Boundary-layer instability on rotating cones: An experiment-based exploration

Boundary-layer instability induces spiral vortices on rotating cones. As they grow along the cone, the vortices enhance mixing of high- and low-momentum fluid, and subsequently, cause the boundary-layer to transition into a turbulent state. This transition process is scientifically enticing as it is one of the classical problems in fluid mechanics. In practice, the transitions of rotating cone boundary-layer are relevant in several engineering applications, including rotating nose-cones of aero-engines.

The instability-induced spiral vortices on rotating aero-engine-nose-cones are expected to influence the aerodynamics at the fan root. This will potentially affect the loss mechanism at junctions between fan blades and the hub (the central rotating body of the engine, including the nose-cone). Accurate assessment of these losses requires knowing the boundary-layer instability behaviour on rotating cones in aero-engine-like flow conditions.

The past literature on this classical instability problem has only focused on low-speed (low-Reynolds number incompressible) axisymmetric inflow conditions. In reality, aero-engine-nose-cones often experience high-speed (high-Reynolds number compressible) inflow during a cruise. Moreover, several concepts of future-aircraft feature engines embedded in the airframe, or engines with ultra high bypass ratio with short nacelles. Owing to the associated inflow distortions, the nose-cones of these engines will experience non-axisymmetric inflow. However, limitations of the past experimental techniques pose hurdles in investigating the boundary-layer instability on rotating cones in non-axisymmetric as well as high-speed inflows.

This dissertation explores the boundary-layer instability on rotating cones with the inflow conditions pertaining to a typical aero-engine, i.e. non-axisymmetric as well as high-speed inflow. First, an experimental method is developed to measure the coherent flow structures on rotating cones. This method uses infrared thermography (IRT) with proper orthogonal decomposition (POD) to detect the thermal footprints of the spiral vortices on rotating cones. The POD modes are selectively used to reconstruct different instability-induced flow features. For this selection, a new criterion is formulated to determine the physical admissibility of the POD modes for reconstructing the flow-feature of interest. This method overcomes the limitations of the past experimental methods and has allowed quantitative measurements of spiral vortex growth, angle and azimuthal number, for the first time in complex flow environment, i.e. axial as well as non-axial inflow and high-speed inflow.

The asymmetry of the non-axial inflow has been found to delay the spiral vortex growth on the investigated case of a rotating slender cone (half-cone angle ψ=15º). Here, the spiral vortex growth appears at higher local Reynolds number Re_l and local rotational speed ratio S compared to the axial inflow case at same operating conditions. It is postulated that the azimuthal asymmetry of the flow conditions (local Re_l and S) disturbs the azimuthal coherence of the instability characteristics, i.e. angle and wavelength of the dominant mode. This inhibits the spiral vortex growth. However, at high rotational speed ratio S, when the instability characteristics approach the azimuthal coherence, the spiral vortices are found to be growing in the asymmetric flow field.

Furthermore, the dissertation extends the axial flow investigations from the most addressed case of a rotating slender cone of ψ=15º to the broader cones of ψ=22.5º, 30º, 45º, and 50º. Here, the boundary-layer instability mechanism changes from the centrifugal instability for slender cones ψ ≤ 30º to the cross-flow instability for the broad cones ψ ≥ 30º. The exact half-cone angle where this change occurs still remains unclear. While the past literature majorly focused on rotating slender cones in axial inflow, theoretical studies expressed the lack of experimental data for the rotating broad cones in axial inflow. This dissertation has provided this experimental data on the instability-induced spiral vortices for the rotating broad cones of ψ=45º and 50º in axial inflow.

The experimental method developed in this work has enabled studying the boundary-layer instability behaviour on rotating cones, for the first time in high-speed conditions, i.e. local Reynolds number Re_l =0—3 × 10⁶, rotational speed ratio S<1—1.5, and inflow Mach number M=0.5. These conditions are typically expected on the aero-engine-nose-cones during the transonic cruise of a large passenger aircraft (like A320, A350, etc.). These high-speed measurements revealed that the spiral vortices grow on the investigated rotating cones (ψ=15º, 30º and 40º) as expected from the low-speed studies. This confirms that the right circular type nose-cones of the transonic cruise aircraft will experience the spiral vortex growth in transitional boundary-layer.

The dissertation also conceptually discusses the potential effects of the spiral vortices on the fan aerodynamics. The spiral vortices are expected to influence the aerodynamics within the blade passage, especially, near the hub. Flow at the hub and fan-blade junction corner often separates on the suction side of the blade. This reduces the total pressure rise and efficiency of the engine. Presence of the spiral vortices is expected to affect the local aerodynamics at the hub, including the hub-corner separation, however, quantifying this effect needs further investigation. Furthermore, the dissertation has also shown a typical asymmetric flow field around the nose-cones when the fan is subjected to an inflow distortion. The fan-driven redistribution of the distorted inflow reduces the flow-field asymmetry near the nose-cone wall in the symmetry plane. This is a favourable condition for the spiral vortex growth.

Overall, this doctoral research has presented a new experimental approach to the classical problem of the boundary-layer instability on rotating cones. This has allowed furthering the fundamental knowledge about the instability-induced spiral vortex growth on rotating cones in following parameters: local Reynolds number Re_l =0—3 × 10⁶, rotational speed ratio S=0—250, inflow Mach number M=0—0.5, inflow incidence angle α=0º—10º and half-cone angle ψ=15º—50º.