On a New Theory of free Turbulence

1943 ◽  
Vol 47 (390) ◽  
pp. 167-176 ◽  
Author(s):  
H. Reichardt
Keyword(s):  
Differential Equation ◽  
Turbulent Flows ◽  
Turbulent Mixing ◽  
Thermal Conduction ◽  
Phenomenological Theory ◽  
Rational Application ◽  
Turbulent Momentum ◽  
Molecular Balance

Measurements of momentum in regions of turbulent mixing show that an analogy exists between the processes of turbulent and molecular balance which enables a rational application of the differential equation of thermal conduction to the propagation of turbulent momentum to be made. This fact forms the basis of a new phenomenological theory of free turbulent flows.

scholarly journals A Shear-Based Parameterization of Turbulent Mixing in the Stable Atmospheric Boundary Layer

2015 ◽  
Vol 72 (5) ◽  
pp. 1713-1726 ◽  
Author(s):  
Jordan M. Wilson ◽  
Subhas K. Venayagamoorthy
Keyword(s):  
Boundary Layer ◽  
Stress Intensity ◽  
Kinetic Energy ◽  
Atmospheric Boundary Layer ◽  
Turbulent Mixing ◽  
Intensity Ratio ◽  
Eddy Diffusivity ◽  
Stable Atmospheric Boundary Layer ◽  
Turbulent Momentum ◽  
Shear Production

Abstract In this study, shear-based parameterizations of turbulent mixing in the stable atmospheric boundary layer (SABL) are proposed. A relevant length-scale estimate for the mixing length of the turbulent momentum field is constructed from the turbulent kinetic energy and the mean shear rate S as . Using observational data from two field campaigns—the Surface Heat Budget of the Arctic Ocean (SHEBA) experiment and the 1999 Cooperative Atmosphere–Surface Exchange Study (CASES-99)— is shown to have a strong correlation with . The relationship between and corresponds to the ratio of the magnitude of the tangential components of the turbulent momentum flux tensor to , known as stress intensity ratio, . The field data clearly show that is linked to stability. The stress intensity ratio also depends on the flow energetics that can be assessed using a shear-production Reynolds number, , where P is shear production of turbulent kinetic energy and is the kinematic viscosity. This analysis shows that high mixing rates can indeed persist at strong stability. On this basis, shear-based parameterizations are proposed for the eddy diffusivity for momentum, , and eddy diffusivity for heat, , showing remarkable agreement with the exact quantities. Furthermore, a broader assessment of the proposed parameterizations is given through an a priori evaluation of large-eddy simulation (LES) data from the first GEWEX Atmospheric Boundary Layer Study (GABLS). The shear-based parameterizations outperform many existing models in predicting turbulent mixing in the SABL. The results of this study provide a framework for improved representation of the SABL in operational models.

scholarly journals Bubbles and Superbubbles: Observations and Theory

2007 ◽  
Vol 3 (S250) ◽  
pp. 341-354 ◽  
Author(s):  
You-Hua Chu
Keyword(s):  
Turbulent Mixing ◽  
Thermal Conduction ◽  
Massive Stars ◽  
Ambient Medium ◽  
Surrounding Medium ◽  
Shell Structures ◽  
Stellar Winds ◽  
Hot Gas ◽  
Dense Shell ◽  
Supernova Explosions

AbstractMassive stars inject energy into the surrounding medium and form shell structures. Bubbles are blown by fast stellar winds from individual massive stars, while superbubbles are blown by fast stellar winds and supernova explosions from groups of massive stars. Bubbles and superbubbles share a similar overall structure: a swept-up dense shell with an interior filled by low-density hot gas. Physical properties of a bubble/superbubble can be affected by magnetic field, thermal conduction, turbulent mixing, inhomogeneous ambient medium, etc. I will review recent progresses on observations and compare them to theoretical expectations for (1) swept-up dense shells, (2) hot interiors, and (3) interface between a dense shell and its interior hot gas.

Chaotic stirring in quasi-turbulent flows

2007 ◽  
Vol 365 (1861) ◽  
pp. 3061-3084 ◽  
Author(s):  
Francois Lekien ◽  
Chad Coulliette
Keyword(s):  
Turbulent Flows ◽  
Turbulent Mixing ◽  
Pollution Source ◽  
Laminar Flows ◽  
Coastal Pollution ◽  
Monterey Bay ◽  
Thin Filaments ◽  
Isotropic Mixing ◽  
Recent Developments ◽  
The Impact

Transport in laminar flows is governed by chaotic stirring and striation in long thin filaments. In turbulent flows, isotropic mixing dominates and tracers behave like stochastic variables. In this paper, we investigate the quasi-turbulent, intermediate regime where both chaotic stirring and turbulent mixing coexist. In these flows, the most common in nature, aperiodic Lagrangian coherent structures (LCSs) delineate particle transport and chaotic stirring. We review the recent developments in LCS theory and apply these techniques to measured surface currents in Monterey Bay, California. In the bay, LCSs can be used to optimize the release of drifting buoys or to minimize the impact of a coastal pollution source.

Transport processes In liquids

1952 ◽  
Vol 215 (1120) ◽  
pp. 29-36 ◽  
Keyword(s):  
Differential Equation ◽  
Probability Distribution ◽  
Thermal Conduction ◽  
Intermolecular Forces ◽  
Transport Processes ◽  
Modern Theory ◽  
Brownian Movement ◽  
Average Flow ◽  
Large Particles ◽  
Quantitative Results

The object of the modern theory is to find the average flow of mass, momentum or energy, as observed in diffusion, viscous flow or thermal conduction, by means of the probability distribution for the co-ordinates and momenta of a representative molecule or pair of molecules. Transmission of momentum or energy in liquids, as distinct from gases, is due to the action of intermolecular forces. The probability distribution is determined by a differential equation similar to the equation of Fokker and Planck. Frequently it is sufficient to find the probability distribution in space co-ordinates only, by solving the equation of Smoluchowski. These equations are known to apply to the Brownian movement of large particles suspended in a liquid. Their validity for the movement of molecules was established only recently by combining the principles of statistics and dynamics and invoking a hypothesis of molecular chaos. The friction constants entering as parameters into the differential equations can, in principle, be derived from intermolecular forces; in practice this involves considerable difficulties. Even in its present incomplete stage the theory yields quantitative results comparing reasonably well with experiment. In addition it provides criteria for assessing the significance of viscosity formulae as put forward by previous authors.

Investigation of the Agglomeration and the Break-Up of Isolation Material

2009 ◽  
Author(s):  
Stefan Renger
Keyword(s):  
Differential Equation ◽  
Turbulent Flows ◽  
Nuclear Power ◽  
Heat Dissipation ◽  
Cfd Simulation ◽  
Reactor Core ◽  
Equation System ◽  
Differential Equation System ◽  
Complex Flow ◽  
Break Up

The description of the complex flow of coolant water with particles is necessary to evaluate safety relevant effects of the sedimentation of isolation material on sump-sieves in nuclear power station. Classifying and modeling of the different phenomena maybe important in the case of a coolant accident, because the isolation material can be transported into the reactor containment, the building sump of the containment and into the associated systems [1]. In order to ensure the heat dissipation from the reactor core and the containment the cooling systems transport the water from the sump into the condensation chamber and then into the reactor pressure vessel. The functionality of the pumps can be affected by a high allocation of the sieves with fractionated isolation material. In this case the heat dissipation from fuel elements is not guaranteed. The transport of the material will be simulated with the CFD-code. The modeling of the flow with particles is very complex, because of the structure of the particles and their interaction with the fluid. There are different classes of particles with different attributes, e.g. sinking velocity. So one needs more than one disperse phase to describe the whole process, which is associated with a lot of computing power and not realizable for large geometries. The paper deals with experimental and methodical activities for the description of the agglomeration and the break-up of isolation material in fluid flow. The aim of this work is to describe the evolution of the volume parts of the different particle classes turbulent flows depending on the time in. The modeling phase starts with a very simple model to describe 3 particle classes (x, y, z) and results in a differential equation system with 3 equations. To describe all classes the model has to be expanded. Therefore the Lindenmayer-System approach has been adopted. These systems can be taken in cases where self-similarity takes place. The result is a differential equation system with iterations for the three classes (x(i), y(i), z(i)), with i as the parameter for the number of subclasses. The values for the agglomeration and break-up rates will be taken from experiments. As a result a model has been created which describes the evaluation of the different particles classes in turbulent flow. It helps to choose the correct particle class in the CFD simulation depending on the situation to simulate.

A Linearized Turbulent Lubrication Theory

1965 ◽  
Vol 87 (3) ◽  
pp. 675-682 ◽  
Author(s):  
Chung-Wah Ng ◽  
C. H. T. Pan
Keyword(s):  
Differential Equation ◽  
Experimental Data ◽  
Eddy Viscosity ◽  
Shear Flows ◽  
Momentum Transport ◽  
Turbulent Shear ◽  
New Approach ◽  
Turbulent Shear Flows ◽  
Governing Differential Equation ◽  
Turbulent Momentum

The “law of wall” for turbulent shear flows has been adapted to analyze turbulent lubrication. This new approach takes into account many well-established facts concerning turbulent shear flows. Isotropy of turbulent momentum transport (eddy viscosity) is assumed in treating nonplanar mean flows. A linearized version of the governing differential equation is established. Sample results agree well with available experimental data.

scholarly journals On the phenomenological theory of magnetic storms

2016 ◽  
Vol 2 (2) ◽  
pp. 29-34
Author(s):  
Анатолий Гульельми ◽  
Anatol Guglielmi
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Phase Transitions ◽  
Integral Representation ◽  
Wide Class ◽  
Phenomenological Theory ◽  
Azimuthal Component ◽  
Explosive Instability ◽  
Threshold Phenomena ◽  
Threshold Point

This article addresses methodical issues concerning the modeling of the Dst variation in a geomagnetic storm. We describe the so-called RBM (Russell — Burton — McPherron) model representing an ordinary differential equation with solutions simulating the relation between the Dst variation and the azimuthal component of the interplanetary electric field. Special attention is paid to the threshold nature of Dst variation excitation. We would like to emphasize the necessity of stochastic extension of the RBM model by allowing for fluctuations inherent to any physical system. The integral representation of a Dst variation bifurcation diagram is given. This enables us to account for the effect of fluctuations which eliminate the diagram root singularity and cause a threshold point shift. The Dst variation is shown to be typical of the wide class of threshold phenomena similar to second-order phase transitions. We draw an analogy with threshold phenomena in the Earth’s magnetosphere, atmosphere, and lithosphere. In addition, we briefly discuss the issue about soft and hard passages through the threshold, as well as about explosive instability in geophysical media.

Modeling the Transport of Fuel Mixture Perturbations and Entropy Waves in the Linearized Framework

2020 ◽  
Author(s):  
Thomas Ludwig Kaiser ◽  
Kilian Oberleithner
Keyword(s):  
Turbulent Flows ◽  
Channel Flow ◽  
Turbulent Mixing ◽  
Equivalence Ratio ◽  
Stokes Equations ◽  
Turbulent Channel Flow ◽  
Passive Scalar ◽  
Computational Domain ◽  
Reynolds Stresses ◽  
Mean Flow

Abstract In this paper a new method is introduced to model the transport of entropy waves and equivalence ratio fluctuations in turbulent flows. The model is based on the Navier-Stokes equations and includes a transport equation for a passive scalar, which may stand for entropy or equivalence ratio fluctuations. The equations are linearized around the mean turbulent fields, which serve as the input to the model in addition to a turbulent eddy viscosity, which accounts for turbulent diffusion of the perturbations. Based on these inputs, the framework is able to predict the linear response of the flow velocity and passive scalar to harmonic perturbations that are imposed at the boundaries of the computational domain. These in this study are fluctuations in the passive scalar and/or velocities at the inlet of a channel flow. The code is first validated against analytic results, showing very good agreement. Then the method is applied to predict the convection, mean flow dispersion and turbulent mixing of passive scalar fluctuations in a turbulent channel flow, which has been studied in previous work with Direct Numerical Simulations (DNS). Results show that our code reproduces the dynamics of coherent passive scalar transport in the DNS with very high accuracy and low numerical costs, when the DNS mean flow and Reynolds stresses are provided. Furthermore, we demonstrate that turbulent mixing has a significant effect on the transport of the passive scalar fluctuations. Finally, we apply the method to explain experimental observations of transport of equivalence ratio fluctuations in the mixing duct of a model burner.

Simulation of turbulent mixing rate in simulated subchannels of a reactor rod bundle

Kerntechnik ◽  
2021 ◽  
Vol 86 (3) ◽  
pp. 210-216
Author(s):  
M. P. Sharma ◽  
A. Moharana
Keyword(s):  
Turbulent Flows ◽  
Turbulent Mixing ◽  
Flow Behavior ◽  
Three Dimensional ◽  
Reynolds Stress Model ◽  
Momentum Equation ◽  
Mixing Rate ◽  
Mixing Coefficient ◽  
Rod Bundle ◽  
Subchannel Analysis

Abstract Subchannel analysis codes are widely used for the thermal-hydraulic design of nuclear reactor rod bundle. The effectiveness of subchannel analysis codes depends on turbulent mixing between these subchannels. Turbulent mixing has no direct contribution to the axial mass flow rate through subchannel but it will cause exchange of momentum and energy between the neighboring subchannels. Thus, it is important to evaluate the turbulent mixing coefficient for reactor rod bundle as it is a significant factor in the lateral energy and momentum equation for subchannel analysis codes like COBRA IIIC, COBRA-IV and MATRA LMR-FB. With the rapid developments in computational fluid dynamics and computer performance, three-dimensional analyses of turbulent flows occurring in the nuclear rod bundle have become more prominent. Several numerical analyses have already been attempted to investigate the flow behavior in rod bundles of different reactors. Much of these are dedicated to find out the structure of turbulence in rod bundle but a few analyses has been done to evaluate the magnitude of the turbulent mixing coefficient. In view of this, CFD analyses were carried out to determine the turbulent mixing coefficient in the simulated sub-channels of the reactor rod bundle. Previous studies on the structure of turbulence reveals that it is highly anisotropic. Hence, the Reynolds Stress Model (RSM), finer mesh and near wall distance ( y + ≤ 2) is required to capture turbulent mixing phenomena. The validation of results is done by comparing with subchannel mixing experiments.

Sign in / Sign up

Export Citation Format

Share Document