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Technical Brief

A Simplified Model Predicting the Kelvin–Helmholtz Instability Frequency for Laminar Separated Flows

[+] Author and Article Information
Daniele Simoni

DIME-Università di Genova,
Via Montallegro 1,
Genova I-16145, Italy
e-mail: daniele.simoni@unige.it

Marina Ubaldi

DIME-Università di Genova,
Via Montallegro 1,
Genova I-16145, Italy
e-mail: marina.ubaldi@unige.it

Pietro Zunino

DIME-Università di Genova,
Via Montallegro 1,
Genova I-16145, Italy
e-mail: pietro.zunino@unige.it

1Corresponding author.

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received January 19, 2015; final manuscript received November 24, 2015; published online December 29, 2015. Assoc. Editor: Rolf Sondergaard.

J. Turbomach 138(4), 044501 (Dec 29, 2015) (6 pages) Paper No: TURBO-15-1014; doi: 10.1115/1.4032162 History: Received January 19, 2015; Revised November 24, 2015

A semi-empirical model for the estimation of the Kelvin–Helmholtz (KH) instability frequency, in the case of short laminar separation bubbles over airfoils, has been developed. To this end, the Thwaites's pressure gradient parameter has been adopted to account for the effects induced by the aerodynamic loading distribution as well as by the Reynolds number on the separated shear layer thickness at separation. The most amplified frequency predicted by linear stability theory (LST) for a piecewise linear profile, which can be considered as the KH instability frequency, has been related to the shear layer thickness at separation, hence to the Reynolds number and the aerodynamic loading distribution through the Thwaites's pressure gradient parameter. This procedure allows the formulation of a functional dependency between the Strouhal number of the shedding frequency based on exit conditions and the dimensionless parameters. Experimental results obtained in different test cases, characterized by different Reynolds numbers and aerodynamic loading distributions, have been used to validate the model, as well as to identify the regression curve best fitting the data. The semi-empirical correlation here derived can be useful to set the activation frequency of active flow control devices for the optimization of boundary layer separation control strategies.

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References

Figures

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Fig. 1

Piecewise linear profile (left); growth rate of disturbances as a function of dimensionless wave number for different dimensionless distances from the wall (center); and phase velocity of instability waves (right)

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Fig. 2

Static pressure coefficient distributions: FPTS (on the left); HL cascade (on the center); and UHL cascade (on the right)

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Fig. 3

Velocity spectra: FPTS (continuous line); HL cascade (dashed line)

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Fig. 4

KH frequency dimensionless parameters versus Reynolds number: Strouhal number (on the left); Strouhal number combined with the dimensionless loading parameters (on the right)

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