NASA has recently undertaken a very high fidelity, detailed experiment focused on flow separation at the junction of a wing and its fuselage. It is well known that Reynolds-averaged Navier-Stokes (RANS) models, especially linear eddy viscosity models, struggle to predict this type of flow. Since large eddy simulation (LES) models can be considerably more expensive, hybrid turbulence models are of interest. These hybrid models rely on RANS modeling of all attached flow regions, therefore the first study of this paper confirms that a grid independent Spalart-Allmaras turbulence model predicts the flow well in all but separated region near the wing/fuselage junction. Grid independence is verified by performing a uniform refinement of an unstructured grid boundary layer mesh employing 71 million elements resulting in a 567 million element mesh. The second study undertaken in this paper is a preliminary Delayed Detached Eddy Simulation (DDES) on the 71 million element mesh to obtain an initial assessment of the prediction of such a hybrid model even before additional resolution is added to the separated flow regions that switch over from RANS to scale-resolving mode. Simulation predictions of surface pressure, velocity profiles, and oil flow separation are compared with those from the experiment and discussed.