Abstract: According to the conditions proposed by Donalson which should be satisfied for the numerical turbulence models, a non - linear composition of vorticity tensor which is symmetrical and whose trace is zero is added to the constitutive relation between Reynolds stress and time -averaged quantities of flow field, and a new constitutive equation of Reynolds stress is given. For the turbulent flows in a straight pipe with square cross section and in a straight pipe with circular cross section, the theoretical calculation results indicate that the new constitutive equation of Reynolds stress can properly predict the existence of secondary flow and significantly improve the predictions in terms of Reynolds normal stresses and their anisotropy. The new constitutive equation of Reynolds stress has an advantage over that of standard k - 6 model, and is different from some other modified k - 8 models in which the effects of vorticity are added to turbulence kinetic energy equation and/or to its dissipation rate equation. It can be applied to establishing a new numerical turbulence model or to modifying the existing turbulence calculation roodels, which provides useful information on practical approaches to the modeling of Reynolds stress.
2008, Vol. 23 
