Gas annular seals are commonly adopted for leakage control in turbomachinery applications. Honeycomb seals are attractive from the viewpoints of leakage control as well as rotordynamic stability. To improve our understanding of thermo-fluid-physics in such seals, a computational capability is developed for low Mach number, compressible, turbulent flows. The emphases of the present study include (i) development of an original numerical scheme with periodic boundary conditions for flows around repeated geometries, (ii) evaluation of a low Reynolds number version of the k-epsilon turbulence model suitable for the operating conditions of honeycomb seals, and (iii) 3-D computations to assess the implications of the numerical predictions for practical configurations including velocity, pressure, temperature characteristics and loss mechanisms.