Computation of Flow Between Two Disks Rotating at Different Speeds

Disks 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 disk to that of the faster one then Γ=−1, 0 and +1 represents the three important cases of contra-rotating disks, rotor-stator systems and co-rotating disks, 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 disks 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 disk, 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 disks and a rotating core between. Where available, measured velocity distributions are in good agreement with the computed values.