A Structure-Based Model for the Rapid Distortion of Homogeneous Turbulence.

Computer Science

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Scientific paper

A good one-point turbulence model should behave as an eddy-viscosity model for flows with slow mean deformation rates and as rapid distortion theory (RDT) for flows with rapid deformations. RDT is a linear theory, which is closed for two-point correlations but which needs modeling at the one-point level because of the non-locality of the pressure fluctuations. The structure-based model is based on the distinction between structure dimensionality (D) and componentality (C) and the need for turbulence models to carry information about both. In this model, a 3D-3C turbulence field is built as a superposition of 2D-3C flows or eddies. Each 2D field is characterized by an axis of independence (or eddy axis) and two scalar parameters giving the velocity components along and around the axis. Averaging over all the eddies produces the one-point, structure-based model in which an algebraic equation of state relates the Reynolds stresses to the eddy-axis tensor a_{ij }, and two scalar parameters, the turbulence -jetting parameter phi and the turbulence -helix parameter gamma. One evolves aij, phi, and gamma and uses the algebraic constitutive equation to get the stresses. Here the rapid version of the structure-based model is constructed. The evolution equations for phi and gamma, as obtained from the Navier-Stokes equations, exhibit the correct fixed points under all forms of mean deformation. Additional terms were added to capture the transients in flows with mean rotation. These terms were selected and tuned by reference to exact RDT carried out with a new technique, the particle representation model (PRM) of RDT, which is also developed here. The rapid version of the structure-based model is compared to RDT. Results from a large number of test cases suggest that the rapid structure-based model provides accurate modeling of the stresses under all forms of irrotational deformation, exact modeling of the RDT fixed points for all combinations of strain and rotation, and satisfactory modeling of the stresses during transitions to the fixed points. The model exhibits material indifference for 2D turbulence rotating about the axis of independence and gives realizable turbulent stresses under all conditions tested.

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