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Numerical Heat Transfer, Part A: Applications
An International Journal of Computation and Methodology
Volume 69, 2016 - Issue 2
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Original Articles

Assessment of a common nonlinear eddy-viscosity turbulence model in capturing laminarization in mixed convection flows

, &
Pages 146-165 | Received 22 Dec 2014, Accepted 14 Jan 2015, Published online: 30 Nov 2015
 

ABSTRACT

Laminarization is an important topic in heat transfer and turbulence modeling. Recent studies have demonstrated that several well-known turbulence models failed to provide accurate prediction when applied to mixed convection flows with significant re-laminarization effects. One of those models, a well-validated cubic nonlinear eddy-viscosity model, was observed to miss this feature entirely. This paper studies the reasons behind this failure by providing a detailed comparison with the baseline Launder–Sharma model. The difference is attributed to the method of near-wall damping. A range of tests have been conducted and two noteworthy findings are reported for the case of flow re-laminarization.

Nomenclature

Bo=

= buoyancy parameter, 8 × 104Gr/(Re 3.425 Pr0.8)

cf=

= local friction coefficient

Cμ=

= constant in eddy-viscosity models

D=

= pipe diameter

Eϵ=

= near-wall source term

fμ=

= damping function

gi=

= acceleration due to gravity

Gr=

= Grashof number,

k=

= turbulent kinetic energy,

Nu=

= Nusselt number,

p=

= pressure

Pk=

= rate of shear-production of k,

Pr=

= Prandtl number, cpμ/λ

=

= wall heat flux

R=

= pipe radius

Re=

= Reynolds number, UbD/v

Ret=

= turbulent Reynolds number,

S=

= strain parameter

T=

= temperature

T+=

= non-dimensional temperature, (TwT)/Tτ

Tτ=

= friction temperature, /ρ.cp.Uτ

U+=

= non-dimensional velocity, U/Uτ

Uτ=

= friction velocity,

Ui, ui=

= mean, fluctuating velocity components in Cartesian tensors

=

= Reynolds stress tensor

=

= turbulent heat flux

x, y=

= streamwise and wall-normal coordinates

y+=

= dimensionless distance from the wall, yUτ/v

Greek Symbols=
B=

= coefficient of volumetric expansion

δij=

= Kronecker delta

E=

= rate of dissipation of k

Λ=

= thermal conductivity

μ=

= dynamic viscosity

ν=

= kinematic viscosity, μ/ρ

νt=

= turbulent viscosity

ρ=

= density

σt=

= turbulent Prandtl number

τw=

= wall shear stress

Subscripts=
0=

= forced convection

b=

= bulk

t=

= turbulent

w=

= wall

Nomenclature

Bo=

= buoyancy parameter, 8 × 104Gr/(Re 3.425 Pr0.8)

cf=

= local friction coefficient

Cμ=

= constant in eddy-viscosity models

D=

= pipe diameter

Eϵ=

= near-wall source term

fμ=

= damping function

gi=

= acceleration due to gravity

Gr=

= Grashof number,

k=

= turbulent kinetic energy,

Nu=

= Nusselt number,

p=

= pressure

Pk=

= rate of shear-production of k,

Pr=

= Prandtl number, cpμ/λ

=

= wall heat flux

R=

= pipe radius

Re=

= Reynolds number, UbD/v

Ret=

= turbulent Reynolds number,

S=

= strain parameter

T=

= temperature

T+=

= non-dimensional temperature, (TwT)/Tτ

Tτ=

= friction temperature, /ρ.cp.Uτ

U+=

= non-dimensional velocity, U/Uτ

Uτ=

= friction velocity,

Ui, ui=

= mean, fluctuating velocity components in Cartesian tensors

=

= Reynolds stress tensor

=

= turbulent heat flux

x, y=

= streamwise and wall-normal coordinates

y+=

= dimensionless distance from the wall, yUτ/v

Greek Symbols=
B=

= coefficient of volumetric expansion

δij=

= Kronecker delta

E=

= rate of dissipation of k

Λ=

= thermal conductivity

μ=

= dynamic viscosity

ν=

= kinematic viscosity, μ/ρ

νt=

= turbulent viscosity

ρ=

= density

σt=

= turbulent Prandtl number

τw=

= wall shear stress

Subscripts=
0=

= forced convection

b=

= bulk

t=

= turbulent

w=

= wall

Acknowledgments

The authors are pleased to acknowledge the contribution of their colleagues in the School of Mechanical, Aerospace and Civil Engineering (MACE) at the University of Manchester, especially Dr. M.A. Cotton and Professor D. Laurence.