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#### Numerical simulation of shock-disturbances interaction in high-speed compressible inviscid flow over a blunt nose using weighted essentially non-oscillatory scheme

, Article Wave Motion ; Volume 88 , 2019 , Pages 167-195 ; 01652125 (ISSN) ; Rahmani, S ; Sharif University of Technology
Elsevier B.V
2019

Abstract

In the present study, shock-disturbances interaction in high-speed compressible inviscid flow is simulated utilizing the weighted essentially non-oscillatory (WENO) scheme by employing the shock-capturing technique. For this aim, the two-dimensional Euler equations in strong conservative form are discretized by using the explicit third-order TVD Runge–Kutta scheme in time and the fifth-order WENO finite difference scheme in space. The main advantage of using the WENO scheme is its capability for properly solving the discontinuities in the domain without needing any artificial viscosity, limiter function or filter. Hence, this scheme is stable, and thus, it is suitable for simulating very...

#### An assessment of shock-disturbances interaction considering real gas effects

, Article Journal of Fluids Engineering, Transactions of the ASME ; Volume 141, Issue 1 , 2019 ; 00982202 (ISSN) ; Rahmani, S ; Sharif University of Technology
American Society of Mechanical Engineers (ASME)
2019

Abstract

In this study, a theoretical analysis is performed to assess the interaction of freestream disturbances with a plane normal shock considering real gas effects. Such effects are important in a field with high velocities and high temperatures. To perform the theoretical analysis, the downstream disturbances field is expressed as a mathematical function of the upstream one by incorporating real gas effects in the formulation. Here, the linearized one-dimensional perturbed unsteady Euler equations are used for the classification of the downstream/upstream disturbances field and the linearized one-dimensional perturbed Rankine-Hugoniot equations are applied to provide a relationship between the...

#### Numerical Simulation of Natural Convection Using Smoothed Particle Hydrodynamics with Artificial Compressibility Method

, M.Sc. Thesis Sharif University of Technology ; Hejranfar, Kazem (Supervisor)
Abstract

In this research, the numerical simulation of the natural convection is performed by using the smoothed particle hydrodynamics based on the artificial compressibility method. For this aim, the formulation of the artificial compressibility method in the Eulerian reference frame for the mass and momentum equations is written in the Lagragian reference frame and the Lagrangin form of the energy equation is also considered to compute the thermal effects. The benefit of the artificial compressibility-based incompressible SPH (ACISPH) method over the weakly compressible SPH (WCSPH) method for computing the natural convection is that there is no need in the formulation considered here to use any...

#### A high-order accurate unstructured spectral difference lattice Boltzmann method for computing inviscid and viscous compressible flows

, Article Aerospace Science and Technology ; Volume 98 , 2020 ; Ghaffarian, A ; Sharif University of Technology
Elsevier Masson SAS
2020

Abstract

In the present work, the spectral difference lattice Boltzmann method (SDLBM) is implemented on unstructured meshes for the solution methodology to be capable of accurately simulating the compressible flows over complex geometries. Both the inviscid and viscous compressible flows are computed by applying the unstructured SDLBM. The compressible form of the discrete Boltzmann–BGK equation with the Watari model is considered and the solution of the resulting system of equations is obtained by applying the spectral difference method on arbitrary quadrilateral meshes. The accuracy and robustness of the unstructured SDLBM for simulating the compressible flows are demonstrated by simulating four...

#### Development of Characteristic Boundary Conditions with Artificial Compressibility Method by Compact Finite-Difference Discretization

, Ph.D. Dissertation Sharif University of Technology ; Hejranfar, Kazem (Supervisor)
Abstract

In the present study, the preconditioned incompressible Navier‐Stokes equations with the artificial compressibility (AC) method formulated in the generalized curvilinear coordinates are numerically solved by using a high‐order compact finite‐difference scheme for accurately and efficiently computing the incompressible flows. A fourth‐order compact finite‐difference scheme is utilized to discretize the spatial derivative terms of the resulting system of equations and the time integration is carried out based on the dual time‐stepping method. The capability of the proposed solution methodology for computing the steady and unsteady incompressible viscous flows in a wide range of Reynolds...

#### An assessment of shock-disturbances interaction considering real gas effects

, Article Journal of Fluids Engineering, Transactions of the ASME ; Volume 141, Issue 1 , 2019 ; 00982202 (ISSN) ; Rahmani, S ; Sharif University of Technology
American Society of Mechanical Engineers (ASME)
2019

Abstract

In this study, a theoretical analysis is performed to assess the interaction of freestream disturbances with a plane normal shock considering real gas effects. Such effects are important in a field with high velocities and high temperatures. To perform the theoretical analysis, the downstream disturbances field is expressed as a mathematical function of the upstream one by incorporating real gas effects in the formulation. Here, the linearized one-dimensional perturbed unsteady Euler equations are used for the classification of the downstream/upstream disturbances field and the linearized one-dimensional perturbed Rankine-Hugoniot equations are applied to provide a relationship between the...

#### A coupled prescribed wake-Euler solver for efficient computing helicopter rotor flows in hover

, Article 25th Congress of the International Council of the Aeronautical Sciences 2006, Hamburg, 3 September 2006 through 8 September 2006 ; Volume 3 , 2006 , Pages 1670-1681 ; Mohammadi, M ; Sharif University of Technology
Curran Associates Inc
2006

Abstract

A numerical solution technique is developed to simulate the flowfield of hovering helicopter rotor. The present method uses a coupled prescribed wake-Euler solver to efficiently allow the vortical wake effects. The threedimensional Euler equations written in a rotating coordinate frame are solved by using a cell-centered finite volume scheme that is based on the Roe's flux-difference splitting on unstructured meshes. High-order accuracy is achieved via the reconstruction of flow variables using the MUSCL interpolation technique. Calculations are carried out for an isolated rotor in hover for two operating conditions of subsonic and transonic tip Mach numbers, Mtip = 0.44 and Mtip = 0.877 ,...

#### Numerical Simulation of 2D Compressible Cavitation Flow Using Compact Finite-Difference Method

, M.Sc. Thesis Sharif University of Technology ; Hejranfar, Kazem (Supervisor)
Abstract

In the present study, the numerical simulation of 2D inviscid compressible cavitation flow is performed by using the compact finite-difference method. The problem formulation is based on the multiphase compressible Euler equations with the assumption of the homogeneous equilibrium model and the system of baseline differential equations is comprised of the continuity, momentum and energy equations for the vapor-liquid mixture. To complete the system of governing equations, the ideal gas relation is used for the vapor phase and the Tait relation is applied for the liquid phase, and therefore, the compressibility effects are considered for both the vapor and liquid phases. To analyze the flow...

#### Aerodynamic Analysis of Dual Rotors Using Potential Method and Free Wake Modeling

, M.Sc. Thesis Sharif University of Technology ; Hejranfar, Kazem (Supervisor)
Abstract

Potential flow solvers simplify the mathematical formulation and achieve efficient solutions. The prediction of aerodynamic of dual rotor systems using computational fluid dynamic methods is difficult task due to the interference effects between the wakes shed from the rotors. In the present work, a free wake vortex lattice method is used to predict the vertical wake and blade loading of dual rotors in hover. In this approach the blades are modeled as flat plates with zero thickness and ring vortices are distributed on the surface of each blade. When the blades rotate, vortices are shed into the wake and freely move with a local velocity induced by the effects of the vortices on the blades...

#### Numerical Solution of Hypersonic Axisymmetric Flows Including Real Gas Effects Using Compact Finite-Difference Scheme

, M.Sc. Thesis Sharif University of Technology ; Hejranfar, Kazem (Supervisor)
Abstract

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...

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...

#### Numerical Simulation of 2D Inviscid Compressible Magnetohydrodynamic Flows by Spectal Difference Method

, M.Sc. Thesis Sharif University of Technology ; Hejranfar, Kazem (Supervisor)
Abstract

In the present study, the numerical solution of 2D inviscid compressible ideal magnetohydrodynamic (MHD) flows by using the spectral difference (SD) method on unstructured meshes is performed. The SD method combines the most desirable features of structured and unstructured grid methods to have computational efficiency and geometric flexibility to accurately compute flow over complex geometries. In the SD method, two sets of structured points, namely “unknown points” and “flux points”, are defined in each cell to support the reconstruction of given order of accuracy. The differential form of the conservation laws is satisfied at nodal unknown points while the flux derivatives expressed in...

#### Developing a Compact Finite Difference Method for Solving Fluid - Solid Interaction in Incompressible Flow

, M.Sc. Thesis Sharif University of Technology ; Hejranfar, Kazem (Supervisor)
Abstract

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...

#### Numerical Simulation Cavitating Flows Using Compact Finite-difference Scheme

, M.Sc. Thesis Sharif University of Technology ; Hejranfar, Kazem (Supervisor)
Abstract

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...

#### Numerical Simulation of Incompressible Flows over two Dimensional Geometries by Means of Immersed Boundary Method

, M.Sc. Thesis Sharif University of Technology ; Hejranfar, Kazem (Supervisor)
Abstract

Two-dimensional incompressible flow analysis is one the most important applied issues in engineering and applied science field. Numerical solution of governing equations of flow requires exact computational grid generation.In complex geometries, generation of the grid which is coincident to the body is very difficult and time consuming. Immersed boundary method is an appropriate superseded method of body conformal grid generation in flow field numerical solution. In this method a grid which is not coincidentto bodyis generated and flow field properties are modified on points adjacent to the boundary of the object (Ghost Cell Method) to satisfy boundary conditions.

The purpose of this...

The purpose of this...

#### Numerical Simulation of Cavitating Flows with Compressibility Effects

, M.Sc. Thesis Sharif University of Technology ; Hejranfar, Kazem (Supervisor)
Abstract

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...

#### Numerical Simulation of Two-dimensional Compressible Flow by Central Difference Finite Volume Scheme and Immersed Boundary Method

, M.Sc. Thesis Sharif University of Technology ; Hejranfar, Kazem (Supervisor)
Abstract

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...

#### Numerical Simulation of Compressible Viscous Flows Using Central Difference Finite Volume Lattice Boltzmann Method

, M.Sc. Thesis Sharif University of Technology ; Hejranfar, Kazem (Supervisor)
Abstract

In this study, 2-D compressible viscous and inviscid flows are simulated by using a finite volume Lattice Boltzmann method. Two different models, namely, the Qu model and Watari model are employed for compressible flows simulations. The first model includes 13 discrete velocity vectors and 2 energy levels in which the Maxwellian function is replaced with a simple function for describing the distribution function that is suitable for inviscid flow simulations. The second model is a thermal multi-velocity model with isotropic tensors up to seventh rank that is suitable for compressible viscous and inviscid flow simulations with arbitrary specific heats ratio. In both the models, lattice...

#### Numerical Simulation of Turbulent Cavitating Flows Using Two-Equation k-ϵ Turbulence Model

, M.Sc. Thesis Sharif University of Technology ; Hejranfar, Kazem (Supervisor)
Abstract

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...

#### Assessment of three preconditioning schemes for solution of the two-dimensional Euler equations at low Mach number flows

, Article International Journal for Numerical Methods in Engineering ; Volume 89, Issue 1 , 2012 , Pages 20-52 ; 00295981 (ISSN) ; Kamali Moghadam, R ; Sharif University of Technology
2012

Abstract

Three preconditioners proposed by Eriksson, Choi and Merkel, and Turkel are implemented in a 2D upwind Euler flow solver 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 other. For this purpose, these preconditioning schemes are expressed in a unified formulation. A cell-centered finite volume Roe's method is used for the discretization of the preconditioned Euler equations. The accuracy and performance of these preconditioning schemes are examined by computing steady low Mach number flows over a NACA0012 airfoil and a two-element...

#### Implementing a high-order accurate implicit operator scheme for solving steady incompressible viscous flows using artificial compressibility method

, Article International Journal for Numerical Methods in Fluids ; Volume 66, Issue 8 , July , 2011 , Pages 939-962 ; 02712091 (ISSN) ; Khajeh Saeed, A ; Sharif University of Technology
2011

Abstract

This paper uses a fourth-order compact finite-difference scheme for solving steady incompressible flows. The high-order compact method applied is an alternating direction implicit operator scheme, which has been used by Ekaterinaris for computing two-dimensional compressible flows. Herein, this numerical scheme is efficiently implemented to solve the incompressible Navier-Stokes equations in the primitive variables formulation using the artificial compressibility method. For space discretizing the convective fluxes, fourth-order centered spatial accuracy of the implicit operators is efficiently obtained by performing compact space differentiation in which the method uses block-tridiagonal...