Method for measuring and calculating restoring force caused by surface tension of liquid fuel in storage tank

Abstract

The invention relates to a method for measuring and calculating restoring force caused by surface tension of liquid fuel in a storage tank, which comprises the following steps: a ground scaling storage tank control group is manufactured, the scaling storage tank control group comprises three groups of scaling storage tanks, and every two scaling storage tanks filled with different test solutions form one group; carrying out a ground shaking test on a ground scaling storage tank control group, and recording a first-order shaking fundamental frequency; the first-order resonance generation process of each ground scaling storage tank in the ground shaking test is equivalent by a simple pendulum model; according to the same shrinkage ratio storage tank radius, the proportional relation of gravitational acceleration gmn between control groups formed by different test solutions, and the proportional relation of equivalent acceleration # imgabs0 # generated by internal liquid surface tension; and solving the equivalent acceleration # imgabs1 # generated by the surface tension of the liquid in each ground scaling storage tank, and extrapolating the equivalent acceleration generated by the surface tension of the internal liquid under the actual on-orbit working condition according to the principle that the spacecraft liquid-filled storage tank is in direct proportion to the Bond number of the on-orbit environment, thereby converting the equivalent acceleration into the restoring force caused by the surface tension of the liquid fuel in the storage tank.

Description

Technical Field

[0001] The present invention belongs to the field of liquid fuel sloshing and redistribution analysis in an on-orbit spacecraft tank, and relates to a method for measuring the magnitude of the force acting on the surface tension of the liquid fuel in the tank to maintain an initial equilibrium position in consideration of the on-orbit microgravity environment. The method can be used as an effective reference for estimating the on-orbit fuel sloshing frequency of a spacecraft in a microgravity environment and for accurate modeling of rigid-liquid coupling dynamics. Background Art

[0002] Traditional high-orbit satellites, spacecraft and deep space probes carry a large amount of liquid fuel. Considering the low / microgravity environment on orbit, the surface tension of liquid fuel will have a more significant impact on its distribution and dynamic characteristics (compared with the normal gravity environment on the ground). 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 inertia) will increase significantly, and no matter what state it is in, the surface tension potential energy always has a tendency to decrease and remain at the minimum state. However, the on-orbit maneuvering process will inevitably cause disturbances to the liquid fuel inside the tank, which will bring two adverse effects: (1) The disturbed liquid may leave the initial equilibrium position and relocate to other positions inside the tank; since the liquid outlet inside the tank is fixed, the relocated position may not cover the liquid outlet, resulting in reduced liquid outlet efficiency or even engine ignition failure; (2) The shaking of the disturbed liquid fuel will in turn affect the maneuvering process of the spacecraft (such as attitude jitter), which will undoubtedly reduce the maneuvering efficiency and accuracy, and even lead to mission failure.

[0003] The first type of impact 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 redistribution of the liquid fuel. Whether the liquid will be redistributed depends mainly on whether the lateral (perpendicular to the normal of the liquid free surface) disturbance force on the liquid can exceed the restoring force generated by the surface tension of the liquid. Considering that the surface tension action process is complex in low / microgravity environments, it is challenging to obtain the magnitude of the force of the surface tension on maintaining the initial equilibrium position.

[0004] The second type of impact is more common in the field of aerospace engineering. Usually, an equivalent sloshing model (such as a simple pendulum model) is 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 the liquid fuel into the equivalent sloshing model. This is also rarely seen in previous sloshing-related engineering application models.

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

[0006] The technical problem solved by the present invention is: to overcome the shortcomings of the prior art and provide a method for measuring the restoring force caused by the surface tension of liquid fuel in a tank. By using a ground-scaled tank control group sway test method, the restoring force generated by the surface tension of liquid fuel inside the spacecraft tank is measured and estimated, which 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.

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

[0008] A ground scaled tank control group is prepared, the scaled tank control group includes six scaled tanks, the shape of the scaled tanks is the same as a cylindrical test tube with a hemispherical bottom; every two scaled tanks with the same characteristic radius form a group, and two types of test solutions with different surface tension coefficients are respectively filled in the same group of scaled tanks; different groups of scaled tanks have different characteristic radii, corresponding to different on-orbit environmental Bond numbers of the liquid-filled tanks;

[0009] A ground shaking test was carried out on the ground scale tank control group to observe the process of the first-order resonance of each ground scale tank and record the corresponding excitation frequency, which is recorded as the first-order shaking fundamental frequency f mn , m represents the type of test solution inside the scaled tank, m = 1, 2; n is the serial number of the scaled tank control group, n = 1 to 3;

[0010] The first-order resonance process of each ground-scale tank in the equivalent ground sway test is simulated by using a single pendulum model, and the gravitational acceleration g in the equivalent single pendulum model is assumed to be mn is the local gravity acceleration g at the location where the ground shaking test is carried out and the equivalent acceleration caused by the surface tension of the liquid inside the ground-scale tank sum;

[0011] The gravitational acceleration g between the control groups formed by the same scale tank radius and different test solutions mn The proportional relationship between the internal liquid surface tension and the equivalent acceleration The proportional relationship is used to solve the equivalent acceleration caused by the surface tension of the liquid inside the tank at each scaled-down level.

[0012] According to the principle that the Bond number of the spacecraft liquid-filled tank is proportional to the on-orbit environment, the equivalent acceleration generated by the internal liquid surface tension under actual on-orbit conditions is extrapolated and 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 tank is distilled water or anhydrous ethanol.

[0014]

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

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

[0017]

[0018] Among them, B in-orbit is the internal bond number of the tank corresponding to the on-orbit condition; x is the serial number of the control group formed by the same scaled tank radius and different test solutions participating in the extrapolation calculation, x = 1, 2 or 3, B x1 and B x2 The number of bonds inside the first scaled tank and the number of bonds inside the second scaled tank in the control group; and are the equivalent accelerations caused by the surface tension of the liquid inside the first scaled tank and the second scaled tank 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] Among them, m slosh It is the mass of the fuel inside the tank that participates in the sloshing when on orbit.

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

[0023]

[0024] Where ρ is the density of the liquid fuel inside the tank, in kg / m 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 It is the acceleration of the liquid-filled tank due to the inertial force on orbit.

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

[0026] Preferably, the acceleration a generated by the inertial force on the liquid-filled tank in orbit is in-orbit for:

[0027]

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

[0029] Preferably, the characteristic radii of the three groups of scaled tanks are: r1>r2>r3, and the radius corresponding to the actual on-orbit environment Bond number of the spacecraft liquid-filled tank is taken as the reference radius, wherein the characteristic radius r3 of the third group of scaled tanks differs from it by no more than five times the reference radius and no less than 1 / 5 of the reference radius.

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

[0031] The beneficial effects of the present invention compared with the prior art are:

[0032] (1) The present invention provides a method for measuring and estimating the restoring force generated by the surface tension of liquid fuel inside a spacecraft tank through a ground-scale tank control group sloshing test, which can effectively deepen the understanding of the surface tension force of fuel inside the tank in the field of aerospace engineering and enhance the practical value of related engineering models.

[0033] (2) The method of the present invention can be extended to the evaluation of the fuel redistribution state of a spacecraft carrying liquid fuel and requiring on-orbit maneuvers, and the optimization of the corresponding sloshing equivalent mechanical model taking into account the influence of the surface tension of the liquid fuel. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 The figure is a flow chart of a method for calculating the restoring force caused by the surface tension of liquid fuel inside a tank according to an embodiment of the present invention. DETAILED DESCRIPTION

[0035] The present invention will be further described below in conjunction with the embodiments.

[0036] Example 1

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

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

[0039] The calculation method for the acceleration of the liquid-filled tank caused by the inertial force on orbit is as follows:

[0040]

[0041] Among them, F t is the thrust of the spacecraft's on-orbit engine, in N, such as the thrust of a geosynchronous orbit satellite to maintain its position on orbit; M is the dry weight of the spacecraft excluding liquid fuel, in kg; m l is the total weight of liquid fuel in the spacecraft, in kg. If there are multiple tanks, it is the total weight of the liquid fuel in each tank; a in-orbit The acceleration generated by the inertial force inside the tank, in m / s 2 .

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

[0043] The actual on-orbit environmental Bond number of the spacecraft liquid tank is calculated as follows:

[0044]

[0045] Where ρ is the density of the liquid fuel inside the tank, in kg / m 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 internal radius of the tank. For a column crown (cylindrical in the middle and hemispherical at both ends) commonly used in aerospace engineering, the characteristic radius is the internal radius of the hemisphere at the end of the tank; B N It is a dimensionless Bond number. In the 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: According to the actual on-orbit environment Bond number of the spacecraft liquid-filled tank, establish a ground-based scaled tank control group and determine the scaled tank radius and test solution.

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

[0048] 32) Considering that there is a certain degree of curvature of the free liquid surface in the low Bond number environment, it is difficult to observe the sloshing process under external stimulation. Therefore, it is necessary to make a control group of at least three scaled tanks. The scaled tanks have a test tube with a spherical head at the bottom. Every two scaled tanks form a group, and two scaled tanks are filled with two types of test solutions with different densities respectively; the characteristic radius of each group of scaled tanks is different, corresponding to different on-orbit environmental Bond numbers of the liquid-filled tanks; the characteristic radii of the three groups of scaled tanks are: r1>r2>r3, the radius corresponding to the actual on-orbit environmental Bond number of the spacecraft liquid-filled tank is taken as the reference radius, among which the characteristic radius r3 of the third group of scaled tanks is not more than five times the reference radius and not 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 vibration exciter.

[0050] A ground shaking test observation platform should be established. The platform should basically include a uniaxial exciter, a scaled 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 stage. At the same time, the excitation frequency of the uniaxial exciter should cover the range of 0.1Hz to 20Hz, and the frequency adjustment accuracy should reach 0.01Hz.

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

[0052] 51) Carry out the sloshing fundamental frequency observation test of the control group in the order of the scaled tank radius from large to small;

[0053] 52) All control group observation tests were completed using distilled water and anhydrous ethanol respectively, and the excitation frequencies of the control groups (r1, r2, r3) formed by the same scaled tank radius and different test solutions when the first-order resonance occurred were recorded in turn, and determined as the first-order sloshing fundamental frequency f of the above controls in turn. mn , m represents the type of test solution inside the scaled tank, m = 1, 2; n is the serial number of the scaled tank control group, n = 1 to 3; in the actual observation process, the first-order resonance state is when the liquid free surface wave height reaches the highest and no significant liquid surface breakage and rotational shaking occur;

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

[0055] Step 6: Use a single pendulum model to evaluate the first-order resonance of each ground-scale tank in the equivalent ground shaking test.

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

[0057]

[0058] Among them, m is 1 and 2, representing distilled water and anhydrous ethanol respectively; n is 1, 2, and 3, representing each reference group; L mn is the pendulum length of the single pendulum model corresponding to each reference group, which is only related to the tank filling depth and radius; g mn is 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 the same type of force as the gravity restoring force.

[0060] Assuming that surface tension and gravity provide the restoring force for the free surface of the liquid to return to its static equilibrium position, the equivalent gravitational acceleration g mentioned in step 6 is mn It consists of two parts:

[0061]

[0062] Among them, g is the gravitational acceleration in the equivalent simple pendulum model; It is the equivalent acceleration caused by the surface tension of the liquid inside the scaled tank.

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

[0064] 81) When the filling ratio of the liquid-filled tank is the same, even if different solutions are used, the first-order sloshing frequency is only related to the surface tension coefficient and the viscosity coefficient, and has nothing to do with the density. Considering that the first-order resonance measurement under forced vibration can be ignored, the influence of the viscosity coefficient can be ignored. Therefore, only the surface tension coefficient is the single influencing factor, then

[0065]

[0066] 82) The surface tension restoring force inside the scaled tank is proportional to the radius of the free surface of the liquid and the surface tension coefficient. Ignoring the curvature of the free surface in the microgravity environment, there is

[0067]

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

[0069]

[0070]

[0071] You can also get

[0072]

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

[0074] Step 9: Based on the principle that the Bond number of the spacecraft liquid-filled tank is proportional to the on-orbit environment, the equivalent acceleration generated by the internal liquid surface tension under actual on-orbit conditions is extrapolated, thereby converting 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 internal liquid surface tension under actual on-orbit conditions for:

[0076]

[0077] Among them, B in-orbit is the internal bond number of the tank corresponding to the on-orbit condition; x is the serial number of the control group formed by the same scaled tank radius and different test solutions participating in the extrapolation calculation, x = 1, 2 or 3, B x1 and B x2 The number of bonds inside the first scaled tank and the number of bonds inside the second scaled tank in the control group; and are the equivalent accelerations caused by the surface tension of the liquid inside the first scaled tank and the second scaled tank in the control group, respectively.

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

[0079]

[0080] Among them, mslosh It is the mass of the fuel inside the tank that participates in the sloshing when on orbit.

[0081] If the liquid filling ratio inside the tank is less than 40%, the mass m of the fuel inside the tank that participates in the sloshing in the on-orbit state slosh Equal to the mass of all the fuel inside the tank.

[0082] For the calculation of the mass of the part involved in sloshing in a high liquid filling ratio tank, 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 as above in the form of a preferred embodiment, it is not intended to limit the present invention. Any person skilled in the art may make possible changes and modifications to the technical solution of the present invention by using the methods and technical contents disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention shall fall within the protection scope of the technical solution of the present invention.

Claims

1. A method for calculating the restoring force caused by the surface tension of liquid fuel in a tank, characterized in that The steps include: A ground scaled tank control group is prepared, the scaled tank control group includes six scaled tanks, the shape of the scaled tanks is the same as that of a cylindrical test tube with a hemispherical bottom; two scaled tanks form a group, and two scaled tanks are respectively filled with two types of test solutions with different surface tension coefficients; the characteristic radius of each group of scaled tanks is different, corresponding to different on-orbit environment Bond numbers of the liquid-filled tanks; A ground shaking test was carried out on the ground scale tank control group to observe the process of the first-order resonance of each ground scale tank and record the corresponding excitation frequency, which is recorded as the first-order shaking fundamental frequency f mn , m represents the type of test solution inside the scaled tank, m = 1, 2; n is the serial number of the scaled tank control group, n = 1 to 3; The first-order resonance process of each ground-scale tank in the equivalent ground sway test is simulated by using a single pendulum model, and the gravitational acceleration g in the equivalent single pendulum model is assumed to be mn is the local gravity acceleration g at the location where the ground shaking test is carried out and the equivalent acceleration caused by the surface tension of the liquid inside the ground-scale tank sum; The gravitational acceleration g between the control groups formed by the same scale tank radius and different test solutions mn The proportional relationship between the internal liquid surface tension and the equivalent acceleration The proportional relationship is used to solve the equivalent acceleration caused by the surface tension of the liquid inside the tank at each scaled-down level. According to the principle that the Bond number of the spacecraft liquid-filled tank is proportional to the on-orbit environment, the equivalent acceleration generated by the internal liquid surface tension under actual on-orbit conditions is extrapolated and converted into the restoring force caused by the surface tension of the liquid fuel inside the tank.

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

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

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

5. A method for calculating the restoring force caused by the surface tension of liquid fuel in a tank according to claim 1, characterized in that: Restoring force caused by surface tension of liquid fuel inside the tank The calculation formula is: Among them, m slosh It is the mass of the fuel inside the tank that participates in the sloshing when on orbit.

6. A method for calculating the restoring force caused by the surface tension of liquid fuel in a tank according to claim 1, characterized in that: The actual on-orbit environmental Bond number of the spacecraft liquid tank is: Where ρ is the density of the liquid fuel inside the tank, in kg / m 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 It is the acceleration of the liquid-filled tank due to the inertial force on orbit.

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

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

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

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

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