A Validation Study for a Turbulent Mixing Model Based on the Probability Density Function Approach

The purpose of the present study is a to demonstrate and validate the use of the conserved scalar/assumed pdf approach to simulate turbulent mixing. To achieve this goal a numerical simulation of an experimental bench-mark problem is performed. A two-dimensional finite volume axisymmetric model numerically simulates the steady state passive scalar/air mixing. The computational study is conducted by solving the Reynolds Averaged Navier Stokes (RANS) flowfield governing transport equations. The turbulent fluctuations are computed by the two-equation k-e model. In addition to the flowfield variables, the model also solves for the mean and variance of the passive scalar concentration. To calculate the mean density, the probability density function (pdf) of the mixture fraction is assumed to follow the Beta-function distribution. The mean density is then computed by the convolution integral of the instantaneous density over the mixture fraction space. The moments of the pdf are determined from the mean and variance of the mixture fraction. The computational results are compared to the detailed measurements for the mean and turbulent quantities in the mixing flowfield as well as to the measured pdf of the mixture fraction. Effects of intermittency factor on mixing are also studied and compared to the experimentally observed intermittency. In general the computations are in reasonable agreement with the published measurements. The computed pdf assuming Beta function is also found to be, generally, in acceptable agreement with measurements. This detailed validation study indicates the ability of the present model to describe the basic features of the turbulent mixing including the intermittent behavior. However, the computations also show that a single assumed pdf shape is not able to represent all of the mixing stages.