CN115640696A - On-orbit prediction method and prediction system for total impulse margin of Hall thruster - Google Patents
On-orbit prediction method and prediction system for total impulse margin of Hall thruster Download PDFInfo
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Abstract
The invention relates to an on-orbit prediction method and a prediction system for the total impulse allowance of a Hall thruster, wherein the radial component of a magnetic field under excitation current is given according to the Hall drift current density and the fixed design parameters of the thruster, and the on-orbit thrust of the Hall thruster at each moment in a first time period is calculated by using an on-orbit thrust calculation model to obtain a plurality of on-orbit thrust values; calculating a time-averaged thrust value of a first time period; calculating a first calibration value of the propellant allowance in the gas storage tank at the first moment, calculating a second calibration value at the second moment and calculating the time-average flow rate of the first time period according to the capacity of the gas storage tank and the first density at the first moment; and finally, calculating the total impulse allowance predicted value at the second moment according to the time-averaged thrust value, the second calibration value and the time-averaged flow. The method can predict the predicted value of the total impulse allowance of the Hall thruster at the target moment, provides a reference standard for evaluating the residual service life of the Hall thruster, and is beneficial to further development and application of the Hall thruster.
Description
Technical Field
The invention relates to the field of Hall thruster on-orbit performance evaluation, in particular to an on-orbit prediction method and a prediction system for Hall thruster total impulse allowance.
Background
The Hall thruster is a function conversion device for providing kinetic energy for the propellant through the combined action of an electric field and a magnetic field. Is one of the most used electric thrusters in space propulsion. The further development and application of the Hall thruster greatly depend on the on-orbit performance monitoring of the thruster, the total impulse is used as an important standard for measuring the completion of a planning task of a Hall thruster service space platform, and the prediction of the residual quantity is the premise for grasping the residual service life of the Hall thruster. Therefore, the on-orbit prediction method of the total impulse margin is one of the important points to be researched by the hall thruster.
Disclosure of Invention
The invention aims to provide an on-orbit prediction method and a prediction system for the total impulse allowance of a Hall thruster, which can predict the predicted value of the total impulse allowance of the Hall thruster at a target moment, provide a reference standard for the evaluation of the residual service life of the Hall thruster and are beneficial to the further development and application of the Hall thruster.
In order to achieve the purpose, the invention provides the following scheme:
the invention provides an on-orbit prediction method for the total impulse allowance of a Hall thruster, which comprises the following steps of:
according to the Hall drift current density and the fixed design parameters of the thruster, the radial component of a magnetic field under excitation current is given, and the on-orbit thrust of the Hall thruster at each moment in the first time period is calculated by using an on-orbit thrust calculation model to obtain a plurality of on-orbit thrust values; the on-orbit thrust calculation model is used for representing the relation among Hall drift current density, radial magnetic field intensity and on-orbit thrust; the Hall drift current density is calculated by utilizing a static magnetic field inversion method according to the magnetic field intensity; the magnetic field intensity is the magnetic field intensity induced by Hall drift current in a discharge channel of the Hall thruster in the discharge process, and the magnetic field intensity is captured by a magnetic sensor array; the first time interval is an interval between a first time and a second time;
calculating the time-averaged thrust value of the first time period according to the on-orbit thrust values;
calculating a first calibration value of the propellant allowance in the air storage tank at the first moment according to the capacity of the air storage tank and the first density at the first moment; the first density is obtained by calculation according to a first temperature remote measurement value, a first pressure remote measurement value and a relation curve, wherein the relation curve is a relation curve between xenon density and temperature and pressure; the first temperature remote measuring value and the first pressure remote measuring value are measured by a remote measuring system; the air storage tank is an air storage tank of the Hall thruster;
calculating a second calibration value of the propellant allowance in the air storage tank at a second moment according to the capacity of the air storage tank and a second density at the second moment;
calculating the time-average flow of a first time period according to the first calibration value and the second calibration value;
and calculating a total impulse allowance predicted value at a second moment according to the time-averaged thrust value, the second calibration value and the time-averaged flow.
Optionally, before the radial component of the magnetic field under the excitation current is given according to the hall drift current density and the fixed design parameter of the thruster, calculating the on-orbit thrust of the hall thruster at each moment in the first time period by using an on-orbit thrust calculation model, and obtaining a plurality of on-orbit thrust values, the method further includes:
acquiring the magnetic field intensity induced by Hall drift current in a discharge channel of the Hall thruster in the discharge process; the magnetic field strength is captured by a magnetic sensor array;
and calculating the Hall drift current density in the discharge channel by using a static magnetic field inversion method according to the magnetic field intensity.
Optionally, the matrix equation of the static magnetic field inversion method is as follows:
f(J H )＝min{||AJ H -B|| 2 +λ{||L rr J H || 2 +2||L rz J H || 2 +||L zz J J || 2 }}
wherein, J H Spreading and tiling a Hall drift current density distribution condition j (r, z) to obtain a column vector; b is a vector constructed by the magnetic field intensity at the positions of a plurality of sensor measuring points in the Hall drift current induced magnetic field; a is a Green matrix which links current density distribution with magnetic field intensity of each sensor measuring point; the Green matrix is determined by a calibration experiment; λ is the control regularization term { | | | L rr J H || 2 +2||L rz J H || 2 +||L zz J H || 2 Relative to the residual term | | | AJ H -B|| 2 Regularization parameters of the weights; r is a radial position coordinate in a discharge channel of the Hall thruster; z represents an axial position coordinate in a discharge channel of the Hall thruster; l is rr Representing a second derivative operator obtained by carrying out two derivatives on the radial position in the discharge channel of the Hall thruster; l is zz Represents a second derivative operator L obtained by carrying out two derivatives on the axial position in the discharge channel of the Hall thruster rz And the second derivative operator is obtained by carrying out first derivation on the radial position in the discharge channel of the Hall thruster and carrying out first derivation on the axial position in the discharge channel of the Hall thruster.
Optionally, the static magnetic field inversion method considers a nonnegativity constraint and a zero boundary constraint;
the non-negative constraint means that the azimuth current of the acceleration channel of the Hall thruster flows along the same azimuth direction;
the zero boundary constraint means that the Hall drift current density on the boundary of the discharge chamber of the Hall thruster is zero; the boundary of the discharge chamber of the Hall thruster comprises a wall surface of a discharge channel of the Hall thruster and an anode plane of the Hall thruster.
Optionally, the formula of the on-orbit thrust calculation model includes:
T＝∫ V |J H B r |dV
wherein T is on-orbit thrust; j is a unit of H The Hall drift current density is obtained, and V is the volume of a discharge channel of the Hall thruster; b r The radial component of the magnetic field under the given excitation current is measured by a Gauss meter under the given excitation current of the fixed design parameters of the thruster.
Optionally, the calculation formula for calculating the total impulse margin predicted value at the second time according to the time-averaged thrust value, the second calibration value, and the time-averaged flow is as follows:
wherein, I teva Is a total impulse margin predicted value at the second moment,
is a time-averaged thrust value, mp 1 Is a second calibrated value and is a second calibrated value,
the flow rate is time-averaged.
Optionally, each magnetic sensor in the magnetic sensor array is located outside the plume region, and the magnetic field gradient is greater than a set threshold.
Optionally, the arrangement manner of the magnetic sensors in the magnetic sensor array includes radial arrangement and axial arrangement.
Optionally, the magnetic sensor array uses a tunneling magneto-resistance TMR as a sensing element.
The invention also provides an on-orbit prediction system of the total impulse allowance of the Hall thruster, which comprises the following steps:
the on-orbit thrust calculation module is used for giving the radial component of the magnetic field under the excitation current according to the Hall drift current density and the fixed design parameters of the thruster, calculating the on-orbit thrust of the Hall thruster at each moment in a first time period by using an on-orbit thrust calculation model, and obtaining a plurality of on-orbit thrust values; the on-orbit thrust calculation model is used for representing the relation among Hall drift current density, radial magnetic field intensity and on-orbit thrust; the Hall drift current density is calculated by utilizing a static magnetic field inversion method according to the magnetic field intensity; the magnetic field intensity is the magnetic field intensity induced by Hall drift current in a discharge channel of the Hall thruster in the discharge process, and the magnetic field intensity is captured by a magnetic sensor array; the first time interval is an interval between a first time and a second time;
the time-averaged thrust calculation module is used for calculating the time-averaged thrust value of the first time period according to a plurality of on-orbit thrust values;
the first time propellant residual amount value calculating module is used for calculating a first calibration value of the propellant residual amount in the gas storage tank at the first time according to the capacity of the gas storage tank and the first density at the first time; the first density is obtained by calculation according to a first temperature remote measuring value, a first pressure remote measuring value and a relation curve, wherein the relation curve is a relation curve between the xenon density and the temperature and the pressure; the first temperature remote measurement value and the first pressure remote measurement value are both measured by a remote measuring system; the air storage tank is an air storage tank of the Hall thruster;
the propellant residual quantity value calculation module at the second moment is used for calculating a second calibration value of the propellant residual quantity in the air storage tank at the second moment according to the capacity of the air storage tank and the second density at the second moment;
the time-average flow calculation module is used for calculating the time-average flow of a first time period according to the first calibration value and the second calibration value;
and the total impulse allowance predicted value calculating module is used for calculating the total impulse allowance predicted value at the second moment according to the time-averaged thrust value, the second calibration value and the time-averaged flow.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the invention provides an on-orbit prediction method and a prediction system for the total impulse allowance of a Hall thruster, which comprises the steps of firstly, giving the radial component of a magnetic field under excitation current according to the Hall drift current density and the fixed design parameters of the thruster, and calculating the on-orbit thrust of the Hall thruster at each moment in a first time period by using an on-orbit thrust calculation model to obtain a plurality of on-orbit thrust values; calculating a time-averaged thrust value in a first time period according to the on-orbit thrust values; then, according to the capacity of the gas storage tank and the first density at the first moment, calculating a first calibration value of the propellant allowance in the gas storage tank at the first moment, calculating a second calibration value at the second moment by adopting the same method as the first calibration value, and calculating the time-average flow rate of the time period between the first moment and the second moment according to the first calibration value and the second calibration value; and finally, calculating the total impulse allowance predicted value at the second moment according to the time-averaged thrust value, the second calibration value and the time-averaged flow. The method can predict the predicted value of the total impulse allowance of the Hall thruster at the target moment, provides a reference standard for evaluating the residual service life of the Hall thruster, and is beneficial to further development and application of the Hall thruster.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without creative efforts.
Fig. 1 is a flowchart of an on-orbit prediction method for a total impulse margin of a hall thruster provided in embodiment 1 of the present invention;
fig. 2 is a schematic diagram of an on-orbit thrust calculation method of a hall thruster in the on-orbit prediction method of total impulse margin of the hall thruster provided in embodiment 1 of the present invention;
fig. 3 is a distribution diagram of a magnetic field radial component at a given excitation current in fixed design parameters of a thruster in a discharge channel of a hall thruster provided in embodiment 1 of the present invention;
fig. 4 is a contour diagram of a hall drift current density distribution provided in embodiment 1 of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to provide an on-orbit prediction method and a prediction system for the total impulse allowance of a Hall thruster, which provide a reference standard for the estimation of the residual service life of the Hall thruster and are beneficial to the further development and application of the Hall thruster.
According to the definition formula of the Hall thruster total impulse, the on-orbit prediction of the total impulse margin is inseparable from the on-orbit estimation of the thruster thrust and the margin on-orbit calibration of the propellant. In order to provide an on-orbit prediction method for the total impulse margin of the Hall thruster, firstly, an on-orbit evaluation method for the thrust of the Hall thruster and an on-orbit calibration method for the margin of the propellant need to be researched.
Currently, the mainstream methods for thrust on-track assessment can be divided into two categories: orbit estimation and attitude estimation. The orbit estimation method establishes a relation between the undetectable thrust information and the measurable satellite orbit information through a global satellite navigation system, and then calculates the thrust of the thruster according to the satellite orbit change information; the attitude estimation method measures angular motion data of a satellite by using a satellite-borne high-precision attitude sensing device, and then calculates thrust. However, the thrust provided by the hall thruster has the same magnitude as the environmental disturbance force applied to the spacecraft when the spacecraft runs in orbit, so that once the environmental disturbance moment is not fully considered, a relative error between the estimated thrust value and the true thrust value is large.
A common on-orbit calibration method for the propellant allowance of the electric propulsion system is a billing method, and is a working medium allowance calibration method developed and formed according to the principle that the mass of a working medium in a constant volume system is in direct proportion to the density of the working medium. The density of the propellant is determined by telemetering the temperature and the pressure in the propellant gas storage tank and combining the physical characteristics of the propellant measured on the ground, and then the mass of the residual propellant in the tank is obtained by multiplying the density by the volume of the gas storage tank. For the electric propulsion system with multiple gas storage tanks, the propellant allowance of each gas storage tank is calculated by respectively applying a billing method, and finally, the sum is carried out.
In order to make the aforementioned objects, features and advantages of the present invention more comprehensible, the present invention is described in detail with reference to the accompanying drawings and the detailed description thereof.
Example 1
The present embodiment provides an on-orbit prediction method for a total impulse margin of a hall thruster, please refer to fig. 1, which includes:
s1, according to Hall drift current density and a thruster fixed design parameter, giving a radial component of a magnetic field under an excitation current, and calculating on-orbit thrust of a Hall thruster at each moment in a first time period by using an on-orbit thrust calculation model to obtain a plurality of on-orbit thrust values; the on-orbit thrust calculation model is used for representing the relation among Hall drift current density, radial magnetic field intensity and on-orbit thrust; the Hall drift current density is calculated by using a static magnetic field inversion method according to the magnetic field intensity; the magnetic field intensity is the magnetic field intensity induced by Hall drift current in a discharge channel of the Hall thruster in the discharge process, and the magnetic field intensity is captured by a magnetic sensor array; the first time period is a time period between a first time and a second time.
The on-orbit prediction of the total impulse margin is inseparable from the on-orbit estimation of the thruster thrust and the margin on-orbit calibration of the propellant. In order to provide an on-orbit prediction method of the total impulse margin of the Hall thruster, firstly, an on-orbit evaluation method of the thrust of the Hall thruster and an on-orbit calibration method of the margin of propellant need to be researched.
The on-orbit evaluation method of the thrust of the Hall thruster is described as follows:
as an optional implementation, before S1, the method further includes:
s01, acquiring the magnetic field intensity induced by Hall drift current in a discharge channel of the Hall thruster in the discharge process; the magnetic field strength is captured by a magnetic sensor array;
and S02, calculating the Hall drift current density in the discharge channel by using a static magnetic field inversion method according to the magnetic field strength.
It should be noted that the on-orbit estimation method of the thrust of the hall thruster includes steps S01, S02, and S1.
As an alternative embodiment, the magnetic sensor array mentioned in S1 uses a tunneling magneto-resistance TMR as a sensing element.
Specifically, the magnetic sensor can be a TMR2701 chip from the multi-dimensional technologies of jiangsu.
In the step S01, a magnetic sensor array which takes a TMR2701 chip of Jiangsu multidimensional technology company as a magnetic induction element is used for capturing a magnetic field induced by Hall drift current in a channel of a Hall thruster in the discharging process, a voltage signal on the sensor is captured by a data acquisition card of a USB-5817 model of Mohua technology (China) Limited company, and then magnetic field information of a corresponding position is obtained by an upper computer program written by Labview. A data acquisition card of a USB-5817 model is placed outside a vacuum tank where the Hall thruster is located.
Optionally, each magnetic sensor in the magnetic sensor array is located outside the plume region, and the magnetic field gradient is greater than a set threshold.
It should also be noted that the magnetic sensor installation position should comply with the basic principle of the normal operating conditions of the magnetic sensor, for example, the temperature of the magnetic sensor installation position should meet the temperature of the normal operating conditions of the magnetic sensor, i.e., be lower than 80 ℃.
As an alternative embodiment, the arrangement of the magnetic sensors in the magnetic sensor array includes a radial arrangement and an axial arrangement.
According to the setting conditions of the magnetic sensors, through numerical simulation, the present embodiment sets 8 magnetic sensor positions, please refer to fig. 2, in which 4 radial sensors measure the axial component of the magnetic field, and the other 4 axial sensors measure the radial component of the magnetic field; the magnetic sensor array is integrally close to the plane of the outlet of the thruster and is placed in a vacuum tank. The specific placement positions of the 8 magnetic sensors are: and by taking a point on an intersection line of the outer wall of the channel and the outer magnetic pole piece as a zero point, establishing an abscissa axis in a plane where the outer magnetic pole piece is located, and establishing an ordinate axis in an extension plane of the outer wall of the channel, the position coordinates of the 4 axial sensors are (50, 10), (30, 20), (50, 20), (45, 30), and the position coordinates of the 4 radial sensors are (20, 10), (30, 10), (40, 20).
As an alternative embodiment, the matrix equation of the static magnetic field inversion method in step S02 is:
f(J H )＝min{||AJ H -B|| 2 +λ{||L rr J H || 2 +2||L rz J H || 2 +||L zz J H || 2 }}
wherein, J H Spreading and tiling a Hall drift current density distribution condition j (r, z) to obtain a column vector; b is a vector constructed by the magnetic field intensity at the positions of a plurality of sensor measuring points in the Hall drift current induced magnetic field; a is a Green matrix which links the current density distribution with the magnetic field intensity of each sensor measuring point; the Green matrix is determined by a calibration experiment; λ is the control regularization term { | | L rr J H || 2 +2||L rz J H || 2 +||L zz J H || 2 Relative to the residual term | | | AJ H -B|| 2 Regularization parameters of the weights; r is a radial position coordinate in a discharge channel of the Hall thruster; z represents an axial position coordinate in a discharge channel of the Hall thruster; l is rr Representing a second derivative operator obtained by carrying out two derivatives on the radial position in the discharge channel of the Hall thruster; l is a radical of an alcohol zz Represents a second derivative operator L obtained by carrying out two-time derivation on the axial position in the discharge channel of the Hall thruster rz Shows that the radial position in the discharge channel of the Hall thruster is subjected to one derivation and the axial direction in the discharge channel of the Hall thrusterAnd (5) carrying out first derivation on the position to obtain a second derivative operator.
It should be noted that, magnetic field information captured by the magnetic sensor array and the digital acquisition device is a known quantity, and the distribution characteristic of the hall drift current in the channel during the discharge process of the hall thruster is solved through the known magnetic field information, and the magnetostatic inverse problem can be expressed as a matrix equation: f (J) H )＝min||AJ H -B|| 2 . In consideration of the discontinuity of the solution, smoothing the problem by using Tikhonov regularization to obtain a stable and applicable Hall drift current density distribution solution; the equation to be solved of the magnetostatic inversion problem after processing becomes f (J) H )＝min{||AJ H -B|| 2 +λ{||L rr J H || 2 +2||L rz J H || 2 +||L zz J H || 2 }}。
After smoothing the inverse problem with the regularization constraint method, two additional constraints, namely a non-negativity constraint and a zero boundary constraint, need to be added in order to obtain a useful stable solution.
As an alternative embodiment, the static magnetic field inversion method takes into account non-negativity constraints and zero boundary constraints;
the non-negative constraint means that the azimuth current of the acceleration channel of the Hall thruster flows along the same azimuth direction;
the zero boundary constraint means that the Hall drift current density on the boundary of the discharge chamber of the Hall thruster is zero; the boundary of the discharge chamber of the Hall thruster comprises a wall surface of a discharge channel of the Hall thruster and an anode plane of the Hall thruster.
When solving the matrix equation of the static magnetic field inversion method, firstly, a Green matrix A representing the mathematical relationship between the Hall current density distribution in the discharge channel and the magnetic field intensity of each measuring point is determined through calibration. The specific implementation scheme is as follows: winding copper wires with the diameter of phi 1mm into 5 turns, and enabling the copper wires to be radially and equidistantly distributed on the same axial plane in a thruster channel, wherein the minimum diameter is 75mm, and the maximum diameter is 95mm, so that Hall drift current in the channel when the thruster runs is simulated; when calibration is started, the coil in the thruster is firstly suppliedElectrifying for 2.4A, electrifying for the outer coil for 1.4A, supplying power for the sensor for 1.4V, and recording the background magnetic field B generated by the thruster at each sensor position b (ii) a Then 4A of current is applied to each copper wire, and the magnetic field B at each sensor position is recorded again w The difference B between them Δ ＝B w -B b The magnetic field increment at each measuring point position excited by the simulated Hall drift current is obtained; then moving the wire to the exit plane of the thruster along the axis of the thruster and repeating the calibration process, and taking a calibration plane at intervals of 5mm from the plane 15mm away from the anode plane of the thruster, wherein the total number of the calibration planes is 10; according to the Hall drift currents with known magnitude at 50 positions in the channel and the magnetic field intensity at 8 measuring points in the induction magnetic field, a Green matrix A is obtained 8×50 The specific expression of the matrix is
Constituent element B Δ (r i ，z j ，S k ) Wherein i can take 1,2,3,4,5 to represent 5 radial position coordinates; j may take 1,2,3, \8230; \ 8230;, 10, representing 10 axial position coordinates; k can take 1,2,3, \8230;, 8, representing magnetic sensors at 8 measurement points.
Solving a matrix equation, writing an MATLAB script by utilizing an fmincon function to execute the regularization algorithm, and assigning an initial value of current density as a zero vector; solving the solution J of the obtained Hall drift current density H Is a 50 x 1 column vector, which is rearranged in a manner opposite to the stacking of the rows in the green matrix, so that a contour map of the hall drift current density distribution in the discharge channel is obtained. According to the method, in the specific embodiment, when the cathode flow rate of the Hall thruster is 3sccm, the anode flow rate is 30sccm, the cathode relative angle is 180 degrees, the exciting currents of the inner coil and the outer coil are respectively 2.4A and 1.4A, and the discharge voltage is 300V, the contour diagram of the Hall drift current density distribution is obtained as shown in FIG. 4.
When the magnetic field intensity of 8 measuring point positions is measured, 8 sensors are respectively connected in series with a passive resistor, all the sensors share the same power bus, and the voltage drop is indirectly measured through the passive resistor; the power supply of the sensor array is arranged outside the vacuum tank. A graphite cover is arranged outside a circuit board of the magnetic sensor to protect the sensor from being influenced by plasma sputtering near the exit plane of the thruster, and meanwhile, the graphite also plays a role in heat dissipation.
For the radial magnetic field component in S1, in a specific embodiment, when the inner and outer coil exciting currents are given as 2.4A and 1.4A, respectively, the distribution of the radial magnetic field component under the fixed design parameters of the thruster measured by a gauss meter is shown in fig. 3.
The embodiment is used for realizing on-orbit evaluation on the thrust of the Hall thruster by combining the basic principle that the Hall drift current and the radial magnetic field interact to generate the thrust, and the principle corresponds to an on-orbit thrust calculation model.
As an alternative embodiment, the formula of the on-orbit thrust calculation model includes:
T＝∫ V |J H B r |dV
wherein T is on-orbit thrust; j is a unit of H Is the Hall drift current density (i.e. the solution of the above matrix equation), and V is the Hall thruster discharge channel volume; b r And measuring the radial component of the magnetic field under the given excitation current by a Gauss meter under the given excitation current of the fixed design parameters of the thruster.
In a specific embodiment, when the cathode flow of the Hall thruster is 3sccm, the anode flow is 30sccm, the cathode relative angle is 180 degrees, the exciting currents of the inner coil and the outer coil are respectively 2.4A and 1.4A, and the discharge voltage is 300V, the calculated thrust value is 23.10mN; at this time, the thrust value measured by the three-wire torsional pendulum type thrust test bench was 22.45mN, and the relative error was only 2.90%.
In the on-orbit evaluation process of the thrust of the Hall thruster, the magnetic field intensity of the second level can be measured by using the magnetic sensing array, the on-orbit thrust is calculated according to the magnetic field intensity of the second level, and then the real-time on-orbit thrust is obtained, so that the defect of poor evaluation real-time performance caused by the fact that the existing on-orbit thrust evaluation method needs to be combined with satellite orbit change information or angular displacement change information to evaluate the thrust is overcome.
And S2, calculating the time-averaged thrust value in the first time period according to the on-orbit thrust values.
The spacecraft on-orbit t is obtained by the method for estimating the thrust of the Hall thruster on-orbit 0 Time to t 0 A thrust value for a first period (Δ t) between times + Δ t. Let T =80mN be the estimated thrust value at the start of a certain spatial mission. Wherein t is 0 The time is the first time t 0 The + Δ t time is the second time.
The thrust evaluation value T in the delta T time period is subjected to integral average to obtain the time-average thrust value in the time period
Namely that
Assuming that the time average thrust value measured and calculated in the time period
The method for on-track calibration of the propellant residual quantity is described as follows:
s3, calculating a first calibration value of the propellant allowance in the air storage tank at the first moment according to the capacity of the air storage tank and the first density at the first moment; the first density is obtained by calculation according to a first temperature remote measurement value, a first pressure remote measurement value and a relation curve, wherein the relation curve is a relation curve between xenon density and temperature and pressure; the first temperature remote measuring value and the first pressure remote measuring value are measured by a remote measuring system; the air storage tank is of a Hall thruster.
First, t is obtained by a telemetry system 0 And (4) measuring the temperature and the pressure in the air storage tank of the Hall thruster at any moment. Suppose that the remote temperature value of the air storage tank is T t0 =37 ℃ and a pressure telemetry value P 0 ＝10Mpa。
Then, the user can use the device to perform the operation,by using an accounting method, firstly, the performance test data of the ground thruster is utilized to correspondingly obtain the density rho of the propellant, and then the volume t of the known gas storage tank is combined to calculate 0 In-tank propellant allowance calibration value Mp at any moment 0 . Specifically, the temperature of the air storage tank is T according to the remote measurement value t0 =37 ℃, pressure telemetry value is P 0 =100bar, and p is obtained by referring to the xenon density and temperature and pressure relation curve 0 ＝1.5150g/cm 3 On the premise that the volume V =4L of the air storage tank is known, t can be obtained 0 In-tank propellant allowance calibration value Mp at any moment 0 ＝ρ 0 V＝6.0600kg。
And S4, calculating a second calibration value of the residual quantity of the propellant in the air storage tank at the second moment according to the capacity of the air storage tank and the second density at the second moment.
The second density is calculated according to a second temperature remote measurement value, a second pressure remote measurement value and a relation curve, wherein the relation curve is a relation curve between the xenon density and the temperature and the pressure; the second temperature remote measurement value and the second pressure remote measurement value are both measured by a remote measurement system; the air storage tank is of a Hall thruster.
After delta t =600s, the billing method is applied again to obtain t 0 + delta t time in-tank propellant residual quantity calibration value Mp 1 . Specifically, let t 0 The remote measurement value of the temperature of the air storage tank at the + delta T moment is T t1 =37 ℃, pressure telemetry value is P 1 =99.95bar, and p is obtained by referring to the relation curve of xenon density and temperature and pressure 1 =1.5142g/ml, and when the volume of the air storage tank is V =4L, t is determined 0 And (4) calibrating value Mp of residual quantity of propellant in tank at + delta t moment 1 ＝ρ 1 V＝6.0568kg。
And S5, calculating the time-average flow in the first time period according to the first calibration value and the second calibration value.
Time-averaged flow over a period of at
Instead of actual flow at any time during the time period
Under the working conditions, the time average flow in the delta t time period.
And S6, calculating a total impulse allowance predicted value at a second moment according to the time-averaged thrust value, the second calibration value and the time-averaged flow.
As an alternative, the calculation formula of step S6 is:
wherein the content of the first and second substances,
is a predicted value of the total impulse margin at the second moment,
time-averaged thrust value, mp 1 Is a second calibrated value and is a second calibrated value,
the flow rate is time-averaged.
Under the working condition, the Hall thruster is at t 0 Total impulse margin predicted value at + delta t moment
It should be further noted that the derivation process of the calculation formula of the total impulse margin predicted value is as follows:
the definition formula of the Hall thruster total impulse allowance is as follows:
in the formula I t Is t 0 Time (t) 0 Is an arbitrary value) of total impulse allowance of the Hall thruster, and T is T 0 The thrust generated by the Hall thruster at the moment is equal to t 0 Propellant consumption rate in discharge channel of Hall thruster at any moment
Product of the effective discharge velocity c at the discharge channel outlet, t max The maximum working time of the Hall thruster under the current thrust depends on the propellant allowance in the air storage tank of the Hall thruster system; propellant consumption rate in Hall thruster discharge channel
Is considered to be in contact with the air supply rate of the propellant in the air storage tank of the Hall thruster system
Equality, i.e. neglecting incomplete ionization of the neutral propellant in the discharge channel, there are
Mp t And (4) indicating the propellant allowance in the air storage tank of the Hall thruster system at the time t.
I in the above formula t ＝c·Mp t Wherein c is t 0 The effective exhaust speed of the propellant at the outlet of the discharge channel of the Hall thruster at the moment can be known from the content in the previous paragraph
Effective exhaust velocity with propellant
Replacement of t 0 Actual valid row of time instantsThe gas velocity c.
Mean time to effective exhaust velocity for propellant
A short time period delta t is taken from the time t, and the time-average thrust in the delta t time period is defined
Mean gas supply rate of propellant
So that the mean effective exhaust velocity of the propellant during the delta t time period can be obtained
Mean gas feed rate in propellant
Middle, mp 0 The residual quantity of the propellant in the air storage tank of the Hall thruster system is t 0 Calibration value of time, mp 1 The residual quantity of the propellant in the air storage tank of the Hall thruster system is t 0 A calibration value at time + Δ t.
According to the derivation, the final predicted value of the total impulse allowance of the Hall thruster at the time of t + delta t is obtained as
The on-orbit prediction method for the total impulse margin of the Hall thruster provided by the embodiment can predict the predicted value of the total impulse margin of the Hall thruster at the target moment, provides a reference standard for evaluating the residual service life of the Hall thruster, and is beneficial to further development and application of the Hall thruster.
Example 2
The embodiment provides an on-orbit prediction system for the total impulse margin of a Hall thruster, which comprises:
the on-orbit thrust calculation module is used for giving the radial component of the magnetic field under the excitation current according to the Hall drift current density and the fixed design parameters of the thruster, calculating the on-orbit thrust of the Hall thruster at each moment in a first time period by using an on-orbit thrust calculation model, and obtaining a plurality of on-orbit thrust values; the on-orbit thrust calculation model is used for representing the relation among Hall drift current density, radial magnetic field intensity and on-orbit thrust; the Hall drift current density is calculated by utilizing a static magnetic field inversion method according to the magnetic field intensity; the magnetic field intensity is the magnetic field intensity induced by Hall drift current in a discharge channel of the Hall thruster in the discharge process, and the magnetic field intensity is captured by a magnetic sensor array; the first time interval is a time interval between a first moment and a second moment;
the time-averaged thrust calculation module is used for calculating the time-averaged thrust value of the first time period according to the on-orbit thrust values;
the first time propellant residual amount value calculating module is used for calculating a first calibration value of the propellant residual amount in the gas storage tank at the first time according to the capacity of the gas storage tank and the first density at the first time; the first density is obtained by calculation according to a first temperature remote measuring value, a first pressure remote measuring value and a relation curve, wherein the relation curve is a relation curve between the xenon density and the temperature and the pressure; the first temperature remote measuring value and the first pressure remote measuring value are measured by a remote measuring system; the air storage tank is an air storage tank of the Hall thruster;
the second moment propellant residual quantity value calculating module is used for calculating a second calibration value of the propellant residual quantity in the gas storage tank at the second moment according to the capacity of the gas storage tank and the second density at the second moment;
the time-average flow calculation module is used for calculating the time-average flow of a first time period according to the first calibration value and the second calibration value;
and the total impulse allowance predicted value calculating module is used for calculating the total impulse allowance predicted value at the second moment according to the time-averaged thrust value, the second calibration value and the time-averaged flow.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.
Claims (10)
1. An on-orbit prediction method for the total impulse margin of a Hall thruster is characterized by comprising the following steps of:
according to the Hall drift current density and the fixed design parameters of the thruster, the radial component of a magnetic field under excitation current is given, and the on-orbit thrust of the Hall thruster at each moment in the first time period is calculated by using an on-orbit thrust calculation model to obtain a plurality of on-orbit thrust values; the on-orbit thrust calculation model is used for representing the relation among Hall drift current density, radial magnetic field intensity and on-orbit thrust; the Hall drift current density is calculated by utilizing a static magnetic field inversion method according to the magnetic field intensity; the magnetic field intensity is the magnetic field intensity induced by Hall drift current in a discharge channel of the Hall thruster in the discharge process, and the magnetic field intensity is captured by a magnetic sensor array; the first time interval is a time interval between a first moment and a second moment;
calculating the time-average thrust value of the first time period according to the plurality of on-orbit thrust values;
calculating a first calibration value of the propellant allowance in the air storage tank at the first moment according to the capacity of the air storage tank and the first density at the first moment; the first density is obtained by calculation according to a first temperature remote measurement value, a first pressure remote measurement value and a relation curve, wherein the relation curve is a relation curve between xenon density and temperature and pressure; the first temperature remote measurement value and the first pressure remote measurement value are both measured by a remote measuring system; the air storage tank is an air storage tank of the Hall thruster;
calculating a second calibration value of the propellant allowance in the air storage tank at a second moment according to the capacity of the air storage tank and a second density at the second moment;
calculating the time-average flow of a first time period according to the first calibration value and the second calibration value;
and calculating a total impulse allowance predicted value at a second moment according to the time-averaged thrust value, the second calibration value and the time-averaged flow.
2. The method of claim 1, wherein before calculating the on-orbit thrust of the hall thruster at each moment in the first time period by using an on-orbit thrust calculation model to obtain a plurality of on-orbit thrust values, before the radial component of the magnetic field under the given excitation current according to the hall drift current density and the fixed design parameters of the thruster, the method further comprises:
acquiring the magnetic field intensity induced by Hall drift current in a discharge channel of the Hall thruster in the discharge process;
and calculating the Hall drift current density in the discharge channel by using a static magnetic field inversion method according to the magnetic field intensity.
3. The method of claim 2, wherein the matrix equation of the static magnetic field inversion method is:
f(J H )＝min{||AJ H -B|| 2 +λ{||L rr J H || 2 +2||L rz J H || 2 +||L zz J H || 2 }}
wherein, J H Spreading and tiling a Hall drift current density distribution condition j (r, z) to obtain a column vector; b is several channels in magnetic field induced by Hall drift currentA vector constructed by the magnetic field intensity at the position of the measuring point of the sensor; a is a Green matrix which links current density distribution with magnetic field intensity of each sensor measuring point; the Green matrix is determined by a calibration experiment; λ is the control regularization term { | | | L rr J H || 2 +2||L rz J H || 2 +||L zz J H || 2 Relative to the residual term | | AJ H -B|| 2 Regularization parameters of the weights; r is a radial position coordinate in a discharge channel of the Hall thruster; z represents an axial position coordinate in a discharge channel of the Hall thruster; l is a radical of an alcohol rr Representing a second derivative operator obtained by carrying out two derivatives on the radial position in the discharge channel of the Hall thruster; l is zz Represents a second derivative operator L obtained by carrying out two derivatives on the axial position in the discharge channel of the Hall thruster rz And the second derivative operator is obtained by carrying out first derivation on the radial position in the discharge channel of the Hall thruster and carrying out first derivation on the axial position in the discharge channel of the Hall thruster.
4. The method of claim 3, wherein the static magnetic field inversion method takes into account non-negativity constraints and zero boundary constraints;
the non-negative constraint means that the azimuth current of the acceleration channel of the Hall thruster flows along the same azimuth direction;
the zero boundary constraint means that the Hall drift current density on the boundary of the discharge chamber of the Hall thruster is zero; the boundary of the discharge chamber of the Hall thruster comprises a wall surface of a discharge channel of the Hall thruster and an anode plane of the Hall thruster.
5. The method of claim 1, wherein the formula for the on-orbit thrust force calculation model comprises:
T＝∫ V |J H B r |dV
wherein, T is on-orbit thrust; j. the design is a square H The Hall drift current density is obtained, and V is the volume of a discharging channel of the Hall thruster; b is r For a given radial component of the magnetic field at the excitation current, by means of a GaussmeterThe thruster is obtained by measuring fixed design parameters under the condition of given exciting current.
6. The method according to claim 1, wherein the calculation formula for calculating the predicted total impulse margin value at the second time point according to the time-averaged thrust value, the second calibration value and the time-averaged flow rate is as follows:
wherein the content of the first and second substances,
is a total impulse margin predicted value at the second moment,
is a time-averaged thrust value, mp 1 Is a second calibrated value and is a second calibrated value,
the flow rate is time-averaged.
7. The method of claim 1, wherein each magnetic sensor of the array of magnetic sensors is located outside of a plume region, and the magnetic field gradient is greater than a set threshold.
8. The method of claim 1, wherein the magnetic sensors of the magnetic sensor array are arranged in a manner that includes a radial arrangement and an axial arrangement.
9. The method of claim 1, wherein the magnetic sensor array has a tunneling magnetoresistive TMR as a sensing element.
10. An on-orbit prediction system for the total impulse margin of a Hall thruster is characterized by comprising the following components:
the on-orbit thrust calculation module is used for giving the radial component of the magnetic field under the excitation current according to the Hall drift current density and the fixed design parameters of the thruster, calculating the on-orbit thrust of the Hall thruster at each moment in a first time period by using an on-orbit thrust calculation model, and obtaining a plurality of on-orbit thrust values; the on-orbit thrust calculation model is used for representing the relation among Hall drift current density, radial magnetic field intensity and on-orbit thrust; the Hall drift current density is calculated by using a static magnetic field inversion method according to the magnetic field intensity; the magnetic field intensity is the magnetic field intensity induced by Hall drift current in a discharge channel of the Hall thruster in the discharge process, and the magnetic field intensity is captured by the magnetic sensor array; the first time interval is an interval between a first time and a second time;
the time-averaged thrust calculation module is used for calculating the time-averaged thrust value of the first time period according to a plurality of on-orbit thrust values;
the first time propellant residual amount value calculating module is used for calculating a first calibration value of the propellant residual amount in the air storage tank at a first time according to the capacity of the air storage tank and the first density at the first time; the first density is obtained by calculation according to a first temperature remote measurement value, a first pressure remote measurement value and a relation curve, wherein the relation curve is a relation curve between xenon density and temperature and pressure; the first temperature remote measurement value and the first pressure remote measurement value are both measured by a remote measuring system; the air storage tank is an air storage tank of the Hall thruster;
the propellant residual quantity value calculation module at the second moment is used for calculating a second calibration value of the propellant residual quantity in the air storage tank at the second moment according to the capacity of the air storage tank and the second density at the second moment;
the time-average flow calculation module is used for calculating the time-average flow of a first time period according to the first calibration value and the second calibration value;
and the total impulse allowance predicted value calculating module is used for calculating the total impulse allowance predicted value at the second moment according to the time-averaged thrust value, the second calibration value and the time-averaged flow.
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| CN117451238B (en) * | 2023-12-19 | 2024-04-09 | 哈尔滨工业大学 | On-orbit optical detection method and device for propeller thrust fluctuation based on neural network |
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