We report on a numerical study of the vortex structure modifications and drag reduction in a flow over a rotationally oscillating circular cylinder at a high subcritical Reynolds number, Re=1:4×10⁵. Considered are eight forcing frequencies f=f_e/f₀=0:5, 1, 1.5, 2, 2.5, 3, 4, 5 and three forcing amplitudes Δ_e=ΔD/2U_∞ =1, 2, 3, non-dimensionalized with f₀, which is the natural vortex-shedding frequency without forcing, U_∞ the free-stream velocity, D the diameter of the cylinder. In order to perform a parametric study of a large number of cases (24 in total) with affordable computational resources, the three-dimensional unsteady computations were performed using a wall-integrated (WIN) second-moment (Reynolds-stress) Reynolds-averaged Navier-Stokes (RANS) turbulence closure, verified and validated by a dynamic large-eddy simulations (LES) for selected cases (f = 2.5,Δ = 2 and f = 4, Δ = 2), as well as by the earlier LES and experiments of the flow over a stagnant cylinder at the same Re number described in Palkin et al. (Flow Turbul. Combust., vol. 97 (4), 2016, pp. 1017-1046). The drag reduction was detected at frequencies equal to and larger than f =2.5, while no reduction was observed for the cylinder subjected to oscillations with the natural frequency, even with very different values of the rotation amplitude. The maximum reduction of the drag coefficient is 88% for the highest tested frequency f = 5 and amplitude Δ = 2. However, a significant reduction of 78% appears with the increase of f already for f = 2.5 and Δ = 2. Such a dramatic reduction in the drag coefficient is the consequence of restructuring of the vortex-shedding topology and a markedly different pressure field featured by a shrinking of the low pressure region behind the cylinder, all dictated by the rotary oscillation. Despite the need to expend energy to force cylinder oscillations, the considered drag reduction mechanism seems a feasible practical option for drag control in some applications for Re>10⁴, since the calculated power expenditure for cylinder oscillation under realistic scenarios is several times smaller than the power saved by the drag reduction.

We perform a finely resolved Large-eddy simulation to study coherent vortical structures populating the initial (near-nozzle) zone of a pipe jet at the Reynolds number of 5300. In contrast to ‘top-hat’ jets featured by Kelvin-Helmholtz rings with the non-dimensional frequency St≈0.3−0.6, no high-frequency dominant mode is observed in the near field of a jet issuing from a fully-developed pipe flow. Instead, in shear layers we observe a relatively wide peak in the power spectrum within the low-frequency range (St≈0.14) corresponding to the propagating helical waves entering with the pipe flow. This is confirmed by the Fourier transform with respect to the azimuthal angle and the Proper Orthogonal Decomposition complemented with the linear stability analysis revealing that this low-frequency motion is not connected to the Kelvin-Helmholtz instability. We demonstrate that the azimuthal wavenumbers m=1−5 contain the most of the turbulent kinetic energy and that a common form of an eigenmode is a helical vortex rotating around the axis of symmetry. Small and large timescales are identified corresponding to “fast” and “slow” rotating modes. While the “fast” modes correspond to background turbulence and stochastically switch from co- to counter-rotation, the “slow” modes are due to coherent helical structures which are long-lived and have low angular velocities, in agreement with the previously described spectral peak at low St.

Mixing characteristics and coherent structures populating the near-nozzle area of a rotating-pipe jet at the Reynolds number of 5300 were studied by Large-eddy simulation (LES). The swirl rate, defined as the ratio of the tangential velocity of the inner pipe wall to the bulk axial velocity, varied from 0 to 1, corresponding to a weak-to-moderate swirl intensity, insufficient to induce reverse flow near the nozzle. The visualization shows that for the non-swirling jet the near-wall streaky structures generated in the pipe interact with the shear layer, evolving into hairpin-like structures that become tilted at low rotation rates. For higher swirl, they cannot be recognized as they are destroyed at the nozzle exit. No large-scale coherent structures akin to Kelvin–Helmholtz vortical rings in the ‘top-hat’ jets are identifiable close to the nozzle. Using the single and joint probability density functions of velocity and passive scalar (temperature) fields we quantify the events responsible for the intensive entrainment at various swirl numbers. The isosurface of the temperature field indicates the meandering and precessing motion of the rotating jet core at the axial distance of 6D downstream, where D is the diameter of the pipe. The Fourier analysis with respect to the azimuthal angle and time reveals an interplay between the co- and counter-rotating modes. These findings explain the previously detected but not fully clarified phenomenon of the weakly counter-rotating jet core at low swirl rates.

We study the flow over an infinite cylinder at high sub-critical Reynolds numbers of Re = 1.4 × 10⁵ using the second-moment closure Reynolds Stress Model. The model of Jakirlić and Hanjalić [1] has been previously validated against large-eddy simulations (LES) and experimental data [2]. The focus is on the control of drag and lift forces acting on the cylinder by rotary oscillations of the bluff body with a set amplitude and frequency. We show that, although at low frequencies the drag force fluctuates around the same value as for the non-rotating case, the recirculating bubble behind the cylinder shrinks for sufficiently large amplitudes of oscillations. The results agree with the data from the literature for lower Reynolds numbers suggesting the investigation of the effect of drag reduction at higher frequencies of rotation.

To unravel the widespread perception that the RANS (Reynolds-averaged Navier-Stokes) concept is unreliable in predicting the dynamics of separated flows, we assessed the performance of two RANS closure levels, the linear eddy-viscosity (LEVM) and the second-moment (Reynolds stress, RSM) approaches in a massively separated generic flow over a bluff body. Considered is the canonical, zero-turbulence, cross-flow over an infinite cylinder with reference to our LES and the available DNS and experiments at two Reynolds numbers, Re = 3.9 × 10³ and 1.4 × 10⁵, both within the sub-critical regime with laminar separation. Both models capture successfully the vortex shedding frequency, but the low frequency modulations are detected only by the RSM. At high Reynolds numbers the RSM is markedly superior to the LEVM showing very good agreement with the LES and experimental data. The RSM, accounting naturally for the stress anisotropy and phase lag between the stress and strain eigenvectors, is especially successful in reproducing the growth rate of the turbulent kinetic energy in the initial shear layer which proved to be crucial for accurate prediction of the separation-induced transition. A scrutiny of the unsteady RANS (URANS) stress terms based on the conditional phase-averaged LES data shows a remarkable similarity of the normalized coherent and stochastic (modeled) stress components for the two Reynolds numbers considered. The mixed (cross) correlations, while non-negligible at the low Re number, diminish fast relative to the stochastic ones with increasing Reynolds number and, in the whole, are not significant to undermine the URANS concept and its applicability to high Re flows of industrial relevance.

We describe the low Mach variable-density Navier-Stokes numerical iterative solution procedure implemented in the finite-volume unstructured T-FlowS code. As the test cases we use a number of analytic manufactured solutions and Rayleigh-Taylor instability problem from the literature for algorithm verification purposes. The tests show that the code is second-order accurate in agreement with the spatial discretization scheme. We outline the recent combustion ADEF model implemented in the program.