A local thermal nonequilibrium analysis was made to assess the potential use of bi-disperse porous walls for a transpiration cooling system. A three-energy equation model successfully used for the transient thermal analysis of bi-disperse packed bed thermocline storage systems was introduced to investigate various heat transfer aspects of transpiration cooling through a bi-disperse porous wall made of combination of large and small particles. Three independent energy balance equations, namely, the energy equation of the coolant gas phase, that of the solid phase of large particles, and that of small particles are coupled with one another to obtain a set of exact expressions for all three individual temperature distributions across the porous wall for given thermal boundary conditions of the third kind. It has been revealed that the solid wall temperature of the bi-disperse porous wall stays lower than that of the monodisperse porous wall in the high Peclet number range, resulting in a higher overall cooling efficiency for a given blowing flowrate. Furthermore, the analysis provides a suitable range of the Peclet number, under which the transpiration cooling should be operated to suppress excessive heat loss to the coolant reservoir at the same time to ensure a high overall cooling efficiency.

In the present study, we conducted a conjugate heat transfer (CHT) analysis for double-wall cooling with impingement and effusion, incorporating various types of ribs, using the Reynolds-averaged Navier–Stokes (RANS) method and the modified shear stress transport (SST) turbulence closure model (SST-KIC), accounting for the Kato-Launder modification (K), intermittency (I), and crossflow (C) transition effects. We comprehensively discussed the impact of slit type (parallel, inclined, convergent, and divergent), open-area ratio (β = 5%, 20%, and 40%), and jet Reynolds number on the turbulent flow and heat transfer in a double-wall cooling with slit ribs. Our findings indicated that the introduction of slit ribs significantly improved heat transfer and its uniformity on the target wall, albeit with a slight increase in pressure loss. The overall Nusselt number and thermal-hydraulic performance (THP) in cases with slit ribs gradually decreased with β, yet remained up to 17% and 13% higher than those observed on a smooth target wall. Notably, the open-area ratio of the slit rib exhibited a more pronounced effect on heat transfer over the target plate. For the divergent slit rib within the Reynolds number range of 4000–16 000, the heat transfer enhancement ratio reached the highest value at β of 0.05. In addition, we computed the entropy production caused by fluid friction and heat transfer, as well as the overall entropy production in double-wall cooling at different β and Re. The analysis revealed that the slit rib target plate performed better than the solid rib target plate, showing a distinct advantage in terms of total entropy production.

Diffusion shaped holes are widely used on aero-engine turbine blades for film cooling. The effect of the spanwise-expansion angle and spanwise width of the hole exit on the film cooling effectiveness of diffusion shaped holes was investigated in this study. The film cooling effectiveness was obtained through the pressure-sensitive paint (PSP) technique on a plate model at five momentum ratios (0.11, 0.43, 0.97, 1.73, and 2.71). A numerical simulation was performed to analyze the flow mechanism. The laid-back fan-shaped (LBFS) holes and the fan-shaped holes with three spanwise-expansion angles (FS-A: 7 deg, 11 deg, and 15 deg) and with three spanwise widths of the hole exits (FS-B: 1.7d, 2.3d, and 3.4d) were used for the study. The results revealed that the film cooling effectiveness of fan-shaped holes (FS-A) increases monotonically as the spanwise-expansion angle increases, while the film cooling effectiveness of the LBFS holes increases first and then decreases as the spanwise-expansion angle increases. However, the film cooling effectiveness of the two kinds of holes (LBFS and FS-B) both increase first and then decrease with the increase of the spanwise width of hole exit. The mainstream intrusion occurred at the same spanwise width of the hole exit of 3.4d for both kinds of holes. The laid-back fan-shaped hole possessed high resistance to cooling performance decline. The importance of the spanwise width of the hole exit as a key parameter was emphasized in this study.