This note shows that when studying geometric pro perties, a polynomial system is defined as a line field on a projective space such that its singular set has co dimension at least 2. By this definition, the concept ...This note shows that when studying geometric pro perties, a polynomial system is defined as a line field on a projective space such that its singular set has co dimension at least 2. By this definition, the concept of the degree of a polynomial system does not coincide with the usual one. The usual degenerate polynomial system of degree n+1 should be regarded as a system of degree n . Note that the definition is independent coordinate system. And, by this definition, some geometric properties concerning polynomial vector fields turn out to be evident.展开更多
An accurate and complete geometric model was constructed to simulate the combustion, flow and temperature environment in the radiant section of the steam cracking furnace. Simulation of flow and radiation status has u...An accurate and complete geometric model was constructed to simulate the combustion, flow and temperature environment in the radiant section of the steam cracking furnace. Simulation of flow and radiation status has utilized the standard k-ε model and P1 model. The finite-rate/eddy-dissipation (finite-rate/ED) combustion model and non-premixed combustion model were both used to simulate accurately the combustion and the operation status of the steam cracking furnace. Three different surfaces of the steam cracking furnace were obtained from the simulation, namely:the flue gas temperature field of the entrance surface in long flame burners, the central surface location of tubes, and the crossover section surface. Detailed information on the flue gas temperature and the mass concentration fraction of these different surfaces in the steam cracking furnace can also be obtained by the simulation. This paper analyzed and compared the simulation results with the two combustion models, estimated the operation status of the steam cracking furnace, and reported that the finite-rate/ED model is appropriate to simulate the steam cracking furnace by comparing key simulation data with actual test data. This work has also provided a theoretical basis for simulating and operating the steam cracking furnace.展开更多
Spatial correlation of sound pressure and particle velocity of the surface noise in horizontally stratified media was demonstrated, with directional noise sources uniformly distributed on the ocean surface. In the eva...Spatial correlation of sound pressure and particle velocity of the surface noise in horizontally stratified media was demonstrated, with directional noise sources uniformly distributed on the ocean surface. In the evaluation of particle velocity, plane wave approximation was applied to each incident ray. Due to the equivalence of the sound source correlation property and its directivity, solutions for the spatial correlation of the field were transformed into the integration of the coherent function generated by a single directional source. As a typical horizontally stratified media, surface noise in a perfect waveguide was investigated. Correlation coefficients given by normal mode and geometric models show satisfactory agreement. Also, the normalized covariance between sound pressure and the vertical component of particle velocity is proportional to acoustic absorption coefficient, while that of the surface noise in semi-infinitely homogeneous space is zero.展开更多
文摘This note shows that when studying geometric pro perties, a polynomial system is defined as a line field on a projective space such that its singular set has co dimension at least 2. By this definition, the concept of the degree of a polynomial system does not coincide with the usual one. The usual degenerate polynomial system of degree n+1 should be regarded as a system of degree n . Note that the definition is independent coordinate system. And, by this definition, some geometric properties concerning polynomial vector fields turn out to be evident.
基金supported by the technology development fund of China Petroleum & Chemical Corporation (Sinopec 409045)
文摘An accurate and complete geometric model was constructed to simulate the combustion, flow and temperature environment in the radiant section of the steam cracking furnace. Simulation of flow and radiation status has utilized the standard k-ε model and P1 model. The finite-rate/eddy-dissipation (finite-rate/ED) combustion model and non-premixed combustion model were both used to simulate accurately the combustion and the operation status of the steam cracking furnace. Three different surfaces of the steam cracking furnace were obtained from the simulation, namely:the flue gas temperature field of the entrance surface in long flame burners, the central surface location of tubes, and the crossover section surface. Detailed information on the flue gas temperature and the mass concentration fraction of these different surfaces in the steam cracking furnace can also be obtained by the simulation. This paper analyzed and compared the simulation results with the two combustion models, estimated the operation status of the steam cracking furnace, and reported that the finite-rate/ED model is appropriate to simulate the steam cracking furnace by comparing key simulation data with actual test data. This work has also provided a theoretical basis for simulating and operating the steam cracking furnace.
基金Supported by the National Natural Science Foundation of China under Grant No.（50909028）.
文摘Spatial correlation of sound pressure and particle velocity of the surface noise in horizontally stratified media was demonstrated, with directional noise sources uniformly distributed on the ocean surface. In the evaluation of particle velocity, plane wave approximation was applied to each incident ray. Due to the equivalence of the sound source correlation property and its directivity, solutions for the spatial correlation of the field were transformed into the integration of the coherent function generated by a single directional source. As a typical horizontally stratified media, surface noise in a perfect waveguide was investigated. Correlation coefficients given by normal mode and geometric models show satisfactory agreement. Also, the normalized covariance between sound pressure and the vertical component of particle velocity is proportional to acoustic absorption coefficient, while that of the surface noise in semi-infinitely homogeneous space is zero.
