**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 7, 2012**

**Issue 1, Volume 7, January 2012**

Title of the Paper: **Analysis of Flow Field Across Blunt Fin with Dimples – Experimentation**

Authors: **Muthu Kumara Samy Sekaran, B. Achu Naik**

Abstract: Experimental studies are made on the hemi – cylindrically blunted fins for Mach 2.2 to examine the effect of dimples on shock wave / boundary layer interaction. Flow field details around hemi – cylindrically blunted fin has been captured using oil flow visualization, measurements of static and total pressures and the lambda shock has been captured by shadowgraphy. Configuration indicate nonstart. The effect of the number of holes, hole diameter and height of the blunt fin on the separation region has been investigated.

Keywords: Fins, Dimples, shadowgraphy, oil flow visualization, lambda shock wave, boundary layer

Title of the Paper: **One Approach to Adaptive Control of a Tubular Chemical Reactor**

Authors: **Petr Dostál, Vladimír Bobál, Ji?í Vojt?šek, Zden?k Babík**

Abstract: The paper deals with continuous-time adaptive control of a tubular chemical reactor with the countercurrent cooling as a nonlinear single input – single output process. The mean reactant temperature and the output reactant temperature are chosen as the controlled outputs, and, the coolant flow rate as the control input. The nonlinear model of the reactor is approximated by an external linear model with a structure chosen on the basis of controlled outputs step responses. Its parameters are estimated via corresponding delta model. The control system structure with two feedback controllers is considered. The resulting controllers are derived using polynomial approach. The method is tested on a mathematical model of the tubular chemical reactor.

Keywords: Nonlinear system, tubular chemical reactor, approximate linear model, parameter identification, polynomial approach, pole assignment

Title of the Paper: **MGD Application to a Blunt Body in Two-Dimensions**

Authors: **Edisson Sávio De Góes Maciel**

Abstract: In this paper, the Euler and Navier-Stokes equations are solved, according to a finite volume formulation and symmetrical structured discretization, applied to the problem of a blunt body in two-dimensions. The work of Gaitonde is the reference one to present the fluid dynamics and Maxwell equations of electromagnetism based on a conservative and finite volume formalisms. The MacCormack and the Jameson and Mavriplis symmetrical schemes are applied to solve the conserved equations. Two types of numerical dissipation models are applied, namely: Mavriplis and Azevedo. A spatially variable time step procedure is employed aiming to accelerate the convergence of the numerical schemes to the steady state solution. The results have proved that, when the Jameson and Mavriplis scheme is employed, an increase in the shock standoff distance is observed, which guarantees a minor increase in the temperature at the blunt body nose, and a minor increase in the drag aerodynamic coefficient.

Keywords: Euler and Navier-Stokes equations, Magnetogasdynamics formulation, MacCormack algorithm, Jameson and Mavriplis algorithm, Finite volumes, Two-dimensional space

**Issue 2, Volume 7, April 2012**

Title of the Paper: **MathCAD Solutions for Problem of Laminar Boundary-Layer Flow **

Authors: **Daniela Cârstea **

Abstract: The problem of laminar boundary-layer flow past a flat plate is presented from the viewpoint of an engineer where the numerical results are of great interest. We compute the velocity profile in the boundary layer and other relevant physical parameters. We also compute the temperature distribution in the thermal boundary layer associated with the forced flow. We consider some algorithmic skeletons both for uncoupled fields and coupled fields. The natural coupling between the velocity field and thermal field can lead to sophisticated algorithms and these aspects are considered in our target example. The non-linear partial differential equations of the laminar boundary-layer flow past a flat plate are transformed into a system of ordinary differential equations by using usual similarity transformations. This system is solved numerically using a software product as MathCAD. Blasius problem is presented from the computational viewpoint and direct transformation and inverse transformations are presented. In the study of the simplified model one encounters what is called a two-point boundary-value problem. Shooting method is effective for this case using functions in MathCAD software.

Keywords: Boundary layer; Similarity solutions; Blasius equation; Numerical simulation; MathCAD

Title of the Paper: **A New Solution of Euler's Equation of Motion with Explicit Expression of Helicity **

Authors: **Tsutomu Kambe **

Abstract: Improving the variational formulation for an ideal compressible fluid, a new expression of velocity field is presented by using vector potentials of frozen field, i.e. the potentials convected by the fluid flow under effect of stretching. This has been deduced from the action principle. It is verified that the system of new expressions in fact satisfies the Euler's equation of motion. The Lagrangian consists of main terms of total kinetic energy and internal energy, together with two terms yielding the equations of continuity and entropy and the third term which provides rotational component of velocity field. The last term leads to an explicit expression of non-vanishing helicity.

Keywords: Ideal fluid, New solution, Variational formulation, Helicity

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

**Issue 3, Volume 7, July 2012**

Title of the Paper: **A Review of Some Numerical Methods to the Euler Equations in Two-Dimensions **

Authors: **Edisson Sávio De Góes Maciel **

Abstract: This work aims to describe the numerical implementation of the Lax and Friedrichs, Lax and Wendroff TVD, Boris and Book, Beam and Warming and MacCormack, on a finite volume and structured spatial discretization contexts, to solve the Euler equations in two-dimensions. The Lax and Wendroff algorithm was implemented according to the TVD formulation of Yee. The Beam and Warming scheme was implemented only in its explicit version. Hence, it is possible to distinguish four categories of algorithms studied in this work: symmetrical (Lax and Friedrichs and Beam and Warming), FCT (Boris and Book), Predictor/Corrector (MacCormack) and TVD (Lax and Wendroff). They are applied to the solution of the steady state problem of the moderate supersonic flow along a compression corner. A spatially variable time step procedure is employed to accelerate the convergence of the numerical methods to the steady state condition. This procedure has demonstrated a meaningful gain in terms of convergence ratio, as reported by Maciel. The results have demonstrated that the Beam and Warming scheme, using the nonlinear dissipation operator, provides the best results in terms of quality (good capture of shock wave thickness and wall pressure profile) and quantity (good prediction of the oblique shock wave angle).

Keywords: Symmetrical schemes, FCT scheme, Predictor/Corrector scheme, TVD scheme, Finite volumes, Euler equations, Two-dimensions

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: **Simulation of a Distribution Transformer **

Authors: **Alejandro Roberto Tello Campos, Ignacio Carvajal Mariscal, Saul Garcia Hernandez **

Abstract: Within transformer industry, one of the thermal design key parameters in this type of devices is the determination of the transformer cooling oil temperature. Several researchers, including manufacturers and people from professional associations like IEEE, have proposed thermal models ranging from the simplified analytical to the computational of concentrated parameters which predict the oil temperature within the transformer cooling ducts of the high and low voltage windings of this type of energy conversion device. In this work, a computational thermal model that predicts the oil temperature distribution in winding ducts of a 1000 kVA one-phase transformeris proposed. This model was developed based on the finite volume technique that is used in Fluent ™. It was found that the temperature distribution obtained from the model agrees well with experimental data for a transformer with the same power capacity.

Keywords: Distribution transformer, thermal model, windings, temperature, duct, finite element

**Issue 4, Volume 7, October 2012**

Title of the Paper: **Two-phase Flow of a Third Grade Fluid Between Parallel Plates **

Authors: **A. M. Siddiqui, M. K. Mitkova, A. R. Ansari **

Abstract: The two-phase flow of a third grade fluid between parallel plates is considered in three different cases. The Homotopy Analysis Method (HAM) is used to solve the nonlinear differential equations and the solutions up to second order of approximation are provided in case of Couette, Poiseuille and Couette-Poiseuille flow. The velocity profile is used to study qualitatively the effect of the physical parameters and in particular, of the fluids’ material constants.

Keywords: Fluid mechanics, homotopy analysis method, non-Newtonian fluid, third grade fluid, two-phase flow

Title of the Paper: **Frink, Parikh and Pirzadeh and Liou and Steffen Jr. TVD Algorithms and Implicit Formulations Applied to the Euler Equations in 2D **

Authors: **Edisson Sávio De Góes Maciel **

Abstract: In this work, the Frink, Parikh and Pirzadeh and the Liou and Steffen Jr. schemes are implemented following a MUSCL approach, aiming to guarantee second order accuracy and to achieve TVD properties, and employing an implicit formulation to solve the Euler equations in the two-dimensional space. These schemes are implemented according to a finite volume formulation and using a structured spatial discretization. The former scheme is a flux difference splitting one, whereas the latter is a flux vector splitting scheme. The MUSCL approach employs five different types of nonlinear limiters, which assure TVD properties, namely: Van Leer limiter, Van Albada limiter, minmod limiter, Super Bee limiter and -limiter. All variants of the MUSCL approach are second order accurate in space. The implicit schemes employ an ADI approximate factorization to solve implicitly the Euler equations. Explicit and implicit results are compared, as also the computational costs, trying to emphasize the advantages and disadvantages of each formulation. The schemes are accelerated to the steady state solution using a spatially variable time step, which has demonstrated effective gains in terms of convergence rate according to Maciel. The algorithms are applied to the solution of the physical problem of the moderate supersonic flow along a compression corner. The results have demonstrated that the most accurate solutions are obtained with the Frink, Parikh and Pirzadeh TVD scheme using the Van Leer and Super Bee nonlinear limiters, when implemented in its explicit version.

Keywords: Frink, Parikh and Pirzadeh algorithm, Liou and Steffen Jr. algorithm, MUSCL procedure, Implicit formulation, Flux difference splitting, Flux vector splitting, Euler equations, Two-dimensions

Title of the Paper: **Simulation of Ventilation Effects on Indoor Radon in a Detached House **

Authors: **Keramatollah Akbari, Jafar Mahmoudi, Robert Oman **

Abstract: CFD is widely used in indoor air quality, air flow pattern, indoor pollutant distribution and thermal comfort as a cost effective and powerful tool and it can be used to predict, estimate and visualize the indoor radon level. . The intention of this article is to use computational fluid dynamics (CFD), as a standalone tool to simulate indoor radon distribution and ventilation effects. This technique can be used to predict and visualize radon content and indoor air quality throughout a one family detached house in Stockholm. . In this study a mechanical balanced ventilation system and a continuous radon monitor (CRM) were also used to measure the indoor ventilation rate and radon levels. In numerical approach the FLUENT, CFD package was used to simulate radon entry into the building and ventilation effects. Results of numerical study indicated that indoor pressure made by means of ventilation systems and infiltration through door or window has significant effects on indoor radon content. It is observed that the location of vents can affect the indoor radon level, particularly in breathing (seating) zone. The analytic solution is used to validate numeric results at 3 distinct air change rates. The comparison amongst analytical, numerical and measurement results shows close agreement.

Keywords: Numerical modeling, Simulation, Radon mitigation, Balanced Ventilation, Residential buildings, CFD