The flow around a stepped cylinder with turbulent wake and stable shear layer

Abstract

The turbulent external flow around a three-dimensional stepped cylinder is studied by means of direct numerical simulations with the adaptive mesh refinement technique. We give a broad perspective of the flow regimes from laminar to turbulent wake at $Re_D=5000$ , which is the highest ever considered for this flow case. In particular, we focus on the intermediate Reynolds number $Re_D=1000$ that reveals a turbulent wake coupled with a stable cylinder shear layer (subcritical regime). This flow shows a junction dynamics similar to the laminar $Re_D=150$ , where no hairpin vortex appears around the edges, and just two horseshoe vortices are visible. A new stable vortex in the form of a ring, which coils around the rear area, is also identified. In the turbulent wake, the presence of three wake cells is pointed out: the large and small cylinder cells together with the modulation region. However, the modulation dynamics varies between the subcritical and turbulent regimes. A time-averaged, three-dimensional set of statistics is computed, and spatially coherent structures are extracted via proper orthogonal decomposition (POD). The POD identifies the (long-debated) connection between the N-cell and the downwash behind the junction. Furthermore, as the Reynolds number increases, the downwash phenomenon becomes less prominent. Eventually, a reduced-order reconstruction with the most energetically relevant modes is defined to explain the wake vortex interactions. This also serves as a valuable starting point for simulating the stepped cylinder wake behaviour within complex frameworks, e.g. fluid–structure interaction.

Direct numerical simulation of the turbulent flow around a Flettner rotor

“…The three-dimensional wake develops streamwise structures connecting the shed vortices, with both small-scale braids and large-scale helically twisted patterns downstream in the wake (a result of a mode B three-dimensional wake instability 40 ). Similar patterns have been observed in the context of uniform 41 and stepped 42 , 43 cylinders. In the current case, they not only wrap in the streamwise direction but also develop vertically, carried by the velocity shear.…”

“…The statistical evidence of vortex shedding is quantified by using the vortex formation length, which is defined as the distance between consecutive vortex shedding points. Among the different definitions available in the literature, in this study, the vortex formation length is defined using the location of the maximum time-averaged streamwise velocity fluctuation , following the previous works 42 , 43 , 45 , 46 . In the near wake, two peaks are expected to occur when the Kármán vortex sheet is formed.…”