ISSN:
1089-7666
Source:
AIP Digital Archive
Topics:
Physics
Notes:
Rapid distortion theory is applied to study distortion of homogeneous turbulence subject to two different axisymmetric strain modes: contraction and expansion. Exact expressions for turbulence structural quantities are obtained in closed form by assuming initially isotropic turbulence and the asymptotic behavior at large total strains is also presented. Comparison with numerical simulations at high strain rate shows remarkably good agreement for all the quantities considered. Differences in effects of the two axisymmetric strain modes on evolution of the turbulence statistics are investigated in detail. It is found that (i) both velocity and vorticity fluctuations are enhanced more efficiently by contraction than by expansion; (ii) contraction produces much higher anisotropy in velocity and vorticity than expansion; (iii) root-mean-square pressure is slightly reduced during contraction, whereas it increases rapidly during expansion; and (iv) vortical structures of rodlike shape develop in a contraction flow, while disklike structures develop in an expansion flow. For flows of uniform, time-dependent density ρ(t) at low turbulence Mach number, it is shown that, by a decomposition of mean strain-rate tensor, statistical correlations are related to those in the equivalent incompressible flow, e.g., Rij(e) =(ρ/ρ0)2/3R(small star, filled)ij (e(small star, filled)), where e is the total strain and e(small star, filled) is the corresponding incompressible total strain (ρ0 is the initial density). The decomposition is applied to isotropic, one-dimensional, and two-dimensional dilatation cases to explore the effect of compressibility on turbulence. Terms in the transport equation of the Reynolds-stress tensor are evaluated for axisymmetric strain flows. A simple model for the pressure–strain-rate term is proposed by incorporating structural parameters and history effects based on the rapid distortion analysis. Prediction of the improved model agrees well with the numerical simulation results, even in cases at low strain rate.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.857331
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