Computation of Heat Transfer for Two Discs Rotating at Different Speeds

Computations have been conducted for the case where one rotating disc is heated and the other surfaces are adiabatic. Discs rotating at different speeds are found in the internal cooling-air systems of engines, and it is convenient to define Γ as the ratio of the angular speed of the slower (adiabatic) disc to that of the faster (heated) disc. A finite-volume, axisymmetric, elliptic, multigrid solver, employing a low-Reynolds-number k-ε turbulence model, previously used for a complementary study of the flow structure, has been validated using available heat transfer measurements for Γ = −1, 0 and +1. The effect of Γ (for the range −1 ≤ Γ ≤ +1) on heat transfer is then considered for a generic case in which the rotational Reynolds number, Re_φ, is 1.25 × 10⁶. (Although this is much lower than the values found in practice, the magnitude of the coolant flow rate was chosen to produce an engine-representative flow structure.) Theoretical values of the adiabatic-disc temperature are in reasonable agreement with computed values for Γ > 0. In the source region, at the smaller radii, there is no effect of Γ on the local Nusselt numbers, Nu, which are consistent with a free-disc correlation. For the average Nusselt numbers, Nu_av, the Reynolds analogy shows that the ratio of Nu_av/Re_φC_m, where C_m is the moment coefficient, should be equal to a constant value of 0.259. For Γ ≥ 0, the computed value of this “constant” is within 7% of the theoretical value.