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Title:  High Reynolds Number Flow Over A BackwardFacing Step 
Authors:  Nadge, Pankaj M 
Advisors:  Govardhan, R N 
Keywords:  Fluid Mechanics High Reynolds Number Flow ThreeDimensional Vortical Structures Bubble Structures Backwardfacing Step Flow Flow Field Measurements Unsteady Threedimensional Flow Downstream Threedimensional Unsteady Structures Particle Image Velocimetry (PIV) Hotwire Anemometry Flow Separation Reynolds Number Bubble Schedule 
Submitted Date:  Dec2012 
Series/Report no.:  G25638 
Abstract:  Flow separation and reattachment happens in many fluid mechanical situations occurring in engineering applications as well as in nature. The flow over a backwardfacing step represents a geometrically simple flow situation exhibiting both flow separation and reattachment. Broadly speaking there are only two important parameters in the problem, the Reynolds number(Re) based on the step height(h),and a geometrical parameter, referred to as the Expansion ratio(ER), defined as the downstream channel height to the upstream channel height. In spite of the relative simplicity of this geometry, the flow downstream is quite complex. The main focus of the present work is to elucidate the unsteady threedimensional coherent structures present in this flow at large Re, Re>36,000,based on the step height(h). For this, we use velocity field measurements from Particle Image Velocimetry (PIV)in conjunction with hotwire anemometry measurements.
The timeaveraged structure of this flow is first studied in detail, including the effect of Reynolds number(Re) and Expansion Ratio(ER), on it. These studies show that at sufficiently large Re (Re>20,000), the reattachment length becomes independent of Re. The detailed internal structure of the separation bubble is also found to be independent of Re, but for Revalues that are relatively larger(Re>36,000). At large Re, the main effect of ER ,is found to be on the reattachment length, which increases with ER and saturates for ER values greater than about 1.8. The detailed internal structure of the separation bubble has been mapped at high Re and is found to be nearly the same for all ER, when the streamwise length is normalized by the reattachment length.
In order to elucidate the unsteady coherent vortical structures, PIV measurements are done in two orthogonal planes downstream of the backwardfacing step. These measurements are done for ER= 1.50 at large Re(Re=36,000) and in a large aspect ratio facility(AR= span length/step height= 24); the latter being important to avoid any effects due to spanwise confinement. In the spanwise plane parallel to the lower wall(xz plane),instantaneous velocity fields show counter rotating vortex pairs, which is a signature of the threedimensional vortical structures in this plane. Using conditional averaging, this counterrotating vortex pair signature is captured right from upstream of the step, to well after reattachment. Spatial correlations are used to get the length scale of these coherent vortical structures, which varies substantially from the attached boundary layer before separation to the region after reattachment. The variation of these structures in the crossstream (vertical) direction at reattachment and beyond gives an idea about their three dimensional shape. The circulation of these counterrotating pairs is measured from the conditionally averaged fields, and is found to increase with streamwise distance reaching normalized circulation values (Γ/Uoh) of about 0.5 around reattachment.
Velocity spectra downstream of the step show peaks corresponding to both the shear layer frequency(Stsl)and a relatively lower frequency that corresponds to largescale shedding from the separation bubble (Stb); the latter in particular being quasiperiodic. Small amplitude sinusoidal forcing at the shedding frequency(Stb) is applied close to the step, by blowing and suction, to make the quasiperiodic shedding more regular. Measurements show that this has a very small effect on both the mean separation bubble and on the counterrotating structures in the xz plane. This mild forcing however enables phase locked PIV measurements to be made which shows the bubble shedding phenomenon in the crossstream plane(side view or xy plane).
The phaseaveraged velocity fields show significant variations from phase to phase. Although there is some hint of structures being shed, from these phaseaveraged fields, it is not very clear. One of the primary reasons is the fact that the flow is effectively spanwise averaged, as the threedimensional structures are not locked in the spanwise direction. To get a three dimensional view of the sheddin gphenomenon, it is necessary to lock the spanwise location with respect to the threedimensional vortical structures before averaging across the different phases. We use the condition, u’< urms, to locate the central plane between the counterrotating structures, which in effect are the “legs” of the threedimensional structure. With this condition, we effectively get a slice of the shedding cycle cutting through the “head” of the threedimensional structure. Apart from this cut, we also get a cut between adjacent structures from the weak sweep events, with the condition u’< urms. Using these conditions, on the phaselocked velocity fields, we effectively lock the structures in time, as well as in the spanwise direction. With this ,a clearer picture of the shedding process emerges. The flow is highly threedimensional near reattachment and the shedding of the separation bubble is modulated in the spanwise direction owing to the threedimensional hairpin like vortical structures in the flow. The separation bubble is seen bulged out and lifted high at locations where the head of the hairpin vortex passes, owing to the strong ejection of fluid caused by the vortical structure. On the other hand, outside the hairpin vortices, weak sweep events push the flow towards the wall and make it shallow and less prominent, with the shedding being very weak in this plane. From these observations, a threedimensional picture of the flow is proposed. 
Abstract file URL:  http://etd.ncsi.iisc.ernet.in/abstracts/3297/G25638Abs.pdf 
URI:  http://hdl.handle.net/2005/2542 
Appears in Collections:  Mechanical Engineering (mecheng)

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