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Research Papers

Ultrasonic Doppler Velocimetry Measurement of Flow and Instabilities in a Rotating Lid-Driven Cylinder

[+] Author and Article Information
Zhao C. Kong

BP America
Houston, TX 77079

Brent C. Houchens

Mem. ASME
e-mail: houchens@rice.edu
Department of Mechanical Engineering
and Materials Science,
Rice University,
Houston, TX 77005

1Corresponding author.

Manuscript received May 4, 2012; final manuscript received January 21, 2013; accepted manuscript posted January 28, 2013; published online July 19, 2013. Assoc. Editor: Martin Ostoja-Starzewski.

J. Appl. Mech 80(5), 050904 (Jul 19, 2013) (8 pages) Paper No: JAM-12-1180; doi: 10.1115/1.4023496 History: Received May 04, 2012; Revised January 21, 2013; Accepted January 28, 2013

The steady, axisymmetric base flow and instabilities in a rotating lid-driven cylinder are investigated experimentally via ultrasonic Doppler velocimetry and verified with computations. The flow is governed by two parameters: the Reynolds number (based on the angular velocity of the top lid, the cylinder radius, and kinematic viscosity) and the aspect ratio (cylinder height/radius). Base states and instabilities are explored using ultrasonic Doppler velocimetry in two mixtures of glycerol and water. Velocity profiles in the cylinder are constructed for aspect ratio 2.5 and Reynolds numbers between 1000 and 3000. The results are compared to computational spectral element simulations, as well as previously published findings. The base flow velocity profiles measured by ultrasonic Doppler velocimetry are in good agreement with the numerical results below the critical Reynolds number. The same is true for time-averaged results above the critical Reynolds number. Prediction of the first axisymmetric instability is demonstrated, although not always at the expected critical Reynolds number. Advantages and limitations of ultrasonic Doppler velocimetry are discussed.

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Figures

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Fig. 1

Idealized rotating lid-driven cylinder enclosure

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Fig. 2

Left: close-up cross section of experimental cylinder in the r − z plane. Right: photograph of experimental setup.

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Fig. 3

Characteristic streamlines of the meridional flow over the range of Re where steady flow is expected. Representative UDV beam divergence is superimposed on the Re = 1000 case, with “outer” and “inner” lines representing the maximum beam divergence.

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Fig. 4

Steady state (sample-averaged) experimental vertical velocity vz* along a line offset by r = 0.25 from the centerline, compared to numerical solutions from SEMTEX (left: 24%/76% glycerol/water, right: 50%/50% glycerol/water). The maximum vertical velocity scale is held constant for each mixture.

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Fig. 7

Left: color map of the vertical velocity vz* in time from UDV at Re = 3000 and right: steady state (sample-averaged) vertical velocity vz* from UDV at Re = 3000 for 24% glycerol, 76% water mixture compared with time-averaged numerical simulations at r∈ = 0.25 offset

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Fig. 5

Steady state (sample-averaged) vertical velocity vz* along a line offset by r = 0.75 from the centerline for 24%/76% glycerol/water, compared to numerical solutions from SEMTEX

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Fig. 6

Color maps of the vertical velocity vz* in time (left: numerical solution at Re = 2800, middle: UDV for the 24%/76% glycerol/water at Re = 2500, right: UDV for the 50%/50% glycerol/water mixture at Re = 2900) at offset r = 0.25, with times scaled to match the nondimensional time of the numerical solution. Note that the experimental data extends an arbitrary distance into the lid at the top of the domain.

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