Dynamics of Laminar Separation Bubbles on Low Reynolds Number Airfoils

Abstract

This is a detailed study on the aerodynamics of low Reynolds number airfoils. E387 airfoil that comes under the category of trailing-edge stall is used extensively in this study. The reduction in lift due to low Reynolds number effects can be modeled by the so-called viscous decambering of airfoils. In particular, we show this viscous decambering effect can be subsumed in the zero-lift angle term. It is further demonstrated that leading-edge camber angle plays an important role in explaining the stall characteristics of different airfoils. An attempt has been made to heuristically illustrate the different stall characteristics from thin-airfoil theory, and also to understand the basic design philosophy of low Reynolds number airfoils. Laminar Separation Bubble bursting is a deleterious phenomenon (in turbine blades, airfoils etc.) resulting in a loss of lift and increase of drag at relatively low Reynolds numbers. Bursting of a laminar separation bubble is characterised by a massive loss of lift in an airfoil; the surface pressure distribution departs significantly from the inviscid pressure distribution. There are some criteria in vogue in the literature to characterise onset of the bursting phenomenon. A relatively simple one-parameter criterion that was proposed in the past (Diwan, Chetan, and Ramesh 2006), has been found to be quite successful in characterising bursting and is well cited in the literature, including in unsteady flow contexts. This criterion is revisited and reassessed in the light of our present laminar separation bubble measurements over an Eppler 387 airfoil. Building on these foundations, the pursuit of a more robust bursting criterion that could also be predictive in nature, led to a new simple criterion. According to this, bursting is signalled by the ratio of the freestream velocity at reattachment to that at separation reaching a critical value of 0.86. New engineering correlations for length and height of laminar separation bubbles are also proposed. These correlations, along with the new bursting criterion, should be extremely useful in the design of low Reynolds number aerodynamic configurations. One of the central foci of the thesis is to study the phenomenon of bursting of laminar separation bubbles. A pertinent question to ask, on the physics of bursting, is whether the onset of bursting is coincident with absolutely instability? In this study, it is unequivocally shown that whether the bubble is short, long or transitional it is convectively unstable. The absolute instability characteristics are only seen momentarily in the unforced flow conditions, which change the state of the flow. Low frequency activity is prevalent in all the bubbles, but for the short bubble the amplitude of this activity is small compared to transitional and long bubbles. Impulse response shows absolute instability behavior in the low-frequency part of the flow-field for all the bubbles, reminiscent of some global mode oscillator. At (and post) bursting, the Reynolds shear stress ð€€€u0v0 is found to be negative in the initial region (close to the maximum time-averaged vorticity of the flow) of the transitional and long bubbles. Similar observations were reported by O¨ zkol,Wark, and Fabris (2007), Simoni, Ubaldi, and Zunino (2012), and Lengani et al. (2017). The effect of ð€€€u0v0 < 0 is that one of the turbulent kinetic energy production term, namely ð€€€u0v0 ¶U ¶y , becomes negative. This term is an important contributor to the overall rate of production of turbulent kinetic energy, and if it is negative, development of turbulence is compromised and the reattachment of the separated shear layer is delayed. This provides an explanation of the delayed reattachment for the long and transitional bubble post bursting. This is attributed to the increased curvature of the separated shear layer, and results in the runaway effect. Reduction of drag by passive flow control techniques, like roughness induced flow control, is investigated in this work. Roughness is found to be most effective when it is placed in the vicinity of the locus of inflection points of the base velocity profile. Analysis of receptivity of this flow by the solution of the adjoint Orr-Sommerfeld equation also supports the experimental observation. A more clear flow physics by consideration of the energetics is obtained from the inhomogeneous Orr-Sommerfeld equation. From this, the roughness seems to be effective where the inflection point is close to it and the shear-strain rate of the base flow at the wall is relatively high. This knowledge of passive control study is applied on the next study, where the relative impact of LSBs is investigated. The conventional wisdom says that LSBs deteriorate the performance of an aerodynamic system. Here, we systematically study the LSB in the Reynolds number range of 40,000 to 200,000. We find that for lower Reynolds number of 40,000 to 60,000, suppressing LSBs by tripping the boundary layer is beneficial to the overall performance of the airfoil. On the other hand, for Reynolds number of 100,000 and above, suppression of LSBs deteriorates the performance further. So, it seems that LSBs at these Reynolds numbers of 100,000 and 200,000 act as efficient switches of the oncoming laminar flow to transition to a turbulent flow, and it is not ideal in trying to suppress them by boundary layer trips. Whereas, for lower Reynolds number of 40,000 and 60,000, the trip is recommended as it is able to bring down the drag, and increase the lift on the airfoil to a considerable extent. The reduction in lift at low Reynolds numbers is attributed to the modification of circulation by the boundary layer vorticity. A non-zero pressure difference across the trailing-edge of an airfoil can be directly related to the integrated flux of counterclockwise vorticity emanating (diffusing) out of the wall. The loss in lift DCl is successfully correlated to this DCP across the trailing edge, and this seems to be true for long bubbles, and even fully separated post-stall flow situations.