Investigation on the vortical structures by the Liutex method in turbulent channels at Re_(τ)=180 with scalloped and triangular riblet control

Riblets are a series of small protrusions formed along the flow direction,which have been extensively studied as a passive turbulent drag reduction technique.Experiments and numerical simulations have shown that well-designed riblets can significantly reduce drag in turbulent flows,making them highly promising and valuable for various applications.In this study,we focus on a scalloped riblet,which is designed by smoothly connecting two third-order polynomials,and thus the sharpness of the tip and the curvature of the valley can be well defined.We conduct direct numerical simulations of turbulent channel with smooth plate,scalloped riblet-mounted and triangular riblet-mounted walls.Width in wall units of W^(+)=20 and height-width ratio ofγ=0.5 are selected for both riblet cases.Compared with the smooth plate case,the scalloped riblet case achieves an 8.68%drag reduction,while the triangular riblet case achieves a 4.79%drag reduction.The obtained drag reduction rate of the triangular riblet is consistent with previous experiments and simulations,and the results indicate that the scalloped riblet is more effective in reducing drag and deserves further investigation.We compare turbulent statistics of the scalloped riblet case with those of the triangular riblet case.The mean velocity profiles of riblets are similar,but both the Reynolds shear stress and second-order statistics of velocity fluctuations and Liutex are significantly reduced in the scalloped riblets controlled turbulent channel,indicating that the scalloped riblet can more effectively suppress the spanwise and wall-normal turbulent intensity near the wall.We also compare the pre-multiplied spectra of streamwise velocity and streamwise Liutex component for the three cases to investigate the energy distribution and characteristics of Liutex distribution.The Liutex vortex identification method is also utilized to analyze the instantaneous flow field,which provides insights into the flow field and could be beneficial for the further optimization of riblet.

Identification of vortex boundaries in two-dimensional incompressible flows based on the Liutex-shear interaction

According to the Liutex-shear decomposition,vorticity can be decomposed into a rotational part,i.e.,the Liutex vector,and a residual shear part.With this decomposition,the vorticity transport equation can be used to formulate a governing equation for Liutex easily for two-dimensional incompressible flows with a source term depending on the residual shear.The dynamics of Liutex-identified structures is then studied in a Taylor-Green vortex flow and a flow past a cylinder at Reynolds number of 200.It is revealed that such boundaries exist outside which the shear has trivial impact on the evolution of Liutex and inside which enhancing and weakening effects of shear on Liutex can be observed.In addition,there is a strong dissipation effect upon Liutex on these boundaries.Based on the interaction mechanism between Liutex and shear,we argue that the vortex boundaries can be identified by these highly dissipative boundaries.In contrast,traditional methods use iso-surfaces of arbitrarily selected thresholds to represent vortex boundaries.The current method of identifying vortex boundaries based on the Liutex-shear interaction has a clearer theoretical base and avoids the arbitrary selection of thresholds.Extensions to three-dimensional incompressible flows can be made in future following the same procedure but with a slightly more complex vorticity transport equation which includes the velocity gradient induced stretching or tilting term.

A Liutex-based subgrid stress model for large-eddy simulation

The concept of vortex is crucial in both understanding and modeling of turbulence.For large eddy simulation(LES),the effect of small-scale eddies onto the large scales or the resolved flow field is modeled by subgrid stress models.Even though the rotating motions of fluids,i.e.,vortices or eddies are central in developing turbulent models,vortex identification methods are seldom used in these models.In this study,we develop a new subgrid model based on the Liutex vector,a new quantity introduced to decompose fluid motions into rigid rotation,pure shear and stretching,and thus identify vortices.The new model is then applied in a decaying homogeneous isotropic turbulence(DHIT)and a turbulent channel flow at Reynolds number Reτ=180.It is shown that the new model can predict accurate energy spectra compared with experiments in DHIT and give a well-matched velocity profile in turbulent channel flow without changing the form of the model.Future directions include improvement of the Liutex based model,for example developing anisotropic subgrid models,and its applications in various turbulent flows.