Daniel A. Salinas Casanova - salinas@unioeste.br
Universidade Estadual do Oeste do Paraná, Centro de Engenharias e Ciências Exatas
85.855-000, Foz do Iguaçu, PR, Brasil

César J. Deschamps - deschamps@nrva.ufsc.br
Alvaro T. Prata - prata@nrva.ufsc.br
Francisco F. S. Matos - fred@nrva.ufsc.br
Universidade Federal de Santa Catarina, Departamento de Engenharia Mecânica
80.040-900 - Florianópolis, SC, Brasil

The work is a comparative analysis of two k- e turbulence models applied to a flow under the combined effects of stagnation, streamline curvature, stiff pressure gradient and recirculation. For such flow situations, it has been found that standard versions of k- e model fail to predict even the most basic flow features unveiled by experimental data. Recently, a new version of k- e model, developed from Renormalization Group (RNG) theory, has been proposed and successfully applied to a number of flows where other k- e models have shown poor results. The reason for this superior performance of the RNG k- e model cannot be easily explained since most works in the literature focus their attention only on results for quantities associated to the mean velocity field, without any reference to turbulence quantities. In the present investigation, the RNG k- e model is compared to the widely used Launder & Sharma's k- e model in the prediction of a complex flow. An assessment of the superior results found with the RNG k- e model is provided through results for eddy viscosity and turbulence length scale.

Keywords: Renormalization Group (RNG) theory, Eddy viscosity models, Turbulence Modeling
 
 

D. O. A. Cruz, E-mail: doac@ufpa.br
E. N. Macêdo, E-mail: enegrao@ufpa.br
Mechanical Engineering Department, Federal University of Pará - UFPA
Campus Universitário do Guamá, 66075-900, Belém, Pará, Brazil

The purpose of this work is to analyze the problem of the turbulence modeling of non-Newtonian Bingham plastic fluids, through the introduction of a new characteristic flow velocity which is a function of the yield stress. Also, with the aid of the characteristic flow velocity and using some dimensional arguments, a new skin friction equation for non-Newto nian Bingham plastic fluids, together with a new law of the wall that use the new characteristic flow velocity are proposed. A analytical solution of the hydrodynamically developed turbulent equation of motion for flow in circular tubes is obtained. Comparisons with experimental data are made, showing good agreements.

Keywords : Turbulence, Bingham Plastic, law of the wall
 
 

Nicolau A. Branco
Atila P. Silva Freire
Mechanical Engineering Program (PEM/COPPE/UFRJ), C. P. 68503, 21945-970 Rio de Janeiro, Brazil

The dynamics of liquid steel flowing in a tundish is numerically studied for a set of design and operating parameters.  The emphasis here is on assessing the effects that the presence of a large concentration of small particles may have on the turbulence properties of the flow.  The work uses the modified two-equation differential model developed by Rogers and Eaton (Phys. Fluids A, 3, 928-937, 1991) to describe the turbulence.  The work also applies a Lagrangean model to the problem of finding the residence time distribution of particles in a tundish.  Results show that depending on the particle concentration and on the particle diameter a large degree of attenuation can be found for the turbulent kinetic energy levels.

Keywords: tundish, continuous steel casting, Kappa-Epsilon model.
 
 

Juliana B. R. Loureiro
Fernanda S. Vasques
Daniel A. Rodrigues
Rodrigo J. Terra
Atila P. Silva Freire
Mechanical Engineering Program (PEM/COPPE/UFRJ), C. P. 68503, 21945-970 Rio de Janeiro, Brazil

The velocity and temperature fields around smooth and steep two-dimensional hills were experimentally studied in a simulated neutral atmospheric boundary layer in a wind tunnel.  Two different flow patterns were studied, attached and separated flows.  Mean velocity, mean temperature and turbulence quantities were measured at various positions.  The speed up of flow on top of the hill was compared with the theoretical predictions of other authors.  The effects that the velocity field has on the temperature scalar fields is particularly investigated.

Keywords: turbulence, hill, temperature surface flux, stable boundary layer
 
 

Juliana B. R. Loureiro
Fernanda S. Vasques
Daniel A. Rodrigues
Rodrigo J. Terra
Atila P. Silva Freire
Mechanical Engineering Program (PEM/COPPE/UFRJ), C. P. 68503, 21945-970 Rio de Janeiro, Brazil

In the second part of the paper, an experimental study of the velocity and temperature fields around a steep two-dimensional hill was carried out in a wind tunnel simulated neutral atmospheric boundary layer.  The large separated region that forms behind the hill was characterized by smoke visualization.  Mean velocity, mean temperature and turbulence quantities were measured at various positions.  The speed up of flow on top of the hill was compared with the theoretical predictions of other authors.  The effects that turbulent transfer has on near wall scalar fields was particularly investigated.

Keywords: turbulence, hill, temperature surface flux, stable boundary layer
 
 

Marcelo J.S. de-Lemos - e-mail: delemos@mec.ita.br
Departamento de Energia - IEME
Instituto Tecnológico de Aeronáutica - ITA
12228-900 - São José dos Campos - SP - Brasil

The study of flow in porous media has gained an enormous attention lately due to its potential industrial application. Analysis and optimization of Enhanced Oil Recovery systems, cleaning of contaminated soil and improvements of modern fluidized bed combustion systems, are just a few examples of such engineering applications. This paper presents an overview of the major steps taken in developing a general two-equation turbulence model for application in such systems. Transport equations are written for both clear fluid and porous medium and the numerical scheme developed for treating both domains with a single set of equations is discussed.

Keywords: Porous Media, Turbulence Modeling, Numerical Methods
 
 

G. N. Zevallos - gzevallo@mec.puc-rio.br
A. O. Nieckele - nieckele@mec.puc-rio.br
Departamento de Engenharia Mecânica, Pontifícia Universidade Católica - PUC/Rio
R. Marquês de São Vicente 225- Gávea, 22453-900 Rio de Janeiro, RJ, Brasil

Turbulent flows inside curvilinear obstruction tubes are encountered in many engineering situations. The prediction of flows in the presence of separation and reattachment is a difficult task. Several low-Reynolds number turbulence models have been developed aiming a better prediction of the recirculation areas, as well as pressure recovery after the obstruction and shear stress distribution along the duct walls. At the present work, the curvilinear obstruction is described by a cosine curve. For this geometry, the . - e low Reynolds number turbulence model LSH presents a reasonable prediction for the mean flow field and pressure drop, however it fails to predict the turbulent quantities. The objective of the present paper is to analyze the influence of different low-Reynolds correction terms in the LSH model. Therefore, a few modifications were introduced in the original model. The velocity, turbulent kinetic energy and dissipation rate fields obtained by the different model modifications are compared with numeric and experimental data found in the literature. The numeric determination of the fluid flows was accomplished by a finite volume method. Among all model modifications that have been tested, none was able to reproduce exactly the experimental data.

Keywords: Low Reynolds . - e models, curvilinear obstruction
 
 

Danielle Guerra
Daniel O. A. Cruz
Atila P. Silva Freire
Mechanical Engineering Program (PEM/COPPE/UFRJ), C. P. 68503, 21945-970 Rio de Janeiro, Brazil

The characteristics of a turbulent boundary layer near the reattachment point behind a backward-facing step flow are studied here.  The emphasis is on providing experimental data that can be used to validate a previous formulation of the problem advanced by Cruz and Silva Freire (IJHMT, 41, 2097-2111, 1998).  Two different flow visualization techniques are used to find the location of the separation point.  Data for the mean velocity and mean temperature are then presented for the non-recirculation flow region.  A data reduction technique based on the inverse problem method is used to furnish predictions of the local skin friction coefficient and Stanton number.  All results are also compared with the data of Vogel and Eaton (J. Heat Transfer, vol. 107, 922-929, 1985).

Keywords: Turbulence, backward-facing step flow, re-attachment, heat transfer
 
 

J. D. M. Abrunhosa- diniz@mec.puc-rio.br
Angela O. Nieckele - nieckele@mec.puc-rio.br
Departamento de Engenharia Mecânica, Pontifícia Universidade Católica - PUC/Rio

In the present work, an assyntotic and numerical analysis is performed to analyze the behavior of four low Reynolds number turbulence models in the wall region. The numerical results are compared with dada from direct numerical simulation of a flow through a backstep. The correct modeling of the pressure gradient term in the . equation in recirculating flows is investigated, and it is concluded that, at the present stage of development of the low Reynolds number models, this is not a crucial deficiency.

Keywords: Low Reynolds .-e Models. Pressure Gradient.
 
 

Guillermo Vilalta (e-mail: gvilalta@mecanica. ispjae.edu.cu)
Centro de Estudios de Tecnologías Energéticas Renobables, ISPJAE, Marianao 14, CP 19 390,
Habana, Cuba.

Jayme Pinto Ortiz (e-mail: jportiz@usp.br)
Departamento de Engenharia Mecânica, Escola Politécnica da USP, CEP 05508-900
São Paulo, SP, Brasil.
Escola de Engenharia Mauá, IMT, São Caetano do Sul, Brasil.

In this work, an experimental study about the influence of the polymer molecular weight in the turbulent channel flow structure and, consequently, in the drag reduction, is presented. The Iqapac 731, low molecular weight polymer was used in the tests, that were carried out at four concentrations of the polimeric solutions and at different Reynolds numbers in the range between 8x10 3 e 10 5. The results showed that polymers with low molecular weight, lower than 10 6 , are able to drag reduction, although the effects are smaller if compared to the high molecular weight polymers. By mean of rheological analysis it is estimated that the viscous properties are more important than elastic properties.
 
 

Marcello A. Faraco de Medeiros { e-mail: marcello@pucminas.br
Instituto Politecnico da Universidade Catolica { IPUC
Pontificia Universidade Catolica de Minas Gerais { PUC-MG
Av. Dom Jos_e Gaspar, 500, Belo Horizonte, 30535-610 - MG - Brazil.

The in uence of streamwise modulation on the evolution of three-dimensional wavetrains in boundary layers is experimentally investigated. The results show that for slowly modulated wavetrains the _rst nonlinear signature a mean ow distortion that resembles the mean ow distortion observed in continuous wavetrains. At some stage of the nonlinear evolution all the modulated signals displayed a band of frequencies close to the subharmonic. The spanwise wavenumber of this band was similar to the spanwise
wavenumber of the mean ow distortion in continuous wavetrain. Some of the results suggest that the mechanisms that produce the mean ow distortion in three-dimensional continuous wavetrains might provide a deterministic seed for subharmonic resonance. Others indicated that subharmonic band is detached from the fundamental one.

Keywords: Hydrodynamic instability, laminar-turbulent transition, boundary layers, hot-wire anemometry, experimental uid mechanics
 
 

Paulo Seiji Kumon Zandonade - paulo@vortex.enm.unb.br
Universidade de Brasília, Departamento de Engenharia Mecânica

Campus Darcy Ribeiro - 70000-000 - Brasília, DF, Brasil
José Luiz Alves da Fontoura Rodrigues - fontoura@orion.enm.unb.br
Universidade de Brasília, Departamento de Engenharia Mecânica
Campus Darcy Ribeiro - 70000-000 - Brasília, DF, Brasil

Two nonlinear algebraic models for the Reynolds tensor are used in the simulation of the turbulent flow over a backwards-facing step, a case where the linear model for the Reynolds tensor, the Boussinesq hypothesis, is not valid and yields unsatisfactory results. The goal of this paper is to evaluate the performance of non-linear models of the Reynolds tensor in the experimental configuration of Driver & Seegmiller (1985). A collocated finite volume code was used to solve the time-averaged incompressible Navier-Stokes equations while using various models for the Reynolds tensor to solve the closure problem. The computational data obtained through three different explicit models for the Reynolds tensor  - Boussinesq hypothesis, Gatski-Speziale, Girimaji - are compared with experimental data. The non-linear models achieve a more consistent representation of the transport of turbulence in the region immediately downstream of the sudden expansion, while consuming approximately 50% more computation time, when compared to the linear model. The improved representation of the transport of turbulence following the step allowed the estimation of the reattachment distance of the flow to within 3% of the experimental value, which may be compared with the 26% margin observed when applying the Boussinesq hypothesis.

Keywords: Fluid Mechanics, Turbulence, Numerical Simulation, Turbulence Models, Reynolds  Tensor Models
 
 

Marcio T. Mendonca
Centro Tecnico Aeroespacial - Instituto de Atividades Espaciais
Pc Mal. Eduardo Gomes, 50 - 12228-904 - Sao Jose dos Campos - SP- Brazil
email: marcio tm@yahoo.com

Marcello A. F. de Medeiros
Pontificia Universidade Catolica de Minas Gerais - Engenharia Mec^anica
Av. Dom Jose Gaspar, 500 - 30535-610 - Belo Horizonte - MG - Brazil
email: marcello@pucminas.br

In this paper a numerical model based on the parabolized stability equations is used to investigate the characteristics of subharmonic and fundamental secondary instabilities. In order to identify which instability mode is dominant, the classic K-type and H-type secondary instability experiments are repeated including both fundamental and subharmonic oblique modes in the initial condition. The results show that, depending on the initial amplitude of the two-dimensional Tollmien-Schlichting (TS) wave, both oblique modes are destabilized and that the subharmonic oblique wave has a stronger nonlinear growth. Linearly unstable oblique modes are also studied showing that, due to its higher frequency, the fundamental mode grows faster and interact more strongly with the twodimensional TS wave. Which secondary instability mode will prevailes depends on the relative amplitude of the disturbances and on their growth rates.

Keyword: hydrodynamic instability, transition to turbulence, K-type secondary instability, H-type secondary instability, Tollmien-Schlichting waves
 
 

Mila R. Avelino
Department of Mechanical Engineering, UERJ, Rua São Francisco Xavier, 524/5023A, 20550-013, Rio de Janeiro, Brazil

Atila P. Silva Freire
Mechanical Engineering Program (PEM/COPPE/UFRJ), C. P. 68503, 21945-970 Rio de Janeiro, Brazil

The present work reports the dynamic and thermal behaviour of flows that develop over surfaces which show a sudden change in surface temperature and roughness.  A particular interest of this study is to investigate any existing relationship between the error in origin for both the velocity and temperature profiles, so that any analogy between the logarithmic laws for the velocity and the temperature profiles can be assessed.  Then, by considering the validity of Coles's law of the wake for the outer part of the boundary layer, a robust algebraic equation for the estimation of Stanton number is proposed.  Three different types of surfaces are considered here: two 'K' type of surfaces and one 'D' type of surface.  The flow is made to pass from a cold smooth surface to a hot rough surface.  Measurements are presented for the mean velocity and temperature profiles.  Also, all global parameters that characterize the velocity and the temperature fiels are presented.  The results show that for surfaces of type 'K' the behaviour of epsilon and epsilon_t are very similar; for surface of type 'D', however, their behaviour is quite different.

Keywords: turbulence, thermal boundary layer, roughness, error in origin.
 
 

Marcelo Assato - e-mail: assato@mec.ita.br
Marcelo J.S. de-Lemos - e-mail: delemos@mec.ita.br
Departamento de Energia - IEME, Instituto Tecnológico de Aeronáutica - ITA
12228-900 São José dos Campos - SP - Brasil

This work deals with numerical predictions of turbulence-driven secondary flow that appear in ducts of non-circular cross section. These small currents are caused by differences between normal stresses. Fully developed flow was calculated making use of a non-linear k- e turbulence model. Governing equation for the mean and turbulent fields were discretized with the help of the control-volume method. A non-orthogonal grid mapped the computational domain. The SIMPLE method was employed for relaxing the dependent variables. Results for the fully developed flow field in a square duct were compared with experiments. An extensive analysis of the turbulence structure in such flow was carried out.
 
 

Rigoberto E. M. Morales - rmorales@fem.unicamp.br
Eugênio S. Rosa - erosa@fem.unicamp.br
FEM/DE UNICAMP CP 6122
13083-970 - Campinas, SP, Brasil

É realizado uma simulação numérica do escoamento turbulento completamente desenvolvido em um canal helicoidal de seção retangular. As equações de conservação são discretizadas para um sistema ortogonal local, e resolvidas utilizando o método numérico de volumes finitos com o esquema híbrido de interpolação. A interface livre é calculado utilizando o algoritmo HOL (Height-Of-Liquid). A turbulência é modelada utilizando o modelo de turbulência para baixo números de Reynolds. As simulações mostraram que o método utilizado, quando comparado com dados experimentais, calcula satisfatoriamente a localização da interface. Apresenta-se os campos da velocidade média e da energia cinética turbulenta.

Palavras-chave: Canal Helicoidal, Superfície livre, Turbulência, . - e LB
 
 

J. Pontes jopontes@paladium.metalmat.ufrj.br
Metallurgy and Materials Engineering Department { EE/COPPE/UFRJ
PO Box 68505 21945-970 Rio de Janeiro RJ, Brazil
N. Mangiavacchi norberto@icmc.sc.usp.br
Institute of Mathematical and Computational Sciences USP { S. Carlos
PO Box 668 13560-161 S.Carlos, SP, Brazil
O. E. Barcia barcia@metalmat.ufrj.br
Institute of Chemistry { UFRJ 21945-970 Rio de Janeiro, Brazil
O. R. Mattos omattos@metalmat.ufrj.br
Metallurgy and Materials Engineering Department { COPPE/UFRJ
PO Box 68505 21945-970 Rio de Janeiro RJ, Brazil
B.Tribollet
UPR15 { CNRS, Physique des Liquides et Electrochimie
4 place Jussieu, 75252 Paris Cedex 05, France
D. Walgraef dwaelgr@ulb.ac.be
Center for Nonlinear Phenomena and Complex Systems
Universit_e Libre de Bruxelles CP 231 B-1050 Brussels, Belgium

The stability of the hydrodynamic _eld developed close to the axis of a rotating disk electrode in an electrochemical cell is considered. This cell is used in the study of
anodic dissolution of iron electrodes in sulfuric acid media. Polarization curves (applied voltage _ current) obtained experimentally from such cells display a current instability region within the range of applied voltage in which the current is controlled by mass transport of the electrolyte. According to the literature (Barcia et. al., 1992) the electrodissolution process leads to the existence ofaviscosity gradient in the interface metal-solution, which changes the velocity pro_les and may a_ect the stability of the hydrodynamical _eld. The purpose of this work is to investigate whether this viscosity gradient may lead to a hydrodynamic instability. The results show that the neutral stability curves are signi_cantly modi_ed by the presence of a viscosity gradient and that the critical Reynolds number, above which the considered class of perturbations are linearly unstable, is clearly reduced. The existence of unstable hydrodynamic modes at Reynolds numbers on the order of those found in the experimental setup may originate the observed current unstability.

Keywords: Electrochemistry, Hydrodynamic Stability, Boundary Layers, Rotating Disk
 
 

Marcelo Assato * - e-mail: assato@mec.ita.br
Francisco D. Rocamora Jr. ** - e-mail: rocamora@mec.ita.br
Marcelo J.S. de-Lemos * - e-mail: delemos@ita.cta.br
*Departamento de Energia - IEME, Instituto Tecnológico de Aeronáutica - ITA
12228-900 São José dos Campos - SP - Brasil
**Depto. de Energia Nuclear, Instituto de Estudos Avançados - IEAv/CTA
12231-970, São José dos Campos - SP - Brasil

Numerical results for turbulent flow and heat transfer are here presented. It is shown that the non-linear k- e model predicts values closer to experimental data, for both hydrodynamic and thermal fields, when compared to their linear counterpart. Wall functions for velocity and temperature are used in order to bypass fine computation close to the wall. The control volume approach is employed for discretizing the flow governing equation and the SIMPLE algorithm is used for relaxing the solution. Results for turbulent flow in a channel with an abrupt expansion are presented. The recirculating length and mean flow quantities are better predicted with the use of a non-linear relationship between the shear stresses and the deformation rate tensor.
 
 
 

Pedro H. de A. Barbosa
Marcio Cataldi
Atila P. Silva Freire
Mechanical Engineering Program (PEM/COPPE/UFRJ), C. P. 68503, 21945-970 Rio de Janeiro, Brazil

The present work discusses various types of turbulence generators which can be used to generate thick turbulent boundary layers.  The experimental assessment of the generators was carried out considering the integral properties of the flow, skin-friction, mean velocity profiles in inner and outer coordinates and turbulence.  Designs based on triangular wedge, elliptic wedge and cylindrical rod generators are analyzed.  The paper describes in detail the experimental arrangement, including the features of the wind tunnel and of the instrumentation.  The results are compared with naturally developed flow and with experimental data from other authors.

Keywords: Turbulence, roughness, boundary layer, atmospheric flows