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A numerical model for two-phase debris flows is developed in this paper, on the basis of understanding of the physical characteristics of debris flows from field investigations and experiments. Employing a moving coordinate, the kinetic energy equation of gravel particles in unit volume in debris flow is developed by considering the potential energy of the particles, energy from the liquid phase, energy consumption due to inner friction-collision between the particles, energy dispersion through collisions between particles, energy for inertia force, energy consumption due to the friction with the rough bed and energy consumption at the debris front. The model is compared with measured results of two-phase debris flow experiments and the calculated velocity profiles agree well with the measured profiles. The gravel’s velocity at the debris flow head is much smaller than that of particles in the following part and the velocity profile at the front of the debris flow wave is almost linear, but the profile in the main flow shows an inverse ‘s’ shape. This is because the gravel particles in the main flow accelerate as they receive energy from the gravitational energy and flowing liquid and decelerate as they transmit the energy to the debris flow head and consume energy due to collision with the channel bed.

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In this study, a single bubble behavior in dielectric viscous fluid under the uniform magnetic field has been simulated numerically by using a level set method in two-phase bubbly flow. The two-phase bubbly flow considered to be laminar and homogenous. Deformation of the bubble was considered due to buoyancy and magnetic forces induced from the external applied magnetic field. A computer code was developed to solve the problem with flow field, interface of two-phases, and the magnetic field. The Finite Volume method was applied using SIMPLE algorithm to differentiate the governing equations. Using this algorithm enables us to calculate the pressure parameter which was eliminated by previous researchers due to complexity of the two-phase flow. The Finite Difference method was used to solve the magnetic field equation. The results outlined in the present study well agree with the existing experimental data and numerical results. The results show that the magnetic field affects and controls the shape, size, velocity and location of the bubble.

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Two-phase flow modeling has been the subject of many investigations. However, fewer studies are corresponded for two-phase flow within a porous medium, because of additional complications. In this paper, two-phase flow with the density and viscosity ratio of 1, within a porous medium is simulated by Shan and Chen model. Due to inherent limitations and weaknesses of this approach in an independent control of surface tension, investigation of parameters such as Reynolds number, Froude and Weber is not applicable. However, porous medium parameters such as Darcy number and contact angle could be studied by changing the porous medium and contact angle. Competition between opposing forces against the drop and the capillary effect because of increasing the number of particles in the porous media is described using the Darcy number. Also the effect of the contact angle between liquid-gas phases and the solid surface is evaluated on the droplet penetration inside the porous medium.

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Abstract It has been proved that developing a supercaviting flow over under-water projectiles has an important role on their drag reduction, so many of researchers have focused on this subject during recent decade. In this research, the geometrical characteristics of supercavitaties developed behind three different conical cavitators with conic angles of 30, 45 and 60 degrees are studied numerically and experimentally. The experiments were done in an open-loop water tunnel. The fluid flow velocity in the test section was between 27 to 38 m/s. Also the 3D multiphase fluid flow over the cavitators within the test section are modeled and analyzed numerically by solving the corresponding governing equations using finite volume method and mixture model. Good agreement was observed in comparison between the numerical and experimental results. Finally, effects of some important parameters .i.e. the cavitation index, inlet velocity and conic angle of the cavitators on the geometrical characteristics of the supercavities are discussed

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This study is an experimental investigation of two-phase water-air flow in hilly-terrain duct.The inclination angles for hill and valley configuration is ±7.5o. Review of the related literature showstheir results are limited to slug regime only. In the present study, flow regime map and pressure traces are investigated. This study reveals that the possible slug flow behavior categories exist along a valley and hill configuration are four and two, respectively. In an attempt to relate the qualitative flow behavior at a valley and hill to the flow pattern maps of upstream and downstream, this qualitative classification is superimposed on flow pattern maps where obtained independently for the upstream and downstream sections. The results show, flow has different behavior in hill in compare to valley at relatively low gas flow rates. However, at higher gas velocity, difference between hill and valley behavior decreases.It can be concluded, that the effect of hill and valley behavior are similar on flow regime at relatively high gas flow rates.

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In this article, two-phase slug flow is simulated numerically in a horizontal duct with rectangular cross-section using Volume Of Fluid (VOF) method. Conservation equations of mass, momentum and advection equation are solved in open source OpenFOAM code accompanying k-ω SST turbulence equations. Simulation is conducted based on the experimental results in the duct with rectangular cross-section. The results shows, due to Kelvin-Helmholtz (K-H) instability criteria slug initiation forms in the air-water interface during three dimensional turbulence modeling. Water level was increased slightly at interface in both numerical simulation and experiment. This level increase satisfies the K-H instability to generate a slug at interface. During slug initiation, the pressure behind slug is increased significantly. Big pressure gradient at the beginning of the slug in compare to the end of it causes the slug length to be increased as propagate along the duct. The numerical simulation of present research is capable of predicting the slug length accurately in accordance with experiment; however, the slug position with 22% inaccuracy was obtained. Comparison of the results with the numerical and experimental results of other researchers confirms higher accuracy of flow prediction in the present work.

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Experimental investigation conducted on Taylor bubble characteristics in a large bend including three consecutive inclinations. For this purposes, flow maps were obtained for the bend and horizontal section of upstream of the bend to define the area of this regime and mechanism of Taylor bubble formation. The effect of superficial gas-liquid velocities and the duct slope were studied on average velocity, length and frequency of bubbles. The results show, the bubble velocity and length increase as gas superficial velocity increases and the duct slope decreases. However, liquid velocity increase has decreasing effect on this characteristics. Bubble frequency is independent of slope change and reduces as gas superficial velocity increase. However, bubble frequency reduces at first and then increase as liquid superficial velocity increases. Regarding the safety regulation for industry, the minimum of the bubble frequency should be generated for the required liquid mass flow rate. Meanwhile, for the gas velocity, some optimization is required between frequency reductions with Taylor bubble velocity increase in addition to bubble length reduction. Regarding the background of the present field with shortage of results on Taylor bubbles frequency, some correlations based on the superficial Reynolds number of phases were presented for each inclination.

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Experimental investigation of two-phase air-water flow was conducted at consecutive inclinations of a large bend (with three equal slopes in respect to each other) and including the horizontal sections of the inlet and outlet of the bend. The results show that the elongated bubble regime flows without any effect of duct inclination change and consistent for all three zones of horizontal sections of before and after the bend and the bend itself. It was also noticed, as the duct inclination decreases along the route, vortex misty flow transmits to misty annular flow at higher gas flow rates. The annular flow regime was noticed only at the first slop of the bend. Slug flow was observed at the horizontal sections upstream and downstream of the bend. The slug flow at the upstream generated by the interfacial instabilities but at the downstream formed by Taylor bubbles. Slug flow area in the flow diagram increases as liquid flow rate increase at both horizontal sections. In addition, the void fraction change rate with phases mass flow rate was considered at the duct inlet.

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In this paper, two-phase air–water flow was investigated experimentally and simulated numerically using VOF method. The tests are conducted in Multiphase Flow Lab. of Tarbiat Modares University. In order to evaluate the rib effect on flow regimes, experimental investigation was conducted with ribs of different width and pitch where assembled on front and back side walls (side walls) of the duct during different test runs. The rib width and pitch were held constant during each test. The experimental work considered for different regimes of wavy, plug and slug which generated in the ducts with and without rib applying various phase velocities. The effects of using ribs on regime boundaries are presented in the flow diagrams and discussed in details. Compared to the smooth duct, the ribbed duct affects the different regime boundary positions noticeabily. The results showed that in the duct with small sizes ribs, the first slug initiates at longer time and distance in compare to the duct equipped with bigger size ribs. The results show that for normal operational flow velocities, the ribbed duct decreases the slug area on flow diagram map in compare to smooth duct. However, ribs facilitate the slug regime initiation for phase velocities in accordance with slug generation, which is not benefit of operational condition.

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This Study presents a numerical investigation of the hydro-thermal behavior of a Non-Newtonian ferrofluid (non-Newtonian base fluid and 4% Vol. Fe3O4) in a rectangular vertical duct in the presence of different magnetic fields, using two-phase mixture model, power-law model, and control volume technique. Considering the electrical conductivity of the base fluid, in addition to the ferrohydrodynamics principles, the magnetohydrodynamics principles have also been taken into account. To study the effects of non-Newtonian base fluid using power-law model, assuming the same flow consistency index with viscosity of Newtonian fluid, two different power law indexes (i.e., n=0.8 and 0.6), have been investigated and the results have been compared with that of Newtonian ones (i.e., n=1). Three cases for magnetic field have been considered to study mixed convection of the ferrofluid: non-uniform axial field, uniform transverse field and another case when both fields are applied simultaneously. The results indicate that the overall influence of magnetic fields on Nusselt number and friction factor is similar to the Newtonian case, although, by decreasing the power law index, the effect of axial field on velocity profile, Nusselt number and friction factor become more significant. Moreover, the results indicate that electrical conductivity has a significant effect on the behavior of ferrofluid and cannot be neglected and also negative gradient axial field and uniform transverse field act similarly and enhance both the Nusselt number and the friction factor, while positive gradient axial field decreases them.

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In this paper, a non - isothermal and two-phase flow in the cathode gas diffusion layer (GDL) of PEM fuel cell is modeled. To achieve more accurate boundary conditions, other components of fuel cell (membrane and anode GDL) are modeled. Governing equations including energy, mass and momentum conservation and auxiliary equations are solved by numerical method and the effect of gas mixture pressure in channels, relative humidity and effect of contact and mass exchange between two phases are investigated. Results show, it is necessary that both the contact and mass exchange between the gas and liquid phase to be considered. The performance curve and temperature distribution for single and two phase flow are compared for different amount of cathode channel humidity. The relative value of performance and temperature for single and two phase flow depends on the humidity of cathode channel. With increasing the cathode pressure from 0.5 to 5atm the value of water content in membrane and gas diffusion interface will increase about 20%. With increasing the water content in the membrane therefore the ohmic loss is reduced. With the reduction in the ohmic loss the temperature distribution along the fuel cell decreases but if the anode pressure increases the temperature distribution along the fuel cell increases. Keywords

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In present work, models that predict contact angle of a droplet with a solid surface, are considered and compared with each other. Two phases were assumed to be Newtonian, incompressible and immiscible fluids. OpenFOAM software is applied to simulate the two phases interface by using Color function VOF (CF-VOF) method. Different models for contact angle of a droplet as Tanner and Yokoi models are implemented in the OpenFOAM. In addition, the dynamics and statics contact angle models were used to compare with recent models in order to choose the best one. The outcome of study shows, even though the static contact angle model is simple to understand, however, it could be the best model to predict the droplet behavior in a wide range of different conditions. The fluid viscosity effect was also considered in different models of the present study. It concluded that the fluid viscosity affects the type of pattern of droplet impact and as viscosity of fluid increases; more energy is needed to uplift the droplet again from the surface. Kelvin-Helmholtz instability (K-H) was also simulated and explained in details which initiates on the interface of two fluids due to velocity differences of droplet and the surrounded air.

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Dry Steam flow at blade passages of steam turbines' low pressure stages occurs due to rapid expansion, delay in condensation and the condition of supercooled dry steam and finally after nucleation and condensation shock, phase change from vapor to liquid droplets occurs which is called two-phase or wet steam flow. In this paper, the aim of developing finite-volume flow of wet Jameson is considered for the first time in two-dimensional study by using the advantages of CUSP's numerical method. In this paper, equations governing the formation of liquid phase are combined with equations of survival and by using CUSP's numerical approach in Jameson's finite-volume method (the integrated method) the positive features of both of these methods can be simultaneously used in the modeling of two-phase flow. To calculate nucleation, the classical equation of nucleation with appropriate correction and also Lagrangian solution for growth of droplets are used in integrated method. Additionally, condensation shock effect on the pressure distribution and the droplet size has been calculated and compared with experimental data. Given the importance of areas of shocks on the suction surface of the blade, the focus of integrated method is shifted to this area. The results of integrated two-phase model are examined in subsonic and supersonic flow output .In the shock area on suction surface blade, using the CUSP's method (the integrated method) shows a better coverage in predicting attributes of flow in target area in comparison with the experimental data by a reduction of 20 percent in numerical errors.

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In the present research, two-phase flow is studied adiabatically in vertical plexigalss tubes with inner diameters of 40 mm and 70 mm in heights of 1.73 m and 3.22 m. Flow pattern maps are presented for both tubes and effect of diameter and height on the transition curves between flow patterns is investigated. Air and water are used as working fluids. Superficial velocities of air and water for 40 mm tube are 0.054-9.654 m/s and 0.015-0.877 m/s; and for 70 mm tube are 0.038-20.44 m/s and 0.036-1.530 m/s, respectively. By changing the tube diameter from 40 mm to 70 mm, slug pattern region shrinks considerably. Inlet is designed to be "annular" for which bubbly flow in 70 mm tube is not observed in low water superficial velocities. However, this pattern is observed in higher water and lower air superficial velocities. For both tubes, the main flow regimes observed are bubbly, slug, churn and annular. The results obtained using image processing technique show that bubbly regime in 40 mm can be divided into three sub-patterns called dispersed, agitated and agglomerated bubbly. In addition, two sub-patterns are recognized in slug regime as large slug and small slug. Also semi-annular pattern is observed as an independent flow pattern in tube with inner diameter of 70 mm which has not been analyzed accurately up to now.

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Present research has been done with the aim of investigating hydrodynamic behavior of slug flows in a transparent acrylic tube with inner diameter of 40 mm and height of 3.33 m. The vertical experimental system constructed in Two-Phase Flow lab in Tarbiat Modares University was used to perform needed experiments. By using image processing technique, recorded movies of flow structures were analyzed and some important characteristics of slug flow such as length and velocity of Taylor bubbles and liquid slugs between them were extracted. In addition, the average path line of Taylor bubble nose was computed in a proper range of the tube length. The acquired probability density functions show that there is a direct relationship between the increasing of Taylor bubble length and liquid slug length moving after it. Also rising velocity of shorter Taylor bubbles is more than longer ones. Results show that bubble nose does not violate ± 20 % around the center line of the tube. An experimental correlation based on the Taylor bubble velocity and total superficial velocities of phases is presented which shows that the famous Nicklen correlation does not work well for this tube diameter.

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Phenomenon of dispersion and deposition of nano- and micro-particles in turbulent flows been focused in the past decades. In this paper, particle dispersion and deposition in gas-particle two-phase turbulent flow inside a two-dimensional channel with rectangular artificial roughness is studied using an Eulerian–Lagrangian method. The RSM turbulence model with enhanced wall treatment was used to simulate the anisotropic turbulent gas phase flow. The gas phase flow predictions were validated by comparing the results with available experimental data for a fully developed asymmetric turbulent channel flow. In discrete phase, Lagrangian approach was applied for particle tracking. The Lagrangian equation of particle motion includes drag, gravity, Saffman lift, and Brownian forces. The particle phase simulation results were validated by comparing the present work with available equations and valid data for a gas particles turbulent flow inside a two-dimensional smooth channel. The gas phase simulation results show that by increasing the artificial roughness height, a recirculation region which is created in the space between two ribs, becomes larger. The particle phase results show that the rate of deposition in the channel with artificial roughness is a function of gravity force and flow pattern in the space between two ribs. The rate of deposition for small particle is affected significantly by gas flow pattern in the space between two ribs. However for large particles the gravity force is more dominant.

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In the present research, the high-order DG-ADER method is used to solve governing equations of two-phase drift flux model. The drift flux model is suitable for studying two-phase flows where the phases are strongly coupled. This model is composed of three differential equations including two continuity equations for two phases and a mixture momentum equation. The mixture model uses also an algebraic relation to link the velocity of the phases. The high-order DG-ADER numerical method, which is a new scheme to get high order accuracy of results, is used to solve the governing equations. The DG-ADER is a nonlinear method in which the reconstruction process is performed using WENO method and the time evolution part is achieved by discontinues Galerkine approach. The results are compared with those reported by other researchers. Three problems including two two-phase shock tubes and a pure rarefaction test problem are solved using this method. The results show that DG-ADER method can solve the two-phase flow problems with a very good accuracy even on a coarse grid. The drawback of this method is presenting numerical fluctuations with limited domain at the position of shock waves.

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In this article, a numerical solution of incompressible two-phase flow in isothermal condition, based on wetting pressure-wetting saturation formulation (Pw,Sw) using high order primal discontinuous Galerkin (DG) methods is considered which can capture the shock fronts of two-phase flow in heterogeneous porous media. In this presented model, the velocity field is reconstructed by a H(div) post-process in lowest order of Raviart-Thomas space (RT0). Also in this study, the scaled penalty and weighted average (harmonic average) formulation significantly improve the especial discretization formulation of governing equations which cause to reduce the instabilities in heterogamous media. The modified MLP slope limiter is used to remove the non-physical saturation values at end of each time step. In this study, the slope limiter should be considered as one of the main novelties due to the impressive effects in results stabilization. The proposed model is verified by pseudo 1D Buckley-Leverett and Mcwhorter problems. Two test cases, a problem for modeling the secondary recovery of petroleum reservoirs and other one a problem for detecting immiscible contamination are used to show the abilities of shock capturing two phases interface in porous media.

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Due to increasing the heat transfer surface area and high providing capillary pressure with high permeability, porous structures play a key role in improving the performance of two phase heat transfer devices such as heat pipes. New porous structures (bi-porous structures), have two distinct size distribution of pores of which the small pores provide the capillary pressure required for delivering liquid to the surface and large pores help vapor escape from the surface through increasing its permeability. The main goal is to gain a deeper understanding of the evaporator section of heat pipes and comparison between the performances of two sample biporous structures. Towards this goal first the Kovalev modeling technique is applied to determine the possibility of each phase’s existence in pores of different sizes throughout the computational domain. One dimensional heat transfer in a bi-porous wick is investigated. Inside the domain the conservation equations are solved for each phase and the results such as heat flux versus wall superheat are presented. Thermo-physical properties of the fluid and the matrix like the fluid properties, phase saturation and permeability and the conduction heat transfer coefficient are calculated from the geometry of the matrix and experimental relationships.

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The aim of this paper was to study the thermophoresis effect on the deposition of nano-particles from diesel engine exhaust after the dilution tunnel using a computational modeling approach. Dilution tunnel was used in order to dilute the exhaust gas to the extend that was suitable for the measurement systems. The Lagrangian particle tracking method was used to model the dispersion and deposition of nano-particles. For the range of studied particle diameters (from 5 to 500 nm), the Brownian, thermophoresis, gravity and Saffman Lift forces are considered. After verifying the code, the importance of different forces was evaluated. Due to the temperature gradient between the exhaust gas and the pipe walls, particular attention was given to include the thermophoresis force in addition to the other forces acting on nano-particles. The results showed that for the range of nano-particle diameters studied, the Brownian force was the dominant force for particle deposition. Furthermore, the thermophoresis force was important even for relatively low temperature gradient and cannot be ignorable especially for larger particles. The maximum thermophoresis effect occurred for 100 nm particles. The gravity had negligible effects on nano-particle deposition and can be ignorable for particles with diameter less than 500 nm. The Saffman lift also had negligible effects and its effect was noticeable only for the deposition of 500 nm particles. The results of this paper could provide an understanding of two-phase flow emission from diesel engines especially after the dilution tunnel.