Based on the existing energy-minimization multi-scale(EMMS)model for turbulent flow in pipe,an improved version is proposed,in which not only a new radial velocity distribution is introduced but also the quantificatio...Based on the existing energy-minimization multi-scale(EMMS)model for turbulent flow in pipe,an improved version is proposed,in which not only a new radial velocity distribution is introduced but also the quantification of total dissipation over the cross-section of pipe is improved for the dominant mechanism of fully turbulent flow in pipe.Then four dynamic equality constraints and some other constraints are constructed but there are five parameters involved,leading to one free variable left.Through the compromise in competition between dominant mechanisms for laminar and fully turbulent flow in pipe respectively,the above four constructed dynamic equality constraints can be closed.Finally,the cases for turbulent flow in pipe with low,moderate and high Reynolds number are simulated by the improved EMMS model.The numerical results show that the model can obtain reasonable results which agree well with the data computed by the direct numerical simulation and those obtained by experi-ment.This illustrates that the improved EMMS model for turbulent flow in pipe is reasonable and the compromise in competition between dominant mechanisms is indeed a universal governing principle hidden in complex systems.Especially,one more EMMS model for a complex system is offered,pro-moting the further development of mesoscience.展开更多
基金supported by the State Key Laboratory of Multiphase Complex Systems(grant No.MPCS-2022-A-01)the National Natural Science Foundation of China(grant No.22078327).
文摘Based on the existing energy-minimization multi-scale(EMMS)model for turbulent flow in pipe,an improved version is proposed,in which not only a new radial velocity distribution is introduced but also the quantification of total dissipation over the cross-section of pipe is improved for the dominant mechanism of fully turbulent flow in pipe.Then four dynamic equality constraints and some other constraints are constructed but there are five parameters involved,leading to one free variable left.Through the compromise in competition between dominant mechanisms for laminar and fully turbulent flow in pipe respectively,the above four constructed dynamic equality constraints can be closed.Finally,the cases for turbulent flow in pipe with low,moderate and high Reynolds number are simulated by the improved EMMS model.The numerical results show that the model can obtain reasonable results which agree well with the data computed by the direct numerical simulation and those obtained by experi-ment.This illustrates that the improved EMMS model for turbulent flow in pipe is reasonable and the compromise in competition between dominant mechanisms is indeed a universal governing principle hidden in complex systems.Especially,one more EMMS model for a complex system is offered,pro-moting the further development of mesoscience.
