Velocity/wave-vector probability density function models for inhomogeneous turbulent flows
Abstract
A probability density function (PDF) method for inhomogeneous turbulence, the wave vector model (WVM), is constructed that provides an exact representation of rapidly distorted homogeneous turbulence (RDT). The fundamental quantity modeled is the joint PDF of velocity and wave vector, which is related to the unit wave number vector in Fourier space. With the correspondence to Fourier space, the joint PDF equation provides a spectral model at the level of the directional spectrum which is the integral of the velocity spectrum over the wave number magnitude. The rapid pressure - rate-of-strain correlation from the Reynolds stress equation is closed at the directional spectrum level, and an exact representation of RDT is achieved. Stochastic diffusion models are added to the RDT equations to represent the dissipating and return-to-isotropy behaviors of turbulence, which at the Reynolds stress level are contained in the slow pressure - rate-of-strain correlation and dissipation tensor. The resulting models apply to general homogeneous turbulence and are tested in various cases where a modeled mean dissipation equation is included for closure. A further extension to inhomogeneous flows follows directly from the homogeneous model. For inhomogeneous turbulence, complex phenomena such as external intermittency can play a significant role in the behavior of the flow, and an addition of a particle turbulent frequency into the PDF formulation allows for improved modeling of these processes. A particle turbulent frequency model is developed to treat external intermittency in a natural manner through a conditional mean. At the edges of a temporal shear layer, the pressure transport is demonstrated to have a strong influence on the flow. A PDF model for the pressure transport is constructed that is applicable to general boundary-free shear flows. The cases of a temporal shear layer and swirling/non-swirling co-axial turbulent jets are studied with the WVM, the turbulent frequency model, and the pressure transport model. Direct numerical simulation (DNS) and experimental data are well predicted by the resulting PDF method.
- Publication:
-
Ph.D. Thesis
- Pub Date:
- September 1998
- Bibcode:
- 1998PhDT........63V