# WSEAS Transactions on Fluid Mechanics

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

**Volume 9, 2014**

Notice: As of 2014 and for the forthcoming years, the publication frequency/periodicity of WSEAS Journals is adapted to the 'continuously updated' model. What this means is that instead of being separated into issues, new papers will be added on a continuous basis, allowing a more regular flow and shorter publication times. The papers will appear in reverse order, therefore the most recent one will be on top.

**Volume 9, 2014**

Title of the Paper: **The Linear Stability of Cartesian Plumes in a Bounded Region **

Authors: **Khaled S. M. Al-Mashrafi **

Abstract: The flow and temperature distributions for a column of materially buoyant fluid, referred to as a Cartesian compositional plume, rising in a less buoyant fluid contained between two parallel vertical planes are identified, and the material, heat, and buoyancy fluxes associated with them are discussed. The stability of the system to linear perturbations is investigated. It is found to depend on six dimensionless numbers. The stability is discussed to find that the plume is unstable in the whole parameter space except when the plume is close to a wall and its thickness exceeds a certain value determined by the parameters of the problem, in which case a small region of stability appears in the parameter space.

Keywords: Compositional plumes; flux; stability; growth rate; bounded domain; material diffusion

WSEAS Transactions on Fluid Mechanics, ISSN / E-ISSN: 1790-5087 / 2224-347X, Volume 9, 2014, Art. #20, pp. 217-233

Title of the Paper: **The Effect of Non-Uniform Transverse Friction on the Linear Stability of Shallow Mixing Layers**

Authors: **Irina Eglite, Andrei Kolyshkin, Inta Volodko**

Abstract: Linear stability analysis of mixing layers in shallow water is performed in the present paper under the following assumptions: (a) the fluid contains uniformly distributed heavy small particles, (b) the mixing layer is slightly curved in the longitudinal direction, (c) the friction coefficient changes in the transverse direction. Marginal stability curves are calculated for different base flow velocity profiles which represent both stably and unstably curved mixing layers. The effect of all parameters on the stability characteristics of the flow is investigated.

Keywords: Linear stability, shallow mixing layer, non-uniform friction, curvature

WSEAS Transactions on Fluid Mechanics, ISSN / E-ISSN: 1790-5087 / 2224-347X, Volume 9, 2014, Art. #19, pp. 210-216

Title of the Paper: **Least Squares Finite Element Method for 3D Unsteady Diffusion and Reaction-Diffusion Problems**

Authors: **E. C. Romão, J. A. Martins, L. F. M. Moura**

Abstract: In this paper a study to application of Least Squares Finite Element Method (LSFEM) is made and with auxiliary equations (temperature derivatives) in the solution of Transient Three-dimensional Diffusion-Reaction. In order to do so, two applications are presented and discussed, one of them Pure Diffusion and another Diffusion-Reaction, both solved towards the constructive meshes with hexahedron of 8 and 27 nodes. This analysis uses the standard L (maximum error in all meshes) and L2 (average error in all the meshes) to verify the numerical error committed in the solution.

Keywords: LSFEM, Diffusion, Reaction-Diffusion, Hexaedrals, Error norms

WSEAS Transactions on Fluid Mechanics, ISSN / E-ISSN: 1790-5087 / 2224-347X, Volume 9, 2014, Art. #18, pp. 196-209

Title of the Paper: **The Effect of Internal Profile on Cannula Outflow**

Authors: **Nadia Shaira Shafii, Nofrizalidris Darlis, Jeswant Dillon, Kahar Osman, Ahmad Zahran Md Khudzari**

Abstract: One of the medical devices used during the open heart surgery in cardiopulmonary bypass (CPB) is the aortic curve-tip cannula. The aortic curve-tip cannula is also used in the extracorporeal membrane oxygenator (ECMO) to support patient in intensive care unit. There are few complications caused by the non – physiological jet or dispersed flow from the current cannula design. Thus, a novel designs approach to induce spiral flow and reduce the adverse effect on the aortic wall. The objective of this study is to compare the internal helical designs of curved-tip aortic cannula from three groove internal cannula design and three ribs internal cannula design against the standard cannula design; all with variation of straight and tapered body. A comparative study between six cannulae designs were carried out by computational fluid dynamics (CFD) in a steady state condition. Alls proposed internal helical designs have successfully induced spiral flow. The tapered body with 3 rib design was the best curved-tip aortic cannula design, since wall shear stress induced (2310 dyne/cm2) was below the critical value of wall shear stress (4500 dyne/cm2); while the outflow velocity was only slightly more than the standard cannula design. Also, the pressure drop across the cannula (66 mmHg) was significantly below the safe limit (100 mmHg).

Keywords: Spiral flow, aortic cannula design, internal helical design aortic curved-tip cannula, computational fluid dynamics, cardiopulmonary bypass

WSEAS Transactions on Fluid Mechanics, ISSN / E-ISSN: 1790-5087 / 2224-347X, Volume 9, 2014, Art. #17, pp. 187-195

Title of the Paper: **Hydrodynamic Traffic Flow Models and its Application to Studying Traffic Control Effectiveness**

Authors: **Nickolay Smirnov, Alexey Kiselev, Valeriy Nikitin, Mikhail Silnikov, Anna Manenkova**

Abstract: The present research was motivated by the arising difficulties in rational traffic organization the Moscow Government was faced in the recent years. The decrease of the roads handling capacity in the centre of the city (the Boulevard ring, the Gardens ring) caused by the increase of traffic density brought to necessity of re-organizing the traffic flows and constructing of the third ring road around the centre of the city. The present paper contains the results of investigations on mathematical modeling of essentially unsteady-state traffic flows on ring roads. The developed mathematical model is not limited only by the substance conservation equation and empirical relationships between density and velocity, but contains both the continuity (substance conservation) and momentum equations. It presents a closed form mathematical model and suggests the procedure to develop the model parameters based on technical characteristics of the vehicles. Thus, the available experimental data on the traffic flows observations is used only for validation of the model.

Keywords: Traffic, flow, model, continuous, handling capacity, traffic jam, regulation strategy

WSEAS Transactions on Fluid Mechanics, ISSN / E-ISSN: 1790-5087 / 2224-347X, Volume 9, 2014, Art. #16, pp. 178-186

Title of the Paper: **Generalized Similarity Transformation Model for Power-law Laminar Boundary Layer Fluids with non-Linear Dynamic Viscosity**

Authors: **Jacob Nagler**

Abstract: In this paper, mathematical representation of similarity transformation model has been obtained for the steady laminar boundary layer of non-Newtonian flow with variable dynamic viscosity over a flat plate. The power-law fluid model has been adopted for the non-Newtonian fluid representation. The governing non-dimensional boundary layer equations have been transformed into ordinary differential equations using general similarity transformation. Comparison of different studies transformation models has been made for useful and common special similarity transformation. While excellent compatibility was found. This developed general model can be used as a proof to the current models and basic for future transformation models in a large variety of applications. Moreover, numerical solution procedure using quasi-linearization method for flow equation based on this latter transformation model was developed and presented.

Keywords: Boundary layer, non-Newtonian fluid, Similarity solution transformation, Quasilinearization

WSEAS Transactions on Fluid Mechanics, ISSN / E-ISSN: 1790-5087 / 2224-347X, Volume 9, 2014, Art. #15, pp. 168-177

Title of the Paper: **Modeling of Combustion in Engines Fed by Hydrogen**

Authors: **Nickolay Smirnov, Yurii Phylippov, Valeriy Nikitin, Mikhail Silnikov**

Abstract: Computer aided design of new effective and clean hydrogen engines needs mathematical tools for supercomputer modeling of hydrogen – oxygen components mixing and combustion in rocket or aviation engines. The paper presents the results of developing verification and validation of mathematical model making it possible to simulate unsteady processes of ignition and combustion in RAM or pulse detonation engines. One of peculiarities of hydrogen-oxygen rocket engine is the following. On injecting liquid components fuel (hydrogen) having must lower critical temperature comes pre-evaporated and pre-heated in combustion chamber, while oxygen could be liquid then evaporating inside the chamber. Thus contrary to most types of engines hydrogen engine has an inverse mixture entering combustion chamber, in which fuel is gaseous and oxidant is liquid. Onset of detonation being very dangerous for classical RAM engines could, however, serve the basis for creating new generation of engines - pulse detonating engines (PDE). For this issue the problems of detonation onset and deflagration to detonation transition should be simulated quite accurately, because these processes strongly depend on inlet conditions, mixture composition and geometrical characteristics of combustion chamber.

Keywords: Combustion, ignition delay, non-equilibrium, diffusion, turbulence, mathematical simulation

WSEAS Transactions on Fluid Mechanics, ISSN / E-ISSN: 1790-5087 / 2224-347X, Volume 9, 2014, Art. #14, pp. 154-167

Title of the Paper: **Simulation of the Air-Oil Mixture Flow in the Scavenge Pipe of an Aero Engine using Generalized Interphase Momentum Exchange Models**

Authors: **Stratis Kanarachos, Michael Flouros**

Abstract: Understanding the flow in aero-engine lubrication systems forms an essential part of future designs for aero-engines. This especially applies to scavenge pipes which contain a complex two-phase flow formed by the interaction of sealing airflow and lubrication oil. In the last decade, two phase flows in pipes are increasingly modeled and simulated with 3D Computational Fluid Dynamics (CFD) codes. One of the major challenges is to approximate the different flow morphologies developed (bubbly, stratified, annular, slug, e.t.c.) using a unified CFD model without increasing prohibitively the computational cost. This paper presents a methodology implementing empirically derived generalized interphase momentum exchange models for modeling and simulation of the two phase flow of air and oil in the scavenge pipe of an aero-engine. The advantage of the proposed approach is the simplicity of the computational model which depends mainly on the assumed bubble diameter. Simulation results are presented and discussed for an experimental study performed at MTU Aero Engines facilities. This work is part of the European Union funded research program ELUBSYS (Engine LUBrication System TechnologieS) within the 7th EU Frame Program for Aeronautics and Transport.

Keywords: Two phase flow; interphase momentum exchange model; aero-engine; scavenge pipe

WSEAS Transactions on Fluid Mechanics, ISSN / E-ISSN: 1790-5087 / 2224-347X, Volume 9, 2014, Art. #13, pp. 144-153

Title of the Paper: **Modeling Breaking Waves and Wave-induced Currents with Fully Nonlinear Boussinesq Equations**

Authors: **K. Z. Fang, Z. B. Liu**

Abstract: A Boussinesq-type wave model is developed to numerically investigate the breaking waves and wave-induced currents. All the nonlinear terms are retained in the governing equations to keep fully nonlinearity characteristics and it hence more suitable to describe breaking waves with strong nonlinearity in the nearshore region. The Boussinesq equations are firstly extended to incorporate wave breaking, moving shoreline and bottom friction, and then solved numerically using finite difference method. Using well documented experimental data as a reference, numerical experiments are conducted to investigate the effect of tunable parameter values on the computed results. The developed model is used to simulate breaking waves and wave-induced currents over complex bathymetries and the numerical results are compared against the measurements.

Keywords: Breaking waves, Wave-induced currents, Boussinesq-type wave model, Numerical simulation

WSEAS Transactions on Fluid Mechanics, ISSN / E-ISSN: 1790-5087 / 2224-347X, Volume 9, 2014, Art. #12, pp. 131-143

Title of the Paper: **Mathematical Modeling of Flows in Porous Media**

Authors: **V. R. Dushin, V. F. Nikitin, J. C. Legros, M. V. Silnikov**

Abstract: The paper is aimed at mathematical modeling of flows in porous medium. The results are compared with model experiments performed under microgravity conditions. Numerical investigations of the instability in displacement of viscous fluid by a less viscous one in a twodimensional and three-dimensional geometry were carried out. The effect of the three-dimensional phenomena on instability growth was investigated.

Keywords: Porous medium, seepage, flow, capillary, unstable, microgravity

WSEAS Transactions on Fluid Mechanics, ISSN / E-ISSN: 1790-5087 / 2224-347X, Volume 9, 2014, Art. #11, pp. 116-130

Title of the Paper: **A Comparison of the Density Perforations for the Horizontal Wellbore**

Authors: **Mohammed Abdulwahid, Sadoun Dakhil, Niranjan Kumar**

Abstract: In this paper study the flow behavior in horizontal wellbore with 60 and 150 perforations of perforation densities equivalent to 6 and 12 SPF respectively has been studied. The pressure drops in a perforated pipe that includes the influence of inflow through the pipe walls compares for two pipes that difference in perforation density. 3D numerical simulations for the pipe with two numbers of perforations were investigated by using ANSYS CFX modeling tool with Reynolds number ranging from 28,773 to 90,153 and influx flow rate ranging from 0 to 899 lit/hr to observe the flow through perforated pipe, measure pressure drops. The effect of density perforations on the flow through perforated pipe was conducted. CFD simulations yielded results that are reasonably close to experiments data.

Keywords: Perforation density, pressure, numerical, CFX

WSEAS Transactions on Fluid Mechanics, ISSN / E-ISSN: 1790-5087 / 2224-347X, Volume 9, 2014, Art. #10, pp. 110-115

Title of the Paper: **Numerical Analysis of Unsteady Transonic Flow over Rocket Nose**

Authors: **Somdeb Bandopadhyay, Dong-Hyun Kim**

Abstract: Computational analysis has been performed for unsteady fluid flow in transonic regime over rocket like configurations. Finite volume based numerical method has been used and k-ω SST based turbulence model is applied. The purpose of this work is to analyze the unsteady aerodynamic character of the flow and establish the validity and accuracy of the computational process. The validation has been done by comparing the RMS(root mean square) value of the computed instantaneous pressure at different time step against the experimental results. Apart from this, the PSD (Power Spectral Density) values for the pressure fluctuation are also calculated and compared with experiment. The effects of Mach number and geometry configuration on the location of the shockwave have also been considered and comparison results are presented in detail.

Keywords: k-ω SST, DES, Transonic Flow, Rocket Configuration

WSEAS Transactions on Fluid Mechanics, ISSN / E-ISSN: 1790-5087 / 2224-347X, Volume 9, 2014, Art. #9, pp. 102-109

Title of the Paper: **Effects of MHD Visco-Elastic Fluid Flow Past a Moving Plate with Double Diffusive Convection in Presence of Heat Generation**

Authors: **Rita Choudhury, Paban Dhar**

Abstract: During the course of present investigation, effects of first order homogeneous chemical reaction and thermal radiation on two dimensional MHD flow of a visco-elastic fluid past a moving porous plate by considering double diffusive convection in presence of heat generation has been analyzed. A uniform magnetic field is applied in the direction normal to the moving plate. Also, the plate is considered to be moving with a constant velocity along the flow field. The present theoretical study has been carried out under perturbation approximation. Also, the expressions for velocity, temperature, concentration, shearing stress, rate of heat transfer and rate of mass transfer have been obtained. The velocity profiles and shearing stress for both heated and cooled plate are depicted for various values of flow parameters to observe the visco-elastic effects. The rate of heat transfer i.e. Nusselt number and the rate of mass transfer i.e. Sherwood number are not significantly affected by the visco-elastic parameter.

Keywords: Visco-elastic, Walters liquid (model B׳), Hartmann number, Prandtl number, Grashof number, Soret number

WSEAS Transactions on Fluid Mechanics, ISSN / E-ISSN: 1790-5087 / 2224-347X, Volume 9, 2014, Art. #8, pp. 89-101

Title of the Paper: **Modeling of Special Features of Flow in a Planar Vortex Chamber**

Authors: **D. V. Voronin**

Abstract: The numerical calculations of the flowfield in a planar vortex chamber have been performed. The model is based on conservation laws of mass, momentum and energy for nonsteady two-dimensional compressible gas flow in case of swirl axial symmetry. The processes of viscosity, heat conductivity and turbulence have been taken into account. It was found that transition of kinetic energy of gas into heat due to processes of dissipation generates “hot spots” in boundary layers at the chamber walls. The gas temperature at the spots may exceed the temperature of gas ignition, while the surrounding regions remain still cold. It may be the reason of cold gas self-ignition observed in experiments.

Keywords: modeling, turbulence, compressible flows, hot spots, self-ignition

WSEAS Transactions on Fluid Mechanics, ISSN / E-ISSN: 1790-5087 / 2224-347X, Volume 9, 2014, Art. #7, pp.78-88

Title of the Paper: **The Velocity Potential PDE in an Orthogonal Curvilinear Coordinate System**

Authors: **Richard Selescu**

Abstract: This work studies and clarifies some local physical phenomena in fluid mechanics, in the form of an intrinsic analytic study, regarding the PDEs of the velocity potential and (especially) 2-D “quasi-potential” (their simpler and special forms), over the “isentropic” or the 3-D (V, Ω) surfaces and along the “isentropic & isotachic” space curves, written for any potential and even rotational flow of an inviscid compressible fluid for both steady and unsteady motions. It continues a series of works presented at some conferences and a congress during 2006 – 2012, representing a real deep insight into the still hidden theory of the isoenergetic flow. Applying the advantages offered by the special virtual surfaces (“isentropic” and “polytropic”) and space curves (intersection lines of these surfaces) introduced in the previous works, a simpler PDE of the 2nd order in only two variables, and more, a Laplace’s PDE (for any rotational “pseudo-flow”, using a new smart intrinsic coordinate system), instead of the general PDE (Steichen, 1909, for plane potential supersonic flows only) of the 2nd order in three variables. So far, this equation was known as being written for potential flows only. A model extension for rotational flows of a viscous compressible fluid was given.

Keywords: rotational flows, steady and unsteady flows, inviscid and viscous fluids, compressible fluids, isentropic and polytropic surfaces, Selescu’s isentropic & isotachic vector (dRij), quasi-Laplace lines (quasi-isothermal quasi-potential)

WSEAS Transactions on Fluid Mechanics, ISSN / E-ISSN: 1790-5087 / 2224-347X, Volume 9, 2014, Art. #6, pp.58-77

Title of the Paper: **Unsteady Viscous Flow with Non Linear Free Surface around Oscillating SWATH Ship Sections**

Authors: **Luca Bonfiglio, Stefano Brizzolara**

Abstract: Ship motion problem is approached exploiting the assumption of linearity and subdividing forces acting on the hull in different components; in this paper the focus is on the radiation problem. A fully viscous solver, based on the numerical solution of the Navier-Stokes equation through the finite volume technique, is used to calculate radiation forces on hull surface, with non linear free surface evaluated through the volume of fluid method. Radiation forces are the most influenced by viscous effects, especially for particular hull geometries as SWATH ships. OpenFOAM libraries are used to solve the unsteady flow around one circular and two SWATH two dimensional sections forced to heave in calm water. The comparison with experiments evidence a very good agreement of the forces measured over a wide frequency range including irregular frequencies.

Keywords: Unsteady viscous solvers, free surface, OpenFOAM, SWATH

WSEAS Transactions on Fluid Mechanics, ISSN / E-ISSN: 1790-5087 / 2224-347X, Volume 9, 2014, Art. #5, pp.49-57

Title of the Paper: **New First Integrals for the Continuity, Vorticity and Related Equations**

Authors: **Richard Selescu**

Abstract: This work studies and clarifies some local phenomena in fluid mechanics, in the form of an intrinsic analytic study, regarding the continuity equation, its first integral (the flow rate equation), for inviscid compressible fluids, and the vorticity equation, for viscous incompressible fluids, finding new first integrals. It continues a series of works presented at some conferences and a congress during 2006 – 2012, representing a real deep insight into the still hidden theory of the isoenergetic rotational flow. Several new functions, surfaces and vectors were introduced: the 2-D “quasi-stream” function on the 3-D (V, Ω) surfaces, for the continuity equation; the surfaces of iso-normal mass flux density (over which the continuity equation for the steady flow in a thick stream tube admits the same first integral as for the flow in a thin one, and whose envelope sheets are the sections of uniform flow), for the flow rate equation; the 3-D stream function vector, allowing new local and global forms of continuity equation (the global one similar to Helmholtz’ 2nd theorem about vortices in an ideal fluid); Selescu’s incompressible roto-viscous vector and the zero-work surfaces (for some non-conservative vectors), for the vorticity equation. The dependence “2-D velocity quasipotential <-> 2-D quasi-stream function” was established. The unsteady flow’s continuity equation was analytically integrated.

Keywords: rotational flows, steady and unsteady flows, inviscid and viscous fluids, compressible fluids, isentropic or (V, Ω) surfaces, Selescu’s 3-D stream function vector, surfaces of iso-normal mass flux density, roto-viscous vector and zero-work surfaces

WSEAS Transactions on Fluid Mechanics, ISSN / E-ISSN: 1790-5087 / 2224-347X, Volume 9, 2014, Art. #4, pp.34-48

Title of the Paper: **Second Order Slip Flow of Cu-Water Nanofluid Over a Stretching Sheet With Heat Transfer**

Authors: **Rajesh Sharma, Anuar Ishak**

Abstract: The boundary layer flow of Cu-water based nanofluid with heat transfer over a stretching sheet is numerically studied. Second order velocity slip flow model is considered instead of no-slip at the boundary. The governing partial differential equations are transformed into ordinary one using similarity transformation, before being solved numerically. Numerical solutions of these equations are obtained using finite element method (FEM). The variations of the velocity and temperature distribution as well as the skin friction and the heat transfer coefficients for some values of the governing parameters, namely, the nanoparticle volume fraction and slip parameters are shown graphically and discussed. Comparison with published results for pure fluid flow case is presented and it is found to be in excellent agreement.

Keywords: Nanofluid, Stretching surface, heat transfer, FEM, velocity slip condition

WSEAS Transactions on Fluid Mechanics, ISSN / E-ISSN: 1790-5087 / 2224-347X, Volume 9, 2014, Art. #3, pp.26-33

Title of the Paper: **Laminar Boundary Layer Model for Power-Law Fluids with Non-Linear Viscosity**

Authors: **Jacob Nagler**

Abstract: In this paper, analytical solutions are obtained for the steady laminar boundary layer of non- Newtonian flow with non-linear viscosity over a flat moving plate. The power-law fluid model was adopted for the non-Newtonian fluid representation. The governing non-dimensional boundary layer equations are transformed into ordinary differential equations using similarity transformation which are then solved analytically. The analytical results are obtained for different values of the constant n representing the powerlaw index and flow consistency parameter K which is assumed to be function type of η and n in this study. The effects of various values on the velocity profiles are presented and discussed.

Keywords: Analytical solution, non-Newtonian, non-Linear viscosity, Boundary Layer, Bingham model

WSEAS Transactions on Fluid Mechanics, ISSN / E-ISSN: 1790-5087 / 2224-347X, Volume 9, 2014, Art. #2, pp.19-25

Title of the Paper: **First Integrals for Crocco’s Equation and Hence for the Motion Equation**

Authors: **Richard Selescu**

Abstract: This work studies and clarifies some local phenomena in fluid mechanics, in the form of an intrinsic analytic study, regarding Crocco’s equation and the motion one, for inviscid compressible fluid flows (both steady and unsteady), and finds new first integrals. It continues a series of works presented at some conferences and a congress during 2006 – 2012, representing a real deep insight into the still hidden theory of the isoenergetic rotational flow. Unlike the geometrical point of view (using a smart intrinsic coordinate system tied to flow’s isentropic surfaces) previously approached to eliminate the rotational non-conservative term, this time a thermodynamic point of view is used, to evidence the above term first as a biscalar one, and further as a conservative one. Several new functions and surfaces were introduced: the 2-D velocity quasi-potential, the isentropic 3-D (V, Ω) surfaces, the polytropic integral ones, and the quasi-incompressible quasi-potential (Laplace) lines, for a quasi-uniform rotational pseudoflow of an inviscid compressible fluid. The dependence of gas particle specific entropy on the 2-D velocity quasipotential was established. The PDE of the polytropic special integral surfaces, and that of the isentropic ones (both in Cartesian system) were given. The newly found first integrals for the motion equation are related to D. Bernoulli’s and D. Bernoulli–Lagrange ones. An extension of the new intrinsic model to MHD of a neutral plasma was also given.

Keywords: conservative (irrotational, potential) and biscalar vectors, rotational flows, steady and unsteady flows, inviscid fluids, compressible fluids, isentropic surfaces, polytropic integral surfaces, quasi-Laplace lines

WSEAS Transactions on Fluid Mechanics, ISSN / E-ISSN: 1790-5087 / 2224-347X, Volume 9, 2014, Art. #1, pp.1-18