A Reynolds-averaged Navier-Stokes (RANS) solver developed in-house was used to simulate grazing channel flow past single and multiple cavities. The objective of this investigation was to predict fluid instabilities in hole-pattern stator seals. The numerical results generated with the RANS solver showed good agreement with those obtained using a commercial Large Eddy Simulation (LES) code. In addition, the numerical results agreed well with experimental data. Rossiters formula, a popular semi-empirical model used to predict frequencies of hole-tone acoustic instabilities caused by grazing fluid flow past open cavities, was modified using the RANS solver results to allow for its application to channel flows. This was done by modifying the empirical constant , the ratio of vortex velocity and the freestream velocity. The dominant frequencies predicted using the Rossiters formula with the new value matched well the experimental data for hole-pattern stator seals. The RANS solver accurately captured the salient features of the flow/acoustic interaction and predicted well the dominant acoustic frequencies measured in an experimental investigation. The flow solver also provided detailed physical insight into the cavity flow instability mechanism.