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Flow dynamics of bluff bodies
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posted on 06.02.2017by Rao, Anirudh Narayan
A computational study investigating the flow past bluff bodies in the low Reynolds
numbers range (Re ≤ 750) is presented. Two- and three-dimensional investigations are performed to investigate various flow transitions that occur when canonical bluff bodies such as circular cylinders and spheres are placed near a planar boundary, rotated or a combination of the two effects.
Control parameters such as α, the non-dimensionalised rotation rate, defined as the ratio of the tangential velocity on the body surface to the oncoming fluid velocity, and gap height G/D, the distance between the body and the wall (G) non-dimensionalised by the diameter D, are extensively used together with the Reynolds number. For these investigations, α is varied between ±3, where positive values correspond to prograde rotation and negative values correspond to retrograde rotation. The gap height is varied from G/D = ∞ for bodies in freestream to G/D ~ 0 for bodies near a wall.
A spectral element based solver is used to solve the Navier-Stokes equations in twoand
three-dimensions. Computational domains are constructed so that the evaluated
flow parameters, such as the force coefficients and the shedding frequency, are accurate
to an error of less than 1%. Spatial resolution studies are performed to obtain a tradeoff
between accuracy and computational time. For all investigations, the results vary
by less than 0.5% with respect to the domain with the highest resolution.
The first of these studies investigates the onset of various three-dimensional modes in
the wake of a rotating cylinder in freestream as the rotation rate is varied for α ≤ 2.5 and Re ≤ 400. Two transitions are considered in this study; the first being the transition to periodic flow where vortex shedding occurs. As the rotation rate was increased, the onset of periodic flow was delayed and altogether suppressed for α ≥ 2.1. The second transition considered is the transition to three-dimensionality using a technique known as linear stability analysis. For rotation rates α ≤ 1, the onset of the three-dimensional modes occurs in the unsteady regime, and is identical to that observed for a non-rotating cylinder, although the rotation rate delays the onset of transition to higher Reynolds numbers. For higher rotation rates, the three-dimensional scenario becomes increasingly complex, where three new modes bifurcate from the unsteady base flow and two new modes bifurcate from the steady base flow. The spatio-temporal characteristics and the physical mechanism leading to the instability of these modes are discussed.
A second study investigates the flow dynamics for a circular cylinder translating
along a wall at different gap heights. From the two-dimensional computations, the force
coefficients and the shedding frequencies were quantified. At large spacings, G/D ≥ 0.28, the transition to three-dimensionality was observed on the unsteady base flow, while below this gap height, the three-dimensional transition occurred in the steady regime at Reynolds numbers lower than the transition to periodic flow. Simulations were further carried out to determine the variation of the transitional Reynolds numbers for cylinders rolling along a wall. For forward rolling cases, the transition to unsteady flow occurred at increasingly low Reynolds numbers, while reverse rolling delayed the onset of periodic flow to higher Reynolds numbers and periodic flow was suppressed for α ≤ −1.5. Linear stability analysis indicated that the onset of three-dimensional flow was lowered as the rotation rate was increased to higher positive values of α, while three-dimensionality was suppressed for negative rotation rates of α ≤ −2. For the cylinder sliding along a wall (α = 0), stability analysis at higher Reynolds numbers in the unsteady state shows multiple modes unstable to spanwise perturbations. The three-dimensional simulations indicate that the flow eventually becomes chaotic, possibly due to the interaction between the various modes.
The second study was further extended to investigate the flow past multiple bodies
near a wall. The additional control parameter for this study was the separation distance
S/D, where S is the distance between the cylinders and Reynolds number, while the
rotation rate was fixed at α = 0. For cylinders at very small and very large separations, the flow features were identical to that of the singular cylinder. As Reynolds number was increased, unsteady flow was detected at close spacings, which led to an increase in the drag coefficient on the downstream cylinder. Stability analysis showed similar trends for the limiting cases, while for intermediate spacings, the flow first became unstable, and then restabilised at slightly higher Reynolds number. This flow further became unstable at higher Reynolds number. Three-dimensional simulations over a range of separations show the flow transitioning to a chaotic state akin to the singular cylinder.
The final study investigated the wake of a forward rolling sphere for Re ≤ 500. At Re ~ 140, vortex shedding occurred by the formation of hairpin vortices which moved away from the wall and convected downstream. A secondary transition involving the loss of planar symmetry occurred at Re ~ 192, where the hairpin vortices were displaced laterally along the wake centreline, giving a sinuous structure to the wake when viewed from above. Beyond this transition, the lateral oscillations exhibited a 7 : 3 resonance with the hairpin vortex shedding. As Reynolds number was increased, the flow progressively became more disorganised and chaotic. At the highest tested Reynolds number of 500, the wake was spatio-temporally chaotic, while retaining its sinuous structure.