A method for calculating the restoring force caused by the surface tension of liquid fuel in a storage tank

Abstract

This invention relates to a method for calculating the restoring force caused by the surface tension of liquid fuel in a storage tank: A ground-based scaled-down storage tank control group is constructed, comprising three sets of scaled-down storage tanks, with each set consisting of two tanks filled with different test solutions; a ground swaying test is conducted on the ground-based scaled-down storage tank control group, and the first-order swaying fundamental frequency is recorded; the first-order resonance process of each ground-based scaled-down storage tank in the ground swaying test is equivalent to that of a simple pendulum model; and the gravitational acceleration g between the control groups formed by the same scaled-down storage tank radius and different test solutions is calculated. mn Based on the proportional relationship between the internal liquid surface tension and the equivalent acceleration generated by the internal liquid surface tension, the equivalent acceleration generated by the internal liquid surface tension of the scaled-down tanks in various locations is calculated. According to the principle that the liquid-filled tank of the spacecraft is proportional to the Bond number of the on-orbit environment, the equivalent acceleration generated by the internal liquid surface tension under the actual on-orbit operating conditions is extrapolated, and then converted into the restoring force caused by the surface tension of the liquid fuel inside the tank.

Description

Technical Field

[0001] This invention belongs to the field of analysis of liquid fuel sloshing and redistribution in the tanks of on-orbit spacecraft. It relates to a method for calculating the magnitude of the force that the microgravity environment in on-orbit exerts on the surface tension of liquid fuel in the tank to maintain its initial equilibrium position. It can serve as an effective reference for estimating the frequency of on-orbit fuel sloshing in microgravity environments and for accurate modeling of rigid-liquid coupling dynamics. Background Technology

[0002] Traditional high-orbit satellites, spacecraft, and deep space probes carry large amounts of liquid fuel. Considering the low / microgravity environment in orbit, the surface tension of the liquid fuel has a more significant impact on its distribution and dynamic characteristics (compared to the normal gravity environment on Earth). This is because the ratio of the tension potential energy formed by the surface tension of the liquid to the mechanical potential energy formed by gravity (or inertial force) is significantly increased, and the surface tension potential energy always tends to decrease and remain at a minimum, regardless of the state. However, the in-orbit maneuver inevitably disturbs the liquid fuel inside the tank, resulting in two adverse effects: (1) The disturbed liquid may leave its initial equilibrium position and reposition itself to another location inside the tank; since the outlet inside the tank is fixed, the repositioned location may not cover the outlet, resulting in reduced liquid discharge efficiency or even engine ignition failure; (2) The sloshing of the disturbed liquid fuel will, in turn, affect the maneuvering process of the spacecraft (such as attitude jitter), which will undoubtedly reduce maneuvering efficiency and accuracy, and may even lead to mission failure.

[0003] The first type of influence usually occurs when the liquid fuel filling inside the tank is relatively small. At this time, the inside of the tank is relatively "empty", leaving more space for the liquid fuel to redistribute. Whether the liquid will redistribute depends mainly on whether the lateral (perpendicular to the normal direction of the free liquid surface) disturbance force on the liquid can exceed the restoring force generated by the liquid surface tension. Considering that the surface tension process is complex in low / microgravity environment, it is challenging to obtain the magnitude of the force of surface tension to maintain the initial equilibrium position.

[0004] The second type of influence is common in the field of aerospace engineering. An equivalent sway model (such as a pendulum model) is usually introduced into the spacecraft control system with a certain safety margin. However, when more precise and efficient attitude control is required, it is inevitable to introduce the influence of the restoring force generated by the surface tension of liquid fuel into the equivalent sway model. This is also rare in previous engineering application models related to sway.

[0005] However, the key to solving the problems affecting (1) and (2) is to answer the range of the restoring force generated by surface tension. Therefore, it is meaningful to find a method to measure the restoring force caused by the surface tension of liquid fuel inside the tank. Summary of the Invention

[0006] The technical problem solved by this invention is to overcome the shortcomings of the prior art and provide a method for calculating the restoring force caused by the surface tension of liquid fuel inside the propellant tank. By using a ground-based scaled-down propellant tank control group sway test, the magnitude of the restoring force generated by the surface tension of liquid fuel inside the spacecraft propellant tank can be measured and calculated. This can effectively deepen the understanding of the surface tension force of fuel inside the propellant tank in the aerospace engineering field and enhance the practical value of related engineering models.

[0007] The solution to the technical problem of this invention is: a method for calculating the restoring force caused by the surface tension of liquid fuel in a storage tank, the method comprising the following steps:

[0008] A ground-based scaled-down tank control group was constructed, comprising six scaled-down tanks, each with a shape identical to a cylindrical test tube with a hemispherical bottom. Each group consisted of two scaled-down tanks with the same characteristic radius, and each tank in the same group was filled with two different types of test solutions with different surface tension coefficients. The characteristic radii of the scaled-down tanks in different groups were different, corresponding to different Bond numbers in the on-orbit environment of the filled tanks.

[0009] Ground sway tests were conducted on the ground-scaled tank control group to observe the process of first-order resonance in each ground-scaled tank and record the corresponding excitation frequency, which was denoted as the first-order sway fundamental frequency f. mn m represents the type of test solution inside the scaled-down tank, m = 1, 2; n is the serial number of the control group of the scaled-down tank, n = 1 to 3;

[0010] The first-order resonance process of each scaled-down storage tank in the ground shaking test is equivalent to that of a simple pendulum model, and the gravitational acceleration g in the equivalent simple pendulum model is assumed to be... mn The local gravitational acceleration g at the ground shaking test site and the equivalent acceleration generated by the surface tension of the liquid inside the scaled-down tank at each location. sum;

[0011] Based on the gravitational acceleration g between control groups formed with the same scaled-down tank radius and different test solutions, mn The proportional relationship and the equivalent acceleration generated by the surface tension of the internal liquid The proportional relationship is used to solve for the equivalent acceleration generated by the surface tension of the liquid inside the scaled-down storage tank at various locations.

[0012] Based on the principle that the bond number of a spacecraft's liquid-filled tank is proportional to the bond number of the on-orbit environment, the equivalent acceleration generated by the surface tension of the internal liquid under actual on-orbit conditions is extrapolated, and thus converted into the restoring force caused by the surface tension of the liquid fuel inside the tank.

[0013] Preferably, the test solution inside the scaled-down storage tank is distilled water or anhydrous ethanol.

[0014]

[0015] Wherein, σ1 is the surface tension coefficient of the first test solution inside the scaled-down tank, and σ2 is the surface tension coefficient of the second test solution inside the scaled-down tank.

[0016] Preferably, the equivalent acceleration corresponding to the restoring force generated by the surface tension of the internal liquid under actual on-orbit conditions. for:

[0017]

[0018] Among them, B in-orbit B represents the number of bonds inside the tank corresponding to the on-orbit operating conditions; x represents the control group number formed by different test solutions with the same scaled-down tank radius participating in the extrapolation calculation, x = 1, 2, or 3. x1 and B x2 The number of bonds inside the first scaled-down tank and the number of bonds inside the second scaled-down tank in the control group; and These are the equivalent accelerations generated by the surface tension of the liquid inside the first and second scaled-down tanks in the control group, respectively.

[0019] Preferably, the restoring force caused by the surface tension of the liquid fuel inside the tank. The calculation formula is:

[0020]

[0021] Where, m slosh This refers to the mass of the fuel inside the tank that participates in the sloshing motion while in orbit.

[0022] Preferably, the actual on-orbit Bond number of the spacecraft's liquid-filled tank is:

[0023]

[0024] Where ρ is the density of the liquid fuel inside the tank, in kg / m³. 3 σ is the surface tension coefficient of the liquid fuel inside the tank, in N / m; r is the characteristic radius of the tank, in m; a in-orbit This refers to the acceleration of the liquid-filled storage tank due to inertial forces experienced in orbit.

[0025] Preferably, for a spherical tank, the characteristic radius is the inner radius of the tank; for a cylindrical tank, the characteristic radius is the inner radius of the hemisphere at the end of the tank.

[0026] Preferably, the acceleration α of the liquid-filled tank due to the inertial force it experiences in orbit is... in-orbit for:

[0027]

[0028] Among them, F t M is the on-orbit engine thrust of the spacecraft, in N; M is the dry weight of the spacecraft excluding liquid fuel, in kg; m l The total weight of the spacecraft's liquid fuel, expressed in kg.

[0029] Preferably, the characteristic radii of the three scaled-down tanks are in the order of r1>r2>r3, with the radius corresponding to the actual on-orbit Bond number of the spacecraft's liquid-filled tank as the reference radius. The difference between the characteristic radius r3 of the third scaled-down tank and the reference radius is no more than five times and no less than 1 / 5 of the reference radius.

[0030] Preferably, the first-order oscillation fundamental frequency f mn The measurement accuracy is better than 0.01Hz.

[0031] The advantages of this invention compared to the prior art are:

[0032] (1) This invention provides a method for measuring and calculating the magnitude of the restoring force generated by the surface tension of liquid fuel inside a spacecraft tank through a ground-scaled tank control group sway test. This method can effectively deepen the understanding of the surface tension force of fuel inside the tank in the aerospace engineering field and enhance the practical value of related engineering models.

[0033] (2) The method of the present invention can be extended to the assessment of fuel redistribution status of spacecraft carrying liquid fuel and requiring on-orbit maneuvering, and the optimization of the corresponding sloshing equivalent mechanical model considering the influence of liquid fuel surface tension. Attached Figure Description

[0034] Figure 1 This is a flowchart illustrating the method for calculating the restoring force caused by the surface tension of liquid fuel inside the storage tank according to an embodiment of the present invention. Detailed Implementation

[0035] The present invention will be further described below with reference to the embodiments.

[0036] Example 1

[0037] like Figure 1 The diagram shown is a flowchart of the method of the present invention, and the main steps are as follows:

[0038] Step 1: Calculate the magnitude of the inertial force and acceleration value of the liquid-filled tank in orbit based on the actual on-orbit operating conditions of the spacecraft.

[0039] The method for calculating the magnitude of the acceleration of the liquid-filled tank caused by the inertial force it experiences in orbit is as follows:

[0040]

[0041] Among them, F t The thrust of a spacecraft's on-orbit engine is measured in Newtons (N), such as the position-holding thrust for a geostationary satellite; M is the dry weight of the spacecraft excluding liquid fuel, measured in kilograms; m l This represents the total weight of the spacecraft's liquid fuel, in kg. If there are multiple tanks, it represents the total weight of the liquid fuel in each tank. in-orbit The acceleration inside the tank due to inertial forces, in m / s². 2 .

[0042] Step 2: Calculate the Bond number of the spacecraft's liquid storage tank and the on-orbit environment based on the internal acceleration value of the liquid storage tank.

[0043] The actual on-orbit environment Bond number calculation method for spacecraft liquid-filled tanks is as follows:

[0044]

[0045] Where ρ is the density of the liquid fuel inside the tank, in kg / m³. 3 σ is the surface tension coefficient of the liquid fuel inside the tank, in N / m; r is the characteristic radius of the tank, in m. For a spherical tank, the characteristic radius is the inner radius of the tank; for a cylindrical tank (cylindrical in the middle, hemispherical at both ends) commonly used in aerospace engineering, the characteristic radius is the inner radius of the hemisphere at the end of the tank; B N The Bond number is a dimensionless number. In this technical field, the Bond number is often used to characterize the microgravity environment inside the tank. The smaller the Bond number, the more prominent the influence of the surface tension of the liquid inside the tank, and vice versa.

[0046] Step 3: Based on the actual on-orbit environment Bond number of the spacecraft's liquid-filled tank, establish a ground-based scaled-down tank control group to determine the radius of the scaled-down tank and the solution used for the test.

[0047] 31) Develop a test plan for the scaled-down tank control group, using distilled water and anhydrous ethanol as test solutions; room temperature 20℃, density of distilled water 998 kg / m³. 3 The surface tension coefficient is 7.3 × 10⁻⁶. -2 N / m; at 20℃, the density of anhydrous ethanol is 790 kg / m³. 3 The surface tension coefficient is 2.2 × 10⁻⁶. -2 N / m;

[0048] 32) Considering that the free liquid surface has a certain degree of curvature under low Bond number environment, it is difficult to observe the shaking process under external excitation. Therefore, it is necessary to make no less than three scaled-down tank control groups. The scaled-down tanks are test tubes with ball-shaped bottoms. Each pair of scaled-down tanks is a group, and the two scaled-down tanks are filled with two different types of test solutions of different densities. The characteristic radius of each group of scaled-down tanks is different, corresponding to different Bond numbers in the on-orbit environment of the liquid-filled tanks. The characteristic radii of the three groups of scaled-down tanks are as follows: r1>r2>r3. The radius corresponding to the actual Bond number in the on-orbit environment of the liquid-filled tank of the spacecraft is used as the reference radius. The difference between the characteristic radius r3 of the third group of scaled-down tanks and the reference radius is no more than five times the reference radius and no less than 1 / 5 of the reference radius.

[0049] Step 4: Establish a ground shaking test platform, equipped with: fixtures matching each reference group, high-speed photography observation equipment, and frequency-adjustable exciter.

[0050] Establish a ground shaking test observation platform, which should basically include a single-axis exciter, a scaled-down storage tank fixture, and high-speed photography equipment. In order to more accurately observe the first-order resonance process and the corresponding excitation frequency, it is necessary to combine high-speed photography to capture the details of the resonance occurrence stage. At the same time, the excitation frequency of the single-axis exciter needs to cover the range of 0.1Hz to 20Hz, and the frequency adjustment accuracy should reach 0.01Hz.

[0051] Step 5: Conduct ground sway tests on the ground-scaled tank control group, observe the process of first-order resonance occurring in each ground-scaled tank, and record the corresponding excitation frequency, denoted as the first-order sway fundamental frequency f. mn m represents the type of test solution inside the scaled-down tank, m = 1, 2; n is the serial number of the control group of the scaled-down tank, n = 1 to 3;

[0052] 51) Conduct control group sway fundamental frequency observation tests in descending order of scaled-down tank radius;

[0053] 52) Complete all control group observation experiments using distilled water and anhydrous ethanol respectively. Record the excitation frequencies at which the first-order resonance occurs in the control groups (r1, r2, r3) formed by three identical scaled-down tank radii and different test solutions, and determine them as the first-order sway fundamental frequency f of the above controls. mn m represents the type of test solution inside the scaled-down tank, m = 1, 2; n is the serial number of the control group of the scaled-down tank, n = 1 to 3; in the actual observation process, the state of first-order resonance is defined as the liquid free surface wave height reaching the highest point without significant liquid surface breakage and rotational shaking.

[0054] 53) The first-order fundamental frequency measurement results of the distilled water control group (r1, r2, r3) are denoted as f. 11 f 12 f 13The first-order fundamental frequency measurement results of the anhydrous ethanol control group (r1, r2, r3) are denoted as f. 21 f 22 f 23 ;

[0055] Step 6: The first-order resonance process of each scaled-down storage tank in the ground shaking test equivalent to a simple pendulum model.

[0056] The simple pendulum model commonly used in aerospace engineering is adopted to describe the swaying process. The mathematical model of the simple pendulum swaying is as follows:

[0057]

[0058] Where m is 1 and 2, representing distilled water and anhydrous ethanol, respectively; n is 1, 2, and 3, representing each reference group; L mn The pendulum length of each reference group is related only to the liquid filling depth and radius of the tank; g mn This represents the equivalent gravitational acceleration corresponding to each reference group.

[0059] Step 7: Based on the actual effect of the restoring force caused by surface tension, the restoring force caused by surface tension is equivalent to a force of the same type as the restoring force caused by gravity.

[0060] Assuming that surface tension and gravity simultaneously provide the restoring force for the liquid surface to return to its rest equilibrium position, the equivalent gravitational acceleration g mentioned in step six... mn It consists of two parts:

[0061]

[0062] Where g represents the gravitational acceleration in the equivalent simple pendulum model; The equivalent acceleration generated by the surface tension of the liquid inside the tank is a scaled-down version of the ground surface.

[0063] Step 8: Based on the above equivalent processing method and the observation results of the control group, extract the gravitational acceleration g between the control groups formed by different test solutions with the same scaled-down tank radius. mn The proportional relationship and the equivalent acceleration generated by the surface tension of the internal liquid The proportional relationship is used to solve for the equivalent acceleration generated by the surface tension of the liquid inside the scaled-down storage tank at various locations.

[0064] 81) When the filling ratio is the same, even if different solutions are used, the first-order sloshing frequency of the liquid-filled tank is only related to the surface tension coefficient and viscosity coefficient, and is independent of density. Considering the first-order resonance measurement under forced vibration, the influence of viscosity coefficient can be ignored. Therefore, only the surface tension coefficient is a single influencing factor.

[0065]

[0066] 82) The magnitude of the surface tension restoring force inside the scaled-down tank is proportional to the radius of the free liquid surface and the surface tension coefficient. Ignoring the bending of the free liquid surface under microgravity, then...

[0067]

[0068] 83) Combining 81) and 82), then

[0069]

[0070]

[0071] It is also possible to obtain

[0072]

[0073] Wherein, σ1 is the surface tension coefficient of the first test solution inside the scaled-down tank, and σ2 is the surface tension coefficient of the second test solution inside the scaled-down tank.

[0074] Step 9: Based on the principle that the bond number of the liquid tank in a spacecraft is proportional to the bond number of the on-orbit environment, extrapolate the equivalent acceleration generated by the surface tension of the internal liquid under actual on-orbit conditions, and then convert it into the restoring force caused by the surface tension of the liquid fuel inside the tank.

[0075] The equivalent acceleration corresponding to the restoring force generated by the surface tension of the internal liquid under actual on-orbit conditions for:

[0076]

[0077] Among them, B in-orbit B represents the number of bonds inside the tank corresponding to the on-orbit operating conditions; x represents the control group number formed by different test solutions with the same scaled-down tank radius participating in the extrapolation calculation, x = 1, 2, or 3. x1 and B x2 The number of bonds inside the first scaled-down tank and the number of bonds inside the second scaled-down tank in the control group; and These are the equivalent accelerations generated by the surface tension of the liquid inside the first and second scaled-down tanks in the control group, respectively.

[0078] Restoring force caused by surface tension of liquid fuel inside the tank The calculation formula is:

[0079]

[0080] Where, mslosh This refers to the mass of the fuel inside the tank that participates in the sloshing motion while in orbit.

[0081] If the fuel filling ratio inside the tank is less than 40%, the mass m of the fuel inside the tank involved in sloshing under on-orbit conditions is... slosh It equals the mass of all the fuel inside the tank.

[0082] For calculations of the mass of the sloshing component in high-fill-liquid-ratio tanks, please refer to the professional book "THE NEW 'Dynamic Behavior of Liquids in Moving Containers'" (NASA-SP-106, 2000).

[0083] 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.

Claims

1. A method for calculating the restoring force caused by the surface tension of liquid fuel in a storage tank, characterized in that... Includes the following steps: A ground-based scaled-down tank control group was constructed, comprising six scaled-down tanks, each with a shape identical to a cylindrical test tube with a hemispherical bottom. Each pair of scaled-down tanks formed a group, and the two tanks were filled with two different types of test solutions with different surface tension coefficients. The characteristic radius of each group of scaled-down tanks was different, corresponding to different Bond numbers in the on-orbit environment of the liquid-filled tanks. Ground sway tests were conducted on the ground-scaled tank control group to observe the process of first-order resonance in each ground-scaled tank and record the corresponding excitation frequency, which was denoted as the first-order sway fundamental frequency f. mn m represents the type of test solution inside the scaled-down tank, m = 1, 2; n is the serial number of the control group of the scaled-down tank, n = 1 to 3; The first-order resonance process of each scaled-down storage tank in the ground shaking test is equivalent to that of a simple pendulum model, and the gravitational acceleration g in the equivalent simple pendulum model is assumed to be... mn The local gravitational acceleration g at the ground shaking test site and the equivalent acceleration generated by the surface tension of the liquid inside the scaled-down tank at each location. sum; Based on the gravitational acceleration g between control groups formed with the same scaled-down tank radius and different test solutions, mn The proportional relationship and the equivalent acceleration generated by the surface tension of the internal liquid The proportional relationship is used to solve for the equivalent acceleration generated by the surface tension of the liquid inside the scaled-down storage tank at various locations. Based on the principle that the bond number of a spacecraft's liquid-filled tank is proportional to the bond number of the on-orbit environment, the equivalent acceleration generated by the surface tension of the internal liquid under actual on-orbit conditions is extrapolated, and thus converted into the restoring force caused by the surface tension of the liquid fuel inside the tank.

2. The method for calculating the restoring force caused by the surface tension of liquid fuel in a storage tank according to claim 1, characterized in that, The test solution inside the scaled-down storage tank is distilled water or anhydrous ethanol.

3. The method for calculating the restoring force caused by the surface tension of liquid fuel in a storage tank according to claim 1, characterized in that, Wherein, σ1 is the surface tension coefficient of the first test solution inside the scaled-down tank, and σ2 is the surface tension coefficient of the second test solution inside the scaled-down tank.

4. The method for calculating the restoring force caused by the surface tension of liquid fuel in a storage tank according to claim 1, characterized in that, The equivalent acceleration corresponding to the restoring force generated by the surface tension of the internal liquid under actual on-orbit conditions for: Among them, B in-orbit B represents the number of bonds inside the tank corresponding to the on-orbit operating conditions; x represents the control group number formed by different test solutions with the same scaled-down tank radius participating in the extrapolation calculation, x = 1, 2, or 3. x1 and B x2 The number of bonds inside the first scaled-down tank and the number of bonds inside the second scaled-down tank in the control group; and These are the equivalent accelerations generated by the surface tension of the liquid inside the first and second scaled-down tanks in the control group, respectively.

5. The method for calculating the restoring force caused by the surface tension of liquid fuel in a storage tank according to claim 1, characterized in that, Restoring force caused by surface tension of liquid fuel inside the tank The calculation formula is: Where, m slosh This refers to the mass of the fuel inside the tank that participates in the sloshing motion while in orbit.

6. The method for calculating the restoring force caused by the surface tension of liquid fuel in a storage tank according to claim 1, characterized in that, The actual on-orbit Bond number of the spacecraft's liquid-filled tank is: Where ρ is the density of the liquid fuel inside the tank, in kg / m³. 3 σ is the surface tension coefficient of the liquid fuel inside the tank, in N / m; r is the characteristic radius of the tank, in m; a in-orbit This refers to the acceleration of the liquid-filled storage tank due to inertial forces experienced in orbit.

7. The method for calculating the restoring force caused by the surface tension of liquid fuel in a storage tank according to claim 2, characterized in that, For a spherical tank, the characteristic radius is the inner radius of the tank; for a cylindrical tank, the characteristic radius is the inner radius of the hemisphere at the end of the tank.

8. The method for calculating the restoring force caused by the surface tension of liquid fuel in a storage tank according to claim 1, characterized in that, The liquid-filled tank experiences acceleration α due to inertial forces while in orbit. in-orbit for: Among them, F t M is the on-orbit engine thrust of the spacecraft, in N; M is the dry weight of the spacecraft excluding liquid fuel, in kg; m l The total weight of the spacecraft's liquid fuel, expressed in kg.

9. The method for calculating the restoring force caused by the surface tension of liquid fuel in a storage tank according to claim 1, characterized in that, The characteristic radii of the three scaled-down tanks are as follows: r1>r2>r3. The radius corresponding to the actual on-orbit Bond number of the liquid-filled tank in the spacecraft is taken as the reference radius. The difference between the characteristic radius r3 of the third scaled-down tank and the reference radius is no more than five times and no less than 1 / 5 of the reference radius.

10. The method for calculating the restoring force caused by the surface tension of liquid fuel in a storage tank according to claim 1, characterized in that, First-order oscillation fundamental frequency f mn The experimental measurement accuracy is better than 0.01Hz.

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