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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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A consistent implicit Incompressible Smoothed Particle Hydrodynamics (ISPH) method based on projection approach is proposed for solving violent free surface flow problems. In this way, two consistent discretization schemes are employed for first and second spatial derivatives. In this study, it is shown that in explicit ISPH solvers, the field variables and the positions of particles in the process of numerical differentiation are estimated at two different time steps. So, the incompressibility is not completely satisfied. In the present approach, an iteration loop is implemented, in each time-step. Thus, at the end of each time-step both velocity and the positions used in divergence estimation are at the new time-level. The proposed ISPH method is validated in free surface flow problems involving 2-D dam break benchmarks in which both wet and dry beds are considered. Among the advantages of the present implicit method is being more accurate and stable than the explicit one, despite use of lower number of particles and greater time-step sizes. Also, it provides significant improvement in free surface simulations and pressure distribution results.

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Abstract: In the papers published on compressible fluid using Pseudo Bond Graph approach, isentropic flow is assumed. However in a converging- diverging nozzle, for a specific pressure ratio, the assumption of isentropic flow is invalid. For the purpose of considering normal shock effects, this paper introduces a new field (NIKE-field) to the pseudo bond graph. The output of the new field can be also used to determine normal shock position and to extract momentum equation as well. In the following, the methodology developed in this paper has been applied a simple pedagogic example. Simulation result is validated by comparison with the analytical result. As the new field can be modeled non-isentropic flow, it can be used to for modeling rockets motors and thrusters in transient state. One of another advantage of new field (NIKE-field) is that it can be easily used in many software applications like MS1, SYMBOLS2000 and 20SIM®; therefore, With regard to the systematic derivation of a mathematical model from a bond graph in these softwares, there is no need to derive any state equations and their solutions.

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Two incompressible SPH numerical solvers, including a modified explicit method and a new implicit method have been developed to simulate the sediment-laden free surface flow problems. Using, consistent discretization schemes, the proposed explicit method improves somewhat the accuracy of the usual explicit ISPH methods. The implicit method additionally guarantees the incompressibility condition completely. In the presented methods, the liquid phase is modeled using Navier-Stokes equations and to predict the non-Newtonian behavior of the sediment phase, the Bingham plastic rheological model is used. The accuracy and capabilities of the developed incompressible SPH methods is first validated in comparison with available experimental and numerical results of a single-phase water-sediment mixture flow generated by unsteady dam break problem. Then, they are applied to simulate an eroding dam break problem with a two-phase flow sediment transport. Comparing the obtained results with the available results in the literature shows that the developed methods particularly the implicit one, are very powerful tools for simulation of the problems including sediment transport induced by violent free surface flow, with interactions between flow and sediment and morphological changes in bed.

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In this paper, an implicit high order discretization has been developed for gridless method. In recent decade, gridless method using a distribution of points has become an important research topic in computational fluid dynamics. Gridless method usually uses the first order Taylor series for discretization of the space derivatives at any points. This paper presents an extension of high order for a central difference gridless method and investigates the results accuracy and performance of this method for solving inviscid compressible flows. Euler equations have been solved in two dimensional using second and fourth order artificial dissipation terms. These terms make a fast gridless method. The method of discretization in time, Explicit and dual-time implicit time discretization are used. In order to reduce the computational cost, local time stepping and residual smoothing techniques are utilized to speed up convergence. The capabilities and accuracy of the method are compared with finite volume method and experimental data for airfoils in transonic and supersonic flows. Results show that the second order accuracy solutions with fewer point distributions indicate higher accuracy when compared to the first order accuracy solutions in transonic and supersonic flows.

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In the present Paper, solution methods for simulating compressible flows and shock wave simulation by using Lattice Boltzmann Method(LBM) and simulation of shock wave in the bubble with a moving boundary is evaluated. The standard LBM is found to be incapable of predicting compressible flows and confront instabilities in high Mach number flows. But with some efforts that has been made in recent years, new models for stable solutions of the compressible equations are established. Modified Lax–Wendroff finite difference scheme that has stabale solutions has been used for discretizing Lattice Boltzmann equation. In this study models based on the compressible Euler and compressible multispeed Navier-Stokes to simulate compressible lattice Boltzmann method have been used. The dynamics of compressible bubble busing Rayleigh-Plesset equation have been obtained. Simulation of shock wave in the bubble with other computational fluid dynamics methods has been carried out, However, due to the weakness of the Lattice Boltzmann method for compressible flow, no effort to study the physic of this phenomena has been done with this method. The purpose of this simulation is to achieve a distribution of thermodynamic properties through the radius while collapsing and eventually forming the Sonoluminescence phenomena that caused by the collision of shock waves in the center of the bubble to one other,with lattice boltzmann method.

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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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This article is devoted to the derivation of formulation and isogeometric solution of nonlinear nearly incompressible elastic problems, known as nearly incompressible hyperelasticity. After problem definition, the governing equations are linearized for employing the Newton-Raphson iteration method. Then, the problem is discretized by using concepts of isogeometric analysis method and its solution algorithm is devised. To demonstrate the performance of the proposed approach, the obtained results are compared with finite elements. Due to large deformations in this kind of problems, the finite element method requires a relatively large number of elements, as well as the need for remeshings in some problems, that results in a large system of equations with a high computational cost. In the isogeometric analysis method, using B-Spline and NURBS (Non-Uniform Rational B-Spline) basis functions provides us with a good flexibility in modeling of geometry without any need for further remeshings. The examples studied in this article indicate that by using the isogeometric approach good quality results are obtained with a smaller system of equations and less computational cost. Also, influence of different volumetric functions for the nearly incompressible materials are investigated.

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In this article bubbly flow under the specified axial pressure gradient in a curved channel is studied numerically. To do so, a second order parallelized front-tracking/finite-difference method based on the projection algorithm is implemented to solve the governing equations including the full Navier-Stokes and continuity equations in the cylindrical coordinates system using a uniform staggered grid well fitted to the geometry concerned. In the absence of gravity the mid-plane parallel to the curved duct plane, which is the symmetry plane in the single fluid flow inside the curved duct, separates the bubbly flow into two different flow regions not interacting with each other. Twelve bubbles with diameters of 0.125 wall units are distributed in the equally spaced distances from each other. The numerical results obtained indicate that for the cases studied here, the bubbles reach the statistical steady state with an almost constant final orbital motion path due to the strong secondary field. Furthermore, the effects of different physical parameters such as Reynolds number, and curvature ratio on the flow field at the no slip boundary conditions, are investigated in detail.

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The interactions between vortical structures and spherical particles or droplets is of practical issues in two-phase flows. The interactions bring major changes in the flow field particularly when coupled with particle rotation. It is observed that the heat transfer rate is significantly influenced during the time that the vortices’ cores are in the vicinity of the particle. In this paper, transient heat transfer of a rotating spherical particle interacting with a pair of vortices in incompressible and viscous flow is studied using numerical solution of the Navier-Stokes and energy equations in the range of 20≥Re≤100 and non-dimensional rotational velocities 0≤Ω≤1, by computational code which has been developed by the authors. In order to ensure the accuracy of the calculation, the results are compared with numerical data reported in the literature and good agreement between results was observed. Then the effect of circulation direction of two vortices interacting with a particle by spin on its heat transfer rate was investigated. Also distribution of heat transfer coefficient at the particle surface with separate rotation around three different axes in two cases of interacting and non-interacting with vortices is given and the results of heat transfer coefficient are presented. The results show that particle rotation for Ω≤0.5, in both presence and absence of vortices in flow field has negligible effects on the particle heat transfer rate; however, with increasing of particle spin significant effects on heat transfer coefficient has been observed that due to the circulation direction of vortices, different amounts are obtained.

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One of the main difficulties in employing fully coupled algorithms for solving Navier-Stokes equations is the high computation cost of coefficient matrix determination and solving the linear equation system. Therefore, the number of required iterations and computational costs may be reduced by increasing the convergence rate. This article deals with the formulation and testing of an improved fully coupled algorithm based on physical influence scheme (PIS) for the solution of incompressible fluid flow on cell-centred grid. The discretisation of improved algorithm is investigated and fully clarified, by comparing the methodology with two similar schemes. For a better insight, two benchmark problems are solved. The first problem is a steady lid-driven cavity with different Reynolds numbers between 100 and 10000. The second problem is steady flow over a backward facing step for the specified Reynolds number of 800. The history of residuals for present and previous methods are compared, in order to demonstrate the performance of the new discretization scheme. It is worth mentioning, the presented method is based on nine cells discretization. Therefore, the computational costs and memory usage of the proposed method are almost the same as previous ones. The results indicate that, the improved method converges in fewer iterations in comparison with prior methods. The new scheme can be utilized for development of the computational fluid dynamics solvers based on cell-centred grid arrangement.

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In this paper, a novel model based on the indicial functions concept is presented to calculate the unsteady aerodynamic loads in the incompressible and subsonic compressible flow. Indicial functions represent the two-dimensional airfoil response to a unit step change in the angle of attack or the pitch rate about the reference axis. In contrast to the incompressible flow where the aerodynamic loads can be determined in terms of a single indicial function, four indicial aerodynamic functions are required to find them in the compressible one. If the indicial functions are known, the unsteady loads can then be obtained through the superposition of indicial responses using Duhamel’s integral for any arbitrary motion. For the purpose of combination the aerodynamic loads for the entire subsonic flow speed range, i.e. 0≤M≤0.8, a new, efficient and Mach dependent approximations of the indicial functions are presented by using the analytical as well as numerical data. Using four instead of seven Mach dependent coefficients in the common indicial functions, the required coefficient are decreased from 28 to 16 to fully describe the aerodynamic loads. Utilizing the indicial functions, then a novel and convenient form of unsteady aerodynamic loads and the corresponding state-space representation is presented; having a unified formulation in incompressible and subsonic compressible flight speed regimes. Based on the strip theory as well as the modified lift curve slope, the finite span effect of 3D wings is also included. The generated indicial functions is validated against available results, which shows a good agreement.

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Numerical simulation of multi material or multi-phase flows are one of the most challenging problems between computational fluid dynamics researches. The main difficulty of these problems is producing some unexpected and non-physical oscillation at material interface which causes entering some error in to computation domain. For eliminating this source of error, many sophisticated algorithm have been proposed recently. By neglecting diffusion processes, Euler equations and HLLC reimann solver are applied. In addition, Level set algorithm is implemented to track interferences between two materials. An accurate, easily developed and low computation cost algorithm, proposed by Abgrall and Karni, is used to prevent generating the oscillations in the interfaces. In the current work, the algorithm is developed to 2 dimensional algorithm. Afterwards, the result of 1 and 2 dimensional code are evaluated to verify the developed algorithm by some standard problems such as sod problem. Finally, shock –bubble (Air – Helium) interaction problem is simulated to investigate the effect of the algorithm in 2 dimensional simulation. The comparison shows that the code and its result have very good accuracy with very low computational cost.

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In this study, the effects of Co-Flow jet and injection temperature on the enhancement of airfoil performance in the compressible flow are investigated numerically. Co-Flow jet is a method of increasing lift to drag ratio and varying the Stall Degree which works via injecting the air from the edge of airfoil and suction from the tail. The much number of studied flow changes from 0.4 to 0.6. Clark-Y airfoil has been chosen for this study because of its application in compressible flow, it is the base airfoil for development of new airfoils. A validation is performed for Clark-Y airfoil by comparing the present numerical result and available experimental data in the literature. Results indicate that the enhancement induced by the Co-Flow jet on the compressible flow is less than one in the incompressible flow. The drag and lift coefficients reduces and increases by increasing the jet momentum coefficient, respectively. Using the Co-Flow Jet increase the stall degree. The maximum of lift decrement and drag increment occurs around the stall degree. Increasing the temperature increases lift coefficient slightly where it seems to be better choice in comparison with increment of Jet momentum coefficient due to ease of operation.

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Applications of hollow spherical particles in industry and in thermal spraying process have been developed in recent years. Despite dense droplets, in hollow droplets, the volume changes of the gas play an important role in the dynamics of impact and the shape of the formed splats. In plasma thermal spraying, impact velocities of particles to the surface is in the range of 50 m/s-300 m/s, therefore, changes in pressure and volume of the trapped gas, is important. In this research, impact of hollow droplet on a flat surface and its solidification has been simulated. Volume of fluid model for compressible flows at real thermal spraying condition is used while the impact velocities in the range of 50 m/s-300 is considered. In a few moments after the impact of droplet on the surface, a pressure wave is formed in the air. This wave, increase the vorticity in vicinity of interface of two fluid, which has a great effect on shaping the formed splats. Simulations showed that shape of formed splats vary with velocities in the range of 50 m/s-300 m/s. In higher velocities, the surface of the formed splat is more porous.

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In this paper, an implicit finite element-discontinuous Galerkin method for compressible viscous and inviscid flow is developed using Newton-Krylov algorithm with the objective of increasing the accuracy and convergence rate. For inviscid flows, an artificial viscosity is implemented in sharp gradient flow regions especially at high-order cases, increasing the accuracy of the solution. Moreover, for viscous flows, the accuracy is improved by using compact discontinuous Galerkin discretization method for elliptical terms. To reduce the computing CPU time and increase the convergence rate, an iterative Krylov type preconditioned linear solver is applied. For preconditioning, restarting, Block-Jacobi and block incomplete-LU factorization are employed for solving the linear system of the Jacobian matrix. The Jacobian matrix is constructed via finite difference perturbation technique. In this context, the performance of preconditioning matrix for three types of flow regimes of inviscid subsonic, inviscid transonic and viscous laminar subsonic are studied. In addition to complete the discussions, multigrid smoother with special conditions is applied for all preconditioning matrices. To improve the solver performance for higher order discretization, a lower order solution may be used as higher orders initial condition. Therefore, a middle phase is needed to transfer calculations from low to high order discretized domain and then the final Newton phase is continued. In addition, local time stepping is implemented to improve the rate of convergence. Consequently, the presented numerical method can be used as an efficient algorithm for high-order Discontinuous Galerkin flow simulation, especially for transonic inviscid and laminar viscous flows.

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Piston effect is an important mechanism of heat transfer in a supercritical fluid flow under microgravity condition. In this study, a Lattice Boltzmann Model (LBM) has been introduced to simulate the piston effect. Variations of diffusion coefficient has been accounted for by adding a corresponding term to equilibrium distribution function. To calculate the intermolecular forces and compressibility in the LBM, a van der Waals equation of estate has been employed. Boundary conditions corresponding to compressible LBM at the presence of van der Waals forces have been set to eliminate the speed jump at the wall. It has been shown that such boundary conditions provide high accuracy in problems involving forces with an error of second order of magnitude in terms of space. The developed thermal LBM together with compressible LBM have been applied to simulate the heat transfer to supercritical fluid flows. The piston effect has been modeled by considering van der Waals inter molecular forces. The errors associated with each of the schemes used have been evaluated. A comparison between a pure conduction case and heat transfer due to piston effect has been made. It has been shown that the heat transfer occurs faster once the piston effect is in effect.

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One of the methods for solving Navier-Stokes equations in order to analyse aerodynamic flows is using finite volume method. Since aerodynamic flows are mostly in the range of compressible flows, here one of the density based algorithm (CUSP) have been studied to connecting equations. So here by adding LD (Low diffusion) part to the CUSP method a new method LDE (Low diffusion E-CUSP) have been created which containing new improved discretizations and it has been extended for a unstructured two dimensional mesh. Because of using edge-based data structure it gives the ability to solve the unstructured and structured meshes. Also the discretization of time section is done explicitly by Runge-Kutta method. It has acceptable stability range in compare with the amount of calculation utilized. Then, the results of new improved method (LDE) have been studied for a unstructured 2d mesh and compared with old method which it has been improved for unstructured mesh. The results show that the convergence time and the number of iterations to reach desired error are reduced. Also error percentage of numerical results like pressure coefficient is reduced. Moreover, dissipation of this new method does better than first method in terms of capturing shock location in a proper way.

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In this research, the impact of a completely molten hollow droplet and a semi-molten hollow droplet on a surface is simulated numerically. At first, the production process of hollow particles from the agglomerated particles is addressed analytically. By this model, one can predict the particle diameter, solid core diameter and shell thicknesses of produced particle. The results of this section show that hollow particle may hardly develop at small initial porosity values (p=0.2). Then, the collected data from analytical model is used as input data for numerical simulation. In the numerical model, the central solid core was assumed to be a fluid with high viscosity. Due to high impact velocity, volume and density changes of the trapped gas inside droplet are important. Therefore the compressible form of governing equations is used. The results show that the hydrodynamic and solidification behavior of a completely molten droplet and a semi-molten droplet during impact process are different. In the semi-molten state, the central solid core prevents the formation of a counter jet. For this reason, a hollow semi-molten droplet is solidified faster than a completely molten hollow droplet. The overall time of solidification in the completely molten state is 35 μs and the corresponding time for semi-molten state, is 12 μs. Moreover the splat of a semi-molten hollow droplet is more continues compared with a completely molten droplet

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The system of compressible equations using upstream numerical methods has convergence problem to analyze low-Mach number flow. In this study precondition method is employed in Euler equations to solve convergence problem in low-Mach number flow and this preconditioned equations are used to analyze flow around a two-dimensional body. The preconditioner modifies the transient behavior of the Euler equations in manner that the stiffness of the eigenvalues is removed and allows for a faster convergence to the steady state. So, Turkel precondition method, one of the useful preconditioner matrices, is applied in system of Euler equations. As majority of solvers use conservative variables, precondition matrix is recalculated for conservative variables and is employed in Euler equations. The upstream finite volume Roe method in an unstructured grid is employed for space discretization of equations. Transient part of equations also is discretized with fourth order explicit Runge-Kutta method. The performance of the proposed approach is vetted through an inviscid tow-dimensional flow around the NACA0012 airfoil with different Mach number and the steady state solution is calculated. Numerical results show‎ that Turkel preconditioner allow for a faster convergence to the steady state solution in low-Mach number. . .