Evaluation of Extended Weak-Equilibrium Conditions for Fully Developed Rotating Channel Flow

Abstract

The weak-equilibrium condition, which is the basis in the development of algebraic Reynolds stress models is assessed in the prediction of fully developed turbulent channel flow under the influence of system rotation. The budget of the various terms of the exact transport equation for the anisotropy tensor is evaluated by using a DNS database. Two diffusive transport constraints are evaluated by using the DNS data. The results show that neither of them can hold for the nearwall region. An asymptotic analysis of the near-wall behavior is performed and an alternative form of the diffusive transport constraint is proposed. The analysis shows that the proposed alternative diffusive transport constraint has the potential to improve the predictive ability of the resultant ARSM.

On the weak-equilibrium condition for derivation of algebraic heat flux model

“…It should be noted that when compared with the Reynolds stress case (Qiu et al, 2008), where the extended constraint gave excellent agreement with the DNS data for all Reynolds stress components, the extended constraint developed in the present study yields some noticeable discrepancies with the DNS data in some cases. In both the Reynolds stress and heat flux cases, the production terms are assumed to be negligible.…”

“…Consequently, a question arises whether the usual assumption for diffusive-transport can hold in flows involving rotation and curvature effects. The same question for the diffusive-transport assumption associated with Reynolds stress anisotropy tensor has been recently explored by Qiu et al (2008) using a budget analysis of the Reynolds stress anisotropy equation together with the near-wall asymptotic behavior. For the current study, an analogous strategy will be employed to address the issue of the diffusive-transport assumption associated with turbulent normalized heat flux.…”

“…Qiu et al (2008) attempted to resolve this problem by representing the diffusive-transport by the sum of redistribution and dissipation anisotropy terms associated with the Reynolds stress anisotropy. For current study, this same approach will be extended to the diffusive-transport assumption associated with normalized turbulent heat flux.…”

“…Following (Wikström et al, 2000), an assessment of the diffusive-transport constraint in non-inertial frames can be done by an analysis of the budget of the normalized heat flux equation using DNS data. Qiu et al (2008) proposed a nearwall correction for the diffusive-transport constraint applied to an ARSM based on a budget analysis of the transport equation for the Reynolds stress anisotropy. The current study will extend this work to the modification of the diffusive-transport constraint for an AHFM.…”

Second-moment and scalar flux representations in engineering and geophysical flows

“…In engineering flows, the region where this term is dynamically important is near solid surfaces and where effects of mean shear are negligible. In such flow field regions, the assumption is problematic and improvements are needed (see the recent study by Qiu et al 2008).…”