An Online Strategy for Exploring the Outer Boundary of a Convex Polygon

Author(s):  
Qi Wei ◽  
Jie Sun ◽  
Xuehou Tan ◽  
Xiaolin Yao
2021 ◽  
Vol 11 (4) ◽  
pp. 1936
Author(s):  
Abdel-Hakim Bouzid

The accurate prediction of liquid leak rates in packing seals is an important step in the design of stuffing boxes, in order to comply with environmental protection laws and health and safety regulations regarding the release of toxic substances or fugitive emissions, such as those implemented by the Environmental Protection Agency (EPA) and the Technische Anleitung zur Reinhaltung der Luft (TA Luft). Most recent studies conducted on seals have concentrated on the prediction of gas flow, with little to no effort put toward predicting liquid flow. As a result, there is a need to simulate liquid flow through sealing materials in order to predict leakage into the outer boundary. Modelling of liquid flow through porous packing materials was addressed in this work. Characterization of their porous structure was determined to be a key parameter in the prediction of liquid flow through packing materials; the relationship between gland stress and leak rate was also acknowledged. The proposed methodology started by conducting experimental leak measurements with helium gas to characterize the number and size of capillaries. Liquid leak tests with water and kerosene were then conducted in order to validate the predictions. This study showed that liquid leak rates in packed stuffing boxes could be predicted with reasonable accuracy for low gland stresses. It was found that internal pressure and compression stress had an effect on leakage, as did the thickness change and the type of fluid. The measured leak rates were in the range of 0.062 to 5.7 mg/s for gases and 0.0013 and 5.5 mg/s for liquids.


2007 ◽  
Vol 45 (3) ◽  
pp. 268-272 ◽  
Author(s):  
E. V. Panov ◽  
S. P. Savin ◽  
J. Büchner ◽  
A. Korth

Author(s):  
Lavinia Darlea ◽  
Sylvie Galichet ◽  
Lionel Valet ◽  
Gabriel Vasile ◽  
Emmanuel Trouve
Keyword(s):  

2014 ◽  
Vol 937 ◽  
pp. 695-699
Author(s):  
Hong E Li ◽  
Xiao Xu Dong ◽  
Shun Chu Li ◽  
Dong Dong Gui ◽  
Cong Yin Fan

The similar structure of solution for the boundary value problem of second order linear homogeneous differential equation has been studied. Based on the analysis of the relationship between similar structure of solution, its kernel function, the equation and boundary conditions, similar constructive method (shortened as SCM) of solution is obtained. According to the SCM, the similar structure of solution and its kernel function are constructed for the mathematical model of homogeneous reservoir which considers the influence of bottom-hole storage and skin effect under the infinite outer boundary condition. The SCM is a new and innovative way to solve boundary value problem of differential equation and seepage flow theory, which is especially used in Petroleum Engineering.


2014 ◽  
Vol 29 (21) ◽  
pp. 1450115
Author(s):  
Fahrettin Koyuncu ◽  
Orhan Dönmez

We have solved the General Relativistic Hydrodynamic (GRH) equations using the high resolution shock capturing scheme (HRSCS) to find out the dependency of the disk dynamics to the Mach number, adiabatic index, the black hole rotation parameter and the outer boundary of the computational domain around the non-rotating and rotating black holes. We inject the gas to computational domain at upstream and downstream regions at the same time with different initial conditions. It is found that variety of the mass accretion rates and shock cone structures strongly depend on Mach number and adiabatic index of the gas. The shock cones on the accretion disk are important physical mechanisms to trap existing oscillation modes, thereupon these trapped modes may generate strong X-rays observed by different X-ray satellites. Besides, our numerical approach also show that the shock cones produces the flip–flop oscillation around the black holes. The flip–flop instabilities which are monitored in our simulations may explain the erratic spin behavior of the compact objects (the black holes and neutron stars) seen from observed data.


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