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 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 u0v0 < 0 is that one of the turbulent
kinetic energy production term, namely 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.