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Title:  Dynamics Of Early Stages Of Transition In A Laminar Separation Bubble 
Authors:  Suhas, Diwan Sourabh 
Advisors:  Ramesh, O N 
Keywords:  Laminar Boundary Layers Bubbles Transition Dynamics Smoke Flow Visualization Bubble Bursting Separation Bubbles  Instability Spatial Inviscid Instability Laminar Separation Bubble Parallel Flows 
Submitted Date:  Feb2009 
Series/Report no.:  G22933 
Abstract:  This is an experimental and theoretical study of a laminar separation bubble and the associated transition dynamics in its early stages. The separation of a laminar boundary layer from a solid surface is prevalent in very many flow situations such as over gas turbine blades (especially in the lowpressure turbine stage) and the wings of microaerovehicles (MAVs) that operate at fairly low Reynolds numbers. Flow separation occurs in such cases due to the presence of an adverse pressure gradient. The separated shear layer becomes unstable due to the presence of an inflection point and presumably transitions to turbulence rapidly. Eventually, there is reattachment back to the solid surface further downstream, if conditions are right. The region enclosed by the shear layer is called a laminar separation bubble and has been a subject of many studies in the past.
The present experiments have been conducted in a closedcircuit wind tunnel. A separation bubble was obtained on the upper surface of a flat plate by appropriately contouring the top wall of the tunnel. Four different techniques were used for qualitative and quantitative study viz. surface flow visualisation, smoke flow visualisation, surface pressure measurements and hotwire anemometry. Response of the bubble to both natural as well as artificial (impulsive excitation) disturbance environment has been studied.
Linear stability analyses (both OrrSommerfeld and Rayleigh calculations), in the spatial framework, have been performed for the mean velocity profiles starting from an attached adverse pressure gradient boundary layer all the way up to the front portion of the separation bubble region (i.e. up to the end of the deadair region where linear evolution of disturbances could be expected). The measured velocity profiles (both attached and separated) were fitted with analytical model profiles for doing stability calculations.
A separation bubble consists of aspects of both wallbounded and wallfree shear layers and therefore both viscous and inviscid mechanisms are expected to be at play. Most of the studies in the literature point to the inviscid instability associated with the shear layer to be the main mechanism. The main aim of the present work is to understand the exact origin of the primary instability mechanism responsible for the amplification of disturbances. We argue that at least up to the front portion of the bubble, the instability mechanism is due to the inflectional mode associated with the mean velocity profile. However, the seeds of this inviscid inflectional instability could be traced back to the attached boundary layer upstream of separation. In other words, the inviscid inflectional instability of the separated shear layer should be logically seen as an extension of the instability of the upstream attached adversepressuregradient boundary layer. This modifies the traditional view that pegs the origin of the instability in a separation bubble to the free shear layer outside the bubble with its associated KelvinHelmholtz mechanism. Our contention is that only when the separated shear layer has moved considerably away from the wall (and this happens near the maximum height of the mean bubble) that a description by KelvinHelmholtz instability paradigm with its associated scaling principles could become relevant. We also propose a new scaling for the most amplified frequency for a wallbounded shear layer in terms of the inflection point height and the vorticity thickness, and show its universality.
Next, we theoretically investigate the role played by the recirculating region of the separation bubble in the linear instability regime. In the recirculating region near the wall, associated with the socalled wall mode, the production of disturbance kinetic energy is found to be negative. This is a very interesting observation which has been cursorily noted in earlier studies. Here we show that the nearwall negative production region exerts a stabilising influence on the downstream travelling disturbances. A theoretical support for such a mechanism to exist close to the wall is presented. It is shown that the stabilising wallproximity effect is not a peripheral aspect but has a significant effect on the overall stability especially for the waves close to the upper neutral branch. We demonstrate the appropriateness of inviscid analysis for the stability of the separated flow velocity profile away from the wall, by comparing the numerical solutions of Rayleigh and OrrSommerfeld equations. Following this, the analytical consequences of the Rayleigh equation such as the inflection point criterion and the Fjortoft criterion are derived for the wallbounded inflectional velocity profiles. Furthermore, we also discuss the relevance of the negative production region towards flow control and management for the wallbounded flows.
It appears fruitful to divide the separation bubble region into two parts with respect to the nature of disturbance dynamics: one outside the mean dividing streamline (which behaves as an amplifier) and the other inside the bubble corresponding to the recirculating region (having oscillator type characteristics). To explore the oscillatorlike behaviour of the bubble further, we have carried out spatiotemporal stability analysis of the reversed flow velocity profiles and determined the conditions for the onset of absolute instability. We contend that the presence of the negative production region for the upstream travelling waves has a restraining effect arresting the tendency of the flow (both wallfree and wallbounded) to become absolutely unstable and thereby requiring a particular threshold of the backflow velocity to be crossed for its realisation. Moreover, the delay in the onset of absolute instability for a wallbounded profile as compared to a free shear layer is attributed to a certain ‘negativedrag’ effect of the wall on the overall flow which increases the group velocities for the wallbounded flows.
A related theme in the literature regarding the dynamics of laminar separation bubbles is the socalled ‘bursting’ of the bubble wherein there is a sudden increase in the length and height of the bubble as some critical conditions are reached. Bubbles before bursting are termed as ‘short’ bubbles and those after bursting as ‘long’ bubbles. In this work, we provide a criterion to predict bursting which is a refinement over the existing criteria. The proposed criterion takes into account not just the length of the bubble but also the maximum height and it is shown to be more universal in differentiating short bubbles from the long ones, as compared to the other criteria. We also present a hypothesis regarding the sequence of events leading to bubble bursting by relating its onset to the instability of the recirculating region. For this we observe that as the amount of backflow velocity is increased for a reversed flow velocity profile, the inflection point moves inside the mean dividing streamline and this happens before the onset of absolute instability. This causes a vorticity maximum to develop inside the recirculating region which could lead to the instability of the closed streamlines with respect to twodimensional cylindrical disturbances. The actual bursting process may be expected to involve nonlinear interactions of the disturbances and the long bubble could be a nonlinearly saturated state of the instability of the recirculating region.
In order to explore the threedimensionality associated with the bubble, extensive surface flow visualisation experiments have been performed. The surface streamline pattern is obtained for the entire span of the plate for three different freestream velocities. The patterns have been interpreted using topological ideas and various critical points have been identified. It is shown that the arrangement of critical points satisfies the ‘index theorem’ which is a topological necessity and the streamline patterns are ‘structurally stable’. An interesting observation from these patterns is the presence of threedimensionality upstream of the separation line close to the wall even though the oncoming flow is nominally twodimensional. Using the critical point theory, we propose a hypothesis which could be used to construct a semiempirical model wherein the critical points are assigned with a quantity called ‘strength’ for determining the extent of upstream influence of a given separation line.
Finally, we derive a necessary condition for the existence of inviscid spatial instability in plane parallel flows. It states that for spatial instability the curvature of the velocity profile should be positive in some region of the profile. This includes Rayleigh’s inflection point theorem (which was proposed and proved by Rayleigh for temporal instability) as a special case. It thus provides a rigorous basis for applying the inflection point criterion to the flows in the framework of spatial stability theory (which we have used extensively in the present thesis). Moreover, the condition derived here is more general as it also includes velocity profiles with the curvature positive everywhere which are excluded by Rayleigh’s theorem in the temporal framework. An example of such a profile is presented (CouettePoiseuille flow with adverse pressure gradient) and it is shown that this flow is an exceptional case which is temporally stable but spatially unstable. Eigenvalue calculations as well as energy considerations suggest that the mechanism governing instability of this flow is inviscid and noninflectional in character. This is a new result which could have important implications in understanding the instability dynamics of parallel flows. 
URI:  http://etd.iisc.ernet.in/handle/2005/679 
Appears in Collections:  Aerospace Engineering (aero)

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