Vagesh D. Narasimhamurthy

Cellular vortex shedding behind a tapered circular cylinder.

Vortex shedding behind a tapered circular cylinder with taper ratio 75 placed normal to the inflow has been studied. The Reynolds numbers based on the uniform inflow velocity and the diameter of the cylinder at the wide and narrow ends were 300 and 102, respectively. In the present direct numerical simulation study it was observed that even with a very long time sampling a discrete cellular shedding pattern prevails. This is in contrast to what Parnaudeau et al. [J. Turbulence 8, 13 (2007)] speculated in their tapered cylinder study, where they suggested that with a longer time sampling a diffused cellular pattern might appear. In the present investigation it was found that streamwise vorticity increases as vortex dislocation occurs, an effect also reported by Piccirillo and Van Atta [J. Fluid Mech. 246, 163 (1993)] in their experimental study. Flow visualizations revealed that both modes A and B secondary flow structures coexist along the span of the present tapered cylinder. The wavelength of mode B is ...

Vortex shedding in flow past an inclined flat plate at high incidencea)

The properties of asymmetric wake patterns behind a flat plate inclined at angles of attack 20°, 25°, and 30° are investigated. The Reynolds number based on the inflow velocity and the plate width is 1000. Both two-dimensional and three-dimensional calculations are performed by direct numerical simulations. Compared to the three-dimensional simulations, the two-dimensional calculations predict a significantly lower pressure on the rear surface of the plate, which consequently leads to very high drag and lift forces on the plate. The asymmetric mean wake flow, turbulence properties, and coherent patterns in the three-dimensional simulations are analysed by time- and phase-averaged techniques. Unlike the symmetric wake flow, the vortices shed from the leading and trailing edges of an inclined plate possess unequal strength with the trailing edge vortex having higher strength. It is observed that the present three-dimensional simulations predict results which compare well with the experimental data. In addit...

Cellular vortex shedding in the wake of a tapered plate

(Received 18 December 2007 and in revised form 28 August 2008) Direct numerical simulation (DNS) of vortex shedding behind a tapered plate with the taper ratio 20 placed normal to the inflow has been performed. The Reynolds numbers based on the uniform inflow velocity and the width of the plate at the wide and narrow ends were 1000 and 250, respectively. For the first time ever cellular vortex shedding was observed behind a tapered plate in a numerical experiment (DNS). Multiple cells of constant shedding frequency were found along the span of the plate. This is in contrast to apparent lack of cellular vortex shedding found in the high-Reynoldsnumber experiments by Gaster & Ponsford (Aero. J., vol. 88, 1984, p. 206). However, the present DNS data is in good qualitative agreement with similar high-Reynoldsnumber experimental data produced by Castro & Watson (Exp. Fluids, vol. 37, 2004, p. 159). It was observed that a tapered plate creates longer formation length coupled with higher base pressure as compared to non-tapered (i.e. uniform) plates. The three-dimensional recirculation bubble was nearly conical in shape. A significant base pressure reduction towards the narrow end of the plate, which results in a corresponding increase in Strouhal number, was noticed. This observation is consistent with the experimental data of Castro & Rogers (Exp. Fluids, vol. 33, 2002, p. 66). Pressuredriven spanwise secondary motion was observed, both in the front stagnation zone and also in the wake, thereby reflecting the three-dimensionality induced by the tapering.

Oblique and cellular vortex shedding behind a circular cylinder in a bidirectional shear flow

Vortex shedding in the transitional wake of a circular cylinder in a shear flow has been investigated. The focus has been on the effect of a bidirectional shear, i.e., the oncoming unidirectional flow varied linearly both in the spanwise and cross-stream directions. The computer experiments showed that the bidirectional shear resulted in a wake with oblique and cellular vortex shedding similar to the cylinder wake resulting from spanwise shear alone. The presence of a planar shear, however, gave rise to longer cellular cells. Due to the bidirectional shear inflow, the pressure was higher along the high-velocity side of the cylinder surface than along the low-velocity surface and at the same time exhibited a spanwise variation, which gave rise to secondary motions along the stagnation line and in the base region. Even though the cross-stream shear component was four times larger than the spanwise shear, the latter tended to dominate the three-dimensional wake dynamics.

Three-dimensional wake transition behind an inclined flat platea)

Transition phenomena in the wake of a flat plate at 25° angle of attack are investigated by means of three-dimensional computer simulations. The Strouhal number versus Reynolds number relationship was determined for Re from 275 to 800. The Strouhal number turned out to be independent of the Reynolds number for Re > 400 and distinctly lower than that reported from recent two-dimensional simulations. A first subharmonic frequency was detected already at Re = 300, at which the originally two-dimensional wake also became three-dimensional. The spanwise wavelength of the most energetic three-dimensional mode turned out to be about two times the projected width of the plate and almost independent of Re. The complexities of the vortex shedding increased gradually with increasing Reynolds number until a turbulent-like state with a continuous spectrum of spanwise scales was found. However, while a strict spanwise periodicity was observed for Re = 350, a more irregular wake topology occurred at Re = 325 with two di...

Cellular vortex shedding in the wake of a tapered plate at low Reynolds number

The unsteady near wake behind a linearly tapered plate has been investigated numerically. The tapering made the Reynolds number based on the inflow velocity and the local width of the plate vary from 25 to 100. The wake flow comprised three different flow regimes coexisting side by side. The wake flow was steady behind the narrow end of the plate. Periodic vortex shedding occurred downstream from where the local Reynolds number exceeded 32. Vortex dislocations enabled a cellular shedding pattern with shedding frequency decreasing toward the wide end of the plate. The regular oblique vortex shedding near midspan was subjected to three-dimensional scrambling toward the wide end of the plate which gave rise to streamwise-oriented vortex structures. The Strouhal number was distinctly lower than in the wake of a uniform plate whereas the base pressure coefficient was substantially higher.

On oblique and parallel shedding behind an inclined plate

Three-dimensional wake instabilities in the form of oblique shedding and vortex dislocations in the flow past an inclined flat plate of angle of attack 20° and Reynolds number 1000 have been reported earlier [D. Yang, B. Pettersen, H. I. Andersson, and V. D. Narasimhamurthy, Phys. Fluids 24, 084103 (2012)]10.1063/1.4744982. In the current study, direct numerical simulations were performed to further explore this bifurcation. At lower Reynolds numbers, i.e., well below 525, the three-dimensional wake was found to be stable and in a parallel shedding mode. However, as the Reynolds number increases, it was observed that both parallel and oblique vortex sheddings arose naturally. Vortex dislocations appeared at the juxtaposition of oblique and parallel shedding modes. The velocity signals were analyzed by a wavelet transformation, from which the instantaneous characteristics of three-dimensional vortex shedding were obtained and examined. Results show that the phase difference of shed vortex rollers in the sp...

Floquet stability analysis of the wake of an inclined flat plate

The route from a time-periodic two-dimensional wake flow to a three-dimensional flow has been investigated by means of linear Floquet stability analysis. The critical Reynolds number for the onset of three-dimensional instabilities in the wake behind a flat plate with an angle of attack α in the range from 20° to 30° with respect to the free stream was determined. For all three angles considered, in the lower wavelength range, the two-dimensional base flow first became unstable with respect to the sub-harmonic mode C. Although the critical Reynolds number decreased with increasing angle of attack, the spanwise wavelength remained close to two times the projected plate width. Qualitatively different transition scenarios were obtained for the three angles of attack with a particularly simple scenario for α = 30°.

Three-dimensional transition characteristics in the wake of an inclined flat plate

The transition phenomena in the wake of an inclined flat plate at angle of attack 25 degrees are investigated numerically. The Reynolds number, based on the free-stream velocity, plate width and kinematic viscosity, between 275 and 800 has been considered. The Strouhal number versus Reynolds number curves were plotted and compared with two-dimensional simulation data. In the present three-dimensional simulation results, for Reynolds number above 350, the Strouhal numbers converge to a constant value and multiple basic frequencies are detected at certain Reynolds numbers. The spanwise wavelength of secondary structure is estimated by using the autocorrelation method. In the range of Reynolds numbers investigated the spanwise wavelengths, non-dimensionalized by the plate projected width, have a constant value which is consistent with the second instability wavelength detected in the case with the plate normal to the flow.

Bilateral shear layer between two parallel Couette flows.

We consider an unusual shear layer occuring between two parallel Couette flows. Contrary to the classical free shear layer, the width of the shear zone does not vary in the streamwise direction but rather exhibits a lateral variation. Based on some simplifying assumptions, an analytic solution is derived for this shear layer. These assumptions are justified by a comparison with numerical solutions of the full Navier-Stokes equations, which accord with the analytical solution to better than 1% in the entire domain. An explicit formula is found for the width of the shear zone as a function of the wall-normal coordinate. This width is independent of the wall velocities in the laminar regime. Preliminary results for a cocurrent laminar-turbulent shear layer in the same geometry are also presented. Shear-layer instabilities are then developed and result in an unsteady mixing zone at the interface between the two cocurrent streams.