Session 10: Finite Volume Method

Chairs:

Angela Ourivio Nieckele
Dept. Engenharia Mecânica PUC-Rio

Clovis Raimundo Maliska
Departamento de Engenharia Mecânica Universidade Federal de Santa Catarina






s10p01

MOULD FILLING SIMULATION USING FINITE VOLUME METHOD BASED ON VORONOI DISCRETIZATION

João Flávio Vieira de Vasconcellos
LEMA - Laboratório de Experimentação e Simulação Numérica em Transferência de Calor e Massa
Instituto Politécnico da UERJ, Cx. P. 97.282 - CEP 28.601- 970, Nova Friburgo - Rio de Janeiro - Brasil

Clovis Raimundo Maliska
SINMEC - Laboratório de Simulação Numérica em Mecânica dos Fluidos e Transferencia de Calor
Universidade Federal de Santa Catarina, Cx. P. 476 - CEP 88.040-900, Florianópolis - Santa Catarina - Brasil

This paper presents numerical results obtained when validating a finite volume methodology using the well-known VOF method for capturing the fluid interface in a moving boundary problem. This methodology uses an additional equation for capturing the front and Voronoi grids for the finite volume scheme. It is shown comparisons with analytical solutions demonstrating the potentiality of the methodology.

Keywords: Finite Volume Method, Moving Fronts, Non-newtonian Fluid, Mold Filling
 
 



s10p03

ANALYSIS OF A VOLUME BASED FINITE ELEMENT METHODOLOGY IN VIEW OF THE INTERPOLATION FUNCTION EMPLOYED AND COUPLING CHARACTERISTICS

Jeferson A. Souza – [email protected]
Clóvis R. Maliska – [email protected]
Computational Fluid Dynamics Laboratory – SINMEC -Federal University of Santa Catarina
88040-900 – Florianópolis –SC – Brasil - Phone: 0xx48 331 9562 - Fax: 0xx48 234 1519

Abstract. The search for computational methods to the solution of the fluid mechanical and heat transfer problems that could deal with all the difficulties in a “strong” way, combine with the growing capabilities of processing and memory storage of the modern computers, make the control volume finite element methods, associated with a coupled solution of the Navier-Stokes and continuity equations, of great interest of the scientific community. This work studies one of these methods known as FIELDS, and discusses some of its important private characteristics with respect to the interpolation functions and the discretization of the diffusive term of the Navier-Stokes equations. The applicability of the method for unstructured grid will also be discussed.

Key words: Control-volume, Interpolation functions, Simultaneous solution
 
 
 



s10p06

NUMERICAL SOLUTION OF NON-ISOTHERMAL LAMINAR JET FLOW USING THE MULTIGRID METHOD

Maximilian S. Mesquita - 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

Heated laminar jet flow is numerically investigated using the multigrid method. Numerical analysis is based on the finite volume discretization scheme applied to structure orthogonal regular meshes. Performance of the correction storage (CS) multigrid is compared for different Reynolds number at inlet and distinct number of grids. Up to three grids were used for both V- and W-cycles. Simultaneous and segregated temperature-velocity solution schemes were investigated. Advantages in using more than one grid are discussed. For simultaneous solution, results indicate an increase in the computational effort for higher inlet Reynolds numbers. Optimal number of intermediate relaxation sweeps within both V-and W-cycles are discussed.

Keywords: Sudden Expansion, Multigrid, CFD, Numerical Methods
 
 



s10p07

NUMERICAL SIMULATION OF THE FLOW AROUND A SQUARE CYLINDER AT LOW REYNOLDS NUMBER: THE DOMAIN SIZE INFLUENCE

Odenir de Almeida [email protected]
Sérgio Said Mansur [email protected]
UNESP -Faculdade de Engenharia de Ilha Solteira, Departamento de Engenharia Mecânica
15385-000 - Ilha Solteira, SP, Brasil

Aristeu da Silveira Neto [email protected]
UFU -Faculdade de Engenharia Mecânica, Departamento de Engenharia Mecânica
38400-902 - Uberlândia, MG, Brasil

The flow around a square cylinder at low Reynolds numbers has been simulated with different configurations, in order to study the effects of domain size on the fluid motion. Numeric two-dimensional calculations have been performed with FLUENT .5.0 software by means of a finite-volume method employing a structured grid. An incompressible SIMPLEC algorithm has been employed for the velocity-pressure coupling, and the third-order QUICK scheme has been used for the treatment of convective terms. The influence of blockage ratio, as well as inlet and outlet location on the flow, has been investigated. Numerical flow patterns are also presented by means of streamlines and vorticity contours for the blockage ratios studied. Quantitative parameters as Strouhal number, lift, drag and pressure coefficients have been calculated for each case, showing that the values obtained depend strongly of the domain size. Keywords: Numerical simulation, finite-volume method, calculation domain, square cylinder, vortex street.
 
 



s10p08

SIMULATION OF STEEL BILLETS HEATING IN A REHEAT FURNACE - REAL TIME MODEL

Cynara V. Magalhães - [email protected]
Márcio Ziviani - [email protected]
Ricardo J. Silva - [email protected]
Universidade Federal de Minas Gerais, Departamento de Engenharia Mecânica
Av. Antônio Carlos, 6627 - 31270-901 - Belo Horizonte, MG, Brasil

In this work, the heating of steel billets in a walking beam reheat furnace is investigated. The numerical model is validated with respect to a full-scale experimental data carry out in the industry. The heating of the stocks is simulated inside the furnace in real time. Temperatures of all the billets are presented in the furnace in different times, with the purpose to evaluate the differentiated heating of the pieces during the test. The knowledge of the thermal process proves to be a promising and valuable tool to control the furnace operation aiming to save energy and to improve quality to the final product.

Keywords: Reheat furnace, Walking beam, Finite volume, Metallurgical industry
 
 



s10p09

AN FINITE VOLUME PROCEDURE FOR SIMULATING NON-NEWTONIAN FLUID FLOWS WITH MOVING FRONTS

João Flávio Vieira de Vasconcellos
LEMA - Laboratório de Experimentação e Simulação Numérica em Transferência de Calor e Massa
Instituto Politécnico da UERJ, Cx. P. 97.282 - CEP 28.601- 970, Nova Friburgo - Rio de Janeiro - Brasil

Clovis Raimundo Maliska
SINMEC - Laboratório de Simulação Numérica em Mecânica dos Fluidos e Transferencia de Calor
Universidade Federal de Santa Catarina, Cx. P. 476 - CEP 88.040-900, Florianópolis - Santa Catarina - Brasil

Abstract. This paper presents a transient three-dimensional model for simulating the injection mold flow inside a cavity. The non-newtonian behavior is represented by a power-law equation and the difficulty associated with the determination of the moving front is solved using the VOF method. Results are compared with commercial software designed for the simulation of plastic injection flows.

Keywords: Finite Volume Method, Moving Fronts, Non-newtonian Fluid, Mold Filling
 
 



s10p11

TWO-PHASE POLYSTYRENE INJECTION WITH SOLIDIFICATION IN RETANGULAR MOLDS USING VOF-TVD METHODOLOGY: INFLUENCES OF TEMPERATURE PROFILE

Carlos E. Fontes
Paulo L. C. Lage
José C. Pinto
Programa de Engenharia Química, COPPE/UFRJ
CP 68502 - CEP 21945-970 - Rio de Janeiro, RJ, Brazil

Simulations of the injection of melt polymer in molds were performed aiming the study of the filling pattern. The fluid flow equations for a pseudo-continuous fluid in a rectangular cavity were solved using Finite-Volume techniques and the SIMPLER scheme. The energy conservation equation was also solved and the interface was tracked by a VOF-TVD scheme. Polymer melt freezing was empirically accounted for in the code. Simulations for melt polystyrene injection in a water filled mold were performed. The influence of the flow initial condition, mold cooling and displaced fluid viscosity on the filing patterns were analyzed. The results show that the displaced fluid viscosity value does not appreciably affect the filling pattern. The initial flow condition slightly affects the filling pattern, while mold cooling can dramatically change the filling pattern.

Keywords: Mold filling, TVD schemes, VOF schemes, computational fluid dynamics (CFD), heat transfer.
 
 



s10p13

A FINITE VOLUME FORMULATION USING UNSTRUCTURED AND HYBRID GRIDS

Fábio Alencar Schneider - [email protected]
Clovis Raimundo Maliska - [email protected]
SINMEC - Lab. de Simulação Numérica em Mecânica dos Fluidos e Transferência de Calor
Universidade Federal de Santa Catarina, Departamento de Engenharia Mecânica
Cx. P. 476 - 88040-900 - Florianópolis, SC, Brasil

The use of unstructured grids for domain discretization has increased significantly in recent years. These grids have better adaptative ness for complex domains. However, the use of structured grids, when possible, reduces significantly the computational effort. This work proposes a numerical solution for the convection-diffusion equation for a scalar variable using the Finite Volume Method in hybrid grids, i.e., a grid composed by quadrilateral and triangles. The method result from a combination of the FIELDS method (Schneider & Raw, 1987) and CVFEM method (Baliga and Patankar, 1988).

Keywords: Numerical Method, Unstructured grids, Fluid Flow.
 
 



s10p16

UTILIZATION OF THE FINITE VOLUME METHOD IN THE SOLUTION OF THE FLOW IN CYCLONES USING GENERALIZED COORDINATES

Dilênio P. de Souza - [email protected]
Universidade Federal de Santa Catarina - Departamento de Engenharia Química e Engenharia de Alimentos, LABSIN - Laboratório de Simulação Numérica de Sistemas Químicos
CEP 88040-900 - Caixa Postal 476, Florianópolis, SC, Brasil

Henry F. Meier - [email protected]
Universidade Regional de Blumenau - Departamento de Engenharia Química, LFC - Laboratório de Fluidodinâmica Computacional
CEP 89010-971 - Caixa Postal 1507, Blumenau, SC, Brasil

Antonio A. Ulson de Souza - [email protected] *
Universidade Federal de Santa Catarina - Departamento de Engenharia Química e Engenharia de Alimentos, LABSIN - Laboratório de Simulação Numérica de Sistemas Químicos
CEP 88040-900 - Caixa Postal 476, Florianópolis - SC

This work presents a study of the turbulent flow in cyclones using the Computational Fluid Dynamics techniques. The developed mathematical model is based on the conservation equations of the mass and momentum, in the conservative form, transformed for the generalized coordinates system. It is considered the turbulent, isothermal, monophasic flow. The domain discretization is made using the coordinate coincident with boundary of the physical problem, with a structured grid. The governing equations are treated with the technique of finite volumes, with co-located variables arrangement. For the pressure-velocity coupling, the method SIMPLEC is used. The results of the numerical model present good agreement when compared with the experimental data of the literature.

Keywords: Cyclones, Computational Fluid Dynamics, Generalized Coordinates
 
 



s10p17

APPLICATION OF TEH ALL-SPEED METHOD TO STEADY AND UNSTEADY ROWS ON STRUCTUDED GRIDS

Wladimyr M. C. Dourado  [email protected]
Centro Técnico Aeroespacial, Instituto de Aeronáutica e Espaço
CTA/IAE/ASA-P, 12228-904  São José dos Campos  SP  BRASIL
João Luiz F. Azevedo  [email protected]
Centro Técnico Aeroespacial, Instituto de Aeronáutica e Espaço
CTA/IAE/ASE-N, 12228-904  São José dos Campos  SP  BRASIL
Pascal Bruel  [email protected]
Centre National de la Recherche Scienti?que
Laboratoire de Combustion et de Détonique
BP 40109 - 86961 Futuroscope Chasseneuil Cedex  FRANCE

A numerical method based on the all-speed approach is proposed to calculate low Mach number separated and unsteady rows. The Navier-Stokes equations are solved on hybrid and non-hybrid unstructured meshes. The results are compared with analytical solutions and experimental data available in the literature.

Key Words: Aerodynamics, All speed methods, Finite volume method, Unstructured grids, Recirculating rows, Unsteady rows.