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The final stages of transition and the reattachment region in transitional separation bubbles

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Abstract

The final stages of transitional phenomena in laminar separation bubbles play a key role in their reattachment process, and they condition the boundary layer properties and flow structure after reattachment. In this experimental study, the evolution of the perturbation velocity spectra found in this zone is first presented, showing the nonlinear growth of instabilities in their path to develop fully turbulent spectra. The study of the average flow field allows the scaling of the reattachment region, both in its extension and in the characterization of the integral boundary layer magnitudes. Experimental laws are proposed for the evolution of the momentum thickness and of the shape factor. In addition, a universal, wake-like mean velocity profile is found shortly after the reattachment station. The phase-locked characterization technique allows measurements conditioned to the presence of a fluid event. This technique is used to track the evolution of large-scale structures, whose dynamics is seen to dominate the fluid behavior in the reattachment zone. The simultaneous existence of two vortex blobs is found to characterize this flow region, with the longest lived one being convected toward the wall and stretched. This process results in the fast breakdown of the large-scale vorticity structure and the sudden formation of 3-D, small scales that promote the rapid flow evolution toward a fully developed turbulent state.

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Abbreviations

E :

Power spectral density

f :

Frequency

h ω :

LSB height defined from maximum vorticity wall normal distance

h dmax :

LSB height defined from separation streamline wall normal distance

L I :

Length of the laminar region

L II :

Length of the average reattachment region

L d :

Inviscid velocity characteristic deceleration length

Q :

2-D Q-criterion scalar \(Q=\frac{\partial u}{\partial x}\frac{\partial v}{\partial y}-\frac{\partial u}{\partial y}\frac{\partial v}{\partial x}\)

Re Ld :

Reynolds number based on L d and maximum edge velocity

t :

Time

T :

Period

u, v :

Streamwise and wall normal velocity components

u c :

Vortex blobs convection velocity

u e :

Streamwise edge velocity

u inv :

Inviscid solution streamwise velocity over the plate

\(\overline{u^{\prime2}},\overline{v^{\prime2}},\overline{u'v'}\) :

Reynolds stresses

x, y, z :

Streamwise, wall normal, spanwise coordinates

δ :

Flag function

λ :

Wavelength

θ :

Momentum thickness

ϕ :

Generic variable

\(\varphi\) :

Phase and phase information signal

()0 :

Value at the beginning of deceleration (test section throat)

()I :

Value at the end of the laminar region

()s :

Value at separation

()II :

Value at the average reattachment station

\(\widetilde{\phi}\) :

Non-dimensional variable

\(\overline{\phi}\) :

Temporal averaged value

\(\phi^{\prime}\) :

Temporal fluctuating part of a variable

\(\hat{\phi}\) :

Phase-averaged value

\(\breve{\phi}\) :

Filtered signal

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Acknowledgements

This work has been partially supported by the Spanish Ministry of Education (under projects TRA2005-01249, and TRA2009-09404, and PhD internship BES-2006-13926), the European Commission through the Sixth Framework Program project “Environmentally Friendly Aeroengines (VITAL)”, and Grants P020130430 and P060130077 from “Industria de Turbo Propulsores S.A. (ITP)”.

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  1. J. Serna

    Present address: University Center of Defence at the Spanish Air Force Academy, MDE-UPCT, Calle Coronel López Peña, s/n, 30720, Santiago de la Ribera, Murcia, Spain

Authors and Affiliations

  1. School of Aeronautics, Universidad Politécnica de Madrid, 28040, Madrid, Spain

    J. Serna & B. J. Lázaro

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  1. J. Serna
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  2. B. J. Lázaro
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Serna, J., Lázaro, B.J. The final stages of transition and the reattachment region in transitional separation bubbles. Exp Fluids 55, 1695 (2014). https://doi.org/10.1007/s00348-014-1695-7

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