A new second-order moment model for turbulent combustion is applied in the simulation of methane-air turbulent jet flame. The predicted results are compared with the experimental results and with those predicted using...A new second-order moment model for turbulent combustion is applied in the simulation of methane-air turbulent jet flame. The predicted results are compared with the experimental results and with those predicted using the well-known EBU-Arrhenius model and the original second-order moment model. The comparison shows the advantage of the new model that it requires almost the same computational storage and time as that of the original second-order moment model, but its modeling results are in better agreement with experiments than those using other models. Hence, the new second-order moment model is promising in modeling turbulent combustion with NOx formation with finite reaction rate for engineering application.展开更多
Let(Z_(n))be a branching process with immigration in a random environmentξ,whereξis an independent and identically distributed sequence of random variables.We show asymptotic properties for all the moments of Z_(n) ...Let(Z_(n))be a branching process with immigration in a random environmentξ,whereξis an independent and identically distributed sequence of random variables.We show asymptotic properties for all the moments of Z_(n) and describe the decay rates of the n-step transition probabilities.As applications,a large deviation principle for the sequence log Z_(n) is established,and related large deviations are also studied.展开更多
A full second-order moment (FSM) model and an algebraic stress (ASM) two-phase turbulence modelare proposed and applied to predict turbulent bubble-liquid flows in a 2D rectangular bubble column. Predictiongives the b...A full second-order moment (FSM) model and an algebraic stress (ASM) two-phase turbulence modelare proposed and applied to predict turbulent bubble-liquid flows in a 2D rectangular bubble column. Predictiongives the bubble and liquid velocities, bubble volume fraction, bubble and liquid Reynolds stresses and bubble-liquidvelocity correlation. For predicted two-phase velocities and bubble volume fraction there is only slight differencebetween these two models, and the simulation results using both two models are in good agreement with the particleimage velocimetry (PIV) measurements. Although the predicted two-phase Reynolds stresses using the FSM are insomewhat better agreement with the PIV measurements than those predicted using the ASM, the Reynolds stressespredicted using both two models are in general agreement with the experiments. Therefore, it is suggested to usethe ASM two-phase turbulence model in engineering application for saving the computation time.展开更多
For continuous-state branching processes in Lévy random environments, the recursion of n-moments and the equivalent condition for the existence of general f-moments are established, where f is a positive continuo...For continuous-state branching processes in Lévy random environments, the recursion of n-moments and the equivalent condition for the existence of general f-moments are established, where f is a positive continuous function satisfying some standard conditions.展开更多
A two-scale second-order moment two-phase turbulence model accounting for inter-particle collision is developed, based on the concepts of particle large-scale fluctuation due to turbulence and particle small-scale flu...A two-scale second-order moment two-phase turbulence model accounting for inter-particle collision is developed, based on the concepts of particle large-scale fluctuation due to turbulence and particle small-scale fluctuation due to collision and through a unified treatment of these two kinds of fluctuations. The proposed model is used to simulate gas-particle flows in a channel and in a downer. Simulation results are in agreement with the experimental results reported in references and are near the results obtained using the sin- gle-scale second-order moment two-phase turbulence model superposed with a particle collision model （USM-θ model） in most regions.展开更多
By using Lamperti＇s bijection between self-similar Markov processes and L@vy processes~ we prove finiteness of moments and asymptotic behavior of passage times for increasing self-similar Markov processes valued in ...By using Lamperti＇s bijection between self-similar Markov processes and L@vy processes~ we prove finiteness of moments and asymptotic behavior of passage times for increasing self-similar Markov processes valued in （0, ~）. We Mso investigate the behavior of the process when it crosses a level. A limit theorem concerning the distribution of the process immediately before it crosses some level is proved. Some useful examples are given.展开更多
A two-scale second-order moment two-phase turbulence model accounting for inter-particle collision is developed, based on the concept of particle large-scale fluctuation due to turbulence and particle small-scale fluc...A two-scale second-order moment two-phase turbulence model accounting for inter-particle collision is developed, based on the concept of particle large-scale fluctuation due to turbulence and particle small-scale fluctuation due to collision. The proposed model is used to simulate gas-particle downer reactor flows. The computational results of both particle volume fraction and mean velocity are in agreement with the experimental results. After analyzing effects of empirical coefficient on prediction results, we can come to a conclusion that, inside the limit range of empirical coefficient, the predictions do not reveal a large sensitivity to the empirical coefficient in the downer reactor, but a relatively great change of the constants has important effect on the prediction.展开更多
The USM-θ model of Bingham fluid for dense two-phase turbulent flow was developed, which combines the second-order moment model for two-phase turbulence with the particle kinetic theory for the inter-particle collisi...The USM-θ model of Bingham fluid for dense two-phase turbulent flow was developed, which combines the second-order moment model for two-phase turbulence with the particle kinetic theory for the inter-particle collision. In this model, phases interaction and the extra term of Bingham fluid yield stress are taken into account. An algorithm for USM-θ model in dense two-phase flow was proposed, in which the influence of particle volume fraction is accounted for. This model was used to simulate turbulent flow of Bingham fluid single-phase and dense liquid-particle two-phase in pipe. It is shown USM-θ model has better prediction result than the five-equation model, in which the particle-particle collision is modeled by the particle kinetic theory, while the turbulence of both phase is simulated by the two-equation turbulence model. The USM-θ model was then used to simulate the dense two-phase turbulent up flow of Bingham fluid with particles. With the increasing of the yield stress, the velocities of Bingham and particle decrease near the pipe centre. Comparing the two-phase flow of Bingham-particle with that of liquid-particle, it is found the source term of yield stress has significant effect on flow.展开更多
Let Ls be the last exit time from a compact set B of an elliptic diffusion process X. A moderate estimate for the distribution of Ls is obtained, and the sufficient and necessary condition for E^x（L^κB） 〈∞ is pr...Let Ls be the last exit time from a compact set B of an elliptic diffusion process X. A moderate estimate for the distribution of Ls is obtained, and the sufficient and necessary condition for E^x（L^κB） 〈∞ is proved.展开更多
plane with the strike of 127°, the dip of 79° and the rake of 171°. The rupture process inversion result of MS=7.9 earthquake shows that the total rupture duration is about 37 s, the scalar moment tenso...plane with the strike of 127°, the dip of 79° and the rake of 171°. The rupture process inversion result of MS=7.9 earthquake shows that the total rupture duration is about 37 s, the scalar moment tensor is M0=0.97 × 1020 N·m. Rupture mainly occurred on the shallow area with 110 km long and 30 km wide, the location in which the rupture initiated is not where the main rupture took place, and the area with slip greater than 0.5 m basically lies within 35 km deep middle-crust under the earth surface. The maximum static slip is 3.6 m. There are two distinct areas with slip larger than 2.0 m. We noticed that when the rupture propagated towards northwest and closed to the area around the MS=7.3 hypocenter, the slip decreased rapidly, which may indicate that the rupture process was stopped by barriers. The consistence of spatial distribution of slip on the fault plane with the distribution of aftershocks also supports that the rupture is a heterogeneous process owing to the presence of barriers.展开更多
基金The project sponsored by the Foundation for Doctorate Thesis of Tsinghua Universitythe National Key Project in 1999-2004 sponsored by the Ministry of Science and Technology of China
文摘A new second-order moment model for turbulent combustion is applied in the simulation of methane-air turbulent jet flame. The predicted results are compared with the experimental results and with those predicted using the well-known EBU-Arrhenius model and the original second-order moment model. The comparison shows the advantage of the new model that it requires almost the same computational storage and time as that of the original second-order moment model, but its modeling results are in better agreement with experiments than those using other models. Hence, the new second-order moment model is promising in modeling turbulent combustion with NOx formation with finite reaction rate for engineering application.
基金partially supported by the National Nature Science Foundation of China(11601286,11501146)。
文摘Let(Z_(n))be a branching process with immigration in a random environmentξ,whereξis an independent and identically distributed sequence of random variables.We show asymptotic properties for all the moments of Z_(n) and describe the decay rates of the n-step transition probabilities.As applications,a large deviation principle for the sequence log Z_(n) is established,and related large deviations are also studied.
基金Supported by the Special Funds for Major State Basic Research Projects, PRC(G1999-0222-08) and the National Natural Science Foundation of China(No. 19872039).
文摘A full second-order moment (FSM) model and an algebraic stress (ASM) two-phase turbulence modelare proposed and applied to predict turbulent bubble-liquid flows in a 2D rectangular bubble column. Predictiongives the bubble and liquid velocities, bubble volume fraction, bubble and liquid Reynolds stresses and bubble-liquidvelocity correlation. For predicted two-phase velocities and bubble volume fraction there is only slight differencebetween these two models, and the simulation results using both two models are in good agreement with the particleimage velocimetry (PIV) measurements. Although the predicted two-phase Reynolds stresses using the FSM are insomewhat better agreement with the PIV measurements than those predicted using the ASM, the Reynolds stressespredicted using both two models are in general agreement with the experiments. Therefore, it is suggested to usethe ASM two-phase turbulence model in engineering application for saving the computation time.
基金supported by the National Natural Science Foundation of China(11531001)
文摘For continuous-state branching processes in Lévy random environments, the recursion of n-moments and the equivalent condition for the existence of general f-moments are established, where f is a positive continuous function satisfying some standard conditions.
基金The project supported by the Special Funds for Major State Basic Research,China(G-1999-0222-08)the Postdoctoral Science Foundation(2004036239)
文摘A two-scale second-order moment two-phase turbulence model accounting for inter-particle collision is developed, based on the concepts of particle large-scale fluctuation due to turbulence and particle small-scale fluctuation due to collision and through a unified treatment of these two kinds of fluctuations. The proposed model is used to simulate gas-particle flows in a channel and in a downer. Simulation results are in agreement with the experimental results reported in references and are near the results obtained using the sin- gle-scale second-order moment two-phase turbulence model superposed with a particle collision model （USM-θ model） in most regions.
基金supported in part by the National Natural Science Foundation of China(1117126211171263)
文摘By using Lamperti＇s bijection between self-similar Markov processes and L@vy processes~ we prove finiteness of moments and asymptotic behavior of passage times for increasing self-similar Markov processes valued in （0, ~）. We Mso investigate the behavior of the process when it crosses a level. A limit theorem concerning the distribution of the process immediately before it crosses some level is proved. Some useful examples are given.
基金Project supported by China Post-Doctoral Science Foundation(No.2004036239)
文摘A two-scale second-order moment two-phase turbulence model accounting for inter-particle collision is developed, based on the concept of particle large-scale fluctuation due to turbulence and particle small-scale fluctuation due to collision. The proposed model is used to simulate gas-particle downer reactor flows. The computational results of both particle volume fraction and mean velocity are in agreement with the experimental results. After analyzing effects of empirical coefficient on prediction results, we can come to a conclusion that, inside the limit range of empirical coefficient, the predictions do not reveal a large sensitivity to the empirical coefficient in the downer reactor, but a relatively great change of the constants has important effect on the prediction.
基金Project supported by the National Key Basic Research and Development Program of China(No.G1999-0222-08)
文摘The USM-θ model of Bingham fluid for dense two-phase turbulent flow was developed, which combines the second-order moment model for two-phase turbulence with the particle kinetic theory for the inter-particle collision. In this model, phases interaction and the extra term of Bingham fluid yield stress are taken into account. An algorithm for USM-θ model in dense two-phase flow was proposed, in which the influence of particle volume fraction is accounted for. This model was used to simulate turbulent flow of Bingham fluid single-phase and dense liquid-particle two-phase in pipe. It is shown USM-θ model has better prediction result than the five-equation model, in which the particle-particle collision is modeled by the particle kinetic theory, while the turbulence of both phase is simulated by the two-equation turbulence model. The USM-θ model was then used to simulate the dense two-phase turbulent up flow of Bingham fluid with particles. With the increasing of the yield stress, the velocities of Bingham and particle decrease near the pipe centre. Comparing the two-phase flow of Bingham-particle with that of liquid-particle, it is found the source term of yield stress has significant effect on flow.
基金Research supported in part by Tianyuan Fund ofr Mathematics of NSFC (10526021)A Grant from Ministry of Education
文摘Let Ls be the last exit time from a compact set B of an elliptic diffusion process X. A moderate estimate for the distribution of Ls is obtained, and the sufficient and necessary condition for E^x（L^κB） 〈∞ is proved.
基金The Specialized Funds for National Key Basic Study (G1998040704), the Dual Project of China Earthquake Admini-stration (9691309020301) and National Natural Science Foundation of China (46764010).
文摘plane with the strike of 127°, the dip of 79° and the rake of 171°. The rupture process inversion result of MS=7.9 earthquake shows that the total rupture duration is about 37 s, the scalar moment tensor is M0=0.97 × 1020 N·m. Rupture mainly occurred on the shallow area with 110 km long and 30 km wide, the location in which the rupture initiated is not where the main rupture took place, and the area with slip greater than 0.5 m basically lies within 35 km deep middle-crust under the earth surface. The maximum static slip is 3.6 m. There are two distinct areas with slip larger than 2.0 m. We noticed that when the rupture propagated towards northwest and closed to the area around the MS=7.3 hypocenter, the slip decreased rapidly, which may indicate that the rupture process was stopped by barriers. The consistence of spatial distribution of slip on the fault plane with the distribution of aftershocks also supports that the rupture is a heterogeneous process owing to the presence of barriers.
