15th European Conference on Turbomachinery Fluid dynamics & Thermodynamics

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Guglielmo Vivarelli  - Imperial College London, United Kingdom
Joao Anderson Isler - Imperial College London, United Kingdom
Francesco Montomoli - Imperial College London, United Kingdom
Spencer Sherwin - Imperial College London, United Kingdom
Paolo Adami - Rolls-Royce Deutschland
Raul Vazquez-Diaz - Rolls-Royce plc


During the early phases of the turbomachinery design process, it is often the case that various simplifications and assumptions can be made when attempting to understand the boundary layer behaviour subject to pressure gradients. For example, simplified boundary-layer models, which neglect the effect of surface curvature and/or density variations, while retaining the non-dimensional pressure distribution over the suction surface, can be employed to appreciate losses incurred to understand the flow behaviour over gas turbine components. The objective of this paper is understand and quantify the implication of those simplifications on this type of flow. The effect of the compressibility on a boundary layer over a flat plate under representative pressure gradient was investigated and presented in a separate paper. To gain further insight into the effect of this simplification, here we extend our previous work to a more representative case. A set of 2D fan profiles, representing the pressure distribution found at 70% and 90% span of a modern Low Speed fan for a UHBP turbofan, are analysed at cruise conditions. In order to investigate the effects of compressibility the two profiles were redesigned to achieve exactly the same non-dimensional pressure distribution over the suction side at incompressible conditions. The resulting boundary layer quantities will be compared explaining the necessary scaling required along with the reasons behind the discrepancies, such as the effect of density variations. To investigate the curvature ramifications, the results from these fan profiles will be compared with those of a flat plate with the same non-dimensional pressure gradient subject to the same high-Reynolds number incoming flow. The second test-case considered is a flat plate with a strong adverse pressure gradient subject to a high-Reynolds number incoming flow. This particular geometry is the same for both compressible and incompressible computations as the peak Mach number is just shy of the 0.3 threshold in a restricted region outside the boundary layer. In this case, the flow behaviour is much more complex: to start with, the adverse pressure gradient causes a separation bubble to appear. Viscous instabilities in the form of Tollmien–Schlichting waves materialise along the free-flow/bubble interface; these are then followed by Kelvin-Helmholtz inviscid instabilities in the form of 2D cylindrical structures. The latter interact with the secondary vortical instabilities ejected from the bubble. Consequently, turbulent transition develops downstream. For this particular geometry, the comparison will detail the reasons behind the separation point and any turbulent transition differences. Similarities in terms of the overall behaviour will be highlighted, thus allowing us to determine whether the incompressible boundary layer assumption may be valid and what sort of inaccuracies are being introduced. All test-cases will be analysed by means of the spectral/hp-element flow solver Nektar++. This is a high-order finite-element method type code having both compressible and incompressible formulations. Employing this kind of software will allow to reach Direct Numerical Simulation range for all the simulations carried out in this work, that would otherwise be unobtainable with lower-order discretisations typically found in industry.


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