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Heat and Mass Transfer

, Volume 51, Issue 12, pp 1655–1667 | Cite as

Partially-averaged Navier–Stokes method for turbulent thermal plume

  • Rajesh Kumar
  • Anupam DewanEmail author
Original

Abstract

In this paper, the partially-averaged Navier–Stokes (PANS) simulation is performed for a turbulent thermal plume. The aim of the paper is to assess the PANS method for modeling buoyancy-driven flows at a reasonable computational cost. PANS is a turbulence closure model which is developed to be used as a bridging model ranging from the direct numerical simulation to the Reynolds-averaged Navier–Stokes simulation by varying the level of resolution. The PANS computations are performed for various values of the filter-width to evaluate the sensitivity of the filter-widths to the computed flow statistics. The present simulations have been carried out employing a source code buoyantPimpleFOAM based on the OpenFOAM platform. In order to capture the effect of buoyancy on turbulence, the generalized gradient diffusion hypothesis is employed to model the production of turbulence due to buoyancy. A detailed comparison of the time-averaged and turbulent statistics obtained from the PANS simulations with the experimental data and LES results reported in the literature has been presented. The present results have also been compared with the results of the unsteady Reynolds-averaged Navier–Stokes solutions. The PANS model is shown to enhance the computing capability significantly in predicting buoyancy-driven flows compared with those of URANS model. Finally, various important unsteady flow structures of turbulent thermal plume have been visualized from the instantaneous flow statistics obtained using the PANS simulations.

Keywords

Large Eddy Simulation Direct Numerical Simulation RANS Filter Parameter Thermal Plume 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols

Bu

Production of turbulence due to buoyancy (kg/ms3)

g

Acceleration due to gravity (m/s2)

h

Specific enthalpy (J/kg)

k

Turbulent kinetic energy (m2/s2)

ku

Unresolved turbulent kinetic energy (m2/s2)

p

Total pressure (N/m2)

pd

Component of total pressure, \(p_{d} = p - \rho \varvec{g} \cdot \varvec{X}\) (N/m2)

Pu

Production of turbulence due to shear (kg/ms3)

r

Radius (m)

S

Strain rate (s−1)

Sij

Strain rate tensor (s−1)

T

Temperature (K)

ui

Velocity component in the ith direction (m/s)

W

Time-averaged velocity in the axial direction (m/s)

z

Vertical distance (m)

δij

Kronecker delta (dimensionless)

μu

Unresolved turbulent viscosity (kg/ms)

σt

Turbulent Prandtl number (dimensionless)

τij

Shear stress tensor (N/m2)

ɛ

Turbulent dissipation rate (m2/s3)

ɛu

Unresolved turbulent dissipation rate (m2/s3)

μ

Molecular viscosity (kg/ms)

ρ

Density (kg/m3)

Subscripts

Properties of the ambient

i

Vector direction

c

Quantities at the centerline

Superscripts

\(\bar{\varphi }\)

Partially-averaged quantity

φ

Unresolved fluctuation

\(\tilde{\varphi }\)

Favre-averaged quantity

φ

Fluctuation (Favre statistics)

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of Applied MechanicsIndian Institute of Technology DelhiNew DelhiIndia

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