In this research we have implemented the Random vortex Method to calculate velocity fields of fluids inside open cavities in both turbulent and laminar flows. the Random vortex Method is a CFD method (in both turbulent and laminar fields) which needs the Schwarz-Christoffel transformation formula to map the physical geometry into the upper half plane. In some complex geometries like the flow inside cavity, the Schwarz-Christoffel mapping which transfers the cavity into the upper half plane cannot be achieved easily. In this paper, the mentioned mapping function for a square cavity is obtained numerically. Then, the instantaneous and the average velocity fields are calculated inside the cavity using the RVM. Reynolds numbers for laminar and turbulent flows are 50 and 50000, respectively. In both cases, the velocity distribution of the model is compared with the FLUENT results that the results are very satisfactory. Also, for aspect ratio the cavity (α ) equal 2, the same calculation was done for Re=50 and 50000. The advantage of this modelling is that for calculation of velocity at any point of the geometry, there is no need to use meshing in all of the flow field and the velocity in a special point can be obtained directly and with no need to the other points.

This research describes unsteady two-dimensional reacting flow around a circular cylinder. The numerical solution combines Random vortex method for incompressible two dimensional viscous fluid flow with a Simple Line Interface Calculation (SLIC) algorithm for propagation of flame interface. To simplify the governing equations, two fundamental assumptions namely Low Mach Number and Thin Flame Thickness are used. Numerical and graphical representation of vorticity field, velocity variation on the wake axis, the effect of combustion on stream line pattern and location of vortex element at Reynolds numbers of 3000 and 9500 are discussed. The numerical results for the non-reacting flows fall within the range of the experimental measurements while the results of the reacting case are qualitatively following the physics.

Direct numerical simulation of the wake flow around and behind a planar ellipse using a Random vortex method is presented. Fluid is considered incompressible and the aspect ratios of ellipse and the angles of attacks are varied. This geometry can be a logical prelude to the more complex geometries, but less time dependent experimental measurements are available to validate the numerical results. Therefore, the key figures of the averaged values of selected cases are chosen to check the accuracy of the results. Based on the results, the general behavior of the flow around an ellipse at the zero angle of attack is almost similar to that around a circle. But, at the other angle of attacks, the asymmetry of the flow is dominant and pronounced clearly.

In this paper, numerical simulation for a two-dimensional viscous and incompressible flow past the elliptical airfoil is presented by Random vortex Blob (RVB). RVB is a numerical technique to solve the incompressible, two-dimensional and unsteady Navier-Stocks equations by converting them to rotational non-primitive formulations. In this method, the velocity vector at a certain point can be calculated without considering any grid around it, so the RVB method can be treated as a meshless method. Accordingly, the turbulent flow past a cylinder as well as an elliptical airfoil is investigated. In both cases, the obtained mean time velocities are compared with available numerical and experimental results where an acceptable agreement is observed. Having known the velocity field, by employing momentum balance, the drag and lift coefficients caused by flow past the elliptical airfoil with different diameter ratios and Re=105 are calculated and compared with experimental data where a good consistency is achieved.

In this paper the turbulent, incompressible and unsteady viscous flow around a circular cylinder is numerically simulated and the imposed fluid forces are calculated. The Random vortex Method (RVM) with the using of a Large-Eddy Simulation (LES), as a turbulence modelling, is developed to investigate the fluid flow around a circular cylinder. A LES of turbulent flow is applied to account for the effect of turbulence in the wake. The Navier-Stokes equations are filtered by LES and transformed to computational domain by a general conformal transformation. The fil- tered equations are solved by an operator splitting where the velocity is found from Cloud-in-Cell (CIC) method and the diffusion equation is modeled by Random walks (RW). The numerical results lift, darg coefficients and Strouhal number are in reasonable agreement with experimental results.

Analysis of the flow passing cylindrical obstacles is one of the basic issues in fluid dynamics and is of great importance. Many surveys have been conducted to investigate the velocity field in potential and viscous flows, as a basis for finding pressure field, and investigation of forces exerted by fluid on obstacles such as uplift and drag forces in different flow regimes. Since the nature of formation of vortexes behind the obstacles is absolutely depended on time, the conventional turbulent models which are based on average time, do not justify, and the use of direct solution of Navier Stocks equations is inevitable. One of the presented models which can solve time-dependent Navier Stocks equations in wide range of Reynolds numbers, is Random vortex Method (RVM). Since in this method velocity field is instantly calculated, it can be used to simulate turbulent flows with a time-dependent nature. In this paper, vorticity equations gained from Navier Stocks equations are solved in both convection and diffusion phases. In this study, the flow on three cylinders with Re=140000 is investigated and field of average and instant velocity is shown along with streamlines. Also by drawing instant distribution of vortex fields and streamlines, it is possible to provide a revealing presentation of vortex behind cylinders.

Direct numerical simulation of turbulent flow behind a cylinder, wake flow, using the Random vortex method for an incompressible fluid in two dimensions is presented. In the Random vortex method, the primary variable is vorticity of the flow field. After generation on the cylinder wall, it is followed in two fractional time step in a Lagrangian system of coordinates, namely convection and diffusion. No closure model is used and the instantaneous results are calculated without any a priori modeling. Regarding the Lagrangian nature of the method, there is a very good compatibility between the numerical method and physics of the flow. The numerical results are presented for a wide range of Reynolds number, 40-9500. In the initial stages, there is only an unstable symmetrical flow behind the cylinder and the vortex shedding is not started yet. But, in the high Reynolds number flows, two distinctive flow patterns, namely a and b are detected. The mechanism of generation of the primary and the secondary eddies can be related to the production, convection and diffusion of the vorticity field and the time dependent structure of the flow field in the wake zone behind the cylinder. The length of the computational domain, downstream of the cylinder, is selected 25 times of the cylinder's diameter. Regarding such a lengthy computational domain it is possible to detect the mechanism of generation, pairing and growth of the large scale structure, eddies. Although the instantaneous numerical results are calculated, no coresponding comparable results are available. Therefore, the validity of the results in this stage is only qualitative. For the quantitative comparison of the results, after the establishment of the stationary state, time averaged based indicators such as separation angle, drag coefficient, lift coefficient, Strophe umber and ... are calculated. The numerical results accurately fall within the range of the experimental measurements.

Flow-induced vibration is the effective factor in mechanical destruction of structures that are exposed to fluid flow. In this study, Random vortex- boundary element methods (RVM-BEM), is used to simulate two-dimensional laminar fluid flow around four one/two-degrees-of-freedom cylindrical cylinders in a rectangular arrangemen. Hydrodynamic force coefficients, streamlines and cylinder displacements were plotted. The vorticity distribution is separated into blob-vortexes and its changes are studied by tracking these vortexes in the Lagrangian approach by considering two mechanisms of convection and diffusion in each time step. Satisfying no-slip boundary condition, vortex sheets were created on boundary. The cylinder vibrations were modeled as a system of mass, spring, and damper. The results showed that for 1 and 2DoF compared to the stationary cylinder, the average drag coefficient changes are 0.84 and 0.97, respectively. The rear cylinders vibrations amplitude were less than in the front cylinders. The y-amplitude was three times larger than x-amplitude. The maximum x-amplitude vibration of 1DoF cylinders was 1.51 times larger than 2DoF ones. Solving flow over 2DoF single cylinder by BEM(no need for homodis mapping or considering the vortexe images) with a similar solution in Ansys-Fluent software, showed 25% reduction in runtime and 2.3% increase in calculations accuracy.

The oscillations of cylinders are due to formation of vortices in the make region, which has come to attention of researches in the last decades. The calculation of aerodynamics forces acting on the cylinderical shape bedies is of prime interest in the industry and especially the indestanding of the nature of these farces ourll be helpful to design the off-shose structures, the electrical transport lines and other industrial applications. On the other hand in the flows with high Reynalds numbers the experimental values o the aerodynamics Forces coefficients are very expensive and therefore the theoretical calculations of the coefficients will be of prime interest.It is the aim of this paper to calculate the airedynamic forces coefficients using the numerical methods combining the large Eddy Simulation (LES) and the Random vortex Method (RVM). The comparison of the calculated values with the experemantal results shows good agreement.

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.