As a continuation of a recent linear analysis by Mao et al.(Acta Mech Sin,2010,26:355),in this paper we propose a general theoretical formulation for the compressing process in complex Newtonian fluid flows,which cove...As a continuation of a recent linear analysis by Mao et al.(Acta Mech Sin,2010,26:355),in this paper we propose a general theoretical formulation for the compressing process in complex Newtonian fluid flows,which covers gas dynamics,aeroacoustics,nonlinear thermoviscous acoustics,viscous shock layer,etc.,as its special branches.The principle on which our formulation is based is the maximally natural and dynamic Helmholtz decomposition of the Navier-Stokes equation,along with the kinematic Helmholtz decomposition of the velocity field.The central results are the new dilatation equation and velocity-potential equation,which are the counterparts of vorticity transport equation and vector stream-function equation for the shearing process,respectively.Various couplings of the compressing process with shearing and thermal processes,including its physical sources,are carefully identified.While the possible applications and influences of the new formulation are yet to be explored,our preliminary discussion on the pros and cons of previous formulations pertain to acoustic analogy and that on the process splitting and coupling in highly compressible turbulence indicates that at least the formulation can serve as a new frame of reference by which one may gain some additional insight and thereby develop new approaches to the multi-process complex flow problems.展开更多
On the basis of the plasma, electric and magnetic fields jointly observed by Cluster and the Double Star TC-I spacecraft in the Earth＇s magnetotail, we have investigated the earthward flow bursts by introducing the m...On the basis of the plasma, electric and magnetic fields jointly observed by Cluster and the Double Star TC-I spacecraft in the Earth＇s magnetotail, we have investigated the earthward flow bursts by introducing the momentum equation in the X-direction in the ideal conditions of magneto hydrodynamics （MHD）. One earthward flow burst with a peak in excess of 500 km/s was selected, when the four spacecraft of Cluster were located around -16 RE and TC-1 was located around -10 RE in the X-direction. The inter-spacecraft distances in Y and Z directions were smaller than the statistical spatial scales of the bursty bulk flows. When the Y components of E and -VxB were compared, there was no clear breakdown of the frozen-in condition during the earthward flow burst. With the measured plasma and magnetic parameters from two spacecraft at different positions in the magnetotail, the X component of the pressure gradient was calculated. Magnetic tension was calculated using the mag- netic field measured at four points, which could be compared with the assumed constant in the past research with single satel- lite. When the pressure gradient and the magnetic tension were put into the MHD momentum equation, some samples of the earthward flow bursts were accelerated and some were decelerated. The braking process of the earthward flow burst was more complicated than what the past results had shown. The accelerated samples accounted for about one third of the whole earth- ward flow bursts and discontinuously located among the decelerated elements. The original single earthward flow burst event might be split into several short flow bursts when it was moving to the Earth. Our results may partly illustrate that the duration of fast flows during three phases of substorm becomes short near the Earth. The results are consistent with the past results that fast flows intrude to places earthward the typical braking region.展开更多
In this paper, by introducing the flow velocity item into the classical Rayleigh-Plesset dynamic equation, a newequation, which does not involve the time term and can describe the motion of cavitation bubble in the st...In this paper, by introducing the flow velocity item into the classical Rayleigh-Plesset dynamic equation, a newequation, which does not involve the time term and can describe the motion of cavitation bubble in the steadycavitating flow, has been obtained. By solving the new motion equation using Runge-Kutta fourth order methodwith adaptive step size control, the dynamic behaviors of cavitation bubble driven by the varying pressure fielddownstream of a venturi cavitation reactor are numerically simulated. The effects of liquid temperature (correspondingto the saturated vapor pressure of liquid), cavitation number and inlet pressure of venturi on radial motionof bubble and pressure pulse due to the radial motion are analyzed and discussed in detail. Some dynamicbehaviors of bubble different from those in previous papers are displayed. In addition, the internal relationshipbetween bubble dynamics and process intensification is also discussed. The simulation results reported in thiswork reveal the variation laws of cavitation intensity with the flow conditions of liquid, and will lay a foundationfor the practical application of hydrodynamic cavitation technology.展开更多
The average-passage equation system(APES)provides a rigorous framework to account for the deterministic unsteady effects by the so-called deterministic correlations(DC),which include both deterministic stress correlat...The average-passage equation system(APES)provides a rigorous framework to account for the deterministic unsteady effects by the so-called deterministic correlations(DC),which include both deterministic stress correlations(DCS)and deterministic total enthalpy correlations(DCH).These correlations should be modeled to close the system of equations.In this paper,the distribution of DC in a transonic centrifugal compressor is presented,and its relative importance is revealed.The assumption made by Adamczyk that the pure unsteady fluctuation is significantly smaller than the spatial fluctuation is verified at the impeller-diffuser interface.The decomposition of DCH is also discussed to determine its two different physical mechanisms.Finally,the transport equations in terms of DCS in cylindrical coordinates are derived,and the terms are evaluated to determine the ones that are necessary to model.All these analyses significantly contribute to our model development for DC in centrifugal compressors.展开更多
It is showed that, as the Mach number goes to zero, the weak solution of the compressible Navier-Stokes equations in the whole space with general initial data converges to the strong solution of the incompressible Nav...It is showed that, as the Mach number goes to zero, the weak solution of the compressible Navier-Stokes equations in the whole space with general initial data converges to the strong solution of the incompressible Navier-Stokes equations as long as the later exists. The proof of the result relies on the new modulated energy functional and the Strichartz's estimate of linear wave equation.展开更多
基金supported by the Ministry of Science and Technology of China's Turbulence Program (Grant No.2009CB724101)the National Basic Research Program of China (Grant No.2007CB714600)the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (Grant No.10921202)
文摘As a continuation of a recent linear analysis by Mao et al.(Acta Mech Sin,2010,26:355),in this paper we propose a general theoretical formulation for the compressing process in complex Newtonian fluid flows,which covers gas dynamics,aeroacoustics,nonlinear thermoviscous acoustics,viscous shock layer,etc.,as its special branches.The principle on which our formulation is based is the maximally natural and dynamic Helmholtz decomposition of the Navier-Stokes equation,along with the kinematic Helmholtz decomposition of the velocity field.The central results are the new dilatation equation and velocity-potential equation,which are the counterparts of vorticity transport equation and vector stream-function equation for the shearing process,respectively.Various couplings of the compressing process with shearing and thermal processes,including its physical sources,are carefully identified.While the possible applications and influences of the new formulation are yet to be explored,our preliminary discussion on the pros and cons of previous formulations pertain to acoustic analogy and that on the process splitting and coupling in highly compressible turbulence indicates that at least the formulation can serve as a new frame of reference by which one may gain some additional insight and thereby develop new approaches to the multi-process complex flow problems.
基金supported by the National Natural Science Foundation of China (Grant Nos. 40931054, 41174141 and 40904042)the National Basic Research Program of China ("973" Project)(Grant No. 2011CB811404)+1 种基金Specialized Research Fund for State Key Laboratories (Grant No. KP201104)supported by Chinese Academy of Sciences (CAS) visiting Professorship for Senior International Scientists (Grant No. 2009S1-54)
文摘On the basis of the plasma, electric and magnetic fields jointly observed by Cluster and the Double Star TC-I spacecraft in the Earth＇s magnetotail, we have investigated the earthward flow bursts by introducing the momentum equation in the X-direction in the ideal conditions of magneto hydrodynamics （MHD）. One earthward flow burst with a peak in excess of 500 km/s was selected, when the four spacecraft of Cluster were located around -16 RE and TC-1 was located around -10 RE in the X-direction. The inter-spacecraft distances in Y and Z directions were smaller than the statistical spatial scales of the bursty bulk flows. When the Y components of E and -VxB were compared, there was no clear breakdown of the frozen-in condition during the earthward flow burst. With the measured plasma and magnetic parameters from two spacecraft at different positions in the magnetotail, the X component of the pressure gradient was calculated. Magnetic tension was calculated using the mag- netic field measured at four points, which could be compared with the assumed constant in the past research with single satel- lite. When the pressure gradient and the magnetic tension were put into the MHD momentum equation, some samples of the earthward flow bursts were accelerated and some were decelerated. The braking process of the earthward flow burst was more complicated than what the past results had shown. The accelerated samples accounted for about one third of the whole earth- ward flow bursts and discontinuously located among the decelerated elements. The original single earthward flow burst event might be split into several short flow bursts when it was moving to the Earth. Our results may partly illustrate that the duration of fast flows during three phases of substorm becomes short near the Earth. The results are consistent with the past results that fast flows intrude to places earthward the typical braking region.
基金support of the National Natural Science Foundation of China (Grant No. 50806078)the National High-Tech Research and Development Program of China (863 Program, Grant No. 2006AA05Z203).
文摘In this paper, by introducing the flow velocity item into the classical Rayleigh-Plesset dynamic equation, a newequation, which does not involve the time term and can describe the motion of cavitation bubble in the steadycavitating flow, has been obtained. By solving the new motion equation using Runge-Kutta fourth order methodwith adaptive step size control, the dynamic behaviors of cavitation bubble driven by the varying pressure fielddownstream of a venturi cavitation reactor are numerically simulated. The effects of liquid temperature (correspondingto the saturated vapor pressure of liquid), cavitation number and inlet pressure of venturi on radial motionof bubble and pressure pulse due to the radial motion are analyzed and discussed in detail. Some dynamicbehaviors of bubble different from those in previous papers are displayed. In addition, the internal relationshipbetween bubble dynamics and process intensification is also discussed. The simulation results reported in thiswork reveal the variation laws of cavitation intensity with the flow conditions of liquid, and will lay a foundationfor the practical application of hydrodynamic cavitation technology.
基金supported by the National Natural Science Foundation of China(Grant Nos.51376001,51006006,51420105008 and 51376014)the National Basic Research Program of China("973"Project)(Grant Nos.2012CB720205,2014CB046405)+2 种基金the Aeronautical Science Foundation of China(Grant No.2012ZB51014)the Beijing Higher Education Young Elite Teacher Projectthe Fundamental Research Funds for the Central Universities
文摘The average-passage equation system(APES)provides a rigorous framework to account for the deterministic unsteady effects by the so-called deterministic correlations(DC),which include both deterministic stress correlations(DCS)and deterministic total enthalpy correlations(DCH).These correlations should be modeled to close the system of equations.In this paper,the distribution of DC in a transonic centrifugal compressor is presented,and its relative importance is revealed.The assumption made by Adamczyk that the pure unsteady fluctuation is significantly smaller than the spatial fluctuation is verified at the impeller-diffuser interface.The decomposition of DCH is also discussed to determine its two different physical mechanisms.Finally,the transport equations in terms of DCS in cylindrical coordinates are derived,and the terms are evaluated to determine the ones that are necessary to model.All these analyses significantly contribute to our model development for DC in centrifugal compressors.
基金supported by the National Natural Science Foundation of China (Nos. 10431060, 10701011,10501047) the Nanjing University Talent Development Foundation
文摘It is showed that, as the Mach number goes to zero, the weak solution of the compressible Navier-Stokes equations in the whole space with general initial data converges to the strong solution of the incompressible Navier-Stokes equations as long as the later exists. The proof of the result relies on the new modulated energy functional and the Strichartz's estimate of linear wave equation.
