Lagrangian-based investigation of the transient flow structures around a pitching hydrofoil

The objective of this paper is to address the transient flow structures around a pitching hydrofoil by com- bining physical and numerical studies. In order to predict the dynamic behavior of the flow structure effectively, the Lagrangian coherent structures （LCS） defined by the ridges of the finite-time Lyapunov exponent （FTLE） are utilized under the framework of Navier-Stokes flow computations. In the numerical simulations, the k-w shear stress trans- port （SST） turbulence model, coupled with a two-equation F-Reo transition model, is used for the turbulence closure. Results are presented for a NACA66 hydrofoil undergoing slowly and rapidly pitching motions from 0° to 15° then back to 0° at a moderate Reynolds number Re = 7.5 × 105. The results reveal that the transient flow structures can be observed by the LCS method. For the slowly pitching case, it consists of five stages： quasi-steady and laminar, transition from laminar to turbulent, vortex development, large-scale vortex shedding, and reverting to laminar. The observation of LCS and Lagrangian particle tracers elucidates that the trailing edge vortex is nearly attached and stable during the vortex development stage and the interaction between the leading and trailing edge vortex caused by the adverse pres- sure gradient forces the vortexes to shed downstream during the large-scale vortex shedding stage, which corresponds to obvious fluctuations of the hydrodynamic response. For the rapidly pitching case, the inflection is hardly to be observed and the stall is delayed. The vortex formation, interaction, and shedding occurred once instead of being repeated three times, which is responsible for just one fluctuation in the hydrody- namic characteristics. The numerical results also show that the FTLE field has the potential to identify the transient flows, and the LCS can represent the divergence extent of infinite neighboring particles and capture the interface of the vortex region.

Variable Coefficient KdV Equation and the Analytical Diagnoses of a Dipole Blocking Life Cycle

A variable coefficient Korteweg de Vries （VCKdV） system is derived by considering the time-dependent basic flow and boundary conditions from the well-known Euler equation with an earth rotation term. The analytical solution obtained from the VCKdV equation can be successfully used to explain fruitful phenomena in fluid and other physical fields, for instance, the atmospheric blocking phenomena. In particular, a diploe blocking case happened during 9 April 1973 to 18 April 1973 read out from the National Center for Environmental Prediction/National Center for Atmospheric Research （NCEP/NCAR） reanalysis data is well described by the analytical solution.

Coherent Spanwise Structures in Turbulent Boundary Layer over Drag-Reducing Riblets

The time series of velocity vector fields and their statistics in the turbulent boundary layer(TBL)over riblets and smooth plate were measured by utilizing a time-resolved particle image velocimetry(TR-PIV)system. The mean velocity profiles of the TBL were compared in the case of 0.13 m/s(the riblets with dimensionless peakto-peak spacing being approximately s?≈21)and 0.19 m/s( s?≈28)for these two kinds of plates, respectively. Two kinds of drag-reducing velocity profiles were illustrated and analyzed. Then the spatial topologies of the physical vorticity for the coherent spanwise structures were detected and extracted at the fourth scale by utilizing an improved quadrant splitting method(IQSM). Results revealed that nearly 6.17%, and 10.73%, of a drag reduction was separately achieved over the riblets surface. Besides, it was visualized that the drag-reduction was acquired by the riblets influencing the bursting ejection(Q2)and sweep(Q4)events of the coherent spanwise vortex structures, the Q4 events in particular. Based on such two drag-reducing cases of the riblets, lastly, a simplified KelvinHelmholtz-like linear instability model proposed initially by García-Mayoral and Jiménez(2011)has been discussed. It is still difficult to establish with certainty whether the observed phenomena, the appearance of coherent spanwise structures found at around or below y?≈20 in both cases of s?≈21 and s?≈28 and their topological changes, were consequences or causes of the breakdown of the viscous regime. We prefer to suggest that the interactions between those structures and the riblets, which contain the coherent spanwise structures extending toward the wall and penetrating into the riblet grooves, are the root causes.