scholarly journals Role of Conservation Laws in the Development of Nonequilibrium and Emergence of Turbulence

2018 ◽  
Vol 14 (2) ◽  
pp. 7682-7690
Author(s):  
Ludmila Ivanovna Petrova
Keyword(s):  
Conservation Laws ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Coordinate Systems ◽  
Navier Stokes Equations ◽  
Equations Of Mathematical Physics ◽  
Physical Quantities ◽  
Numerical And Analytical Methods ◽  
Turbulent Pulsations

It turns out that the equations of mathematical physics, which consist equations of the conservation laws for energy, linear momentum, angular momentum, and mass, possess additional, hidden, properties that enables one to describe not only a variation of physical quantities (such as energy, pressure, density) but also processes such as origination of waves, vortices, turbulent pulsations and other ones. It is caused by the conservation laws properties. In present paper the development of nonequilibrium in gasdynamic systems, which are described by the Euler and Navier-Stokes equations, will be investigated.  Under studying the consistence of conservation laws equations, from the Euler and Navier-Stokes equations it can be obtained the evolutionary relation for entropy (as a state functional).  The evolutionary relation possesses a certain peculiarity, namely, it turns out to be nonidentical. This fact points out to inconsistence of the conservation law equations and noncommutativity of conservation laws. Such a nonidentical relation discloses peculiarities of the solutions to the Navier-Stokes equations due to which the Euler and Navier-Stokes equations can describe the processes the development of nonequilibrium and emergence of vortices and turbulence. It has been shown that such processes can be described only with the help of two nonequivalent coordinate systems or by simultaneous using numerical and analytical methods.

Numerical Investigation of the Effect of Balancing-Hole on the Axial Force of a Partial Emission Pump

2014 ◽  
Author(s):  
Zhang Lisheng ◽  
Jiang Jin ◽  
Xiao Zhihuai ◽  
Li Yanhui
Keyword(s):  
Axial Force ◽  
Stokes Equations ◽  
Dominant Role ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Design Parameters ◽  
Navier Stokes Equations ◽  
Computational Fluid Dynamics Cfd ◽  
The Cost

In this paper numerical simulations were conducted to analyze the effects of design parameters and distribution of balancing-hole on the axial-force of a partial emission pump. The studied pump is a single stage pump with a Barske style impeller. Based on the original impeller, we designed 7 pumps with different balancing-hole diameters and the partial emission pump equipped with different impellers were simulated employing the commercial computational fluid dynamics (CFD) software Fluent 12.1 to solve the Navier-Stokes equations for three-dimensional steady flow. A sensitivity analysis of the numerical model was performed with the purpose of balancing the contradiction of numerical accuracy and the cost of calculation. The results showed that, with increasing of the capacity, the axial force varies little. The diameter of the inner balancing-hole plays a dominant role of reducing axial-force of partial emission pump, the axial-force decreases with increasing of inner balancing-hole diameter on the whole range of operation, the axial-force of impeller without inner balancing-hole is approximately 3 times larger than that of impeller with inner balancing-hole. While the diameter of outer balancing-hole has a reverse effects compared with that of inner balancing-hole. With increasing of outer balancing-hole, the axial force increases accordingly.

Scouring Below Pipelines: The Role of Vorticity and Turbulence

2010 ◽  
Author(s):  
Matteo Mattioli ◽  
Alessandro Mancinelli ◽  
Giuseppina Colicchio ◽  
Maurizio Brocchini
Keyword(s):  
Numerical Model ◽  
Lift Force ◽  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Offshore Pipeline ◽  
Temporal Averaging ◽  
Force Components

A numerical study on the turbulence and vorticity of local scour underneath an offshore pipeline placed on a non-cohesive sandy seabed and forced by a steady flow current is presented. The numerical model solves the Navier-Stokes equations using an innovative Level Set technique. The model predicts the behavior of the movable sediments through both drift and lift force components. Mean and turbulent flow quantities were extracted by temporal averaging. Results on the distribution and evolution of turbulent kinetic energy and vorticity will be illustrated at the conference.

scholarly journals Competition between Chaotic Advection and Diffusion: Stirring and Mixing in a 3D Eddy Model

2018 ◽  
Author(s):  
Genevieve Jay Brett ◽  
Larry Pratt ◽  
Irina Rypina ◽  
Peng Wang
Keyword(s):  
Turbulent Diffusion ◽  
Stokes Equations ◽  
Effective Diffusivity ◽  
Eddy Diffusivity ◽  
Chaotic Advection ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Spatially Varying ◽  
Future Work

Abstract. The importance of chaotic advection relative to turbulent diffusion is investigated in an idealized model of a 3D swirling and overturning ocean eddy. Various measures of stirring and mixing are examined in order to determine when and where chaotic advection is relevant. Turbulence is alternatively represented by: 1) an explicit, observation–based, scale–dependent eddy diffusivity, 2) stochastic noise, added to a deterministic velocity field, or 3) explicit and implicit diffusion in a spectral numerical model of Navier–Stokes equations. Lagrangian chaos in our model occurs only within distinct regions of the eddy, including a large chaotic ‘sea’ that fills much of the volume near the perimeter and central axis of the eddy, and much smaller ‘resonant’ bands. The size and distribution of these regions depends on factors such as the degree of axial asymmetry of the eddy and the Ekman number. The relative importance of chaotic advection and turbulent diffusion within the chaotic regions is quantified using three measures: the ratio of the tracer filament arrest scale to the width of the chaotic region, the rate of dispersal of closely spaced fluid parcels, and the Nakamura effective diffusivity. The role of chaotic advection in the stirring of a passive tracer is generally found to be most important within the larger chaotic ‘seas’, at intermediate times, with small diffusivities, and for eddies with strong asymmetry. In contrast, in thin chaotic regions, turbulent diffusion at oceanographically relevant rates is at least as important as chaotic advection. Future work should address anisotropic and spatially–varying representations of turbulence for more realistic models.

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