Applying laser Doppler anemometry inside a Taylor–Couette geometry using a ray-tracer to correct for curvature effects

Huisman, Sander G.; Gils, Dennis van; Sun, Chao

doi:10.1016/j.euromechflu.2012.03.013

Cited by 33 publications

(36 citation statements)

References 37 publications

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“…We measure the azimuthal velocity component by focusing two beams in the radial-azimuthal plane. We correct for curvature effects of the outer cylinder by using a ray-tracer, see Huisman et al (2012a). The velocities are measured at midheight (z = L/2) unless specified otherwise.…”

Section: Methodsmentioning

confidence: 99%

Optimal Taylor–Couette flow: radius ratio dependence

et al. 2014

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Taylor-Couette flow with independently rotating inner (i) & outer (o) cylinders is explored numerically and experimentally to determine the effects of the radius ratio η on the system response. Numerical simulations reach Reynolds numbers of up to Re i = 9.5 · 10 3 and Re o = 5 · 10 3 , corresponding to Taylor numbers of up to T a = 10 8 for four different radius ratios η = r i /r o between 0.5 and 0.909. The experiments, performed in the Twente Turbulent Taylor-Couette (T 3 C) setup, reach Reynolds numbers of up to Re i = 2 · 10 6 and Re o = 1.5 · 10 6 , corresponding to T a = 5 · 10 12 for η = 0.714−0.909. Effective scaling laws for the torque J ω (T a) are found, which for sufficiently large driving T a are independent of the radius ratio η. As previously reported for η = 0.714, optimum transport at a non-zero Rossby number Ro = r i |ω i − ω o |/[2(r o − r i )ω o ] is found in both experiments and numerics. Ro opt is found to depend on the radius ratio and the driving of the system. At a driving in the range between T a ∼ 3 · 10 8 and T a ∼ 10 10 , Ro opt saturates to an asymptotic η-dependent value. Theoretical predictions for the asymptotic value of Ro opt are compared to the experimental results, and found to differ notably. Furthermore, the local angular velocity profiles from experiments and numerics are compared, and a link between a flat bulk profile and optimum transport for all radius ratios is reported.

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Section: Methodsmentioning

confidence: 99%

Optimal Taylor–Couette flow: radius ratio dependence

et al. 2014

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“…Due to the curvature of the outer cylinder we have to correct the measured velocity by multiplying it with a constant factor. We find this constant numerically by ray-tracing [17] the LDA beams in our optical geometry.…”

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confidence: 99%

Statistics of turbulent fluctuations in counter-rotating Taylor-Couette flows

2013

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The statistics of velocity fluctuations of turbulent Taylor-Couette flow are examined. The rotation rate of the inner and outer cylinder are varied while keeping the Taylor number fixed to 1.49 × 10 12(O(Re) = 10 6 ). The azimuthal velocity component of the flow is measured using laser Doppler anemometry (LDA). For each experiment 5 × 10 6 datapoints are acquired and carefully analysed. Using extended self-similarity (ESS) [1] the longitudinal structure function exponents are extracted, and are found to weakly depend on the ratio of the rotation rates. For the case where only the inner cylinder rotates the results are in good agreement with results measured by Lewis and Swinney [2] using hot-film anemometry. The power spectra shows clear −5/3 scaling for the intermediate angular velocity ratios −ωo/ωi ∈ {0.6, 0.8, 1.0}, roughly −5/3 scaling for −ωo/ωi ∈ {0.2, 0.3, 0.4, 2.0}, and no clear scaling law can be found for −ω0/ωi = 0 (inner cylinder rotation only); the local scaling exponent of the spectra has a strong frequency dependence. We relate these observations to the shape of the probability density function of the azimuthal velocity and the presence of a neutral line.Taylor-Couette (TC) flow, among others like RayleighBénard convection, and von Kármán, pipe, channel and plate flow, played a pivatol role in exploring fundamental concepts in fluid mechanics [3]. In a TC apparatus, fluid is confined between two independently rotating coaxial cylinders, see fig. 1. The TC geometry is best described with cylindrical coordinates: radial distance ρ, azimuth θ, and height z. The driving of the TC apparatus is given by two Reynolds numbers:where ω is the angular velocity defined as u θ /ρ, ρ the radius, ν the kinematic viscosity, and i and o subscripts denote quantities related to the inner and outer cylinder, respectively. Another way of describing the flow is by a Taylor number Ta =, which is the ratio of centrifugal forces to viscous forces, along with a parameter describing the ratio of the driving velocities, for which we have chosen:σ is defined as ((1 + η)/ √ 4η) 4 with the radius ratio η = ρ i /ρ o . By measuring the torque T [2, 4-10], required to maintain constant angular velocity of both cylinders, we can find the power input (P ) of our system using P = T |ω i − ω o |. Note that we can measure the torque on either cylinder as it has the same magnitude on the inner and the outer cylinder [11]. As all the energy that enters the system globally will be dissipated by viscous * Electronic address: s.g.huisman@gmail.com † Electronic address: d.lohse@utwente.nl ‡ Electronic address: c.sun@utwente.nl dissipation, the torque can be related to the average energy dissipate rate:where ρ fluid is the density of the working fluid, and L the length of the cylinders. Using the energy dissipation rate and the viscosity we can now find the average Kolmogorov length scale [12,13] in our flow: η K = ν 3 /ǫ 1/4 .

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“…At each measurement position, 100000 samples are acquired, with a limiting time acquisition of 40 s. The data rate lies in the range 800 − 10000 Hz, while the validation rate is upper than 60%. In dealing with velocity measurements in liquid Taylor-Couette flow by mean of LDA technique, the presence of flat or curved interface introduces a shift of the measurement volume and an underestimation of some components of the flow velocity (Huisman et al [16]). In this study a ray tracer program has been used to calculate the measurement volume displacement and velocity correction factors.…”

Section: Ldv Measurementmentioning

confidence: 99%

“…The elliptical shape of these vortices depends on the strength of inward and outward fluid. According to Tokgoz et al [16] the birth and death of new vortices always takes place at these boundaries. For the present geometry, Reynolds number and acceleration rate (∂Re i /∂τ ), the local axial wavelength of the vortices obtained at midheight of the apparatus is around 4.4d, comparable to the value reported by Ravelet et al [17] for Re i = 14000 in an experiment with a slightly different gap ratio.…”

Section: Ldv Measurementmentioning

confidence: 99%