MODELING THE SEPARATION PROCESS IN A HYDROCYCLONE

2020 ◽  
Author(s):  
Сергей Ильдусович Валеев ◽  
Владимир Александрович Савчук
Keyword(s):  
Stokes Equation ◽  
Effective Viscosity ◽  
Numerical Study ◽  
Separation Process ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Light Impurities

На основе уравнения Навье-Стокса проведено численное исследование эффективной вязкости в цилиндрическом гидроциклоне для разделения эмульсий с малым содержанием легких примесей. Установлено, что эффективная вязкость в гидроциклоне возрастает с увеличением разгрузочного соотношения. On the basis of the Navier-Stokes equation, a numerical study of the effective viscosity in a cylindrical hydrocyclone for the separation of emulsions with a low content of light impurities is carried out. It was found that the effective viscosity in a hydrocyclone increases with an increase in the unloading ratio.

On the Effective Viscosity Expression for Modeling Squeeze-Film Damping at Low Pressure

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Maria F. Pantano ◽  
Leonardo Pagnotta ◽  
Salvatore Nigro
Keyword(s):  
Experimental Data ◽  
Stokes Equation ◽  
Effective Viscosity ◽  
Optimization Procedure ◽  
Low Pressure ◽  
Squeeze Film ◽  
Navier Stokes ◽  
Fluid Viscosity ◽  
Navier Stokes Equation ◽  
Squeeze Film Damping

While at high pressure, the classical Navier–Stokes equation is suitable for modeling squeeze-film damping, at low pressure, it needs some modification in order to consider fluid rarefaction. According to a common approach, fluid rarefaction can be included in this equation by substituting the standard fluid viscosity with a fictitious quantity, known as effective viscosity, for which different formulations were proposed. In order to identify which expression works better, the results obtained when either formulation is implemented inside the Navier–Stokes equation (that is then solved by both analytical and numerical means) are compared with already available experimental data. At the end, a novel expression is discussed, derived from a computer-assessed optimization procedure.

scholarly journals Space Analyticity and Bounds for Derivatives of Solutions to the Evolutionary Equations of Diffusive Magnetohydrodynamics

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1789
Author(s):  
Vladislav Zheligovsky
Keyword(s):  
Stokes Equation ◽  
Arbitrary Order ◽  
Numerical Study ◽  
A Priori ◽  
Auxiliary Problem ◽  
Time Derivative ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Evolutionary Equations ◽  
Derivatives Of

In 1981, Foias, Guillopé and Temam proved a priori estimates for arbitrary-order space derivatives of solutions to the Navier–Stokes equation. Such bounds are instructive in the numerical investigation of intermittency that is often observed in simulations, e.g., numerical study of vorticity moments by Donzis et al. (2013) revealed depletion of nonlinearity that may be responsible for smoothness of solutions to the Navier–Stokes equation. We employ an original method to derive analogous estimates for space derivatives of three-dimensional space-periodic weak solutions to the evolutionary equations of diffusive magnetohydrodynamics. Construction relies on space analyticity of the solutions at almost all times. An auxiliary problem is introduced, and a Sobolev norm of its solutions bounds from below the size in C3 of the region of space analyticity of the solutions to the original problem. We recover the exponents obtained earlier for the hydrodynamic problem. Moreover, the same approach is followed here to derive and prove similar a priori bounds for arbitrary-order space derivatives of the first-order time derivative of the weak MHD solutions.

Numerical Study of Cavitation on Hydrofoils

2010 ◽  
Vol 44-47 ◽  
pp. 2001-2005
Author(s):  
Jing Hu ◽  
Xian Zhou Wang ◽  
Ming Yue Liu ◽  
Zhi Guo Zhang ◽  
Qi Zhou
Keyword(s):  
Numerical Simulation ◽  
Stokes Equation ◽  
Turbulence Model ◽  
Volume Fraction ◽  
Numerical Study ◽  
Navier Stokes ◽  
Special Focus ◽  
Navier Stokes Equation ◽  
The Relationship ◽  
Incompressible Navier Stokes Equation

Based on CFD technology, flow around a 2-dimentional hydrofoil of highly skewed propeller and NACA series hydrofoils are simulated using 2D incompressible Navier-Stokes equation with Realizable k- turbulence model. In the numerical simulation, the vapor volume fraction is calculated for different cavitation numbers and angles of attack by adding the mixture model. The hydrofoil’s performance and the relationship with hydrofoil parameter are qualitatively analyzed. Special focus is given to the influence of the cavitation numbers and angle of attack on cavitation characteristics.

Wavelet-distributed approximating functional method for solving the Navier-Stokes equation

1998 ◽  
Vol 115 (1) ◽  
pp. 18-24 ◽  
Author(s):  
G.W. Wei ◽  
D.S. Zhang ◽  
S.C. Althorpe ◽  
D.J. Kouri ◽  
D.K. Hoffman
Keyword(s):  
Stokes Equation ◽  
Functional Method ◽  
Navier Stokes ◽  
Navier Stokes Equation

scholarly journals Generalized Navier–Stokes Equations and Dynamics of Plane Molecular Media

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 288
Author(s):  
Alexei Kushner ◽  
Valentin Lychagin
Keyword(s):  
Carbon Dioxide ◽  
Internal Structure ◽  
Stokes Equation ◽  
Hydrogen Cyanide ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations

The first analysis of media with internal structure were done by the Cosserat brothers. Birkhoff noted that the classical Navier–Stokes equation does not fully describe the motion of water. In this article, we propose an approach to the dynamics of media formed by chiral, planar and rigid molecules and propose some kind of Navier–Stokes equations for their description. Examples of such media are water, ozone, carbon dioxide and hydrogen cyanide.

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