Sharif Digital Repository

In the present study, a high-order accurate numerical solution of steady incompressible slip flow and heat transfer in 2D microchannels is presented. The numerical method used is an alternating direction implicit operator scheme which is efficiently implemented to solve the incompressible Navier-Stokes equations in the primitive variables formulation using the artificial compressibility method. To stabilize the numerical solution, numerical filters are used. The present methodology considers the solution of the Navier-Stokes equations with¬ employing different slip boundary condition¬¬ (Maxwell,¬ ¬¬Hyperbolic tangent function of Knudsen number¬ and Beskok slip models)¬ ¬¬on the wall to model... 

The numerical solution of the parabolized Navier-Stokes (PNS) equations for accurate computation of hypersonic axisymmetric flowfield with real gas effects is obtained by using the fourth-order compact finite-difference method. The PNS equations in the general curvilinear coordinates are solved by using the implicit finite-difference algorithm of Beam and Warming type with a high-order compact accuracy. A shock fitting procedure is utilized in the compact PNS scheme to obtain accurate solutions in the vicinity of the shock. To stabilize the numerical solution, numerical dissipation term and filters are used. The main advantage of the present formulation is that the basic flow variables... 

In this study, the solution of compressible flows is performed using finite volume lattice Boltzmann method (FVLBM). A model associated with 13 discrete velocity vectors and 2 energy levels is used and the Boltzmann transport equation is solved using a cell-centered finite volume on structured meshes. The values of distribution functions on each cell faceare determined by averaging from their values at the two control points located on the center of two neighboring cells. The fourth-order Runge-Kutta time-stepping scheme is applied to discretize temporal derivative term. The second- and fourth-order numerical dissipation termsareadded to the algorithm to stabilize the solution when solving... 

The study of evaporation of fuel droplet and determination of the rate of vaporization are important in designing combustion chambers. For achieving high performance of a combustor, the evaporation of fuel droplets takes place within a high pressure environment. At these conditions, the use of low-pressure models is not appropriate and many effects that are assumed negligible at low ambient pressures become very important. For example, the solubility of the ambient gas into the liquid phase is increased by increasing the ambient pressure. In addition, the ideal gas assumption is not valid for these conditions and one should use an appropriate equation of state (EOS) that can predict the... 

Nowadays, one of the most important desires of the human being is to reduce his living environmental pollution. Using the diluted combustion systems in new gas turbines in order to produce the minimum amount of has been done to satisfy this desire. It should be noted that reducing this amount and using the lower flame temperature will result in some consequences. The most important problem occurred in industrial and aerial gas turbines are the instability of the combustion due to dilution of the fuel to air mixture which it results in heat release fluctuations. If the heat release fluctuations and acoustic pressure are in the same phases, the amplitude of the fluctuations will increase which... 

In this study, fluid-solid interaction (FSI) is simulated computationally by using a high-order accurate numerical method. The two-dimensional incompressible viscous flows are considered in the fluid domain. The primary problem with solutions of the incompressible Navier–Stokes equations is the difficulty of coupling changes in the velocity field with changes in the pressure field while satisfying the continuity equation. Herein, the artificial compressibility method is used to overcome this difficulty. Preconditioning is implemented to reduce the stiffness of the system of equations to increase the convergence rate of the solution. Using preconditioning, physical solutions even at low... 

In this study, the numerical simulation of natural and ventilated cavitating flows is performed. The algorithm employs the homogenous, multiphase Navier-Stokes equations with appropriate mass transfer terms.The base line differential equations system is comprised of the mixture volume, mixture momentum and constituent volume fraction equations. A three species differential formulation is considered for constituent volume fraction transport/generation of liquid, condensable vapor and non-condensable gas fields.The system of governing equations is discretized using a cell-centered finite volume Roe’s upwind scheme. Both laminar and turbulent cavitating flows are considered in this study. For... 

In the present study, the numerical simulation of the compressible inviscid flow around helicopter rotor is performed using the solution of the preconditioned Euler equations. Three preconditioners proposed by Eriksson, Choi and Merkel, and Turkel are implemented in two- and three-dimensional upwind Euler flow solvers on unstructured meshes. The mathematical formulations of these preconditioning schemes for different sets of primitive variables are drawn and their eigenvalues and eigenvectors are compared with each others. For this aim, these preconditioning schemes are expressed in a unified formulation. A cell-centered finite volume Roe's upwind method is used for the discretization of the... 

In the study, the simulation of two-dimensional cavitating flows is performed by applying a high-order accurate numerical method to the preconditioned, homogenous, multiphase Navier-Stokes equations. The baseline differential equations system is comprised of the mixture volume, mixture momentum and constituent volume fraction equations. A coordinate transformation is applied and the resulting system of governing equations in curvilinear coordinates is discretized using a fourth-order compact finite-difference scheme. The high-order accurate numerical scheme employing the suitable linear and nonlinear filters to account for density jumps across the cavity interface is shown to yield an... 

In this study, the simulation of two-dimensional supersonic flows through microchannels in slip flow regime is performed using a lattice Boltzmann model (LBM). Traditional LB models have been used to simulate incompressible fluid flows and there are not suitable for modeling compressible or thermo-fluid flows. Herein, a recently developed LB model, namely, the finite difference lattice Boltzmann method (FDLBM), is employed to simulate compressible flows with embedded shocks. In this model, one can select particle velocities independently from the lattice configuration, and therefore, a correct and numerically stable multispeed thermal model by adopting more isotropic particle velocities can... 

In this study, the numerical simulation of cavitating flows for cryogens fluids is performed. The algorithm employs the homogenous, multiphase Euler/Navier-Stokes equations with the interface capturing method. The thermodynamic and thermal effects substantially impact the cavitation dynamics of cryogenic fluids and therefore these effects should be considered by solving the energy equation in conjunction with the mass and momentum conservation, and updating the fluid physical properties. Here, two cavitation modeling strategies, namely, the barotropic cavitation model and the transport equation-based model are used. Both laminar and turbulent cavitating flows are studied in this work. For... 

In the present work, the numerical simulation of 2D inviscid compressible flows by using the spectral difference (SD) method on quadrilateral meshes is performed. The SD method combines the most desirable features of structured and unstructured grid methods to attain computational efficiency and geometric flexibility. Similar to the discontinuous Galerkin (DG) and spectral volume (SV) methods, the SD scheme utilizes the concept of discontinuous and high-order local representations to achieve conservation and high accuracy. The SD method is based on the finite-difference formulation and thus its formulation is simpler than the DG and SV methods ... 

In this study, the numerical simulation of cavitating flows with compressibility effects is performed. The algorithm employs the multiphase Euler equations with homogeneous equilibrium model. The baseline differential equations system is similar to the one-phase system of equations and comprised of the mixture density, mixture momentums and mixture energy equations. Thephases considered for cavitating flows is liquid-vapor and liquid-gas fields. The system of governing equations is discretized using a cell-centered finite volume AUSM’s upwind scheme. The computations are presented for steady noncavitating/cavitating flows around 1D/2Dproblems for different conditions. A sensitivity study is... 

In the current study, the numerical simulation of the turbulent cavitating flows is performed by solving the preconditioned, homogenous, multiphase Navier-Stokes equations. For the turbulence modeling, the standard two-equation k-ϵ model is used. The baseline differential equations system is comprised of the mixture volume, mixture momentum and constituent volume fraction equations together with two equations for the turbulence kinetic energy k and the turbulence energy dissipation rate ϵ. For the calculation of the eddy viscosity near the wall boundary, appropriate turbulence damping functions are applied to modify the source terms of the ϵ equation. The system of governing equations is... 

In the present study, the simulation of incompressible Electro-Magneto-hydrodynamic flows is performed using a finite volume lattice Boltzmann method (FVLBM). The Boltzmann transport equation is solved using a cell-centered finite volume method on structured meshes. A central difference scheme is used to discretize the spatial derivatives and the fourth-order numerical dissipation term is added to stabilize the solution. To discretize the temporal derivative, the fourth-order Runge-Kutta time stepping scheme is applied. The standard collision-streaming lattice Boltzmann method has been used to simulate EMHD flows in the literature, however, it has several deficiencies such as the... 

In the present work, the deformation and collapse of a single cavitating bubble near solid boundaries is simulated by solving the preconditioned, homogenous, multiphaseNavier-Stokes equations. Up to now, all studies in the literature performed by the volume of fluid (VOF)approach to capture the bubble surface have been based on the pressure-based category in which the flow variables are calculated through solving the Poisson equation. Here, the density-based category is applied and the solution methodology is based on the artificial compressibility approach. The compressible form of the Navier-Stokes equations is applied inside the bubble and the liquid phase is assumed to be incompressible.... 

In this study,thecut-cells method is developed for simulating two-dimensional, inviscid, compressible flows with immersed boundaries. A finite volume method based on the second-order accurate central-difference scheme and the Runge-Kutta time stepping scheme is used. The key aspects that require to be considered in thedevelopment of such a solver are implementation of boundary conditions on the immersed boundaries and correct discretizing the governing equations in those cells cut by the boundaries. An appropriate interpolation procedure is applied to preserve the second-order spatial accuracy of the solver. The solution procedure is validated vs. well documented test problems for a wide... 

In the present work, the numerical solution of 2D inviscid compressible Magneto-hydrodynamic flow is performed by using the spectral difference (SD) method on quadrilateral grids. In this numerical method, similar to the discontinuous Galerkin (DG) and spectral volume (SV) methods, the concept of the discontinuous and high-order local representations is used to achieve conservation property and high-order accuracy. In the SD method, the test function or the surface integral is not involved and thus it has a simpler formulation than the DG and SV methods. In this numerical method, two sets of structured points, namely unknown points and flux points, are defined in each cell to support the... 

In this study, the numerical simulation of the two-dimensional incompressible flow around an oscillating airfoil is performed. For this aim, the incompressible Navier-Stokes equations based on the artificial compressibility approach written in the arbitrary Lagrangian-Eulerian form are considered. Then, the vorticity confinement method is incorporated in the formulation and the resulting system of equations is solved by a second-order central-difference finite volume method with the controllable dissipation terms. For the time integration, the implicit dual-time stepping scheme is implemented. At first, the numerical solution of the incompressible flow over the oscillating NACA0012 airfoil... 

In this study, an accurate numerical solution of the two-dimensional incompressible viscous flows is performed by using the spectral difference method on structured grids. The system of equations to be solved here is the preconditioned incompressible Navier-Stokes equations in the primitive variable formulation with the artificial compressibility approach. In the spectral difference method, two sets of the structured points, namely, “solution points” and “flux points” are defined in each cell for supporting the reconstruction of desirable order of accuracy. Here, the formulation of the spectral difference method is derived and the representative form of the solution and flux points for...