Project
Interaction of supersonic nozzle flows with solid objects in the context of vertical landing vehicle
Supersonic jets impinging on nearby surfaces generate complex shock structures, intense pressure fluctuations, acoustic emissions, and localized mechanical and thermal loads. These phenomena are particularly relevant to reusable launch vehicles and vertical take-off and landing systems, where high-energy exhaust jets interact with landing surfaces during terminal descent. Under certain operating conditions, a hydrodynamic–acoustic feedback loop develops between the nozzle shear layer and the impingement region, producing strong self-sustained oscillations and discrete-frequency tones. Despite extensive experimental and numerical research, the parameters governing the onset and suppression of these oscillations remain insufficiently understood. This project investigates the separate effects of nozzle pressure ratio, convective Mach number, and nozzle-to-plate spacing on the feedback mechanism. High-performance computing (HPC) is essential because resolving the three-dimensional, compressible, unsteady flow requires high-order numerical methods, fine computational grids, very small time steps, and simulations over sufficiently long physical times to obtain statistically and spectrally meaningful results.
Project Details
Project term
November 8, 2024–December 4, 2025
Affiliations
RWTH Aachen University
Institute
Chair of High Pressure Gas Dynamics
Principal Investigator
Methods
The project employed high-order numerical simulations using the in-house compressible-flow solver KICK. The three-dimensional compressible Navier–Stokes equations for a calorically perfect gas were solved numerically. Inviscid fluxes were discretized using a fifth-order Weighted Essentially Non-Oscillatory (WENO-5) finite-difference scheme with Lax–Friedrichs flux-vector splitting, while viscous terms were evaluated using a sixth-order central-difference scheme. Temporal integration was performed with an explicit third-order TVD Runge–Kutta method. Non-reflecting characteristic boundary conditions were applied to minimize artificial wave reflections that could interfere with the physical feedback mechanism. A systematic parametric study investigated nozzle pressure ratio, convective Mach numbers ranging from approximately 0.82 to 1.20, and nozzle-to-plate spacings of 30, 40, and 50 mm. Pressure signals recorded near the nozzle were analyzed using Fourier transforms to determine dominant frequencies and Strouhal numbers. Numerical schlieren visualizations based on density gradients were additionally used to examine shock structures and upstream-propagating acoustic waves.
Results
The simulations successfully reproduced both self-sustained pulsating and stable impinging-jet regimes. In the baseline pulsating configuration, numerical schlieren images revealed a complete feedback cycle in which disturbances generated near the impingement region propagated upstream toward the nozzle, excited the shear layer, and initiated subsequent downstream-travelling structures. The pressure spectrum contained a strong narrowband tone of approximately 15 kHz with a Strouhal number near 0.32. Changing the nozzle pressure ratio while maintaining the other parameters did not suppress the feedback mechanism and produced only limited changes in the dominant frequency. The convective Mach number was identified as the primary parameter governing the existence of self-sustained oscillations. Strong discrete tones occurred for subsonic convective Mach numbers, whereas the oscillations weakened as the convective Mach number approached unity. At and above approximately unity, the narrowband pulsations collapsed and the pressure spectra became predominantly broadband. Variations in nozzle-to-plate spacing primarily influenced the oscillation amplitude and selected frequency while the feedback mechanism remained active.
Discussion
The results demonstrate that the convective Mach number provides the clearest control parameter for the onset and suppression of self-sustained fluctuations in the investigated supersonic impinging jet. The transition from strong narrowband oscillations to broadband behavior near a convective Mach number of unity indicates that the ability of acoustic disturbances to propagate upstream and interact with the nozzle shear layer is fundamental to maintaining the feedback cycle. In comparison, nozzle pressure ratio primarily modifies the flow and shock structure without independently determining whether the feedback loop remains active. Plate spacing influences the effective propagation path, oscillation strength, and frequency selection, but its role is secondary to that of the convective Mach number. These findings provide useful guidance for controlling jet-induced acoustic and mechanical loads in reusable launch vehicles and other propulsion systems operating near surfaces. Future work should extend the investigated parameter range, employ higher-resolution simulations, examine additional nozzle and surface geometries, and compare the numerical predictions with experimental measurements.
Additional Project Information
DFG classification: 404-03 Fluid Mechanics
Software: ParaView
Cluster: CLAIX
Publications
Muhammad Bilal, Igor Klioutchnikov, Karl Alexander Heufer,
Numerical Investigation of Self-Sustained Fluctuations in a Supersonic Impinging Jet,
https://dx.doi.org/10.11159/icffts25.140, October 2025