**WSEAS Transactions on
Fluid Mechanics**

**Contents:**

2016 | 2015 | 2014 | 2013 | 2012 | 2011 | 2010 | 2009 | 2008 | Pre-2008

**Print ISSN: 1790-5087
E-ISSN: 2224-347X**

**Volume 8, 2013**

**Issue 1, Volume 8, January 2013**

Title of the Paper: **Chemical Non-Equilibrium Reentry Flows in Two-Dimensions – Part I **

Authors: **Edisson Sávio De Góes Maciel, Amilcar Porto Pimenta **

Abstract: This work presents a numerical tool implemented to simulate inviscid and viscous flows employing the reactive gas formulation of thermal equilibrium and chemical non-equilibrium. The Euler and Navier-Stokes equations, employing a finite volume formulation, on the context of structured and unstructured spatial discretizations, are solved. The aerospace problem involving the hypersonic flow around a blunt body, in two-dimensions, is simulated. The reactive simulations will involve an air chemical model of five species: N, N2, NO, O and O2. Seventeen chemical reactions, involving dissociation and recombination, will be simulated by the proposed model. The algorithm employed to solve the reactive equations was the Van Leer, first- and second-order accurate ones. The second-order numerical scheme is obtained by a “MUSCL” (Monotone Upstream-centered Schemes for Conservation Laws) extrapolation process in the structured case. The algorithm is accelerated to the steady state solution using a spatially variable time step procedure, which has demonstrated effective gains in terms of convergence rate, as reported in Maciel. The results have demonstrated that the most correct aerodynamic coefficient of lift is obtained by the Van Leer first-order accurate scheme in the inviscid, structured, blunt body simulation. Moreover, the shock position is closer to the geometry as using the reactive formulation than the ideal gas formulation. It was verified in the inviscid and viscous cases.

Keywords: Euler and Navier-Stokes equations

Title of the Paper: **Spatial Evolution of Mixing Layers: Effects of Shear and Convection **

Authors: **Mohammed A. Azim **

Abstract: This paper has reported the effects of shear velocity, convection velocity and shear rate on the spatial evolution of turbulent axisymmetric mixing layers. The types of mixing layers investigated are with the variation of convection velocity under the constant shear velocity, with the variation of shear velocity under the constant convection velocity and with the variation of shear or convection velocity under the constant shear rate. The closed form equations governing the mixing layer flows are obtained by the standard k −ε model and solved by using Fully Implicit Scheme and TDMA (Tridiagonal Matrix Algorithm). Obtained results show that the mixing layer thickness and momentum thickness evolve streamwise, and the shape and level of mean velocity, turbulent shear stress, mean vorticity and turbulence kinetic energy evolve streamwise but not radially with the changes in operating conditions at constant rate of shear. While changes in operating conditions affect the evolution of mixing layers in both directions under the constant shear or convection velocity.

Keywords: Axisymmetric mixing layer, Turbulent flow, Spatial evolution, Shear velocity, Convection velocity, Shear rate, Computational fluid dynamics

Title of the Paper: **Simultaneous Inversion for Dispersion Coefficients and Space-Dependent Source Magnitude in 2D Solute Transportation **

Authors: **Dali Zhang, Hezhong Lou, Gongsheng Li, Xianzheng Jia, Huiling Li **

Abstract: This paper deals with an inverse problem of simultaneously determining the dispersion coefficients and the space-dependent source magnitude in 2D advection dispersion equation with finite observations at the final time. The forward problem is solved by using the alternating direction implicit (ADI) finite difference scheme, and then the optimal perturbation algorithm with the regularization parameter chosen by a Sigmoid-type function is introduced to solve the simultaneous inversion problem numerically. Numerical inversions are presented, and several factors having influences on realization of the algorithm are discussed. The inversion solutions are in good approximations to the exact solutions demonstrating that the optimal perturbation algorithm with the Sigmoid-type regularization parameter is efficient for the simultaneous inversion problem in 2D solute transportation.

Keywords: 2D advection dispersion equation, simultaneous inversion, optimal perturbation algorithm, regularization parameter, numerical simulation

**Issue 2, Volume 8, April 2013**

Title of the Paper: **A Note on the Shoaling of Acoustic-Gravity Waves **

Authors: **Usama Kadri, Michael Stiassnie **

Abstract: A mathematical solution of the two dimensional linear problem of an acoustic–gravity wave propagating over a rigid and slowly-varying bathymetry, in an acoustically homogeneous and slightly compressible ocean, is resented. Expressions for the far and near flow fields are derived. The present note enriches our knowledge about acoustic–gravity waves in a way that could assist, among others, in the early detection of tsunami.

Keywords: Acoustic–gravity waves, shoaling, turning point, early detection of tsunami

Title of the Paper: **Chemical Non-Equilibrium Reentry Flows in Two-Dimensions – Part II **

Authors: **Edisson Sávio De Góes Maciel, Amilcar Porto Pimenta **

Abstract: This work, second part of this study, presents two numerical tools implemented to simulate inviscid and viscous flows employing the reactive gas formulation of thermal equilibrium and chemical non-equilibrium. The Euler and Navier-Stokes equations, employing a finite volume formulation, on the context of structured and unstructured spatial discretizations, are solved. The aerospace problems involving the hypersonic flow around a blunt body, around a double ellipse, and around a re-entry capsule, in two-dimensions, are simulated. The reactive simulations will involve an air chemical model of five species: N, N2, NO, O and O2. Seventeen chemical reactions, involving dissociation and recombination, will be simulated by the proposed model. The algorithms employed to solve the reactive equations were the Van Leer and the Liou and Steffen Jr., first- and second-order accurate ones. The second-order numerical scheme is obtained by a “MUSCL” (Monotone Upstream-centered Schemes for Conservation Laws) extrapolation process in the structured case. The algorithms are accelerated to the steady state solution using a spatially variable time step procedure, which has demonstrated effective gains in terms of convergence rate, as reported in Maciel. The results have demonstrated that the most correct aerodynamic coefficient of lift to the re-entry problem is obtained by the Van Leer first-order accurate scheme in the viscous, structured simulation. The Van Leer scheme is also the most robust being able to simulate the major part of the studied problems.

Keywords: Euler and Navier-Stokes equations, Chemical non-equilibrium, Five species model, Hypersonic flow, Van Leer algorithm, Liou and Steffen Jr. algorithm

Title of the Paper: **A Study on the Mathematical Modeling of Water Quality in "River-Type" Aquatic Systems **

Authors: **Galina Marusic **

Abstract: This paper deals with the problem of pollution in "river-type" aquatic systems. We discuss prediction methods of pollution and water quality determination, and the concept of "water quality". It examines the main sources of pollution in the river. It presents an analysis of scientific work in the field of river pollution. It addresses the problem of mathematical modeling of hydrodynamics and pollutant dispersion in "river-type" systems. It summarizes the scientific work in the field of river water quality modeling.

Keywords: Water quality, river, turbulent motion, punctate pollution, diffuse pollution, mathematical modeling, numerical model

**Issue 3, Volume 8, July 2013**

Title of the Paper: **Tsunami Wave Simulation Models Based on Hexagonal Cellular Automata **

Authors: **E. Syed Mohamed, S. Rajasekaran **

Abstract: The devastating effect of tsunamis on mankind has clearly established that many improvements are needed in disaster management. In this work we propose a new hexagonal cellular automata model based on the transfer of fractional traversed area. The rates of spread of tsunami waves for both homogeneous and non homogeneous oceans under different topological conditions are derived. Graphical representation of rate of spread has been found successfully.

Keywords: Tsunami wave, Simulation, Homogeneous, Non-homogeneous, Cellular automata, Discrete time step, Primary wave front, Secondary wave front

Title of the Paper: **TVD and ENO Applications to Supersonic Flows in 3D – Part II **

Authors: **Edisson Sávio De Góes Maciel **

Abstract: In this work, second part of this study, the high resolution numerical schemes of Yee and Harten, of Yang second order, of Yang third order, and of Yang and Hsu are applied to the solution of the Euler and Navier-Stokes equations in three-dimensions. All schemes are flux difference splitting algorithms. The Yee and Harten is a TVD (“Total Variation Diminishing”) second order accurate in space and first order accurate in time algorithm. The Yang second order is a TVD/ENO (“Essentially Nonoscillatory”) second order accurate in space and first order accurate in time algorithm. The Yang third order is a TVD/ENO third order accurate in space and first order accurate in time algorithm. Finally, the Yang and Hsu is a UNO (Uniformly Nonoscillatory) third order accurate in space and first order accurate in time algorithm. The Euler and Navier- Stokes equations, written in a conservative and integral form, are solved, according to a finite volume and structured formulations. A spatially variable time step procedure is employed aiming to accelerate the convergence of the numerical schemes to the steady state condition. It has proved excellent gains in terms of convergence acceleration as reported by Maciel. The physical problems of the supersonic flows along a compression corner and along a ramp are solved, in the inviscid case. For the viscous case, the supersonic flow along a ramp is again solved. In the inviscid case, an implicit formulation is employed to marching in time, whereas in the viscous case, a time splitting or Strang approaches are used. The results have demonstrated that the Yang and Hsu UNO third order accurate algorithm has presented the best solutions in the problems studied herein. Moreover, it is also the best as comparing with the numerical schemes of Part I of this study.

Keywords: Yee and Harten algorithm, Yang second order TVD/ENO algorithm, Yang third order TVD/ENO algorithm, Yang and Hsu UNO algorithm, Euler and Navier-Stokes equations, Finite Volumes

Title of the Paper: **Large Eddy Simulation of Low Subcritical Reynolds NumberFlow across a Rotating Circular Cylinder **

Authors: **K. Mobini, M. Niazi **

Abstract: In this study, unsteady turbulent flow across a counterclockwise rotating circular cylinder is computed using Large Eddy Simulation (LES). The spinratio varies between 0 and 2 and The Reynolds number changes from 3900 to 10000. Time integration of the flow equations is carried out for a very large dimensionless time. Smagorinsky subgrid scale model with Cs=0.1 is used to resolve the residual stresses. Variations of the mean drag and lift coefficients, and the flow structure with spin ratio and Reynolds number are studied. It is found that by increase ofspin ratioor decrease of Reynolds number, both the stagnation point and the wake region move upward along the cylinder. As a result,the mean drag decreases and the mean lift increases. Length of the vortices behindthe cylinder is also increased by increase of bothspin ratio and Reynolds number. The computed results are compared with the results from the other numerical or experimental works, showing a good correspondence. It was found that the LES method is an accurate and convenient method for computation of highly recirculating flows.

Keywords: Large Eddy Simulation, Rotating circular cylinder, unsteady flow, drag coefficient, lift coefficient, subcritical flow

**Issue 4, Volume 8, October 2013**

Title of the Paper: **Comparative Study Compact Scheme for the Case of Shock Tube Problem **

Authors: **Mahmod Abd Hakim Mohamad, Mahathir Mohamad **

Abstract: In this work, a high-order compact upwind scheme is developed for solving one-dimensional Euler equation. A detailed investigation was conducted to assess the performance of the basic third-order compact central discretization schemes. From this observation, discretization of the convective flux terms of the Euler equation is based on a hybrid flux-vector splitting, known as the advection upstream splitting method (AUSM) scheme which combines the accuracy of flux-difference splitting and the robustness of flux-vector splitting. In one-dimensional problem for the first order schemes, an explicit method is adopted by using time integration method. In addition to that, development and modification of source code for the one-dimensional flow is validated with two test cases namely, unsteady shock tube and quasi-one-dimensional supersonic-subsonic nozzle flow were using as a comparative study. Further analysis had also been done in comparing the characteristic of AUSM scheme against experimental results, obtained from previous works and also comparative analysis with computational results generated by van Leer, KFVS and AUSMPW schemes. Furthermore, there is a remarkable improvement with the extension of the AUSM scheme from first-order to third-order accuracy in terms of shocks, contact discontinuities and rarefaction waves.

Keywords: High-order compact schemes, finite difference methods, flux-difference splitting, flux-vector splitting, Euler equations, One-dimensional

Title of the Paper: **On the Steady Two-Dimensional Flow of Blood with Heat Transfer in the Presence of a Stenosis **

Authors: **Azhar Mirza, Ali R Ansari, Abdul M Siddiqui, Tahira Haroon **

Abstract: In the present study, we consider the steady two-dimensional flow of blood in an axisymmetric artery having a constriction, referred to as a stenosis, of cosine shape with heat transfer. Blood is assumed to behave like an incompressible Newtonian fluid. The governing Navier-Stokes equations are transformed and solved an- alytically by the regular perturbation technique. The results thus obtained are presented graphically in the form of stream lines, wall shear stress, separation point, pressure distribution, velocity components and temperature distribution. It is observed that an increase in the height of the constriction, increases the velocity of blood, wall shear stress, pressure and temperature. A parametric study of the blood flow behavior is presented and some of the results are compared with published literature.

Keywords: Heat transfer, wall shear stress, pressure distribution

Title of the Paper: **Analysis of Laminar Boundary Layer Flow along a Stretching Cylinder in the Presence of Thermal Radiation **

Authors: **Vikas Poply, Phool Singh, K. K. Chaudhary **

Abstract: An analysis has been carried out to obtain the effects of thermal radiation on axi-symmetric laminar boundary layer flow of a viscous incompressible fluid along a stretching cylinder. Rosseland approximation has been use to model the radiative heat transfer. Using the similarity transformation, the partial differential equations corresponding to the momentum and heat equations have been transformed to a set of non-linear ordinary differential equations. These equations have been solved numerically using Runge-Kutta Fehlberg method with shooting technique. In the present reported work, the effects of radiation parameter, curvature parameter, Prandtl number and temperature exponent parameter on flow and heat transfer characteristics have been discussed. Variations of these parameters have been graphically presented. The reported results have been found to be in good agreement with the available published work in the literature.

Keywords: Laminar flow, boundary layer, stretching cylinder, radiation