Rayleigh-Taylor (RT) Instability has a growing importance in many fields including aircraft industry and astrophysics. The development and the growth of RT Instability were investigated using sinusoidal disturbances with different wavelength at the interface of the two fluids. Numerical simulations were performed by solving Navier-Stokes unsteady equations with the VOF formulation. Results of the 2D simulation are compared with experimental results.It is shown that beyond a critical time, not captured experimentally, the mushroom shape of RT Instability turns into a helical path or breaks down into a patchy shape depending on the shape of disturbance. Nonlinear instabilities responsible for such behavior are apparent when the wavelength exceeds 10 times the length scale introduced in this study.

In this paper, recommended spiral passive micromixer was designed and simulated. spiral design has the potential to create and strengthen the centrifugal force and the secondary flow. A series of simulations were carried out to evaluate the effects of channel width, channel depth, the gap between loops, and flowrate on the micromixer performance. These features impact the contact area of the two fluids and ultimately lead to an increment in the quality of the mixture. In this study, for the flow rate of 25 μl/min and molecular diffusion coefficient of 1×10-10 m2/s, mixing efficiency of more than 90% is achieved after 30 (approximately one-third of the total channel length). Finally, the optimized design fabricated using proposed 3D printing method.

The stability of CJ detonations has been investigated Numerically with a two-step kinetics model. The reaction model consists of a non-heat release induction step, followed by an exothermic step. Both steps are governed by the Arrhenius kinetics model. The effect of activation energies associated with these steps on the detonation front behavior has been studied. This study was arranged in two stages. At each stage, one of the activation energies was kept constant and the other one was changed. In the steady detonation structure, the activation energies of the first and second steps (Ea1, Ea2) control the induction and reaction lengths, respectively. Increasing Ea1 (for a fixed Ea2) increases induction length and destabilizes a detonation, the same behavior as a one-step model. Increasing Ea2 first increases reaction length and has a stabilizing effect (i.e., the amplitude of oscillation decreases). Further increasing Ea2 has a destabilizing effect. The present study shows that the ratio of the reaction length to the induction length characterizes general features of detonation stability.

Kelvin-Helmholtz Instability is a hydrodynamic Instability generated by the relative motion of immiscible, irrotational, incompressible, and inviscid fluids. In the present study, the Kelvin-Helmholtz Instability is assessed for Newtonian and non-Newtonian fluids by solving two-dimensional Navier-Stokes equations using the finite volume method. ANSYS FLUENT software is used to simulate the two-phase flow field. The Numerical method is the finite volume method. Using the semi-implicit method for pressure-linked equations algorithm, the velocity and pressure fields are coupled and the Navier-Stokes equations are solved. The second-order upwind method is used to discretize the convection terms in Navier-Stokes equations and the central difference method is employed to approximate the time derivative. In the case of Newtonian fluids, it was found that for  the growth rate of Kelvin-Helmholtz Instability depends on the surface tension when the surface tension is in the range of 0.000192-0.000993 N/m. The results demonstrate that the critical wavenumber is enhanced by increasing the power-law index (n) for shear-thinning and shear-thickening non-Newtonian fluids; however, at a specific time, the amount of critical wavenumber for shear-thickening fluids is smaller than that for shear-thinning ones. It is also concluded that as the power-law index increases, the wave stability can be reached more rapidly.

Prediction of fluid-elastic Instability is a great matter of importance in designing cross-flowtube bundles from the perspective of vibration. In the present paper, the threshold of fluid-elastic Instability has been Numerically predicted via simulation of incompressible, unsteady, and turbulent cross-flow through a tube bundle in a normal triangular arrangement. The conditions of simulation is the same as a previous experiment. A finite volume solver, based on Cartesian-staggered grid, has been implemented and the interactions between fluid and structure are solved fully coupled method of solving flow and structure equations in each time step. The fluid elastic Instability was predicted and analyzed by presenting the structural responses, trajectory of flexible cylinders, and critical reduced velocities.

Buried pipelines are used to transport water, liquid fuel, gas, oil, etc and they must remain in service in all circumstances such as permanent transverse ground deformation caused by slope Instability. In the literature, modeling of soil-pipe interaction is carried out by using two methods of soil-equivalent springs and continuum. In this paper, Numerical simulation in domain of continuum is applied to predict the behavior of the pipe embedded inside the slope. Problem modeling has been done in the FLAC 3D software by using finite difference method. The effect of parameters such as pipe diameter and thickness, width of the slope, soil adhesion and internal friction angle of soil on soil and pipe interactions were investigated. Comparison of the present Numerical model with other Numerical, analytical and physical models, indicates that the maximum displacement of the transverse ground and pipe occurs in the center of the area and reaches zero in the sides. Also, the anchor and force in the pipe are symmetric to the center of the model and reach a maximum value in the center. By taking steps such as increasing the diameter of the pipe, increasing the thickness of the pipe wall and reducing the angle of the slope, the displacements, tensions and strains created in the pipe can be reduced to some extent. On the other hand, the internal angle of friction of the soil and cohesion are effective in increasing the soil's resistance and also reducing the deformations in the pipe.

In this paper, miscible viscous fingering Instability in a Darcy and non-Darcy porous media was studied through Numerical solution and the formation and growth of finger patterns were discussed. According to the porosity coefficient, the media can be divided into Darcy and non-Darcy categories. Also, flow velocity and fluid used (Newtonian or non-Newtonian) are the factors that limit the use of Darcy’ s relation. In this simulation, against most previous studies which had been used the two-phase Darcy’ s structural equation to approximate examination of instabilities, a two-dimensional model was used. This model was based on coupling flow equations in porous media (Darcy or Brinkman) and transport of diluted species. The effects of increasing injection rates and viscosity changes were investigated based on Peclet non-dimensional number and viscous ratio on instabilities. Besides, a comparison was done between the results of Darcy’ s and Brinkman’ s solution at different porosity coefficient and viscosity ratio. Image processing techniques were performed to measure the break through time, perimeter of the interface, fractal dimension and sweep efficiency. With increasing viscosity in Darcy and Brinkman solution, the perimeter of the interface and fractal dimension were increased and more complex fingers generated. As a result, the sweep efficiency of the porous media reduces. In addition, the growth of the media porosity led to sweep efficiency. Finally, it was observed that with increasing injection velocity in Brinkman’ s solution, the fingers complexity and perimeter of the interface increased and sweep efficiency decreased.