Hairpin vortices in the largest scale of turbulent boundary layers

We have conducted direct numerical simulations of a turbulent boundary layer for the momentum-thickness-based Reynolds number ${\mathit{Re}}_{\theta }$ = 180–4600. To extract the largest-scale vortices, we coarse-grain the fluctuating velocity fields by using a Gaussian filter with the filter width comparable to the boundary layer thickness. Most of the largest-scale vortices identified by isosurfaces of the second invariant of the coarse-grained velocity gradient tensor are similar to coherent vortices observed in low-Reynolds-number regions, that is, hairpin vortices or quasi-streamwise vortices inclined to the wall. We also develop a percolation analysis to investigate the threshold-dependence of the isosurfaces and objectively identify the largest-scale hairpin vortices in terms of the coarse-grained vorticity, which leads to the quantitative evidence that they never disappear even in fully developed turbulent regions. Hence, we conclude that hairpin vortices exist in the largest-scale structures irrespective of the Reynolds number.     

Numerical investigation of the effect of convex transverse curvature and concave grooves on the turbulent boundary layer along a cylinder in axial flow

Axisymmetric turbulent boundary layers that develop around streamwise oriented long cylinder-like objects can be found in many applications, such as towed array sonars or marine seismic streamers. In many of these applications, turbulent fluctuations within the boundary layer flow can have a negative impact compared with laminar flow conditions. The aim of the present work is to design a surface modification that influences the turbulent boundary layer around a cylinder in axial flow in order to reduce turbulent fluctuations. To design the surface we consider recent findings regarding the turbulence damping effects of groove-like surface structures and combine these insights with the effect of convex transverse curvature on turbulence. We use large-eddy simulations to investigate the flow around a cylinder of modified design and around a reference circular cylinder. Both flows have a radius-based Reynolds number of ${\text{Re}}_a\approx 1.23\cdot 10^4$. The modified design leads to a 20 % decrease in the average wall shear stress and results in local reductions in the turbulent intensities, Reynolds stress, the temporal velocity spectrum, and the turbulent dissipation rate. The analysis within the anisotropy-invariant space reveals a tendency towards flow relaminarization. However, the new design has no effect on turbulent pressure fluctuations. We provide suggestions on how to further improve the surface design to achieve even greater flow stabilization.     

A formulation of PANS capable of mimicking IDDES

The partially averaged Navier–Stokes (PANS) model, proposed in Girimaji (2006), allows to simulate turbulent flows either in RANS, LES or DNS mode. The PANS model includes $f_k$ which denotes the ratio of modeled to total kinetic energy. In RANS, $f_k=1$ while in DNS it tends to zero. In the present study we propose an improved formulation for $f_k$ based on the H-equivalence introduced by Friess et al. (2015). In this formulation the expression of $f_k$ is derived to mimic Improved Delayed Detached Eddy Simulation (IDDES). This new formulation behaves in a very similar way as IDDES, even though the two formulations use different mechanisms to separate modeled and resolved scales. They show very similar performance in separated flows as well as in attached boundary layers. In particular, the novel formulation is able to (i) treat attached boundary layers as properly as IDDES, and (ii) “detect” laminar initial/boundary conditions, in which case it enforces RANS mode. Furthermore, it is found that the new formulation is numerically more stable than IDDES.     

Evolution of a wall-attached buoyant plume in confined boxes: Direct numerical simulations,entrainment coefficient and an integral model

The evolution of a wall-attached plume in a confined box is studied here with the aid of three dimensional direct numerical simulations (DNS). The plume originates from a local line heat source of length, L, placed at the bottom left corner of the box. The Reynolds number of the wall plume, based on box height and buoyant velocity scale, is ${\mathit{Re}}_H=14530$ and boxes of two different aspect ratios (ratio of box width to height) for a particular value of L are simulated. We observe that the plume develops along the vertical sidewall while remaining attached to it before spreading across the top wall to form a buoyant fluid layer and eventually moving downwards and filling the whole box. The original filling box model of Baines and Turner (1969) is modified to incorporate the wall shear stress, and the results from the DNS are compared against the new model. In modelling plumes, we find that the entrainment coefficient ($\alpha$) for wall-attached plumes is reduced to approximately half of that in the free plume, and the main reason is a diminished contribution of turbulence production to $\alpha$ resulting from a restricted ability of the large-scale eddies to transport momentum. Also, unlike the free plume where away from the source inertial forces balances buoyancy forces, here in our simulations of wall-attached plumes this balance is marginally off, likely due to wall friction. A reasonable agreement is observed between our model and DNS data for the volume and momentum fluxes in the quiescent uniform environment and also for the time-dependent buoyancy profile calculated far away from the plume.