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Abstract: Applications of two-phase flow in nuclear power plants, transmission lines, oil and gas have been considered in recent decades. Different models have been introduced that can contribute to the current two-phase flow approach to numerical analysis. Two-fluid model is the most widely used and most accurate model for predicting two-phase flow in channels during different regimes of unstable flow. This study addressed the PFM model Hyperbolicity. Hyperbolicity of this model is the most important for the well-posed condition; otherwise the model is in ill-posed condition and the results are unstable numerically. Hydrodynamic instability of two-phase gas-liquid by using the PFM model is calculated and discussed.

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In this article, for the first time the numerical solution of Godunov method with HLLC Riemann solver is extended for a hyperbolic five equations two-fluid model. The flow field is considered for two-space dimensional case. So far, two main difficulties include non-monotonic behavior of mixture sound relation and inability of shock transition from interface was mentioned during working with this model. In this research these difficulties were overcome by selecting an appropriate mixture sound relation and appropriate discretization of non-conservative term. The mutual effect of shock wave impact with a droplet and two droplets with different diameters were simulated and studied. During the shock wave impact with 1.47 and 6 Mach with the droplet, a complicated shape of interface was formed with high pressure zone and low pressure zone of cavitations. The results obtained from the present attempt were compared with the experimental and related similar results of that obtained by the other numerical methods and models. The comparison of the results was good. It was also concluded that the numerical method used in the present work has enough accuracy with high capability in capturing two-phase flow interfacial instability and shock wave impact transmission from the droplet.

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This paper is concerned with the conduction heat transfer between two parallel plates filled with a multi-layer porous medium under a Local Thermal non - equilibrium condition. Analytical solution is obtained for both fluid and solid temperature fields in the porous channel incorporating the effects of thermal conductivity ratio, porosity, and a non-dimensional heat transfer coefficient at the pore level. The effects of the variable porosity on the temperature distribution are completely shown and compared with the constant porosity model. The presented method for analysis of heat transfer in a multi-layer porous medium is a generalized solution which is valid for arbitrary number of internal porous layers. The local temperature difference between fluid and solid phases is also calculated for a wide range of parameters. The results confirmed that the conductivity ratio and the porosity of the internal layers have significant role in the thermal modeling of the porous channel.

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Abstract-Two-fluid models are the most accurate and complex models for analysis of two-phase flows. There are two different two-fluid models for analyzing compressible isothermal two-phase flows which are Single Pressure Model (SPM) and Two-Pressure Model (TPM). In spite of capabilities of these models in capturing two-phase flow behavior, it is not possible to express them in conservative form due to existence of non-conservative term in momentum equation of phases. Therefore, the classical Rankine-Hugoniot condition across discontinuities in the flow filed is not applicable for these equations and there would be difficulty in using classical numerical methods for solving these equations. In this paper a new path-conservative method is used to overcome this difficulty. In this method, one can apply general Rankine-Hugoniot condition along a path connecting left and right states of the discontinuity. After expressing path-conservative form of the employed central numerical methods which are Lax-Fridriches, Lax-Wendroff and Rusanove, water faucet and large relative velocity shock tube problems are solved by using these schemes. Grid independence was achieved using different grid sizes. For water faucet problem, comparison of numerical results with analytical solution show good agreement and for shock tube problem, the results indicate that this method is highly capable in capturing discontinuities in two-phase flow.

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In the PEM fuel cells, gas phase (air and vapour) and liquid water could simultaneously flow through the cathode Gas Diffusion Layer (GDL). On the other hand, the performance of fuel cell and the main characteristic parameters of the flow can be influenced by the interaction of these gas and liquid phases. In the present study, the main parameters of two-phase flow in the GDL such as capillary pressure, mole concentrations of gas species, gas velocity and liquid velocity have been evaluated by considering the interactional effects of the aforementioned two phases. Also, the impact of changing the value of cathode channel humidity and fuel cell temperature on the value of the mentioned parameters has been investigated. The results indicated that decreasing of relative humidity in the cathode channel causes an increase in the rate of water vaporization. Thus, this leads to a decrease in the liquid water velocity, capillary pressure gradient and saturation gradient in the GDL. Also, increasing the temperature causes an increase in the rate of water vaporization and a decrease in the gas velocity and gas pressure gradient.

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In this study, the collision of two drops using Lattice Boltzmann numerical method in two-phase flow has been investigated. The simulation for incompressible fluid is based on the model represented by Lee. The prominent feature of this model is to simulate fluids with high density ratios. Thus, the model has easily been compared with experimental results and its validity has been investigated. Using this simulation, the variation of non-dimensional parameters such as Weber number, Reynolds number, Impact parameter, density ratio, kinematic viscosity ratio, diameter ratio and velocity ratio of two drops were studied. Considering the results, it was shown that the Reynolds number, density ratio and relative velocity ratio have no effect on separation or coalescence of drops collision; while the variation of Weber number, Impact Parameter and kinematic viscosity ratio results in separation or coalescence. Moreover, by increase in Weber number, Reynolds number or density ratio or decrease in kinematic viscosity, the number of oscillations and the time needed to reach equilibrium increases. Likewise, the amplitude of oscillation and the deformation of the drops increase when the Weber number, Reynolds number or density ratio rise or the kinematic viscosity lowers.

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In present paper the Inamuro Model based on free energy approach of the Lattice Boltzmann Method (LBM) was used to simulate the motion of bubble and coalescence of two bubbles under buoyancy force. By combining the Tanaka and Inamuro models, three-dimensional model of Inamuro was used in two-dimension for decreasing the computational cost. Firstly it was ensured that the surface tension effect and Laplace low for two density ratio 50 and 1000 were properly implemented. Secondly in next step, effect of governing dimensionless numbers problem such as Etvos number and Morton number on Reynolds number and terminal shape of bubble were investigated. Different flow patterns in various dimensionless numbers were obtained and by changing the dimensionless number, terminal change of bubble’s shape was seen. Finally, motion of two bubbles and terminal shape of coalescence of two bubbles were studied in different dimensionless number, which shape of first bubble was same to single bubble, but it was seen that second bubble experienced various shapes due to its location in wake of first bubble and less difference pressure on two sides of this bubble.

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Fluid-Elastic Instability is the most important mechanism among the vibration excitations in heat exchanger tube bundles subjected to cross flow. Flows through the heat exchanger are mostly two phase flow like air-water, vapor-water or Freon. Tow phase numerical methods are so complicated because of some parameters like VOF and interaction between two phases. Experimental studies are so problem and costly. Therefore, numerical methods are so important for studying two phase flow. In this Article, threshold of vibration has been numerically predicted by simulation of incompressible, viscose, and unsteady cross flow through a tube bundle in normal triangular arrangement. Interactions between the fluid and the structure has been counted in a fully coupled manner. HEM was used for analyzing two phase flow, In HEM method treats no difference in velocity between gas and fluid. In this study, two phase flow with HEM was solved around a single flexible cylinder surrounded by rigid and flexible tubes of bundle. Eventually, the flow through tube bundle has been simulated and analyzed by monitoring critical reduced velocity. Result shows that with increasing VoF, amplitude decreased and the critical velocity increased.

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Nowadays boiling phenomenon has been an important issue in various fields such as petroleum industries and nuclear power plants due to enhancement of the total heat transfer coefficient. One method to increase the level of heat transfer coefficient is to add certain nanoparticles such as 〖Al〗_2 O_3 to the base fluid. The present paper concerns the effect of nanoparticles on forced convective boiling within the general- purpose computational fluid dynamics (CFD) solver FLUENT. The governing equations solved are generalized phase continuity, momentum and energy equations. Wall boiling phenomena are modeled using the baseline mechanistic nucleate boiling model developed in Rensselaer Polytechnic Institute (RPI). To simulate the critical heat flux phenomenon, the RPI model is extended to the departure from nucleate boiling by partitioning wall heat flux to both liquid and vapor phases considering the existence of thin liquid wall film. In addition to validating the subcooled boiling phenomenon, the effect of aluminum oxide 〖Al〗_2 O_3 nanoparticles on heat transfer coefficients has been analyzed. It is concluded that by increasing the volume fraction of 〖Al〗_2 O_3 nanoparticles in the base fluid, wall temperature has been dropped and the heat transfer coefficients have been increased significantly.

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Computational Fluid Dynamics (CFD) implementations are also classified as the Lagrangian and Eulerian methods. Smoothed Particle Hydrodynamics (SPH) is a mesh free particle method based on Lagrangian formulation with a number of advantages. This method is obtained approximate numerical solutions of the equations of the fluid dynamics by replacing the fluid with a set of particles. All particles carry their properties and then the advection is taken care automatically. In contrast, Eulerian mesh based numerical methods have difficulties such as the problem of numerical diffusion due to advection terms. Because of the simplicity and robustness of SPH, this numerical method has been extended to complex fluid and solid mechanics problems. The important advantage of SPH is that the muli-phase flows can be modeled by SPH and each particle can be assigned to a different phase. In this paper, the SPH method is used for simulating water and sediment flow in dam break problem. The government equations are momentum and continuity equations which are described in a Lagrangian framework. Also, the compressible flows are modeled as a weakly compressible flow via the equation of state. The XSPH equation is applied for each particle movement at each time step. The Wendland kernel is applied as smoothing function. Sediments are treated as non-Newtonian fluid and for simulating them the non-Newtonian models are used. In this paper, the combination of two rheological models named Bingham and Cross is used. The predictor- corrector algorithm is applied. The time step is controlled by Courant condition (CFL), the forcing terms and the viscous diffusion terms. On the other hand, the laboratory experiment of dam break is performed and the new experimental set up was built. At first, the column of water with a height of 0.5 m and the wide of 0.25 m is blocked by a partition gate. The bottom of the water column is covered with non cohesive sediments. The sediments are sands with d50=1.4 mm. The partition gate separates the water column from the downstream channel and the speed of partition gate is more important. Then the partition gate is removed with a specific velocity. The partition gate opens completely from above with a constant speed of 0.6 m/s. The flow motion is recorded by digital camera system. Finally, a comparison between experimental results and computational results is carried out and the errors are calculated. The error of sediment height variations in specific horizontal distances (x=5 cm and 14 cm) in reservoir are 6.55% and 5.94%, respectively. Also, the sediment surface profiles are shown in different times. The comparisons are shown good agreements between numerical and experimental results. The good agreement proves the ability of the present SPH model to simulating two phase flows.

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The prediction of distillation zone is very important in steam turbine blades and steam nozzles. In identification of distillery with equilibrium method, as the steam flow contacts the two-phase dome, the second phase formes and flow properties will pass the distillery without any jumping, therefor after crossing the saturation curve, the droplet formation transpires, but in non-equilibrium method by a sudden increase in pressure, called “condensation shock” a discontinuity in the flow characteristics is seen and after crossing the saturation curve, the formation of droplets starts. In this paper, numerical analysis of a vapor-liquid two-phase transonic flow in a convergent-divergent nozzle with and without shock is investigated. Effects of stagnation temperature at nozzle inlet, viscosity and geometry is studied using thermodynamic equilibrium and non-equilibrium methods and results compared with experimental datas. Roe numerical method is used for vapor-liquid two-phase flow numerical solution. The main properties of the flow at the boundary of elements is extrapolated by MUSCL third order acuracy and time discretization is performed using Lax-Wendroff explicit two-step method of second order accuracy. It is observed that the results of non-equilibrium solution, has more correspondence to experimental results and Condensation starts earlier in the nozzle with further expansion rate. By increasing the temperature at nozzle inlet, the place at which condensation starts goes forward. Also in comparision with non-viscous flow, the shock location in viscous flow comes closed to the throat.

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In the current study, the streamline simulation technique is used for definition of a new objective function to optimize the production rates during water injection process. The streamline simulation technique, in comparison with common numerical methods for simulation of multi-phase flow in porous media, is much faster with less computational memory requirement. This method represents the key parameter of “Time of Flight” which helps to consider complex heterogeneity of porous media in a more easy way. In order to optimization of oil production rates from reservoir, a function based on averaged time of flight has been introduced which minimization of this function can be used to have uniform fronts of water for flooding of oil. For this target, two optimization techniques; the Artificial Bee Colony (ABC) and the Sequential Quadratic Programming (SQP) method are employed to optimize the objective function and their results are compared with each other. Advantages and disadvantages of these two methods are investigated and based on their advantages, a new hybrid approach is proposed which utilizes the benefits of both techniques to converge to the optimum solution. In the hybrid approach the SQP algorithm is initialized with the ABC method. In order to validate the mathematical model, a 2D homogeneous model used for optimization. Next a 2D heterogeneous model and a 3D complex reservoir model are investigated. In all the mentioned problems, it is observed that the hybrid approach, in comparision with the two other methods, can approach the optimum point with better accuracy and speed.

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In this study, falling ferrofluid droplet behavior in nonmagnetic viscous fluid under the uniform magnetic field in two-phase flow is studied numerically. To this approach, a hybrid lattice-Boltzmann base shan-chen model and finite-volume method is used. The lattice Boltzmann equation with the magnetic force term is solved to update the flow field while the magnetic induction equation is solved using the finite volume method to calculate the magnetic field. To validate the flow field solution two tests have been considered: the free bubble rising and Laplace law. In order to validate the magnetic field, permeable circle and deformation of static drop under magnetic field is simulated. The comparison of results between present study and previous researches shows that there is a good agreement between the results. The effects of the magnetic Bond number, susceptibility and magnetic field direction on deformation of the falling droplet are investigated. The results show that increase in the magnetic Bond number or susceptibility leads to a larger deformation of the droplet. Also in horizontal magnetic field, the falling process takes more time in compared to the vertical magnetic field.

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This paper presents a numerical study using two-fluid model in order to compare the effect of hydrodynamic and hydrostatic models for pressure correction term in two-fluid model in modeling gas-liquid two-phase flows to provide a more accurate model. Two-fluid model is solved by Godunov Approximate Riemann Solver. The two-fluid model is applied using both hydrodynamic pressure correction term and hydrostatic pressure correction term for four sample examples including Water Faucet Case, Water-Air Separation Case, Toumi’s Shock Tube Case, and Large Relative Velocity Shock Tube Case. Hydrostatic pressure correction term is neglected for vertical geometry, therefore, in this geometry; two-fluid model cannot be hyperbolic. Thus, hydrostatic pressure correction term is not a stabilizing term. Also, in horizontal pipe and for atmospheric conditions, hydrostatic pressure correction term presents better results than hydrodynamic pressure correction term. But, in non-atmospheric conditions, hydrodynamic pressure correction term presents better results. Therefore, in order to select a suitable pressure correction term for two-fluid model, we consider geometry (vertical or horizontal) and flow conditions (atmospheric or under-pressure). Also, hydrodynamic pressure correction term in two-fluid equations system is hyperbolic in a boarder range than hydrostatic pressure correction term.

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In this work, axial vibration of nanorod was analyzed based on two phase integro-differential nonlocal elasticity theory using isogeometric method. Two phase integro-differential nonlocal elasticity theory not only shows the nonlocal property in an integrated manner based on kernel weight function, but also combines local and nonlocal linear curvature for a two phase nonlocal elastic material. The new isogeometric approach combines finite element method with computational geometry and can present an accurate geometric model for the problem. Also, using b-spline basis functions with arbitrary continuity order, it can be a better alternative for classical finite element methods. The obtained results indicated that isogeometric approach was superior to finite element method in term of speed and convergence quality. Moreover, in this model, the effects of phase and nonlocal parameters on the natural frequencies of the nanorod were investigated and it was shown that increase of parameters of local phase and nonlocal length scale, respectively, increased and decreased the values of natural frequencies of nanorods. Finally, for two special cases, asymptotic frequencies for a single type of nonlocal rod, two phase integro-differential was obtained and the results were compared with corresponding available differential Eringen results.

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In the present study two-phase flow within the effervescent atomizer has been simulated by the volume of fluid interface tracing model using 0.08%, 0.32%, 1.24%, and 4.9% gas-to-liquid mass ratios and 0.38 L/min liquid flow rate. The purpose of this simulation is to study two-phase flow regimes within the effervescent atomizer and their effect on the atomization quality. This study also considers the gas-liquid interface instabilities in different two-phase flow regimes inside the atomizer. The compressibility of gas phase which is rear in literature survey included in gas-to-liquid mass ratios of 1.24% and 4.9%, due to the high gas phase velocity in constant liquid flow rate and high gas-to-liquid mass ratios. The effect of gravitational force is considered in all simulations. The results of the simulation indicate that by increasing the gas-to-liquid mass ratio, the two-phase flow regime inside the discharge passage transfers from bubbly flow regime with long bubbles to annular flow regime. In addition to decreasing the liquid film thickness coming out from discharge orifice (during transform of the flow regime from bubbly flow to annular flow), the liquid interface instabilities increase in the annular flow regime and besides, where segregated ligaments from the liquid interface become shorter, thinner and more unstable. This type of regime is the most efficient flow behavior for the effervescent atomizer.

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Underbalanced drilling and managed pressure drilling with foam have been gained attention of the world oil companies due to its many benefits. The advantages of this method include oil and gas production during drilling, high-speed drilling, drill bit life increase, better cutting transfer and reduced formation damage. In this paper cutting handling by foam was investigated in which foam was assumed to be a homogeneous, single-phase, compressible and non-Newtonian fluid whose rheological properties can be well described by power law model. The assumptions and governing equations of transient two-fluid model were expressed in Euler-Euler coordinate for fluid-particle (foam-cuttings). The upstream method is used to discretizing the equations and the results of the numerical solution are reported in the form of pressure, speed, cutting concentration, quality and density of the foam logs along the well. The impact of back-pressure, ROP, injection rate of gas and liquid, shape and size of cuttings, water influx and oil production on cutting concentration and bottom-hole pressure have been investigated. With increasing parameters such as back-pressure, liquid and gas flow rate, size of the cuttings and ROP, bottom hole pressure and cutting concentration increases. Cutting concentration decreases with increasing liquid and gas flow rate and increases by increasing back-pressure, cutting size and ROP. For validating, the results of the numerical solution are compared with field data obtained from well FR-1 located in the Santa Catarina state of Brazil which show about 16.5 percent errors.

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A spillway is a hydraulic structure that is provided at storage and detention dams to release surplus or flood water that cannot be safely stored in the reservoir. In this paper, two-dimensional simulation of gas-liquid two-phase flow on stepped spillway in different discharge rate is studied. The VOF model and the two-fluid model are used in order to simulate numerically and then the results of the two models are compared. In order to study the influence of aeration in stepped spillway, two different physics are proposed. In the first geometry it is assumed that there is no air intake via stairs and in second geometry air intake and its effect on the flow over the spillway is studied by embedding hole in the top edge of stair. The air pressure is assumed to be atmospheric. The results showed that VOF model provide more accurate result than that of two-fluid model in low discharge rate. However, in cases where aeration is studied, because of mixing phases, this model is not able to simulate fluid flow as well as two-fluid model. The two-fluid model is more accurate due to solving equations for both phases (air and water). For verification, numerical results have been compared with experimental values and determined that numerical models are able to predict the total energy loss within an error range of %10 compared with the measured experimental data.

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Ice slurry is called a mixture of fine ice particles with a fluid carrier such as water. The phase change ability of this mixture attracts the strong attention in the areas of thermal storage and refrigerant cooling of the secondary cycle. In this research, flow of ice slurry in horizontal tubes during the phase change is numerically investigated using FLUENT software. The two-phase nature of ice slurry mixture is studied using the Euler-Euler two-phase model based on kinetic theory of granular flows. The effect of ice particles phase change on heat and mass transfer between phases are investigated, the obtained results show that the local heat transfer coefficient for the use of the icy slurry mixture is increased 12% compare to the pure water. It is also determined by examining heat and mass transfer rate along tube, that the heat transfer coefficient for the pipe lengths larger than 10-15 times pipe diameter, remains constant. The variation of mean mass transfer is maximum at distance of 10-15 times of pipe diameter. The maximum value is 2-5 times larger than mean mass transfer in the pipe outlet. At the 20% end of the pipe, the decreasing trend of mass transfer accelerates.

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In this paper, the three dimensional ventilated cavitating flow in the steady condition around a projectile model is simulated using CFD method combined with a sst k-ω turbulence model and volume-of-fluid technique, With the aid of CFD software ANSYS CFX. The numerical model is validated using comparisons between numerical predictions and existing experimental data and fairly good agreement is revealed. The numerical results show that with increasing the ventilation gas rate at constant Froude number, the cavity length gradually increases to a critical value and then remains fixed upon further increase in gas ventilation rate. Also, it has been observed that rear portion of larger cavity moves upwards due to gravitational effect. With increasing the ventilation gas rate, the gas leakage mechanism at rear portion of ventilated supercavity changes from the re-entrant jet closure mode to twin vortex closure mode. The variation of ventilation gas rate versus cavity length is a function of Froude number and the critical ventilation gas rate increases linearly with Froude number.