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Annals of the Assembly for International Heat Transfer Conference 13

ISBN 1-56700-225-0 / CD 1-56700-226-9

Volumes per year:

various

Year 2006

DOI: 10.1615/IHTC13.p1

PREDICTION OF RICHARDSON NUMBER EFFECTS ON STABLY-STRATIFIED TURBULENCE WITH SECOND-MOMENT CLOSURES

J. C. F. Pereira
Instituto Superior Técnico / Technical University of Lisbon, Department of Mechanical Engineering / LASEF, Av. Rovisco Pais, 1049-001 Lisbon, Portugal

J. M. P. Rocha
Instituto Superior Técnico / Technical University of Lisbon, Department of Mechanical Engineering / LASEF, Av. Rovisco Pais, 1049-001 Lisbon, Portugal

ABSTRACT

The performance of second moment turbulence closures based on differential transport equations is critically evaluated in order to access the process of collapsed state of stable stratified shear turbulence. This state occurs typically for gradient Richardson number Ri greater than 0.25. The process of turbulence collapse includes the extinction of vertical over turning, counter gradient heat and momentum flux phenomena an formation of gravity waves in the early stages of Ri supercritical regime.
Focus of present paper is on predicting the Richardson number effects on turbulence mixing properties up to the transition region. The modelling of pressure-strain, pressure-temperature gradient terms in Reynolds stress and heat flux equations incorporate two different levels of closure, namely linear and non-linear power expansion on anisotropy terms.
The predictions describe satisfactorily DNS data for low Ri numbers, up to critical Richardson number. As Richardson number increases, the behaviour of the models deteriorates once in the vicinity of Ri transition. The effect of Ri on the growth rate of turbulent kinetic energy follows the same trend. The mixing efficiency, characterised by the Richardson flux number R_f, is well predicted across whole Ri range considered. However, the models do not predict the strong increase of Reynolds stress anisotropy that occurs when stratification intensity increases up to Richardson transition point. Suggestion is made that it is very likely that this drawback of the models may be related with a deficient response of pressure-strain model to increase of stratification intensity.