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This paper presents a new and accurate methodology for transient and dynamic behavior of slug hydrodynamic instability modeling in horizontal and inclined channels. The base of this methodology is on numerical solution of hyperbolic two fluid model equations by means of a class of high resolution shock capturing methods. The privilege of this method is that it can model and predict initiation and growth of slug in stratified flow automatically and directly by solving the flow field differential equations. The well-defined test case considered for the verification and validation of the results is the Ransom Water Faucet case. The results obtained for slug flow modeling in horizontal duct were compared with two sets of experimental results. The good agreement of the present modeling results with the experimental results of own and other investigators and also grid independency study show the model is capable of slug tracking and slug capturing and the numerical method which is used here can predict with high enough accuracy.

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In this paper; reduced order modeling (ROM) of unsteady two-phase flows is performed based upon two-fluid models and a proper-orthogonal decomposition (POD) method. The four-equation two-phase flow model is used as a mathematical model to describe physics of the problem. After presenting the governing equations, direct numerical solution of the problem is introduced using AUSMDV* method. Then, the POD method is introduced as a mathematical tool to reduce computational time of the transient problems. In the present research, an equation free/Galerkine free POD method is used for ROM of the unsteady two-phase flows. In this approach, the singular value decomposition (SVD) method is used to compute the base vectors of the reduced space. A shock tube and water-air separation two-phase problems are solved using the present ROM method. Results show that this approach can reduce computational time of unsteady simulations about 35%. Reduction of the computational time directly depends on the size of the computational gird. The results also indicate that application of POD method on the fine grids is more efficient than on the coarse grids.

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Subcooled flow boiling has many industrial applications such as nuclear engineering and energy generation. The study of the subcooled flow boiling provides a lot of information about the void fraction of vapor on the wall and also the critical heat flux. In this paper, the sub cooled flow boiling in a 2D vertical corrugated channel has been investigated numerically. The two-fluid model and the finite volume method have been used in this investigation. The obtained results show that with increasing of nanoparticles in the base fluid, the void fraction and bubbles departure reduced, However, the wall temperature increases due to heat flux evaporation decreases. Also, with increasing the wavy amplitude, the wall temperature and void fraction increases. that increasing the water temperature on the wall decreases its density and the fluid velocity increases in the vicinity of the wall because the momentum of the flow is constant in the transverse cross section of the channel. Furthermore, because of the variations of the velocity due to the variations of the channel's cross section, the void fraction of the vapor increases in the converging areas of the corrugated channel.

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Numerical modeling of compressible two-phase flow is a challenging and important subject in practical cases and research problems. In these problems, mutual effect of shock wave interaction creates a discontinuity in fluid properties and interface of two fluids as a second discontinuity lead to some difficulties in numerical approximations and estimating an accurate interface during hydro-dynamical capturing process. The objective of this research is to increase the accuracy of numerical simulation of two-phase flow using two dimensional five-equation two-fluid model. For this purposes, MUSCL strategy was used for increasing the Godunov numerical scheme accuracy from 1st order to 2nd order. The privilege of this method is high accuracy, low numerical oscillation and low numerical diffusion. The problems considered for the verification of the results are the water-air shock tube, a square bubble with moving interface in a uniform flow and a shock wave with 1.72 Mach having interaction with an air bubble in a water pool. The obtained numerical results showed that, the results that have been obtained by second order accuracy have less diffusion in the two-phase flow interface.

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In this paper, gas-liquid two-phase flow in the annulus of a real well during under-balanced drilling operations is simulated numerically. Oil and gas flow from the reservoir in to the annulus is considered due to under-balanced drilling condition. A numerical code based on one-dimensional form of steady-state single pressure two-fluid model in the Eulerian frame of reference is developed and its results are validated using experimental data from two real wells. The results of numerical simulation show better accuracy in comparison with other researches. Given the importance of prediction and control of the bottom-hole pressure and the amount of oil and gas production during the drilling operations, the effects of controlling parameters such as liquid and gas injection flow rate and choke pressure are discussed. Also, the effects of different controlling parameters on the characteristics of two-phase flow pattern, including liquid and gas void fractions, liquid and gas velocities and pressure distribution along with the annulus are discussed. According to the results, the effects of choke pressure and injected liquid flow rate on the production of the oil from the reservoir are independent of the values of each other and are dependent on the injected gas flow rate.

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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 the current study, two-phase flow of water and air over a stepped spillway is probed in the form of a two-dimensional incompressible viscous flow. A novel numerical approach is used for the numerical simulation which is a combination of two models: volume of fluid (VOF) which uses an interface tracking algorithm for the simulation of the two-phase flow and two-fluid model which is based on time and space averaged equations and cannot track the interface explicitly. The most important issue in the introduced approach is to couple the two basic methods and select a proper criterion for status change between two basic methods. The latter criterion is based on an approximation from local distribution of the interface at each cell. In the hybrid method. In order to investigate the aeration effect in the stepped spillway, the air suction is generated by designing some holes at the upper edge of the steps and considering atmosphere pressure for these areas. The obtained results divulge the amount of dispersion is low at the beginning part of the step and also the hybrid model take more advantages from VOF, while in the lower steps where the flow disperses two-fluid model has hegemony. The results are compared in the form of pressure contours and streamlines as well as volume fraction counters. The comparison shows that the results of the proposed method is closer to the experimental results with respect to each of the basic model.