CN114662417B - Thrust density distribution calculation method of Hall thruster - Google Patents
Thrust density distribution calculation method of Hall thruster Download PDFInfo
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Abstract
The thrust density distribution calculation method of the Hall thruster comprises the following steps: step one, building a Hall thruster thrust distribution physical model; step two, obtaining a thrust density distribution expression of the Hall thruster: wherein the total thrust density distribution of the Hall thruster is the sum of thrust density distribution generated by monovalent ions, doubly charged ions and charge-exchanged ions; step three, obtaining motion parameters of each component ion in the beam particles sprayed by the Hall thruster: obtaining plasma flow field parameters after calculation stabilization by adopting a PIC-MCC method, and defining a surface with potential 0 in the flow field as an interface S1 to obtain motion parameter data; step four, obtaining thrust density distribution of each component ion in the beam particles sprayed by the Hall thruster; and fifthly, calculating thrust density distribution of beam particles sprayed by the Hall thruster. The method solves the problem of solving the thrust density distribution characteristic of the Hall thruster, realizes the quantitative calculation of the thrust density distribution characteristic, and provides a basis for the optimization and evaluation of the thrust performance of the Hall thruster.
Description
Technical Field
The invention relates to the technical field of calculation of Hall thrusters, in particular to a calculation method of thrust density distribution of a Hall thruster.
Background
The Hall thruster obtains thrust mainly by jetting high-speed particles, and the beam current comprises: multicomponent particles such as monovalent ions, doubly charged ions, charge-exchanged ions, electrons, neutral atoms, and the like. In the working process, ions generated by ionization in the channel are sprayed out of the channel under the action of an accelerating electric field, and the ions possibly touch the inner wall surface and the outer wall surface of the channel in the accelerating process to change the direction, and meanwhile, the high-speed ions and neutral atoms generate charge exchange collision to generate charge exchange ions; a small amount of non-ionized atoms escape from the channel outlet in a thermal diffusion motion; electrons are attracted by the anode high voltage to travel into the channel and are confined by the magnetic field. The large difference in the spatial density distribution and velocity distribution of the ejected particle streams makes the thrust density of the thruster complex.
Compared with the ion thruster, the Hall thruster gets rid of the limitation of space charge to realize higher thrust density, but the non-uniformity of the output thrust density distribution of the Hall thruster is more prominent due to larger divergence angle of the Hall thruster, and meanwhile, the non-axisymmetry is accompanied, so that the thrust eccentric effect is generated. The small magnitude of the thrust off-axis is sufficient to cause a disturbing moment on the spacecraft, which, if not corrected, can cause the attitude and orbit of the spacecraft to deviate from the predetermined orbit for a long time.
The existing theoretical model is mainly used for modeling and calculating the total thrust of the Hall thruster, and does not consider the characteristic parameter of thrust density distribution of the thruster; therefore, how to quantitatively calculate the thrust density distribution of the hall thruster is a problem to be solved at present.
Disclosure of Invention
The invention aims to overcome the defects in the prior art and provide a method for calculating the thrust density distribution of a Hall thruster. According to the method, the thrust density generated by monovalent ions, double charged ions and charge exchange ions in the beam of the Hall thruster is calculated and analyzed, the thrust density distribution of the Hall thruster is obtained, and a support is provided for the performance optimization of the Hall thruster.
The technical scheme of the invention is as follows: the thrust density distribution calculating method of the Hall thruster comprises the following steps,
step one, building a Hall thruster thrust model
The thrust of the Hall thruster mainly generates thrust through jetting out beam particles, the momentum balance relation between the Hall thruster and the jetting out beam particles in space is met, and according to Newton's third law, the thrust expression generated in the axial direction when the Hall thruster works is as follows:
wherein F is total The unit is N, which is the total thrust;for mass flow of the ejected beam particles, the unit is kg/s,the unit is m/s for the average velocity of the ejected beam particles.
Step two, obtaining a thrust density expression of the Hall thruster
The mass of electrons in the ejected beam particles is far less than that of ions, and the velocity of neutral atoms is far less than that of ions, so that the thrust generated by electrons and atoms is ignored. Namely, the axial thrust of the Hall thruster mainly comes from monovalent ions, double charged ions and charge exchange ions, and the thrust expression is as follows:
wherein,mass flow rates of monovalent ions, doubly charged ions and charge-exchanged ions, respectively, in kg/s; />Respectively are provided withThe average velocity in m/s for monovalent ions, doubly charged ions and charge-exchanged ions.
The thrust density is defined as the axial thrust generated on the unit area, and then the calculation formula for further obtaining the thrust density is as follows:
wherein f 0 Is the total thrust density f of the Hall thruster 1 、f 2 、f 3 The thrust densities produced by the monovalent ions, the doubly charged ions and the charge-exchanged ions, respectively, are all in mN/cm 2 。
Step three, obtaining motion parameters of each component ion in beam particles sprayed by the Hall thruster
Acquiring plasma flow field parameters of beam particles ejected by a Hall thruster, extracting potential distribution in the acquired plasma flow field parameters, defining a surface with potential 0 in the flow field as an interface S1, and respectively acquiring the following data:
statistics of monovalent ion flux information at S1 and acquisition of monovalent ions at different positions at the S1 interfaceThe density distribution, speed distribution, moving direction and axial angle of the parts are respectively marked as +.>
Counting the information of the double charged ion flow on the S1, and obtaining different positions of the double charged ions on the S1 interfaceThe density distribution, speed distribution and the angle between the moving direction and the axial direction are respectively marked as +.>
Statistics of charge-exchanged ions at S1Flow information and obtain the different positions of charge-exchanged ions on the S1 interfaceThe density distribution, speed distribution and the angle between the moving direction and the axial direction are respectively marked as +.>
Step four, obtaining thrust density distribution of each component ion in beam particles sprayed by the Hall thruster
According to formula (1), at the S1 interfaceLocation infinitesimal area->The axial thrust dF generated is expressed as:
wherein m is xe Is ion mass, unit kg; n is ion density in units of individual/m 3 ；The average velocity of the ion flow is expressed as m/s; θ is the angle between the ion movement direction and the axial direction of the Hall thruster, and β is the angle between the infinitesimal area normal and the axial direction of the thruster;
the thrust density is:
namely, the axial thrust density distribution of the Hall thruster is as follows:
the thrust density distribution of the multicomponent ions in the ejected particle stream is further obtained as follows:
step five, calculating thrust density distribution of beam particles sprayed by the Hall thruster
Space within the hall thruster from the interface S1The thrust density distribution calculation expression at the position is:
the thrust density distribution of the hall thruster is calculated.
The invention further adopts the technical scheme that: and the method comprises the steps of obtaining plasma flow field parameters of beam particles sprayed by the Hall thruster, establishing a numerical model of the plasma extraction of the Hall thruster by adopting a PIC-MCC method, and carrying out simulation calculation by combining the working electrical parameters of the Hall thruster to obtain the plasma flow field parameters after calculation stability.
Compared with the prior art, the invention has the following characteristics: according to the invention, the thrust distribution physical model is established to sum the space thrust density distribution of the particles with various components, so that the thrust density distribution of the Hall thruster is obtained, the quantitative calculation of the thrust distribution characteristics of the Hall thruster is realized, and conditions are provided for further optimizing and evaluating the thrust performance of the Hall thruster.
The detailed structure of the present invention is further described below with reference to the accompanying drawings and detailed description.
Drawings
FIG. 1 is a flow chart of a calculation method of the present invention;
FIG. 2 is a graph showing the calculation of the thrust density distribution of monovalent ions in the particles of an ejected beam according to the first embodiment;
FIG. 3 is a graph showing the calculation of thrust density distribution of doubly charged ions in ejected beam particles according to the first embodiment;
FIG. 4 is a graph showing the calculation of thrust density distribution of charge-exchanged ions in ejected beam particles according to the first embodiment;
fig. 5 is a graph showing a thrust density distribution calculation of a hall thruster according to an embodiment.
Detailed Description
In a first embodiment, as shown in fig. 1-5, a method for calculating thrust density distribution of a hall thruster, taking a 200W hall thruster as an example, includes the following steps:
step one, building a Hall thruster thrust model
The hall thruster thrust mainly generates thrust by ejecting beam particles, wherein the ejected beam particles comprise: the momentum balance relation between the Hall thruster and the ejected beam particles in the space is satisfied, and according to Newton's third law, when the Hall thruster operates in space, the thrust satisfies the following formula:
wherein F is total The unit is N, which is the total thrust;for mass flow of the ejected beam particles, the unit is kg/s,the average velocity of beam particles is given in m/s.
Step two, obtaining a thrust density expression of the Hall thruster
Because the sprayed beam particles have different acceleration mechanisms, the density distribution and the speed distribution of each group of different particles are different.
Such as monovalent ions and double chargesIons are mainly concentrated near the central axis of the Hall thruster and are distributed in a spike shape; the charge exchange ion groups are distributed around the outlet of the Hall thruster and are distributed in a scattered manner; electrons are mainly distributed near the plasma bridge between the cathode outlet and the channel; and neutral atoms escape from the outlet of the annular channel, and are dispersed in the space. And the diagnosis result of the beam plasma shows that: the ion current density near the central axis of the Hall thruster is about 2.0mA/cm 2 And a current density of about 0.01mA/cm in the vicinity of the outer diameter 2 The test results verify this non-uniform distribution characteristic. In addition, the results of the beam particle energy measurement show that: the monovalent ion velocity is about 15000-20000 m/s, the doubly charged ion velocity is about 20000-28000 m/s, the charge exchanged ion velocity is about 5000-10000 m/s, and the neutral atom thermal motion velocity is typically about 340-400 m/s. From the above-described test results, it can be known that there is also a significant difference in the velocity of each component particle in the ejected beam particles. Thus, the thrust output by the hall thruster exhibits a significant non-uniform distribution characteristic.
The working medium gas of the hall thruster is generally xenon, and the mass of single atoms or ions is about: 2.6e-25kg and an electron mass of about 9.1e-31kg, the electron mass being much smaller than the ion and atomic mass; at the same time, the neutral atom speed is far smaller than the ion speed, so that the thrust generated by electrons and neutral atoms is ignored, and the beam multicomponent particles for generating the thrust mainly comprise: monovalent ions, doubly charged ions, charge-exchanged ions, thrust expressions are as follows:
wherein,mass flow rates of monovalent ions, doubly charged ions and charge-exchanged ions respectively, wherein the unit is kg/s; />Respectively monovalent ionsAverage velocity of the doubly charged, charge-exchanged ions in m/s.
And further deriving a thrust density formula as follows:
wherein f 0 For thrust density distribution of Hall thruster, f 1 、f 2 、f 3 Thrust density distribution generated by monovalent ions, double charged ions and charge exchange ions respectively, and units are mN/cm 2 。
Step three, obtaining motion parameters of each component ion in beam particles sprayed by the Hall thruster
Establishing a Hall thruster plasma numerical model by adopting a PIC-MCC method, and respectively carrying out particle tracking on monovalent ions, double charged ions and charge exchange ions; and (3) carrying out simulation calculation by combining the working electrical parameters of the Hall thruster to obtain the plasma flow field parameters after stable calculation.
On this basis, the spatial potential distribution is extracted and the interface S1 is defined as the surface with potential 0 in the flow field. The PIC-MCC method was used to model a 200W hall thruster plasma number, enabling the existence of an interface S1 with a potential of 0 at a position about 4.7 channel length (z/l=4.7) from the channel outlet. Because the potential of the anode of the hall thruster is high, the typical value is 300V, and the potential is gradually reduced along the axial direction from the outlet of the discharge channel, a higher potential distribution still exists in the plume near-field region, which causes a stronger accelerating electric field to exist in the plume near-field region, so that the ejected beam particles are continuously accelerated, that is, interaction still exists between the ejected high-speed particle flow and the hall thruster body, and a larger error exists in calculating the thrust in the region by utilizing the velocity of the ejected beam particles. In the model, the zero-potential interface in the plume near-field region of the Hall thruster is defined as the interface S1 for calculation, so that the sprayed beam particles on the interface and the Hall thruster body are thoroughly separated, the interaction between the particles is avoided, and the accuracy of a calculation result can be ensured.
The following data were obtained:
statistics of monovalent ion information at S1, further obtaining monovalent ion in spaceThe density distribution, velocity distribution and the angle between the direction of movement and the axial direction at the location are respectively marked +.>
Counting the information of the double charged ions on S1 to further obtain the space of the double charged ionsThe density distribution, velocity distribution and the angle between the direction of movement and the axial direction at the location are respectively marked +.>
Counting charge exchange ion information at S1 to further obtain space of charge exchange ionsThe density distribution, velocity distribution and the angle between the direction of movement and the axial direction at the location are respectively marked +.>
Step four, acquiring thrust density distribution interfaces S1 of all component ions in beam particles sprayed by the Hall thrusterLocation infinitesimal area->The axial thrust dF generated is expressed as:
wherein m is xe Is ion mass, unit kg; n is ion density in units of individual/m 3 ；The average velocity of the ion flow is expressed as m/s; θ is the angle between the ion movement direction and the axial direction of the Hall thruster, and β is the angle between the infinitesimal area normal and the axial direction of the thruster;
the thrust density is:
namely, the axial thrust density distribution of the Hall thruster is as follows:
the thrust density distribution of the multicomponent particles in the ejected particle stream is further obtained as follows:
figures 2-4 show calculated thrust density profiles for monovalent ions, doubly charged ions, and charge-exchanged ions, respectively, in an ejected beam particle.
Step five, calculating thrust density distribution of beam particles sprayed by the Hall thruster
Space within the hall thruster from the interface S1The thrust density distribution calculation expression at the position is:
from this, the thrust density distribution of the hall thruster was calculated, and fig. 5 shows a graph of the calculation of the thrust density distribution of the particles of the ejected beam of the 200W hall thruster.
The calculated thrust density distribution of different positions of the Hall thruster is applied to performance evaluation and optimization when the actual Hall thruster operates, so that the space orbit is ensured to be maintained at the correct position, and deviation is corrected in time, and the method has very important influence on control of the spacecraft.
Claims (2)
1. The thrust density distribution calculation method of the Hall thruster is characterized by comprising the following steps of: comprises the following steps of the method,
step one, building a Hall thruster thrust model
The thrust of the Hall thruster mainly generates thrust through jetting out beam particles, the momentum balance relation between the Hall thruster and the jetting out beam particles in space is met, and according to Newton's third law, the thrust expression generated in the axial direction when the Hall thruster works is as follows:
wherein F is total The unit is N, which is the total thrust;for the mass flow of the ejected beam particles, the unit is kg/s, < >>The unit is m/s for the average speed of the ejected beam particles;
step two, obtaining a thrust density expression of the Hall thruster
The mass of electrons in the ejected beam particles is far smaller than that of ions, the speed of neutral atoms is far smaller than that of the ions, and the thrust generated by electrons and atoms is ignored; namely, the axial thrust of the Hall thruster mainly comes from monovalent ions, double charged ions and charge exchange ions, and the thrust expression is as follows:
wherein,mass flow rates of monovalent ions, doubly charged ions and charge-exchanged ions, respectively, in kg/s; />Average velocities of monovalent ions, doubly charged ions, and charge-exchanged ions, respectively, in m/s;
the thrust density is defined as the axial thrust generated on the unit area, and then the calculation formula for further obtaining the thrust density is as follows:
wherein f 0 Is the total thrust density f of the Hall thruster 1 、f 2 、f 3 The thrust densities produced by the monovalent ions, the doubly charged ions and the charge-exchanged ions, respectively, are all in mN/cm 2 ；
Step three, obtaining motion parameters of each component ion in beam particles sprayed by the Hall thruster
Acquiring plasma flow field parameters of beam particles ejected by a Hall thruster, extracting potential distribution in the acquired plasma flow field parameters, defining a surface with potential 0 in the flow field as an interface S1, and respectively acquiring the following data:
statistics of monovalent ion flux information at S1 and acquisition of monovalent ions at different positions at the S1 interfaceThe density distribution, speed distribution, moving direction and axial included angle of the position are dividedLet it be->
Counting the information of the double charged ion flow on the S1, and obtaining different positions of the double charged ions on the S1 interfaceThe density distribution, speed distribution and the angle between the moving direction and the axial direction are respectively marked as +.>
Counting charge exchange ion flow information at S1 and obtaining different positions of charge exchange ions at S1 interfaceThe density distribution, speed distribution and the angle between the moving direction and the axial direction are respectively marked as +.>
Step four, obtaining thrust density distribution of each component ion in beam particles sprayed by the Hall thruster
According to formula (1), at the S1 interfaceLocation infinitesimal area->The axial thrust dF generated is expressed as:
wherein m is xe Is ion mass, unit kg; n is ion density in units of individual/m 3 ；The average velocity of the ion flow is expressed as m/s; θ is the angle between the ion movement direction and the axial direction of the Hall thruster, and β is the angle between the infinitesimal area normal and the axial direction of the thruster;
the thrust density is:
namely, the axial thrust density distribution of the Hall thruster is as follows:
the thrust density distribution of the multicomponent particles in the ejected particle stream is further obtained as follows:
step five, calculating thrust density distribution of beam particles sprayed by the Hall thruster
Space within the hall thruster from the interface S1The thrust density distribution calculation expression at the position is:
the thrust density distribution of the hall thruster is calculated.
2. The method for calculating the thrust density distribution of the hall thruster according to claim 1, wherein: and the method comprises the steps of obtaining plasma flow field parameters of beam particles sprayed by the Hall thruster, establishing a numerical model of the plasma extraction of the Hall thruster by adopting a PIC-MCC method, and carrying out simulation calculation by combining the working electrical parameters of the Hall thruster to obtain the plasma flow field parameters after calculation stability.
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| CN106772543A (en) * | 2016-12-07 | 2017-05-31 | 哈尔滨工业大学 | Hall thruster plume divergence angle measurement modification method |
| CN113465494A (en) * | 2021-06-29 | 2021-10-01 | 哈尔滨工业大学 | Thrust vector eccentricity calculation method for Hall thruster |
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| CN104061137A (en) * | 2014-07-11 | 2014-09-24 | 哈尔滨工业大学 | Method for correcting on-rail flight hall thruster thrust parameters according to ground experiment parameters |
| CN106772543A (en) * | 2016-12-07 | 2017-05-31 | 哈尔滨工业大学 | Hall thruster plume divergence angle measurement modification method |
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