University of Manitoba
Winnipeg, Manitoba, Canada
A modified k-$\varepsilon-\gamma$ model that is valid down to a solid wall has been developed and applied to the developing turbulent pipe flow. In contrast to the Byggstoyl and Kollman's [1] intermittency model which employs conditional zone averaged moments, this k-$\varepsilon-\gamma$ model is based on the conventional Reynolds averaged moments. It is a more economical model compared with Byggstoyl and Kollman's [1] intermittency model because it halves the number of partial differential equations which need to be solved. This modified k-$\varepsilon-\gamma$ model eliminates the need for wall functions which makes it more generally applicable compared with Cho and Chung's [2] k-$\varepsilon-\gamma$ model.
Tests were performed for a smooth circular pipe with a length-to-diameter ratio of 83.8 for bulk Reynolds numbers of 75,000 and 300,000. Results show that the predictions for the mean axial velocity and the turbulent kinetic energy obtained by the present k-$\varepsilon-\gamma$ model are in better agreement with the experimental data than those obtained by Chien's [3] k-$\varepsilon$ model, therefore the capability of the modified k-$\varepsilon-\gamma$ model for predicting the internal flows is confirmed. Furthermore, the distributions of the intermittency factor for the developing pipe flow are presented with details for the first time and they seem to be physically realistic.
References:
[1] Byggstoyl, S., and Kollmann, W., ``Closure Model for Intermittent Turbulent Flows,'' {\it International Journal of Heat Mass Transfer}, Vol. 24, No. 11, 1981, pp. 18 11-1822.
[2] Cho, J. R., and Chung, M. K., ``A k-$\varepsilon-\gamma$ Equation Turbulence Model,'' {\it Journal of Fluid Mechanics}, Vol. 237, 1992, pp. 301-322.
[3] Chien, K. Y., ``Predictions of Channel and Boundary-Layer Flows with a Low-Reynolds-Number Turbulent Model,'' {\it AIAA Journal}, Vol. 20, No. 1, 1982, pp. 33-38.