A two-dimensional panel in subsonic flow with stochastic excitation is studied by assuming that the aerodynamic pressure contains random pressure fluctuations.Based on the global properties,the sensitivities of system...A two-dimensional panel in subsonic flow with stochastic excitation is studied by assuming that the aerodynamic pressure contains random pressure fluctuations.Based on the global properties,the sensitivities of system parameters and noise intensities are presented.Firstly,the parameter region with multiple coexisting attractors under different dynamic pressures is obtained.It is found that the coexistence of multiple attractors extensively appears and the basin structure may be complex.Then the periodic time history diagrams are calculated by simulating the random pressure fluctuation as Poisson white noise.The results show that under typical bistable conditions,the noise sensitivity of the subsonic panel system is related to the basin structures and the disposition of the coexisting attractors to the saddle.The transition between two attractors diffuses along the unstable manifold and tends to the position where the basin boundary curvature is relatively large.The findings underscore the importance of global analysis in assessing the noise load carrying capacity,which provides some valuable insights into the safety design of subsonic panel systems.展开更多
In this article, we study irrotational subsonic and subsonic-sonic flows with gen- eral conservative forces in the infinity long nozzle. For the subsonic case, the varified Bernoulli law leads a modified cut-off syste...In this article, we study irrotational subsonic and subsonic-sonic flows with gen- eral conservative forces in the infinity long nozzle. For the subsonic case, the varified Bernoulli law leads a modified cut-off system. Because of the local average estimate, conservative forces do not need any decay condition. Afterwards, the subsonic-sonic limit solutions are constructed by taking the extract subsonic solutions as the approximate sequences.展开更多
In this paper,we investigate two dimensional subsonic and subsonic-sonic spiral flows outside a porous body.The existence and uniqueness of the subsonic spiral flow are obtained via variational formulation,which tends...In this paper,we investigate two dimensional subsonic and subsonic-sonic spiral flows outside a porous body.The existence and uniqueness of the subsonic spiral flow are obtained via variational formulation,which tends to a given radially symmetric subsonic spiral flow at far field.The optimal decay rate at far field is also derived by Kelvin ’s transformation and some elliptic estimates.By extracting spiral subsonic solutions as the approximate sequences,we obtain the spiral subsonic-sonic limit solution by utilizing the compensated compactness.The main ingredients of our analysis are methods of calculus of variations,the theory of second-order quasilinear equations and the compensated compactness framework.展开更多
To deal with the effect of compressible fluids on the supercavitating flow over the subsonic disk cavitator of a projectile, a finite volume method is formulated based on the ideal compressible potential theory. By us...To deal with the effect of compressible fluids on the supercavitating flow over the subsonic disk cavitator of a projectile, a finite volume method is formulated based on the ideal compressible potential theory. By using the continuity equation and Tait state equation as well as Riabouchinsky closure model, an“inverse problem”solution is presented for the supercavitating flow. According to the impenetrable condition on the surface of supercavity, a new iterative method for the supercavity shape is designed to deal with the effect of compressibility on the supercavity shape, pressure drag coefficient and density field. By this method, the very low cavitation number can be computed. The calculated results agree well with the experimental data and empirical formula. At the subsonic condition, the fluid compressibility will make supercavity length and radius increase. The supercavity expands, but remains spheroid. The effect on the first 1/3 part of supercavity is not obvious. The drag coefficient of projectile increases as the cavitation number or Mach number increases. With Mach number increasing, the compressibility is more and more significant. The compressibility must be considered as far as the accurate calculation of supercavitating flow is concerned.展开更多
The aerodynamic drag on a train running in an evacuated tube varies with tube air pressure, train speed and shape, as well as blockage ratio. This paper uses numerical simulations to study the effects of different fac...The aerodynamic drag on a train running in an evacuated tube varies with tube air pressure, train speed and shape, as well as blockage ratio. This paper uses numerical simulations to study the effects of different factors on the aerodynamic drag of a train running at subsonic speed in an evacuated tube. Firstly, we present the assumption of a steady state, two dimensional, incompressible viscous flow with lubricity wall conditions. Subsequently, based on the Navier-Stokes equation and the k-c turbulent models, we calculate the aerodynamic drag imposed on the column train with a 3-meter diameter running under different pressure and blockage ratio conditions in an evacuated tube transporta- tion （ETT） system. The simulation is performed with FLUENT 6.3 software package. An analyses of the simulation re- sults suggest that the blockage ratio for ETT should be in the range of 0.25-0.7, and the tube internal diameter in the range of 2-4 m, with the feasible vacuum pressure in the range of 1-10 000 Pa for the future subsonic ETT trains.展开更多
Turbo-machineries,as key components,have wide applications in civil,aerospace,and mechanical engineering.By calculating natural frequencies and dynamical deformations,we have explained the rationality of the series fo...Turbo-machineries,as key components,have wide applications in civil,aerospace,and mechanical engineering.By calculating natural frequencies and dynamical deformations,we have explained the rationality of the series form for the aerodynamic force of the blade under the subsonic flow in our earlier studies.In this paper,the subsonic aerodynamic force obtained numerically is applied to the low pressure compressor blade with a low constant rotating speed.The blade is established as a pre-twist and presetting cantilever plate with a rectangular section under combined excitations,including the centrifugal force and the aerodynamic force.In view of the first-order shear deformation theory and von-K′arm′an nonlinear geometric relationship,the nonlinear partial differential dynamical equations for the warping cantilever blade are derived by Hamilton’s principle.The second-order ordinary differential equations are acquired by the Galerkin approach.With consideration of 1:3 internal resonance and 1/2 sub-harmonic resonance,the averaged equation is derived by the asymptotic perturbation methodology.Bifurcation diagrams,phase portraits,waveforms,and power spectrums are numerically obtained to analyze the effects of the first harmonic of the aerodynamic force on nonlinear dynamical responses of the structure.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
A new method of preparation of biomaterial composite coating by the techniqueof subsonic thermal spraying was discussed in this paper. Ti_6Al_4V and pure Ti were chosen assubstrate and sublayer material respectively a...A new method of preparation of biomaterial composite coating by the techniqueof subsonic thermal spraying was discussed in this paper. Ti_6Al_4V and pure Ti were chosen assubstrate and sublayer material respectively and the working layer was sprayed with biomaterialhydroxyapatite (HAP), forming the composite coating. The experiments of heat shock and tensilestrength showed that the bonding strength between coating and substrate is almost as same as that ofspecimen in which Ni/Al powder was adopted as sublayer. The phases of TiN, TiO_2, and Ti_2O_3 wereformed in the sublayer, which are free of toxic and have no side effects. The powder of workinglayer HAP was decomposed partly during spraying, but it can be solved by later treatment.展开更多
An improved mean surtace method (IMSM) for propeller noise predictionis presented, based on solving the Ffowes Williams & Hawking (FW & H) equation intime domain. Numerical calculation results show that the IM...An improved mean surtace method (IMSM) for propeller noise predictionis presented, based on solving the Ffowes Williams & Hawking (FW & H) equation intime domain. Numerical calculation results show that the IMSM needs only 50% ofCPU time and memory of subsonic full surface method (SFSM), 50%～ 60% of CPUtime and meinory of old nican surfacc method (OMSM) and 10%～ 13% of CPU timeof transonic collapse spliere method (TCSM) while the calculation accuracy can be as-sured. Thus, the IMSM given in this paper could be a good alternative method forsubsonic propeller noise prediction. especially in preliminary aeroacoustics design of anew propeller.展开更多
An overview of recent experimental results on instability and dynamics of jets at low Reynolds numbers is given. Round and plane, macro and micro jets are under the consideration. Basic features of their evolution aff...An overview of recent experimental results on instability and dynamics of jets at low Reynolds numbers is given. Round and plane, macro and micro jets are under the consideration. Basic features of their evolution affected by initial conditions at the nuzzle outlet and environmental perturbations are demonstrated.展开更多
As a continuation of[Li,J.and Wang,Y.N.,Structural stability of steady subsonic Euler flows in 2D finitely long nozzles with variable end pressure,J.Differential Equations,413,2014,70-109],in this paper,the authors st...As a continuation of[Li,J.and Wang,Y.N.,Structural stability of steady subsonic Euler flows in 2D finitely long nozzles with variable end pressure,J.Differential Equations,413,2014,70-109],in this paper,the authors study the structural stability of three dimensional axisymmetric steady subsonic Euler flows in finitely long curved nozzles.The reference flow is a general subsonic shear flow in a three dimensional regular cylindrical nozzle with general size of vorticity and without stagnation points.The problem is described by the well-known steady compressible Euler system.With a class of admissible physical conditions and prescribed pressure at the entrance and the exit of the nozzle respectively,they establish the structural stability of this kind of axisymmetric subsonic shear flow with no-zero swirl velocity.Due to the hyperbolic-elliptic coupled form of the Euler system in subsonic regions,the problem is reformulated via a twofold normalized process,including straightening the lateral boundary of the nozzle under the natural Cartesian coordinates and reformulating the problem under the cylindrical coordinates.Accordingly,the Euler system is decoupled into an elliptic mode and three hyperbolic modes with some artificial singular terms under the cylindrical coordinates.The elliptic mode is a mixed type boundary value problem of first order elliptic system for the pressure and the radial velocity angle.Meanwhile,the hyperbolic modes are transport type to control the total energy,the specific entropy and the swirl velocity,respectively.The estimates as well as well-posedness are executed in a Banach space with optimal regularity under the natural Cartesian coordinates in place of the cylindrical coordinates.The authors develop a systematic framework to deal with the artificial singularity and the non-zero swirl velocity in three dimensional axisymmetric case.Their strategy is helpful for other three dimensional problems under axisymmetry.展开更多
In this paper,we consider a uniformly accurate compact finite difference method to solve the quantum Zakharov system(QZS)with a dimensionless parameter 0<ε≤1,which is inversely proportional to the acoustic speed....In this paper,we consider a uniformly accurate compact finite difference method to solve the quantum Zakharov system(QZS)with a dimensionless parameter 0<ε≤1,which is inversely proportional to the acoustic speed.In the subsonic limit regime,i.e.,when 0<ε?1,the solution of QZS propagates rapidly oscillatory initial layers in time,and this brings significant difficulties in devising numerical algorithm and establishing their error estimates,especially as 0<ε?1.The solvability,the mass and energy conservation laws of the scheme are also discussed.Based on the cut-off technique and energy method,we rigorously analyze two independent error estimates for the well-prepared and ill-prepared initial data,respectively,which are uniform in both time and space forε∈(0,1]and optimal at the fourth order in space.Numerical results are reported to verify the error behavior.展开更多
In this paper, we study the irrotational subsonic and subsonic-sonic fows with general conservative forces in the exterior domains. The conservative forces indicate the new Bernoulli law naturally. For the subsonic ca...In this paper, we study the irrotational subsonic and subsonic-sonic fows with general conservative forces in the exterior domains. The conservative forces indicate the new Bernoulli law naturally. For the subsonic case, we introduce a modified cut-off system depending on the conservative forces which needs the varied Bers skill, and construct the solution by the new variational formula. Moreover, comparing with previous results, our result extends the pressure-density relation to the general case. Afterwards we obtain the subsonic-sonic limit solution by taking the extract subsonic solutions as the approximate sequences.展开更多
Increasing demand for downsizing of engines to improve CO2 emissions has resulted in renewed efforts to improve the efficiency and expend the stable operating range of the centrifugal compressors used in petro-chemica...Increasing demand for downsizing of engines to improve CO2 emissions has resulted in renewed efforts to improve the efficiency and expend the stable operating range of the centrifugal compressors used in petro-chemical equipment and turbochargers. The losses in these compressors are dominated by tip clearance flow. In this paper, the tip clearance flow in the subsonic impeller is numerically investigated. The nature of the tip clearance in inducer, axial to radial bend and exducer are studied in detail at design and off-design conditions by examining the detailed flow field through the clearance and the interaction of the clearance flow with the shear effect with the endwalls. The correlation between blade loading and span wise geometry and clearance flow at different locations are presented.展开更多
In this paper, under some assumptions on the flow with a low Mach number, we study the nonexistence of a global nontrivial subsonic solution in an unbounded domain Ω which is one part of a 3D ramp. The flow is assume...In this paper, under some assumptions on the flow with a low Mach number, we study the nonexistence of a global nontrivial subsonic solution in an unbounded domain Ω which is one part of a 3D ramp. The flow is assumed to be steady, isentropic and irrotational, namely, the movement of the flow is described by the potential equation. By establishing a fundamental a priori estimate on the solution of a second order linear elliptic equation in Ω with Neumann boundary conditions on Ω and Dirichlet boundary value at some point of Ω, we show that there is no global nontrivial subsonic flow with a low Mach number in such a domain Ω.展开更多
The gas turbine is the main power equipment for naval ship and special civil ship,while the compressor is one of the core structures of the gas turbine.The existing tip clearance could prevent the compressor blade and...The gas turbine is the main power equipment for naval ship and special civil ship,while the compressor is one of the core structures of the gas turbine.The existing tip clearance could prevent the compressor blade and casing collision.Therefore,the flow loss in the tip region caused by the tip clearance will degrade the performance of the compressor.To improve the variable clearance characteristics of the high subsonic compressor cascades,the cascades with tip clearances of 1%,2%and 3%chord length are studied through experimental measurements and numerical calculations.The research results prove that the pressure surface tip winglet can cause a significant improvement effect under most working conditions.If the blade tip clearance size is gradually increasing within a reasonable range,the improvement effect becomes more remarkable,and the optimal tip winglet case changes.When tip clearance is 1%chord length,the PTW1.0 case(the width of the pressure surface tip winglet is 1.0 time of the original tip)reduces the flow loss by 3.09%compared with the NTW case(No Tip Winglet).When tip clearance is 2%chord length,the flow loss of PTW1.5 case(the width of the pressure surface tip winglet is 1.5 times of the original tip)is reduced by 3.46%.When tip clearance is 3%chord length,all alternative tip winglets reduce the total pressure loss,and PTW2.0 case(the width of the pressure surface tip winglet is 2.0 times of the original tip)is the best choice,which has a 6.53%degree of improvement.展开更多
The purpose of this paper is to prove the uniform stability of multidimensional subsonic phase transitions satisfying the viscosity-capillarity criterion in a van der Waals fluid, and further to establish the local ex...The purpose of this paper is to prove the uniform stability of multidimensional subsonic phase transitions satisfying the viscosity-capillarity criterion in a van der Waals fluid, and further to establish the local existence of phase transition solutions.展开更多
An algorithm composed of an iterative modified approximate factorization(MAF(k)) method with Navier-Stokes characteristic boundary conditions(NSCBC) is proposed for solving subsonic viscous flows.A transformation on t...An algorithm composed of an iterative modified approximate factorization(MAF(k)) method with Navier-Stokes characteristic boundary conditions(NSCBC) is proposed for solving subsonic viscous flows.A transformation on the matrix equation in MAF(k) is made in order to impose the implicit boundary conditions properly.To be in consistent with the implicit solver for the interior domain,an implicit scheme for NSCBC is formulated.The performance of the developed algorithm is investigated using spatially evolving zero pressure gradient boundary layer over a flat plate and a wall jet mixing with a cross flow over a flat plate with a square hole as the test cases.The numerical results are compared to the existing experimental datasets and a number of general correlations,together with other available numerical solutions,which demonstrate that the developed algorithm possesses promising capacity for simulating the subsonic viscous flows with large CFL number.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.52225211 and 12172284)the Natural Science Foundation of Chongqing,China(Grant No.cstc2021jcyjmsxmX0738)the Fundamental Research Funds for the Central Universities.
文摘A two-dimensional panel in subsonic flow with stochastic excitation is studied by assuming that the aerodynamic pressure contains random pressure fluctuations.Based on the global properties,the sensitivities of system parameters and noise intensities are presented.Firstly,the parameter region with multiple coexisting attractors under different dynamic pressures is obtained.It is found that the coexistence of multiple attractors extensively appears and the basin structure may be complex.Then the periodic time history diagrams are calculated by simulating the random pressure fluctuation as Poisson white noise.The results show that under typical bistable conditions,the noise sensitivity of the subsonic panel system is related to the basin structures and the disposition of the coexisting attractors to the saddle.The transition between two attractors diffuses along the unstable manifold and tends to the position where the basin boundary curvature is relatively large.The findings underscore the importance of global analysis in assessing the noise load carrying capacity,which provides some valuable insights into the safety design of subsonic panel systems.
基金supported in part by NSFC(11601305)supported in part by NSFC(11601401)the Fundamental Research Funds for the Central Universities(WUT:2017IVA072 and 2017IVB066)
文摘In this article, we study irrotational subsonic and subsonic-sonic flows with gen- eral conservative forces in the infinity long nozzle. For the subsonic case, the varified Bernoulli law leads a modified cut-off system. Because of the local average estimate, conservative forces do not need any decay condition. Afterwards, the subsonic-sonic limit solutions are constructed by taking the extract subsonic solutions as the approximate sequences.
基金partially supported by National Natural Science Foundation of China(11701431,11971307,12071359)。
文摘In this paper,we investigate two dimensional subsonic and subsonic-sonic spiral flows outside a porous body.The existence and uniqueness of the subsonic spiral flow are obtained via variational formulation,which tends to a given radially symmetric subsonic spiral flow at far field.The optimal decay rate at far field is also derived by Kelvin ’s transformation and some elliptic estimates.By extracting spiral subsonic solutions as the approximate sequences,we obtain the spiral subsonic-sonic limit solution by utilizing the compensated compactness.The main ingredients of our analysis are methods of calculus of variations,the theory of second-order quasilinear equations and the compensated compactness framework.
基金Foundation item： Supported by the National Natural Science Foundation of China （Grant No. 51309230）, and China Postdoctoral Science Foundation （Nos. 2014T70992 and 2013 M542531）We would like to thank Dr. Tao Miao for closely following our work and making several useful suggestions.
文摘To deal with the effect of compressible fluids on the supercavitating flow over the subsonic disk cavitator of a projectile, a finite volume method is formulated based on the ideal compressible potential theory. By using the continuity equation and Tait state equation as well as Riabouchinsky closure model, an“inverse problem”solution is presented for the supercavitating flow. According to the impenetrable condition on the surface of supercavity, a new iterative method for the supercavity shape is designed to deal with the effect of compressibility on the supercavity shape, pressure drag coefficient and density field. By this method, the very low cavitation number can be computed. The calculated results agree well with the experimental data and empirical formula. At the subsonic condition, the fluid compressibility will make supercavity length and radius increase. The supercavity expands, but remains spheroid. The effect on the first 1/3 part of supercavity is not obvious. The drag coefficient of projectile increases as the cavitation number or Mach number increases. With Mach number increasing, the compressibility is more and more significant. The compressibility must be considered as far as the accurate calculation of supercavitating flow is concerned.
基金supported by the National Natural Science Foundation of China (No. 50678152)the Scientific Plan Fund of Shaanxi Province(No. 2009K09-24)
文摘The aerodynamic drag on a train running in an evacuated tube varies with tube air pressure, train speed and shape, as well as blockage ratio. This paper uses numerical simulations to study the effects of different factors on the aerodynamic drag of a train running at subsonic speed in an evacuated tube. Firstly, we present the assumption of a steady state, two dimensional, incompressible viscous flow with lubricity wall conditions. Subsequently, based on the Navier-Stokes equation and the k-c turbulent models, we calculate the aerodynamic drag imposed on the column train with a 3-meter diameter running under different pressure and blockage ratio conditions in an evacuated tube transporta- tion （ETT） system. The simulation is performed with FLUENT 6.3 software package. An analyses of the simulation re- sults suggest that the blockage ratio for ETT should be in the range of 0.25-0.7, and the tube internal diameter in the range of 2-4 m, with the feasible vacuum pressure in the range of 1-10 000 Pa for the future subsonic ETT trains.
基金Project supported by the National Natural Science Foundation of China(Nos.11372015,11832002,11290152,11427801,and 11972051)。
文摘Turbo-machineries,as key components,have wide applications in civil,aerospace,and mechanical engineering.By calculating natural frequencies and dynamical deformations,we have explained the rationality of the series form for the aerodynamic force of the blade under the subsonic flow in our earlier studies.In this paper,the subsonic aerodynamic force obtained numerically is applied to the low pressure compressor blade with a low constant rotating speed.The blade is established as a pre-twist and presetting cantilever plate with a rectangular section under combined excitations,including the centrifugal force and the aerodynamic force.In view of the first-order shear deformation theory and von-K′arm′an nonlinear geometric relationship,the nonlinear partial differential dynamical equations for the warping cantilever blade are derived by Hamilton’s principle.The second-order ordinary differential equations are acquired by the Galerkin approach.With consideration of 1:3 internal resonance and 1/2 sub-harmonic resonance,the averaged equation is derived by the asymptotic perturbation methodology.Bifurcation diagrams,phase portraits,waveforms,and power spectrums are numerically obtained to analyze the effects of the first harmonic of the aerodynamic force on nonlinear dynamical responses of the structure.
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.
基金This project is financially supported by the Natural Science Foundation ofHeilongjiang Province (No. E0232)
文摘A new method of preparation of biomaterial composite coating by the techniqueof subsonic thermal spraying was discussed in this paper. Ti_6Al_4V and pure Ti were chosen assubstrate and sublayer material respectively and the working layer was sprayed with biomaterialhydroxyapatite (HAP), forming the composite coating. The experiments of heat shock and tensilestrength showed that the bonding strength between coating and substrate is almost as same as that ofspecimen in which Ni/Al powder was adopted as sublayer. The phases of TiN, TiO_2, and Ti_2O_3 wereformed in the sublayer, which are free of toxic and have no side effects. The powder of workinglayer HAP was decomposed partly during spraying, but it can be solved by later treatment.
文摘An improved mean surtace method (IMSM) for propeller noise predictionis presented, based on solving the Ffowes Williams & Hawking (FW & H) equation intime domain. Numerical calculation results show that the IMSM needs only 50% ofCPU time and memory of subsonic full surface method (SFSM), 50%～ 60% of CPUtime and meinory of old nican surfacc method (OMSM) and 10%～ 13% of CPU timeof transonic collapse spliere method (TCSM) while the calculation accuracy can be as-sured. Thus, the IMSM given in this paper could be a good alternative method forsubsonic propeller noise prediction. especially in preliminary aeroacoustics design of anew propeller.
文摘An overview of recent experimental results on instability and dynamics of jets at low Reynolds numbers is given. Round and plane, macro and micro jets are under the consideration. Basic features of their evolution affected by initial conditions at the nuzzle outlet and environmental perturbations are demonstrated.
基金supported by the National Key Research and Development Program of China(No.2024YFA1013301)。
文摘As a continuation of[Li,J.and Wang,Y.N.,Structural stability of steady subsonic Euler flows in 2D finitely long nozzles with variable end pressure,J.Differential Equations,413,2014,70-109],in this paper,the authors study the structural stability of three dimensional axisymmetric steady subsonic Euler flows in finitely long curved nozzles.The reference flow is a general subsonic shear flow in a three dimensional regular cylindrical nozzle with general size of vorticity and without stagnation points.The problem is described by the well-known steady compressible Euler system.With a class of admissible physical conditions and prescribed pressure at the entrance and the exit of the nozzle respectively,they establish the structural stability of this kind of axisymmetric subsonic shear flow with no-zero swirl velocity.Due to the hyperbolic-elliptic coupled form of the Euler system in subsonic regions,the problem is reformulated via a twofold normalized process,including straightening the lateral boundary of the nozzle under the natural Cartesian coordinates and reformulating the problem under the cylindrical coordinates.Accordingly,the Euler system is decoupled into an elliptic mode and three hyperbolic modes with some artificial singular terms under the cylindrical coordinates.The elliptic mode is a mixed type boundary value problem of first order elliptic system for the pressure and the radial velocity angle.Meanwhile,the hyperbolic modes are transport type to control the total energy,the specific entropy and the swirl velocity,respectively.The estimates as well as well-posedness are executed in a Banach space with optimal regularity under the natural Cartesian coordinates in place of the cylindrical coordinates.The authors develop a systematic framework to deal with the artificial singularity and the non-zero swirl velocity in three dimensional axisymmetric case.Their strategy is helpful for other three dimensional problems under axisymmetry.
基金supported by the Project for the National Natural Science Foundation of China(No.12261103).
文摘In this paper,we consider a uniformly accurate compact finite difference method to solve the quantum Zakharov system(QZS)with a dimensionless parameter 0<ε≤1,which is inversely proportional to the acoustic speed.In the subsonic limit regime,i.e.,when 0<ε?1,the solution of QZS propagates rapidly oscillatory initial layers in time,and this brings significant difficulties in devising numerical algorithm and establishing their error estimates,especially as 0<ε?1.The solvability,the mass and energy conservation laws of the scheme are also discussed.Based on the cut-off technique and energy method,we rigorously analyze two independent error estimates for the well-prepared and ill-prepared initial data,respectively,which are uniform in both time and space forε∈(0,1]and optimal at the fourth order in space.Numerical results are reported to verify the error behavior.
基金The research of Xumin Gu was supported in part by NSF of China under Grant 12031006The research of Tian-Yi Wang was supported in part by NSF of China under Grant 11971024 and 12061080。
文摘In this paper, we study the irrotational subsonic and subsonic-sonic fows with general conservative forces in the exterior domains. The conservative forces indicate the new Bernoulli law naturally. For the subsonic case, we introduce a modified cut-off system depending on the conservative forces which needs the varied Bers skill, and construct the solution by the new variational formula. Moreover, comparing with previous results, our result extends the pressure-density relation to the general case. Afterwards we obtain the subsonic-sonic limit solution by taking the extract subsonic solutions as the approximate sequences.
基金supported by the National Natural Science Foundation of China (Grant No. 51276125)the National Basic Research Program of China ("973" Project) (Grant No. 2012CB720101)
文摘Increasing demand for downsizing of engines to improve CO2 emissions has resulted in renewed efforts to improve the efficiency and expend the stable operating range of the centrifugal compressors used in petro-chemical equipment and turbochargers. The losses in these compressors are dominated by tip clearance flow. In this paper, the tip clearance flow in the subsonic impeller is numerically investigated. The nature of the tip clearance in inducer, axial to radial bend and exducer are studied in detail at design and off-design conditions by examining the detailed flow field through the clearance and the interaction of the clearance flow with the shear effect with the endwalls. The correlation between blade loading and span wise geometry and clearance flow at different locations are presented.
基金supported by National Basic Research Programm of China (Grant No.2006CB805902)National Natural Science Foundation of China (Grant No. 10871096)
文摘In this paper, under some assumptions on the flow with a low Mach number, we study the nonexistence of a global nontrivial subsonic solution in an unbounded domain Ω which is one part of a 3D ramp. The flow is assumed to be steady, isentropic and irrotational, namely, the movement of the flow is described by the potential equation. By establishing a fundamental a priori estimate on the solution of a second order linear elliptic equation in Ω with Neumann boundary conditions on Ω and Dirichlet boundary value at some point of Ω, we show that there is no global nontrivial subsonic flow with a low Mach number in such a domain Ω.
基金supported by the National Natural Science Foundation of China(Grant Nos.51906134 and 51436002)。
文摘The gas turbine is the main power equipment for naval ship and special civil ship,while the compressor is one of the core structures of the gas turbine.The existing tip clearance could prevent the compressor blade and casing collision.Therefore,the flow loss in the tip region caused by the tip clearance will degrade the performance of the compressor.To improve the variable clearance characteristics of the high subsonic compressor cascades,the cascades with tip clearances of 1%,2%and 3%chord length are studied through experimental measurements and numerical calculations.The research results prove that the pressure surface tip winglet can cause a significant improvement effect under most working conditions.If the blade tip clearance size is gradually increasing within a reasonable range,the improvement effect becomes more remarkable,and the optimal tip winglet case changes.When tip clearance is 1%chord length,the PTW1.0 case(the width of the pressure surface tip winglet is 1.0 time of the original tip)reduces the flow loss by 3.09%compared with the NTW case(No Tip Winglet).When tip clearance is 2%chord length,the flow loss of PTW1.5 case(the width of the pressure surface tip winglet is 1.5 times of the original tip)is reduced by 3.46%.When tip clearance is 3%chord length,all alternative tip winglets reduce the total pressure loss,and PTW2.0 case(the width of the pressure surface tip winglet is 2.0 times of the original tip)is the best choice,which has a 6.53%degree of improvement.
基金Supported by the Zheng Ge Ru Foundation when Ya-guang Wang was visiting the Institute of Mathematical Sciences in the Chinese University of Hong KongThe work of Wang is also partially supported by the National Natural Science Foundation of China, the
文摘The purpose of this paper is to prove the uniform stability of multidimensional subsonic phase transitions satisfying the viscosity-capillarity criterion in a van der Waals fluid, and further to establish the local existence of phase transition solutions.
文摘An algorithm composed of an iterative modified approximate factorization(MAF(k)) method with Navier-Stokes characteristic boundary conditions(NSCBC) is proposed for solving subsonic viscous flows.A transformation on the matrix equation in MAF(k) is made in order to impose the implicit boundary conditions properly.To be in consistent with the implicit solver for the interior domain,an implicit scheme for NSCBC is formulated.The performance of the developed algorithm is investigated using spatially evolving zero pressure gradient boundary layer over a flat plate and a wall jet mixing with a cross flow over a flat plate with a square hole as the test cases.The numerical results are compared to the existing experimental datasets and a number of general correlations,together with other available numerical solutions,which demonstrate that the developed algorithm possesses promising capacity for simulating the subsonic viscous flows with large CFL number.
