scholarly journals Scaling bounds on dissipation in turbulent flows

2015 ◽  
Vol 777 ◽  
pp. 591-603 ◽  
Author(s):  
Christian Seis
Keyword(s):  
Fluid Dynamics ◽  
Turbulent Flows ◽  
Dissipation Rate ◽  
Equations Of Motion ◽  
Average Energy ◽  
Energy Dissipation Rate ◽  
Porous Medium Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Rigorous Method

We propose a new rigorous method for estimating statistical quantities in fluid dynamics such as the (average) energy dissipation rate directly from the equations of motion. The method is tested on shear flow, channel flow, Rayleigh–Bénard convection and porous medium convection.

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.

Experimental assessment of fractal scale similarity in turbulent flows. Part 4. Effects of Reynolds and Schmidt numbers

1998 ◽  
Vol 377 ◽  
pp. 169-187 ◽  
Author(s):  
RICHARD D. FREDERIKSEN ◽  
WERNER J. A. DAHM ◽  
DAVID R. DOWLING
Keyword(s):  
Turbulent Flows ◽  
Dissipation Rate ◽  
Single Point ◽  
Energy Dissipation Rate ◽  
Scalar Dissipation ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Outer Scale ◽  
Scale Invariant ◽  
Scale Similarity

Experimental results are presented for the influence of Reynolds number on multifractal scale similarity in turbulent flows. These are obtained from single-point measurements of a dynamically passive Sc≈1 conserved scalar quantity ζ(t) in a turbulent shear flow at outer-scale Reynolds numbers of 14000[les ]Reδ[les ]110000. Statistical criteria based on the maximum allowable scale-to-scale variation L1(ε) in multiplier distributions P(Mε) from multifractal gauge sets allow accurate discrimination between multifractal and non-multifractal scaling. Results show that the surrogate scalar energy dissipation rate χs(t)≡(dζ/dt)2is found to display a scale-invariant similarity consistent with a random multiplicative cascade characterized by a bilinear multiplier distribution P(Mε) over a range of scales extending downward from the outer scaleTδ. For a range of scales extending upward from the inner (diffusive) scale TD, the dissipation rate displays a different scale-invariant similarity characterized by a uniform multiplier distribution. The former scale-invariance becomes evident in the present Sc≈1 data only when Reδ is sufficiently large. Comparisons with results from Sc 1 data indicate that this scale-invariant similarity applies when the outer-to-inner scale ratio Tδ/TD≈0.09 Re3/4δSc1/2 is greater than about 400. In contrast to the scalar dissipation rate field, the scalar field is found to lack any multifractal scale similarity.

scholarly journals Temperature profiles measurements in turbulent Rayleigh-Bénard convection by optical fibre system at the Barrel of II-menau

2018 ◽  
Vol 180 ◽  
pp. 02020
Author(s):  
Jakub Drahotský ◽  
Pavel Hanzelka ◽  
Věra Musilová ◽  
Michal Macek ◽  
Ronald du Puits ◽  
...  
Keyword(s):  
Turbulent Flows ◽  
Optical Fibre ◽  
Large Scale ◽  
Temperature Profiles ◽  
Vertical Temperature ◽  
Thin Glass ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Modelling of large-scale natural (thermally-generated) turbulent flows (such as the turbulent convection in Earth’s atmosphere, oceans, or Sun) is approached in laboratory experiments in the simplified model system called the Rayleigh-Bénard convection (RBC). We present preliminary measurements of vertical temperature profiles in the cell with the height of 4:7 m, 7:15m in diameter, obtained at the Barrel of Ilmenau (BOI), the worldwide largest experimental setup to study highly turbulent RBC, newly equipped with the Luna ODiSI-B optical fibre system. In our configuration, the system permits to measure the temperature with a high spatial resolution of 5mm along a very thin glass optical fibre with the length of 5m and seems to be perfectly suited for measurement of time series of instantaneous vertical temperature profiles. The system was supplemented with the two Pt100 vertically movable probes specially designed by us for reference temperature profiles measurements.

Determination of hydraulic resistance of channels using spectral geometry methods

2021 ◽  
Author(s):  
Alex Baron
Keyword(s):  
Hydraulic Resistance ◽  
Cross Section ◽  
Dissipation Rate ◽  
Average Energy ◽  
Energy Dissipation Rate ◽  
High Accuracy ◽  
Spectral Geometry ◽  
Constant Cross Section ◽  
Theoretical Justification

Abstract In this paper, we propose a new method for calculation of hydraulic resistance of channels with constant cross-section. The method is based on the obtained estimates for the average energy dissipation rate in a turbulent flow. The first part of the paper is devoted to theoretical justification of the method. The second part is devoted to calculation of hydraulic resistance of various channels using the abovementioned method and comparison of these values with the known results. The proposed method allows for calculation of hydraulic resistance of various channels with sufficiently high accuracy and is based only on the information about the channel geometry.

Observations of Small-Scale Processes Associated with the Internal Tide Encountering an Island

2005 ◽  
Vol 35 (9) ◽  
pp. 1553-1567 ◽  
Author(s):  
Craig L. Stevens ◽  
Edward R. Abraham ◽  
C. Mark Moore ◽  
Philip W. Boyd ◽  
Jonathan Sharples
Keyword(s):  
Dissipation Rate ◽  
East Coast ◽  
Average Energy ◽  
Internal Tide ◽  
Propagation Speed ◽  
Energy Dissipation Rate ◽  
Nonstationary Time Series ◽  
Small Scale ◽  
Vertical Diffusivity ◽  
Order Of Magnitude

Abstract Current-meter, temperature, and microstructure observations of the large-amplitude internal tide shoaling on the continental shelf of the east coast of northern New Zealand show the complexity of the internal kinematics and mixing. The propagation speed of the main internal wave was around 0.3 m s−1, and nonstationary time series analysis was used to locate the trailing short-wavelength internal waves in frequency (periods of around 40 min) and tidal-phase space. The average energy dissipation rate (5 × 10−8 m2 s−3) was an order of magnitude smaller than that observed on the open shelf in other studies, but peaks in dissipation rate were measured to be much greater. The vertical diffusivity of heat was around 10−4 m2 s−1, comparable to, or greater than, other studies. Examples of the scale and sporadic nature of larger mixing events were observed. The behavior was complicated by the nearby steeply shoaling coast of the Poor Knight Islands. Consistent reflected wave energy was not apparent.

scholarly journals Data-driven reduced modelling of turbulent Rayleigh–Bénard convection using DMD-enhanced fluctuation–dissipation theorem

2018 ◽  
Vol 852 ◽  
Author(s):  
M. A. Khodkar ◽  
Pedram Hassanzadeh
Keyword(s):  
Turbulent Flows ◽  
Data Driven ◽  
High Dimensional ◽  
Dynamic Mode ◽  
Fluctuation Dissipation ◽  
Fluctuation Dissipation Theorem ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

A data-driven model-free framework is introduced for the calculation of reduced-order models (ROMs) capable of accurately predicting time-mean responses to external forcings, or forcings needed for specified responses, e.g. for control, in fully turbulent flows. The framework is based on using the fluctuation–dissipation theorem (FDT) in the space of a limited number of modes obtained from dynamic mode decomposition (DMD). Use of the DMD modes as the basis functions, rather than the commonly used proper orthogonal decomposition modes, resolves a previously identified problem in applying FDT to high-dimensional non-normal turbulent flows. Employing this DMD-enhanced FDT method ($\text{FDT}_{DMD}$), a linear ROM with horizontally averaged temperature as state vector is calculated for a 3D Rayleigh–Bénard convection system at a Rayleigh number of$10^{6}$using data obtained from direct numerical simulation. The calculated ROM performs well in various tests for this turbulent flow, suggesting$\text{FDT}_{DMD}$as a promising method for developing ROMs for high-dimensional turbulent systems.

scholarly journals Assessment of Solution Algorithms for LES of Turbulent Flows Using OpenFOAM

Fluids ◽  
2019 ◽  
Vol 4 (3) ◽  
pp. 171 ◽  
Author(s):  
Santiago López Castaño ◽  
Andrea Petronio ◽  
Giovanni Petris and Vincenzo Armenio 
Keyword(s):  
Turbulent Flows ◽  
Mixed Model ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Subgrid Scale ◽  
Reynolds Analogy ◽  
Navier Stokes Equations ◽  
Hexahedral Meshes ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

We validate and test two algorithms for the time integration of the Boussinesq form of the Navier—Stokes equations within the Large Eddy Simulation (LES) methodology for turbulent flows. The algorithms are implemented in the OpenFOAM framework. From one side, we have implemented an energy-conserving incremental-pressure Runge–Kutta (RK4) projection method for the solution of the Navier–Stokes equations together with a dynamic Lagrangian mixed model for momentum and scalar subgrid-scale (SGS) fluxes; from the other side we revisit the PISO algorithm present in OpenFOAM (pisoFoam) in conjunction with the dynamic eddy-viscosity model for SGS momentum fluxes and a Reynolds Analogy for the scalar SGS fluxes, and used for the study of turbulent channel flows and buoyancy-driven flows. In both cases the validity of the anisotropic filter function, suited for non-homogeneous hexahedral meshes, has been studied and proven to be useful for industrial LES. Preliminary tests on energy-conservation properties of the algorithms studied (without the inclusion of the subgrid-scale models) show the superiority of RK4 over pisoFoam, which exhibits dissipative features. We carried out additional tests for wall-bounded channel flow and for Rayleigh–Bènard convection in the turbulent regime, by running LES using both algorithms. Results show the RK4 algorithm together with the dynamic Lagrangian mixed model gives better results in the cases analyzed for both first- and second-order statistics. On the other hand, the dissipative features of pisoFoam detected in the previous tests reflect in a less accurate evaluation of the statistics of the turbulent field, although the presence of the subgrid-scale model improves the quality of the results compared to a correspondent coarse direct numerical simulation. In case of Rayleigh–Bénard convection, the results of pisoFoam improve with increasing values of Rayleigh number, and this may be attributed to the Reynolds Analogy used for the subgrid-scale temperature fluxes. Finally, we point out that the present analysis holds for hexahedral meshes. More research is need for extension of the methods proposed to general unstructured grids.

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