Method, system and program for analyzing combustion state of hybrid rocket engine

Abstract

To provide a method, system and program for analyzing a combustion state of a hybrid rocket engine, which can obtain time history of O / F of the hybrid rocket engine in real time with relatively high accuracy.SOLUTION: A method for analyzing a combustion state of a hybrid rocket engine acquires test data including fuel consumption data Mf,ex in a combustion test. The method obtains a theoretical characteristic exhaust speed c*th for multiple values of O / F in advance by a combination of fuel and oxidizer contained in a propellant used in the combustion test, and approximates c*th×{1+1 / (O / F)} with a first power function with O / F as a variable. The method calculates, based on the test data and the first power function, a fuel consumption Mf for any multiple values of characteristic exhaust speed efficiency ηc*, and approximates it with a second power function with ηc* as a variable. The method obtains, based on the second power function and the fuel consumption data Mf,ex, the value of ηc* in the combustion test, and obtains time history of O / F in the combustion test.SELECTED DRAWING: Figure 2

Description

[Technical field]

[0001] The present invention relates to a combustion state analysis method, a combustion state analysis system, and a combustion state analysis program for 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 propellant rocket engines are easier to control combustion 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] In rocket engines, the propellant mass flow rate, which is the sum of the mass flow rate of the oxidizer and the mass flow rate of the fuel, is one of the important combustion data. In liquid propellant rocket engines, the propellant mass flow rate can be easily measured because both the fuel and the oxidizer are liquid. In solid propellant rocket engines, the gasification rate of the solid propellant corresponds to the propellant mass flow rate, which is difficult to measure directly, but the O / F (the mass flow rate ratio of the oxidizer to the fuel) has already been investigated for each composition of solid propellant and is known. Since the O / F is known, the composition of the combustion gas flowing through the nozzle can be obtained by chemical equilibrium calculations, and the history of the propellant mass flow rate can be easily obtained from the pressure history of the combustion chamber and the area of ​​the nozzle throat.

[0004] In contrast, in hybrid rocket engines, the mass flow rate of the oxidizer, which is either gas or liquid, can be easily measured, but the mass flow rate of the fuel is difficult to measure directly because it is given by the gasification rate of the fuel. If the mass flow rate of the fuel cannot be measured, the O / F is also unknown, and the mass flow rate of the propellant cannot be calculated from the pressure of the combustion chamber and the area of ​​the nozzle throat, as in solid propellant rocket engines. For this reason, in hybrid rocket engines, when obtaining combustion data, it has been common to measure the weight of the fuel before and after combustion, and divide the mass difference by the combustion time to obtain the mass average fuel mass flow rate.

[0005] However, because the fuel regression rate and fuel gasification rate of an actual hybrid rocket engine are not constant during combustion and have nonlinearity, there is a problem that errors occur when using the weight-average fuel mass flow rate. Therefore, in the past, methods proposed to obtain the fuel flow rate and O / F history of a hybrid rocket engine include a method of directly measuring the thickness and weight of the solid fuel, and a method (reproduction method) of estimating from the history of the combustion chamber pressure and oxidizer flow rate, which are easily measurable.

[0006] Direct measurement methods that have been developed include, for example, a method in which the fuel regression rate during combustion is photographed with a camera to obtain a time- and space-resolved fuel regression rate (see, for example, Non-Patent Document 1); a method in which the fuel thickness is measured with an ultrasonic sensor mounted on the rocket combustion chamber to obtain a time-resolved fuel regression rate inside the rocket combustion chamber (see, for example, Non-Patent Document 2); a method in which solid fuel is measured with time and partial space resolution by performing X-ray measurement on tubular solid fuel (see, for example, Non-Patent Document 3); and a method in which a fuel with an electrode network is formed by blending a conductive material with a non-conductive solid fuel using a 3D printer, and the physical quantities of the electrode network are measured to obtain a time- and partial space-resolved fuel regression rate (see, for example, Patent Document 1).

[0007] However, among these direct measurement methods, the method described in Non-Patent Document 1 is for a combustion test using rectangular fuel, and not only is there a limit to the fuel that can be used, but there is also a problem that it is difficult to apply it to a combustion test of a rocket engine. In addition, the method described in Non-Patent Document 2 is a point measurement, so there is a problem that it is not possible to obtain the time history of O / F in the entire rocket engine. In addition, the method described in Non-Patent Document 3 is also a measurement in a part of the solid fuel, so there is also a problem that it is not possible to obtain the time history of O / F in the entire rocket engine. In addition, the method described in Patent Document 1 requires 3D printer modeling to insert an electrode inside the solid fuel, so there are problems such as limitations on the type of fuel that can be used, and problems such as not being able to obtain the time history of O / F in the entire rocket engine.

[0008] In contrast, the reproduction method uses combustion test data and chemical equilibrium calculations to perform two-stage convergence calculations, making it possible to obtain the O / F (time history of O / F) of the entire rocket engine at each time regardless of the type of solid fuel used, thus solving the problems of the direct measurement method. In the reproduction method, the time history of O / F can be obtained as follows (see, for example, Non-Patent Documents 3 to 5).

[0009] In other words, the characteristic pumping speed efficiency is 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 fuel consumption data from the combustion test is M f,ex Then, the following equations (a) and (b) hold. In addition, the fuel consumption M f is expressed by formula (c) using O / F. Here, m f is the fuel mass, dm f / dt is the fuel mass flow rate (hereinafter m f" with a dot over it is the same.

[0010]

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[0011] Therefore, in the reproduction method, as shown in FIG. 10, first, after obtaining the combustion test data (step 51), the characteristic exhaust velocity efficiency η c* Assuming (step 52), the combustion chamber pressure P c and oxidizer mass flow rate dm o Based on / dt, the theoretical characteristic pumping speed c is calculated by chemical equilibrium. * th Then, using equation (a), O / F at each combustion time is iteratively calculated (steps 53 to 54), and the fuel mass flow rate at each combustion time is calculated (step 55).

[0012] After obtaining the O / F and fuel mass flow rate up to the time of the end of combustion (step 56), the fuel consumption M is calculated by integrating the O / F at each combustion time over the entire combustion time using equation (c). f (Step 57), and the fuel consumption data M obtained in the actual combustion test f,ex (Step 58). Fuel consumption M f and fuel consumption data M f,ex The characteristic pumping speed efficiency η c* While changing, steps 52 to 58 are repeated repeatedly. f and M. f,ex If they match, the characteristic exhaust speed efficiency η c* and O / F at each combustion time are expressed as the characteristic exhaust velocity efficiency η c* and the time history of O / F is obtained (step 59). In this way, the reproduction method can obtain the time history of O / F.

[0013] As a chemical equilibrium calculation program capable of performing chemical equilibrium calculations in the combustion chamber of a rocket engine and combustion calculations for various chemical species, for example, NASA-CEA (Chemical Equilibrium with Applications) in Non-Patent Document 6 is provided. With NASA-CEA, for example, chemical equilibrium calculations can be performed based on the combination of solid fuel and oxidizer contained in the propellant used in the combustion test of a hybrid rocket engine. Also, a method for evaluating a hybrid rocket engine by performing a numerical combustion test has been developed (for example, see Non-Patent Document 7). [Prior art documents] [Non-patent literature]

[0014] [Non-Patent Document 1] 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 2] Lestrade et al., “Liquefying fuel regression rate modeling in hybrid propulsion”, Aerospace Science and Technology, 2015, 42 [Non-Patent Document 3] 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 4] Nagata et al., “Accuracy and applicable range of a reconstruction technique for hybrid rockets”, Advances in aircraft and spacecraft science, 1.3.2014 [Non-Patent Document 5] Saito et al., “The accuracy of reconstruction techniques for determining hybrid rocket fuel regression rate”, 2018 Joint Propulsion Conference, 2018 [Non-Patent Document 6] 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 7] 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]

[0015] [Patent Document 1] Patent Publication No. 2021-063501 Summary of the Invention [Problem to be solved by the invention]

[0016] However, the reproduction method described in Non-Patent Documents 3 to 5 requires two-stage convergence calculation, which results in high calculation costs, time-consuming convergence, and difficulty in determining the time history of O / F in real time. In addition, as described in Non-Patent Documents 3 and 4, the reproduction method also has the problem that, when performing convergence calculation, a so-called "multiple solution problem" occurs in which multiple solutions exist in the O / F region to be set due to the performance of the rocket engine, and the analysis accuracy of the O / F decreases. Non-Patent Document 5 describes a method for solving the multiple solution problem by assuming that the characteristic exhaust speed is constant during combustion, but when the O / F fluctuates during combustion, this assumption does not hold, and there is also the problem that the analysis accuracy is significantly deteriorated.

[0017] The present invention has been made with a focus on such problems, and aims to provide a combustion state analysis method, combustion state analysis system, and combustion state analysis program for a hybrid rocket engine that can determine the time history of the O / F of a hybrid rocket engine in real time with relatively high accuracy. [Means for solving the problem]

[0018] In order to achieve the above object, the present invention provides a method for analyzing the combustion state of a hybrid rocket engine, comprising: f,ex A data acquisition step for acquiring test data including the theoretical characteristic pumping speed c * th When the mass flow ratio of the oxidizer to the fuel is O / F, the c for multiple values ​​of O / F was calculated in advance by the combination of the fuel and oxidizer contained in the propellant used in the combustion test. * th Search for c * th The first approximation step is to approximate ×{1+1 / (O / F)} by the first power function with O / F as a variable, and the characteristic pumping speed efficiency is η c*, then, based on the test data acquired in the data acquisition step and the first power function approximated in the first approximation step, c* Fuel consumption for the value of M f Calculate the fuel consumption M f η c* a second approximation step of approximating the fuel consumption data M obtained in the data acquisition step using a second power function having a variable, f,ex Based on this, η in the combustion test c* a characteristic exhaust speed efficiency calculation step for calculating the value of η c* and an O / F calculation step of calculating a time history of O / F in the combustion test based on the value of the first power function approximated in the first approximation step, the test data acquired in the data acquisition step, and the first power function approximated in the first approximation step.

[0019] The hybrid rocket engine combustion state analysis system according to the present invention is a system for analyzing fuel consumption data M f,ex A data acquisition means for acquiring test data including the theoretical characteristic pumping speed c * th When the mass flow ratio of the oxidizer to the fuel is O / F, the c for multiple values ​​of O / F was calculated in advance by the combination of the fuel and oxidizer contained in the propellant used in the combustion test. * th Search for c * th The first approximation method is to approximate ×{1+1 / (O / F)} by the first power function with O / F as a variable, and the characteristic pumping speed efficiency is η c* Then, based on the test data acquired by the data acquisition means and the first power function approximated by the first approximation means, any number of η c* Fuel consumption for the value of M f Calculate the fuel consumption M f η c*a second approximation means for approximating the second power function with a variable, the second power function approximated by the second approximation means, and the fuel consumption data M acquired by the data acquisition means. f,ex Based on this, η in the combustion test c* a characteristic exhaust speed efficiency calculation means for calculating a value of η c* and an O / F calculation means for calculating a time history of O / F in the combustion test based on the value of the first power function approximated by the first approximation means, the test data acquired by the data acquisition means, and the first power function approximated by the first approximation means.

[0020] The hybrid rocket engine combustion state analysis program according to the present invention is a program for causing a computer to input fuel consumption data M in a combustion test of a hybrid rocket engine. f,ex A data acquisition means for acquiring test data including the theoretical characteristic pumping speed c * th When the mass flow ratio of the oxidizer to the fuel is O / F, the c for multiple values ​​of O / F was calculated in advance by the combination of the fuel and oxidizer contained in the propellant used in the combustion test. * th Search for c * th The first approximation method is to approximate ×{1+1 / (O / F)} by the first power function with O / F as a variable, and the characteristic pumping speed efficiency is η c* Then, based on the test data acquired by the data acquisition means and the first power function approximated by the first approximation means, any number of η c* Fuel consumption for the value of M f Calculate the fuel consumption M f η c* a second approximation means for approximating the second power function with a variable, the second power function approximated by the second approximation means, and the fuel consumption data M acquired by the data acquisition means f,ex Based on this, η in the combustion test c* a characteristic exhaust speed efficiency calculation means for calculating a value of η determined by the characteristic exhaust speed efficiency determination means; c*The present invention is characterized in that the O / F calculation means functions as an O / F calculation means for calculating the time history of O / F in the combustion test based on the value of the first power function approximated by the first approximation means, the test data acquired by the data acquisition means, and the first power function approximated by the first approximation means.

[0021] The hybrid rocket engine combustion state analysis method, combustion state analysis system, and combustion state analysis program according to the present invention use an approximation of the first power function and the second power function, which eliminates the need for convergence calculations as in the reproduction method, and can reduce calculation costs. In addition, it is possible to prevent the occurrence of multiple solution problems as in the reproduction method. Therefore, the hybrid rocket engine combustion state analysis method, combustion state analysis system, and combustion state analysis program according to the present invention can obtain the time history of the O / F of the hybrid rocket engine in real time with relatively high accuracy.

[0022] In the combustion state analysis method for a hybrid rocket engine according to the present invention, the test data is a combustion chamber pressure P c and the nozzle throat cross-sectional area A t and oxidizer mass flow rate dm o / dt, and the first approximation step approximates the first power function by * th ×{1+1 / (O / F)}=A(O / F) B and the second approximation step is performed by calculating the values ​​of A and B using the arbitrary number of η c* Calculate the value of O / F using equation (1) and then calculate the fuel consumption M f Calculate the value of (where dm f / dt is the fuel mass flow rate),

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[0023] In the combustion state analysis method for a hybrid rocket engine according to the present invention, the first approximation step uses a chemical equilibrium calculation to calculate c for a plurality of O / F values. * thIn the combustion state analysis system and the combustion state analysis program for a hybrid rocket engine according to the present invention, the first approximation means uses a chemical equilibrium calculation to calculate c for a plurality of O / F values. * th In this case, the chemical equilibrium calculation is preferably configured to calculate c for a given O / F value. * th Any method may be used as long as it can calculate the above. For example, the chemical equilibrium calculation program NASA-CEA described in Non-Patent Document 6 can be used. Effect of the Invention

[0024] According to the present invention, it is possible to provide a combustion state analysis method, a combustion state analysis system, and a combustion state analysis program for a hybrid rocket engine, which can determine the time history of the O / F of a hybrid rocket engine in real time with relatively high accuracy. [Brief description of the drawings]

[0025] [Figure 1] FIG. 1 is a longitudinal sectional view showing a hybrid rocket engine used in a combustion test according to an embodiment of the present invention. [Diagram 2] 1 is a block diagram showing a configuration of a combustion state analysis system for a hybrid rocket engine according to an embodiment of the present invention; [Diagram 3] 1 is a graph showing an example of the relationship between c*th×{1+1 / (O / F)} and O / F (solid line) in the first approximation means of the combustion state analysis system for a hybrid rocket engine according to an embodiment of the present invention, and the first power function (dashed line) obtained. [Figure 4] This is a graph showing an example of the fuel consumption Mf when the characteristic exhaust velocity efficiency ηc*=0.6, 0.8, and 1.0 in the second approximation means of the combustion state analysis system for a hybrid rocket engine of an embodiment of the present invention, and the obtained second power function (dashed line). [Diagram 5]1 is a flowchart showing a processing procedure of a combustion state analysis method for a hybrid rocket engine according to an embodiment of the present invention. [Figure 6] 1 is a graph showing the time history of the fuel regression rate (rdot), O / F, and combustion chamber pressure Pc obtained by a numerical combustion test, which are used in the combustion state analysis method of the hybrid rocket engine according to an embodiment of the present invention. [Figure 7] Graphs showing (a) the time history of O / F when the characteristic exhaust velocity efficiency ηc* is set to 0.6, 0.8, and 1.0, (b) the fuel consumption Mf, and the obtained second power function (dashed line), (c) the time history of the O / F finally obtained ("Present Invention" in the figure), and the time history of O / F obtained by a numerical combustion test ("Numerical Test" in the figure) of the combustion state analysis method of a hybrid rocket engine of an embodiment of the present invention. [Figure 8] 1 is a graph showing a time history of an oxidizer mass flow rate dmo / dt and a combustion chamber pressure Pc obtained by a combustion test, which are used in a combustion state analysis method of a hybrid rocket engine according to an embodiment of the present invention. [Figure 9] 1 is a graph showing (a) the time history of O / F when the characteristic exhaust speed efficiency ηc* is set to 0.6, 0.8, and 1.0, (b) the fuel consumption Mf, and the obtained second power function (dashed line), (c) the time history of the finally obtained O / F ("present invention" in the figure), and the time history of O / F (Oxidizer to fuel mass ratio) obtained by the conventional reproduction method ("reproduction method" in the figure), in the combustion state analysis method of a hybrid rocket engine of an embodiment of the present invention. [Figure 10] 1 is a flowchart showing a processing procedure of a conventional reproduction method. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0026] Hereinafter, an embodiment of the present invention will be described with reference to the drawings. 1 to 9 show a hybrid rocket engine combustion state analysis method, a combustion state analysis system, and a combustion state analysis program according to an embodiment of the present invention. The hybrid rocket engine combustion state analysis method according to an embodiment of the present invention is a method that is preferably implemented by the hybrid rocket engine combustion state analysis system according to an embodiment of the present invention, and can be executed by a computer using the hybrid rocket engine combustion state analysis program.

[0027] As shown in FIG. 1, the hybrid rocket engine 40 uses, for example, a cylindrical solid fuel 41 as a propellant, and is configured to supply an oxidizer OX from an injector 43 attached to the front of the hybrid rocket engine 40 to the inside of the solid fuel 41 arranged inside a combustion chamber 42, so that the oxidizer OX reacts with the vaporized solid fuel 41 and burns by boundary layer combustion. The propellant is not limited to a cylindrical shape, and may be a solid fuel of any shape. The hybrid rocket engine 40 is configured to obtain thrust or driving force by choking and discharging the combustion gas to the outside through a nozzle 44. In addition, it is configured to perform nitrogen purging at the end of combustion to promote the end of combustion.

[0028] 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 41 of the hybrid rocket engine 40. 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.

[0029] In the combustion test of the hybrid rocket engine 40, the oxidizer mass flow rate dm was calculated by measuring the amount of oxidizer OX supplied from the injector 43. o The time change of / dt is acquired, and the combustion chamber pressure P cAfter the combustion test is completed, the solid fuel 41 is removed from the combustion chamber 42, and fuel consumption data M is obtained from the mass difference before and after the combustion test. f,ex are beginning to demand more.

[0030] As shown in FIG. 2, a hybrid rocket engine combustion state analysis system 10 according to an 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.

[0031] 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 o The storage means 12 is configured to temporarily store the test data input by the input means 11 and the various parameters calculated by the main control unit 14 for a necessary period of time.

[0032] The display means 13 displays the test data and various parameters stored in the storage means 12, and the characteristic exhaust speed efficiency η c* It is configured to display the time history of operation and maintenance, etc., in graphs and numbers.

[0033] The main control unit 14 has a data acquisition means 21, a first approximation means 22, a second approximation means 23, a characteristic exhaust speed efficiency calculation means 24, and an O / F calculation means 25. The data acquisition means 21 is configured to acquire each test data in a combustion test of the hybrid rocket engine via the input means 11, and store the data in the storage means 12.

[0034] The first approximation means 22 calculates the theoretical characteristic pumping speed c for a plurality of values ​​of O / F as follows. * th and obtain a first power function with O / F as a variable as an approximation equation. That is, by transforming the above equation (a) and combining the test data stored in the storage means 12 on the left side, equation (4) is obtained.

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[0035] On the right side of equation (4), c * th ×{1+1 / (O / F)} is approximated by the first power function O / F, A(O / F) B That is, c * th ×{1+1 / (O / F)}=A(O / F) B By approximating it as above, we obtain equation (5). Note that c * th is the combustion chamber pressure P c Therefore, in this approximation, the combustion chamber pressure P c The impact of

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[0036] Here, for example, by using the chemical equilibrium calculation program NASA-CEA, c for multiple values ​​of O / F was calculated based on the combination of solid fuel and oxidizer contained in the propellant used in the combustion test. * th This gives c * thA graph showing the relationship between ×{1+1 / (O / F)} and O / F can be obtained. As a specific example, the solid fuel is PMMA (acrylic resin), the oxidizer is gas oxygen, and the combustion chamber pressure P c When is 0.5 MPa, c * th The relationship between ×{1+1 / (O / F)} and O / F was calculated and is shown by the solid line in Figure 3.

[0037] Next, for the graph obtained, use, for example, the least squares method to approximate the equation A(O / F) B The values ​​of A and B are calculated so that the best fit is obtained. The approximate equation calculated for the example shown in Figure 3 is shown by the dashed line in Figure 3. The dashed line graph shows A = 3087.9 and B = -0.389. The coefficient of determination (R 2 ) is 0.9552. In this manner, the first approximation means 22 determines the first power function, which is an approximation formula.

[0038] The second approximation means 23 calculates the fuel consumption M f , the characteristic exhaust speed efficiency η c* The second power function is calculated by approximating the O / F with a variable, and the second power function is calculated. In other words, when formula (5) is calculated for O / F, the above formula (1) is obtained. In addition, by integrating O / F over the entire combustion time using formula (2) above, the fuel consumption M f Therefore, we can obtain any number of η c* For the value of , calculate the value of O / F using equation (1), and then calculate the fuel consumption M f Calculate the value of

[0039] As a specific example, the solid fuel is PMMA (acrylic resin), the oxidizer is gaseous oxygen, and the oxidizer mass flow rate dm o / dt is 2 g / s, the nozzle throat diameter is 4 mm (nozzle throat cross-sectional area A t is 12.57 mm 2 ), combustion chamber pressure P c When is 0.5 MPa, from equations (1) and (2), η c* Fuel consumption when M = 0.6, 0.8, 1.0f was calculated and is shown in Figure 4.

[0040] Calculated fuel consumption M f and η c* Since the relationship with is a monotonic function, M f η c* The second power function, C(η c* ) D By approximating with, we obtain equation (6).

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[0041] Any multiple η c* and the calculated fuel consumption M f For example, the least squares method is used to find the values ​​of C and D that best fit equation (6). The approximate equation found in the example shown in Figure 4 is shown by the dashed line in Figure 4. The dashed line graph shows C = 3.9722 and D = -2.571. The coefficient of determination (R 2 ) is 1. In this way, the second approximation means 23 obtains the second power function, which is an approximation formula. Note that, in order to obtain the second power function with high accuracy, it is necessary to use three or more η c* For the value of M f It is preferable to obtain

[0042] The characteristic exhaust speed efficiency calculation means 24 calculates the fuel consumption M f is the actual fuel consumption M f,ex Then, the above formula (3) is obtained, and the values ​​of C and D of the second power function approximated by the second approximation means 23 and the fuel consumption data M stored in the storage means 12 can be calculated by the formula (3). f,ex Based on the above, the characteristic exhaust velocity efficiency η c* The method is configured to find the value of

[0043] The O / F calculation means 25 calculates the characteristic exhaust speed efficiency η c*The time history of O / F in the combustion test is obtained by substituting the values ​​of , each test data stored in the memory means 12, and the values ​​of A and B of the first power function approximated by the first approximation means 22 into equation (1).

[0044] Alternatively, since equation (7) is obtained by substituting equation (3) into equation (1), the O / F calculation means 25 may be configured to obtain the time history of O / F in the combustion test by substituting each test data stored in the memory means 12, the values ​​A and B of the first power function approximated by the first approximation means 22, and the values ​​C and D of the second power function approximated by the second approximation means 23 into equation (7).

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[0045] Next, a method for analyzing the combustion state of a hybrid rocket engine according to an embodiment of the present invention, which is a processing procedure of the hybrid rocket engine combustion state analysis system 10 according to an embodiment of the present invention, will be described with reference to Fig. 5. As shown in Fig. 5, 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 O / dt is acquired and stored in the storage means 12. In addition, the first approximation means 22 calculates theoretical characteristic exhaust velocities c for a plurality of values ​​of O / F in advance based on the combination of the solid fuel and the oxidizer contained in the propellant used in the combustion test. * th Find c * th ×{1+1 / (O / F)} is approximated by the first power function on the right hand side of equation (5) with O / F as a variable, and the values ​​of A and B of the first power function are found (step 31).

[0046] Next, the second approximation means 23 calculates a plurality of arbitrary characteristic exhaust speed efficiencies η based on each test data stored in the storage means 12 and the values ​​A and B of the first power function approximated by the first approximation means 22. c* Select values ​​of η c* For the value of , calculate the value of O / F using equation (1) (step 33), and then calculate the fuel consumption M f The value of is calculated (step 34).

[0047] Furthermore, the second approximation means 23 calculates M f η c* The second power function on the right side of the equation (6) is used as a variable to approximate the second power function, and the values ​​of C and D of the second power function are obtained. Next, the characteristic exhaust speed efficiency calculation means 24 calculates the values ​​of C and D of the second power function approximated by the second approximation means 23 and the fuel consumption data M stored in the storage means 12. f,ex Based on this, the characteristic exhaust velocity efficiency η c* The value of is calculated (step 35).

[0048] Next, the O / F calculation means 25 calculates the η c* The time history of O / F in the combustion test is obtained by substituting the values ​​of A, B of the first power function approximated by the first approximation means 22, each test data stored in the storage means 12, and the values ​​of A and B of the first power function approximated by the first approximation means 22 into equation (1) (step 36). Alternatively, the time history of O / F in the combustion test is obtained by substituting the values ​​of A, B of the first power function approximated by the first approximation means 22, and the values ​​of C and D of the second power function approximated by the second approximation means 23 into equation (7) by the O / F calculation means 25 (step 36).

[0049] The hybrid rocket engine combustion state analysis system 10 and the combustion state analysis method according to the embodiment of the present invention can uniquely calculate O / F from equations (1) and (7) by using an approximation of the first power function on the right side of equation (5) and the second power function on the right side of equation (3). This eliminates the need for convergent calculations as in the reproduction method, and can reduce calculation costs. In addition, it is possible to prevent the occurrence of multiple solution problems as in the reproduction method. Therefore, the hybrid rocket engine combustion state analysis system 10 and the combustion state analysis method according to the embodiment of the present invention can calculate the time history of O / F of a hybrid rocket engine in real time with relatively high accuracy. EXAMPLES

[0050] A numerical combustion test was conducted using a known evaluation method for hybrid rocket engine combustion tests, and the time history of each test data and O / F was obtained. Using each test data obtained in the numerical combustion test, the time history of O / F was obtained using the combustion state analysis method of the hybrid rocket engine of the embodiment of the present invention shown in Figure 5, and a comparison was made with the time history of O / F obtained in the numerical combustion test.

[0051] The numerical combustion test was carried out using the method described in Non-Patent Document 7. In the numerical combustion test, a cylindrical propellant was used, the solid fuel contained in the propellant was HDPE (high density polyethylene), the oxidizer was oxygen gas, the length of the propellant was 200 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 30 seconds.

[0052] Numerical combustion test results showed that the fuel consumption f,ex is 265 g, characteristic exhaust speed efficiency η c* The fuel regression rate (rdot), O / F, and combustion chamber pressure P c The time history of is shown in Figure 6.

[0053] Next, the time history of O / F was calculated using each test data obtained in the numerical combustion test by the combustion state analysis method of the hybrid rocket engine of the embodiment of the present invention shown in Figure 5. c* When is set to 0.6, 0.8, and 1.0, the value of O / F is calculated using equation (1) in step 33 and the fuel consumption M f The results of calculating the value of and the second power function on the right-hand side of equation (3) obtained in step 35 are shown in Figure 7(b). At this time, the values ​​of A and B of the first power function on the right-hand side of equation (5) obtained in step 31 were A = 3183.3 and B = -0.321, respectively. Furthermore, the values ​​of C and D of the second power function on the right-hand side of equation (3) obtained in step 35 were C = 158.9 and D = -2.98, respectively. Furthermore, the coefficient of determination (R 2 ) was 0.9995.

[0054] Furthermore, in step 35, the η calculated by equation (3) c* was 0.83. The time history of O / F calculated in step 36 using equation (1) or equation (7) is shown in Fig. 7(c) (indicated as "present invention" in the figure). Fig. 7(c) also shows the time history of O / F obtained in a numerical combustion test (indicated as "numerical test" in the figure).

[0055] When the results obtained by the combustion state analysis method of the hybrid rocket engine according to the embodiment of the present invention are compared with the results of the numerical combustion test, as shown in Figure 7(c), it was confirmed that the average error of the time history of O / F with respect to the results of the numerical combustion test is 0.4%, and that they are in relatively good agreement. In addition, the characteristic exhaust velocity efficiency η c* The value of was 0.86 in the numerical combustion test and 0.83 in the method of the present invention, confirming a relatively good agreement. EXAMPLES

[0056] A combustion test was conducted on the hybrid rocket engine, and the time history of O / F was obtained and compared using the combustion state analysis method of the hybrid rocket engine according to the embodiment of the present invention shown in Fig. 5 and the conventional reproduction method shown in Fig. 10. In the combustion test, a cylindrical propellant was used, the solid fuel contained in the propellant was HDPE, the oxidizer was oxygen gas, the length of the propellant was 190 mm, the initial inner diameter was 30 mm, and the density was 950 kg / m 3 The nozzle throat diameter was 8 mm and the combustion time was 40 seconds.

[0057] Combustion test results showed that fuel consumption was M f,ex The oxidizer mass flow rate dm o / dt, and chamber pressure P c The time history of is shown in Figure 8.

[0058] The combustion state analysis method for the hybrid rocket engine according to the embodiment of the present invention shown in FIG. 5 was used to obtain the time history of O / F by using each test data obtained in the combustion test. c* When is set to 0.6, 0.8, and 1.0, the value of O / F is calculated using equation (1) in step 33 and the fuel consumption M f The results of calculating the value of and the second power function on the right-hand side of equation (3) obtained in step 35 are shown in Figure 9(b). At this time, the values ​​of A and B of the first power function on the right-hand side of equation (5) obtained in step 31 were A = 3183.3 and B = -0.321, respectively. Furthermore, the values ​​of C and D of the second power function on the right-hand side of equation (3) obtained in step 35 were C = 62.40 and D = -3.115, respectively. Furthermore, the coefficient of determination (R 2 ) was 1.

[0059] Furthermore, in step 35, the η calculated by equation (3) c*was 0.966. The time history of O / F (Oxidizer to fuel mass ratio) calculated in step 36 using equation (1) or equation (7) is shown in FIG. 9(c) (labeled "present invention" in the figure). The time history of O / F was calculated using the test data obtained in the combustion test by the conventional reproduction method shown in FIG. 10, and the results are also shown in FIG. 9(c) (labeled "reproduction method" in the figure). Note that η c* The value was 0.970.

[0060] When comparing the results obtained by the hybrid rocket engine combustion state analysis method of the embodiment of the present invention with the results of the conventional reproduction method, as shown in Figure 9 (c), it was confirmed that the average error of the time history of O / F compared to the results of the conventional reproduction method was 5.0%, and that they were in relatively good agreement. In addition, the characteristic exhaust velocity efficiency η c* The value of was 0.966 in the method of the present invention, while 0.970 in the conventional reproduction method, and it was confirmed that they were in relatively good agreement. In addition, the conventional reproduction method and the method of the present invention used the same computer for analysis, and when comparing the calculation time, it took about 2 hours in the conventional reproduction method, whereas the method of the present invention obtained results instantly after inputting each test data, confirming that calculation costs can be significantly reduced.

[0061] The hybrid rocket engine combustion state analysis program 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 hybrid rocket engine combustion state analysis program from the communication line or recording medium, transfer it to the internal storage device of the computer, and store it for use. In addition, the hybrid rocket engine combustion state analysis program 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.

[0062] 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.

[0063] The application program as the combustion state analysis program of the hybrid rocket engine according to the embodiment of the present invention includes a program code that is 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]

[0064] 10 Hybrid rocket engine combustion state analysis system 11 Input methods 12 Memory means 13 Display means 14 Main control unit 21 Data Acquisition Methods 22 First approximation means 23 Second approximation means 24. Characteristic exhaust speed efficiency calculation method 25 O / F calculation means 40 Hybrid Rocket Engine 41 Solid fuel 42 Combustion chamber 43 Injector OX Oxidizing agent 44 Nozzle 45 Pressure Sensor

Claims

1. Fuel consumption data for hybrid rocket engine combustion tests ｆ，ｅｘ A data acquisition step of acquiring test data including: The theoretical characteristic pumping speed is c ＊ ｔｈ When the mass flow ratio of the oxidizer to the fuel is O / F, the c for a plurality of values ​​of O / F was calculated in advance by the combination of the fuel and the oxidizer contained in the propellant used in the combustion test. ＊ ｔｈ Find c ＊ ｔｈ a first approximation step of approximating ×{1+1 / (O / F)} by a first power function with O / F as a variable; Characteristic exhaust speed efficiency η ｃ＊ , then, based on the test data acquired in the data acquisition step and the first power function approximated in the first approximation step, ｃ＊ Fuel consumption for the value of M ｆ Calculate the fuel consumption M ｆ η ｃ＊ a second approximation step of approximating with a second power function having a variable The second power function approximated in the second approximation step and the fuel consumption data M acquired in the data acquisition step ｆ，ｅｘ Based on this, η in the combustion test ｃ＊ A characteristic exhaust speed efficiency calculation step for calculating the value of The η determined in the characteristic exhaust speed efficiency determination step ｃ＊ an O / F calculation step of calculating a time history of O / F in the combustion test based on the value of A method for analyzing the combustion state of a hybrid rocket engine, comprising:

2. 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 / dt and The first approximation step is to approximate the first power function by ＊ ｔｈ ×{1+1 / (O / F)}=A(O / F) Ｂ Then, calculate the values ​​of A and B. The second approximation step is ｃ＊ Calculate the value of O / F using equation (1) and calculate the fuel consumption amount M ｆ Calculate the value of m ｆ is the fuel mass), [0010] The second power function to be approximated is M ｆ = C (η ｃ＊ ) Ｄ Then, calculate the values ​​of C and D. The characteristic exhaust speed efficiency calculation step is carried out by calculating η ｃ＊ Find the value of [0025] The O / F calculation step is to obtain a time history of O / F in the combustion test by using the formula (1).

2. The method for analyzing the combustion state of a hybrid rocket engine according to claim 1.

3. The first approximation step uses chemical equilibrium calculations to calculate c for a plurality of O / F values. ＊ ｔｈ 3. The method for analyzing the combustion state of a hybrid rocket engine according to claim 1, further comprising the steps of:

4. Fuel consumption data for hybrid rocket engine combustion tests ｆ，ｅｘ A data acquisition means for acquiring test data including: The theoretical characteristic pumping speed is c ＊ ｔｈ When the mass flow ratio of the oxidizer to the fuel is O / F, the c for a plurality of values ​​of O / F was calculated in advance by the combination of the fuel and the oxidizer contained in the propellant used in the combustion test. ＊ ｔｈ Find c ＊ ｔｈ a first approximation means for approximating ×{1+1 / (O / F)} by a first power function having O / F as a variable; Characteristic exhaust speed efficiency η ｃ＊ Then, based on the test data acquired by the data acquisition means and the first power function approximated by the first approximation means, any number of η ｃ＊ Fuel consumption for the value of M ｆ Calculate the fuel consumption M ｆ η ｃ＊ A second approximation means for approximating the second power function with The second power function approximated by the second approximation means and the fuel consumption data M acquired by the data acquisition means ｆ，ｅｘ Based on this, η in the combustion test ｃ＊ A characteristic exhaust speed efficiency calculation means for calculating the value of The characteristic exhaust speed efficiency η determined by the characteristic exhaust speed efficiency determining means ｃ＊ an O / F calculation means for calculating a time history of O / F in the combustion test based on the value of the first power function approximated by the first approximation means, the test data acquired by the data acquisition means, and the first power function approximated by the first approximation means; A combustion state analysis system for a hybrid rocket engine, comprising:

5. 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 / dt and The first approximation means approximates the first power function by c ＊ ｔｈ ×{1+1 / (O / F)}=A(O / F) Ｂ Then, calculate the values ​​of A and B. The second approximation means is ｃ＊ Calculate the value of O / F using equation (1) and then calculate the fuel consumption amount M ｆ Calculate the value of m ｆ is the fuel mass), [0010] The second power function to be approximated is M ｆ = C (η ｃ＊ ) Ｄ Then, calculate the values ​​of C and D. The characteristic exhaust speed efficiency calculation means calculates η ｃ＊ Find the value of [0025] The O / F calculation means calculates the time history of O / F in the combustion test by using the formula (1).

5. The combustion state analysis system for a hybrid rocket engine according to claim 4.

6. The first approximation means calculates c for a plurality of O / F values ​​using a chemical equilibrium calculation. ＊ ｔｈ 6. The combustion state analysis system for a hybrid rocket engine according to claim 4, wherein the combustion state analysis system is configured to obtain a combustion state of the hybrid rocket engine.

7. Computer, Fuel consumption data for hybrid rocket engine combustion tests ｆ，ｅｘ A data acquisition means for acquiring test data, The theoretical characteristic pumping speed is c ＊ ｔｈ When the mass flow ratio of the oxidizer to the fuel is O / F, the c for a plurality of values ​​of O / F was calculated in advance by the combination of the fuel and the oxidizer contained in the propellant used in the combustion test. ＊ ｔｈ Find c ＊ ｔｈ a first approximation means for approximating ×{1+1 / (O / F)} by a first power function having O / F as a variable; Characteristic exhaust speed efficiency η ｃ＊ Then, based on the test data acquired by the data acquisition means and the first power function approximated by the first approximation means, any number of η ｃ＊ Fuel consumption for the value of M ｆ Calculate the fuel consumption M ｆ η ｃ＊ a second approximation means for approximating the vector by a second power function having a variable The second power function approximated by the second approximation means and the fuel consumption data M acquired by the data acquisition means ｆ，ｅｘ Based on this, η in the combustion test ｃ＊ A characteristic exhaust speed efficiency calculation means for determining the value of The characteristic exhaust speed efficiency η determined by the characteristic exhaust speed efficiency determining means ｃ＊ an O / F calculation means for calculating a time history of O / F in the combustion test based on the value of (a), the test data acquired by the data acquisition means, and the first power function approximated by the first approximation means; A combustion state analysis program for a hybrid rocket engine, characterized by functioning as follows.

8. 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 / dt and The first approximation means approximates the first power function by c ＊ ｔｈ ×{1+1 / (O / F)}=A(O / F) Ｂ Then, calculate the values ​​of A and B. The second approximation means is ｃ＊ Calculate the value of O / F using equation (1) and calculate the fuel consumption amount M ｆ Calculate the value of m ｆ is the fuel mass), [0010] The second power function to be approximated is M ｆ = C (η ｃ＊ ) Ｄ Then, calculate the values ​​of C and D. The characteristic exhaust speed efficiency calculation means calculates η ｃ＊ Find the value of [0025] The O / F calculation means calculates the time history of O / F in the combustion test by using the formula (1).

8. The combustion state analysis program for a hybrid rocket engine according to claim 7.

9. The first approximation means calculates c for a plurality of O / F values ​​using a chemical equilibrium calculation. ＊ ｔｈ 9. The combustion state analysis program for a hybrid rocket engine according to claim 7 or 8, characterized in that it is configured to obtain the following:

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