Rapid calculation method for steady-state liquid level and liquid remaining amount in storage tank under microgravity

Abstract

The invention relates to a method for rapidly calculating a steady-state liquid level and a liquid residual amount in a storage tank under microgravity, which comprises the following steps of: deriving from a populus-Laplacian equation to obtain a theoretical expression of the steady-state liquid level in the storage tank with a central column and a theoretical expression of the steady-state liquid level in the storage tank without the central column under the microgravity; according to the theoretical expression of the steady-state liquid level in the storage box containing the central column and the theoretical expression of the steady-state liquid level in the storage box not containing the central column, in combination with the structural size of the storage box containing the central column and the structural size of the storage box not containing the central column, the volume expression of liquid in the storage box containing the central column and the volume expression of liquid in the storage box not containing the central column are obtained; according to the steady-state liquid level theoretical expression and the liquid volume expression in the storage tank containing the central column, the steady-state liquid level or the liquid remaining amount in the storage tank containing the central column is obtained; and according to the theoretical expression of the steady-state liquid level in the storage tank without the central column and the expression of the liquid volume, the steady-state liquid level or the liquid remaining amount in the storage tank without the central column is obtained. And rapid evaluation of the liquid surface morphology and the liquid residual amount is realized.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of spacecraft propulsion systems, and relates to a rapid calculation method for a steady-state liquid surface and a liquid residual amount in a tank under microgravity. BACKGROUND

[0002] Satellite life is an important factor affecting whether a satellite can fully play its value, and the main factor restricting the satellite life is the propellant carrying amount. Accurate and reliable detection of satellite propellant is not only an inevitable requirement for the development of aerospace technology, but also an important condition for ensuring the effective use of satellites and the overall completion of aerospace missions. The liquid surface morphology in the tank under microgravity is obviously different from that on the ground, and the liquid surface will exhibit obvious bending characteristics. The liquid residual amount measurement method commonly used on the ground cannot be used to measure the satellite propellant. In recent years, a propellant residual amount measurement method based on the thermal response characteristics of the tank wall has been developed. The measurement method is to paste heating sheets and temperature measuring points on the tank wall, heat the tank, and use the difference in thermal response characteristics when the wall is immersed in liquid and not immersed in liquid to identify the liquid surface position, so as to calculate the liquid residual amount in the tank. However, due to the obvious bending of the liquid surface under microgravity (microgravity: less than 10 -4 g), a clear conversion relationship is needed to calculate the liquid residual amount according to the position of the liquid surface on the wall. Previously, a finite element model needed to be established for each tank to carry out simulation analysis, so as to obtain the liquid surface morphology and the corresponding liquid residual amount under different working conditions. This work is tedious and inefficient. Therefore, it is necessary to use a new rapid calculation method to quickly evaluate the liquid surface morphology and the liquid residual amount. SUMMARY

[0003] The technical problem solved by the application is to overcome the shortcomings of the prior art and provide a liquid surface morphology and liquid residual amount rapid calculation method based on a mathematical model, which can quickly and accurately evaluate the liquid residual amount in a plate-type full management tank according to the liquid surface position, and overcome the shortcomings of the prior art that the simulation technology is used to predict the liquid surface morphology, which is time-consuming and inefficient.

[0004] The technical solution provided by the application is as follows:

[0005] A rapid calculation method for a steady-state liquid surface and a liquid residual amount in a tank under microgravity, comprising:

[0006] A steady-state liquid surface theoretical expression in a tank with a center column under microgravity and a steady-state liquid surface theoretical expression in a tank without a center column are obtained from the Young-Laplace equation;

[0007] According to the theoretical expression of the steady-state liquid surface in the center-column-containing tank and the structural size of the center-column-containing tank, the liquid volume expression in the center-column-containing tank is obtained; according to the theoretical expression of the steady-state liquid surface in the center-column-free tank and the structural size of the center-column-free tank, the liquid volume expression in the center-column-free tank is obtained;

[0008] For the center-column-containing tank, the steady-state liquid surface or the liquid residual amount in the center-column-containing tank is obtained according to the theoretical expression of the steady-state liquid surface in the center-column-containing tank and the liquid volume expression in the center-column-containing tank; for the center-column-free tank, the steady-state liquid surface or the liquid residual amount in the center-column-free tank is obtained according to the theoretical expression of the steady-state liquid surface in the center-column-free tank and the liquid volume expression in the center-column-free tank.

[0009] Further, the theoretical expression of the steady-state liquid surface in the center-column-containing tank is:

[0010]

[0011] In the formula, for the center-column-containing tank, the intersection point of the inner wall of the tank and the lowest point of the rotating shaft is taken as the center point O, the rotating shaft of the tank is taken as the z axis, and the axis perpendicular to the z axis and passing through the point O is taken as the r axis to obtain the cylindrical coordinate system rOz; the intersection point of the liquid surface profile and the center column is defined as point A, the lowest point or the highest point of the liquid surface profile is defined as point B, and the intersection point of the liquid surface profile and the inner wall of the tank is defined as point C; the coordinates of the point A are (r1, z1), the coordinates of the point B are (r2, z2), and the coordinates of the point C are (r3, z3); r1 and r3 are the horizontal coordinates of the points A and C respectively; the coordinates of any point on the liquid surface are (r, z); θ i represents the contact angle of the liquid and the center column, α i represents the inclination angle of the center column, θ o represents the contact angle of the liquid and the tank wall, α o represents the inclination angle of the tank wall, represents the inclination angle of the liquid surface at (r, z); r i is the radius of the center column at z, r o is the radius of the outer wall at z.

[0012] Further, the theoretical expression of the steady-state liquid surface in the center-column-containing tank is:

[0013]

[0014] In the formula, for the tank without the central column, the lowest point of the inner wall of the tank is taken as the center point O', the rotation axis of the tank is taken as the z' axis, and the axis passing through the point O' and perpendicular to the z' axis is taken as the r' axis to obtain the cylindrical coordinate system r'O'z'; the coordinates of any point on the liquid surface are (r, z); θ represents the contact angle of the liquid on the wall, α represents the wall inclination angle, and r0 is the radius of the spherical tank; the intersection point of the liquid surface profile and the rotation axis of the tank is defined as the D point, the intersection point of the liquid surface profile and the inner wall of the tank is defined as the E point, and the coordinates of the D point are (0, z4) and the coordinates of the E point are (r5, z5).

[0015] Further, the liquid volume expression in the tank with the central column is:

[0016] V l = V1+V2+V3

[0017]

[0018] In the formula, V l is the liquid volume in the tank without the central column.

[0019] Further, the liquid volume expression in the tank without the central column is: V l = V4-V5

[0020] In the formula, V l is the liquid volume, V4 is the spherical cap volume with the point E as the height, and V5 is the volume enclosed by the liquid surface profile around the rotation axis of the tank.

[0021] Further, for the tank with the central column, the steady-state liquid surface or the liquid remaining amount in the tank with the central column is obtained according to the steady-state liquid surface theoretical expression in the tank with the central column and the liquid volume expression in the tank with the central column, and includes:

[0022] S1, it is known that: given the tank configuration, r i , r o , given the liquid volume V l , and the liquid contact angles θ i and θ o , the C coordinate range is estimated according to the actual situation, and a plurality of C coordinates are determined.

[0023] S2, the A coordinate range is estimated according to the actual situation, and a plurality of A coordinates are determined.

[0024] S3, a C coordinate and a plurality of A coordinates corresponding to the C coordinate are substituted into the steady-state liquid surface theoretical expression in the tank with the central column to obtain the tangent value of the liquid surface inclination angle at the C coordinate and the A coordinate; whether the tangent value of the liquid surface inclination angle at the C coordinate and the A coordinate satisfies the boundary condition of the liquid surface profile inclination angle is judged, and the C coordinate and the A coordinate satisfying the boundary condition of the liquid surface profile inclination angle are combined as the correct C coordinate and A coordinate combination.

[0025] S4, repeat step S3 to calculate a plurality of correct C coordinate and A coordinate combinations; bring the plurality of correct C coordinate and A coordinate combinations into the theoretical expression of the steady-state liquid level in the center column-containing storage tank to calculate the corresponding complete liquid level profile; calculate the estimated liquid level volume according to the complete liquid level profile and the liquid volume expression in the center column-containing storage tank, and compare the estimated liquid level volume with the given liquid volume V l Obtain the closest estimated liquid level volume, and take the complete liquid level profile corresponding to the closest estimated liquid level volume as the correct complete liquid level profile.

[0026] Further, the plurality of C coordinates are respectively an estimated coordinate range initial value and sequentially increase by 0.01 mm from the estimated coordinate range initial value; and the plurality of A coordinates are respectively an estimated coordinate range initial value and sequentially increase by 0.01 mm from the estimated coordinate range initial value.

[0027] Further, for the center column-containing storage tank, the steady-state liquid level or the liquid remaining amount in the center column-containing storage tank is obtained according to the theoretical expression of the steady-state liquid level in the center column-containing storage tank and the liquid volume expression in the center column-containing storage tank, including:

[0028] S1, known: given storage tank configuration z = h(r), liquid volume V i , r o , given point C coordinate and liquid contact angle θ i and θ o , estimate the range of point A coordinate according to the actual situation, and determine a plurality of A coordinates;

[0029] S2, calculate the tangent value of the liquid level inclination at the C coordinate and the A coordinate according to the theoretical expression of the steady-state liquid level in the center column-containing storage tank by substituting the C coordinate (r3, z3) and the corresponding plurality of A coordinates; judge whether the tangent value of the liquid level inclination at the C coordinate and the A coordinate satisfies the boundary condition of the liquid level profile inclination, and the A coordinate that satisfies the boundary condition of the liquid level profile inclination is the combination under the given C coordinate, which is taken as the correct C coordinate and A coordinate combination;

[0030] S3, bring the correct C coordinate and A coordinate combination into the theoretical expression of the steady-state liquid level in the center column-containing storage tank to calculate the corresponding complete liquid level profile and liquid volume. Further, for the center column-free storage tank, the steady-state liquid level or the liquid remaining amount in the center column-free storage tank is obtained according to the theoretical expression of the steady-state liquid level in the center column-free storage tank and the liquid volume expression in the center column-free storage tank, including:

[0031] S1, known: given storage tank configuration z = h(r), liquid volume V land liquid contact angle θ, according to the actual situation, the estimated point E coordinate range is determined, and a plurality of E coordinates are determined; the plurality of E coordinates are respectively the initial value of the estimated coordinate range, and the initial value of the estimated coordinate range is increased by 0.01mm in turn; K is solved according to the estimated E coordinate; the point E coordinate is (r5, z5), then the liquid surface theoretical expression is solved in the range of 0≤r≤r5, and the liquid surface profile D point is obtained when r=0; the curve from point D to point E is the liquid surface profile; S2, according to the liquid surface profile and the shape function of the tank wall, the estimated liquid surface volume under the current point E coordinate is calculated, and the estimated liquid surface volume is compared with the liquid remaining amount (V l ) to obtain the closest estimated liquid surface volume, and the liquid surface corresponding to the closest estimated liquid surface volume is the correct liquid surface.

[0032] Further, for the tank without a central column, the steady-state liquid surface or the liquid remaining amount in the tank without a central column is obtained according to the steady-state liquid surface theoretical expression in the tank without a central column and the liquid volume expression in the tank without a central column, comprising:

[0033] S1, known: given tank configuration z=h(r), point E coordinate and liquid contact angle θ, according to the point E coordinate (r5, z5), the liquid surface theoretical expression is solved in the range of 0≤r≤r5, and the liquid surface profile D point is obtained when r=0; the curve from point D to point E is the liquid surface profile;

[0034] S2, according to the liquid surface profile and the shape function of the tank wall, the liquid volume under the current point E coordinate can be calculated.

[0035] The liquid surface profile and the liquid remaining amount can be quickly obtained according to certain input.

[0036] In summary, the present application at least includes the following beneficial technical effects:

[0037] The theoretical model of the liquid surface profile in the tank under microgravity established by the method is accurate, simple and easy to popularize; the calculation code is simple and clear, the calculation amount is small, the resource occupation is less, and the universality is strong. According to the tank shape, the liquid contact angle, and the liquid surface endpoint coordinate (or the liquid volume) under the actual working condition of the satellite, the steady-state liquid surface profile and the liquid remaining amount in the tank under microgravity can be calculated. The present application can provide technical guidance for the design of satellite propellant tanks and space station water tanks, and provide a calculation tool for on-orbit propellant remaining measurement, which can be applied to satellite platforms with plate-type full management tanks, and has considerable economic benefits and application prospects. BRIEF DESCRIPTION OF DRAWINGS

[0038] Figure 1 (a) steady-state liquid surface between coaxial rotating bodies under microgravity, (b) steady-state liquid surface in a rotating body under microgravity;

[0039] Figure 2 Three liquid regions V1, V2, V3 are shown in the figure;

[0040] Figure 3 In the figure Figure 3 (a) with central column tank, same filling rate, contact angle is 0°, 30°, 60°, 90°, 120°, 150°, 180° respectively, 3(b) without central column tank, same filling rate, contact angle is 5°, 25° and 45° respectively. DETAILED DESCRIPTION

[0041] In order to make the purpose, technical scheme and advantages of the present application more clear, the embodiments disclosed by the present application will be further described in detail below with reference to the drawings.

[0042] The embodiment of the present application discloses a method for quickly calculating the steady-state liquid level and the liquid remaining amount in a tank under microgravity. In a space environment, the effect of gravity is almost disappeared, and the liquid in a plate-type full management tank is mainly affected by surface tension, so the liquid surface is obviously curved. Since the tank is a rotating body, the liquid surface also has the characteristics of a rotating body, so a mathematical model of the two-dimensional liquid surface profile can be established, and the complete three-dimensional liquid surface topography can be obtained.

[0043] Since the plate-type tank can be divided into two configurations with and without a central column, first, the liquid surface topography schematic diagram of the tank with and without a central column under microgravity is created, as shown in (a) and (b) of the drawings. For the tank with a central column, the intersection point of the inner wall surface of the tank and the lowest point of the rotation axis is taken as the center point O, the rotation axis of the tank is taken as the z axis, and the axis passing through the point O and perpendicular to the z axis is taken as the r axis to obtain the cylindrical coordinate system rOz. For the tank without a central column, the intersection point of the inner wall surface of the tank and the lowest point of the rotation axis of the tank is taken as the center point O', the rotation axis of the tank is taken as the z' axis, and the axis passing through the point O' and perpendicular to the z' axis is taken as the r' axis to obtain the cylindrical coordinate system r'O'z'. The shaded area in the figure represents the liquid. Figure 1

[0044] The cylindrical coordinate system rOz is used for theoretical derivation, and the mathematical model of the liquid surface topography in the two tanks is established by starting from the Young-Laplace equation.

[0045] The theoretical expression of the steady-state liquid surface in the tank with a central column under microgravity is:

[0046]

[0047] In the formula, the intersection point of the liquid surface profile and the central column is point A, the lowest point or the highest point of the liquid surface profile is point B, and the intersection point of the liquid surface profile and the inner wall surface of the tank is point C. The coordinates of point A are (r1, z1), the coordinates of point B are (r2, z2), and the coordinates of point C are (r3, z3). r1 and r3 are the horizontal coordinates of points A and C respectively. θ i ​represents the contact angle between the liquid and the central column, α i represents the inclination angle of the central column, θ o Represents the contact angle between the liquid and the tank wall, α o represents the inclination angle of the tank wall, represents the liquid surface inclination angle at the point (r, z); r i is the radius of the central column at z, r o is the outer wall radius at z.

[0048] like Figure 2 As shown, the expression for liquid volume is:

[0049] V l =V1+V2+V3(2.1)

[0050]

[0051] In the formula, V1, V2 and V3 represent the three regions of the liquid, such as Figure 2 shown.

[0052] The theoretical expression of the steady-state liquid level in a tank without a central column under microgravity is:

[0053]

[0054] Here, θ represents the contact angle of the liquid on the wall, α represents the wall inclination, r0 is the radius of the spherical tank, r5 is the abscissa of point E, (r, z) are the coordinates of any point on the steady-state liquid surface within the tank, point D has coordinates (0, z4), and point E has coordinates (r5, z5). The above formula shows that the liquid surface morphology is only related to the wall geometry, the liquid contact angle, and the liquid volume.

[0055] Then, according to the mathematical model, the calculation program is compiled using the shooting method. There are two types of calculation programs. The first type is to calculate the liquid contact angle (θ, θ) under a given tank configuration. i ,θ o ) and the remaining liquid volume (V l ), the second method is to quickly solve the liquid surface morphology when the tank configuration and liquid contact angle (θ, θ i ,θ o ) and the liquid surface endpoint coordinates C or E, quickly solve the remaining liquid amount.

[0056] For tanks with center columns:

[0057] The calculation process of the first program is as follows (given: given tank configuration, r i , r o , given the liquid volume V l Contact angle θ with liquid i ,θ o ):

[0058] 1. Estimate the coordinate range of point C according to the actual situation, determine multiple C coordinates, and the multiple C coordinates are respectively the initial value of the estimated coordinate range and the initial value of the estimated coordinate range increased by 0.01 mm in turn;

[0059] 2. Estimate the coordinate range of point A according to the actual situation, determine multiple A coordinates, and the multiple A coordinates are respectively the initial value of the estimated coordinate range and the initial value of the estimated coordinate range increased by 0.01 mm in turn;

[0060] 3. Substitute one C coordinate and the corresponding multiple A coordinates into the liquid surface profile expression (1.1) to calculate the tangent value of the liquid surface inclination angle at the C coordinate and the A coordinate, judge whether the boundary condition of the liquid surface profile inclination angle is satisfied, and combine the C coordinate and the A coordinate that satisfy the boundary condition of the liquid surface profile inclination angle as the correct combination of the C coordinate and the A coordinate;

[0061] 4. Repeat step 3 to calculate each C coordinate to obtain multiple correct combinations of C coordinates and A coordinates; bring the multiple correct combinations of C coordinates and A coordinates into the liquid surface profile expression (1.1), that is, use the ODE45 program (or other ordinary differential equation solving method) to solve formula (1.1) to obtain the corresponding complete liquid surface profile; according to the complete liquid surface profile and formulas (2.1)-(2.4), calculate the estimated liquid surface volume, compare the estimated liquid surface volume with the liquid remaining amount (V l ), obtain the closest estimated liquid surface volume, and the liquid surface corresponding to the closest estimated liquid surface volume is the correct liquid surface.

[0062] The second program calculation process is as follows (known: given tank configuration, r i , r o , given point C coordinate, liquid contact angle θ i , θ o ):

[0063] 1. First, estimate the coordinate range of point A according to the actual situation, determine multiple A coordinates, and the multiple A coordinates are respectively the initial value of the estimated coordinate range and the initial value of the estimated coordinate range increased by 0.01 mm in turn;

[0064] 2. Substitute the C coordinate and the corresponding multiple A coordinates into the liquid surface profile expression (1.1) to calculate the tangent value of the liquid surface inclination angle at the C coordinate and the A coordinate, judge whether the boundary condition of the liquid surface profile inclination angle is satisfied, and the A coordinate that satisfies the boundary condition of the liquid surface profile inclination angle is the combination under the given C coordinate;

[0065] 3. The correct C coordinates and A coordinates are combined into the liquid surface profile expression (1.1), that is, the formula (1.1) is solved by using the ODE45 program (or other ordinary differential equation solving method) to obtain the corresponding complete liquid surface profile; the liquid volume is calculated according to the complete liquid surface profile and the formulas (2.1)-(2.4).

[0066] For the tank without a central column:

[0067] The first procedure is calculated as follows (known: given tank configuration z = h(r), given liquid volume V l , liquid contact angle θ):

[0068] The E coordinate range is estimated according to the actual situation, and the calculation is performed every 0.01 mm from the initial value of the estimated coordinate range. The formula (3.1) is an analytical solution of the liquid surface profile, and there is only one unknown constant K in the formula, which can be solved according to the estimated E coordinate. Then the formula (3.1) is directly solved in the range of 0≤r≤r5, and r = 0 is the liquid surface profile D point. The curve from the point D to the point E is the liquid surface profile;

[0069] According to the liquid surface profile and the tank wall surface shape function, the estimated liquid volume at the current point E coordinate can be calculated. The estimated liquid volume is compared with the remaining liquid volume (V l ), and the closest estimated liquid volume is obtained, and the liquid surface corresponding to the closest estimated liquid volume is the correct liquid surface.

[0070] The second procedure is calculated as follows (known: given tank configuration z = h(r), given point E coordinate, liquid contact angle θ):

[0071] According to the point E coordinate (r5, z5), the formula (3.1) is solved in the range of 0≤r≤r5, and r = 0 is the liquid surface profile D point. The curve from the point D to the point E is the liquid surface profile;

[0072] According to the liquid surface profile and the tank wall surface shape function, the liquid volume at the current point E coordinate can be calculated.

[0073] The liquid surface profiles of the same liquid volume and different contact angles calculated by the first procedure are shown in Figs. Figure 3 (a) and 3(b), and the curves in the figures represent the liquid surface profile.

[0074] The method has two embodiments. In the first embodiment, the method is embedded in the software for calculating the remaining propellant on the satellite, and the parameters such as the configuration of the tank and the contact angle of the liquid are configured according to the actual situation on the satellite. When the on-orbit hot spot method is enabled, the liquid surface position identified by the hot spot method is inputted, and the remaining liquid is automatically calculated. In the second embodiment, the parameters such as the configuration of the tank and the contact angle of the liquid are configured according to the actual situation on the satellite, and the liquid surface morphology and the remaining liquid corresponding to different liquid surface positions are calculated, so as to compile an engineering parameter table. When the on-orbit hot spot method is enabled, the liquid surface position identified by the hot spot method is inputted, and the remaining liquid is obtained by inquiring the engineering parameter table.

[0075] The contents not described in detail in the specification of the present application are the known technologies of those skilled in the art.

[0076] The present application is described in detail above in combination with the specific embodiments and exemplary examples, but these descriptions cannot be understood as limitations of the present application. Those skilled in the art understand that the technical solutions and embodiments of the present application can be variously replaced, modified or improved without departing from the spirit and scope of the present application, and these all fall within the scope of the present application. The protection scope of the present application is subject to the appended claims.

Claims

1. A method for rapidly calculating the steady-state liquid level and the remaining amount of liquid in a tank under microgravity, characterized in that: include: The theoretical expressions of steady-state liquid level in a tank with a central column and without a central column under microgravity are derived from the Young-Laplace equation. According to the theoretical expression of the steady-state liquid level in the tank containing the central column and the structural dimensions of the tank containing the central column, the expression of the liquid volume in the tank containing the central column is obtained; Based on the theoretical expression of the steady-state liquid level in the tank without a central column and the structural dimensions of the tank without a central column, the expression of the liquid volume in the tank without a central column is obtained; For a storage tank containing a central column, the steady-state liquid level or the remaining liquid amount in the storage tank containing the central column is obtained based on the theoretical expression of the steady-state liquid level in the storage tank containing the central column and the expression of the liquid volume in the storage tank containing the central column; for a storage tank not containing a central column, the steady-state liquid level or the remaining liquid amount in the storage tank not containing a central column is obtained based on the theoretical expression of the steady-state liquid level in the storage tank not containing a central column and the expression of the liquid volume in the storage tank not containing a central column.

2. The method for rapidly calculating the steady-state liquid level and the remaining amount of liquid in a tank under microgravity according to claim 1, characterized in that: The theoretical expression of the steady-state liquid level in the tank containing the central column is: In the formula, for a tank with a central column, the intersection of the tank inner wall and the lowest point of the rotation axis is taken as the center point O, the tank rotation axis is taken as the z-axis, and the axis passing through point O and perpendicular to the z-axis is taken as the r-axis to obtain the cylindrical coordinate system rOz; the intersection of the liquid surface profile and the central column is defined as point A, the lowest or highest point of the liquid surface profile is defined as point B, and the intersection of the liquid surface profile and the tank inner wall is defined as point C; the coordinates of point A are (r1, z1), the coordinates of point B are (r2, z2), and the coordinates of point C are (r3, z3); ​​r1 and r3 are the horizontal coordinates of points A and C, respectively; the coordinates of any point on the liquid surface are (r, z); θ i represents the contact angle between the liquid and the central column, α i represents the inclination angle of the central column, θ o Represents the contact angle between the liquid and the tank wall, α o represents the inclination angle of the tank wall, represents the liquid surface inclination angle at (r, z); r i is the radius of the central column at z, r o is the outer wall radius at z.

3. The method for rapidly calculating the steady-state liquid level and the remaining amount of liquid in a tank under microgravity according to claim 1, characterized in that: The theoretical expression of the steady-state liquid level in the tank without the central column is: Wherein, for a tank without a central column, the cylindrical coordinate system r'O'z' is obtained with the lowest point of the tank inner wall as the center point O', the tank rotation axis as the z'-axis, and the axis passing through point O' and perpendicular to the z'-axis as the r'-axis. The coordinates of any point on the liquid surface are (r, z); θ represents the contact angle of the liquid on the wall, α represents the inclination angle of the wall, and r0 is the radius of the spherical tank. The intersection of the liquid surface contour and the tank rotation axis is defined as point D, and the intersection of the liquid surface contour and the tank inner wall is defined as point E. The coordinates of point D are (0, z4), and the coordinates of point E are (r5, z5).

4. The method for rapidly calculating the steady-state liquid level and the remaining amount of liquid in a tank under microgravity according to claim 2, characterized in that: The liquid volume in the tank containing the central column is expressed as follows: V l =V1+V2+V3 Where V l It is the volume of liquid in the tank excluding the center column.

5. The method for rapidly calculating the steady-state liquid level and the remaining amount of liquid in a tank under microgravity according to claim 3, characterized in that: The volume of the liquid in the tank without the central column is expressed as: V l =V4-V5 Where V l is the volume of the liquid, V4 is the volume of the spherical cap with point E as the height, and V5 is the volume enclosed by the liquid surface contour around the rotation axis of the tank.

6. The method for rapidly calculating the steady-state liquid level and the remaining amount of liquid in a tank under microgravity according to claim 2, characterized in that: For the storage tank containing the central column, obtaining the steady-state liquid level or the remaining amount of liquid in the storage tank containing the central column according to the theoretical expression of the steady-state liquid level in the storage tank containing the central column and the expression of the liquid volume in the storage tank containing the central column includes: S1. Given: given tank configuration, r i 、r o , given liquid volume V l and the liquid contact angle θ i and θ o When the point C coordinate range is estimated according to the actual situation, multiple C coordinates are determined; S2. Estimate the coordinate range of point A according to the actual situation and determine multiple A coordinates; S3. Substituting a C coordinate and corresponding multiple A coordinates into a theoretical expression for the steady-state liquid level in a tank containing a central column to perform calculations, obtaining the tangent values ​​of the liquid surface inclination angles at the C coordinates and the A coordinates; determining whether the tangent values ​​of the liquid surface inclination angles at the C coordinates and the A coordinates meet the boundary conditions of the liquid surface contour inclination angle, and determining the C coordinate and A coordinate combination that meets the boundary conditions of the liquid surface contour inclination angle as the correct C coordinate and A coordinate combination; S4. Repeat step S3 and calculate each C coordinate to obtain multiple correct C coordinate and A coordinate combinations; bring the multiple correct C coordinate and A coordinate combinations into the theoretical expression of the steady-state liquid level in the tank containing the central column to calculate and obtain the corresponding complete liquid surface morphology; calculate the estimated liquid surface volume based on the complete liquid surface morphology and the liquid volume expression in the tank containing the central column, and compare the estimated liquid surface volume with the given liquid volume V l By comparison, the closest estimated liquid surface volume is obtained, and the complete liquid surface morphology corresponding to the closest estimated liquid surface volume is taken as the correct complete liquid surface morphology.

7. The method for rapidly calculating the steady-state liquid level and the remaining amount of liquid in a tank under microgravity according to claim 6, characterized in that: The multiple C coordinates are respectively the initial values ​​of the estimated coordinate range, and are sequentially increased by 0.01 mm from the initial values ​​of the estimated coordinate range; the multiple A coordinates are respectively the initial values ​​of the estimated coordinate range, and are sequentially increased by 0.01 mm from the initial values ​​of the estimated coordinate range.

8. The method for rapidly calculating the steady-state liquid level and the remaining amount of liquid in a tank under microgravity according to claim 2, characterized in that: For the storage tank containing the central column, obtaining the steady-state liquid level or the remaining amount of liquid in the storage tank containing the central column according to the theoretical expression of the steady-state liquid level in the storage tank containing the central column and the expression of the liquid volume in the storage tank containing the central column includes: S1. Given: given tank configuration, r i 、r o , given point C coordinates and liquid contact angle θ i and θ o When , estimate the coordinate range of point A according to the actual situation and determine multiple A coordinates; S2. Substituting the coordinates (r3, z3) of point C and the corresponding multiple A coordinates into the theoretical expression of the steady-state liquid level in the tank containing the central column for calculation, obtain the tangent values ​​of the liquid surface inclination angles at the C coordinates and the A coordinates; determining whether the tangent values ​​of the liquid surface inclination angles at the C coordinates and the A coordinates meet the boundary conditions of the liquid surface profile inclination angle. The A coordinate that meets the boundary conditions of the liquid surface profile inclination angle is the combination under the given C coordinate, which is regarded as the correct C coordinate and A coordinate combination; S3. Substitute the correct C coordinate and A coordinate combination into the theoretical expression of the steady-state liquid level in the tank containing the central column for calculation to obtain the corresponding complete liquid surface morphology and liquid volume.

9. The method for rapidly calculating the steady-state liquid level and the remaining amount of liquid in a tank under microgravity according to claim 3, characterized in that: For the storage tank without a central column, obtaining the steady-state liquid level or the remaining amount of liquid in the storage tank without a central column according to the theoretical expression of the steady-state liquid level in the storage tank without a central column and the expression of the liquid volume in the storage tank without a central column includes: S1. Given: tank configuration z = h(r), liquid volume V l and the liquid contact angle θ, estimate the coordinate range of the point E according to the actual situation, and determine multiple E coordinates; the multiple E coordinates are the initial value of the estimated coordinate range, and the initial value of the estimated coordinate range is increased by 0.01mm; K is obtained by solving the estimated E coordinate; the coordinate of the point E is (r5, z5), and then the theoretical expression of the liquid surface is solved in the range of 0≤r≤r5. When r=0, it is the liquid surface contour point D, and the curve from point D to point E is the liquid surface contour; S2, according to the liquid surface contour and the tank wall shape function, calculate the estimated liquid surface volume at the current point E coordinate, and compare the estimated liquid surface volume with the liquid remaining amount (V l ) for comparison to obtain the closest estimated liquid level volume, and the liquid level corresponding to the closest estimated liquid level volume is the correct liquid level.

10. The method for rapidly calculating the steady-state liquid level and the remaining amount of liquid in a tank under microgravity according to claim 3, characterized in that: For the storage tank without a central column, obtaining the steady-state liquid level or the remaining amount of liquid in the storage tank without a central column according to the theoretical expression of the steady-state liquid level in the storage tank without a central column and the expression of the liquid volume in the storage tank without a central column includes: S1. Given the tank configuration z = h(r), the coordinates of point E, and the liquid contact angle θ, solve the theoretical expression for the liquid surface in the range 0 ≤ r ≤ r 5 based on the coordinates of point E (r5, z5). When r = 0, the liquid surface contour is point D. The curve from point D to point E is the liquid surface contour. S2. Based on the liquid surface contour and the tank wall shape function, the liquid volume at the current point E coordinate can be calculated.

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