This article addresses the design of the trajectory transferring from Earth to Halo orbit, and proposes a timing closed-loop strategy of correction maneuver during the transfer in the frame of circular restricted thre...This article addresses the design of the trajectory transferring from Earth to Halo orbit, and proposes a timing closed-loop strategy of correction maneuver during the transfer in the frame of circular restricted three body problem （CR3BP）. The relation between the Floquet multipliers and the magnitudes of Halo orbit is established, so that the suitable magnitude for the aerospace mission is chosen in terms of the stability of Halo orbit. The stable manifold is investigated from the Poincar6 mapping defined which is different from the previous researches, and six types of single-impulse transfer trajectories are attained from the geometry of the invariant manifolds. Based on one of the trajectories of indirect transfer which are ignored in the most of literatures, the stochastic control theory for imperfect information of the discrete linear stochastic system is applied to design the trajectory correction maneuver. The statistical dispersion analysis is performed by Monte-Carlo simulation,展开更多
Compared with the one-dimensional trajectory correction technology which adjusts longitudinal range, not only does the two-dimensional trajectory correction technology adjust the force in velocity direction, but also ...Compared with the one-dimensional trajectory correction technology which adjusts longitudinal range, not only does the two-dimensional trajectory correction technology adjust the force in velocity direction, but also need to modulate the lateral force or trajectory (perpendicular to the vertical plane of fire direction). Therefore, the structure of control cabin of two-dimensional trajectory correction projectile (TDTCP) is more complicated than that of one-dimensional trajectory correction projectile (ODTCP). To simplify the structure of control cabin of TDTCP and reduce the cost, a scheme of adding a damping disk to the control cabin of ODTCP has been developed recently. The damping disk is unfolded at the right moment during its flight to change the ballistic drift of spin stabilized projectile. For this technical scheme of TDTCP, a fast and accurate impact point prediction method based on extended Kalman filter is presented. An approximate formula for predicting the ballistic drift and trajectory correction quantity is deduced. And the lateral correction capability for different fire angles and its influencing factors are analyzed. All the work is valuable for further research.展开更多
This paper presents an actuator used for the trajectory correction fuze,which is subject to high impact loadings during launch.A simulation method is carried out to obtain the peak-peak stress value of each component,...This paper presents an actuator used for the trajectory correction fuze,which is subject to high impact loadings during launch.A simulation method is carried out to obtain the peak-peak stress value of each component,from which the ball bearings are possible failures according to the results.Subsequently,three schemes against impact loadings,full-element deep groove ball bearing and integrated raceway,needle roller thrust bearing assembly,and gaskets are utilized for redesigning the actuator to effectively reduce the bearings’stress.However,multi-objectives optimization still needs to be conducted for the gaskets to decrease the stress value further to the yield stress.Four gasket’s structure parameters and three bearings’peak-peak stress are served as the four optimization variables and three objectives,respectively.Optimized Latin hypercube design is used for generating sample points,and Kriging model selected according to estimation result can establish the relationship between the variables and objectives,representing the simulation which is time-consuming.Accordingly,two optimization algorithms work out the Pareto solutions,from which the best solutions are selected,and verified by the simulation to determine the gaskets optimized structure parameters.It can be concluded that the simulation and optimization method based on these components is effective and efficient.展开更多
Aiming at the yaw problem caused by inertial navigation system errors accumulation during the navigation of an intelligent aircraft,a three-dimensional trajectory planning method based on the particle swarm optimizati...Aiming at the yaw problem caused by inertial navigation system errors accumulation during the navigation of an intelligent aircraft,a three-dimensional trajectory planning method based on the particle swarm optimization-A star(PSO-A*)algorithm is designed.Firstly,an environment model for aircraft error correction is established,and the trajectory is discretized to calculate the positioning error.Next,the positioning error is corrected at many preset trajectory points.The shortest trajectory and the fewest correction times are regarded as optimization goals to improve the heuristic function of A star(A*)algorithm.Finally,the index weights are continuously optimized by the particle swarm optimization algorithm.The optimal trajectory is found by the A*algorithm under the current evaluation index,so the ideal trajectory is planned.The experimental results show that the PSO-A*algorithm can quickly search for ideal trajectories in different environment models,indicating that the algorithm has certain feasibility and adaptability,and verifies the rationality of the proposed trajectory planning model.The PSO-A*algorithm has better convergence accuracy than the A*algorithm,and the search efficiency is significantly better than the grid search A star(GS-A*)algorithm.The PSO-A*algorithm proposed in this paper has certain engineering application value.The researchers will study the real-time and systematic nature of the algorithm.展开更多
The two-dimensional trajectory correction needs to adjust not only the force in velocity direction,but also the lateral force or lateral trajectory (normal to the perpendicular plane of fire direction) . Therefore,its...The two-dimensional trajectory correction needs to adjust not only the force in velocity direction,but also the lateral force or lateral trajectory (normal to the perpendicular plane of fire direction) . Therefore,its structure of control cabin is more complicated than that of one-dimensional trajectory correction projectiles (ODTCP). In order to simplify the structure and reduce the cost,a scheme of adding a damping disc to the control cabin of ODTCP has been developed recently. The damping disc will unfold at the right moment during its flight to change the ballistic drift of rotary projectiles. Aimed at this technical scheme,a mathematical model of two-dimensional trajectory corrections was discussed according to the theory of exterior ballistics. An approximate formula for predicting the ballistic drift and trajectory correction was deduced. The capability of lateral trajectory correction and the flight stability of TDTCP were also analyzed. All the work is valuable for further research.展开更多
The optimization method of the canard trajectory correction fuze's controlled trajectory phase is researched by using the aerodynamics of aerocraft and the optimal control theory, the trajectory parameters of the ...The optimization method of the canard trajectory correction fuze's controlled trajectory phase is researched by using the aerodynamics of aerocraft and the optimal control theory, the trajectory parameters of the controlled trajectory phase based on the least energy cost are determined. On the basis of determining the control starting point and the target point, the optimal trajectory and the variation rule of the normal overload with the least energy cost are provided, when there is no time restriction in the simulation process. The results provide a theoretical basis for the structure design of the canard mechanism.展开更多
The research on multiple launch rocket system(MLRS)is now even more demanding in terms of reducing the time for dynamic calculations and improving the firing accuracy,keeping the cost as low as possible.This study emp...The research on multiple launch rocket system(MLRS)is now even more demanding in terms of reducing the time for dynamic calculations and improving the firing accuracy,keeping the cost as low as possible.This study employs multibody system transfer matrix method(MSTMM),to model MLRS.The use of this method provides effective and fast calculations of dynamic characteristics,initial disturbance and firing accuracy.Further,a new method of rapid extrapolation of ballistic trajectory of MLRS is proposed by using the position information of radar tests.That extrapolation point is then simulated and compared with the actual results,which demonstrates a good agreement.The closed?loop fire correction method is used to improve the firing accuracy of MLRS at low cost.展开更多
The longitudinal dispersion of the projectile in shooting tests of two-dimensional trajectory corrections fused with fixed canards is extremely large that it sometimes exceeds the correction ability of the correction ...The longitudinal dispersion of the projectile in shooting tests of two-dimensional trajectory corrections fused with fixed canards is extremely large that it sometimes exceeds the correction ability of the correction fuse actuator.The impact point easily deviates from the target,and thus the correction result cannot be readily evaluated.However,the cost of shooting tests is considerably high to conduct many tests for data collection.To address this issue,this study proposes an aiming method for shooting tests based on small sample size.The proposed method uses the Bootstrap method to expand the test data;repeatedly iterates and corrects the position of the simulated theoretical impact points through an improved compatibility test method;and dynamically adjusts the weight of the prior distribution of simulation results based on Kullback-Leibler divergence,which to some extent avoids the real data being"submerged"by the simulation data and achieves the fusion Bayesian estimation of the dispersion center.The experimental results show that when the simulation accuracy is sufficiently high,the proposed method yields a smaller mean-square deviation in estimating the dispersion center and higher shooting accuracy than those of the three comparison methods,which is more conducive to reflecting the effect of the control algorithm and facilitating test personnel to iterate their proposed structures and algorithms.;in addition,this study provides a knowledge base for further comprehensive studies in the future.展开更多
In conventional technical trajectory correction schemes,continuous attitude adjusting mechanisms, such as canards, are inferior in terms of response time and efficiency of executing instructions. Discontinuous attitud...In conventional technical trajectory correction schemes,continuous attitude adjusting mechanisms, such as canards, are inferior in terms of response time and efficiency of executing instructions. Discontinuous attitude adjusting mechanisms, such as the lateral pulse jet, have complex impact on the airflow layer of the projectile surface caused by the thrust vector jet flow. An improved two-dimensional trajectory correction mechanism is designed based on the principle of firing mass blocks by a tailor-made propellant. The mechanical properties of the thrust force(namely the correction force) is analyzed. The trajectory correction model is established to analyze the effects of correction starting moment and correction phase angle of a thrust force on the projectile's trajectory. According to the trajectory correction scheme, an improved genetic algorithm is employed to this work. The scheme is tested in the simulation. The results show that the correction scheme is effective to reduce target dispersion and increase the precision of the impact point.展开更多
A prototype of impulse thruster for radial thrust trajectory correction munitions is designed. It adopts semiconductor bridge (SCB) as ignition element,Ti/KClO4 (TK) as ignition charge and ammonium perchlorate/alumini...A prototype of impulse thruster for radial thrust trajectory correction munitions is designed. It adopts semiconductor bridge (SCB) as ignition element,Ti/KClO4 (TK) as ignition charge and ammonium perchlorate/aluminium (NA) or potassium picate/RDX (KR) as main charge. A thrust test device of impulse thruster is also designed. The output performance of the impulse thruster prototype is tested by the device. The tested results show that it can meet the safety requirements of 1A1W/5 min no-fire level and produce 0.2-0.6 N·s thrust impulse within 3ms of action time under certain test conditions; the corresponding ignition delay time is less than 0.5 ms.展开更多
The system composition, the operational principle of terminal correction mortar projectiles （TCMP） and the concept planning design of TCMP are researched in this paper. An overall design and aerodynamic configuratio...The system composition, the operational principle of terminal correction mortar projectiles （TCMP） and the concept planning design of TCMP are researched in this paper. An overall design and aerodynamic configuration layout for TCMP are made in this paper, and its aerodynamic coefficients are calculated by using computational fluid dynamics （CFD） software. Test results of TCMP simulated ballistic projectiles indicate the designed TCMP can satisfy the interior ballistic demand and has a fine flight stability. The drag coefficients identified from the radar velocity-time data are in accord with the CFD computed results. According to the exposure frequency of the ground laser designator, a four-quadrant impulse correction scheme and a high exposure frequency impulse correction scheme are brought. The latter can calculate the target azimuth angle by counting the times of the facula passing through one quadrant. Simulation results also show that the guidance precision of the velocity pursuit is higher than that of the body pursuit, and the detector axis is less circuitous. Researches on the typical trajectory indicate that the terminal impulse correction can improve the hit precision of TCMP remarkably.展开更多
The branching corrected surface hopping(BCSH)has been demonstrated as a robust approach to improve the performance of the traditional fewest switches surface hopping(FSSH)for nonadiabatic dynamics simulations of stand...The branching corrected surface hopping(BCSH)has been demonstrated as a robust approach to improve the performance of the traditional fewest switches surface hopping(FSSH)for nonadiabatic dynamics simulations of standard scattering problems[J.Chem.Phys.150,164101(2019)].Here,we study how reliable populations of both adiabatic and diabatic states can be interpreted from BCSH trajectories.Using exact quantum solutions and FSSH results as references,we investigate a series of one-dimensional two-level scattering models and illustrate that excellent timedependent populations can be obtained by BCSH.Especially,we show that different trajectory analysis strategies produce noticeable differences in different representations.Namely,the method based on active states performs better to get populations of adiabatic states,while the method based on wavefunctions produces more reliable results for populations of diabatic states.展开更多
In the one-dimensional renewing warranty period,the quality of the spares for product is likely to be improved during the warranty period.Therefore,upgrading maintenance becomes more and more common.Then the manufactu...In the one-dimensional renewing warranty period,the quality of the spares for product is likely to be improved during the warranty period.Therefore,upgrading maintenance becomes more and more common.Then the manufacturers(customers) may have to decide whether or not to provide(buy) the warranty considering upgrading maintenance.This paper presents a mathematical model considering upgrading maintenance for products with multiple failure modes.Upgrading maintenance is taken into account with the assumption that the warranted item is upgraded one time during the warranty cycle.The upgrading maintenance is carried out,when the corrective maintenance is taken place.After upgrading maintenance,the high-quality spares are used to replace the failed item.In the numerical example,the results of the models are calculated.Monte Carlo simulation results are compared with the analytical results to demonstrate the correctness and efficiency of the proposed models considering upgrading maintenance.展开更多
A simple one-dimensional planar model for ejection was set up based on experiments.And numerical simulation was performed on this model with particle trajectory model method.An Eulerian finite volume method was conduc...A simple one-dimensional planar model for ejection was set up based on experiments.And numerical simulation was performed on this model with particle trajectory model method.An Eulerian finite volume method was conducted to resolve gas field.And Lagrangian method was imposed to track each particle.The interaction between gas and particles was responded as source terms in governing equations which were induced by forces.The effects of total spraying mass,particle size and other factors on the mixture of particles and gas were investigated.The spatial distributions of particle mass and velocity at different time were presented.The result shows that the numerical results are qualitatively consistent to those of experiments.展开更多
基金National Natural Science Foundation of China (10702003)Innovation Foundation of Beijing University of Aeronautics and Astronautics for Ph.D. Graduates
文摘This article addresses the design of the trajectory transferring from Earth to Halo orbit, and proposes a timing closed-loop strategy of correction maneuver during the transfer in the frame of circular restricted three body problem （CR3BP）. The relation between the Floquet multipliers and the magnitudes of Halo orbit is established, so that the suitable magnitude for the aerospace mission is chosen in terms of the stability of Halo orbit. The stable manifold is investigated from the Poincar6 mapping defined which is different from the previous researches, and six types of single-impulse transfer trajectories are attained from the geometry of the invariant manifolds. Based on one of the trajectories of indirect transfer which are ignored in the most of literatures, the stochastic control theory for imperfect information of the discrete linear stochastic system is applied to design the trajectory correction maneuver. The statistical dispersion analysis is performed by Monte-Carlo simulation,
文摘Compared with the one-dimensional trajectory correction technology which adjusts longitudinal range, not only does the two-dimensional trajectory correction technology adjust the force in velocity direction, but also need to modulate the lateral force or trajectory (perpendicular to the vertical plane of fire direction). Therefore, the structure of control cabin of two-dimensional trajectory correction projectile (TDTCP) is more complicated than that of one-dimensional trajectory correction projectile (ODTCP). To simplify the structure of control cabin of TDTCP and reduce the cost, a scheme of adding a damping disk to the control cabin of ODTCP has been developed recently. The damping disk is unfolded at the right moment during its flight to change the ballistic drift of spin stabilized projectile. For this technical scheme of TDTCP, a fast and accurate impact point prediction method based on extended Kalman filter is presented. An approximate formula for predicting the ballistic drift and trajectory correction quantity is deduced. And the lateral correction capability for different fire angles and its influencing factors are analyzed. All the work is valuable for further research.
基金The authors would like to acknowledge National Defense Pre-Research Foundation of China(Grant No.41419030102)to provide fund for conducting experiments.
文摘This paper presents an actuator used for the trajectory correction fuze,which is subject to high impact loadings during launch.A simulation method is carried out to obtain the peak-peak stress value of each component,from which the ball bearings are possible failures according to the results.Subsequently,three schemes against impact loadings,full-element deep groove ball bearing and integrated raceway,needle roller thrust bearing assembly,and gaskets are utilized for redesigning the actuator to effectively reduce the bearings’stress.However,multi-objectives optimization still needs to be conducted for the gaskets to decrease the stress value further to the yield stress.Four gasket’s structure parameters and three bearings’peak-peak stress are served as the four optimization variables and three objectives,respectively.Optimized Latin hypercube design is used for generating sample points,and Kriging model selected according to estimation result can establish the relationship between the variables and objectives,representing the simulation which is time-consuming.Accordingly,two optimization algorithms work out the Pareto solutions,from which the best solutions are selected,and verified by the simulation to determine the gaskets optimized structure parameters.It can be concluded that the simulation and optimization method based on these components is effective and efficient.
文摘Aiming at the yaw problem caused by inertial navigation system errors accumulation during the navigation of an intelligent aircraft,a three-dimensional trajectory planning method based on the particle swarm optimization-A star(PSO-A*)algorithm is designed.Firstly,an environment model for aircraft error correction is established,and the trajectory is discretized to calculate the positioning error.Next,the positioning error is corrected at many preset trajectory points.The shortest trajectory and the fewest correction times are regarded as optimization goals to improve the heuristic function of A star(A*)algorithm.Finally,the index weights are continuously optimized by the particle swarm optimization algorithm.The optimal trajectory is found by the A*algorithm under the current evaluation index,so the ideal trajectory is planned.The experimental results show that the PSO-A*algorithm can quickly search for ideal trajectories in different environment models,indicating that the algorithm has certain feasibility and adaptability,and verifies the rationality of the proposed trajectory planning model.The PSO-A*algorithm has better convergence accuracy than the A*algorithm,and the search efficiency is significantly better than the grid search A star(GS-A*)algorithm.The PSO-A*algorithm proposed in this paper has certain engineering application value.The researchers will study the real-time and systematic nature of the algorithm.
文摘The two-dimensional trajectory correction needs to adjust not only the force in velocity direction,but also the lateral force or lateral trajectory (normal to the perpendicular plane of fire direction) . Therefore,its structure of control cabin is more complicated than that of one-dimensional trajectory correction projectiles (ODTCP). In order to simplify the structure and reduce the cost,a scheme of adding a damping disc to the control cabin of ODTCP has been developed recently. The damping disc will unfold at the right moment during its flight to change the ballistic drift of rotary projectiles. Aimed at this technical scheme,a mathematical model of two-dimensional trajectory corrections was discussed according to the theory of exterior ballistics. An approximate formula for predicting the ballistic drift and trajectory correction was deduced. The capability of lateral trajectory correction and the flight stability of TDTCP were also analyzed. All the work is valuable for further research.
文摘The optimization method of the canard trajectory correction fuze's controlled trajectory phase is researched by using the aerodynamics of aerocraft and the optimal control theory, the trajectory parameters of the controlled trajectory phase based on the least energy cost are determined. On the basis of determining the control starting point and the target point, the optimal trajectory and the variation rule of the normal overload with the least energy cost are provided, when there is no time restriction in the simulation process. The results provide a theoretical basis for the structure design of the canard mechanism.
基金supported by the Na- tional Natural Science Foundation of China (No. 11472135)the Science Challenge Project (No. JCKY2016212A506- 0104)
文摘The research on multiple launch rocket system(MLRS)is now even more demanding in terms of reducing the time for dynamic calculations and improving the firing accuracy,keeping the cost as low as possible.This study employs multibody system transfer matrix method(MSTMM),to model MLRS.The use of this method provides effective and fast calculations of dynamic characteristics,initial disturbance and firing accuracy.Further,a new method of rapid extrapolation of ballistic trajectory of MLRS is proposed by using the position information of radar tests.That extrapolation point is then simulated and compared with the actual results,which demonstrates a good agreement.The closed?loop fire correction method is used to improve the firing accuracy of MLRS at low cost.
基金the National Natural Science Foundation of China(Grant No.61973033)Preliminary Research of Equipment(Grant No.9090102010305)for funding the experiments。
文摘The longitudinal dispersion of the projectile in shooting tests of two-dimensional trajectory corrections fused with fixed canards is extremely large that it sometimes exceeds the correction ability of the correction fuse actuator.The impact point easily deviates from the target,and thus the correction result cannot be readily evaluated.However,the cost of shooting tests is considerably high to conduct many tests for data collection.To address this issue,this study proposes an aiming method for shooting tests based on small sample size.The proposed method uses the Bootstrap method to expand the test data;repeatedly iterates and corrects the position of the simulated theoretical impact points through an improved compatibility test method;and dynamically adjusts the weight of the prior distribution of simulation results based on Kullback-Leibler divergence,which to some extent avoids the real data being"submerged"by the simulation data and achieves the fusion Bayesian estimation of the dispersion center.The experimental results show that when the simulation accuracy is sufficiently high,the proposed method yields a smaller mean-square deviation in estimating the dispersion center and higher shooting accuracy than those of the three comparison methods,which is more conducive to reflecting the effect of the control algorithm and facilitating test personnel to iterate their proposed structures and algorithms.;in addition,this study provides a knowledge base for further comprehensive studies in the future.
基金supported by the National Natural Science Foundation of China(11372142)
文摘In conventional technical trajectory correction schemes,continuous attitude adjusting mechanisms, such as canards, are inferior in terms of response time and efficiency of executing instructions. Discontinuous attitude adjusting mechanisms, such as the lateral pulse jet, have complex impact on the airflow layer of the projectile surface caused by the thrust vector jet flow. An improved two-dimensional trajectory correction mechanism is designed based on the principle of firing mass blocks by a tailor-made propellant. The mechanical properties of the thrust force(namely the correction force) is analyzed. The trajectory correction model is established to analyze the effects of correction starting moment and correction phase angle of a thrust force on the projectile's trajectory. According to the trajectory correction scheme, an improved genetic algorithm is employed to this work. The scheme is tested in the simulation. The results show that the correction scheme is effective to reduce target dispersion and increase the precision of the impact point.
基金the Ministerial Level Advanced Research Foundation (51305080302)
文摘A prototype of impulse thruster for radial thrust trajectory correction munitions is designed. It adopts semiconductor bridge (SCB) as ignition element,Ti/KClO4 (TK) as ignition charge and ammonium perchlorate/aluminium (NA) or potassium picate/RDX (KR) as main charge. A thrust test device of impulse thruster is also designed. The output performance of the impulse thruster prototype is tested by the device. The tested results show that it can meet the safety requirements of 1A1W/5 min no-fire level and produce 0.2-0.6 N·s thrust impulse within 3ms of action time under certain test conditions; the corresponding ignition delay time is less than 0.5 ms.
基金the Ministerial Level Advanced Research Foundation (40406030101)
文摘The system composition, the operational principle of terminal correction mortar projectiles （TCMP） and the concept planning design of TCMP are researched in this paper. An overall design and aerodynamic configuration layout for TCMP are made in this paper, and its aerodynamic coefficients are calculated by using computational fluid dynamics （CFD） software. Test results of TCMP simulated ballistic projectiles indicate the designed TCMP can satisfy the interior ballistic demand and has a fine flight stability. The drag coefficients identified from the radar velocity-time data are in accord with the CFD computed results. According to the exposure frequency of the ground laser designator, a four-quadrant impulse correction scheme and a high exposure frequency impulse correction scheme are brought. The latter can calculate the target azimuth angle by counting the times of the facula passing through one quadrant. Simulation results also show that the guidance precision of the velocity pursuit is higher than that of the body pursuit, and the detector axis is less circuitous. Researches on the typical trajectory indicate that the terminal impulse correction can improve the hit precision of TCMP remarkably.
基金supported by the National Natural Science Foundation of China(No.21922305 and No.21873080)。
文摘The branching corrected surface hopping(BCSH)has been demonstrated as a robust approach to improve the performance of the traditional fewest switches surface hopping(FSSH)for nonadiabatic dynamics simulations of standard scattering problems[J.Chem.Phys.150,164101(2019)].Here,we study how reliable populations of both adiabatic and diabatic states can be interpreted from BCSH trajectories.Using exact quantum solutions and FSSH results as references,we investigate a series of one-dimensional two-level scattering models and illustrate that excellent timedependent populations can be obtained by BCSH.Especially,we show that different trajectory analysis strategies produce noticeable differences in different representations.Namely,the method based on active states performs better to get populations of adiabatic states,while the method based on wavefunctions produces more reliable results for populations of diabatic states.
基金the National Society Science Foundation of China(No.14GJ003-135)the National Natural Science Foundation of China(No.71401173)
文摘In the one-dimensional renewing warranty period,the quality of the spares for product is likely to be improved during the warranty period.Therefore,upgrading maintenance becomes more and more common.Then the manufacturers(customers) may have to decide whether or not to provide(buy) the warranty considering upgrading maintenance.This paper presents a mathematical model considering upgrading maintenance for products with multiple failure modes.Upgrading maintenance is taken into account with the assumption that the warranted item is upgraded one time during the warranty cycle.The upgrading maintenance is carried out,when the corrective maintenance is taken place.After upgrading maintenance,the high-quality spares are used to replace the failed item.In the numerical example,the results of the models are calculated.Monte Carlo simulation results are compared with the analytical results to demonstrate the correctness and efficiency of the proposed models considering upgrading maintenance.
基金Project(10672151) supported by the National Natural Science Foundation of China
文摘A simple one-dimensional planar model for ejection was set up based on experiments.And numerical simulation was performed on this model with particle trajectory model method.An Eulerian finite volume method was conducted to resolve gas field.And Lagrangian method was imposed to track each particle.The interaction between gas and particles was responded as source terms in governing equations which were induced by forces.The effects of total spraying mass,particle size and other factors on the mixture of particles and gas were investigated.The spatial distributions of particle mass and velocity at different time were presented.The result shows that the numerical results are qualitatively consistent to those of experiments.
