scholarly journals EQUIATION OF ENERGY WITH ALLOWANCE OF EFFECTS OF DISSIPATION IN CYLINDRYCAL COORDINATE SYSTEM

2017 ◽  
pp. 109-113
Author(s):  
N. V. Nesterovich ◽  
A. G. Obukhov
Keyword(s):  
Coordinate System ◽  
Energy Equation ◽  
Stokes Equations ◽  
Complete System ◽  
Cylindrical Coordinate System ◽  
Navier Stokes ◽  
Heat Conducting ◽  
Complex Flows ◽  
Navier Stokes Equations ◽  
Cylindrical Coordinate

Complex flows of a viscous compressible heat-conducting gas in ascending swirling flows have a pro-nounced axial symmetry. Therefore, for the numerical solution of the complete system of Navier - Stokes equations to describe such gas flows, it is desirable to use a cylindrical coordinate system. The paper describes the transformation of the energy equation for a complete system of Navier - Stokes equations with allowance for the dissipative properties of a moving continuous medium. The result of the transformation is the formulation of the energy equation in a cylindrical coordinate system.

scholarly journals FIRST PROJECTION OF THE EQUATION OF MOTION IN THE CYLINDRICAL COORDINATE SYSTEM

2016 ◽  
pp. 90-92
Author(s):  
A. G. Obukhov ◽  
R. E. Volkov
Keyword(s):  
Coordinate System ◽  
Stokes Equations ◽  
Equation Of Motion ◽  
Cylindrical Coordinate System ◽  
Navier Stokes ◽  
Gas Flows ◽  
Heat Conducting ◽  
Complex Flows ◽  
Navier Stokes Equations ◽  
Cylindrical Coordinate

It is proved that complex flows of the viscous compressible heat-conducting gas, arising during heating the vertical field, have a pronounced axial symmetry. Therefore, for the numerical solution of the full Navier-Stokes equations for description of such gas flows it are advisable to use a cylindrical coordinate system. This paper describes the transformation of the first projection of the equation of motion of the full Navier-Stokes equations system. The result of the transformation is a record of the first projection of the equation of a continuous medium motion in the cylindrical coordinate system.

scholarly journals THE SECOND PROJECTION OF THE MOTION EQUATION IN THE CYLINDRICAL COORDINATE SYSTEM

2016 ◽  
pp. 83-85
Author(s):  
D. D. Barannikova ◽  
A. G. Obukhov
Keyword(s):  
Coordinate System ◽  
Stokes Equations ◽  
Motion Equation ◽  
Cylindrical Coordinate System ◽  
Navier Stokes ◽  
Gas Flows ◽  
Heat Conducting ◽  
Complex Flows ◽  
Navier Stokes Equations ◽  
Cylindrical Coordinate

The complex flows of viscous compressible heat-conducting gas arising during heating the vertical field, have a pronounced axial symmetry. Therefore, for the numerical solution of the complete Navier-Stokes equations system to describe such gas flows it is advisable to use a cylindrical coordinate system. This paper describes a transformation of the second projection of the motion equation of the complete Navier-Stokes equations system. The result of this transformation is writing of the second projection of the equation of a continuous medium motion in the cylindrical coordinate system.

THE THIRD PROJECTION OF THE MOTION EQUATION IN THE CYLINDRICAL COORDINATE SYSTEM

2017 ◽  
pp. 109-112
Author(s):  
D. D. Barannikova ◽  
A. G. Obukhov
Keyword(s):  
Coordinate System ◽  
Stokes Equations ◽  
Equation Of Motion ◽  
Cylindrical Coordinate System ◽  
Navier Stokes ◽  
Gas Flows ◽  
Heat Conducting ◽  
Navier Stokes Equations ◽  
The Third ◽  
Cylindrical Coordinate

Sophisticated viscous compressible heat-conducting gases arising during heating the vertical field, have a pronounced axial symmetry. Therefore, for the numerical solution of the full Navier-Stokes equations to describe such gas flows is advisable to use a cylindrical coordinate system. This paper describes the transformation of the third projection of the equation of motion of the full Navier-Stokes equations. The result of the transformation is to record the third projection of the equation of motion of a continuous medium in a cylindrical coordinate system.

scholarly journals EQUATION OF CONTINUITY IN THE CYLINDRICAL COORDINATES SYSTEM

2016 ◽  
pp. 119-122
Author(s):  
A. G. Obukhov ◽  
N. V. Chunikhina
Keyword(s):  
Coordinate System ◽  
Continuity Equation ◽  
Stokes Equations ◽  
Cylindrical Coordinate System ◽  
Navier Stokes ◽  
Gas Flows ◽  
Heat Conducting ◽  
Navier Stokes Equations ◽  
Vertical Field ◽  
Cylindrical Coordinate

Sophisticated viscous compressible heat-conducting gases arising during heating the vertical field, have a pronounced axial symmetry. Therefore, for the numerical solution of the full Navier - Stokes equations to describe such gas flows is advisable to use a cylindrical coordinate system. This paper describes the transformation of the first equation of the full Navier - Stokes equations. The result of the transformation is to write the continuity equation in the cylindrical coordinate system.

scholarly journals NUMERICAL CALCULATION OF CONVECTIVE FLOW OF GAS AT CIRCULAR-TYPE SCHEME OF HEATING

2015 ◽  
pp. 87-93
Author(s):  
E. M. Sorokina ◽  
A. G. Obukhov
Keyword(s):  
Convective Flow ◽  
Stokes Equations ◽  
Complete System ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Heat Conducting ◽  
Boundary Condi Tions ◽  
Navier Stokes Equations ◽  
Viscous Heat ◽  
Condi Tions

To investigate the convective flows of polytropic gas a complete system of Navier - Stokes equations is consid-ered. As the initial and boundary conditions the specific ratios are offered. The proposed initial and boundary condi-tions realization is carried out at construction of the numerical solution of the complete system of Navier - Stokes equations for modeling the unsteady state three-dimensional convection flows of the compressible viscous heat-conducting gas in the isolated cubic area. Three components of the velocity vector are calculated for the initial stage of the convective flow. It is shown that the velocity components are complex and depend essentially on the heating shape, height and time.

scholarly journals THREE-DIMENSIONAL INSTANTANEOUS STREAMLINESOF GAS FLOWS FOR SIMULATION THE STEADY-STATE OUTPUT OF AN ARTIFICIAL TORNADO

2018 ◽  
pp. 71-76
Author(s):  
R. E. Volkov ◽  
A. G. Obukhov
Keyword(s):  
Steady State ◽  
Stokes Equations ◽  
Complete System ◽  
Three Dimensional ◽  
Unsteady Flows ◽  
Navier Stokes ◽  
Gas Flows ◽  
Heat Conducting ◽  
Navier Stokes Equations ◽  
Coriolis Forces

The method of parallelizing a numerical solution of the complete system of Navier - Stokes equations is used to describe three-dimensional unsteady flows of a viscous compressible heat-conducting gas in ascending swirling flows. In this case the action of gravity and Coriolis forces is taken into account, and the coefficients of viscosity and thermal conductivity are assumed to be constant. The results of the numerical construction of instantaneous streamlines characterizing complex three-dimensional flows are presented for simulation the steady-state output of an ascend-ing swirling air flow in an artificial tornado.

Numerical Modeling of Flow in a Vertical Cooling Crystallizer

1999 ◽  
Vol 121 (1) ◽  
pp. 148-154 ◽  
Author(s):  
M. A. Sima ◽  
J. A. Harris
Keyword(s):  
Numerical Modeling ◽  
Temperature Distribution ◽  
Flow Field ◽  
Prandtl Number ◽  
Coordinate System ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Low Grade ◽  
Navier Stokes Equations ◽  
Cylindrical Coordinate

Simulations of the flow field and temperature distribution in a low grade vertical continuous cooling sugar crystallizer were carried out by numerically solving the Navier-Stokes equations in a cylindrical coordinate system. The model results indicate highly nonuniform massecuite cooling, primarily due to the massecuite’s large Prandtl number, and significant short-circuiting of flow between inlet and outlet. Modifications to the crystallizer design are proposed and demonstrated to be successful in improving the performance of the vessel.

scholarly journals Mathematical Model of Spool Valve with Rectangular Grooves

2018 ◽  
Vol 36 (3) ◽  
pp. 516-521
Author(s):  
Jia Chen ◽  
Zhaohui Yuan ◽  
Qiang Guo
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Coordinate System ◽  
Stokes Equations ◽  
Lateral Force ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Cylindrical Coordinate ◽  
Spool Valve ◽  
The Mathematical Model

A spool valve of aerospace hydraulic breaks down because of uneven pressure distribution between sleeve and spool, which is called as hydraulic lock. The rectangular grooves on the spool surface can effectively weaken the lateral force, thereby preventing the hydraulic lock. So the mathematical model of spool valve with rectangular grooves is established according to the Navier-Stokes equations based on the cylindrical coordinate system. To verify the effectivity of the mathematical model, the numerical simulation is compared and used to modified the mathematical model.

scholarly journals PARALLEL COMPUTATIONS IN STUDIES OF DEPENDENCE OF GAS DYNAMIC PARAMETERS OF UPWARD SWIRLING FLOW OF GAS ON BLOWING VELOCITY

2016 ◽  
pp. 92-97
Author(s):  
R. E. Volkov ◽  
A. G. Obukhov
Keyword(s):  
Stokes Equations ◽  
Swirling Flow ◽  
Initial Conditions ◽  
Exact Analytical Solution ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Heat Conducting ◽  
Computational Domain ◽  
Navier Stokes Equations ◽  
Gas Dynamic

The rectangular parallelepiped explicit difference schemes for the numerical solution of the complete built system of Navier-Stokes equations. These solutions describe the three-dimensional flow of a compressible viscous heat-conducting gas in a rising swirling flows, provided the forces of gravity and Coriolis. This assumes constancy of the coefficient of viscosity and thermal conductivity. The initial conditions are the features that are the exact analytical solution of the complete Navier-Stokes equations. Propose specific boundary conditions under which the upward flow of gas is modeled by blowing through the square hole in the upper surface of the computational domain. A variant of parallelization algorithm for calculating gas dynamic and energy characteristics. The results of calculations of gasdynamic parameters dependency on the speed of the vertical blowing by the time the flow of a steady state flow.

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