RANS models in CFD are used to predict the liner wall heat transfer characteristics of a gas turbine annular combustor with radial swirlers, over a Reynolds number range from 50,000 to 840,000. A three dimensional hybrid mesh of around twenty five million cells is created for a periodic section of an annular combustor with a single radial swirler. Different turbulence models are tested and it is found that the RNG k-e model with swirl correction gives the best comparisons with experiments. The Swirl number is shown to be an important factor in the behavior of the resulting flow field. The swirl flow entering the combustor expands and impinges on the combustor walls, resulting in a peak in heat transfer coefficient. The peak Nusselt number is found to be quite insensitive to the Reynolds number only increasing from 1850 at Re=50,000 to 2200 at Re=840,000, indicating a strong dependence on the Swirl number which remains constant at 0.8 on entry to the combustor. Thus the peak augmentation ratio calculated with respect to a turbulent pipe flow decreases with Reynolds number. As the Reynolds number increases from 50,000 to 840,000, not only does the peak augmentation ratio decrease but it also diffuses out, such that at Re=840,000, the augmentation profiles at the combustor walls are quite uniform once the swirl flow impinges on the walls. It is surmised with some evidence that as the Reynolds number increases, a high tangential velocity persists in the vicinity of the combustor walls downstream of impingement, maintaining a near constant value of the heat transfer coefficient. The computed and experimental heat transfer augmentation ratios at low Reynolds numbers are within 30-40% of each other.