A universal prediction of stall onset for airfoils at a wide range of Reynolds number flows
Abstract
The inception of leadingedge stall on twodimensional, smooth, thin airfoils at various Reynolds number flows in the range O(103) to O(107) is investigated by an asymptotic approach and numerical simulations. The theory demonstrates that a subsonic flow about a thin airfoil can be described in terms of an outer region, around most of the airfoil chord, and an inner region, around the nose, that asymptotically match each other. The flow in the outer region is dominated by the classical thin airfoil theory. Scaled coordinates and a modified Reynolds number ReM, both based on the nose radius of curvature, are used to account for the nonlinear behavior and extreme velocity changes in the nose region, where stagnation and high suction occur. It results in a reducedorder model problem of a uniform, compressible, viscous flow past a semiinfinite canonic parabola. The inner farfield is governed by a circulation parameter A that is related to the airfoil's angle of attack, nose radius of curvature, thickness ratio, camber, and flow Mach number. The model parabola problem is solved numerically for various ReM and A using two methods. The first technique uses the steady ReynoldsAveraged NavierStokes (RANS) equations with the SpalartAllmaras turbulence model for simulating moderate to high ReM flows. The second method applies direct numerical simulation (DNS) of the unsteady and incompressible NavierStokes equations for low to moderate ReM flows. In both methods, the critical value As is determined when a large separation zone first appears in the nose flow and the minimum pressure coefficient suddenly drops. The change of As with ReM is determined and these values indicate the onset of stall on the airfoil. The DNS results show that As decreases with ReM for ReM < ∼250, in agreement with Marginal Separation Theory (MST). However, calculations display the appearance of unsteady waves above a limiting value ReMcrit ∼250, where A s reaches a minimum of ∼1.55. For ReM > 250, these waves delay in the mean flow the onset of large separation to values of A s that increase with ReM, in contrast to MST predictions, and overlap the As RANS predictions. The RANS computed A s shows a continuing increase with ReM and good agreement for a wide range of Reynolds number with much available experimental data for the stall of airfoils. The simulations also exhibit the existence of stall hysteresis loops between As and a reattachment value of A, which is greater than MST stall prediction for a given ReM . The reducedorder model is also applied to predict the onset of leadingedge sheet cavitation on thin, smooth, hydrofoils. The approach determines the minimum pressure coefficient and a universal criterion for the critical cavitation number as function of hydrofoil's geometry, Reynolds number, and fluid thermodynamic properties. Predictions show agreement with results from available experimental data.
 Publication:

Ph.D. Thesis
 Pub Date:
 2009
 Bibcode:
 2009PhDT.......146M