E​RCOFTAC PC Belgium

Self-Sustained Oscillations in a Supersonic Cascade: Coupled Shock-Boundary Layer Dynamics

Authors: Ludovic TAGUEMA
(Cenaero France, Moissy-Cramayel, France)

Yves MARICHAL
(Safran Aero Booster, Liège, Belgium)

Andrea ROCCA, Michel RASQUIN, Thomas TOULORGE
(​Cenaero Belgium, Charleroi, Belgium)

Koen HILLEWAERT
(Aerospace and Mechanics Department, University of Liège, Belgium; Cenaero Belgium, Charleroi, Belgium)

Wall-resolved Large-Eddy Simulation (LES) using Cenaero’s high-order discontinuous Galerkin solver reveals strongly unsteady flow in a supersonic compressor cascade, with persistent selfsustained oscillations at 960 Hz. Shown are normalized density gradients over four blades (detached bow shocks, expansion fans, passage shocks, turbulent shocklets), followed by Machnumber contours and boundary-layer velocity profiles. The results demonstrate the absence of a steady-state solution for this operating condition. Note: Blade geometry hidden for confidentiality (Safran Aero Boosters proprietary).

Research Context and Industrial Motivation

This visualization originates from comprehensive research investigating shock-boundary layer interactions (SBLI) and self-sustained oscillations in supersonic turbomachinery, addressing critical knowledge gaps for next-generation Geared Turbofan (GTF) low-pressure compressor design. As traditional turbofan designs approach efficiency limits, supersonic blade configurations offer potential performance gains through reduced blade count and enhanced aerodynamic loading capabilities. However, the extension of design methodologies based on steady-state Reynolds- Averaged Navier-Stokes (RANS) approaches, typically used for subsonic cascades, to supersonic regimes rests on an unverified premise: that supersonic cascades admit physically meaningful steady-state solutions.

Computational Methodology

The visualization captures data from wall-resolved implicit Large Eddy Simulation (wr-iLES) of a supersonic compressor cascade at industrially-relevant conditions: inlet Mach number Min = 1.2 and inlet-chord Reynolds number Rec,in = 300,000. The computational campaign relied on highorder discontinuous Galerkin (DG) methods with polynomial degree p = 3, implemented in the ArgoDG solver developed at Cenaero.

The computational domain consists of a single blade prismatic passage with periodic boundaries in pitch and spanwise directions, with inlet and outlet planes positioned three chords upstream and downstream of the blade to isolate the flow from boundary effects. The unstructured hexahedral mesh contains approximately 61 million degrees of freedom, achieving wall-normal 1 resolution with y+ < 1 throughout the domain and satisfying wall-resolved LES requirements without wall modeling.

Key Findings

The investigation revealed that supersonic cascade flows exhibit fundamental, inherent unsteadiness that cannot be eliminated. Extended temporal integration over 120 bladepassage times shows no convergence toward steady state: the cascade operates in perpetual oscillatory motion as its natural flow condition. Spectral analysis of 5,400 probe signals identifies a dominant frequency f0 = 960 Hz (Strouhal number St = 0.121 based on chord length and inlet velocity) appearing ubiquitously across all monitored quantities: inlet/outlet mass flow rates, blade aerodynamic forces, reference plane measurements, and near-wall pressure fluctuations on both blade surfaces.

Three coupled physical mechanisms drive this behaviour and sustain cascade-wide oscillations:
(1) Shocklet formation and aggregation: Turbulent fluctuations in transitional boundary layers, combined with vortex shedding from the suction-side recirculation bubble and trailingedge region, generate small compression waves that steepen into shocklets as they propagate upstream through the passage. These disturbances coalesce with the passage normal shock, creating accumulated pressure perturbations exceeding 2500 Pa that periodically destabilize the shock system. Characteristic decomposition reveals upstream-propagating fluctuations (Δp−) dominating the passage interior, with shocklets originating predominantly from the aft region between the normal shock and trailing edge where vortex shedding is most intense.

(2) Recirculation bubble pressure surges: The suction-side SBLI induces a large separated shear layer (up to 25% chord) that undergoes periodic expansion-contraction cycles. When the bow shock standoff reaches maximum values, reduced adverse pressure gradients allow the bubble to expand until violent eruption ejects low-momentum fluid into the main flow. These breathing cycles produce pressure surges up to 2500 Pa that propagate upstream through the SBLI region, directly loading the bow shock and contributing to its periodic repositioning. Coherent vortical structures continuously shed from the separation region, propagating downstream to interact with the trailing-edge shock system and wake, further modulating the passage shock dynamics through their acoustic radiation.

(3) Unique incidence feedback loops: Supersonic cascades with subsonic axial velocity exhibit a geometric constraint: for given geometry and inlet Mach number, only one inlet flow angle yields spatially periodic flow. Blockage or mass flow fluctuations alter the required inlet angle, forcing cascade-wide adjustment via bow shock repositioning. Pressure waves from shocklet coalescence, recirculation surges, and vortex shedding propagate upstream along bow shock corridors, where locally subsonic post-shock conditions permit acoustic communication despite globally supersonic inlet flow, enforcing sequential realignment that couples blade passages into synchronized oscillation.

Selected Publications

1. Taguema, L., Marichal, Y., Rocca, A., Rasquin, M., Hillewaert, K., and Toulorge, T.: “High-Fidelity Analysis of Shock-Boundary Layer Interactions and Periodic Flow Unsteadiness in a Supersonic Compressor Cascade,” ASME Turbo Expo 2026, GT2026-175179 (submitted, under revision).
2. Taguema, L., Marichal, Y., Rasquin, M., Hillewaert, K., and Toulorge, T.: “Multi-Fidelity Assessment of Supersonic Cascade Unsteadiness,” ERCOFTAC DLES-15 Workshop, 2026 (submitted).
3. Partial results presented: SU2 Conference 2024 and 2025.