The Solution Of 2D Hydrodynamic Equations In The Boussinesq Approximation: A Mechanism Of Hydrocarbons Transport To The Earth’s Surface

Author(s):  
Sergei V. Gavrilov ◽  
◽  
Andrey L. Kharitonov ◽  
Water ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 1254
Author(s):  
Fei Yang ◽  
Xuejun Shao ◽  
Xudong Fu ◽  
Ehsan Kazemi

In this study, the coupled effects of sediment inertia and stratification on the pattern of secondary currents in bend-flows are evaluated using a 3D numerical model. The sediment inertia effect, as well as the stratification effect induced by the non-uniform distribution of suspended sediment, is accounted for by adopting the hydrodynamic equations without the Boussinesq approximation. The 3D model is validated by existing laboratory experimental results. Simulation results of a simplified meandering channel indicate that sediment stratification effect enhances the intensity of secondary flow via reducing eddy viscosity, while sediment inertia effect suppresses it. The integrated effects result in an increase and a reduction in the secondary flow, respectively, at lower and higher concentrations (near-bed volumetric concentrations of 0.015 and 0.1 are, respectively, considered in this study). This suggests that the dominance of the suspended sediment effect depends on the sediment concentration profile. With the increase of concentration under a specific sediment size, the secondary flow rises to reach a maximum, and then decreases. Moreover, as the sediment concentration increases, an exponentially decaying rate has been found for the secondary flow. It is concluded that in the numerical simulation of flow in meandering channels, when concentration is high, the variable-density hydrodynamic equations without the Boussinesq approximation should be considered.


1988 ◽  
Vol 49 (7) ◽  
pp. 1119-1125 ◽  
Author(s):  
M. Jorand ◽  
E. Dubois-Violette ◽  
B. Pansu ◽  
F. Rothen

2016 ◽  
Vol 11 (2) ◽  
pp. 218-225
Author(s):  
V.S. Kuleshov

The results of a numerical modeling of thermo-gravitational convection of abnormally thermo-viscous fluid in a closed square cavity with two vertical adiabatic walls and two horizontal isothermal walls are presented. A model Newtonian liquid for which the dependence of viscosity on temperature is described by a bell function (Gaussian curve) is considered. The natural convection of inhomogeneous liquid is described by the closed mathematical model based on the continuous mechanics equations written in Oberbeck-Boussinesq approximation, where the fluid density is a linear function of temperature. To simulate the fluid flow dynamics, the modified computer code based on the implicit finite volume method and SIMPLE-type algorithm with the second-order temporal accuracy is realized using multiprocessor technology. The effect of the viscosity abnormality on stationary modes of convective flows are studied, the integral heat transfer coefficients in a flat cell are calculated.


2016 ◽  
Vol 11 (2) ◽  
pp. 205-209
Author(s):  
D.T. Siraeva

Invariant submodel of rank 2 on the subalgebra consisting of the sum of transfers for hydrodynamic equations with the equation of state in the form of pressure as the sum of density and entropy functions, is presented. In terms of the Lagrangian coordinates from condition of nonhyperbolic submodel solutions depending on the four essential constants are obtained. For simplicity, we consider the solution depending on two constants. The trajectory of particles motion, the motion of parallelepiped of the same particles are studied using the Maple.


Author(s):  
Klaus Morawetz

The classical non-ideal gas shows that the two original concepts of the pressure based of the motion and the forces have eventually developed into drift and dissipation contributions. Collisions of realistic particles are nonlocal and non-instant. A collision delay characterizes the effective duration of collisions, and three displacements, describe its effective non-locality. Consequently, the scattering integral of kinetic equation is nonlocal and non-instant. The non-instant and nonlocal corrections to the scattering integral directly result in the virial corrections to the equation of state. The interaction of particles via long-range potential tails is approximated by a mean field which acts as an external field. The effect of the mean field on free particles is covered by the momentum drift. The effect of the mean field on the colliding pairs causes the momentum and the energy gains which enter the scattering integral and lead to an internal mechanism of energy conversion. The entropy production is shown and the nonequilibrium hydrodynamic equations are derived. Two concepts of quasiparticle, the spectral and the variational one, are explored with the help of the virial of forces.


2020 ◽  
Vol 330 ◽  
pp. 01005
Author(s):  
Abderrahmane AISSA ◽  
Mohamed Amine MEDEBBER ◽  
Khaled Al-Farhany ◽  
Mohammed SAHNOUN ◽  
Ali Khaleel Kareem ◽  
...  

Natural convection of a magneto hydrodynamic nanofluid in a porous cavity in the presence of a magnetic field is investigated. The two vertical side walls are held isothermally at temperatures Th and Tc, while the horizontal walls of the outer cone are adiabatic. The governing equations obtained with the Boussinesq approximation are solved using Comsol Multiphysics finite element analysis and simulation software. Impact of Rayleigh number (Ra), Hartmann number (Ha) and nanofluid volume fraction (ϕ) are depicted. Results indicated that temperature gradient increases considerably with enhance of Ra and ϕ but it reduces with increases of Ha.


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