scholarly journals Turbulence strength in ultimate Taylor–Couette turbulence

2017 ◽  
Vol 836 ◽  
pp. 397-412 ◽  
Author(s):  
Rodrigo Ezeta ◽  
Sander G. Huisman ◽  
Chao Sun ◽  
Detlef Lohse
Keyword(s):  
Reynolds Number ◽  
Dissipation Rate ◽  
Velocity Structure ◽  
Field Measurements ◽  
Azimuthal Velocity ◽  
Energy Dissipation Rate ◽  
Local Flow ◽  
Kolmogorov Length Scale ◽  
Taylor’S Hypothesis ◽  
Taylor Couette

We provide experimental measurements for the effective scaling of the Taylor–Reynolds number within the bulk $\mathit{Re}_{\unicode[STIX]{x1D706},\mathit{bulk}}$, based on local flow quantities as a function of the driving strength (expressed as the Taylor number $\mathit{Ta}$), in the ultimate regime of Taylor–Couette flow. We define $Re_{\unicode[STIX]{x1D706},bulk}=(\unicode[STIX]{x1D70E}_{bulk}(u_{\unicode[STIX]{x1D703}}))^{2}(15/(\unicode[STIX]{x1D708}\unicode[STIX]{x1D716}_{bulk}))^{1/2}$, where $\unicode[STIX]{x1D70E}_{bulk}(u_{\unicode[STIX]{x1D703}})$ is the bulk-averaged standard deviation of the azimuthal velocity, $\unicode[STIX]{x1D716}_{bulk}$ is the bulk-averaged local dissipation rate and $\unicode[STIX]{x1D708}$ is the liquid kinematic viscosity. The data are obtained through flow velocity field measurements using particle image velocimetry. We estimate the value of the local dissipation rate $\unicode[STIX]{x1D716}(r)$ using the scaling of the second-order velocity structure functions in the longitudinal and transverse directions within the inertial range – without invoking Taylor’s hypothesis. We find an effective scaling of $\unicode[STIX]{x1D716}_{\mathit{bulk}}/(\unicode[STIX]{x1D708}^{3}d^{-4})\sim \mathit{Ta}^{1.40}$, (corresponding to $\mathit{Nu}_{\unicode[STIX]{x1D714},\mathit{bulk}}\sim \mathit{Ta}^{0.40}$ for the dimensionless local angular velocity transfer), which is nearly the same as for the global energy dissipation rate obtained from both torque measurements ($\mathit{Nu}_{\unicode[STIX]{x1D714}}\sim \mathit{Ta}^{0.40}$) and direct numerical simulations ($\mathit{Nu}_{\unicode[STIX]{x1D714}}\sim \mathit{Ta}^{0.38}$). The resulting Kolmogorov length scale is then found to scale as $\unicode[STIX]{x1D702}_{\mathit{bulk}}/d\sim \mathit{Ta}^{-0.35}$ and the turbulence intensity as $I_{\unicode[STIX]{x1D703},\mathit{bulk}}\sim \mathit{Ta}^{-0.061}$. With both the local dissipation rate and the local fluctuations available we finally find that the Taylor–Reynolds number effectively scales as $\mathit{Re}_{\unicode[STIX]{x1D706},\mathit{bulk}}\sim \mathit{Ta}^{0.18}$ in the present parameter regime of $4.0\times 10^{8}<\mathit{Ta}<9.0\times 10^{10}$.

Shape optimization of a split-and-recombine micromixer by the local energy dissipation rate

2020 ◽  
Vol 234 (3) ◽  
pp. 243-251
Author(s):  
Eshaq Ebnereza ◽  
Kamran Hassani ◽  
Mahmoud Seraj ◽  
Katayoun Gohari Moghaddam
Keyword(s):  
Reynolds Number ◽  
Energy Dissipation ◽  
Objective Function ◽  
Dissipation Rate ◽  
Computation Time ◽  
Energy Dissipation Rate ◽  
Local Energy ◽  
Number Range ◽  
Design Variables ◽  
Wide Range

A passive split-and-recombine micromixer was developed based on the concept of lamellar structure and advection mixing type for a serpentine structure. The flow patterns and mixing performance were analyzed using numerical simulation in Reynolds number range of 10≤ Reynolds ≤170. Two design variables, defining the shape of the split-and-recombine branch, were optimized by the local energy dissipation rate as the objective function. The reduction of computation time and the absence of numerical diffusion were the advantages of using the energy dissipation rate as the objective function. At each Reynolds number, 64 sample data was generated on the design space uniformly. Then a model was used based on the Radial basis neural network for the prediction of the objective function. The optimum values of the design variables within the constraint range were found on the response surface. The optimization study was performed at five Reynolds numbers of 10, 50, 90, 130, 170 and the mixing index was improved 0.156, 0.298, 0.417, 0.506, and 0.57, respectively. The effect of design variables on the objective function and the concentration pattern was presented and analyzed. Finally, the mixing characteristic of the split-and-recombine micromixer was studied in a wide range of Reynolds number and the flow was categorized to stratify and show the vortex regime based on the Reynolds number. The optimized split-and-recombine micromixer could be integrated by any system depending on the desired velocity and Reynolds number.

Velocity profiles, flow structures and scalings in a wide-gap turbulent Taylor–Couette flow

2017 ◽  
Vol 831 ◽  
pp. 330-357 ◽  
Author(s):  
A. Froitzheim ◽  
S. Merbold ◽  
C. Egbers
Keyword(s):  
Reynolds Number ◽  
Nusselt Number ◽  
Couette Flow ◽  
Outer Cylinder ◽  
Azimuthal Velocity ◽  
Cylinder Wall ◽  
Taylor Vortices ◽  
Wide Gap ◽  
Taylor Couette ◽  
Taylor Couette Flow

Fully turbulent Taylor–Couette flow between independently rotating cylinders is investigated experimentally in a wide-gap configuration ($\unicode[STIX]{x1D702}=0.5$) around the maximum transport of angular momentum. In that regime turbulent Taylor vortices are present inside the gap, leading to a pronounced axial dependence of the flow. To account for this dependence, we measure the radial and azimuthal velocity components in horizontal planes at different cylinder heights using particle image velocimetry. The ratio of angular velocities of the cylinder walls $\unicode[STIX]{x1D707}$, where the torque maximum appears, is located in the low counter-rotating regime ($\unicode[STIX]{x1D707}_{max}(\unicode[STIX]{x1D702}=0.5)=-0.2$). This point coincides with the smallest radial gradient of angular velocity in the bulk and the detachment of the neutral surface from the outer cylinder wall, where the azimuthal velocity component vanishes. The structure of the flow is further revealed by decomposing the flow field into its large-scale and turbulent contributions. Applying this decomposition to the kinetic energy, we can analyse the formation process of the turbulent Taylor vortices in more detail. Starting at pure inner cylinder rotation, the vortices are formed and strengthened until $\unicode[STIX]{x1D707}=-0.2$ quite continuously, while they break down rapidly for higher counter-rotation. The same picture is shown by the decomposed Nusselt number, and the range of rotation ratios, where turbulent Taylor vortices can exist, shrinks strongly in comparison to investigations at much lower shear Reynolds numbers. Moreover, we analyse the scaling of the Nusselt number and the wind Reynolds number with the shear Reynolds number, finding a communal transition at approximately $Re_{S}\approx 10^{5}$ from classical to ultimate turbulence with a transitional regime lasting at least up to $Re_{S}\geqslant 2\times 10^{5}$. Including the axial dispersion of the flow into the calculation of the wind amplitude, we can also investigate the wind Reynolds number as a function of the rotation ratio $\unicode[STIX]{x1D707}$, finding a maximum in the low counter-rotating regime slightly larger than $\unicode[STIX]{x1D707}_{max}$. Based on our study it becomes clear that the investigation of counter-rotating Taylor–Couette flows strongly requires an axial exploration of the flow.

Assessment of Simple RANS Turbulence Models for Stall Delay Applications at Low Reynolds Number

2017 ◽  
Vol 863 ◽  
pp. 260-265
Author(s):  
M. Arif Mohamed ◽  
Y. Wu ◽  
Martin Skote
Keyword(s):  
Reynolds Number ◽  
Wind Tunnel ◽  
Kinetic Energy ◽  
Dissipation Rate ◽  
Radial Flow ◽  
Turbulence Models ◽  
Energy Dissipation Rate ◽  
Rotating Blade ◽  
Rans Turbulence Models ◽  
Delay Phenomenon

This paper assesses the performance of three two-equation turbulence models viz. the SST k-ω, the RNG and realizable k-εfor the simulations of a rotating blade in a wind tunnel experiment where k, ε and ω are turbulent kinetic energy, dissipation rate and specific dissipation respectively. The experiments showed the stall-delay phenomenon at the inboard of the rotating blade at a Reynolds number of 4800. This trend of suction peaks was captured by all three turbulence models albeit not matching the experimental coefficient of pressure accurately. All three models also showed radial flow at the inboard which is consistent with the experiments while the SST predicted the least k at low wall values.

scholarly journals Modelling the breakup of solid aggregates in turbulent flows

2008 ◽  
Vol 612 ◽  
pp. 261-289 ◽  
Author(s):  
MATTHÄUS U. BÄBLER ◽  
MASSIMO MORBIDELLI ◽  
JERZY BAŁDYGA
Keyword(s):  
Energy Dissipation ◽  
Dissipation Rate ◽  
Critical Value ◽  
Energy Dissipation Rate ◽  
Length Scale ◽  
Order Kinetic ◽  
Local Energy ◽  
Hydrodynamic Stress ◽  
First Order ◽  
Kolmogorov Length Scale

The breakup of solid aggregates suspended in a turbulent flow is considered. The aggregates are assumed to be small with respect to the Kolmogorov length scale and the flow is assumed to be homogeneous. Further, it is assumed that breakup is caused by hydrodynamic stresses acting on the aggregates, and breakup is therefore assumed to follow a first-order kinetic where KB(x) is the breakup rate function and x is the aggregate mass. To model KB(x), it is assumed that an aggregate breaks instantaneously when the surrounding flow is violent enough to create a hydrodynamic stress that exceeds a critical value required to break the aggregate. For aggregates smaller than the Kolmogorov length scale the hydrodynamic stress is determined by the viscosity and local energy dissipation rate whose fluctuations are highly intermittent. Hence, the first-order breakup kinetics are governed by the frequency with which the local energy dissipation rate exceeds a critical value (that corresponds to the critical stress). A multifractal model is adopted to describe the statistical properties of the local energy dissipation rate, and a power-law relation is used to relate the critical energy dissipation rate above which breakup occurs to the aggregate mass. The model leads to an expression for KB(x) that is zero below a limiting aggregate mass, and diverges for x → ∞. When simulating the breakup process, the former leads to an asymptotic mean aggregate size whose scaling with the mean energy dissipation rate differs by one third from the scaling expected in a non-fluctuating flow.

scholarly journals MODEL TESTS ON LITTORAL SAND TRANSPORT RATE

1982 ◽  
Vol 1 (18) ◽  
pp. 80
Author(s):  
J.W. Kamphuis ◽  
O.F.S.J. Sayao
Keyword(s):  
Energy Dissipation ◽  
Wave Energy ◽  
Dissipation Rate ◽  
Field Measurements ◽  
Energy Dissipation Rate ◽  
Transport Rate ◽  
Sand Transport ◽  
Similarity Parameter ◽  
Wave Energy Dissipation ◽  
Mobile Bed

This paper is an analysis of two sets of experimental results on littoral sand transport. A littoral sand transport expression is proposed, relating littoral transport rate to surf similarity parameter and hence to wave energy dissipation rate. The expression indicates that the "constant' in the CERC formula is dependent on the mobile bed beach slope and on the breaker index. The expression is also compared with some of the few published field measurements.

Three-component vorticity measurements in a turbulent grid flow

1998 ◽  
Vol 374 ◽  
pp. 29-57 ◽  
Author(s):  
R. A. ANTONIA ◽  
T. ZHOU ◽  
Y. ZHU
Keyword(s):  
Energy Dissipation ◽  
Dissipation Rate ◽  
Velocity Structure ◽  
Transverse Velocity ◽  
Longitudinal Velocity ◽  
Energy Dissipation Rate ◽  
Grid Turbulence ◽  
Local Isotropy ◽  
Velocity Increments ◽  
The Mean

All components of the fluctuating vorticity vector have been measured in decaying grid turbulence using a vorticity probe of relatively simple geometry (four X-probes, i.e. a total of eight hot wires). The data indicate that local isotropy is more closely satisfied than global isotropy, the r.m.s. vorticities being more nearly equal than the r.m.s. velocities. Two checks indicate that the performance of the probe is satisfactory. Firstly, the fully measured mean energy dissipation rate 〈ε〉 is in good agreement with the value inferred from the rate of decay of the mean turbulent energy 〈q2〉 in the quasi-homogeneous region; the isotropic mean energy dissipation rate 〈εiso〉 agrees closely with this value even though individual elements of 〈ε〉 indicate departures from isotropy. Secondly, the measured decay rate of the mean-square vorticity 〈ω2〉 is consistent with that of 〈q2〉 and in reasonable agreement with the isotropic form of the transport equation for 〈ω2〉. Although 〈ε〉≃〈εiso〉, there are discernible differences between the statistics of ε and εiso; in particular, εiso is poorly correlated with either ε or ω2. The behaviour of velocity increments has been examined over a narrow range of separations for which the third-order longitudinal velocity structure function is approximately linear. In this range, transverse velocity increments show larger departures than longitudinal increments from predictions of Kolmogorov (1941). The data indicate that this discrepancy is only partly associated with differences between statistics of locally averaged ε and ω2, the latter remaining more intermittent than the former across this range. It is more likely caused by a departure from isotropy due to the small value of Rλ, the Taylor microscale Reynolds number, in this experiment.

scholarly journals Taylor–Couette turbulence at radius ratio : scaling, flow structures and plumes

2016 ◽  
Vol 799 ◽  
pp. 334-351 ◽  
Author(s):  
Roeland C. A. van der Veen ◽  
Sander G. Huisman ◽  
Sebastian Merbold ◽  
Uwe Harlander ◽  
Christoph Egbers ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Outer Cylinder ◽  
Azimuthal Velocity ◽  
Velocity Profiles ◽  
Radius Ratio ◽  
Taylor Number ◽  
Turbulent Regime ◽  
Counter Rotation ◽  
Taylor Couette ◽  
Cylinder Rotation

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 $6.2\times 10^{9}$. The extracted angular velocity profiles follow a log law more closely than the azimuthal velocity profiles due to the strong curvature of this ${\it\eta}=0.5$ set-up. 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 ${\it\eta}=0.71$ case, for which the ultimate regime sets in at much lower Taylor number. 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 cylinders 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.

scholarly journals Inertia–Gravity Waves Breaking in the Middle Atmosphere at High Latitudes: Energy Transfer and Dissipation Tensor Anisotropy

2020 ◽  
Vol 77 (9) ◽  
pp. 3193-3210
Author(s):  
Tiago Pestana ◽  
Matthias Thalhammer ◽  
Stefan Hickel
Keyword(s):  
Reynolds Number ◽  
Energy Transfer ◽  
Energy Dissipation ◽  
Kinetic Energy ◽  
Gravity Waves ◽  
Energy Budget ◽  
Dissipation Rate ◽  
Scaling Law ◽  
Energy Dissipation Rate ◽  
Inertia Gravity Waves

Abstract We present direct numerical simulations of inertia–gravity waves breaking in the middle–upper mesosphere. We consider two different altitudes, which correspond to the Reynolds number of 28 647 and 114 591 based on wavelength and buoyancy period. While the former was studied by Remmler et al., it is here repeated at a higher resolution and serves as a baseline for comparison with the high-Reynolds-number case. The simulations are designed based on the study of Fruman et al., and are initialized by superimposing primary and secondary perturbations to the convectively unstable base wave. Transient growth leads to an almost instantaneous wave breaking and secondary bursts of turbulence. We show that this process is characterized by the formation of fine flow structures that are predominantly located in the vicinity of the wave’s least stable point. During the wave breakdown, the energy dissipation rate tends to be an isotropic tensor, whereas it is strongly anisotropic in between the breaking events. We find that the vertical kinetic energy spectra exhibit a clear 5/3 scaling law at instants of intense energy dissipation rate and a cubic power law at calmer periods. The term-by-term energy budget reveals that the pressure term is the most important contributor to the global energy budget, as it couples the vertical and the horizontal kinetic energy. During the breaking events, the local energy transfer is predominantly from the mean to the fluctuating field and the kinetic energy production is in balance with the pseudo kinetic energy dissipation rate.

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