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A subsurface drainage network mainly carries unsteady flow and data are not usually available for model parameters calibration in such networks. In the present research, the finite volume method using the time splitting scheme was employed to develop a computer code for solving the one dimensional unsteady flow equations. Using corrugated sub drainage pipes, an experimental prototype setup was constructed to examine the numerical model response in predicting the observed unsteady data in such circumstances. The experimental setup components and the model parameters were calibrated in place based on steady state flow condition. The results revealed satisfactory performance by the abovementioned method and the scheme employed and justified its validity for field application.

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Accurate estimation of the pressure losses for non-Newtonian drilling fluids inside annulus is quite important to determine pump rates and select mud pump systems during wellbore drilling operation. The aim of this study is to simulate non-Newtonian (power law and Herschel-Bulkly) foam flow in underbalanced drilling condition through wellbore annulus using finite volume method. The effect of various operational parameters on pressure loss such as fluid rheology, foam fluid velocity, foam quality, drillpipe rotation and wellbore eccentricity, have been considered. Simulation results were compared with the previously published experimental data. The agreement was close with a relative error less than 5%. The results of numerical method are closer to experimental data for Herschel Bulkly model for foam fluid. Also, the results of numerical method, showed that pressure drop increases with increasing the foam fluid velocity and quality and it decreases with increasing eccentricity, but drillpipe rotation don’t have noticeable effect on pressure drop.

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In the present paper,by performing a two-dimensional simulation,the heat transfer from a hot cylinder to a cold square enclosure has been studied parametrically and the consequent effect of changing in cylinder diameter has been investigated. The 2-D governing equations have been solved using the finite volume method and TDMA in an ADI procedure for different diameters of cylinder inside a square enclosure with a constant characteristic length for two different Rayleigh numbers of 104 and 105.Results showed that the patterns of streamlines, isotherms and the Nusselt number values depend strongly on the Rayleigh number and also ratio of cylinder diameter to characteristic length of enclosure (2R/H). In this case, the centers of vortices created around the cylinder appear in bottom half of enclosure in 2R/H=0.4 for Ra=104 and in 2R/H= 0.5 for Ra=105. Moreover, it is observed that increasing the Rayleigh number and 2R/H ratio, the heat transfer rate from the enclosure is also increased.For example,in 2R/H=0.5, by increasing the Rayleigh number from 104 to 105, the average Nusselt enhances about 30 percent of its initial value and in Ra=105, by changing the 2R/H ratio from 0.2 to 0.5, the average Nusselt climbs almost 35 percent of its initial value.

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The aim of this research is to study effective parameters of incompressible, viscous and unsteady flow in Turbomachinary cascades using the Spalart-Allmaras (SA) RANS-Based Delayed Detached Eddy Simulation method. Detached Eddy Simulation is a hybrid RANS-LES method that was purposed in order to reduce LES computational cost. In this method, near wall, in boundary layer, RANS turbulence model is used and away from the wall, method automatically switches to LES. To develop original DES method (DES97), DDES was purposed to solve modeled stress depletion problem. A new function is introduced to the DDES model to make the transition from RANS to LES grid cell size independent. The numerical method that is used for discretization is staggered finite-volume and the grid is Cartesian. Also hybrid differencing scheme (the scheme compound of central differencing scheme and upwind scheme) to discretization of convection terms in Navier-Stokes is used. The results of this study compared with the results of simulation with SA turbulence model.

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In this study hydrodynamics and noise behavior of a marine propeller is analyzed through numerical and experimental methods. In order to find out the conditions of initiation and development of cavitation, numerical analysis is carried out through finite volume method (FVM) for various rotational velocities. Moreover, hydrodynamics of the propeller is tested in the cavitation tunnel and the results are compared against numerical simulations. Second, the flow results obtained in the first step were used as the input to extract the sound pressure levels (SPLs) in the Ffowcs Williams–Hawkings (FW-H) formulation, to predict the far field noise. In addition, the behavior of the obtained SPL was studied and a good agreement was observed between our data and the previous works results. Similarly, experimental results collected from two hydrophones are compared with numerical simulations. In this case, cavitation is initiated and developed by either increasing the propeller’s rotational velocity in fixed pressure or dropping pressure while keeping the velocity constant. The signals registered at the two hydrophones are then filtered within one-third octave bands. The outcomes demonstrate a negligible deviation between numerical and experimental results for both noise and hydrodynamics tests.

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In this paper, a numerical study has been performed to investigate the effect of geometrical parameters of a viscous micro-pump on the flow rate and entropy generation. The present research has been carried out for three geometrical parameters of micro-pump including eccentricity (), sizes (S) of rotors and also their distance from each other (L) in the range of 0.1 to 0.9, 1.5 to 3.5 and 0.85 to 4.5, respectively. The results show that with increasing , the micro-pump flow rate also increases. On size variation effects, it is observed that decreasing the downstream rotor diameter, while keeping constant the upstream rotor diameter, the flow rate decreases exponentially. By increasing L, a steep increase in flow rate is initially observed, which becomes almost constant, when rotors are sufficiently far apart. With regard to entropy analysis, the effect of above geometrical parameters has been investigated on the entropy generation. The parameter RS indicating the ratio of the gradient of the entropy production rate to the related flow rate is introduced as a tool for entropy analysis. Also in this paper, for obtaining the maximum flow rate at the minimum frictional dissipation, optimal geometrical parameters are extracted. In this regard, the values of L=2, ε=0.5, S_1=1.5 and S_2=2.5 are selected as the optimum geometrical parameters of viscous micro-pump.

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Abstract In this research, a finite volume-Lattice Boltzmann Method (FVLBM) for simulation of inviscid compressible flows in 1-D and 2-D structured curvilinear coordinate system is presented. In this simulation, LBM, with new method of Circular Function idea instead of expansion or correction of Maxwelian function was implemented for evaluation of equilibrium distribution functions, moreover, in order to capture discontinuities in the flow field, 3rd order MUSCL scheme was implemented for approximation of convective term. Since in lattice Boltzmann method time step is extremely limited by relaxation time (Knudsen number), we improved performance of FVLBM with a third-order IMEX Rung-Kutta scheme for temporal discretization of BGK-model for archiving greater time step and lower CPU time. Consequently, the present work can be used widely for simulation of actual engineering problems in aerodynamics. Various gas dynamics benchmark problems and applied engineering unsteady problems in curvilinear coordinate grid is solved for validation. The numerical results of the presented method are compared with experimental dates and the results of FVM Euler solutions; there is good agreement between the results of the present method and those of the references.

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The panel flutter is concentrated with aerospace researchers, because of fatigue failure on structures. The usage of the numerical simulation is good company with analytical method. The 2D cylindrical panel flutter is simulated with navierstocks equations for fluid flow with finite volume theory. Also, Simulation is prepared with piston theory for analytical solution. Comparison of full numerical finite volume and assume mode method in post flutter domain is produced. Non-linear shell with the effect of in-plane load, thermal load and aerodynamic load with 3rd order piston theory is modeled to solve with assume mode method. The numerical method is 4th order rung-kutta to solve ODEs. With increasing shell camber, limite cycle oscillation change to random motion. The effect of expansion waves made decrease in second half of shell in analytical method in compare to numerical. The most important output depend on equal result for flat plate and different result on curve plate with numerical and analytical method. With increasing shell camber, limite cycle oscillation change to random motion. The effect of expansion waves made decrease in second half of shell in analytical method in compare to numerical. Amplitude of oscillation and flutter speed respectively is increase and decrease in numerical method despite of analytical one.

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In this paper two automated and robust algorithms for generation of unstructured grids suitable for miltiscale finite volume method in oil reservoirs is presented. The multiscale finite volume method is an efficient numerical method for flow simulation in porous media. The multiscale finite volume method has been extensively studied on structured grids. In this research multiscale finite volume method is extended to unstructured grids. Development of the MSFV method to unstructured grids provides advantages of flexibility and compatibility with geological structures. In this method calculations are carried out on three grids, fine grid, primal coarse grid and dual coarse grid. One of the main challenges to extend the multiscale finite volume method to unstructured grids is to generate primal and dual coarse grids. In this paper an algorithm for partitioning of unstructured grid and generating primal coarse grid is proposed. Also a new algorithm for generating dual coarse grid is presented. Finally, the proposed algorithms for generating multiscale unstructured grids are employed for flow simulations in porous media. Numerical results show that the multiscale finite volume method with generated multiscale unstructured grids of this research can accurately predict the fine scale solution.

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In the present study, the pressure equation associated with two-phase, incompressible and immiscible flow in porous media is solved by the multi-scale finite volume method (MsFV) for 2D problems. The MsFV method along with its main source of errors is mathematically and physically described. Associated with the computational grids used in the MsFV method, a set of two-scale isotropic permeability domains is designed. These permeability domains are produced to show how and where the errors are initiated in the pressure domain of the MsFV method. For each permeability domain, the pressure and velocity solutions obtained by the multi-scale method are compared with those of the standard finite volume method (as the reference solutions). The numerical results indicate that the MsFV method is sensitive to the fine cells with low permeability data located at the faces and corners of the dual grid blocks. The most errors is observed when the corners of the dual blocks are located on fine cells with low permeability value. In addition. By introducing the adjusted boundary condition, the effects of the permeability averaging for the edges and corners of the dual blocks on the MsFV errors are also investigated.

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The use of metal hydrides is one of the hydrogen storage methods. In this research, the process of hydrogen desorption from metal hydride storages with high diameter and constant flow rate was investigated using numerical simulation. A two-dimensional model with finite volume method is applied for simulation of hydrogen desorption. Simulation results were compared with available experimental data and a good agreement was observed between them. In this study, a special design of metal hydride storage was investigated. This design allows the application of metal hydride beds with large diameter for a specific hydrogen outlet flow rate by using aluminum fins. The simulation results verified the heat transfer enhancement effect of aluminum fins and showed the storage diameter can even be increased to 60 cm by using this design. The comparison between the result of applying LaNi5 and C5 alloys revealed that the energy efficiency could be increased by using C5 alloys due to need of heating fluid with lower temperature. Moreover, the results showed that by increasing the outlet volumetric flow rate from 230 to 460 (Nlit/min), the storage diameter should be limited and therefore the smaller storage must be selected.

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Dynamic of variation of the hydraulic parameters in the transient operating regime of the liquid propellant rocket engine (LPRE) depends on many factors. In this paper some of these factors such as pump inertia, power balance of pumps with turbine, temperature rise of working fluid in pump passages and variation of pump efficiency with the turbopump rotational speed are simulated. For the first time, filling of the inlet main pipeline and filling of the internal hydraulic channels of pump along with main pump equations are also simulated. To achieve this purpose, governing differential equations of each factor are derived, coupled with each other, and then solved by means of Finite Volume method in Simulink-MATLAB software. Results of this mathematical model are compared with experimental data of a real turbopump and shown that, without considering the internal hydraulic channels of the pump, “ the delay time of the turbopump” is not matched with real results, but by taking the mentioned hydraulic effects into consideration, acceptable agreement would be achieved. Also shown, by changing the resistance and inductance values of internal channels of pump, the settling time of turbopump could be changed, and used as a good factor to optimize the LPRE start process.

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Aerodynamic study of flows at low Reynolds for special applications such as micro unmanned underwater vehicles, underwater robots and explorers are interested. In this paper, an improved progressive preconditioning method named power-law preconditioning method, for analyzing unsteady laminar flows around hydrofoils is presented. In this method, the 2D Navier-Stokes equations modifies by altering the time derivative terms of the governing equations. The preconditioning matrix is adapted from the velocity flow-field by a power-law relation. The governing equation is integrated with a numerical resolution derived from the cell-centered Jameson’s finite volume algorithm and a dual-time implicit procedure is applied for solution of unsteady flows. The stabilization is achieved via the second- and fourth-order artificial dissipation scheme. Explicit four-step Runge–Kutta time integration is applied to achieve the steady-state condition. The computations are presented for unsteady laminar flows around NACA0012 hydrofoil at various angles of attack and Reynolds number. Results presented in the paper focus on the velocity profiles, lift and drag coefficient and effect of the power-law preconditioning method on convergence speed. The results show satisfactory agreement with numerical works of others and also indicate that using the power-law preconditioner improves the convergence rate and decreases the computational cost, significantly.

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In the present study, the incompressible flow through highly heterogeneous porous media is modeled by the Multi-resolution Multi-scale Finite Volume (MrMsFV) method. In order to focus on the effects of the absolute permeability structure on the accuracy and performance of the MrMsFV method, the single phase flow is considered and the effects of the gravity and variation of fluid viscosity and density are ignored. The accuracy of the MrMsFV method is examined by comparing its numerical results with those of the standard finite volume method. These permeability fields are extracted from the tenth comparative study problem of the society of petroleum engineering. For the permeability fields in which the permeability varies smoothly, it is shown that the MrMsFV method produces acceptable results. On the other hand, the numerical results along with mathematical analyses show that the MrMsFV method may produce pressure fields with unphysical peaks for channelized permeability fields. In these cases sufficient conditions for the monotonicity and boundedness of the solution are violated. In fact, the coarse scale transmissibilities may be computed in such a way that the coefficient matrix of the coarse scale pressure equation not to be a so-called M-matrix.

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The main task in finite volume methods (FVM) is to estimate proper values on the cell faces based on the calculated values on the nodes or cell centers. In this way, upwinding schemes are the most successful schemes for estimation of values on the control volume faces. These schemes have been developed in FVM for various techniques with proper accuracy on different kinds of structured and unstructured grids. In this research, the physical influence scheme (PIS) is developed to the cell-centered FVM in an implicit coupled solver and the results are compared with other two main branches of upwinding methods: exponential differencing scheme (EDS) and skew upwind differencing scheme (SUDS). Accuracy of these schemes is evaluated in lid-driven cavity flow at Re = 400-10000 and backward-facing step flow at Re = 800. Simulations show considerable difference between the of results EDS scheme with benchmarks, especially for lid-driven cavity flow at high Reynolds numbers which occurs due to false diffusion. Comparing SUDS and PIS schemes shows relatively close results in backward-facing step flow and different results in lid-driven cavity flow. The poor results of SUDS in cavity flow can be related to its non-pressure sensitivity between cell face and upwind points which is critical for such vortex dominant flows. Instead, the PIS scheme by applying a momentum equation between the cell face and upwind points, is able to capture flow vortices properly and matching well with benchmarks.

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Supercritical fluids have substituted non-super critical fluids in some areas of industry because of their unique characteristics and have been the subject of numerous experimental, numerical and analytic studies since their discovery. In this study laminar natural convection between a hot vertical tube with constant temperature and supercritical carbon dioxide with uniform temperature at inlet is simulated by utilizing a numerical model. The simulation is a two-dimensional, pseudo-transient numerical model based on finite volume method. The main objective of this study is to investigate and analyze the effect of severe property variations of supercritical carbon dioxide on the flow and temperature field of natural convection that ultimately affect heat transfer rates with respect to non-critical natural convection. Numerical simulations have been carried out for temperature and pressure ranges of 305K to 312K and 7.5MPa to 9MPa respectively. Span and Wanger’s multi-parameter equation of state have been used directly to determine carbon dioxide properties around pseudo critical temperature for the first time. Results indicate an increased rate of total heat transfer up to 160% near pseudo-critical temperature and 118% in other temperatures for supercritical natural convection with respect to ideal gas assumption.

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The cavity problem always has been considered as a classic and fundamental problem. Specific materials like Bingham viscoplastic which is sort of Non-newtonian fluids shows resistance in a certain range of stress, calling yield stress, and almost acts like rigid body in this limited area. In case of increase applied stress, flows like fluid. Considering heat transfer in this type of material and investigate it, yield stress and viscosity variations with temperature as in practice we face will not be far-fetched. In the present work the numerical solution of the problem of Bingham material inside lid-driven cavity, investigating fluid flow and heat transfer in view of the changes in material properties has been done and results have shown with change in dimensionless numbers and parameters of Re=10-1000, Bn=1-2000, Pr=0.01-100 and E=5000-50000. In this study, using the finite volume method to discretize governing equations and the use of collocated grid, effect of viscosity and yield stress dependence to temperature compared with independence mode and then distribution of horizontal and vertical components of velocity, yield areas and flow inside cavity, center of vortex and then heat transfer due to the stream lines next to side walls, have been analyzed.

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A Finite Volume-Lattice Boltzmann Method (FVLBM) for simulation of viscous laminar compressible flows in 2-D structured curvilinear coordinate system has been developed. In the present study, validation of the presented software and accuracy assessment of four new 2D lattices D2Q9L2, D2Q13L2, D2Q17L2 and D2Q21L2 based on increasing discrete velocities of lattice has been studied and the optimum lattice has been introduced. The presented LBM has developed using new method of circular function idea instead of expansion or correction of Maxwelian function for evaluation of equilibrium distribution functions. Moreover, in order to capture discontinuities in the flow field, 3rd order MUSCL scheme has been implemented for approximation of convective term. The laminar compressible viscous flow over the NACA0012 airfoil has been simulated in the curvilinear coordinate system for two angle of attacks, 0 and 10 Deg. The obtained results have been compared with validated N.S. solutions. Although the results have desirable accuracy in comparison of those of the N.S. solutions, limitation of the presented method and results assessment obtained by the different lattices have been investigated.

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In the present paper a new numerical simulation method based on finite volume is developed for calculating hydrodynamic pressure distribution in the reservoir of dams during earthquake excitation. An explicit finite volume scheme is applied for discretization of dynamic governs equation. In the proposed method the asymmetry effect of reservoir shape on hydrodynamic pressure distribution can be considered. In the simulation quadrilateral elements with center cell algorithm is used. Because of the negligible changing of hydrodynamic pressure in the cross direction with averaging, the average differential partial equation in central vertical plan of reservoir is solved. The absorption effects of bottom sediment and lateral wall are included in the analysis and an exact far end boundary condition is applied in the truncation boundary. Different approaches to the solution of the coupled field problems exist solution of the entire set of equations as one discretized system, referred to as the monolithic approach. This approach is often inefficient due to its attempt to capture with one discretization methodology the completely different spatial and temporal characteristics of fluid and the structure. The second approach often mentioned is the notion of strong coupling, referring to solvers which might use different discretizations for the fluid and the structure but which employ sub-iteration in each time step to enforce coupling between the fluid and the structure. In these methods, the governing equations for fluid and structure are discretized separately in each of the sub-domains and coupled using a synchronization procedure both in time and in space without sub-iteration. Weakly –coupled schemes have been extensively applied to a variety of different fluid-structure interaction problems of engineering interest in past ten years. wo vital issues when coupling two domains are: the method of data transformation between domains and what information must be transferred. The property of fluid adjacent of a structure such as density and viscosity are also key parameters in the efficiency of a numerical scheme.A dense fluid coupled with a structure cause a strong coupling and required some special technique to overcome corresponding difficulties. Key questions with this approach include properly enforcing boundary conditions at the solid-fluid interface, and accurately transmitting tractions between the solid and fluid. The biggest complaint about the explicit staggered partitioned solution procedure is the typical instability associated with the method,that is generally caused by the time lag between the integration of the fluid and structure equations. In the typical partitioned method, the fluid and the structure equations are integrated in time, and the interface conditions are enforced asynchronously. In the solution of coupled problems using partitioned methods, it is necessary to find a cost-minimization (optimization) compromise between a few passes solution with small time steps and a more iterated solution with larger time steps. This compromise may depend, among other things, in the degree of nonlinearity of the structural problem, which may require equilibrium iterations independently of the interaction effects. From the computational point of view, a one–pass solution with no iteration would be optimal, but stability consideration may prove this impractical.

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This paper presents a non-hydrostatic two-dimensional vertical (2DV) numerical model for the simulation of wave-porous structure problems. The flow in both porous and pure fluid regions is described by the extended Navier-Stokes equations, in which the resistance to flow through a porous medium is considered by including the additional terms of drag and inertia forces. The finite volume method (FVM) in an arbitrary Lagrangian-Eulerian (ALE) description is employed to discretize the flow and transport equations. A two-step fractional method has been deployed to solve the governing equations. In the first step, the momentum equations in the absence of pressure field were solved to compute an intermediate velocity. The second fractional step consisted of bringing the pressure terms back into the equations, and calculating the pressure field by solving the extended continuity equation and the momentum equations excluding advective and diffusive terms and drag force components. By substitution of the approximations of the pressure derivatives into momentum equations, and subject to the continuity constraint, the pressure Poisson equation was obtained. The solution of the pressure Poisson equation led to a linear system of equations in the form of a block tri-diagonal matrix with the pressures as unknowns. The second step was completed by computing the updated velocity values. In the present numerical model, two types of boundary conditions, namely Dirichlet and Neumann boundary conditions were adapted to solve the governing equations. The Dirichlet boundary condition was set to zero for normal velocities at impermeable bottom and the Neumann boundary condition was considered to be equal to zero for normal gradient of the tangential velocities at impermeable bed and also the left side of the computational domain. At open boundaries, where required, by setting the dynamic pressure equal to zero at the end of the numerical domain, a free exit for water was considered. The newly developed model in the absence of porous medium was verified by comparing the numerical simulations with the analytical solutions of a solitary wave propagation in a constant water depth. The newly developed model was then employed to simulate the solitary wave interaction with a permeable submerged breakwater. Based on the numerical results, when the solitary wave front reaches the offshore side of the submerged breakwater, due to the hydraulic jump formation, the flow is separated from the top of the obstacle and small clockwise vortices are generated at the leading edge of the breakwater. As the wave passes over the breakwater, the primary vortex grows in size and penetrates into the deeper layers of water. It was also seen that, due to the drag and inertia resistance forces of the porous medium, the velocity inside the permeable breakwater was noticeably smaller than that on the top of the breakwater. The comparisons between the numerical results and experimental measurements for time histories of water displacements, spatial distributions of free surface elevation, velocity fields and velocity profiles in both horizontal and vertical components, showed the capability of the newly developed model in predicting wave interaction with permeable submerged breakwater.