Method for estimating on-orbit xenon remaining amount of an electric propulsion system

Abstract

The application discloses an on-orbit xenon residual amount estimation method of an electric propulsion system, and relates to the technical field of electric propulsion systems, in particular to an on-orbit xenon residual amount estimation method of an electric propulsion system. The method comprises the following steps: obtaining the pressure of a xenon bottle of the electric propulsion system; judging the relationship between the obtained pressure of the xenon bottle of the electric propulsion system and a preset pressure; when the obtained pressure of the xenon bottle of the electric propulsion system is less than or equal to the preset pressure, calculating the residual amount of xenon in the xenon bottle and pipelines of the electric propulsion system based on the theory of comparative state; and when the obtained pressure of the xenon bottle of the electric propulsion system is greater than the preset pressure, calculating the residual amount of xenon in the xenon bottle and pipelines of the electric propulsion system according to the initial xenon filling amount of the electric propulsion system and the xenon consumption amount of each working process. The application can effectively evaluate the residual amount of xenon and further evaluate the service life of a spacecraft.

Description

Technical Field

[0001] This invention belongs to the technical field of spacecraft electric propulsion systems, and particularly relates to a method for estimating the remaining amount of xenon gas in an electric propulsion system in orbit. Background Technology

[0002] Currently, there are many types of propulsion systems in orbit. Among them, electric propulsion systems have developed rapidly in recent years due to their high specific impulse, especially Hall effect electric propulsion systems and ion electric propulsion systems, which are often used in geostationary orbit satellite platforms to perform tasks such as north-south position maintenance, attitude control (momentum wheel unloading), orbit control, and even geostationary orbit transfer. In addition, electric propulsion systems can accomplish tasks that conventional propulsion systems cannot, such as deep space exploration, interstellar travel and other missions requiring large Δy values, as well as precise attitude control of satellites and microsatellites and satellite constellation networking control.

[0003] Hall effect electric propulsion systems and ion electric propulsion systems in spacecraft mostly use high-purity xenon as the propellant, which is added before satellite launch. During the spacecraft's on-orbit operation, the electric propulsion continuously consumes the xenon propellant. Estimating the remaining xenon propellant quantity during the spacecraft's on-orbit operation is a crucial task in on-orbit management. The accuracy of the xenon propellant quantity prediction affects the estimation of the spacecraft's remaining lifespan and the selection of deorbit timing, which is of great significance for maximizing the spacecraft's value. This is especially true for geostationary satellites with limited orbital resources and satellites with limited xenon propellant capacity, possessing significant strategic and economic benefits.

[0004] Traditional methods for measuring propellant remaining quantity in single- and dual-component chemical propulsion systems mainly include the Book-K (BK) method and the Pressure-Volume-Temperature (PVT) method. These methods are primarily used for estimating the remaining propellant quantity in spacecraft using single-component anhydrous hydrazine and dual-component nitrogen tetroxide / methylhydrazine propellants. Single- and dual-component propellants are stored in liquid form in tanks filled with a pressurized extrusion gas (usually helium). During in-orbit operation, under the influence of the extrusion gas, the propellant flows out of the tank and, through pipelines and valves, ultimately enters the downstream thrusters and engines, generating the thrust required for spacecraft attitude and orbit adjustments. The Book-K method calculates the propellant consumption by recording the thruster ignition time and combining it with flow rate measurements taken during ground calibration. Given the initial propellant load, the remaining propellant quantity in the tank can be determined. The PVT method assumes that the compressed helium gas is an ideal gas during on-orbit operation. With measurable pressure and temperature, the helium volume is obtained using the ideal gas law and the pressure and temperature changes. Given a known tank volume and density, the volume and density of the liquid propellant can be calculated, thus determining the remaining propellant quantity. In practical on-orbit applications, two calculation methods are used to verify the remaining propellant quantity, and the overall calculation accuracy is comprehensively evaluated.

[0005] For electric propulsion systems, the working propellant is xenon, which is stored in xenon cylinders in a supercritical or gaseous state during orbit. Xenon is supplied downstream to the Hall effect and ion thrusters via pressure and flow management by the xenon's own pressure and the storage unit. The differences between electric propulsion xenon storage and usage and chemical propulsion are:

[0006] 1) Electric propulsion xenon cylinders store only a single xenon working medium (supercritical or gaseous); chemical propulsion tanks contain not only liquid propellant but also compressed gas.

[0007] 2) The BK method is used to estimate the remaining amount of chemical propulsion propellant. However, since the entire process of electric propulsion during on-orbit use is quite complex, xenon consumption consists of system pretreatment consumption, xenon leakage, xenon consumption in preheating mode, and thruster ignition consumption. Therefore, the single BK method cannot fully cover the needs of estimating the remaining amount of electric propulsion.

[0008] 3) For the PVT method (i.e., calculating the volume of the squeezed gas helium through the ideal gas equation of state) used to estimate the remaining amount of chemical propulsion, due to the special physical properties of xenon during the on-orbit use of electric propulsion, and the fact that the xenon cylinder contains only a single xenon working medium, the conventional PVT calculation method cannot be used. Summary of the Invention

[0009] The technical problem solved by this invention is to overcome the shortcomings of the prior art and provide a method for estimating the remaining xenon in an electric propulsion system in orbit, which can effectively assess the remaining xenon and the lifespan of the spacecraft.

[0010] To address the aforementioned technical problems, this invention discloses a method for estimating the remaining xenon gas in an electric propulsion system in orbit, comprising:

[0011] To obtain the pressure of the xenon cylinder in the electric propulsion system;

[0012] Determine the relationship between the pressure of the xenon cylinder in the electric propulsion system and the preset pressure;

[0013] When the pressure of the xenon cylinder of the electric propulsion system is less than or equal to the preset pressure, the remaining amount of xenon in the xenon cylinder and pipeline of the electric propulsion system is calculated based on the comparative state theory.

[0014] When the pressure of the xenon cylinder of the electric propulsion system is greater than the preset pressure, the remaining amount of xenon in the xenon cylinder and pipeline of the electric propulsion system is calculated based on the initial xenon filling amount of the electric propulsion system and the xenon consumption amount in each working process.

[0015] In the above-mentioned method for estimating the remaining xenon gas in the electric propulsion system, based on the contrastive state theory, the remaining xenon gas in the xenon cylinder and pipeline of the electric propulsion system is calculated, including:

[0016] To obtain the temperature and pressure of xenon gas in the xenon cylinders and pipelines of the electric propulsion system;

[0017] The temperature and pressure of xenon gas in the xenon cylinder and pipeline of the electric propulsion system were dimensionlessly processed to obtain dimensionless temperature T and dimensionless pressure P of xenon gas.

[0018] Substituting the dimensionless temperature T and dimensionless pressure P of the obtained xenon gas into the BWR equation, the dimensionless density ρ of methane was calculated.

[0019] According to the theory of contrastive states, the dimensionless density ρ of methane calculated is divided by the critical point density of xenon to obtain the density of xenon in the xenon cylinder and pipeline at a specific temperature and pressure.

[0020] The calculated density of xenon gas in the xenon cylinder and pipeline at a specific temperature and pressure is multiplied by the volume of the xenon cylinder and pipeline, respectively; the two products are added together to obtain the remaining amount of xenon gas in the electric propulsion system.

[0021] In the above-mentioned method for estimating the remaining xenon gas in the electric propulsion system, the temperature and pressure of the xenon gas in the xenon cylinder and pipeline of the electric propulsion system are processed to be dimensionless, resulting in dimensionless temperature T and dimensionless pressure P of the xenon gas, including:

[0022] Determine the critical point temperature T0 and critical point pressure P0 of xenon.

[0023] The temperature and pressure of the xenon gas in the xenon cylinder and pipeline of the electric propulsion system are obtained by dividing the critical point temperature T0 and critical point pressure P0, respectively, to obtain the dimensionless temperature T and dimensionless pressure P of the xenon gas.

[0024] In the above method for estimating the remaining on-orbit xenon gas in an electric propulsion system, the BWR equation is expressed as follows:

[0025]

[0026] Among them, A n The coefficients of the BWR equation are r = 0.0096.

[0027] In the above-mentioned methods for estimating the remaining on-orbit xenon gas in electric propulsion systems

[0028] A1 = R v T

[0029] A2 = N1T + N2T 1 / 2 +N3+N4 / T+N5 / T 2

[0030] A3 = N6 + N7 + N8 / T + N9 / T 2

[0031] A4 = N 10 T+N 11 +N 12 / T

[0032] A5 = N 13

[0033] A6 = N 14 / T+N 15 / T 2

[0034] A7 = N 16 / T

[0035] A8 = N 17 / T+N 18 / T 2

[0036] A9 = N 19 / T 2

[0037] A 10 =N 20 / T 2 +N 21 / T 3

[0038] A 11 =N 22 / T 2 +N 23 / T 4

[0039] A 12 =N 24 / T 2 +N 25 / T 3

[0040] A 13 =N 26 / T 2 +N 27 / T 4

[0041] A 14 =N 28 / T 2 +N 29 / T 3

[0042] A 15 =N 30 / T 2 +N 31 / T 3 +N 32 / T 4

[0043] Among them, R v The ideal gas constant is a number; N 1～32 Given the known quantities, refer to the parameter values ​​of fluid CH4.

[0044] In the above method for estimating the remaining on-orbit xenon in an electric propulsion system, N 1～32 =

[0045] [-1.184347314485E-2,7.540377272657E-1,-1.225769717554E+1,6.260681393432E+2 ,-3.490654409121E+4,5.301046385532E-4,-2.875764479978E-1,5.011947936427E+1 ,-2.821562800903E+2,-2.064957753744E-3,1.285951844828E-2,-1.106266656726E+ 0,3.060813353408E-4,-3.174982181302E-3,5.191608004779E+0,-3.074944210271E- 4,1.071143181503E-5,-9.290851745353E-3,1.610140169312E-4,3.469830970789E+4 ,-1.370878559048E+6,1.790105676252E+2,1.615880743238E+6,6.265306650288E-1, 1.820173769533E+1,1.449888505811E-3,-3.159999123798E+1,-5.290335668451E-6, 1.694350244152E-3, 8.612049038886E-9, -2.598235689063E-6, 3.153374374912E-5].

[0046] In the above-mentioned method for estimating the remaining amount of xenon gas in the electric propulsion system, the relative state theory states that for all substances, their state variables, after being dimensionless, follow universal laws of change.

[0047] In the above-mentioned method for estimating the remaining xenon gas in an electric propulsion system, the remaining xenon gas in the xenon cylinders and pipelines of the electric propulsion system is calculated based on the initial xenon gas loading and the xenon gas consumption during each operating process. This includes:

[0048] The initial xenon gas loading amount m0 ​​of the electric propulsion system was obtained by weighing using an electronic scale.

[0049] Based on the leakage rate of the electric propulsion system and the on-orbit time, the xenon leakage amount m2 was calculated.

[0050] Based on the xenon flow rate and the working time of each working stage, the xenon consumption m1 under the pretreatment condition, the xenon consumption m3 under the preheating mode condition, and the xenon consumption m4 under the ignition condition are obtained.

[0051] Based on m0, m1, m3, and m4, the remaining amount of xenon gas m in the xenon cylinder and pipeline of the electric propulsion system is calculated.

[0052] In the above method for estimating the remaining amount of xenon gas in the electric propulsion system, m = m0 - m1 - m2 - m3 - m4.

[0053] In the above method for estimating the remaining xenon gas in the electric propulsion system, the preset pressure is 5 MPa.

[0054] The present invention has the following advantages:

[0055] (1) Currently, there are mature calculation methods for the remaining propellant in chemical propulsion systems in China. However, for electric propulsion systems, due to their new technology and limited on-orbit applications, there is no mature method for calculating the remaining xenon. This invention proposes an on-orbit xenon remaining quantity estimation method for electric propulsion systems, which is applicable to estimating the remaining xenon working propellant in electric propulsion systems. It can effectively assess the remaining xenon quantity and evaluate the spacecraft's lifespan.

[0056] (2) For the PρT method based on the physical properties of xenon, the study on the physical properties of xenon covering the on-orbit operation of electric propulsion has been completed in the early stage, and complete experimental data has been obtained. Therefore, the remaining amount of xenon can be calculated based on flight data such as on-orbit temperature and pressure. For the integrated electric propulsion on-orbit xenon consumption method, it can be calculated based on data such as system leakage rate, on-orbit time, and ignition duration.

[0057] (3) The accuracy of the two calculation methods can be accurately evaluated, thereby enabling accurate prediction of the state of the spacecraft's electric propulsion system. Attached Figure Description

[0058] Figure 1 This is a flowchart illustrating the steps of a method for estimating the remaining amount of xenon gas in an electric propulsion system according to an embodiment of the present invention.

[0059] Figure 2 This is a PρT relationship diagram of Xe in an embodiment of the present invention. Detailed Implementation

[0060] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments disclosed in the present invention will be described in further detail below with reference to the accompanying drawings.

[0061] One of the core ideas of this invention is to disclose a method for estimating the remaining amount of xenon in an electric propulsion system in orbit. This method is based on two calculation methods: the PρT (pressure density temperature) method based on the physical properties of xenon and the integrated electric propulsion method for on-orbit xenon consumption. In practical applications, the calculation accuracy of the two methods is compared at a specific time based on on-orbit flight data, and the method with higher measurement accuracy is used to estimate the remaining amount of xenon working propellant.

[0062] like Figure 1 In this embodiment, the method for estimating the remaining on-orbit xenon gas in the electric propulsion system includes:

[0063] Step 1: Obtain the pressure of the xenon cylinder for the electric propulsion system.

[0064] Step 2: Determine the relationship between the pressure of the xenon cylinder of the electric propulsion system and the preset pressure.

[0065] In this embodiment, when the pressure of the xenon cylinder of the electric propulsion system is less than or equal to the preset pressure, step 3 is executed; when the pressure of the xenon cylinder of the electric propulsion system is greater than the preset pressure, step 4 is executed. Preferably, the preset pressure can be 5 MPa.

[0066] Step 3: Based on the contrastive state theory, calculate the remaining amount of xenon gas in the xenon cylinder and pipeline of the electric propulsion system.

[0067] In this embodiment, the relative state theory refers to the fact that for all matter, its state variables, after being dimensionless, follow universal laws of change. The specific implementation process of step 3 is as follows:

[0068] Sub-step 301: Obtain the temperature and pressure of the xenon gas in the xenon cylinder and pipeline of the electric propulsion system.

[0069] Sub-step 302 involves dimensionlessly processing the obtained temperature and pressure of the xenon gas in the xenon cylinder and pipeline of the electric propulsion system to obtain dimensionless temperature T and dimensionless pressure P of the xenon gas.

[0070] In this embodiment, firstly, the critical point temperature T0 and critical point pressure P0 of xenon are determined. Then, the obtained temperatures and pressures of xenon in the xenon cylinder and pipeline of the electric propulsion system are divided by the critical point temperature T0 and critical point pressure P0, respectively, to obtain the dimensionless temperature T and dimensionless pressure P of xenon.

[0071] In sub-step 303, the dimensionless temperature T and dimensionless pressure P of the obtained xenon gas are substituted into the BWR equation to calculate the dimensionless density ρ of methane.

[0072] In this embodiment, the BWR (Benedict Webb Rubinequation) equation is expressed as follows:

[0073]

[0074] Among them, A n The coefficients of the BWR equation are r = 0.0096.

[0075] Further:

[0076] A1=R v T

[0077] A2=N1T+N2T 1 / 2 +N3+N4 / T+N5 / T 2

[0078] A3=N6+N7+N8 / T+N9 / T 2

[0079] A4=N 10 T+N 11 +N 12 / T

[0080] A5=N 13

[0081] A6=N 14 / T+N 15 / T 2

[0082] A7=N 16 / T

[0083] A8=N 17 / T+N 18 / T 2

[0084] A9=N 19 / T 2

[0085] A 10 =N 20 / T 2 +N 21 / T 3

[0086] A 11 =N 22 / T 2 +N 23 / T 4

[0087] A 12 =N 24 / T 2 +N 25 / T 3

[0088] A 13 =N 26 / T 2 +N 27 / T 4

[0089] A 14 =N 28 / T 2+N 29 / T 3

[0090] A 15 =N 30 / T 2 +N 31 / T 3 +N 32 / T 4

[0091] Among them, R v The ideal gas constant is a number; N 1～32 Given the known quantities, refer to the parameter values ​​of fluid CH4.

[0092] Furthermore, N 1～32 =

[0093] [-1.184347314485E-2,7.540377272657E-1,-1.225769717554E+1,6.260681393432E+2 ,-3.490654409121E+4,5.301046385532E-4,-2.875764479978E-1,5.011947936427E+1 ,-2.821562800903E+2,-2.064957753744E-3,1.285951844828E-2,-1.106266656726E+ 0,3.060813353408E-4,-3.174982181302E-3,5.191608004779E+0,-3.074944210271E- 4,1.071143181503E-5,-9.290851745353E-3,1.610140169312E-4,3.469830970789E+4 ,-1.370878559048E+6,1.790105676252E+2,1.615880743238E+6,6.265306650288E-1, 1.820173769533E+1,1.449888505811E-3,-3.159999123798E+1,-5.290335668451E-6, 1.694350244152E-3, 8.612049038886E-9, -2.598235689063E-6, 3.153374374912E-5].

[0094] Sub-step 304: According to the theory of contrastive states, the calculated dimensionless density ρ of methane is divided by the critical point density of xenon to obtain the density of xenon in the xenon cylinder and pipeline at a specific temperature and pressure.

[0095] Sub-step 305: Multiply the calculated density of xenon gas in the xenon cylinder and pipeline at a specific temperature and pressure by the volume of the xenon cylinder and pipeline, respectively; add the two product results to obtain the remaining amount of xenon gas in the electric propulsion system.

[0096] Step 4: Calculate the remaining xenon amount in the xenon cylinder and pipeline of the electric propulsion system based on the initial xenon filling amount and the xenon consumption amount in each working process.

[0097] In this embodiment, the specific implementation process of step 4 is as follows:

[0098] Sub-step 401: Obtain the initial xenon gas filling amount m0 ​​of the electric propulsion system by weighing using an electronic scale.

[0099] Sub-step 402: Based on the leakage rate of the electric propulsion system and the on-orbit time, the xenon leakage amount m2 is calculated.

[0100] Sub-step 403: Based on the xenon flow rate and the working time of each working stage, obtain the xenon consumption m1 under the pretreatment condition, the xenon consumption m3 under the preheating mode condition, and the xenon consumption m4 under the ignition condition.

[0101] Sub-step 404: Based on m0, m1, m3 and m4, calculate the remaining amount of xenon gas m in the xenon cylinder and pipeline of the electric propulsion system: m = m0 - m1 - m2 - m3 - m4.

[0102] As can be seen from the above embodiments, the present invention employs two schemes to estimate the remaining amount of xenon in orbit: the PρT (pressure density temperature) method based on the physical properties of xenon and the on-orbit xenon consumption method based on integrated electric propulsion. The specific implementation process of the two estimation methods is described in detail below.

[0103] I. PρT Method Based on Xenon Physical Properties

[0104] 1) Calculation principle

[0105] All substances, under different combinations of pressure and temperature, may exhibit various states, including solid, liquid, gas-liquid mixture, gas, and supercritical state, with corresponding definite densities. For Xe, its phase transition (density) and the relationship between pressure and temperature are as follows: Figure 2 As shown. By Figure 2It is known that xenon is in a gaseous state when the temperature is above 16.6℃, and in a supercritical state when the pressure is above 5.84MPa. In the supercritical state, xenon exhibits a liquid-like density but flows like a gas. During in-orbit operation, the xenon cylinder for electric propulsion operates at a temperature of 20–45℃ and a pressure of 15–0.5MPa. Within this temperature and pressure range, xenon exists in both supercritical and gaseous states, preventing the formation of liquid xenon and ensuring a continuous and stable flow rate of xenon working fluid for the electric thruster. Since the volume of the xenon cylinder remains constant, and the xenon density is determined by its temperature and pressure, the mass of xenon within the cylinder can be obtained in real-time by measuring its temperature and pressure in orbit.

[0106] This invention, through experimental research on the physical properties of xenon, obtains a method for calculating the physical properties of xenon based on the principle of contrastive states, achieving high-precision solution of the xenon physical property parameters using the non-analytical BWR equation. When solving for the density of Xe using the principle of contrastive states, the temperature and pressure parameters of Xe are first dimensionlessly processed. Then, the parameters corresponding to the reference fluid CH4 are obtained using the contrastive state theory. Based on this, the density of CH4 is obtained by inversely solving the BWR equation, and finally, the state parameters of Xe are obtained according to the contrastive state theory.

[0107] The BWR equation combines the temperature polynomial with the power series and exponent of density, and its specific form is as follows:

[0108]

[0109] 2) Calculation accuracy analysis

[0110] Depend on Figure 2 It is known that, under the same temperature conditions, the density of xenon gas exhibits a non-linear change with pressure. Furthermore, when the pressure exceeds 5 MPa, there is a sharp increase in density caused by pressure changes, with the degree and extent of this increase varying at different temperatures. Therefore, when the pressure exceeds 5 MPa, using the PρT method to assess the remaining xenon gas quantity will result in significant deviations.

[0111] Currently, the onboard pressure transmission accuracy is 0.5%, and the temperature measurement accuracy is 0.5℃. Tables 1-3 calculate the maximum density deviation caused by pressure and temperature differences, using temperatures of 20℃, 30℃, and 40℃ as examples. As the temperature increases, the slope of the density-pressure curve decreases, and the maximum error also decreases. The maximum error reaches 7.6% at 20℃, but is only 0.7% at 20℃.

[0112]

[0113] Table 1. Error Analysis of Xenon Density at 20℃

[0114]

[0115] Table 2. Error Analysis of Xenon Density at 30℃

[0116]

[0117] Table 3. Error Analysis of Xenon Density at 40℃

[0118] II. On-orbit Xenon Consumption Method Based on Integrated Electric Propulsion

[0119] 1) Calculation principle

[0120] The on-orbit consumption of xenon propellant for electric propulsion mainly consists of system pretreatment consumption, xenon leakage, xenon consumption during preheating mode, and thruster ignition consumption. Therefore, the formula for calculating the remaining xenon quantity can be determined as follows:

[0121] m = m0 - m1 - m2 - m3 - m4

[0122] 2) Calculation accuracy analysis

[0123] Ignition consumption accounts for more than 90% of the total xenon consumption in orbit. Therefore, the accuracy of the calculation of xenon working fluid consumption in orbit is mainly determined by the accuracy of the calculation of ignition consumption.

[0124] The calculation of ignition consumption can be based on ground calibration of xenon gas flow during electric thruster ignition and telemetry data such as on-orbit ignition duration. This allows for the calculation of xenon propellant consumption for a single thruster, which can then be accumulated to obtain the xenon propellant consumption for all thrusters. The xenon propellant required for electric thruster ignition is supplied by the storage and supply unit, with a continuously stable flow rate. Furthermore, electric propulsion on-orbit ignition is essentially a constant steady-state ignition under a fixed flow rate. Therefore, the accuracy of ignition consumption is basically consistent with the flow control accuracy achievable by the storage and supply unit.

[0125] The thruster ignition process is controlled remotely from the ground or autonomously on the spacecraft, and the on-orbit ignition duration can be accurately recorded. Therefore, the accounting method is used to calculate the remaining propellant amount, and its accuracy mainly depends on the flow control accuracy of the storage and supply unit, i.e., 1% to 3%.

[0126] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solutions of the present invention by utilizing the methods and techniques disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solutions of the present invention shall fall within the protection scope of the technical solutions of the present invention.

[0127] The contents not described in detail in this specification are common knowledge to those skilled in the art.

Claims

1. A method for estimating the remaining xenon gas in orbit for an electric propulsion system, characterized in that, include: To obtain the pressure of the xenon cylinder in the electric propulsion system; Determine the relationship between the pressure of the xenon cylinder in the electric propulsion system and the preset pressure; When the pressure of the xenon cylinder in the electric propulsion system is less than or equal to the preset pressure, the remaining amount of xenon in the xenon cylinder and pipeline of the electric propulsion system is calculated based on the contrastive state theory. This includes: obtaining the temperature and pressure of the xenon in the xenon cylinder and pipeline of the electric propulsion system; and performing dimensionless processing on the obtained temperature and pressure of the xenon in the xenon cylinder and pipeline of the electric propulsion system to obtain the dimensionless temperature of the xenon. and dimensionless pressure The dimensionless temperature of the obtained xenon gas. and dimensionless pressure Substituting into the BWR equation, the dimensionless density of methane is calculated. Based on the theory of relative states, the dimensionless density of methane was calculated. Divide by the critical point density of xenon to obtain the density of xenon in the xenon cylinder and pipeline at a specific temperature and pressure; multiply the calculated density of xenon in the xenon cylinder and pipeline at a specific temperature and pressure by the volume of the xenon cylinder and pipeline respectively; add the two products together to obtain the remaining amount of xenon in the electric propulsion system. When the pressure of the xenon cylinder of the electric propulsion system is greater than the preset pressure, the remaining amount of xenon in the xenon cylinder and pipeline of the electric propulsion system is calculated based on the initial xenon filling amount of the electric propulsion system and the xenon consumption amount in each working process. The BWR equation is expressed as follows: ···（1） in, The coefficients of the BWR equation, .

2. The method for estimating the remaining on-orbit xenon gas in an electric propulsion system according to claim 1, characterized in that, The temperature and pressure of the xenon gas in the xenon cylinder and pipeline of the electric propulsion system were obtained by dimensionless processing to obtain the dimensionless temperature of the xenon gas. and dimensionless pressure ,include: Determining the critical point temperature of xenon and critical point pressure ; The obtained temperatures and pressures of the xenon gas in the xenon cylinders and pipelines of the electric propulsion system were divided by the critical point temperature. and critical point pressure The dimensionless temperature of xenon was obtained. and dimensionless pressure .

3. The method for estimating the remaining on-orbit xenon gas in an electric propulsion system according to claim 1, characterized in that, in, The ideal gas constant is a number; Given the known quantities, refer to the parameter values ​​of fluid CH4.

4. The method for estimating the remaining on-orbit xenon gas in an electric propulsion system according to claim 3, characterized in that, [-1.184347314485E-2, 7.540377272657E-1,-1.225769717554E+1,6.260681393432E+2,-3.490654409121E +4,5.301046385532E-4,-2.875764479978E-1,5.011947936427E+1,-2.82156280090 3E+2,-2.064957753744E-3,1.285951844828E-2,-1.106266656726E+0,3.06081335 3408E-4,-3.174982181302E-3,5.191608004779E+0,-3.074944210271E-4,1.071143 181503E-5,-9.290851745353E-3,1.610140169312E-4,3.469830970789E+4,-1.370 878559048E+6,1.790105676252E+2,1.615880743238E+6,6.265306650288E-1,1.820 173769533E+1,1.449888505811E-3,-3.159999123798E+1,-5.290335668451E-6,1. 694350244152E-3, 8.612049038886E-9, -2.598235689063E-6, 3.153374374912E-5].

5. The method for estimating the remaining on-orbit xenon gas in an electric propulsion system according to claim 1, characterized in that, The theory of contrastive states states that for all matter, after being dimensionless, its state variables follow universal laws of change.

6. The method for estimating the remaining on-orbit xenon gas in an electric propulsion system according to claim 1, characterized in that, Based on the initial xenon refueling amount and the xenon consumption during each working process of the electric propulsion system, the remaining xenon amount in the xenon cylinders and pipelines of the electric propulsion system is calculated, including: The initial xenon gas loading amount for the electric propulsion system was determined based on the weighing data obtained from the electronic scale. ; The xenon leakage rate was calculated based on the electric propulsion system leakage rate and on-orbit time. ; Based on the xenon flow rate and the working duration of each stage, the xenon consumption under pretreatment conditions is obtained. Xenon consumption under preheating mode Xenon consumption under ignition conditions ; according to , , and The remaining amount of xenon gas in the xenon cylinders and pipelines of the electric propulsion system was calculated. .

7. The method for estimating the remaining on-orbit xenon gas in an electric propulsion system according to claim 6, characterized in that, 。 8. The method for estimating the remaining on-orbit xenon gas in an electric propulsion system according to claim 1, characterized in that, The preset pressure is 5 MPa.

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