Abstract
A methodology for deriving a pressure–strain correlation model with variable coefficients
is developed. The methodology is based on two important premises: (i) the
extreme states of turbulence – the rapid distortion and equilibrium limits – are more
amenable to mathematically rigorous modelling because of significant simplifications
not possible at other states; and (ii) the models of the extreme states collectively
contain all of the relevant physics so that models for any intermediate state can be
obtained by suitable interpolation. A pressure–strain model of the standard form
is considered and the coefficients are determined from linear analysis in the rapid
distortion limit and from a fixed point analysis in the equilibrium limit. The model
coefficients, which depend on the mean deformation and turbulence state, vary from
flow to flow in a manner consistent with Navier–Stokes physics.The exact causal relationship between the model coefficients and the model's equilibrium
behaviour is established by fixed point analysis performed using representation
theory. Then, the equilibrium values of the model coefficients are chosen to yield the
observed equilibrium behaviour. The values of the model coefficients in the rapid distortion
limit are determined by enforcing consistency with the Crow constraint. The
new variable-coefficient model reduces to the traditional constant-coefficient model in
strain-dominated turbulent flows near equilibrium. The model performance in bench-mark turbulent flows, in which the traditional models have been calibrated extensively,
is preserved intact. The new model is significantly different from the traditional one
in mean vorticity-dominated and non-equilibrium turbulence. These two important
classes of flows, in which traditional models fail, are successfully captured by the new
model.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
40 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献