On the Growth Rate of Turbulent Mixing Layers: A New Parametric Model

Abstract

A new parametric model for the growth rate of turbulent mixing layers is proposed. A database of experimental and numerical mixing layer studies was extracted from the literature to support this effort. The domain of the model was limited to planar, spatial, nonreacting, free shear layers that were not affected by artificial mixing enhancement techniques. The model is split into two parts which were each tuned to optimally fit the database; equations for an incompressible growth rate were derived from the error function velocity profile, and a function for a compressibility factor was generalized from existing theory on the convective Mach number. The compressible model is supported by a detailed evaluation of the currently accepted models and practices, including error analysis of the convective Mach number derivation and a critical analysis of Slessor's renormalization technique which affected his 1998 compressibility parameter. Analysis of the database suggested that a distinction should be made between thickness definitions that are based on the velocity profile and those based on the density profile. Additionally, the accumulation of different normalization approaches throughout the literature was shown to have introduced non-physical variance in the trends. Resolution of this issue through a consistent normalization process has greatly improved the normality and scatter of the data and the goodness-of-fit of the models, resulting in R 2 = 0.9856 for the incompressible model and R 2 = 0.9004 for the compressible model.

Analysis of Aero-Optical Jitter in Convective Turbulent Flows Using Stitching Method

“…The convective velocity of the flow in conjunction with the sampling frequency used in the experiment defines the overlap present in adjacent wave-front images. For certain flows such as boundary layers [14,24,25] and shear layers [26,27], the convective velocity has been extensively studied and can be assumed to be constant and known. More analyses on the assumption of a constant convective velocity in the stitching method can be found in Ref.…”