arXiv subjects

Sander G. Huisman

Publications and source records attributed to Sander G. Huisman.

65 records · Page 4Linked to original sources

arXiv2016

Multiple states in highly turbulent Taylor-Couette flow

The ubiquity of turbulent flows in nature and technology makes it of utmost importance to fundamentally understand turbulence. Kolmogorov's 1941 paradigm suggests that for strongly turbulent flows with many degrees of freedom and its large fluctuations, there would only be \emph{one} turbulent state as the large fluctuations would explore the entire higher-dimensional phase space. Here we report the first conclusive evidence of multiple turbulent states for large Reynolds number $\text{Re}=\mathcal{O}(10^6)$ (Taylor number $\text{Ta}=\mathcal{O}(10^{12})$) Taylor-Couette flow in the regime of ultimate turbulence, by probing the phase space spanned by the rotation rates of the inner and outer cylinder. The manifestation of multiple turbulent states is exemplified by providing combined global torque and local velocity measurements. This result verifies the notion that bifurcations can occur in high-dimensional flows i.e. very large $\text{Re}$) and questions Kolmogorov's paradigm.

physics.flu-dyn↗

arXiv2016

The boiling Twente Taylor-Couette (BTTC) facility: Temperature controlled turbulent flow between independently rotating, coaxial cylinders

A new Taylor-Couette system has been designed and constructed with precise temperature control. Two concentric independently rotating cylinders are able to rotate at maximum rates of $f_i = \pm20$ Hz for the inner cylinder and $f_o = \pm10$ Hz for the outer cylinder. The inner cylinder has an outside radius of $r_i = 75$ mm, and the outer cylinder has an inside radius of $r_o = 105$ mm, resulting in a gap of $d=30$ mm. The height of the gap $L =549$ mm, giving a volume of $V=9.3$l. The geometric parameters are $η= r_i/r_o = 0.714$ and $Γ= L/d = 18.3$. With water as working fluid at room temperature the Reynolds numbers that can be achieved are $\text{Re}_i = ω_i r_i (r_o-r_i)/ν= 2.8 \times 10^5$ and $\text{Re}_o = ω_o r_o (r_o-r_i)/ν= 2 \times 10^5$, or a combined Reynolds number of up to $\text{Re} = (ω_i r_i -ω_o r_o)(r_o-r_i)/ν= 4.8 \times 10^5$. If the working fluid is changed to the fluorinated liquid FC-3284 with kinematic viscosity 0.42 cSt, the combined Reynolds number can reach $\text{Re} = 1.1 \times 10^6$. The apparatus features precise temperature control of the outer and inner cylinder separately, and is fully optically accessible from the side and top. The new facility offers the possibility to accurately study the process of boiling inside a turbulent flow and its effect on the flow.

physics.flu-dyn↗

arXiv2015

Taylor-Couette turbulence at radius ratio $η=0.5$: scaling, flow structures and plumes

Using high-resolution particle image velocimetry we measure velocity profiles, the wind Reynolds number and characteristics of turbulent plumes in Taylor-Couette flow for a radius ratio of 0.5 and Taylor number of up to $6.2\cdot10^9$. The extracted angular velocity profiles follow a log-law more closely than the azimuthal velocity profiles due to the strong curvature of this $η=0.5$ setup. The scaling of the wind Reynolds number with the Taylor number agrees with the theoretically predicted 3/7-scaling for the classical turbulent regime, which is much more pronounced than for the well-explored $η=0.71$ case, for which the ultimate regime sets in at much lower Ta. By measuring at varying axial positions, roll structures are found for counter-rotation while no clear coherent structures are seen for pure inner cylinder rotation. In addition, turbulent plumes coming from the inner and outer cylinder are investigated. For pure inner cylinder rotation, the plumes in the radial velocity move away from the inner cylinder, while the plumes in the azimuthal velocity mainly move away from the outer cylinder. For counter-rotation, the mean radial flow in the roll structures strongly affects the direction and intensity of the turbulent plumes. Furthermore, it is experimentally confirmed that in regions where plumes are emitted, boundary layer profiles with a logarithmic signature are created.

physics.flu-dyn↗

arXiv2015

Azimuthal velocity profiles in Rayleigh-stable Taylor-Couette flow and implied axial angular momentum transport

We present azimuthal velocity profiles measured in a Taylor-Couette apparatus, which has been used as a model of stellar and planetary accretion disks. The apparatus has a cylinder radius ratio of $η= 0.716$, an aspect-ratio of $Γ= 11.74$, and the plates closing the cylinders in the axial direction are attached to the outer cylinder. We investigate angular momentum transport and Ekman pumping in the Rayleigh-stable regime. The regime is linearly stable and is characterized by radially increasing specific angular momentum. We present several Rayleigh-stable profiles for shear Reynolds numbers $Re_S \sim O(10^5) \,$, both for $Ω_i > Ω_o > 0$ (quasi-Keplerian regime) and $Ω_o > Ω_i > 0$ (sub-rotating regime) where $Ω_{i,o}$ is the inner/outer cylinder rotation rate. None of the velocity profiles matches the non-vortical laminar Taylor-Couette profile. The deviation from that profile increased as solid-body rotation is approached at fixed $Re_S$. Flow super-rotation, an angular velocity greater than that of both cylinders, is observed in the sub-rotating regime. The velocity profiles give lower bounds for the torques required to rotate the inner cylinder that were larger than the torques for the case of laminar Taylor-Couette flow. The quasi-Keplerian profiles are composed of a well mixed inner region, having approximately constant angular momentum, connected to an outer region in solid-body rotation with the outer cylinder and attached axial boundaries. These regions suggest that the angular momentum is transported axially to the axial boundaries. Therefore, Taylor-Couette flow with closing plates attached to the outer cylinder is an imperfect model for accretion disk flows, especially with regard to their stability.

physics.flu-dyn↗

arXiv2013

Optimal Taylor-Couette flow: Radius ratio dependence

Taylor-Couette flow with independently rotating inner (i) and 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 x 10^3 and Re_o=5x10^3, corresponding to Taylor numbers of up to Ta=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^3C) setup, reach Reynolds numbers of up to Re_i=2x10^6$ and Re_o=1.5x10^6, corresponding to Ta=5x10^{12} for η=0.714-0.909. Effective scaling laws for the torque J^ω(Ta) are found, which for sufficiently large driving Ta 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 {Ta\sim3\cdot10^8} and {Ta\sim10^{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.

physics.flu-dyn↗

arXiv2013

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

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 $1.49 \times 10^{12}$ ($\mathcal{O}(\text{Re})=10^6$). The azimuthal velocity component of the flow is measured using laser Doppler anemometry (LDA). For each experiment $5\times10^6$ datapoints are acquired and carefully analysed. Using extended self-similarity (ESS) \cite{ben93b} 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 \cite{lew99} using hot-film anemometry. The power spectra shows clear -5/3 scaling for the intermediate angular velocity ratios $-ω_o/ω_i \in \{0.6, 0.8, 1.0\}$, roughly -5/3 scaling for $-ω_o/ω_i \in \{0.2, 0.3, 0.4, 2.0\}$, and no clear scaling law can be found for $-ω_0/ω_i = 0$ (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.

physics.flu-dyn↗

arXiv2013

Logarithmic boundary layers in highly turbulent Taylor-Couette flow

We provide direct measurements of the boundary layer properties in highly turbulent Taylor-Couette flow up to $\text{Ta}=6.2 \times 10^{12}$ using high-resolution particle image velocimetry (PIV). We find that the mean azimuthal velocity profile at the inner and outer cylinder can be fitted by the von Kármán log law $u^+ = \frac 1κ\ln y^+ +B$. The von Kármán constant $κ$ is found to depend on the driving strength $\text{Ta}$ and for large $\text{Ta}$ asymptotically approaches $κ\approx 0.40$. The variance profiles of the local azimuthal velocity have a universal peak around $y^+ \approx 12$ and collapse when rescaled with the driving velocity (and not with the friction velocity), displaying a log-dependence of $y^+$ as also found for channel and pipe flows [1,2].

physics.flu-dyn↗

arXiv2012

Optimal Taylor-Couette turbulence

Strongly turbulent Taylor-Couette flow with independently rotating inner and outer cylinders with a radius ratio of η= 0.716 is experimentally studied. From global torque measurements, we analyse the dimensionless angular velocity flux Nu_ω(Ta, a) as a function of the Taylor number Ta and the angular velocity ratio a = -ω_o/ω_i in the large-Taylor-number regime 10^{11} \lesssim Ta \lesssim 10^{13}. We analyse the data with the common power-law ansatz for the dimensionless angular velocity transport flux Nu_ω(Ta, a) = f(a)Ta^γ, with an amplitude f(a) and an exponent γ. The data are consistent with one effective exponent γ= 0.39\pm0.03 for all a. The amplitude of the angular velocity flux f(a) = Nu_ω(Ta, a)/Ta^0.39 is measured to be maximal at slight counter-rotation, namely at an angular velocity ratio of a_opt = 0.33\pm0.04. This value is theoretically interpreted as the result of a competition between the destabilizing inner cylinder rotation and the stabilizing but shear-enhancing outer cylinder counter-rotation. With the help of laser Doppler anemometry, we provide angular velocity profiles and identify the radial position r_n of the neutral line. While for moderate counter-rotation -0.40 ω_i \lesssim ω_o < 0, the neutral line still remains close to the outer cylinder and the probability distribution function (p.d.f.) of the bulk angular velocity is observed to be monomodal. For stronger counter-rotation the neutral line is pushed inwards towards the inner cylinder; in this regime the p.d.f. of the bulk angular velocity becomes bimodal, reflecting intermittent bursts of turbulent structures beyond the neutral line into the outer flow domain, which otherwise is stabilized by the counter-rotating outer cylinder. Finally, a hypothesis is offered allowing a unifying view for all these various results.

physics.flu-dyn↗

arXiv2012

Applying Laser Doppler Anemometry inside a Taylor-Couette geometry - Using a ray-tracer to correct for curvature effects

In the present work it will be shown how the curvature of the outer cylinder affects Laser Doppler anemometry measurements inside a Taylor-Couette apparatus. The measurement position and the measured velocity are altered by curved surfaces. Conventional methods for curvature correction are not applicable to our setup, and it will be shown how a ray-tracer can be used to solve this complication. By using a ray-tracer the focal position can be calculated, and the velocity can be corrected. The results of the ray-tracer are verified by measuring an a priori known velocity field, and after applying refractive corrections good agreement with theoretical predictions are found. The methods described in this paper are applied to measure the azimuthal velocity profiles in high Reynolds number Taylor-Couette flow for the case of outer cylinder rotation.

physics.flu-dyn↗

arXiv2011

Ultimate Turbulent Taylor-Couette Flow

The flow structure of strongly turbulent Taylor-Couette flow with Reynolds numbers up to Re_i = 2*10^6 of the inner cylinder is experimentally examined with high-speed particle image velocimetry (PIV). The wind Reynolds numbers Re_w of the turbulent Taylor-vortex flow is found to scale as Re_w ~ Ta^(1/2), exactly as predicted for the ultimate turbulence regime, in which the boundary layers are turbulent. The dimensionless angular velocity flux has an effective scaling of Nu_ω ~ Ta^0.38, also in correspondence with turbulence in the ultimate regime. The scaling of Nu_ω is confirmed by local angular velocity flux measurements extracted from high-speed PIV measurements: though the flux shows huge fluctuations, its spatial and temporal average nicely agrees with the result from the global torque measurements.

physics.flu-dyn↗

arXiv2011

Torque Scaling in Turbulent Taylor-Couette Flow with Co- and Counterrotating Cylinders

We analyze the global transport properties of turbulent Taylor-Couette flow in the strongly turbulent regime for independently rotating outer and inner cylinders, reaching Reynolds numbers of the inner and outer cylinders of Re_i = 2 x 10^6 and Re_o = 1.4 x 10^6, respectively. For all Re_i, Re_o, the dimensionless torque G scales as a function of the Taylor number Ta (which is proportional to the square of the difference between the angular velocities of the inner and outer cylinders) with a universal effective scaling law G \propto Ta^{0.88}, corresponding to Nu_omega \propto Ta^{0.38} for the Nusselt number characterizing the angular velocity transport between the inner and outer cylinders. The exponent 0.38 corresponds to the ultimate regime scaling for the analogous Rayleigh-Benard system. The transport is most efficient for the counterrotating case along the diagonal in phase space with omega_o \approx -0.4 omega_i.

physics.flu-dyn↗