Bjørnar Pettersen

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...

Crossflow past a prolate spheroid at Reynolds number of 10000

It is well known that most fluid flows observed in nature or encountered in engineering applications are turbulent and involve separation. Fluid flows in turbines, diffusers and channels with sudden expansions are among the widely observed areas where separation substantially alters the flow field and gives rise to complex flow dynamics. Such types of flows are referred to as internal flows since they are confined within solid surfaces and predominantly involve the generation or utilization of mechanical power. However, there is also a vast variety of engineering applications where the fluid flows past solid structures, such as the flow of air around an airplane or that of water around a submarine. These are called external flows and as in the former case the downstream evolution of the flow field is crucially influenced by separation. The present doctoral thesis addresses both internal and external separated flows by means of direct numerical simulations of the incompressible Navier-Stokes equations. For internal flows, the wall-driven flow in a onesided expansion channel and the pressure-driven flow in a plane channel with a single thin-plate obstruction have been studied in the fully developed turbulent state. Since such geometrical configurations involve spatially developing turbulent flows, proper inflow conditions are to be employed in order to provide a realistic fully turbulent flow at the input. For this purpose, a newly developed technique has been used in order to mimic an infinitely long channel section upstream of the expansion and the obstruction, respectively. With this approach, we are able to gather accurate mean flow and turbulence statistics throughout each flow domain and to explore in detail the instantaneous flow topology in the separated shear layers, recirculation regions as well as the recovery zones. For external flows, on the other hand, the flow past a prolate spheroid has been studied. Here, a wide range of Reynolds numbers is taken into consideration. Based on the characteristics of the vortical structures in the wake, the flow past a prolate spheroid is classified as laminar (steady or unsteady), transitional or turbulent. In each flow regime, the characteristic features of the flow are investigated by means of detailed frequency analysis, instantaneous vortex topology and three-dimensional flow visualizations.

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.

Asymmetries in an obstructed turbulent channel flow

The asymmetric flow pattern caused by a single thin-plate obstruction in a plane channel has been explored by means of direct numerical simulations. The blockage ratio was 1:2 and the bulk Reynolds number about 5700. In order to mimic an infinitely long channel section upstream of the obstruction, realistic dynamic inflow conditions were provided by a promising technique proposed by Barri et al. [“Inflow conditions for inhomogeneous turbulent flows,” Int. J. Numer. Methods Fluids 60, 227 (2009)]. The fluid downstream of the symmetric obstruction was sucked toward one side where a modestly long region of rather strong recirculating flow was observed. The weaker recirculation bubble formed at the opposite side was 17 times longer than the obstruction height and almost four times the size of the shorter bubble. The overall flow pattern turned out to be rather different from that observed in a similar study of channel flow subjected to periodically repeating obstructions by Makino et al. [“Turbulent structure...

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...

Dynamics in the turbulent wake of a curved circular cylinder

Understanding the physics of turbulent wakes is an essential, yet complex task in the study of turbulent flows. In the present paper we investigate the flow past a curved body of circular cross-section. The inflow velocity is aligned with the curvature of the cylinder and directed towards its convex face. We conduct direct numerical simulations at a Reynolds number of 3900 in order to obtain a fully turbulent wake. The instantaneous vortical structures reveal that the primary vortices are roughly aligned with the curved axis. Despite the presence of isolated splitting events in the frequency of the vortex shedding, there is one single shedding frequency that dominates this process. Velocity time-traces confirm that the shear layers exhibit intermittency, which is manifested as large amplitude fluctuations. The intensity of these instabilities is increased by the secondary flow along the recirculation region, thereby influencing the dynamics of the near wake. Several spots of zero mean velocity reside next to the baseline within the recirculation region, displacing the back-flow region further downstream. It is suggested that this displacement is induced by the secondary flow, in combination with the symmetry boundary condition imposed at the top plane.

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°.

Introducing innovative approaches to learning in fluid mechanics : a case study

The purpose of the current article is to examine the impact of laboratory demonstrations and computer visualizations on learning in a third-year fluid mechanics course at Norwegian University of Science and Technology (NTNU). As a first step, on entering the course, students were exposed to a laboratory demonstration focusing on the nature of waves. Students were subsequently taught the theory of wave mechanics in a regular class along with exercises. Finally, the computer algebra system Maple was used to simulate physical properties of the waves using the mathematical equations. The illustrations throughout the paper are examples of some of the pedagogical devices that students were exposed to during the project. The students enjoyed the demonstrations, but there are some indications that the interventions did not help to improve learning of phenomena.