In this paper, energy separation effects in a vortex tube have been investigated using a CFD model. A numerical simulation has been undertaken, due to the complex structure of flow. The governing equations have been solved by the FLUENT TM code in a 2D compressible and turbulent model. Three turbulent models, namely, RSM, Standard k-epsilon and Spalart-Allmaras, have been used. The Spalart-Allmaras turbulent model, which is the first equation, was not so bad in predicting temperature results, although the Standard k-epsilon model better predicts the results in most regions. The effects of geometrical parameters have been investigated. The results have shown that the hot outlet size and its shape do not affect the energy distribution in the vortex tube, and a very small diameter will decrease the temperature separation. Different kinds of gas have been examined for the vortex tube, and it was concluded that using helium as a refrigerant produces the largest energy separation.

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When a vertical liquid jet impacts on a solid and horizontal surface, the liquid starts spreading radially on the surface, until a sudden increase in the fluid height occurs and a circular hydraulic jump (CHJ), easily seen in the kitchen sink, is formed. In this study, the formation of CHJ is numerically simulated by solving the flow governing equations, continuity and momentum equations, along with an equation to track the free surface advection using the volume-of-fluid (VOF) method and Youngs’ algorithm. The numerical model is found to be capable of simulating the jump formation and its different types. Extensive comparisons are performed between the model results and those of the available experiments and modified Watson’s theory. The model is shown to accurately predict the jump location and its behavior. Also a parametric study for the effects of different parameters including volumetric flow rate, downstream height, viscosity and gravity on the jump radius, and its characteristics is carried out. Compared with previous works on CHJ available in the literature, employing the VOF method considering the surface tension effects and performing a full parametric study and a complete comparison with experiments and theory are new in this paper. The simulations are performed for two different liquids, water and ethylene glycol, where it is found that the jump is more stable and its location is less sensitive to the downstream height for the more viscous liquid (ethylene glycol). When the downstream height is increased, the radius of the circular hydraulic jump reduces up to a certain limit after which there would be no stable jump. If the gravity is decreased, the radius of the jump and the length of the transition zone will both increase. The radius of the jump in microgravity conditions is less sensitive to the downstream height than it is in normal gravity.

When a vertical liquid jet impacts on a solid horizontal surface, the first expectation is to have a circular hydraulic jump. However, in some conditions, for highly viscous fluids, the transition from supercritical to subcritical flow occurs with non-circular shapes such as polygons. Indeed, a quick rotational wave appears on the circular jump before the formation of a polygonal form, which may be related to the Rayleigh–Plateau instability. In this paper, stable polygonal jumps are studied to complete this research. The region of stability is defined for polygonal jumps, and the dependence of this region on the flow governing dimensionless groups is determined experimentally. The results confirm the multistability (hysteresis) of the polygonal jumps, and imply that polygonal jumps with different corner numbers can be created in a certain parameter regime. The size and curvature of the sides of the polygons due to variations of flow rate and downstream obstacle height are also investigated. In addition to the stable ones, our experiments reveal a new type of polygonal jump that has an unstable structure and displays a rotational behaviour with a constant angular velocity, which we call it, ‘rotational hydraulic jump’. It is observed that the angular velocity of this kind of jump depends on the jet flow rate, jet radius and downstream height of the jump. Our observations suggest that the nature of the rotational jump is some kind of surface wave along the jump in clockwise or anticlockwise direction. It seems that the rotational jump has a flow structure that is the same as a type IIb jump. The jump dimensions are studied; the inscribed and circumscribed circular radii of each polygon are measured in order to compare the various polygons together and to find a mean jump radius to compare with Watson’s theory.

A new efficient direct simulation Monte Carlo (DSMC) method is proposed for the simulation of microporous media based on the dusty gas model (DGM). Instead of simulating gas flow through a microporous medium with a complex geometry of micropores that mimics the physical pore morphology, the DGM-DSMC method replaces it with the gas flow through a system of randomly distributed motionless virtual particles with simple spherical shapes confined in the considered domain. In addition, the interactions of gas molecules with the porous particles are simulated stochastically. For the aim of our study, the DGM is implemented in Bird’s two-dimensional DSMC code. The obtained results for the average velocity of gas flow through microscale porous media with given porosity are verified for different pressure gradients with those reported in the literature where porous particles are modeled physically in the domain. Thereafter, the effective parameters in porous media such as porosity, particle diameter, and rarefaction on flow behavior including velocity profile, apparent gas permeability, and mass flow rate are investigated. A comparison with the results predicted by the Open source Field Operation and Manipulation (OpenFOAM) software suggests that the employed DGM-DSMC is more accurate in highly porous media and its computational cost is considerably low.