Thermo-hydraulic limits of streamwise rib height grading in high-aspect-ratio cooling channels

Rib turbulators are the standard means of enhancing internal cooling in gas turbine blades, and a recent line of work proposes grading the rib height along the flow so that turbulence is generated where the coolant is coldest. The degree of grading over which this remains beneficial has not been established. The present study quantifies that range for a high-aspect-ratio (AR = 4) rectangular channel with five square ribs mounted on a uniformly heated wall. The grading is described by a single parameter, the rib height ratio RHR, defined as the ratio of the first to the last rib height at a fixed pitch and a fixed downstream rib height, and five configurations from RHR = 1 (uniform) to RHR = 5 are compared on an otherwise identical geometry. Three-dimensional steady RANS simulations with the SST k–ω model are performed for Reynolds numbers from 2 × 10⁴ to 8 × 10⁴. Increasing RHR raises the normalised Nusselt number monotonically, from 1.29 to 1.42 at Re = 8 × 10⁴, but the normalised friction factor rises from 2.05 to 4.30 over the same range, an increase an order of magnitude larger. Both performance criteria therefore fall monotonically with RHR: at Re = 8 × 10⁴ the thermal performance factor η₁ decreases from 1.016 to 0.870, so that under an equal-pumping-power constraint the uniform array outperforms every graded array examined. The flow field identifies the cause: beyond moderate grading the tall leading ribs cease to act as discrete turbulence promoters and collectively deflect the bulk flow away from the heated wall, lifting the shear layer off the surface and leaving a low-momentum, low-Nusselt-number region downstream that offsets much of the upstream gain. Applying η₁ ≥ 1 as a design criterion yields an admissible upper limit that contracts from RHR = 4.41 at Re = 2 × 10⁴ to RHR = 1.36 at Re = 8 × 10⁴. Height grading therefore remains attractive where heat transfer rather than pumping power is the binding constraint, since it delivers up to 10% more heat transfer, but the admissible degree of grading must be selected for the design Reynolds number.