Method, system and program for analyzing space time for solid fuel in hybrid rocket engine

Abstract

To provide a method, system and program for analyzing time space for solid fuel in a hybrid rocket engine, which can easily obtain a time-space resolved fuel regression rate.SOLUTION: A method for analyzing time space for solid fuel in a hybrid rocket engine acquires test data in combustion test of a hybrid rocket engine, and obtains, based on each test data, a fuel consumption Mf(t) of solid fuel at any combustion time t during the combustion test. The method measures a shape R(x,0) of the solid fuel before start of the combustion test, and a shape R(x,tf) of the solid fuel after completion of the combustion test, and obtains, based on the shapes R(x,0) and R(x,tf) and the calculated Mf(t), a shape R(x,t) of the solid fuel during the combustion test.SELECTED DRAWING: Figure 2

Description

[Technical field]

[0001] The present invention relates to a time-space analysis method, a time-space analysis system, and a time-space analysis program for solid fuel of a hybrid rocket engine. [Background technology]

[0002] There are three main types of rocket engines: solid propellant rocket engines, liquid propellant rocket engines, and hybrid rocket engines. Solid propellant rocket engines have a relatively simple structure, are easy to miniaturize, and are easy to store fuel, but combustion is difficult to control. Liquid fuel rocket engines are easier to control than solid propellant rockets, but fuel storage is difficult, there is a high risk of explosion, and the launch process is complicated. Hybrid rocket engines combine the advantages of both, and are particularly safe because they can store the fuel in a solid phase while storing the oxidizer separately.

[0003] Of these, hybrid rocket engines obtain thrust and driving force by using solid fuel, but in order to properly evaluate the performance of a hybrid rocket engine, it is important to understand the regression / gasification rate of the solid fuel (fuel regression rate).

[0004] Conventionally, the boundary layer combustion theory has been proposed to calculate the fuel regression rate of a hybrid rocket engine, where the inner diameter of the cylindrical solid fuel is r [m] and the propellant mass flux is G p [kg / m 2 -s], then, as shown in the following equation (a), the fuel regression rate dr / dt on the left side is G on the right side p It is considered to be proportional to the exponential power of (theoretically to the power of 0.8) and the exponential power of the distance x [m] from one end face of the solid fuel (theoretically to the power of -0.2) (see, for example, Non-Patent Document 1). Note that the value of the proportionality constant differs depending on the type of fuel and the combustion state.

[0005]

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[0006] As shown by the boundary layer combustion theory, the fuel regression rate is not uniform in space during the combustion of solid fuel in an actual hybrid rocket engine. Furthermore, since the propellant mass flux is determined by the inner diameter cross-sectional area of ​​the solid fuel, the fuel regression rate during combustion is not uniform in time and space.

[0007] Although the fuel regression rate is non-uniform in time and space, it has been common to evaluate the fuel regression rate as a time-space average because it is easy to estimate the time-averaged port diameter based on the mass change before and after combustion (see, for example, Non-Patent Document 2). However, this method results in large errors when the combustion time or fuel length is long, so a method has been proposed to move away from the time-space averaged fuel regression rate.

[0008] As such methods, for example, a method in which the fuel regression rate is obtained with time and space resolution by photographing the fuel regression during combustion with a camera (see, for example, Non-Patent Document 3); a method in which the fuel thickness is measured with an ultrasonic sensor mounted on the rocket combustion chamber to obtain the fuel regression rate with time resolution inside the rocket combustion chamber (see, for example, Non-Patent Document 4); a method in which, although there are limitations on the types of fuel that can be used, a fuel in which an electrode network is formed by blending a conductive material with a non-conductive solid fuel by 3D printer modeling, and the physical quantities of the electrode network are measured to obtain the fuel regression rate with time resolution and partial spatial resolution (see, for example, Patent Document 1); and a method in which solid fuel is measured with time resolution and partial spatial resolution by performing X-ray measurements on tubular solid fuel (see, for example, Non-Patent Document 5).

[0009] In addition, from the combustion test data, the fuel mass flow rate dm f / dt[kg / s] (time resolved fuel regression rate; hereafter, "m fA method has also been developed to obtain the characteristic exhaust speed efficiency η c* , the theoretical characteristic pumping speed is c * th , the combustion chamber pressure is P c , the cross-sectional area of ​​the nozzle throat is A t , the mass of the oxidizer is m o , oxidizer mass flow rate in dm o / dt(Hereinafter, "m o (The same applies to the mass flow ratio of the oxidizer and fuel contained in the propellant, O / F.) First, the characteristic exhaust velocity efficiency η c* The value of is assumed, and for example, a chemical equilibrium calculation program such as NASA-CEA (see, for example, Non-Patent Document 7) is used to calculate the chemical equilibrium, and the following equation (b) is converged to obtain O / F. At this time, instead of equation (b), the thrust efficiency η T The O / F may be calculated by assuming the value of and using the thrust equation expressed by the following equation (c).

[0010]

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[0011] Next, using the calculated O / F, the fuel mass flow rate dm is calculated using the following equation (d). f By calculating the time change in / dt and integrating it up to an arbitrary combustion time t using equation (e), the fuel consumption M f (t) is calculated. The end time of the combustion test t is calculated using the formula (e). f Integrate up to M f (t f ) and use this value as fuel consumption data M f,ex and judge whether or not formula (f) is satisfied.

[0012]

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[0013] If formula (f) is not satisfied, the assumed characteristic exhaust speed efficiency η c* or thrust efficiency η T Repeat the calculations from (b) to (e) by changing the value of . If equation (f) is satisfied, calculate the fuel mass flow rate dm f / dt (time resolved fuel regression rate).

[0014] In addition, a method for evaluating hybrid rocket engines by conducting numerical combustion tests has been developed (for example, see Non-Patent Document 8). [Prior art documents] [Non-patent literature]

[0015] [Non-Patent Document 1] Marxman et al., “Turbulent boundary layer combustion in the hybrid rocket”, Symposium (International) on Combustion. Vol. 9(1), 1963 [Non-Patent Document 2] Gregory et al., “Hybrid rocket fuel regression rate data and modeling”, 42nd AIAA / ASME / SAE / ASEE Joint Propulsion Conference & Exhibit, 2006 [Non-Patent Document 3] Dunn et al., “Spatially and temporally resolved regression rate measurements for the combustion of paraffin wax for hybrid rocket motor applications”, Aerospace Science and Technology, 2018, 72 [Non-Patent Document 4] Lestrade et al., “Liquefying fuel regression rate modeling in hybrid propulsion”, Aerospace Science and Technology, 2015, 42 [Non-Patent Document 5] Evans et al., “Instantaneous regression rate determination of a cylindrical x-ray transparent hybrid rocket motor”, 39th AIAA / ASME / SAE / ASEE Joint Propulsion Conference and Exhibit, 2003 [Non-Patent Document 6] Saito et al., “The accuracy of reconstruction techniques for determining hybrid rocket fuel regression rate”, 2018 Joint Propulsion Conference, 2018 [Non-Patent Document 7] Gordon, S., and McBride, B., “Computer Program for Calculation of Complex Chemical Equilibrium Compositions and Applications I. Analysis, NASA RP-1311”, National Aeronautics and Space Administration, Washington, DC, 1994. [Non-Patent Document 8] M. Arif Karabeyoglu et al., “Evaluation of Homologous Series of Normal-Alkanes as Hybrid Rocket Fuels”, 41st AIAA / ASME / ASEE Joint Propulsion Conference, Tucson AZ, July 2005, AIAA 2005-3908 [Patent documents]

[0016] [Patent Document 1] Patent Publication No. 2021-063501 Summary of the Invention [Problem to be solved by the invention]

[0017] However, the method described in Non-Patent Document 3 is for a combustion test using rectangular fuel, and has a problem that it is difficult to apply it to a rocket engine. Also, the method described in Non-Patent Document 4 has a problem that it is a point measurement, and therefore it is not possible to obtain a fuel regression rate with spatial resolution. Also, the method described in Patent Document 1 has a problem that it is a measurement of a part of the solid fuel in which an electrode network is formed, and therefore it is not possible to obtain a fuel regression rate with spatial resolution for the entire rocket engine.

[0018] In addition, the method described in Non-Patent Document 5 measures only a portion of the solid fuel, and thus has a problem in that it is not possible to obtain a fuel regression rate with spatial resolution for the entire rocket engine. In addition, the method described in Non-Patent Document 6 can obtain a time-resolved fuel regression rate, but the fuel regression rate is a spatial average, and therefore has a problem in that it is not possible to obtain a spatially resolved fuel regression rate.

[0019] The present invention has been made with a focus on such problems, and aims to provide a time-space analysis method, a time-space analysis system, and a time-space analysis program for solid fuel in a hybrid rocket engine, which can easily obtain time-space resolved fuel regression rate. [Means for solving the problem]

[0020] In order to achieve the above object, the present invention provides a spatiotemporal analysis method for solid fuel of a hybrid rocket engine, comprising: a time-resolved data acquisition step of acquiring test data in a combustion test of a hybrid rocket engine; and a step of calculating a time-resolved data of an arbitrary spatial position of the solid fuel of the hybrid rocket engine by x, an arbitrary combustion time of the combustion test by t, and an end time of the combustion test by t. f When the shape of the solid fuel during the combustion test is R(x, t), the shape of the solid fuel before the start of the combustion test R(x, 0) and the shape of the solid fuel after the end of the combustion test R(x, t f ) based on the test data acquired in the time-resolved data acquisition step, and a fuel consumption amount M f A fuel consumption calculation step for obtaining R(x,0) and R(x,t f ) and M calculated in the fuel consumption calculation step f and a time-space shape calculation step of calculating R(x,t) based on (t).

[0021] The time-space analysis system for the solid fuel of a hybrid rocket engine according to the present invention includes a time-resolved data acquisition means for acquiring test data in a combustion test of a hybrid rocket engine, and a time-resolved data acquisition means for acquiring test data in a combustion test of the hybrid rocket engine, the time-resolved data acquisition means for acquiring test data in a combustion test of the hybrid rocket engine, and the time-resolved data acquisition means for acquiring test data in a combustion test of the hybrid rocket engine, ... f When the shape of the solid fuel during the combustion test is R(x, t), the shape of the solid fuel before the start of the combustion test R(x, 0) and the shape of the solid fuel after the end of the combustion test R(x, t f ) based on the test data acquired by the spatial resolution data acquisition means, and the fuel consumption M of the solid fuel during the combustion test at any combustion time t based on the test data acquired by the time resolution data acquisition means. f A fuel consumption calculation means for calculating R(x,0) and R(x,t f ) and M calculated by the fuel consumption calculation means f and a time-space shape calculation means for calculating R(x,t) based on (t).

[0022] The time-space analysis program for the solid fuel of a hybrid rocket engine according to the present invention includes a computer, a time-resolved data acquisition means for acquiring test data in a combustion test of a hybrid rocket engine, an arbitrary spatial position of the solid fuel of the hybrid rocket engine being x, an arbitrary combustion time of the combustion test being t, and an end time of the combustion test being t. f When the shape of the solid fuel during the combustion test is R(x, t), the shape of the solid fuel before the start of the combustion test R(x, 0) and the shape of the solid fuel after the end of the combustion test R(x, t f ) based on the test data acquired by the time-resolved data acquisition means, and f a fuel consumption calculation means for calculating R(x,0) and R(x,t f ) and M calculated by the fuel consumption calculation means f(t) based on the time-space shape calculation means for calculating R(x,t).

[0023] The time-space analysis method, time-space analysis system, and time-space analysis program for the solid fuel of a hybrid rocket engine according to the present invention are configured to calculate the shape R(x, 0) of the solid fuel before the start of a combustion test and the shape R(x, t f ) and calculate the fuel consumption M at any given combustion time t of the solid fuel during the combustion test based on the fuel test. f By combining this with (t), the shape of the solid fuel during the combustion test R(x,t) can be obtained, which makes it easy to obtain the time-space resolved fuel regression rate.

[0024] In the time-space analysis method for solid fuel of a hybrid rocket engine according to the present invention, the time-space shape calculation step preferably calculates R(x,t) by equation (1). In the time-space analysis system and time-space analysis program for solid fuel of a hybrid rocket engine according to the present invention, the time-space shape calculation means preferably calculates R(x,t) by equation (1). In this case, R(x,t) can be calculated with relatively high accuracy.

[0025]

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[0026] The method for time-space analysis of solid fuel of a hybrid rocket engine according to the present invention includes a time-space resolution data acquisition step, in which the time-resolved data acquisition step acquires the test data from one combustion test, and the time-space resolution data acquisition step calculates a fuel regression rate and a propellant mass flux G based on the shape R(x, t) of the solid fuel obtained by the time-space shape calculation step and the test data. p and the propellant mass flux G pand an arbitrary spatial position x of the solid fuel. The space-time analysis system and space-time analysis program for the solid fuel of the hybrid rocket engine according to the present invention may be configured to be capable of estimating the fuel regression rate for an infinite number of combinations of the two parameters, i.e., x(x,t) and an arbitrary spatial position x of the solid fuel. The space-time analysis system and space-time analysis program for the solid fuel of the hybrid rocket engine according to the present invention have a space-time resolution data acquisition means, the time resolution data acquisition means acquires the test data from one combustion test, and the space-time resolution data acquisition means calculates a fuel regression rate and a propellant mass flux G based on the shape R(x,t) of the solid fuel calculated by the space-time shape calculation means and the test data. p and the propellant mass flux G p The fuel regression rate may be estimated for an infinite number of combinations of the two parameters R(x,t) and an arbitrary spatial position x of the solid fuel. In this case, for example, by calculating the time derivative of the calculated R(x,t) at an arbitrary spatial position x using equation (2), a spatiotemporal resolved fuel regression rate dr / dt can be obtained. In addition, the propellant mass flux G p (x, t) can be expressed as, for example, the cross-sectional area of ​​the solid fuel and the mass flow rate of the supplied oxidizer dm o / dt and the fuel mass flow rate to the front dm f / dt, it can be calculated by equation (3), where ρf is the density of the solid fuel.

[0027]

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[0028] In this way, the time-space analysis method, time-space analysis system, and time-space analysis program for solid fuel of a hybrid rocket engine according to the present invention can obtain a time-space resolved fuel regression rate without requiring special measuring equipment during a combustion test. Conventionally, only a fuel regression rate averaged at least in time and space could be obtained in one combustion test, and in order to obtain a time-space resolved fuel regression rate, it was necessary to perform the combustion test many times, but according to the present invention, a time-space resolved fuel regression rate can be easily obtained in one combustion test.

[0029] In the spatio-temporal analysis method of the solid fuel of the hybrid rocket engine according to the present invention, the spatio-temporal resolution data acquisition step obtains a fuel regression rate when the combustion of the solid fuel continues by extrapolating the obtained fuel regression rate to a time domain and / or a space domain, or obtains the fuel consumption data M f,ex and the fuel consumption at the end of the combustion test M f (t f In the time-space analysis system and the time-space analysis program for solid fuel of a hybrid rocket engine according to the present invention, the time-space resolution data acquisition means may be configured to obtain a fuel regression rate when the combustion of the solid fuel continues by extrapolating the obtained fuel regression rate to the time domain and / or the space domain based on the ratio of the fuel consumption data M f,ex and the fuel consumption at the end of the combustion test M f (t f ) to obtain a shape of the solid fuel as the combustion of the solid fuel continues. In this case, the time-space evolution of the fuel regression shape as the combustion continues can be estimated. Alternatively, the shape of the solid fuel as the combustion of the solid fuel continues can be obtained by extrapolating the shape of the solid fuel R(x,t) to the time domain and / or the space domain based on the ratio of the shape of the solid fuel R(x,t) to the time domain and / or the space domain. In this case, the time-space evolution of the fuel regression shape as the combustion continues can be estimated. f This makes it possible to grasp the shape of the solid fuel as combustion continues, which will enable prediction of rocket engine performance and contribute to the design of solid fuel and rocket engines.

[0030] In the method for space-time analysis of solid fuel in a hybrid rocket engine according to the present invention, the test data includes the combustion chamber pressure P c and the nozzle throat cross-sectional area A t and oxidizer mass flow rate dm o Changes in fuel consumption data M f,exThe fuel consumption calculation step includes: a ratio O / F of the mass flow rate of the oxidizer to the mass flow rate of the solid fuel and a characteristic exhaust speed efficiency η c* By finding M f In the time-space analysis system and the time-space analysis program for the solid fuel of the hybrid rocket engine according to the present invention, the test data is preferably a combustion chamber pressure P c and the nozzle throat cross-sectional area A t and oxidizer mass flow rate dm o Changes in fuel consumption data M f,ex The fuel consumption calculation means uses a chemical equilibrium calculation to calculate a ratio O / F of a mass flow rate of an oxidizer to a mass flow rate of a solid fuel and a characteristic exhaust speed efficiency η c* By finding M f In this case, the fuel consumption amount M f The method for calculating (t) is to use the data from each combustion test. f Any method can be used as long as it can calculate (t), for example, the regeneration method described in Non-Patent Document 6 can be used. In addition, the chemical equilibrium calculation is performed by calculating O / F and η c* Any method may be used as long as it can determine the above. For example, the chemical equilibrium calculation program NASA-CEA described in Non-Patent Document 7 can be used.

[0031] In the time-space analysis method, time-space analysis system, and time-space analysis program for solid fuel of a hybrid rocket engine according to the present invention, it is preferable that the solid fuel has a shape extending along a predetermined axis, and any spatial position x of the solid fuel represents a position along the axis. It is preferable that the solid fuel has a shape of a revolution such as a cylinder whose central axis is the predetermined axis, or a shape of n-fold rotational symmetry (n is an integer of 3 or more) with respect to the predetermined axis. Effect of the Invention

[0032] According to the present invention, it is possible to provide a time-space analysis method, a time-space analysis system, and a time-space analysis program for solid fuel of a hybrid rocket engine, which can easily obtain a time-space resolved fuel regression rate. [Brief description of the drawings]

[0033] [Figure 1] 1A is a longitudinal sectional view showing a hybrid rocket engine in use in a combustion test according to an embodiment of the present invention, and FIG. 1B is a longitudinal sectional view showing an enlarged portion of the same. [Diagram 2] 1 is a block diagram showing a configuration of a time-space analysis system for solid fuel of a hybrid rocket engine according to an embodiment of the present invention; [Diagram 3] 1 is a flowchart showing a processing procedure of a time-space analysis method for solid fuel of a hybrid rocket engine according to an embodiment of the present invention. [Figure 4] Graphs showing (a) the oxidizer mass flow rate dmo / dt measured in a combustion test, (b) the time history of the combustion chamber pressure Pc, (c) the time history of the calculated O / F, (d) the time history of the fuel consumption Mf(t), and (e) the shape R(x, t) of the solid fuel at the elapsed time t = 10.0 seconds in the combustion test, of the time-space analysis method of the solid fuel of a hybrid rocket engine of an embodiment of the present invention. [Diagram 5] Graphs showing (a) the oxidizer mass flow rate dmo / dt measured in a combustion test, (b) the time history of the combustion chamber pressure Pc, (c) the time history of the calculated O / F, (d) the time history of the fuel consumption Mf(t), and (e) the shape R(x, t) of the solid fuel at the elapsed time t = 30.0 seconds in the combustion test, of the time-space analysis method of the solid fuel of a hybrid rocket engine of an embodiment of the present invention. [Figure 6]Graphs showing (a) the oxidizer mass flow rate dmo / dt measured in a combustion test, (b) the time history of the combustion chamber pressure Pc, (c) the time history of the calculated O / F, (d) the time history of the fuel consumption Mf(t), and (e) the shape R(x, t) of the solid fuel at the elapsed time t = 50.0 seconds in the combustion test, of the time-space analysis method of the solid fuel of a hybrid rocket engine of an embodiment of the present invention. [Figure 7] Graphs showing (a) the oxidizer mass flow rate dmo / dt measured in a combustion test, (b) the time history of the combustion chamber pressure Pc, (c) the time history of the calculated O / F, (d) the time history of the fuel consumption Mf(t), and (e) the shape R(x, t) of the solid fuel at the elapsed time t = 70.0 seconds in the combustion test, of the time-space analysis method of the solid fuel of a hybrid rocket engine of an embodiment of the present invention. [Figure 8] Graphs showing (a) the oxidizer mass flow rate dmo / dt measured in a combustion test, (b) the time history of the combustion chamber pressure Pc, (c) the time history of the calculated O / F, (d) the time history of the fuel consumption Mf(t), and (e) the shape R(x,t) of the solid fuel at the elapsed time t=88.9 seconds in the combustion test, of the time-space analysis method of the solid fuel of a hybrid rocket engine of an embodiment of the present invention. [Figure 9] 1A is a graph showing (a) a 3D display of the space-time resolution of the results obtained in a numerical combustion test, which is a conventional method for evaluating the combustion test of a hybrid rocket engine, and (b) a graph showing a 3D display of the space-time resolution obtained by a space-time analysis method for solid fuel of a hybrid rocket engine according to an embodiment of the present invention. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0034] Hereinafter, an embodiment of the present invention will be described with reference to the drawings. 1 to 9 show a time-space analysis method, a time-space analysis system, and a time-space analysis program for a solid fuel of a hybrid rocket engine according to an embodiment of the present invention. The time-space analysis method for a solid fuel of a hybrid rocket engine according to an embodiment of the present invention is a method that is preferably implemented by the time-space analysis system for a solid fuel of a hybrid rocket engine according to an embodiment of the present invention, and can be executed by a computer using the time-space analysis program for a solid fuel of a hybrid rocket engine.

[0035] As shown in Fig. 1(a), the hybrid rocket engine 50 uses a cylindrical solid fuel 51 as a propellant, and is configured to supply an oxidizer OX from an injector 53 attached to the front of the hybrid rocket engine 50 to the inside of the solid fuel 51 arranged inside a combustion chamber 52, so that the oxidizer OX reacts with the vaporized solid fuel 51 and burns by boundary layer combustion. The hybrid rocket engine 50 is configured to obtain thrust and driving force by choking and discharging the combustion gas to the outside through a nozzle 54. In addition, it is configured to perform nitrogen purging at the end of combustion to promote the end of combustion.

[0036] For example, PMMA (acrylic resin), HDPE (high density polyethylene), WAX (wax)-based fuel, HTPB (hydroxyl-terminated polybutadiene), etc. can be used as the solid fuel 51 of the hybrid rocket engine 50. Also, for example, oxygen, hydrogen peroxide, nitric acid, nitrous oxide, dinitrogen tetroxide, ammonium perchlorate, ammonium nitrate, nitroglycerin, nitrocellulose, etc. can be used as the oxidizer OX.

[0037] In the combustion test of the hybrid rocket engine 50, the oxidizer mass flow rate dm was calculated by measuring the amount of oxidizer OX supplied from the injector 53. o The time change of / dt is acquired, and the combustion chamber pressure P cAfter the combustion test is completed, the solid fuel 51 is removed from the combustion chamber 52, and fuel consumption data M is obtained from the mass difference before and after the combustion test. f,ex are beginning to demand more.

[0038] In addition, as shown in FIG. 1(b), in the combustion test, the three-dimensional shape of the solid fuel 51 is measured by a computer tomography (CT) scan or the like before and after the combustion test, and the shape R(x,0) of the solid fuel 51 at the start of the combustion test (t=0) and the shape R(x,0) at the end of the combustion test (t=t f ) of the shape R(x,t f ) is acquired. In addition, x represents an arbitrary spatial position along the central axis of the cylindrical solid fuel 51, and in the specific example shown in FIG. 1(b), the corner of the solid fuel 51 on the injector 53 side is set as the origin, and the direction toward the nozzle 54 is set as the positive direction.

[0039] As shown in FIG. 2, the hybrid rocket engine solid fuel space-time analysis system 10 according to the embodiment of the present invention is made up of a computer, and has an input means 11, a storage means 12, a display means 13, and a main control unit 14. The input means 11 is made up of a keyboard and a mouse for a user to input various data and information, and a receiving device for acquiring electronic data transmitted from the outside. The storage means 12 is made up of a memory capable of storing various data. The display means 13 is made up of an output device such as a monitor (display) and a printer. The main control unit 14 is made up of a CPU, and has a calculation function and a control function. The main control unit 14 is connected to the input means 11, the storage means 12, and the display means 13, and is configured to be able to control each of them.

[0040] The input means 11 receives fuel consumption data M obtained in a combustion test of a hybrid rocket engine. f,ex , the combustion chamber pressure of the hybrid rocket engine P c Time change of the nozzle throat cross-sectional area A of the hybrid rocket engine t , oxidizer mass flow rate dm oThe test data includes the time change of / dt, the shape of the solid fuel before the start of the combustion test R(x,0), and the shape of the solid fuel after the end of the combustion test R(x,t f The storage means 12 is configured to temporarily or for a necessary period store each test data and shape of the solid fuel input by the input means 11, and various parameters calculated by the main control unit 14.

[0041] The display means 13 is configured to display each test data stored in the memory means 12, the shape of the solid fuel, various parameters, the time-space resolution data of the final solid fuel shape, the time-space resolution data of the fuel regression rate, the time-space resolution data of the propellant mass flux, etc., in the form of graphs, numerical values, images, videos, etc.

[0042] The main control unit 14 has a time-resolved data acquisition means 21, a spatial resolution data acquisition means 22, a fuel consumption calculation means 23, a time-space shape calculation means 24, and a time-space resolution data acquisition means 25. The time-resolved data acquisition means 21 is configured to acquire each test data in a combustion test of the hybrid rocket engine as time-resolved data via the input means 11, and store the data in the storage means 12.

[0043] The spatial resolution data acquisition means 22 acquires, as the solid fuel spatial resolution data, the shape R(x, 0) of the solid fuel of the hybrid rocket engine before the start of the combustion test and the shape R(x, t f ) are acquired by CT measurement or the like and stored in the storage means 12.

[0044] The fuel consumption calculation means 23 calculates the fuel consumption M at any combustion time t of the solid fuel during the combustion test based on each test data acquired by the time-resolved data acquisition means 21 and stored in the storage means 12. f In one specific example, the fuel consumption calculation means 23 is configured to calculate the fuel consumption M f The method is configured to find (t).

[0045] That is, first, the characteristic exhaust speed efficiency η c* Based on the type of solid fuel and oxidizer, the above formula (b) is converged by chemical equilibrium calculation to obtain O / F. At this time, the characteristic exhaust speed efficiency η c* Instead of thrust efficiency η T The value of may be assumed, and the thrust equation expressed by the above equation (c) may be used instead of equation (b) to calculate O / F. Here, for example, the chemical equilibrium calculation program NASA-CEA described in Non-Patent Document 7 may be used for the chemical equilibrium calculation.

[0046] Next, using the calculated O / F, the fuel mass flow rate dm is calculated using the above equation (d). f By calculating the time change in / dt and integrating it up to an arbitrary combustion time t using the above formula (e), the fuel consumption M f (t) is calculated. The end time of the combustion test is t f Integrate up to M f (t f ) and use this value as fuel consumption data M f,ex It is judged whether the above formula (f) is satisfied. If the formula (f) is not satisfied, the assumed characteristic exhaust speed efficiency η c* or thrust efficiency η T The calculations from formula (b) to formula (e) are repeated by changing the value of . If formula (f) is satisfied, the result is adopted. In this way, the fuel consumption calculation means 23 calculates the fuel consumption M f The fuel consumption calculation means 23 calculates the fuel mass flow rate dm f / dt is integrated over time to obtain fuel consumption M f In addition to calculating (t), the fuel consumption M f An approximation of (t) may be found.

[0047] The time-space shape calculation means 24 calculates the solid fuel spatial resolution data R(x, 0) and R(x, tf ) and M calculated by the fuel consumption calculation means 23 f The system is configured to calculate the shape R(x,t) of the solid fuel at an arbitrary spatial position x of the solid fuel and an arbitrary combustion time t based on (t). In a specific example, the system is configured to calculate R(x,t) by the above formula (1) to obtain the spatiotemporal resolution.

[0048] The time-space resolution data acquisition means 25 is configured to obtain the time-space resolved fuel regression rate dr / dt by calculating the time differential of R(x,t) obtained by the time-space shape calculation means 24 using the above formula (2). o From the calculated R(x,t) and the fuel regression rate dr / dt, the propellant mass flux G p (x, t). Furthermore, the spatio-temporal resolution data acquisition means 25 may be configured to obtain a fuel regression rate when the solid fuel continues to burn by extrapolating the obtained fuel regression rate to the time domain and / or the space domain. In addition, the fuel consumption data M f,ex and fuel consumption at the end of the combustion test M f (t f ), and may be configured to determine the shape of the solid fuel as the combustion of the solid fuel continues by extrapolating the shape of the solid fuel R(x,t) to the time domain and / or the space domain based on the ratio of R(x,t) to the time domain and / or the space domain.

[0049] The space-time resolved data R(x,t) of the solid fuel shape, the space-time resolved data dr / dt of the fuel regression rate, and the space-time resolved data G of the propellant mass flux are p (x, t) is stored in the storage means 12 and is configured to be displayed on the display means 13. In order to display the obtained spatiotemporal resolution, the display means 13 may, for example, display the distance in the axial direction of the fuel (the direction from the injector 53 to the nozzle 54) on one axis and the propellant mass flux G p Furthermore, a 3D display may be made by using another axis as the fuel regression rate. Such a 3D display can provide a deeper understanding of the fuel combustion mechanism.

[0050] Next, a spatiotemporal analysis method of a solid fuel of a hybrid rocket engine according to an embodiment of the present invention, which is a processing procedure of the spatiotemporal analysis system 10 of the solid fuel of a hybrid rocket engine according to an embodiment of the present invention, will be described with reference to Fig. 3. As shown in Fig. 3, first, a combustion test of the hybrid rocket engine to be analyzed is performed, and fuel consumption data M f,ex , combustion chamber pressure P c Time change of nozzle throat cross-sectional area A t , oxidizer mass flow rate dm o Each test data including the time change of / dt is acquired and stored in the storage means 12 (step 31). In addition, via the input means 11, the spatial resolution data acquisition means 22 acquires the shape R(x, 0) of the solid fuel before the start of the combustion test and the shape R(x, t f ) and store it in the storage means 12 (step 32).

[0051] Next, the fuel consumption calculation means 23 calculates the characteristic exhaust speed efficiency η c* (Step 33), a chemical equilibrium calculation is used based on each test data stored in the storage means 12 to converge equation (b) to obtain O / F (Step 34), and the fuel mass flow rate dm is calculated from equation (d) using the O / F. f The time change in / dt is calculated (step 35). This is called the end time t f Repeat until the fuel consumption M f (t) and fuel consumption M f (t f ) is calculated (step 36). Furthermore, the calculated fuel consumption M f (t f ) value from the fuel consumption data M f,exand judge whether or not formula (f) is satisfied (step 37). If formula (f) is not satisfied, steps 33 to 36 are repeated until formula (f) is satisfied. If formula (f) is satisfied, the result is adopted, and the time-resolved data M of the fuel consumption is f Obtain (t) (step 38).

[0052] Next, the time-space shape calculation means 24 calculates R(x,0) and R(x,t f ) and M calculated by the fuel consumption calculation means 23 f Based on the above and (t), the shape R(x,t) of the solid fuel at an arbitrary spatial position x of the solid fuel and an arbitrary combustion time t is calculated by equation (1) (step 39). Furthermore, the time-space resolved data acquisition means 25 calculates the time differential of the calculated R(x,t) by the above equation (2) to calculate the time-space resolved fuel regression rate dr / dt. Also, the oxidizer mass flow rate dm o From the calculated R(x,t) and the fuel regression rate dr / dt, the propellant mass flux G p (x, t) is calculated, and thus, time-space resolved data of the solid fuel is obtained (step 40).

[0053] The time-space analysis system 10 and the time-space analysis method of the solid fuel of the hybrid rocket engine according to the embodiment of the present invention are f ) and calculate the fuel consumption M at any given combustion time t of the solid fuel during the combustion test based on the fuel test. f By combining this with (t), the shape R(x,t) of the solid fuel during the combustion test can be obtained without requiring any special measuring equipment, and the time-space resolved fuel regression rate can be easily obtained.

[0054] Conventionally, only a fuel regression rate averaged at least in time or space could be obtained in one combustion test, and in order to obtain a time-space resolved fuel regression rate, it was necessary to perform the combustion test many times. However, according to the time-space analysis system 10 and the time-space analysis method of the solid fuel of the hybrid rocket engine of the embodiment of the present invention, the time-space resolved fuel regression rate can be easily obtained in one combustion test. Furthermore, the time-space analysis system 10 and the time-space analysis method of the solid fuel of the hybrid rocket engine of the embodiment of the present invention can extrapolate the time-space resolved fuel regression rate obtained in the time-space resolved data acquisition means 25 or the time-space resolved data acquisition step to the time domain or the space domain, thereby estimating the time-space development of the fuel regression shape when combustion continues. Furthermore, the fuel consumption data M f,ex and fuel consumption at the end of the combustion test M f (t f ) based on the ratio of the solid fuel shape R(x,t) to the time and space domains, the actual combustion test time t f This makes it possible to grasp the shape of the solid fuel as combustion continues, which will enable prediction of rocket engine performance and contribute to the design of solid fuel and rocket engines. EXAMPLES

[0055] A combustion test of the hybrid rocket engine was conducted, and the shape of the solid fuel R(x,t) during the combustion test was obtained by the space-time analysis method of the solid fuel of the hybrid rocket engine according to the embodiment of the present invention shown in Fig. 3. In the combustion test, the solid fuel was HDPE, the oxidizer was oxygen gas, the length of the propellant was 300 mm, the initial inner diameter was 10 mm, and the density was 950 kg / m 3 The nozzle throat diameter was 8 mm and the combustion time was 90 seconds.

[0056] Oxidizer mass flow rate dm measured in the combustion test o / dt and combustion chamber pressure P c The time history of the calculated O / F and fuel consumption M f4 to 8 show the shape R(x, t) of the solid fuel when the elapsed time (combustion time) of the combustion test (t) is 10.0, 30.0, 50.0, 70.0, and 88.9 seconds.

[0057] As shown in Figures 4 to 8, it was confirmed that the solid fuel was consumed over time during the fuel test, and the shape R(x, t) of the solid fuel, i.e., the inner shape of the cylindrical solid fuel, gradually expanded. It was also confirmed that the rate at which the inner diameter of the solid fuel expanded differed depending on the spatial position x of the solid fuel.

[0058] Applying the obtained results to the above equation (a), which is the equation for the fuel regression rate dr / dt according to boundary layer combustion theory, the multiplier m of x is -0.2391, and the propellant mass flux G p The multiplier n was 0.2784, the proportionality constant was 0.2714, and the coefficient of determination was 0.71. EXAMPLES

[0059] A numerical combustion test, which is a known evaluation method for hybrid rocket engine combustion tests, was performed to obtain the time history of the shape of the solid fuel. Using the time history of the fuel consumption and the initial and final shapes of the solid fuel obtained in the numerical combustion test, the time history of the shape of the solid fuel was obtained by the space-time analysis method of the solid fuel of the hybrid rocket engine according to the embodiment of the present invention shown in Figure 3, and the time history of the shape of the solid fuel was compared with the fuel regression rate obtained in the numerical combustion test.

[0060] Here, the numerical combustion test used a known evaluation method for a hybrid rocket engine combustion test shown in Non-Patent Document 8. It is known that this evaluation method can obtain true values ​​based on the fuel regression characteristics. However, this evaluation method can only be calculated when the fuel regression characteristics are known, and confirmation through a combustion test is essential. In the following, the axial distance x of the fuel, the propellant mass flux G pA method of experimentally confirming the fuel regression characteristics using the three-axis elements of fuel regression rate dr / dt, which was not possible to achieve using conventional numerical combustion tests, is shown to be feasible using the space-time analysis method for solid fuel in a hybrid rocket engine according to an embodiment of the present invention.

[0061] The numerical combustion test was performed using the fuel regression index (n=0.8, m=-0.2) based on Non-Patent Document 1. In the numerical combustion test, the density was 930 kg / m 3 The solid fuel used was a cylinder with a diameter of 10 mm and a length of 100 mm. The combustion time was 100 seconds, and the combustion time and fuel step width were 0.1 seconds and 0.1 mm, respectively.

[0062] Figure 9(a) shows a 3D representation of the time-space resolution of the results obtained in the numerical combustion test (the three axes are the axial distance of the fuel x, the propellant mass flux G p , and the fuel regression rate dr / dt(rdot)). Figure 9(b) shows a 3D display of the time-space resolution obtained by the time-space analysis method of the solid fuel of the hybrid rocket engine of the embodiment of the present invention. Figures 9(a) and (b) show the main range of the combustion time from 1 second to 100 seconds and the fuel length from 5 mm to 99 mm. The fuel regression rate was calculated from equation (2).

[0063] Comparing Figure 9(a) and Figure 9(b), it can be seen that they are very similar. In this case, the relative error obtained by dividing the Frobenius norm of the difference between the two spatio-temporal data by the Frobenius norm of the spatio-temporal data of the numerical combustion test was 2.2%. From this result, it can be said that the fuel regression rate obtained by the spatio-temporal analysis method of the solid fuel of the hybrid rocket engine according to the embodiment of the present invention, using only the time history of the fuel consumption obtained in the numerical combustion test and the initial and final shapes of the solid fuel, can reproduce the true value obtained in the numerical combustion test with high accuracy.

[0064] In this way, according to the method for space-time analysis of solid fuel in a hybrid rocket engine of the embodiment of the present invention, the propellant mass flux Gp It is possible to estimate the fuel regression rate for an infinite number of combinations of the two parameters, namely, the fuel length and the fuel axial distance (fuel length).

[0065] The time-space analysis program for the solid fuel of the hybrid rocket engine according to the embodiment of the present invention may be provided from the outside via a communication line, for example, or may be provided in a form recorded on a computer-readable recording medium such as a CD (CD-ROM, CD-R, CD-RW, etc.), a DVD (DVD-ROM, DVD-RAM, DVD-R, DVD-RW, DVD+R, DVD+RW, etc.), or a USB memory. In these cases, the computer can read the time-space analysis program for the solid fuel of the hybrid rocket engine from the communication line or recording medium, transfer it to an internal storage device of the computer, and store it for use. In addition, the time-space analysis program for the solid fuel of the hybrid rocket engine according to the embodiment of the present invention may be recorded in a storage device (recording medium) such as a magnetic disk, optical disk, or magneto-optical disk, and provided to the computer from the storage device via a communication line.

[0066] Here, a computer is a concept that includes hardware and an OS (operating system), and refers to hardware that operates under the control of the OS. In addition, when an OS is not required and the hardware is operated by an application program alone, the hardware itself corresponds to a computer. The hardware is equipped with at least a microprocessor such as a CPU, and a means for reading computer programs recorded in an internal storage device or a recording medium.

[0067] The application program as the time-space analysis program of the solid fuel of the hybrid rocket engine according to the embodiment of the present invention includes a program code to be executed by the computer as described above. Also, some of the functions may be executed by the OS instead of the application program. [Explanation of symbols]

[0068] 10 Space-time analysis system for solid fuel in hybrid rocket engines 11 Input methods 12 Memory means 13 Display means 14 Main control unit 21 Time-resolved data acquisition methods 22 Means of acquiring spatially resolved data 23 Fuel consumption calculation means 24 Spatiotemporal shape calculation means 25 Means of acquiring spatiotemporal resolution data 50 Hybrid Rocket Engine 51 Solid fuel 52 Combustion chamber 53 Injector OX Oxidizing agent 54 Nozzle 55 Pressure Sensor

Claims

1. A time-resolved data acquisition step of acquiring test data in a combustion test of the hybrid rocket engine; Let x denote an arbitrary spatial position of the solid fuel of the hybrid rocket engine, t denote an arbitrary burning time of the burning test, and t denote the end time of the burning test. ｆ When the shape of the solid fuel during the combustion test is R(x, t), the shape of the solid fuel before the start of the combustion test R(x, 0) and the shape of the solid fuel after the end of the combustion test R(x, t ｆ ) and a spatial resolution data acquisition step of acquiring the spatial resolution data. Based on the test data acquired in the time-resolved data acquisition step, a fuel consumption amount M of the solid fuel during the combustion test at any combustion time t is calculated. ｆ A fuel consumption calculation step for obtaining (t); R(x, 0) and R(x, t ｆ ) and M calculated in the fuel consumption calculation step ｆ and a time-space shape calculation step of calculating R(x, t) based on (t). A method for time-space analysis of solid fuel in a hybrid rocket engine, comprising:

2. The time-space shape calculation step calculates R(x, t) by the formula (1). [0010] 2. The method for space-time analysis of solid fuel in a hybrid rocket engine according to claim 1.

3. The test data is the combustion chamber pressure P ｃ Change in time and nozzle throat cross-sectional area A ｔ and oxidizer mass flow rate dm ｏ Change in time of / dt and fuel consumption data M ｆ，ｅｘ and The fuel consumption calculation step uses a chemical equilibrium calculation to calculate the mass flow ratio O / F of the oxidizer and the fuel and the characteristic exhaust speed efficiency η ｃ＊ By finding ｆ (t) 3. A method for time-space analysis of solid fuel in a hybrid rocket engine according to claim 1 or 2.

4. A spatiotemporal resolution data acquisition step is provided, The time-resolved data acquisition step acquires the test data from one combustion test, The time-space resolution data acquisition step calculates a fuel regression rate and a propellant mass flux G based on the shape R(x, t) of the solid fuel obtained by the time-space shape calculation step and the test data. ｐ and the propellant mass flux G ｐ and that the fuel regression rate can be estimated for an infinite number of combinations of the two parameters at an arbitrary spatial position x of the solid fuel.

4. The method for space-time analysis of solid fuel in a hybrid rocket engine according to claim 3.

5. The time-space resolution data acquisition step obtains a fuel regression rate when the combustion of the solid fuel continues by extrapolating the obtained fuel regression rate to a time domain and / or a space domain, or obtains the fuel consumption data M ｆ，ｅｘ and the fuel consumption at the end of the combustion test M ｆ (t ｆ and determining a shape of the solid fuel as the combustion of the solid fuel continues by extrapolating the shape R(x, t) of the solid fuel to a time domain and / or a space domain based on the ratio of the shape R(x, t) of the solid fuel to the time domain and / or the space domain.

5. The method for space-time analysis of solid fuel in a hybrid rocket engine according to claim 4.

6. The solid fuel has an elongated shape along a predetermined axis, Any spatial position x of the solid fuel represents a position along the axis.

2. The method for space-time analysis of solid fuel in a hybrid rocket engine according to claim 1.

7. A time-resolved data acquisition means for acquiring test data in a combustion test of the hybrid rocket engine; Let x denote an arbitrary spatial position of the solid fuel of the hybrid rocket engine, t denote an arbitrary burning time of the burning test, and t denote the end time of the burning test. ｆ When the shape of the solid fuel during the combustion test is R(x, t), the shape of the solid fuel before the start of the combustion test R(x, 0) and the shape of the solid fuel after the end of the combustion test R(x, t ｆ ) and a spatial resolution data acquisition means for acquiring the spatial resolution data; Based on the test data acquired by the time-resolved data acquisition means, a fuel consumption amount M of the solid fuel during the combustion test at any combustion time t is calculated. ｆ A fuel consumption calculation means for calculating (t); R(x, 0) and R(x, t ｆ ) and M calculated by the fuel consumption calculation means ｆ and a time-space shape calculation means for calculating R(x, t) based on (t). A time-space analysis system for solid fuel of a hybrid rocket engine, comprising:

8. The time-space shape calculation means calculates R(x, t) by the formula (1). [0010] 8. The time-space analysis system for solid fuel of a hybrid rocket engine according to claim 7.

9. The test data is the combustion chamber pressure P ｃ Change in time and nozzle throat cross-sectional area A ｔ and oxidizer mass flow rate dm ｏ Change in time of / dt and fuel consumption data M ｆ，ｅｘ and The fuel consumption calculation means uses a chemical equilibrium calculation to calculate the mass flow ratio O / F of the oxidizer to the fuel and the characteristic exhaust speed efficiency η ｃ＊ By finding ｆ (t) 9. The time-space analysis system for solid fuel of a hybrid rocket engine according to claim 7 or 8.

10. A spatiotemporal resolution data acquisition means is provided; the time-resolved data acquisition means acquires the test data from one combustion test, The space-time resolution data acquisition means calculates a fuel regression rate and a propellant mass flux G based on the shape R(x, t) of the solid fuel calculated by the space-time shape calculation means and the test data. ｐ and the propellant mass flux G ｐ and that the fuel regression rate can be estimated for an infinite number of combinations of the two parameters at an arbitrary spatial position x of the solid fuel.

10. The time-space analysis system for solid fuel of a hybrid rocket engine according to claim 9.

11. The spatio-temporal resolution data acquisition means obtains a fuel regression rate when the combustion of the solid fuel continues by extrapolating the obtained fuel regression rate to a time domain and / or a space domain, or obtains the fuel consumption data M ｆ，ｅｘ and the fuel consumption at the end of the combustion test M ｆ (t ｆ and determining a shape of the solid fuel as the combustion of the solid fuel continues by extrapolating the shape R(x, t) of the solid fuel to a time domain and / or a space domain based on the ratio of the shape R(x, t) of the solid fuel to the time domain and / or the space domain. The time-space analysis system for solid fuel of a hybrid rocket engine according to claim 10.

12. The solid fuel has an elongated shape along a predetermined axis, Any spatial position x of the solid fuel represents a position along the axis.

8. The time-space analysis system for solid fuel of a hybrid rocket engine according to claim 7.

13. Computer, A time-resolved data acquisition means for acquiring test data in a combustion test of the hybrid rocket engine; Let x denote an arbitrary spatial position of the solid fuel of the hybrid rocket engine, t denote an arbitrary burning time of the burning test, and t denote the end time of the burning test. ｆ When the shape of the solid fuel during the combustion test is R(x, t), the shape of the solid fuel before the start of the combustion test R(x, 0) and the shape of the solid fuel after the end of the combustion test R(x, t ｆ ) and a spatial resolution data acquisition means for acquiring the spatial resolution data; Based on the test data acquired by the time-resolved data acquisition means, a fuel consumption amount M of the solid fuel during the combustion test at any combustion time t is calculated. ｆ A fuel consumption calculation means for determining (t); R(x, 0) and R(x, t ｆ ) and M calculated by the fuel consumption calculation means ｆ A time-space shape calculation means for calculating R(x, t) based on A space-time analysis program for solid fuel in a hybrid rocket engine, characterized by functioning as follows.

14. The time-space shape calculation means calculates R(x, t) by the formula (1). [0010] A time-space analysis program for solid fuel of a hybrid rocket engine according to claim 13.

15. The test data is the combustion chamber pressure P ｃ Change in time and nozzle throat cross-sectional area A ｔ and oxidizer mass flow rate dm ｏ Change in time of / dt and fuel consumption data M ｆ，ｅｘ and The fuel consumption calculation means uses a chemical equilibrium calculation to calculate the mass flow ratio O / F of the oxidizer to the fuel and the characteristic exhaust speed efficiency η ｃ＊ By finding ｆ (t) A time-space analysis program for solid fuel of a hybrid rocket engine according to claim 13 or 14.

16. The computer has a function of acquiring time-space resolution data, the time-resolved data acquisition means acquires the test data from one combustion test, The space-time resolution data acquisition means calculates a fuel regression rate and a propellant mass flux G based on the shape R(x, t) of the solid fuel calculated by the space-time shape calculation means and the test data. ｐ and the propellant mass flux G ｐ and that the fuel regression rate can be estimated for an infinite number of combinations of the two parameters at an arbitrary spatial position x of the solid fuel. A time-space analysis program for solid fuel of a hybrid rocket engine according to claim 15.

17. The spatio-temporal resolution data acquisition means obtains a fuel regression rate when the combustion of the solid fuel continues by extrapolating the obtained fuel regression rate to a time domain and / or a space domain, or obtains the fuel consumption data M ｆ，ｅｘ and the fuel consumption at the end of the combustion test M ｆ (t ｆ and determining a shape of the solid fuel as the combustion of the solid fuel continues by extrapolating the shape R(x, t) of the solid fuel to a time domain and / or a space domain based on the ratio of the shape R(x, t) of the solid fuel to the time domain and / or the space domain. A time-space analysis program for solid fuel of a hybrid rocket engine according to claim 16.

18. The solid fuel has an elongated shape along a predetermined axis, Any spatial position x of the solid fuel represents a position along the axis. A time-space analysis program for solid fuel of a hybrid rocket engine according to claim 13.

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