**Session 35: Turbulence**

**Chairs:**

**Aristeu da Silveira Neto**
**Faculdade de Engenharia Mecânica-Universidade
Federal de Uberlândia**

**Cesar J. Deschamps**
**Departamento de Engenharia Mecânica**
**Universidade Federal de Santa Catarina**

**Marcello Augusto Faraco de Medeiros**
**Departamento de Engenharia Mecânica**
**Pontificia Universidade Catolica de
Minas Gerais**

**Marcelo J.S. de_Lemos**
**Departamento de Energia - IEME**
**Instituto Tecnológico de Aeronáutica
- ITA/CTA**

s35p01

**A
COMPARATIVE ANALYSIS OF TURBULENCE MODELS APPLIED TO COMPLEX FLOW**

Daniel A. Salinas Casanova
- [email protected]

Universidade Estadual do
Oeste do Paraná, Centro de Engenharias e Ciências Exatas

85.855-000, Foz do Iguaçu,
PR, Brasil

César J. Deschamps
- [email protected]

Alvaro T. Prata - [email protected]

Francisco F. S. Matos -
[email protected]

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

s35p03

**A
NEW SKIN FRICTION EQUATION FOR TURBULENT FLOWS OF BINGHAM PLASTIC FLUIDS
IN PIPES**

D. O. A. Cruz, E-mail: [email protected]

E. N. Macêdo, E-mail:
[email protected]

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

s35p04

**A
NUMERICAL STUDY OF THE DYNAMICS OF STEEL MELT FLOW IN A TUNDISH**

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.

s35p05

**A
WIND TUNNEL STUDY OF TURBULENT FLOW OVER HILLS. PART I: SMOOTH CHANGES
IN SURFACE ELEVATION**

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

s35p06

**A
WIND TUNNEL STUDY OF TURBULENT FLOW OVER HILLS. PART II: LARGE CHANGES
IN SURFACE ELEVATION**

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

s35p11

**DEVELOPMENT
OF A GENERAL TURBULENCE MODEL FOR HYBRID POROUS MEDIA - CLEAR FLOW DOMAINS**

Marcelo J.S. de-Lemos - e-mail:
[email protected]

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

s35p13

**PERFORMANCE
OF THE LOW-REYNOLDS k-e LSH MODEL TO PREDICT FLOW THROUGH CURVILINEAR OBSTRUCTION**

G. N. Zevallos - [email protected]

A. O. Nieckele - [email protected]

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

s35p15

**HEAT
TRANSFER IN THE RE-ATTACHMENT REGION OF A BACKWARD-FACING STEP FLOW**

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

s35p16

**THE
INFLUENCE OF THE PRESSURE GRADIENT MODELING IN LOW REYNOLDS NUMBER TURBULENCE
MODELS**

J. D. M. Abrunhosa- [email protected]

Angela O. Nieckele - [email protected]

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.

s35p17

**INFLUENCE
OF THE POLYMER MOLECULAR WEIGHT IN THE TURBULENT CHANNEL FLOW STRUCTURE
MODIFICATIONS**

Guillermo Vilalta (e-mail:
[email protected] ispjae.edu.cu)

Centro de Estudios de Tecnologías
Energéticas Renobables, ISPJAE, Marianao 14, CP 19 390,

Habana, Cuba.

Jayme Pinto Ortiz (e-mail:
[email protected])

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.

s35p18

**LAMINAR-TURBULENT
TRANSITION: THE EFFECT OF MODULATION ON THE EVOLUTION OF WAVES IN BOUNDARY
LAYERS**

Marcello A. Faraco de Medeiros
{ e-mail: [email protected]

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

s35p20

**NONLINEAR
MODELS FOR THE REYNOLDS TENSOR IN THE SIMULATION OF WALL-BOUNDED FLOWS**

Paulo Seiji Kumon Zandonade
- [email protected]

Universidade de Brasília,
Departamento de Engenharia Mecânica

Campus Darcy Ribeiro - 70000-000
- Brasília, DF, Brasil

José Luiz Alves da
Fontoura Rodrigues - [email protected]

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

s35p24

**ON
SUBHARMONIC AND FUNDAMENTAL INSTABILITY MODES IN BOUNDARY LAYERS**

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 [email protected]

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: [email protected]

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

s35p27

**RESPONSE
OF A TURBULENT BOUNDARY LAYER TO SUDDEN CHANGES IN WALL TEMPERATURE AND
ROUGHNESS**

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.

s35p28

**ESCOAMENTO
SECUNDÁRIO EM DUTOS DE SEÇÃO NÃO CIRCULAR USANDO
UM MODELO DE TURBULÊNCIA k- e NÃO LINEAR**

Marcelo Assato - e-mail:
[email protected]

Marcelo J.S. de-Lemos -
e-mail: [email protected]

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.

s35p29

**SIMULAÇÃO
NUMÉRICA DO ESCOAMENTO COM SUPERFÍCIE LIVRE EM UM CANAL HELICOIDAL
DE SEÇÃO RETANGULAR**

Rigoberto E. M. Morales -
[email protected]

Eugênio S. Rosa -
[email protected]

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

s35p31

**STABILITY
OF THE HYDRODYNAMIC FIELD CLOSE TO A ROTATING DISK ELECTRODE**

J. Pontes [email protected]

Metallurgy and Materials
Engineering Department { EE/COPPE/UFRJ

PO Box 68505 21945-970 Rio
de Janeiro RJ, Brazil

N. Mangiavacchi [email protected]

Institute of Mathematical
and Computational Sciences USP { S. Carlos

PO Box 668 13560-161 S.Carlos,
SP, Brazil

O. E. Barcia [email protected]

Institute of Chemistry {
UFRJ 21945-970 Rio de Janeiro, Brazil

O. R. Mattos [email protected]

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 [email protected]

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

s35p34

**TRANSFERÊNCIA
DE CALOR TURBULENTA NUM CANAL COM EXPANSÃO ABRUPTA USANDO UM MODELO
k- e NÃO LINEAR**

Marcelo Assato * - e-mail:
[email protected]

Francisco D. Rocamora Jr.
** - e-mail: [email protected]

Marcelo J.S. de-Lemos *
- e-mail: [email protected]

*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.

s35p38

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