# Parametric study of separation and transition characteristics over an airfoil at low Reynolds numbers

## Abstract

Time-resolved surface pressure measurements are used to experimentally investigate characteristics of separation and transition over a NACA 0018 airfoil for the relatively wide range of chord Reynolds numbers from 50,000 to 250,000 and angles of attack from 0° to 21°. The results provide a comprehensive data set of characteristic parameters for separated shear layer development and reveal important dependencies of these quantities on flow conditions. Mean surface pressure measurements are used to explore the variation in separation bubble position, edge velocity in the separated shear layer, and lift coefficients with angle of attack and Reynolds number. Consistent with previous studies, the separation bubble is found to move upstream and decrease in length as the Reynolds number and angle of attack increase. Above a certain angle of attack, the proximity of the separation bubble to the location of the suction peak results in a reduced lift slope compared to that observed at lower angles. Simultaneous measurements of the time-varying component of surface pressure at various spatial locations on the model are used to estimate the frequency of shear layer instability, maximum root-mean-square (RMS) surface pressure, spatial amplification rates of RMS surface pressure, and convection speeds of the pressure fluctuations in the separation bubble. A power-law correlation between the shear layer instability frequency and Reynolds number is shown to provide an order of magnitude estimate of the central frequency of disturbance amplification for various airfoil geometries at low Reynolds numbers. Maximum RMS surface pressures are found to agree with values measured in separation bubbles over geometries other than airfoils, when normalized by the dynamic pressure based on edge velocity. Spatial amplification rates in the separation bubble increase with both Reynolds number and angle of attack, causing the accompanying decrease in separation bubble length. Values of the convection speed of pressure fluctuations in the separated shear layer are measured to be between 35 and 50% of the edge velocity, consistent with predictions of linear stability theory for separated shear layers.

### List of symbols

*C*_{L}Sectional lift coefficient

*C*_{p}Mean surface pressure coefficient

*c*Model chord length

*d*Model height projected onto a streamwise-normal plane

*E*_{pp}Normalized energy spectrum of surface pressure fluctuations

*f*Frequency

*f*_{0}Central frequency of disturbance amplification

*L*Separation bubble length

*n*Exponent in experimental correlations

- \(\tilde{p}\)
RMS surface pressure

- \(\tilde{p}_{\rm max}\)
Maximum RMS surface pressure at a particular α

*q*_{e}Dynamic pressure based on edge velocity, \(q_{e} = \frac{1}{2}\rho U_{e}^2\)

*q*_{∞}Free-stream dynamic pressure, \(q_{\infty} = \frac{1}{2}\rho U_{\infty}^2\)

*Re*Chord Reynolds number,

*Re*=*U*_{∞}*c*/ν*St*Strouhal number for central frequency of disturbance amplification,

*St*=*f*_{0}*d*/*U*_{∞}*U*_{c}Convection speed of surface pressure fluctuations in the separation bubble

*U*_{e}Mean edge velocity in the separated shear layer

*U*_{∞}Free-stream velocity

- \(\tilde{u}\)
RMS free-stream velocity

*x*Distance from the leading edge of the airfoil, measured along the chord

- α
Angle of attack

- ν
Kinematic viscosity

- ρ
Fluid density

- σ
Exponential spatial amplification factor of RMS surface pressure

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