In this paper, we introduce a novel diffraction element for generating any desired arrays of the Vortex and perfect Vortex beam. The method is based on combining radially phase shifted spiral zone plate with different gratings. We show that the element has a great potential in generating a variety of arrays with desired Vortex ring radius and topological charges. We can assemble various Vortex and perfect Vortex beams not only in a lattice array but also in a tilted lattice or circular arrays. Reported Vortex arrays are in the group of vortices having the same topological charge p so the total topological charge of MP which M the number of elements. The experimental results are in good agreement with the simulation predictions.

In this paper, using Vortex blob method (VBM), turbulent flow in a channel is studied and physical concepts of turbulence are obtained and discussed. At first, time-averaged velocities, u and v, and then their fluctuations are calculated. To clarify turbulence structures, velocity fluctuations u and v are plotted. It is observed that turbulence structures occupy different positions and move with convection velocity. To verify the second law of thermodynamics, averaged vorticity and its fluctuations as well as averaged entropy and its fluctuations are calculated. Contours of these fluctuations (  , s ) show that their positions coincide with the positions of turbulence structures and both positions move with the same velocity. Correlation coefficient of velocity fluctuations between two points, and temporal correlation coefficient at a point, which have significant role in understanding physics of turbulence, are calculated and plotted. Having obtained these coefficients, time and spatial micro-scales and then turbulence energy dissipation rate (  ) are obtained. Also, spatial-temporal correlation coefficients is calculated and then for turbulence structures microscale of time (memory), micro-scale of spatial (size) and convection velocity of structures are found. These scales estimate their life and size. Having obtained dual correlation coefficients, spectral studies of the velocity fluctuations, u and v , are performed, which include both frequency amplitude (related to temporal correlation coefficient) and wave number (related to special correlation coefficient). In fact, spectral study of fluctuations is Fourier transform (Cosine) of these fluctuations. Finally, dropping rate of this transform is compared with available data in turbulence literature. In this research, for the first time, the turbulence structures are visualized and presented by employing the vector of velocity fluctuations, vorticity and entropy generation fluctuations.

Annular Vortex tube is a Vortex tube which allows the hot flow pass again over the hot tube. It is introduced for first time in this work. Hot Flow is not allowed to exit after passing conic valve in annular Vortex tube, but it is redirected over hot tube. This back flow absorbs heat from outer wall of hot tube. To study temperature separation which occurs in an annular Vortex tube; the performance of this type of Vortex tube has been experimentally tested and compared with the performance of a typical Vortex tube. Inlet test pressure is 4 bars and natural gas is being used as working fluid. For both type of Vortex tubes, ratio of length to diameter of tube is 10. Cold oriice diameter of Vortex generator is set to 6.4 mm. It was observed that redirecting hot flow over the hot tube in annular Vortex tube improves cooling efficiency up to 24% respect to a typical Vortex tube at the maximum temperature difference. The results show that cold mass fraction in which the coldest temperature occurs is lower for annular Vortex tube comparing with a typical Vortex tube.

For a long time, many efforts have been taken on improving gas turbine performance to increase the propulsive force and keep the chamber walls cool. In this regard, implementation of cyclonic and Vortex engines have been proposed. According to increasing in the engine efficiency and keeping the chamber walls cool, the bidirectional Vortex flow which is exited in the Vortex engine, makes researchers more interested in it. In the Vortex engine, due to its specific geometry, two Vortex layers are established. The combustion occurs in the inner Vortex layer, while the outer layer protects the walls from excessive heat transfer. The Vortex engine with gas fuel and oxidizer has been manufactured in laboratory scale at Virginia Institute of Technology and it is under investigation. Practical usage of the Vortex engine, with both liquid and solid fuels, has its own significance. Investigation and analysis of the flow field in such a chamber have been conducted in different research centers during last five years. The significant results of these studies are the analytical and numerical solution of the flow field by applying many simplifying assumptions. Selecting proper materials, determining the engine dimensions, designing injector plate, and some other parameters in engine manufacturing process require the flow field to be modeled in the combustion chamber which needs the governing equations to be solved. For investigating of the flow field in the Vortex engine, the mass conservation, momentum conservation, and energy equations have to be solved. If the flow is turbulent, the equations become more complicated and many assumptions are needed to simplify the problem. Note that, by assuming the flow to be incompressible, the energy equation becomes segregated from the other equations. At the first stage, the goal of this project is to investigate the previous analytical solution and modify it to become compatible with other numerical and experimental results, provide numerical solution of the governing equations with the least possible assumptions, and compare the obtained numerical and analytical results with each other. Since the governing equations are non-linear and the flow is turbulent, it is impossible to solve the problem analytically in details. The flow will be simulated with respect to the result of numerical solution and applying the conventional methods and the results will be presented. It is to be noted that, if the fuel is liquid, modeling the spray combustion in a two-phase (gas-liquid) flow field is required, which will be described in this project as well. According to the flow field analysis, the propulsive and aero-dynamical results of the engine will be available, which are required to determine the designation parameters and manufacturing of the Vortex engine test rig. Afterwards, by establishing the fundamental requirements for installing the appropriate test rig for the Vortex engine, manufacturing of this test rig with its accessories will be described in details. The obtained results of this project, including the flow field investigation, test rig designation and implementation, are the first steps to achieve mass production of the Vortex engine with both liquid and gas fuels which, according to its innovation and efficiency, has its own significance.

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.