Discs rotating at different speeds are found in the internal cooling-air systems of most gas turbines. Defining Γ as the ratio of the rotational speed of the slower disc to that of the faster one then Γ = −1, 0 and +1 represents the three important cases of contra-rotating discs, rotor-stator systems and co-rotating discs, respectively. A finite-volume, axisymmetric, elliptic, multigrid solver, employing a low-Reynolds-number k-ε turbulence model, is used for the fluid-dynamics computations in these systems. The complete Γ region, −1 ≤ Γ ≤ +1, is considered for rotational Reynolds numbers of up to Reφ = 1.25 × 106, and the effect of a radial outflow of cooling air is also included for nondimensional flow rates of up to Cw = 9720. As Γ → −1, Stewartson-flow occurs with radial outflow in boundary layers on both discs and between which is a core of nonrotating fluid. For Γ ≈ 0, Batchelor-flow occurs, with radial outflow in the boundary layer on the faster disc, inflow on the slower one, and between which is a core of rotating fluid. As Γ → +1, Ekman-layer flow dominates with nonentraining boundary layers on both discs and a rotating core between. Where available, measured velocity distributions are in good agreement with the computed values.

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