Supersonic jet impingement on concave surfaces

The aeroacoustic resonance of round supersonic jets impinging on concave surfaces is investigated using compressible large-eddy simulations, vortex-sheet modelling, and Powell's feedback-loop analysis. The choked jets operate at an ideally expanded Mach number of $1.56$ and a Reynolds number of $6\times10^4$. Six geometries are considered: two flat plates at $L/D=2.08$ and $2.58$, where $L$ is the nozzle-to-wall distance and $D$ the nozzle exit diameter, and four Gaussian concave surfaces of fixed depth and indentation spread $\sigma\in\{0.4,0.8,1.6,4.0\}$. As the indentation narrows, the primary-tone amplitude increases by up to $23\,\mathrm{dB}$ relative to the flat-wall reference at $L/D=2.6$, together with larger wall-pressure fluctuations and moments. A Powell-Tam source-transfer budget attributes this amplification to increased Mach-disk source amplitude and more efficient return of the upstream feedback wave to the nozzle. The stronger upstream-propagating waves are consistent with acoustic focusing by the concave wall. For the helical cases, the measured frequencies and radial eigenfunctions agree closely with the guided jet mode predicted by the vortex-sheet model, supporting its role in closing the upstream feedback path. The same selection is recovered for concave and flat walls alike, so this tone is governed by the shear-layer profile of the equivalent ideally expanded jet rather than by the wall geometry. The axisymmetric frequencies, by contrast, coincide with no guided-mode branch and appear instead to follow Powell's classical loop-length criterion. The results identify distinct frequency-selection mechanisms for helical and axisymmetric screech and demonstrate that wall curvature provides effective control of screech amplitude and surface loading.