Local Energy Dissipation Rate Balances Local Heat Flux in the Center of Turbulent Thermal Convection

2011 ◽  
Vol 107 (17) ◽  
Author(s):  
Rui Ni ◽  
Shi-Di Huang ◽  
Ke-Qing Xia
Keyword(s):  
Heat Flux ◽  
Energy Dissipation ◽  
Thermal Convection ◽  
Dissipation Rate ◽  
Local Heat ◽  
Energy Dissipation Rate ◽  
Local Energy ◽  
Local Heat Flux

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.

Local energy flux and subgrid-scale statistics in three-dimensional turbulence

1998 ◽  
Vol 366 ◽  
pp. 1-31 ◽  
Author(s):  
VADIM BORUE ◽  
STEVEN A. ORSZAG
Keyword(s):  
Energy Transfer ◽  
Energy Dissipation ◽  
Energy Flux ◽  
Dissipation Rate ◽  
Three Dimensional ◽  
Energy Dissipation Rate ◽  
Inertial Range ◽  
Local Energy ◽  
Subgrid Scale ◽  
Velocity Gradients

Statistical properties of the subgrid-scale stress tensor, the local energy flux and filtered velocity gradients are analysed in numerical simulations of forced three-dimensional homogeneous turbulence. High Reynolds numbers are achieved by using hyperviscous dissipation. It is found that in the inertial range the subgrid-scale stress tensor and the local energy flux allow simple parametrization based on a tensor eddy viscosity. This parametrization underlines the role that negative skewness of filtered velocity gradients plays in the local energy transfer. It is found that the local energy flux only weakly correlates with the locally averaged energy dissipation rate. This fact reflects basic difficulties of large-eddy simulations of turbulence, namely the possibility of predicting the locally averaged energy dissipation rate through inertial-range quantities such as the local energy flux is limited. Statistical properties of subgrid-scale velocity gradients are systematically studied in an attempt to reveal the mechanism of local energy transfer.

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.

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.

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