Orbital angular momentum(OAM)can achieve multifold increase of spectrum efficiency,but the hollow divergence characteristic and Line-of-Sight(LoS)path requirement impose the crucial challenges for vortex wave communic...Orbital angular momentum(OAM)can achieve multifold increase of spectrum efficiency,but the hollow divergence characteristic and Line-of-Sight(LoS)path requirement impose the crucial challenges for vortex wave communications.For air-to-ground vortex wave communications,where there exists the LoS path,this paper proposes a multi-user cooperative receive(MUCR)scheme to break through the communication distance limitation caused by the characteristic of vortex wave hollow divergence.In particular,we derive the optimal radial position corresponding to the maximum intensity,which is used to adjust the waist radius.Based on the waist radius and energy ring,the cooperative ground users having the minimum angular square difference are selected.Also,the signal compensation scheme is proposed to decompose OAM signals in air-to-ground vortex wave communications.Simulation results are presented to verify the superiority of our proposed MUCR scheme.展开更多
The influence of the longitudinal acceleration and the angular acceleration of detecting target based on vortex electromagnetic waves in keyhole space are analyzed.The spectrum spreads of different orbital angular mom...The influence of the longitudinal acceleration and the angular acceleration of detecting target based on vortex electromagnetic waves in keyhole space are analyzed.The spectrum spreads of different orbital angular momentum(OAM)modes in different non-line-of-sight situations are simulated.The errors of target accelerations in detection are calculated and compared based on the OAM spectra spreading by using two combinations of composite OAM modes in the keyhole space.According to the research,the effects about spectrum spreads of higher OAM modes are more obvious.The error in detection is mainly affected by OAM spectrum spreading,which can be reduced by reasonably using different combinations of OAM modes in different practical situations.The above results provide a reference idea for investigating keyhole effect when vortex electromagnetic wave is used to detect accelerations.展开更多
In this study, the barotropic stability of vortex Rossby waves （VRWs） in 2D inviscid tropical cyclone （TC）-like vortices is explored in the context of rotational dynamics on an f-plane. Two necessary instable cond...In this study, the barotropic stability of vortex Rossby waves （VRWs） in 2D inviscid tropical cyclone （TC）-like vortices is explored in the context of rotational dynamics on an f-plane. Two necessary instable conditions are discovered： （a） there must be at least one zero point of basic vorticity gradient in the radial scope; and （b） the relative propagation velocity of perturbations must be negative to the basic vorticity gradient, which reflects the restriction relationship of instable energy. The maximum growth rate of instable waves depends on the peak radial gradient of the mean vorticity and the tangential wavenumber （WN）. The vortex-semicircle theorem is also derived to provide bounds on the growth rates and phase speeds of VRWs. The typical basic states and different WN perturbations in a tropical cyclone （TC） are obtained from a high resolution simulation. It is shown that the first necessary condition for vortex barotropic instability can be easily met at the radius of maximum vorticity （RMV）. The wave energy tends to decay （grow） inside （outside） the RMV due mainly to the negative （positive） sign of the radial gradient of the mean absolute vorticity. This finding appears to help explain the developemnt of strong vortices in the eyewall of TCs.展开更多
Using 1958-2002 NCEPNCAR reanalysis data, we investigate stationary and transient planetary wave propagation and its role in wave-mean flow interaction which influences the state of the polar vortex （PV） in the stra...Using 1958-2002 NCEPNCAR reanalysis data, we investigate stationary and transient planetary wave propagation and its role in wave-mean flow interaction which influences the state of the polar vortex （PV） in the stratosphere in Northern Hemisphere （NH） winter. This is done by analyzing the Eliassen-Palm （E-P） flux and its divergence. We find that the stationary and transient waves propagate upward and equatorward in NH winter, with stronger upward propagation of stationary waves from the troposphere to the stratosphere, and stronger equatorward propagation of transient waves from mid-latitudes to the subtropics in the troposphere. Stationary waves exhibit more upward propagation in the polar stratosphere during the weak polar vortex regime （WVR） than during the strong polar vortex regime （SVR）. On the other hand, transient waves have more upward propagation during SVR than during WVR in the subpolar stratosphere, with a domain of low frequency waves. With different paths of upward propagation, both stationary and transient waves contribute to the maintenance of the observed stratospheric PV regimes in NH winter.展开更多
In terms of its dynamics, The Tibetan Plateau Vortex （TPV） is assumed to be a vortex in the botmdary layer forced by diabatic heating and friction. In order to analyze the basic characteristics of waves in the vorte...In terms of its dynamics, The Tibetan Plateau Vortex （TPV） is assumed to be a vortex in the botmdary layer forced by diabatic heating and friction. In order to analyze the basic characteristics of waves in the vortex, the governing equations for the vortex were established in column coordinates with the balance of gradient wind. Based on this, the type of mixed waves and their dispersion characteristics were deduced by solving the linear model. Two numerical simulations with triple-nested domains--one idealized large-eddy simulation and one of a TPV that took place on 14 August 2006---were also carried out. The aim of the simulations was to validate the mixed wave deduced from the governing equations. The high-resolution model output data were analyzed and the results showed that the tangential flow field of the TPV in the form of center heating was cyclonic and convergent in the lower levels and anticyclonic and divergent in the upper levels. The simulations also showed that the vorticity of the vortex is uneven and might have shear flow along the radial direction. The changing vorticity causes the formation and spreading of vortex Rossby （VR） waves, and divergence will cause changes to the n^otion of the excitation and evolution of inertial gravity （IG） waves. Therefore, the vortex may contain what we call mixed ：inertial gravity-vortex Rossby （IG-VR） waves. It is suggested that some strongly developed TPVs should be studied in the future, because of their effects on weather in downstream areas.展开更多
The interactions of cnoidal waves with a submerged quartercircular breakwater are investigated by a ReynoldsAveraged Navier–Stokes(RANS) flow solver with a Volume of Fluid(VOF) surface capturing scheme(RANSVOF) model...The interactions of cnoidal waves with a submerged quartercircular breakwater are investigated by a ReynoldsAveraged Navier–Stokes(RANS) flow solver with a Volume of Fluid(VOF) surface capturing scheme(RANSVOF) model. The vertical variation of the instantaneous velocity indicates that flow separation occurs at the boundary layer near the breakwater. The temporal evolution of the velocity and vorticity fields demonstrates vortex generation and shedding around the submerged quartercircular breakwater due to the flow separation. An empirical relationship between the vortex intensity and a few hydrodynamic parameters is proposed based on parametric analysis. In addition, the instantaneous and time-averaged vorticity fields reveal a pair of vortices of opposite signs at the breakwater which are expected to have significant effect on sediment entrainment, suspension, and transportation,therefore, scour on the leeside of the breakwater.展开更多
Wave ray theory is employed to study features of propagation pathways（rays） of vortex Rossby waves in typhoons with asymmetric basic flow, where the tangential asymmetric basic flow is constructed by superimposing t...Wave ray theory is employed to study features of propagation pathways（rays） of vortex Rossby waves in typhoons with asymmetric basic flow, where the tangential asymmetric basic flow is constructed by superimposing the wavenumber-1 perturbation flow on the symmetric basic flow, and the radial basic flow is derived from the non-divergence equation. Results show that, in a certain distance, the influences of the asymmetry in the basic flow on group velocities and slopes of rays of vortex Rossby waves are mainly concentrated near the radius of maximum wind（RMW）, whereas it decreases outside the RMW. The distributions of radial and tangential group velocities of the vortex Rossby waves in the asymmetric basic flow are closely related to the azimuth location of the maximum speed of the asymmetric basic flow, and the importance of radial and tangential basic flow on the group velocities would change with radius. In addition, the stronger asymmetry in the basic flow always corresponds to faster outward energy propagation of vortex Rossby waves. In short, the group velocities, and thereby the wave energy propagation and vortex Rossby wave ray slope in typhoons, would be changed by the asymmetry of the basic flow.展开更多
The gun-track launch system is a new special launch device that connects the track outside the muzzle.Because it is constrained by the track,the characteristics of development of the muzzle jet differ from those of th...The gun-track launch system is a new special launch device that connects the track outside the muzzle.Because it is constrained by the track,the characteristics of development of the muzzle jet differ from those of the traditional muzzle jet.Specifically,it changes from freely developing to doing so in a constrained manner,where this results in an asymmetric direction of flow as well as spatio-temporal coupling-induced interference between various shock waves and the formation of vortices.In this background,the authors of this article formulate and consider the development and characteristics of evolution of the muzzle jet as it impacts a constrained moving body.We designed simulations to test the gun-track launch system,and established a numerical model based on the dynamic grid method to explore the development and characteristics of propagation of disturbances when the muzzle jet impacted a constrained moving body.We also considered models without a constrained track for the sake of comparison.The results showed that the muzzle jet assumed a circumferential asymmetric shape,and tended to develop in the area above the muzzle.Because the test platform was close to the ground,the muzzle jet was subjected to reflections from it that enhanced the development and evolution of various forms of shock waves and vortices in the muzzle jet to exacerbate its rate of distortion and asymmetric characteristics.This in turn led to significant differences in the changes in pressure at symmetric points that would otherwise have been identical.The results of a comparative analysis showed that the constrained track could hinder the influence of reflections from the ground on the muzzle jet to some extent,and could reduce the velocity of the shock waves inducing the motion of the muzzle as well as the Mach number of the moving body.The work here provides a theoretical basis and the requisite technical support for applications of the gun-track launch system.It also sheds light on the technical bottlenecks that need to be considered to recover high-value warheads.展开更多
Using the NCEP reanalysis at 1°×1° resolution in conjunction with satellite imagery,a study is undertaken of easterly wave related rainstorm events on August 3~4,2001 in seaboards between northern Fujia...Using the NCEP reanalysis at 1°×1° resolution in conjunction with satellite imagery,a study is undertaken of easterly wave related rainstorm events on August 3~4,2001 in seaboards between northern Fujian and southern Zhejiang,expounding the scheme for computing helicity,and exploring the rainstorm evolution and the genesis of the Yandang mountains-triggered a meso-vortex(Duan and Chen,2005) by means of helicity and Q vector divergence.Besides,MM5V2 is employed to simulate the easterly wave caused meso-vorte...展开更多
In a quasi-two-dimensional model, the scattering of incident ordinary electromag- netic waves by a dipole-electrostatic drift vortex is studied with first-order Born approximation. The distribution of the scattering c...In a quasi-two-dimensional model, the scattering of incident ordinary electromag- netic waves by a dipole-electrostatic drift vortex is studied with first-order Born approximation. The distribution of the scattering cross-section and total cross-section are evaluated analytically in different approximate conditions, and the physical interpretations are discussed. When the wavelength of incident wave is much longer than the vortex radius （kia〈〈1）, it is found that the angle at which the scattering cross-section reaches its maxim depends significantly on the approximation of the parameters of the vortex used. It is also found that the total scattering cross-section has an affinitive relation with the parameters of the plasma, while it is irrelevant to the frequency of the incident wave in a wide range of parameters of the vortex. In a totally different range of parameters when incident wave is in the radar-frequency range （then kia 〈〈 1, the wavelength of incident wave is much shorter than the vortex radius）, the numerical procedure is conducted with computer in order to obtain the distribution and the total expression of the scattering crosssection. Then it is found that the total scattering cross-section in the low frequency range is much larger than that in high frequency range, so the scattering is more effective in the low frequency range than in high frequency range.展开更多
In recent ten years high resolution difference schenies for the computation of thefull unsteady Eulerian system of equations for invisid compressible gas finds celebratedprogress. This paper tests furtherly, by a comp...In recent ten years high resolution difference schenies for the computation of thefull unsteady Eulerian system of equations for invisid compressible gas finds celebratedprogress. This paper tests furtherly, by a complex two-dimensional unsteady problem,four recent schemes. to them attentions are paid. The test problem is the initial stageof a two-dimensional diffraction and reflection of a plane shock wave, impinging on arectangular obstacle. At whose top side there are two sharp corners, near which flow.parameters finds severe variation. There is occurrence of expansion fan with a centerand also concentrated vortices. To simulate them well, the schemes should have goodadaptivity. The special shock Mach number M,=2.068 is so chosen, that at this M,the partical velocity behind impinging shock in fixed coordinate system is just equal tothe speed of sound there, this condition also occurs along a curve in the region ofexpansion fan with a center at the corner. This can clarify the computational featureof different schemes in case,when one of the eigenvalues is just zero. Zero eigenvaluemay spoil some schemes locally. Graphical visualization of the computational resultsmay, show features of the tested schemes about the shock wave resolution, schemeviscosity, expansion wave and the ability. to simulate the process of the generation ofunsteadv concentrated vortex.展开更多
Impulsively starting flow, by a sudden attainment of a large angle of attack, has been well studied for incompressible and supersonic flows, but less studied for subsonic flow. Recently,a preliminary numerical study f...Impulsively starting flow, by a sudden attainment of a large angle of attack, has been well studied for incompressible and supersonic flows, but less studied for subsonic flow. Recently,a preliminary numerical study for subsonic starting flow at a high angle of attack displays an advance of stall around a Mach number of 0.5, when compared to other Mach numbers. To see what happens in this special case, we conduct here in this paper a further study for this case, to display and analyze the full flow structures. We find that for a Mach number around 0.5, a local supersonic flow region repeatedly splits and merges, and a pair of left-going and right-going unsteady shock waves are embedded inside the leading edge vortex once it is sufficiently grown up and detached from the leading edge. The flow evolution during the formation of shock waves is displayed in detail. The reason for the formation of these shock waves is explained here using the Laval nozzle flow theory. The existence of this shock pair inside the vortex, for a Mach number only close to 0.5, may help the growing of the trailing edge vortex responsible for the advance of stall observed previously.展开更多
基金supported in part by National Natural Science Foundation of China under Grant 62441115 and 62201427in part by the Ministry of Industry and Information Technology of the People’s Republic of China under Grant CBG01N23-01-04.
文摘Orbital angular momentum(OAM)can achieve multifold increase of spectrum efficiency,but the hollow divergence characteristic and Line-of-Sight(LoS)path requirement impose the crucial challenges for vortex wave communications.For air-to-ground vortex wave communications,where there exists the LoS path,this paper proposes a multi-user cooperative receive(MUCR)scheme to break through the communication distance limitation caused by the characteristic of vortex wave hollow divergence.In particular,we derive the optimal radial position corresponding to the maximum intensity,which is used to adjust the waist radius.Based on the waist radius and energy ring,the cooperative ground users having the minimum angular square difference are selected.Also,the signal compensation scheme is proposed to decompose OAM signals in air-to-ground vortex wave communications.Simulation results are presented to verify the superiority of our proposed MUCR scheme.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11804073 and 61775050).
文摘The influence of the longitudinal acceleration and the angular acceleration of detecting target based on vortex electromagnetic waves in keyhole space are analyzed.The spectrum spreads of different orbital angular momentum(OAM)modes in different non-line-of-sight situations are simulated.The errors of target accelerations in detection are calculated and compared based on the OAM spectra spreading by using two combinations of composite OAM modes in the keyhole space.According to the research,the effects about spectrum spreads of higher OAM modes are more obvious.The error in detection is mainly affected by OAM spectrum spreading,which can be reduced by reasonably using different combinations of OAM modes in different practical situations.The above results provide a reference idea for investigating keyhole effect when vortex electromagnetic wave is used to detect accelerations.
基金supported by the National Basic Research Program of China (Grant No.2009CB421504)the National Natural Science Foundation of China (Grant No. 40830958)+2 种基金the US NSF Grant ATM-0758609the National Youth Science Fund of China (GrantNo. 40905022)the Doctor Start fund of PLA University of Science and Technology
文摘In this study, the barotropic stability of vortex Rossby waves （VRWs） in 2D inviscid tropical cyclone （TC）-like vortices is explored in the context of rotational dynamics on an f-plane. Two necessary instable conditions are discovered： （a） there must be at least one zero point of basic vorticity gradient in the radial scope; and （b） the relative propagation velocity of perturbations must be negative to the basic vorticity gradient, which reflects the restriction relationship of instable energy. The maximum growth rate of instable waves depends on the peak radial gradient of the mean vorticity and the tangential wavenumber （WN）. The vortex-semicircle theorem is also derived to provide bounds on the growth rates and phase speeds of VRWs. The typical basic states and different WN perturbations in a tropical cyclone （TC） are obtained from a high resolution simulation. It is shown that the first necessary condition for vortex barotropic instability can be easily met at the radius of maximum vorticity （RMV）. The wave energy tends to decay （grow） inside （outside） the RMV due mainly to the negative （positive） sign of the radial gradient of the mean absolute vorticity. This finding appears to help explain the developemnt of strong vortices in the eyewall of TCs.
基金supported by the National Basic Research Program of China (Grant Nos2010CB428602 and 2010CB428502)the National Natural Science Foundation of China (Grant No 41005023)the Program for New Century Excellent Talents in University (Grant No NCET-09-0227)
文摘Using 1958-2002 NCEPNCAR reanalysis data, we investigate stationary and transient planetary wave propagation and its role in wave-mean flow interaction which influences the state of the polar vortex （PV） in the stratosphere in Northern Hemisphere （NH） winter. This is done by analyzing the Eliassen-Palm （E-P） flux and its divergence. We find that the stationary and transient waves propagate upward and equatorward in NH winter, with stronger upward propagation of stationary waves from the troposphere to the stratosphere, and stronger equatorward propagation of transient waves from mid-latitudes to the subtropics in the troposphere. Stationary waves exhibit more upward propagation in the polar stratosphere during the weak polar vortex regime （WVR） than during the strong polar vortex regime （SVR）. On the other hand, transient waves have more upward propagation during SVR than during WVR in the subpolar stratosphere, with a domain of low frequency waves. With different paths of upward propagation, both stationary and transient waves contribute to the maintenance of the observed stratospheric PV regimes in NH winter.
基金supported by the National Key Basic Research and Development Project of China(Grant No.2012CB417202)the National Nature Science Fund of China(Grant No.41175045)+1 种基金the Special Fund for Meteorological Research in the Public Interest(Grant Nos.GYHY201006014,GYHY201206042 and GYHY201106003)the Sichuan Meteorological Bureau Fund for Young Scholars(Grant No.2011YOUTH02)
文摘In terms of its dynamics, The Tibetan Plateau Vortex （TPV） is assumed to be a vortex in the botmdary layer forced by diabatic heating and friction. In order to analyze the basic characteristics of waves in the vortex, the governing equations for the vortex were established in column coordinates with the balance of gradient wind. Based on this, the type of mixed waves and their dispersion characteristics were deduced by solving the linear model. Two numerical simulations with triple-nested domains--one idealized large-eddy simulation and one of a TPV that took place on 14 August 2006---were also carried out. The aim of the simulations was to validate the mixed wave deduced from the governing equations. The high-resolution model output data were analyzed and the results showed that the tangential flow field of the TPV in the form of center heating was cyclonic and convergent in the lower levels and anticyclonic and divergent in the upper levels. The simulations also showed that the vorticity of the vortex is uneven and might have shear flow along the radial direction. The changing vorticity causes the formation and spreading of vortex Rossby （VR） waves, and divergence will cause changes to the n^otion of the excitation and evolution of inertial gravity （IG） waves. Therefore, the vortex may contain what we call mixed ：inertial gravity-vortex Rossby （IG-VR） waves. It is suggested that some strongly developed TPVs should be studied in the future, because of their effects on weather in downstream areas.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.51509178 and 51509177)the Natural Science Foundation of Tianjin City(Grant No.14JCYBJC22100)the Natural Science Foundation of Tianjin Education Commission(Grant No.2017KJ046)
文摘The interactions of cnoidal waves with a submerged quartercircular breakwater are investigated by a ReynoldsAveraged Navier–Stokes(RANS) flow solver with a Volume of Fluid(VOF) surface capturing scheme(RANSVOF) model. The vertical variation of the instantaneous velocity indicates that flow separation occurs at the boundary layer near the breakwater. The temporal evolution of the velocity and vorticity fields demonstrates vortex generation and shedding around the submerged quartercircular breakwater due to the flow separation. An empirical relationship between the vortex intensity and a few hydrodynamic parameters is proposed based on parametric analysis. In addition, the instantaneous and time-averaged vorticity fields reveal a pair of vortices of opposite signs at the breakwater which are expected to have significant effect on sediment entrainment, suspension, and transportation,therefore, scour on the leeside of the breakwater.
基金sponsored by the National Natural Science Foundation of China (Grant No.41430426)
文摘Wave ray theory is employed to study features of propagation pathways（rays） of vortex Rossby waves in typhoons with asymmetric basic flow, where the tangential asymmetric basic flow is constructed by superimposing the wavenumber-1 perturbation flow on the symmetric basic flow, and the radial basic flow is derived from the non-divergence equation. Results show that, in a certain distance, the influences of the asymmetry in the basic flow on group velocities and slopes of rays of vortex Rossby waves are mainly concentrated near the radius of maximum wind（RMW）, whereas it decreases outside the RMW. The distributions of radial and tangential group velocities of the vortex Rossby waves in the asymmetric basic flow are closely related to the azimuth location of the maximum speed of the asymmetric basic flow, and the importance of radial and tangential basic flow on the group velocities would change with radius. In addition, the stronger asymmetry in the basic flow always corresponds to faster outward energy propagation of vortex Rossby waves. In short, the group velocities, and thereby the wave energy propagation and vortex Rossby wave ray slope in typhoons, would be changed by the asymmetry of the basic flow.
文摘The gun-track launch system is a new special launch device that connects the track outside the muzzle.Because it is constrained by the track,the characteristics of development of the muzzle jet differ from those of the traditional muzzle jet.Specifically,it changes from freely developing to doing so in a constrained manner,where this results in an asymmetric direction of flow as well as spatio-temporal coupling-induced interference between various shock waves and the formation of vortices.In this background,the authors of this article formulate and consider the development and characteristics of evolution of the muzzle jet as it impacts a constrained moving body.We designed simulations to test the gun-track launch system,and established a numerical model based on the dynamic grid method to explore the development and characteristics of propagation of disturbances when the muzzle jet impacted a constrained moving body.We also considered models without a constrained track for the sake of comparison.The results showed that the muzzle jet assumed a circumferential asymmetric shape,and tended to develop in the area above the muzzle.Because the test platform was close to the ground,the muzzle jet was subjected to reflections from it that enhanced the development and evolution of various forms of shock waves and vortices in the muzzle jet to exacerbate its rate of distortion and asymmetric characteristics.This in turn led to significant differences in the changes in pressure at symmetric points that would otherwise have been identical.The results of a comparative analysis showed that the constrained track could hinder the influence of reflections from the ground on the muzzle jet to some extent,and could reduce the velocity of the shock waves inducing the motion of the muzzle as well as the Mach number of the moving body.The work here provides a theoretical basis and the requisite technical support for applications of the gun-track launch system.It also sheds light on the technical bottlenecks that need to be considered to recover high-value warheads.
基金supported by the National Natural Science Foundation of China(40875025,40875030,40775033,40405009)
文摘Using the NCEP reanalysis at 1°×1° resolution in conjunction with satellite imagery,a study is undertaken of easterly wave related rainstorm events on August 3~4,2001 in seaboards between northern Fujian and southern Zhejiang,expounding the scheme for computing helicity,and exploring the rainstorm evolution and the genesis of the Yandang mountains-triggered a meso-vortex(Duan and Chen,2005) by means of helicity and Q vector divergence.Besides,MM5V2 is employed to simulate the easterly wave caused meso-vorte...
基金National Natural Science Foundation of China(Nos,10375063.40336052)
文摘In a quasi-two-dimensional model, the scattering of incident ordinary electromag- netic waves by a dipole-electrostatic drift vortex is studied with first-order Born approximation. The distribution of the scattering cross-section and total cross-section are evaluated analytically in different approximate conditions, and the physical interpretations are discussed. When the wavelength of incident wave is much longer than the vortex radius （kia〈〈1）, it is found that the angle at which the scattering cross-section reaches its maxim depends significantly on the approximation of the parameters of the vortex used. It is also found that the total scattering cross-section has an affinitive relation with the parameters of the plasma, while it is irrelevant to the frequency of the incident wave in a wide range of parameters of the vortex. In a totally different range of parameters when incident wave is in the radar-frequency range （then kia 〈〈 1, the wavelength of incident wave is much shorter than the vortex radius）, the numerical procedure is conducted with computer in order to obtain the distribution and the total expression of the scattering crosssection. Then it is found that the total scattering cross-section in the low frequency range is much larger than that in high frequency range, so the scattering is more effective in the low frequency range than in high frequency range.
文摘In recent ten years high resolution difference schenies for the computation of thefull unsteady Eulerian system of equations for invisid compressible gas finds celebratedprogress. This paper tests furtherly, by a complex two-dimensional unsteady problem,four recent schemes. to them attentions are paid. The test problem is the initial stageof a two-dimensional diffraction and reflection of a plane shock wave, impinging on arectangular obstacle. At whose top side there are two sharp corners, near which flow.parameters finds severe variation. There is occurrence of expansion fan with a centerand also concentrated vortices. To simulate them well, the schemes should have goodadaptivity. The special shock Mach number M,=2.068 is so chosen, that at this M,the partical velocity behind impinging shock in fixed coordinate system is just equal tothe speed of sound there, this condition also occurs along a curve in the region ofexpansion fan with a center at the corner. This can clarify the computational featureof different schemes in case,when one of the eigenvalues is just zero. Zero eigenvaluemay spoil some schemes locally. Graphical visualization of the computational resultsmay, show features of the tested schemes about the shock wave resolution, schemeviscosity, expansion wave and the ability. to simulate the process of the generation ofunsteadv concentrated vortex.
基金supported by the National Natural Science Foundation of China(No.11472157)
文摘Impulsively starting flow, by a sudden attainment of a large angle of attack, has been well studied for incompressible and supersonic flows, but less studied for subsonic flow. Recently,a preliminary numerical study for subsonic starting flow at a high angle of attack displays an advance of stall around a Mach number of 0.5, when compared to other Mach numbers. To see what happens in this special case, we conduct here in this paper a further study for this case, to display and analyze the full flow structures. We find that for a Mach number around 0.5, a local supersonic flow region repeatedly splits and merges, and a pair of left-going and right-going unsteady shock waves are embedded inside the leading edge vortex once it is sufficiently grown up and detached from the leading edge. The flow evolution during the formation of shock waves is displayed in detail. The reason for the formation of these shock waves is explained here using the Laval nozzle flow theory. The existence of this shock pair inside the vortex, for a Mach number only close to 0.5, may help the growing of the trailing edge vortex responsible for the advance of stall observed previously.
