  In this study, ensembles of experimental data are presented and utilized to
compare and validate two models used in the simulation of variable density,
compressible turbulent mixing. Though models of this kind (Reynolds Averaged
Navier Stokes and Large Eddy Simulations) have been validated extensively with
more canonical flows in previous studies, the present approach offers novelty
in the complexity of the geometry, the ensemble based validation, and the
uniformity of the computational framework on which the models are tested.
Moreover, all experimental and computational tasks were completed by the
authors which has led to a tightly coupled experimental configuration with its
digital twin. The experimental divergent shock tube facility and its data
acquisition methods are described and replicated in simulation space. A 2D
Euler model which neglects the turbulent mixing at the interface is optimized
to experimental data using a Gaussian process. This model then serves as the
basis for both the 2D RANS and 3D LES studies that make comparisons to the
mixing layer data from the experiment. RANS is shown to produce good agreement
with experimental data only at late flow development times. The LES ensembles
generally show good agreement with experimental data, but display sensitivity
to the characterization of initial conditions. Resolution dependent behavior is
also observed for certain higher-order statistics of interest. Overall, the LES
model successfully captures the effects of divergent geometry, compressibility,
and combined non-linear instabilities inherent to the problem. The successful
prediction of mixing width and its growth rate highlight the existence of three
distinct regimes in the development of the instability, each with similarities
to previously studied instabilities.
