Effects of the Reynolds number on a scale-similarity model of Lagrangian velocity correlations in isotropic turbulent flows

A scale-similarity model of a two-point two-time Lagrangian velocity correlation(LVC) was originally developed for the relative dispersion of tracer particles in isotropic turbulent flows(HE, G. W., JIN, G. D., and ZHAO, X. Scale-similarity model for Lagrangian velocity correlations in isotropic and stationary turbulence. Physical Review E, 80, 066313(2009)). The model can be expressed as a two-point Eulerian space correlation and the dispersion velocity V. The dispersion velocity denotes the rate at which one moving particle departs from another fixed particle. This paper numerically validates the robustness of the scale-similarity model at high Taylor micro-scale Reynolds numbers up to 373, which are much higher than the original values(R_λ = 66, 102). The effect of the Reynolds number on the dispersion velocity in the scale-similarity model is carefully investigated. The results show that the scale-similarity model is more accurate at higher Reynolds numbers because the two-point Lagrangian velocity correlations with different initial spatial separations collapse into a universal form compared with a combination of the initial separation and the temporal separation via the dispersion velocity.Moreover, the dispersion velocity V normalized by the Kolmogorov velocity V_η ≡ η/τ_η in which η and τ_η are the Kolmogorov space and time scales, respectively, scales with the Reynolds number R_λ as V/V_η ∝ R_λ^(1.39) obtained from the numerical data.

The Correlation of Gyroscope Axial Velocities

In engineering,all movable expanse revolving objects manifest gyroscopic effects.These effects are created by the action of the outer load on the revolving items whose rotating mass originates eight inertial torques about two axes.Two torques of centrifugal forces,one torque of the Coriolis force originated by the rotating distributed mass,and the torque of the change in the angular momentum of the center mass act about each axis.The inertial torques activate rotations of the gyroscope by the determined correlation.Inertial torques depend on their geometry and orientation at the spatial coordinate system.The known analytical model for the rotation of the revolving disc about axes contains a mechanical error.This error was obtained by the incorrect integration of the centrifugal inertial torque.The corrected inertial torque yields the accurate expression for the interacted rotations of the revolving disc about axes.

Evolution of vortex structure around a wall-mounted rough hemisphere

In this paper,the large eddy simulation(LES)method is used to calculate Reynolds numbers the range in the range of 3000–30000(based on the diameter of the hemisphere D),and then the statistical analysis method is used to study the influence of Re on the characteristics of the flow field around the rough hemisphere and the evolution law of the tail vortex.The effect of the Reynolds number on the structure of the rough hemisphere flow field and the evolution of vortex structure is studied by vorticity distribution,POD method,and correlation analysis.It can be observed that with the increase of Reynolds number,the shear in the recirculating region of the rough hemisphere is enhanced,the large-scale structure is reduced,the small-scale structure is increased,and the angle between the hairpin vortex and the wall is reduced.λ_(ci)vortex identification and the Q-criterion are used to capture the evolution of a periodic vortex structure.Q-criterion gives the three-dimensional vortex structure behind the hemispherical flow.It is found that the horseshoe vortex and arch vortex generated by the incoming flow after passing through the hemisphere will interact with the wall surface to form a hairpin vortex,and the hairpin vortex structure will continue to evolve downstream to form a new vortex structure.