Unsteady flows in cantilever compressor stator tip clearances and the effect of real tip geometry
Direct numerical simulations (DNS) of cantilevered stator blades are performed to identify the unsteady and turbulent flow structure within compressor tip flows. The simulations were performed with clearances of 1.6 and 3.2 percent of chord. The results show that the flow both within the gap and at the exit on the suction side are highly unsteady phenomena controlled by fine-scale turbulent structures. The signature of the classical tip leakage vortex is a consequence of time-averaging and does not exist in the true unsteady flow. The tip leakage flow is shown to be truly unsteady and poorly represented by a mean flow and added perturbation. Despite the complexity of the tip leakage flow, the flow within the tip gap is replicated using a validated quasi-three-dimensional model. This enables a wide range of quasi-3D DNS simulations to study the effects of blade tip corner radius and Reynolds number. Tip corner radius is found to radically alter the unsteady flow in the tip; it affects both separation bubble size and shape, as well as transition mechanisms in the tip flow. These effects can lead to variations in tip mass flow of up to 10 percent. Dissipation varies by a factor of 2 within the tip gap. A quantitative literature review reveals that the compressor efficiency lost with increase in tip gap height for computational studies are 35% lower than experimental studies. This loss of efficiency with increasing tip gap height is termed the "clearance derivative". Reynolds averaged Navier-Stokes (RANS) simulations are conducted and show that variation of blade stagger angle by 20 degrees and camber by 25 degrees causes a variation in clearance derivative of ±30%. The combined effect of blade geometry and radiused tip geometry results in a maximum clearance derivative in line with experimental studies. Thus real geometry is shown to be a likely cause for the remaining discrepancy in clearance derivative between experimental and computational studies. It is recommended that manufacturing processes are tightly controlled to ensure consistent tip geometry.
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