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Research Papers: Fundamental Issues and Canonical Flows

# Application of the $k-ε$ Turbulence Model to Buoyant Adiabatic Wall Plumes

[+] Author and Article Information
Michael A. Delichatsios

FireSERT, University of Ulster, Shore Road, Bt37 0QB, Northern Ireland

C. P. Brescianini, D. Paterson

Fire Science and Technology Laboratory, Construction and Engineering, CSIRO Building, P.O. Box 310, North Ryde, NSW 1670, Sydney, Australia

H. Y. Wang, J. M. Most

Laboratoire de Combustion et de Détonique, UPR 9028 au CNRS, ENSMA, Téléport 2, BP 40109, F-86961 Futuroscope Chasseneuil Cedex, France

J. Fluids Eng 132(6), 061202 (May 19, 2010) (5 pages) doi:10.1115/1.4001642 History: Received July 18, 2009; Revised April 20, 2010; Published May 19, 2010; Online May 19, 2010

## Abstract

Computational fluid dynamics based on Reynolds averaged Navier–Stokes equations is used to model a turbulent planar buoyant adiabatic wall plume. The plume is generated by directing a helium/air source upwards at the base of the wall. Far from the source, the resulting plume becomes self-similar to a good approximation. Several turbulence models based predominantly on the $k-ε$ modeling technique, including algebraic stress modeling, are examined and evaluated against experimental data for the mean mixture fraction, the mixture fraction fluctuations, the mean velocity, and the Reynolds shear stress. Several versions of the $k-ε$ model are identified that can predict important flow quantities with reasonable accuracy. Some new results are presented for the variation in a mixing function for the mixture normal to the wall. Finally, the predicted (velocity) lateral spread is as expected smaller for wall flows in comparison to the free flows, but quite importantly, it depends on the wall boundary conditions in agreement with experiments, i.e., it is larger for adiabatic than for hot wall plumes.

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## Figures

Figure 1

Cross-stream distribution of scaled rms mixture fraction fluctuations in plane buoyant turbulent wall plume. Comparison of high-Re/wall-function model and two-layer k-ε model. Model A represents the simple gradient model for the Gk production term in the k-equation (1).

Figure 2

Cross-stream distribution of scaled mean velocity in plane buoyant turbulent wall plume. Comparison of different turbulence models listed in Table 3. Model A represents the simple gradient model for the Gk production term in the k-equation (1).

Figure 3

Cross-stream distribution of normalized Reynolds shear stress in plane buoyant turbulent wall plume. Comparison of different turbulence models listed in Table 3. Model A represents the simple gradient model for the Gk production term in the k-equation (1).

Figure 4

Cross-stream distribution of mean-square fluctuations of mixture fraction (g¯) normalized by f¯(1.4f¯max−f¯) for a plane buoyant turbulent wall plume. Model A represents the simple gradient model for the Gk production term in the k-equation (1). Model B represents the generalized gradient model for the Gk production term in the k-equation (1).

Figure 5

The lateral spread for two wall buoyant flows with different boundary conditions and for free plane and round buoyant plumes. As expected the lateral spread is smaller for wall flows in comparison to the free flows, but quite importantly, it depends on the wall boundary conditions in agreement with experiments (5-7), i.e., it is larger for adiabatic than for hot wall plumes.

Figure 6

Cross-stream distribution of scaled mean mixture fraction in plane buoyant turbulent wall plume. Comparison of a high-Re/wall-function model and the two-layer k-ε model. This figure is discussed in the conclusions. Model A represents the simple gradient model for the Gk production term in the k-equation (1).

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