Turbulent flow in the bulk of Rayleigh–Bénard convection: aspect-ratio dependence of the small-scale properties

2014 ◽  
Vol 747 ◽  
pp. 73-102 ◽  
Author(s):  
Matthias Kaczorowski ◽  
Kai-Leong Chong ◽  
Ke-Qing Xia
Keyword(s):  
Heat Flux ◽  
Energy Dissipation ◽  
Kinetic Energy ◽  
Aspect Ratio ◽  
Dissipation Rate ◽  
Energy Dissipation Rate ◽  
Thermal Plumes ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Very High

AbstractGeometrical confinement of turbulent Rayleigh–Bénard convection (RBC) in Cartesian geometries is found to reduce the local Bolgiano length scale in the centre of the cell $L_{B,centre}$ and can therefore be used to study cascade processes in the bulk of RBC. The dependence of $L_{B,centre}$ versus $\varGamma $ suggests a cut-off to the local $L_B$, which depends on the Prandtl number $Pr$ and is of the order of the cell’s smallest dimension. It is also observed that geometrical confinement changes the topology of the flow, causing the turbulent kinetic energy dissipation rate and the temperature variance dissipation rate (averaged over the centre of the cell and normalized by their respective global averages) to exhibit a maximum at a certain $\varGamma $, which roughly coincides with the aspect ratio at which the viscous and thermal boundary layers of the two opposite lateral walls merge. As a result the mean heat flux through the core region also exhibits a maximum. Unlike in the cubic case, we find that geometrical confinement of the flow results in a local balance of the heat flux and the turbulent kinetic energy dissipation rate for $Pr= 4.38$ for all values of the Rayleigh number $Ra$ (up to $10^{10}$), while no balance is observed for $Pr= 0.7$. The need for very high bulk resolution to accurately resolve the gradients of the flow field at high $Ra$ is shown by analysing the second-order structure functions of the vertical velocity and temperature in the bulk of RBC. Under-resolution of the temperature field yields a large error in the dissipative range scaling, which is believed to be an effect of intermittently penetrating thermal plumes. The resolution contrast resulting from the requirement to resolve the thermal plumes and the homogeneous and isotropic background turbulence scales as $\delta _T / \langle \eta _k \rangle _{centre} \sim Ra^{0.1}$ and should therefore be taken into account when tackling very high $Ra$. In the case studied here, under-resolution can have a significant effect on the local heat flux through the centre of the cell.

Analysis of sheet-like thermal plumes in turbulent Rayleigh–Bénard convection

2008 ◽  
Vol 599 ◽  
pp. 383-404 ◽  
Author(s):  
OLGA SHISHKINA ◽  
CLAUS WAGNER
Keyword(s):  
Heat Flux ◽  
Aspect Ratio ◽  
Dissipation Rate ◽  
Local Heat ◽  
Thermal Dissipation ◽  
Thermal Plumes ◽  
Vorticity Component ◽  
Local Heat Flux ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Sheet-like thermal plumes are investigated using time-dependent and three-dimensional flow fields obtained from direct numerical simulations and well-resolved large-eddy simulations of turbulent Rayleigh–Bénard convection in water (Prandtl number Pr=5.4) in a cylindrical container with the aspect ratio Γ=1 and for the Rayleigh numbers Ra=2×109 and 2×1010.To analyse quantitatively the physical properties of the sheet-like thermal plumes and the turbulent background and to obtain the temperature threshold which separates these two different flow regions, the temperature dependences of the conditionally averaged local heat flux, thermal dissipation rate and selected components of the velocity and vorticity fields are studied. It is shown that the sheet-like plumes are characterized by high values of the local heat flux and relatively large absolute values of the vertical components of the vorticity and velocity fields. The borders of these plumes are indicated by large values of the thermal dissipation rate and large absolute values of the horizontal vorticity components. In contrast to the sheet-like thermal plumes, the turbulent background is characterized by low values of the thermal dissipation rate, local heat flux and vertical vorticity component. The highest values of the local heat flux and the highest absolute values of the vertical vorticity component are found in the regions where the sheet-like plumes strike against each other. Fluid swirling at these places forms the stems of the mushroom-like thermal plumes which develop in the bulk of the Rayleigh–Bénard cell.Further, formulae to calculate the curvature, thickness and length of the plumes are introduced. Geometrical properties such as plume area, diameter, curvature, thickness and aspect ratio together with the physical properties of the sheet-like plumes such as temperature, heat flux, thermal dissipation rate, velocity and vorticity are investigated.

Evaluation of Turbulent Kinetic Energy Dissipation Rate in a Free Jet Flow from PIV Measurements

2012 ◽  
Vol 7 (1) ◽  
pp. 53-69
Author(s):  
Vladimir Dulin ◽  
Yuriy Kozorezov ◽  
Dmitriy Markovich
Keyword(s):  
Energy Dissipation ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Dissipation Rate ◽  
Energy Dissipation Rate ◽  
Turbulent Velocity ◽  
Small Scale ◽  
Velocity Fluctuations ◽  
Piv Measurements ◽  
Free Jet

The present paper reports PIV (Particle Image Velocimetry) measurements of turbulent velocity fluctuations statistics in development region of an axisymmetric free jet (Re = 28 000). To minimize measurement uncertainty, adaptive calibration, image processing and data post-processing algorithms were utilized. On the basis of theoretical analysis and direct measurements, the paper discusses effect of PIV spatial resolution on measured statistical characteristics of turbulent fluctuations. Underestimation of the second-order moments of velocity derivatives and of the turbulent kinetic energy dissipation rate due to a finite size of PIV interrogation area and finite thickness of laser sheet was analyzed from model spectra of turbulent velocity fluctuations. The results are in a good agreement with the measured experimental data. The paper also describes performance of possible ways to account for unresolved small-scale velocity fluctuations in PIV measurements of the dissipation rate. In particular, a turbulent viscosity model can be efficiently used to account for the unresolved pulsations in a free turbulent flow

A MEMS flow velocity sensor with low kinetic energy dissipation rate

Sensor Review ◽  
2017 ◽  
Vol 37 (3) ◽  
pp. 247-256 ◽  
Author(s):  
Bian Tian ◽  
Huafeng Li ◽  
Ning Yang ◽  
Yulong Zhao ◽  
Pei Chen ◽  
...  
Keyword(s):  
Fluid Flow ◽  
Energy Dissipation ◽  
Kinetic Energy ◽  
Flow Velocity ◽  
Dissipation Rate ◽  
Energy Dissipation Rate ◽  
Flow Sensor ◽  
Ocean Turbulence ◽  
Content Type ◽  
Turbulence Flow

Purpose It is significant to know the real-time indexes about the turbulence flow of the ocean system, which has a deep influence on ocean productivity, distribution of the ocean populations and transmission of the ocean energy, especially the measurement of turbulence flow velocity. So, it is particularly urgent to provide a high-sensitivity, low-cost and reliable fluid flow sensor for industry and consumer product application. This paper aims to design a micro fluid flow sensor with a cross beam membrane structure. The designed sensor can detect the fluid flow velocity and has a low kinetic energy dissipation rate. Design/methodology/approach In this paper, a micro fluid flow sensor with a cross beam membrane structure is designed to measure the ocean turbulence flow velocity. The design, simulation, fabrication and measurement of the designed sensor are discussed. By testing the simply packaged sensor in the fluid flow and analyzing the experiments data, the results show that the designed sensor has favorable performance. Findings The paper describes the tests of the designed sensor, and the experimental results show that the designed sensor can measure the fluid flow velocity and has a sensitivity of 11.12 mV/V/(m/s)2 and a low kinetic energy dissipation rate in the range of 10-6-10-4 W/kg. Originality/value This paper provides a micro-electro-mechanical systems fluid flow sensor used to measure ocean turbulence flow velocity.

scholarly journals Using an ADCP to Estimate Turbulent Kinetic Energy Dissipation Rate in Sheltered Coastal Waters

2015 ◽  
Vol 32 (2) ◽  
pp. 318-333 ◽  
Author(s):  
A. D. Greene ◽  
P. J. Hendricks ◽  
M. C. Gregg
Keyword(s):  
Energy Dissipation ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Cell Size ◽  
Dissipation Rate ◽  
Puget Sound ◽  
Acoustic Doppler Current Profiler ◽  
Energy Dissipation Rate ◽  
Integral Scale ◽  
Thorpe Scale

AbstractTurbulent microstructure and acoustic Doppler current profiler (ADCP) data were collected near Tacoma Narrows in Puget Sound, Washington. Over 100 coincident microstructure profiles have been compared to ADCP estimates of turbulent kinetic energy dissipation rate (ϵ). ADCP dissipation rates were calculated using the large-eddy method with theoretically determined corrections for sensor noise on rms velocity and integral-scale calculations. This work is an extension of Ann Gargett’s approach, which used a narrowband ADCP in regions with intense turbulence and strong vertical velocities. Here, a broadband ADCP is used to measure weaker turbulence and achieve greater horizontal and vertical resolution relative to the narrowband ADCP. Estimates of ϵ from the Modular Microstructure Profiler (MMP) and broadband ADCP show good quantitative agreement over nearly three decades of dissipation rate, 3 × 10−8–10−5 m2 s−3. This technique is most readily applied when the turbulent velocity is greater than the ADCP velocity uncertainty (σ) and the ADCP cell size is within a factor of 2 of the Thorpe scale. The 600-kHz broadband ADCP used in this experiment yielded a noise floor of 3 mm s−1 for 3-m vertical bins and 2-m along-track average (≈four pings), which resulted in turbulence levels measureable with the ADCP as weak as 3 × 10−8 m2 s−3. The value and trade-off of changing the ADCP cell size, which reduces noise but also changes the ratio of the Thorpe scale to the cell size, are discussed as well.

scholarly journals Numerical evidence of anomalous energy dissipation in incompressible Euler flows: towards grid-converged results for the inviscid Taylor–Green problem

2021 ◽  
Vol 932 ◽  
Author(s):  
Niklas Fehn ◽  
Martin Kronbichler ◽  
Peter Munch ◽  
Wolfgang A. Wall
Keyword(s):  
Energy Dissipation ◽  
Kinetic Energy ◽  
Euler Equations ◽  
Spatial Resolution ◽  
Dissipation Rate ◽  
Energy Dissipation Rate ◽  
Incompressible Euler Equations ◽  
Fine Resolution ◽  
Resolution Simulation ◽  
Incompressible Euler

The well-known energy dissipation anomaly in the inviscid limit, related to velocity singularities according to Onsager, still needs to be demonstrated by numerical experiments. The present work contributes to this topic through high-resolution numerical simulations of the inviscid three-dimensional Taylor–Green vortex problem using a novel high-order discontinuous Galerkin discretisation approach for the incompressible Euler equations. The main methodological ingredient is the use of a discretisation scheme with inbuilt dissipation mechanisms, as opposed to discretely energy-conserving schemes, which – by construction – rule out the occurrence of anomalous dissipation. We investigate effective spatial resolution up to $8192^3$ (defined based on the $2{\rm \pi}$ -periodic box) and make the interesting phenomenological observation that the kinetic energy evolution does not tend towards exact energy conservation for increasing spatial resolution of the numerical scheme, but that the sequence of discrete solutions seemingly converges to a solution with non-zero kinetic energy dissipation rate. Taking the fine-resolution simulation as a reference, we measure grid-convergence with a relative $L^2$ -error of $0.27\,\%$ for the temporal evolution of the kinetic energy and $3.52\,\%$ for the kinetic energy dissipation rate against the dissipative fine-resolution simulation. The present work raises the question of whether such results can be seen as a numerical confirmation of the famous energy dissipation anomaly. Due to the relation between anomalous energy dissipation and the occurrence of singularities for the incompressible Euler equations according to Onsager's conjecture, we elaborate on an indirect approach for the identification of finite-time singularities that relies on energy arguments.

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