Three-dimensional stressed state of an unclosed spherical shell

1979 ◽  
Vol 15 (11) ◽  
pp. 1043-1048
Author(s):  
Yu. N. Podil'chuk ◽  
S. A. Goloborod'ko
Keyword(s):  
Stressed State ◽  
Spherical Shell ◽  
Three Dimensional

scholarly journals Investigation of strength of shaped elements of the main gas pipeline

2019 ◽  
Vol 6 (1) ◽  
pp. 14-21
Author(s):  
Ya.V. Doroshenko
Keyword(s):  
Stressed State ◽  
Temperature Difference ◽  
Three Dimensional ◽  
Gas Pipeline ◽  
Cfd Modeling ◽  
Dynamic Processes ◽  
Internal Cavity ◽  
Main Stream ◽  
Gas Dynamic ◽  
Main Gas Pipeline

The research has been carried out for the purpose of a complex numerical three-dimensional modeling of the stressed state of taps and tees of main gas pipelines taking into account the gas-dynamic processes occurring in these shaped elements and the temperature difference in their walls. A 3D modeling of the elbow with a 90° angle and a reinforcing pad on the main line and the drainage of the passage line of the trunk of the main gas pipeline has been carried out. There has been studied the gas flow with 3D models of shaped elements of the main gas pipeline by means of the CFD modeling. The simulation has been рerformed for the equidistant tees in which the entire flow from the main stream flows into its branch. The mathematical model is based on the solution of the Navier–Stokes equation system, continuity equation, closed by a two-parametric k -e model of the Launder–Sharma turbulence with corresponding initial and boundary conditions. The simulation results are visualized in the ANSYS Fluent R18.2 Academic Postprocessor by constructing the pressure fields on the contours and in the longitudinal and transverse sections of shaped elements. The exact values of pressure at different points of the inner cavity of the shaped elements have been determined, the places of rise and fall of pressure identified. There have been performed the simulation of the temperature difference in the walls of the drainage, the trunk of the main gas pipeline in the module ANSYS Transient Thermal. The results of CFD and temperature modeling were imported into the mechanical module ANSYS Static Structural, where the finite element method was used to simulate the stressed state of the shaped elements of the main gas pipeline, taking into account the gas-dynamic processes occurring in their internal cavity and the temperature difference in the walls. The results of the simulation have been visualized by constructing a three-dimensional color fields of equivalent von Mises stresses in the tee and in the elbow. The places of the maximum equivalent stresses in the wall of the studied shaped elements have been revealed. 

scholarly journals Density Stratification Effects on the Thermal Convection in a Rotating Spherical Shell

2001 ◽  
Vol 203 ◽  
pp. 195-197
Author(s):  
N. Nishikawa ◽  
K. Kusano
Keyword(s):  
Spherical Shell ◽  
Thermal Convection ◽  
Structural Transition ◽  
Rotation Axis ◽  
Three Dimensional ◽  
Density Stratification ◽  
Nonlinear Convection ◽  
Solar Convection Zone ◽  
Solar Convection ◽  
The Stability

The density stratification effects on the thermal convection in a rotating spherical shell, which is the representative of the solar convection zone, are investigated by three dimensional numerical simulations. It is found that, the convection structure in the strongly stratified system is switched from parallel cells aligned to the rotation axis to zonal rolles dominated by the longitudinally averaged mode, as the Rayleigh number increases much larger than the stability threshold. Corresponding to this structural transition, the averaged kinetic helicity reverses the sign in each hemisphere (from negative to positive in the northern hemisphere). The results indicate that the density stratification is much important for the nonlinear convection process in the rotating spherical shell.

scholarly journals Coronal ejections from convective spherical shell dynamos

2011 ◽  
Vol 7 (S286) ◽  
pp. 154-158 ◽  
Author(s):  
J. Warnecke ◽  
P. J. Käpylä ◽  
M. J. Mantere ◽  
A. Brandenburg
Keyword(s):  
Magnetic Field ◽  
Spherical Shell ◽  
Large Scale ◽  
Convection Zone ◽  
Three Dimensional ◽  
Simplified Model ◽  
Spherical Coordinates ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Large Scale Magnetic Field

AbstractWe present a three-dimensional model of rotating convection combined with a simplified model of a corona in spherical coordinates. The motions in the convection zone generate a large-scale magnetic field which is sporadically ejected into the outer layers above. Our model corona is approximately isothermal, but it includes density stratification due to gravity.

scholarly journals Viscous dissipation by tidally forced inertial modes in a rotating spherical shell

2010 ◽  
Vol 643 ◽  
pp. 363-394 ◽  
Author(s):  
M. RIEUTORD ◽  
L. VALDETTARO
Keyword(s):  
Spherical Shell ◽  
Shear Layer ◽  
Viscous Dissipation ◽  
Inner Core ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Two Dimensional Model ◽  
Critical Latitude

We investigate the properties of forced inertial modes of a rotating fluid inside a spherical shell. Our forcing is tidal like, but its main property is that it is on the large scales. By numerically solving the linear equations of this problem, including viscosity, we first confirm some analytical results obtained on a two-dimensional model by Ogilvie (J. Fluid Mech., vol. 543, 2005, p. 19); some additional properties of this model are uncovered like the existence of narrow resonances associated with periodic orbits of characteristics. We also note that as the frequency of the forcing varies, the dissipation varies drastically if the Ekman number E is low (as is usually the case). We then investigate the three-dimensional case and compare the results to the foregoing model. The three-dimensional solutions show, like their two-dimensional counterpart, a spiky dissipation curve when the frequency of the forcing is varied; they also display small frequency intervals where the viscous dissipation is independent of viscosity. However, we show that the response of the fluid in these frequency intervals is crucially dominated by the shear layer that is emitted at the critical latitude on the inner sphere. The asymptotic regime, where the dissipation is independent of the viscosity, is reached when an attractor has been excited by this shear layer. This property is not shared by the two-dimensional model where shear layers around attractors are independent of those emitted at the critical latitude. Finally, resonances of the three-dimensional model correspond to some selected least damped eigenmodes. Unlike their two-dimensional counter parts these modes are not associated with simple attractors; instead, they show up in frequency intervals with weakly contracting webs of characteristics. Besides, we show that the inner core is negligible when its relative radius is less than the critical value 0.4E1/5. For these spherical shells, the full sphere solutions give a good approximation of the flows.

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