The film cooling effectiveness of a staggered arrangement of small and large holes was investigated. The small auxiliary holes were located normal to the cooled surface, whereas the large main holes had an inclination angle of 30°. The center points of the small holes were located upstream, downstream, and in the same position as the main holes. A hole pitch (P/D) of 3 and a thickness (t/D) of 3 were considered. The film cooling performance of the hole in trench structure and the cylindrical hole was also determined. The numerical results show that large-scale vortices caused by the auxiliary hole injection inhibit the development of vortices caused by the main hole in the streamwise direction. This result differs from that of anti-Vortex film cooling. Compared to the baseline, the increase in the surface-averaged values is 15-22% for the staggered arrangement, depending on the blowing ratio (0. 5 to 2. 0). The positions of the auxiliary holes have an effect on the spanwise-averaged values.

To investigate the dynamics of droplet-Vortex interactions in particle-laden Karman Vortex street flows, the simulations were carried out by using Euler-Lagrange approach, which was validated by the available experiments and numerical results. Then, the particle dispersion and the dimensionless frequency (Strouhal number) of the wake flow were analyzed to evaluate the particle-Vortex interactions. The particle dispersion was statistically analyzed from both time and space dimensions and the different instantaneous dispersion patterns were explained by the relative slip velocity. Two independent scaling parameters, Stokes number StL and particle-fluid mass loading ratio Φ were revealed, and the particle mean square displacement and the Strouhal number were modelled by using these two scaling parameters, respectively. Finally, the characteristic lengths of the particle-laden wake flow were researched, and the Strouhal number physical model was developed based on the oscillating fishtail model. The results indicated that, firstly, StL and Φ, which constitute a dominant scaling group, can characterize the dynamics of droplet-Vortex interactions in wake flow. Particles gradually separate from the Vortex with the increase of StL due to the centrifugal effect, and the Vortex intensity and regularity get worse with the increase of Φ, which further disperses the droplets for their momentum exchange with irregular Vortex structures. Secondly, the length of the formation region and the width of the free shear layer diffuse are the two simultaneous characteristic lengths of the Strouhal number in oscillating wake. The proposed Strouhal number model gives a physical basis for the frequency determination, and the predicted errors are within ±1. 5% error bands with mean absolute percentage error of 0. 67%.

The main objective of this article is to establish a new model and find some Vortex axisymmetric solutions of finite core size for this model. We introduce the hydrodynamical equations governing the atmospheric circulation over the tropics, the Boussinesq equation with constant radial gravitational acceleration. Solutions are expanded into series of Hermite eigenfunctions. We find the coefficients of the series and show the convergence of them. These equations are critically important in mathematics. They are similar to the 3D Navier-Stokes and the Euler equations. The 2D Boussinesq  equations preserve some important aspects of the 3D Euler and Navier-Stokes equations such as the Vortex stretching mechanism. The inviscid 2D Boussinesq equations are known as the Euler equations for the 3D axisymmetric swirling flows.This model is the most frequently used for buoyancy-driven fluids, such as many largescale geophysical flows, atmospheric fronts, ocean circulation, clued dynamics. In addition, they play an important role in the Rayleigh-Benard convection.

In this paper, formation and development of one of the most dominant Vortex structures, namely, counterrotating Vortex pair (CVP) which is seen in the jet in cross flow are investigated numerically. Influences of the inclination angles between the nozzle (s) and channel on the CVP are presented for three inclination angles, a=30o, 60o and 90o at velocity ratio, R=2.0. Effects of the number of the nozzles on the evolution of CVP is analyzed by considering the single and three side-by-side positioned circular nozzles. In addition to the CVP, some secondary vortices are also reported by considered relatively a narrow channel because their existence cannot be showed in wider channel. Simulations reveal that higher the inclination angle the more jet penetration into the channel in all directions and increasing the inclination angle causes larger CVPs in size.Although the flow structure of the CVP formed in the single and three side-by-side nozzles are similar their evolution is quite different.

This paper presents an original concept of using a composite flexible flapping Vortex generator mounted on a heat sink fin for air side heat transfer augmentation. The main aim is to combine the advantages of hard and soft winglets in a composite one for having the highest possible enhancement. The proposed composite Vortex generator, which is made with a thin elastic sheet is responsible for enhancing heat transfer and mixing quality performances in laminar convection air flow in a heat sink. The merged vortical structures due to oscillation by winglet swept out the thermal boundary layer and enhance thermal mixing between the fluid near the heated fin and the channel core flow. This novel concept is demonstrated using numerical simulation of the flow field with considering a two-way strongly coupled fluid-solid interaction approach in transient condition. The set of governing equations including, the continuity, momentum, and energy for a 2-D forced convection air flow are solved by the finite element method using the COMSOL Multi-Physics. The present findings show 148%, 116%, and 121% increases in the cooling rate by the composite and the two hard and soft homogeneous winglets, respectively. Numerical results are validated against the numerical data reported in the literature.

Wall shear rate and its axial and azimuthal components were evaluated in stable Taylor vortices. The measurements were carried out in a broad interval of Taylor numbers (52-725) and several gap width (R1/R2=0.5 - 0.8) by two three-segment electro diffusion probes and three single probes flush mounted in the wall of the outer fixed cylinder.The axial distribution of wall shear rate components was obtained by sweeping the vortices along the probes using a slow axial flow. The experimental results were verified by CFD simulations. The knowledge of local wall shear rates and its fluctuations is of primordial interest for industrial applications like tangential filtration, membrane reactors and bioreactors containing shear sensitive cells.