FR) task. In the present study, we propose a convolutional autoencoder based neural network model, dubbed FR3D, which enables FR to be carried out for three-dimensional flows around extruded 3D objects with different cross-sections. An innovative mapping approach, whereby multiple fluid domains are mapped to an annulus, enables FR3D to generalize its performance to objects not encountered during training. We conclusively demonstrate this generalization capability using a dataset composed of 80 training and 20 testing geometries, all randomly generated. We show that the FR3D model reconstructs pressure and velocity components with a few percentage points of error. Additionally, using these predictions, we accurately estimate the Q-criterion fields as well lift and drag forces on the geometries.Comment: 29 pages, 10 figures. Accepted at International Journal of Heat and Fluid Flo

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

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Stratified Taylor-Couette flow: nonlinear dynamics

A series of experiments on stratified Taylor–Couette flow in short aspect ratio wide-gap annuli found an intriguing and not-well-understood dynamics: nonlinear coherent structures appearing and disappearing periodically, along with density layering reminiscent of staircase profiles. A detailed numerical study is presented of the nonlinear dynamics near onset of instability in this setting, which explains most of the characteristics found in the experiments. The simulations show that centrifugal instability of the boundary layer on the inner rotating cylinder produces jets of angular momentum forming Taylor cells that are compressed axially due to the strong stratification. These cells are not axisymmetric from the onset, but are in fact two sets of Taylor cells displaced axially that meet in localized azimuthal defect regions where the cells are patched together; the whole structure is a rotating wave with azimuthal wavenumber m=1. The presence of endwalls in this short aspect ratio annulus is critical for the understanding of the dynamics. Their impact cannot be accounted for in idealized axially periodic models. Another key ingredient is the role played by the symmetries of the system. Although the axial reflection symmetry is weakly broken by centrifugal buoyancy effects, following instability there are various branches of solutions corresponding to the different ways the system's symmetries may be broken.Postprint (published version

Experimental and numerical investigation of three equispaced cylinders in cross-flow

Flow around a cluster of three equally spaced cylinders with a spacing ratio of P/D = 1.35 was studied experimentally and numerically. The main focus of this investigation is the effect of cluster orientation on flow characteristics. Two Reynolds numbers were investigated: ReD = 100 and ReD = 2100. Experiments were conducted at the University of Waterloo water flume facility at ReD = 2100 for a range of cluster orientation angles 0◦ ≤ α ≤ 60◦ using hydrogen bubble technique, particle image velocimetry, and laser Doppler velocimetry. The flow was modeled numerically at ReD = 100 and ReD = 2100 for α = 0◦ and 60◦. A laminar model was used for ReD = 100 and a RANS model was used for ReD = 2100. For the RANS case, four turbulence models were evaluated: SST, k−ω, k−ε, and LRR-IP. For all cluster orientations, the experimental results show large scale vortex shedding, similar to single bluff body flows, beyond x/D = 5. Wide and narrow wakes are produced downstream of the cluster due to jets, that form in the passages between the cylinders, exiting the cluster. Small scale vortices are shed from shear layers bounding the narrow wake(s). For α = 0◦, a bistable wake development is present, in which the jet exiting the cluster is directed towards either one of the two downstream cylinders. The asymmetry in the wake development about y = 0 decreases as α increases from 0◦ to 60◦. For α = 60◦, the wake development is symmetric, consisting of two narrow wakes behind the two upstream cylinders and a wide wake behind the downstream cylinder. For all orientations, interactions between the inner shear layer of the wide wake and small scale vortices shed from the shear layers bounding the narrow wake occur. As a results, each large scale structure forming on this side of the wake axis encompasses smaller scale vortices with opposite vorticity sense, which reduces the coherence of the large scale vortices compared to that of their counterparts on the opposite side of the wake for 0◦ ≤ α < 60◦. The small scale vortex shedding frequency increases with increasing α for 0◦ ≤ α ≤ 60◦. For all orientations, the large scale vortex shedding frequency, when scaled by the projected height of the cluster, is equal to that for a single cylinder at the same Reynolds number, suggesting that the cluster behaves like a single bluff body. For ReD = 100, the numerical results show a symmetric wake development for α = 0◦ and 60◦. No bistable wake development is present for α = 0◦. Also, there is no presence of small scale shedding in the near wake of the cluster for both orientations. The Strouhal number based on the projected height of the cluster is equal for both cluster orientations and to that expected for a single cylinder at the same Reynolds number. The total drag on the cluster for α = 0◦ and 60◦ is CP ≈ 1.35 and CP ≈ 1.5, respectively. The maximum drag occurs on the two upstream cylinders for α = 60◦, and is approximately 10% larger than that on a single cylinder. The drag coefficient on all other cylinders is at least 25% lower than that on a single cylinder. Mean lift forces are produced on the two downstream cylinders for α = 0◦ and the two upstream cylinders for α = 60◦. The total RMS for the cluster for α = 0◦ and 60◦ is CL′ ≈ 0.3 and CL′ ≈ 0.5, respectively. The maximum lift RMS occurs on the downstream cylinder for α = 60◦ and is approximately 35% larger than that for a single cylinder. Numerical results for ReD = 2100 show that, out of the four turbulence models tested, the SST and k−ω models perform the best overall when compared to experimental results. Based on the results of the SST model, for α = 0◦ (i.e., the bistable case), the maximum drag occurs on the cylinder producing the narrow wake. For α = 60◦, the maximum drag occurs on cylinders 1 and 3. For both orientations, the total drag coefficient for the cluster is approximately 15% smaller than that for a single cylinder case. Also, the mean lift forces are generated only on the two downstream cylinders for α = 0◦ and the two upstream cylinders for α = 60◦

Vortex shedding characteristics of multi-column structure with or without horizontal connections

Vortex flow around multiple columns of finite length is ubiquitous in engineering. The present work focuses on the basic fluid physics in terms of the vortex shedding flow patterns and their dependence on structural configurations and flow parameters. Though widely documented in the literature, there is no consensus on certain aspects of the wake characteristics immediately behind the obstacles for a multi-column structure at a relative high Reynolds number range. A comprehensive set of numerical simulations has been conducted to investigate the flow interactions with four square section shaped columns in a diamond configuration, which is complimented by experiments using particle image velocimetry and force measurements in a physical model with Reynolds numbers varying from 3.7×104 to 6.0×104. Horizontal structural members called pontoons were added near the end of the columns to alter the interactions with the surrounding fluid. This work reveals further insights of the fluid physics including the interactions of the vortex shedding processes due to the multi-columns and pontoons. The pontoons are seen blocking the vortices shed from the free end of the column by pushing the recirculation region further away from the free end of each column. In addition to the vortex shedding period being increased, further examination of the wake region indicates that the vortex street tends to be tidier and more structured by adding the pontoons to a basic multi-column structure. The findings will lead to better understanding in vortex shedding fluid physics and improved design in new offshore structure development such as deep-draft semi-submersibles and tension leg platforms