The research, led by Xiaolong Zhang of Nanjing University of Aeronautics and Astronautics together with colleagues including Hao Wang of Rongtong Aeroengine Technology and corresponding author Ning Ge, tackles a problem that has challenged engineers since the earliest scramjet experiments of the 1990s. When a shock wave strikes a boundary layer—the thin layer of slowed air hugging a surface—it can thicken that layer dramatically, or even force it to separate from the wall entirely. For film cooling, this is a double-edged sword: a thicker boundary layer might seem to offer more insulation, but separation bubbles create recirculating hot gas that can strip away the coolant film and expose the wall to searing mainstream temperatures. Understanding precisely where and how this happens is essential for designing cooling schemes that survive in hypersonic propulsion systems.

To capture these interactions, the team employed a hybrid turbulence modeling strategy called the Stress-Blended Eddy Simulation, or SBES, coupled with a fifth-order weighted essentially non-oscillatory scheme known as WENO-ZQ. The approach is a compromise between computational necessity and physical fidelity. Full large-eddy simulation, which resolves nearly all turbulent eddies, is extraordinarily expensive for the complex geometries and high Reynolds numbers of engine-relevant flows. Standard Reynolds-averaged methods, meanwhile, average away the very unsteady structures—vortex rings, shear-layer instabilities, separation bubbles—that govern film cooling performance. SBES blends the two: it runs in RANS mode near the wall where turbulence is dominated by small-scale stresses, and switches smoothly to LES mode in the outer regions where large, energy-containing eddies matter. The fifth-order WENO-ZQ scheme, developed originally by Zhu and Qiu, provides the shock-capturing sharpness needed to resolve discontinuities without spurious oscillations.

The validation of this numerical toolkit was itself a significant contribution. The researchers demonstrated that the SST–SBES combination could accurately reproduce the vortex structures and their temporal evolution within the film cooling domain—structures such as the counter-rotating vortex pair that lifts coolant off the wall, the horseshoe vortices that wrap around the jet as it emerges, and the hairpin vortices that trail downstream. These vortical structures are the machinery of mixing: they determine whether the cool air stays pressed against the wall where it protects the surface, or gets churned into the hot mainstream where it is wasted. A turbulence model that cannot capture them cannot be trusted to predict cooling effectiveness, which is precisely why the team invested effort in establishing the method’s resolution and accuracy before drawing physical conclusions.

The geometry at the heart of the study is the 7-7-7 shaped hole, a design whose cross-section expands laterally and vertically in a stepped fashion, resembling a dustpan laid into the surface. Shaped holes of this kind were developed to combat the fundamental weakness of cylindrical holes: the strong counter-rotating vortex pair that lifts the coolant jet away from the wall. By diffusing the jet exit, the shaped hole reduces the jet’s vertical momentum and spreads the coolant laterally, improving coverage. But shaped holes were largely characterized in subsonic conditions. What happens when a shock wave impinges upstream of such a hole, in a supersonic mainstream, remained poorly quantified—especially at different blowing ratios, the ratio of coolant momentum to mainstream momentum.

The team simulated a supersonic flat-plate configuration with the dustpan-shaped hole, examining blowing ratios of 0.5 and 0.65. The first major finding concerns the shock–boundary layer interaction itself. When the shock strikes the incoming boundary layer upstream of the hole, it thickens the layer and can induce a separation bubble—a pocket of recirculating flow detached from the wall. Interestingly, the blowing ratio, which changes the character of the jet emerging from the hole, had only a limited effect on the mainstream pressure distribution. In other words, the shock system upstream behaves largely as if the cooling jet were not there, decoupling the external aerodynamics from the internal cooling problem in a way that simplifies how engineers can think about the two phenomena.

The second key finding is more subtle and concerns the region near the hole’s trailing edge. At the lower blowing ratio of 0.5, the jet does not fill the expanded dustpan exit uniformly. Instead, aerodynamic bulges form within the jet—localized protrusions of high-speed coolant that act like small compression surfaces, generating compression waves of their own. These waves, the study found, intensify localized boundary layer thickening near the trailing edge of the hole, compounding the disturbance already created by the upstream shock. At the higher blowing ratio of 0.65, however, the jet has enough momentum to fill the expanded exit more completely, smoothing out the bulges and alleviating this additional thickening. The practical implication is striking: simply increasing the coolant supply can suppress a secondary shock-generating mechanism, though at the cost of more compressed air diverted from the compressor.

Perhaps the most elegant results come from spectral analysis—the turbulence equivalent of listening to the flow’s frequency signature. The researchers placed monitoring points upstream, midstream, and downstream of the interaction and examined the power spectra of the pressure fluctuations. Upstream and at midstream locations, the spectra displayed a distinctive −7/3 power-law scaling, a slope steeper than the classical Kolmogorov −5/3 law of inertial-range turbulence. The team attributes this anomalous scaling to two mechanisms working together: the compression imposed by the shock wave, which compresses turbulent eddies and steepens their spectra, and the shear-layer instability driven by the interaction between the jet and the mainstream. The −7/3 slope has precedent in pressure spectra of turbulent free shear flows, and its appearance here ties the shock-perturbed cooling flow into a broader family of compressible turbulent phenomena.

Downstream, however, the story changes. The spectra at far-field monitoring points transition toward the classical −5/3 inertial subrange slope, indicating that the violent, shock-dominated disturbances have decayed and the flow has relaxed into a state where turbulent mixing between the jet and the mainstream has saturated. In physical terms, the shock’s fingerprint fades with distance, and the jet-mainstream system settles into ordinary turbulent mixing. This spectral evolution gives engineers a diagnostic tool: by measuring pressure fluctuations at a surface, one can infer how far downstream the shock’s influence on the cooling film persists, and where the protective layer has either recovered or been fully consumed by mixing.

The study, funded by China’s National Science and Technology Major Project, arrives at a moment when hypersonic flight programs worldwide are pushing film cooling technology into regimes where shock interactions are unavoidable rather than exceptional. In a scramjet combustor, shock trains and expansion fans are everywhere, and cooling holes sit directly in their path. The finding that higher blowing ratios can suppress jet-induced compression waves offers a concrete design lever, while the demonstrated fidelity of the SBES–WENO-ZQ framework provides a validated virtual testbed for exploring hole geometries, spacing, and coolant conditions without costly wind-tunnel campaigns. As shaped holes migrate from subsonic turbines into supersonic combustors, studies like this one are building the quantitative foundation that turns a fragile cool blanket into engineering that can be trusted at Mach 5 and beyond.

Subject of Research: Shock wave interaction with shaped-hole film cooling in supersonic boundary layers

Article Title: SBES-Based Study on Aerodynamic Impacts of Upstream Shock Waves on Film Cooling from Dustpan-Shaped Holes

Article References: Zhang, X., Wang, H., Wu, X., & Ge, N. (2026). SBES-Based Study on Aerodynamic Impacts of Upstream Shock Waves on Film Cooling from Dustpan-Shaped Holes. International Journal of Aeronautical and Space Sciences. https://doi.org/10.1007/s42405-026-01272-x

Image Credits: AI Generated

DOI: 10.1007/s42405-026-01272-x

Keywords: film cooling, shock wave, SBES, dustpan-shaped hole, supersonic flow, boundary layer separation, turbulence modeling, WENO scheme, spectral analysis, scramjet, gas turbine, aerodynamics