Numerical simulation of turbulent free surface flow with two-equation k-e eddy-viscosity models

V.G. Ferreira, N. Mangiavacchi, M.F. Tomé, A. Castelo, J.A. Cuminato, S. McKee

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

This paper presents a finite difference technique for solving incompressible turbulent free surface fluid flow problems. The closure of the time-averaged Navier-Stokes equations is achieved by using the two-equation eddy-viscosity model: the high-Reynolds k- (standard) model, with a time scale proposed by Durbin; and a low-Reynolds number form of the standard k- model, similar to that proposed by Yang and Shih. In order to achieve an accurate discretization of the non-linear terms, a second/third-order upwinding technique is adopted. The computational method is validated by applying it to the flat plate boundary layer problem and to impinging jet flows. The method is then applied to a turbulent planar jet flow beneath and parallel to a free surface. Computations show that the high-Reynolds k- model yields favourable predictions both of the zero-pressure-gradient turbulent boundary layer on a flat plate and jet impingement flows. However, the results using the low-Reynolds number form of the k- model are somewhat unsatisfactory.
LanguageEnglish
Pages347-375
Number of pages28
JournalInternational Journal for Numerical Methods in Fluids
Volume44
Issue number4
DOIs
Publication statusPublished - Jan 2004

Fingerprint

Eddy Viscosity
Free Surface Flow
Turbulent Flow
Jet Flow
Viscosity
Numerical Simulation
Low Reynolds number
Flat Plate
Computer simulation
Impinging Jet
Upwinding
Boundary layers
Reynolds number
Turbulent Boundary Layer
Finite Difference Technique
Pressure Gradient
Model
Free Surface
Computational Methods
Fluid Flow

Keywords

  • averaged Navier-Stokes equations
  • finite difference
  • turbulent free surface flow
  • higher-order upwind bounded scheme
  • two-equation k-eddy-viscosity model

Cite this

@article{3dc8b9603eb14a5b995c42fc478539ea,
title = "Numerical simulation of turbulent free surface flow with two-equation k-e eddy-viscosity models",
abstract = "This paper presents a finite difference technique for solving incompressible turbulent free surface fluid flow problems. The closure of the time-averaged Navier-Stokes equations is achieved by using the two-equation eddy-viscosity model: the high-Reynolds k- (standard) model, with a time scale proposed by Durbin; and a low-Reynolds number form of the standard k- model, similar to that proposed by Yang and Shih. In order to achieve an accurate discretization of the non-linear terms, a second/third-order upwinding technique is adopted. The computational method is validated by applying it to the flat plate boundary layer problem and to impinging jet flows. The method is then applied to a turbulent planar jet flow beneath and parallel to a free surface. Computations show that the high-Reynolds k- model yields favourable predictions both of the zero-pressure-gradient turbulent boundary layer on a flat plate and jet impingement flows. However, the results using the low-Reynolds number form of the k- model are somewhat unsatisfactory.",
keywords = "averaged Navier-Stokes equations, finite difference, turbulent free surface flow, higher-order upwind bounded scheme, two-equation k-eddy-viscosity model",
author = "V.G. Ferreira and N. Mangiavacchi and M.F. Tom{\'e} and A. Castelo and J.A. Cuminato and S. McKee",
year = "2004",
month = "1",
doi = "10.1002/fld.641",
language = "English",
volume = "44",
pages = "347--375",
journal = "International Journal of Numerical Methods in Fluids",
issn = "0271-2091",
number = "4",

}

Numerical simulation of turbulent free surface flow with two-equation k-e eddy-viscosity models. / Ferreira, V.G.; Mangiavacchi, N.; Tomé, M.F.; Castelo, A.; Cuminato, J.A.; McKee, S.

In: International Journal for Numerical Methods in Fluids, Vol. 44, No. 4, 01.2004, p. 347-375.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Numerical simulation of turbulent free surface flow with two-equation k-e eddy-viscosity models

AU - Ferreira, V.G.

AU - Mangiavacchi, N.

AU - Tomé, M.F.

AU - Castelo, A.

AU - Cuminato, J.A.

AU - McKee, S.

PY - 2004/1

Y1 - 2004/1

N2 - This paper presents a finite difference technique for solving incompressible turbulent free surface fluid flow problems. The closure of the time-averaged Navier-Stokes equations is achieved by using the two-equation eddy-viscosity model: the high-Reynolds k- (standard) model, with a time scale proposed by Durbin; and a low-Reynolds number form of the standard k- model, similar to that proposed by Yang and Shih. In order to achieve an accurate discretization of the non-linear terms, a second/third-order upwinding technique is adopted. The computational method is validated by applying it to the flat plate boundary layer problem and to impinging jet flows. The method is then applied to a turbulent planar jet flow beneath and parallel to a free surface. Computations show that the high-Reynolds k- model yields favourable predictions both of the zero-pressure-gradient turbulent boundary layer on a flat plate and jet impingement flows. However, the results using the low-Reynolds number form of the k- model are somewhat unsatisfactory.

AB - This paper presents a finite difference technique for solving incompressible turbulent free surface fluid flow problems. The closure of the time-averaged Navier-Stokes equations is achieved by using the two-equation eddy-viscosity model: the high-Reynolds k- (standard) model, with a time scale proposed by Durbin; and a low-Reynolds number form of the standard k- model, similar to that proposed by Yang and Shih. In order to achieve an accurate discretization of the non-linear terms, a second/third-order upwinding technique is adopted. The computational method is validated by applying it to the flat plate boundary layer problem and to impinging jet flows. The method is then applied to a turbulent planar jet flow beneath and parallel to a free surface. Computations show that the high-Reynolds k- model yields favourable predictions both of the zero-pressure-gradient turbulent boundary layer on a flat plate and jet impingement flows. However, the results using the low-Reynolds number form of the k- model are somewhat unsatisfactory.

KW - averaged Navier-Stokes equations

KW - finite difference

KW - turbulent free surface flow

KW - higher-order upwind bounded scheme

KW - two-equation k-eddy-viscosity model

UR - http://dx.doi.org/10.1002/fld.641

U2 - 10.1002/fld.641

DO - 10.1002/fld.641

M3 - Article

VL - 44

SP - 347

EP - 375

JO - International Journal of Numerical Methods in Fluids

T2 - International Journal of Numerical Methods in Fluids

JF - International Journal of Numerical Methods in Fluids

SN - 0271-2091

IS - 4

ER -