Estimation Method and Device for Interior Ballistic Performance of Solid Rocket Motor

Abstract

An embodiment of the present invention discloses a method and device for predicting the interior ballistic performance of a solid rocket motor. The method includes: obtaining a pressure-time curve and a burning surface thickness curve corresponding to the propellant of the solid rocket motor; determining a pressure-burning rate curve corresponding to the propellant of the solid rocket motor according to the burning surface thickness curve, preset parameters, and the pressure-time curve; performing a fitting process on the pressure-burning rate curve to obtain a pressure-burning rate fitting curve; obtaining parameters of a burning rate relationship formula corresponding to the propellant of the solid rocket motor based on the pressure-burning rate fitting curve; and determining a time-pressure comparison curve corresponding to the propellant of the solid rocket motor according to the burning surface thickness curve, preset parameters, and the parameters of the burning rate relationship formula. Through the present invention, the technical problem in the related art that the process of predicting the interior ballistic performance of a solid rocket motor is complex and the calculation effect is not ideal is solved, and the technical effect of improving the accuracy of predicting the interior ballistic performance of a solid rocket motor is achieved.

Description

Technical Field

[0001] The present invention relates to the field of aerospace propulsion technology, and in particular to a method and device for estimating the interior ballistic performance of a solid rocket engine. Background Art

[0002] Solid rocket engines are widely used in various military and civilian spacecraft due to their reliability, economy and design convenience. Their working performance can be reflected in the engine's propulsion speed, working state and output power, which affects the strategic use and service life of the entire aircraft. Solid propellant, as the energy source of the rocket engine, burns in the engine and produces high-temperature and high-pressure gas. The gas is ejected at high speed after passing through the nozzle. According to the principle of action and reaction, the entire aircraft gains forward momentum and reaches a predetermined speed or trajectory. With the continuous development of rocket engine technology, people's requirements for the performance of solid propellants have become more diverse and complex, mainly including the following points: high energy characteristics, good mechanical properties, environmentally friendly combustion products, strong physical and chemical stability, etc.

[0003] As an important technical indicator to measure the combustion performance of propellants, the combustion performance parameters of solid propellants have been determined during their development and production. In order to ensure the normal operation of the engine, the combustion of the propellant in the combustion chamber must be stable and reproducible, and the combustion law must be as free from the influence of environmental factors as possible so that the engine can adapt to various complex working conditions. Different types of engines require propellants with different burning rate ranges. For example, for engines that need to keep working for a long time, the burning rate is generally less than 3mm / s, while for end-burning engines that need to generate large thrust instantly, the burning rate is often higher than 35mm / s.

[0004] Solid propellants can also control the flight speed and range of rockets through the law of their energy release, and also have a certain impact on the working reliability of the engine and the accuracy of the rocket's precision strike. Therefore, the combustion performance of solid rocket engines is very important. The characteristic parameters that characterize the steady-state combustion of solid rocket engines mainly include burning rate, pressure index, burning rate coefficient and temperature sensitivity coefficient. For example, burning rate is one of the important performance parameters of solid propellants. It plays a decisive role in the gas generation of the grain, the thrust generated by the rocket engine, and the combustion surface area required to achieve the predetermined generation and thrust. In recent years, due to the need for high-thrust engines, a large number of new technologies have been invested in the development and production of solid propellant formulations, such as adding metal particles to the propellant to improve its energy characteristics, using 3D printing technology to cast the grain to make the combustion more regular, etc., but this also puts forward new requirements for the testing and verification of the propellant formulation. The test results of the propellant formulation can guide its feasibility and improvement. Therefore, how to improve the burning rate test efficiency of solid propellants is crucial.

[0005] Currently, the commonly used methods for measuring the burning rate of propellants include the target wire method and the underwater acoustic emission method. Both of these methods measure the burning rate of the engine under constant temperature and pressure, and there are certain limitations. This is because under the normal operating conditions of the engine, the pressure and temperature in the combustion chamber are constantly changing, which will cause changes in the burning rate of the propellant. Therefore, there are still errors between the burning rates measured by the two methods in the national military standard and the burning rates of the propellants in solid rocket engines. The burning rate of solid propellants is mainly affected by the surrounding gas pressure. To quantitatively study the magnitude of this influence, the pressure index is defined. In the formulation development of propellants, it is extremely crucial to measure the pressure index of propellants. The national military standard gives a method for measuring the pressure index of propellants, but this method has a relatively cumbersome operation process. It is necessary to test several pressure points of the same propellant, and generally, dozens of single-point burning rate measurements need to be repeated, with low test efficiency and a large consumption of samples.

[0006] The engine method, also known as the scaled-down engine method, can also be used for the burning rate test of solid propellants. It can simulate the test results under real working conditions and conduct combustion performance tests using the actual charge form of the engine. The results obtained by this method are often better than those of the target wire method and the acoustic emission method, but due to the high experimental cost of the engine, it is difficult to perform repeated measurements. The methods for measuring the burning rate in the engine are divided into direct methods and indirect methods. The direct methods can be further divided into the interrupted combustion method, the method of carrying a measuring head in the propellant, the optical instrument observation method, etc.; the indirect method is to use the accurate pressure-time curve obtained in the engine and determine the burning rate through the law of conservation of mass.

[0007] The supersonic method is a method that continuously measures the round-trip time of ultrasonic pulses in solid propellants to observe the movement of the burning surface in the propellant. From the length of the movement of the burning surface under a certain time duration, the corresponding burning rate can be calculated. This method can also be applied to the measurement of the unsteady burning rate, and it can reflect the interior ballistic characteristics and unstable combustion characteristics of the propellant by studying the relationship between the burning rate of the propellant and the pressure response.

[0008] However, for the interior ballistic performance of solid rocket engines, especially the burning rate of propellants on the interior ballistic performance of solid rocket engines, in the existing technology, usually complex burning rate measurement methods such as the supersonic method are used. Not only is the process complex, but the calculation effect is also not ideal, making it difficult to accurately predict the interior ballistic performance of solid rocket engines.

[0009] For the above problems, no effective solutions have been proposed yet. Summary of the Invention

[0010] The embodiments of the present invention provide a method and device for predicting the interior ballistic performance of solid rocket engines, so as to at least solve the technical problems that the process of predicting the interior ballistic performance of solid rocket engines in the related technology is complex and the calculation effect is not ideal.

[0011] According to one aspect of the embodiments of the present invention, a method for predicting the interior ballistic performance of a solid rocket motor is provided, including: obtaining the pressure-time curve and the burning surface thickness curve corresponding to the propellant of the solid rocket motor, wherein the solid rocket motor has different nozzle throat diameters and charging conditions; obtaining the preset parameters of the solid rocket motor, wherein the preset parameters include the free volume including the initial free volume of the combustion chamber, the specific heat ratio of the gas, the characteristic velocity of the charge, and the charge density; determining the pressure-burning rate curve corresponding to the propellant of the solid rocket motor according to the burning surface thickness curve, the preset parameters, and the pressure-time curve; performing a fitting process on the pressure-burning rate curve to obtain a pressure-burning rate fitting curve; obtaining the burning rate relationship parameters corresponding to the propellant of the solid rocket motor based on the pressure-burning rate fitting curve; and determining the time-pressure comparison curve corresponding to the propellant of the solid rocket motor according to the burning surface thickness curve, the preset parameters, and the burning rate relationship parameters.

[0012] Optionally, determining the pressure-burning rate curve corresponding to the propellant of the solid rocket motor according to the burning surface thickness curve, the preset parameters, and the pressure-time curve includes: obtaining the thickness, burning surface, and free volume of the propellant of the solid rocket motor at different times according to the burning surface thickness curve and the preset parameters; calculating the burning rate of the propellant of the solid rocket motor at different times according to the thickness at different times; and obtaining the pressure-burning rate curve according to the pressure-time curve and the burning rate at different times.

[0013] Optionally, performing a fitting process on the pressure-burning rate curve to obtain a pressure-burning rate fitting curve includes: screening out a plurality of segments to be fitted from the pressure-burning rate curve, wherein the segments to be fitted include a fitting starting point and a fitting ending point, the fitting starting point is the point on the pressure-burning rate curve with an obvious linear feature and a starting downward trend, and the fitting ending point is the point on the pressure-burning rate curve with an obvious linear feature and an ending downward trend; and performing a fitting process on the plurality of segments to be fitted respectively to obtain the pressure-burning rate fitting curve.

[0014] Optionally, the burning rate relationship parameters include at least one of the following: the burning rate coefficient and the pressure exponent in different pressure ranges; the burning rate coefficient and the pressure exponent of the first step pressure under different nozzle throat diameters; the burning rate coefficient and the pressure exponent of the second step pressure under different nozzle throat diameters; the burning rate coefficient and the pressure exponent of the third step pressure under different nozzle throat diameters.

[0015] Optionally, determining a time-pressure comparison curve corresponding to the propellant of the solid rocket engine according to the burning surface meat thickness curve, the preset parameters, and the burning rate relational expression parameters includes: calculating the pressures of the propellant of the solid rocket engine at different times according to the burning surface meat thickness curve, the preset parameters, and the burning rate relational expression parameters; generating the time-pressure comparison curve according to the pressures at different times.

[0016] Optionally, calculating the pressures of the propellant of the solid rocket engine at different times according to the burning surface meat thickness curve, the preset parameters, and the burning rate relational expression parameters includes: calculating the generated gas amount and the discharged gas amount of the propellant of the solid rocket engine at different times according to the burning surface meat thickness curve, the preset parameters, and the burning rate relational expression parameters; calculating the pressure change rate of the propellant of the solid rocket engine at different times according to the generated gas amount and the discharged gas amount at different times; calculating the pressure change amount of the propellant of the solid rocket engine at different times according to the pressure change rate at different times; calculating the pressures of the propellant of the solid rocket engine at different times according to the pressure change amount at different times.

[0017] Optionally, obtaining a pressure-time curve and a burning surface meat thickness curve corresponding to the propellant of the solid rocket engine includes: conducting ignition experiments on solid rocket engines under different nozzle throat diameters and charging conditions to obtain experimental data, and respectively recording the experimental data into a first data table and a second data table, where the first data table includes different pressures and the times corresponding to the different pressures, and the first data table includes the meat thicknesses of different propellants and the burning surfaces and free volumes respectively corresponding to the meat thicknesses; obtaining the first data table and generating the pressure-time curve based on the first data table; obtaining the second data table and generating the burning surface meat thickness curve based on the second data table.

[0018] According to another aspect of the embodiments of the present invention, there is also provided a device for predicting the interior ballistic performance of a solid rocket motor, including: a first acquisition module, configured to acquire a pressure-time curve and a burning surface thickness curve corresponding to the propellant of the solid rocket motor, wherein the solid rocket motor has different nozzle throat diameters and charging conditions; a second acquisition module, configured to acquire preset parameters of the solid rocket motor, wherein the preset parameters include the free volume including the initial free volume of the combustion chamber, the specific heat ratio of the gas, the characteristic velocity of the charge, and the charge density; a first determination module, configured to determine a pressure-burning rate curve corresponding to the propellant of the solid rocket motor according to the burning surface thickness curve, the preset parameters, and the pressure-time curve; a fitting processing module, configured to perform fitting processing on the pressure-burning rate curve to obtain a pressure-burning rate fitting curve; a third acquisition module, configured to acquire parameters of a burning rate relationship formula corresponding to the propellant of the solid rocket motor based on the pressure-burning rate fitting curve; a second determination module, configured to determine a time-pressure comparison curve corresponding to the propellant of the solid rocket motor according to the burning surface thickness curve, the preset parameters, and the parameters of the burning rate relationship formula.

[0019] According to another aspect of the embodiments of the present invention, there is also provided a computer-readable storage medium, where the computer-readable storage medium includes a stored program, and when the program runs, it controls the device where the computer-readable storage medium is located to execute the method for predicting the interior ballistic performance of a solid rocket motor described in any one of the above.

[0020] According to another aspect of the embodiments of the present invention, there is also provided a processor, where the processor is used to run a program, and when the program runs, it executes the method for predicting the interior ballistic performance of a solid rocket motor described in any one of the above.

[0021] In an embodiment of the present invention, a pressure-time curve and a burning surface thickness curve corresponding to the propellant of a solid rocket motor are obtained, where the solid rocket motor has different nozzle throat diameters and charging conditions; preset parameters of the solid rocket motor are obtained, where the preset parameters include the free volume including the initial free volume of the combustion chamber, the specific heat ratio of the gas, the characteristic velocity of the charge, and the charge density; according to the burning surface thickness curve, the preset parameters, and the pressure-time curve, a pressure-burning rate curve corresponding to the propellant of the solid rocket motor is determined; the pressure-burning rate curve is fitted to obtain a pressure-burning rate fitting curve; based on the pressure-burning rate fitting curve, burning rate relationship parameters corresponding to the propellant of the solid rocket motor are obtained; according to the burning surface thickness curve, the preset parameters, and the burning rate relationship parameters, a time-pressure comparison curve corresponding to the propellant of the solid rocket motor is determined. That is to say, in the embodiment of the present invention, complex burning rate measurement methods such as the supersonic method do not need to be used. Instead, by conducting ignition experiments on solid rocket motors with different throat diameters under different charging conditions and analyzing the test data, burning rate relationship parameters within different pressure ranges of the propellant are obtained. Then, using the burning surface thickness curve, the preset parameters, and the burning rate relationship parameters, a time-pressure comparison curve corresponding to the propellant of the solid rocket motor is calculated. This time-pressure comparison curve can reflect the interior ballistic performance of the solid rocket motor, thereby predicting the interior ballistic performance of the solid rocket motor, and further solving the technical problems of complex process and unsatisfactory calculation effect in predicting the interior ballistic performance of solid rocket motors in the related art, achieving the technical effect of improving the accuracy of predicting the interior ballistic performance of solid rocket motors. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] The drawings described herein are used to provide a further understanding of the present invention, form a part of this application, and the schematic embodiments and descriptions of the present invention are used to explain the present invention, and do not constitute an improper limitation of the present invention. In the drawings:

[0023] Figure 1 It is a flowchart of a method for predicting the interior ballistic performance of a solid rocket motor provided by an embodiment of the present invention;

[0024] Figure 2 It is a schematic diagram of a pressure-time curve under a nozzle throat diameter of 11.5 provided by an optional embodiment of the present invention;

[0025] Figure 3 It is a schematic diagram of a pressure-burning rate curve under a nozzle throat diameter of 11.5 provided by an optional embodiment of the present invention;

[0026] Figure 4 It is a schematic diagram of a pressure-burning rate fitting curve under a nozzle throat diameter of 11.5 provided by an optional embodiment of the present invention;

[0027] Figure 5Schematic diagram of selecting characteristic points from the burning surface meat thickness curve provided by an alternative embodiment of the present invention;

[0028] Figure 6 Schematic diagram of the calculated pressure-time comparison curve provided by an alternative embodiment of the present invention;

[0029] Figure 7 Schematic diagram of the device for predicting the interior ballistic performance of a solid rocket motor provided by an embodiment of the present invention. Detailed implementation manners

[0030] In order to enable those skilled in the art to better understand the solution of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some, rather than all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0031] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the accompanying drawings are used to distinguish different objects, rather than to limit a specific order.

[0032] According to one aspect of the embodiments of the present invention, a method for predicting the interior ballistic performance of a solid rocket motor is provided. It should be noted that the steps shown in the flowchart of the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although the logical order is shown in the flowchart, in some cases, the steps shown or described can be executed in a different order than here.

[0033] Figure 1 Flowchart of the method for predicting the interior ballistic performance of a solid rocket motor provided by an embodiment of the present invention, as Figure 1 shown, the method includes the following steps:

[0034] Step S102, obtaining the pressure-time curve and the burning surface meat thickness curve corresponding to the propellant of the solid rocket motor, wherein the solid rocket motor has different nozzle throat diameters and charging conditions;

[0035] In an alternative embodiment, obtaining the pressure-time curve and the burning surface thickness curve corresponding to the propellant of a solid rocket motor includes: conducting ignition experiments on solid rocket motors under different nozzle throat diameters and charging conditions to obtain experimental data, and respectively recording the experimental data in a first data table and a second data table, where the first data table includes different pressures and the corresponding times of different pressures, and the first data table includes the thicknesses of different propellants and the corresponding burning surfaces and free volumes respectively; obtaining the first data table, and generating a pressure-time curve based on the first data table; obtaining the second data table, and generating a burning surface thickness curve based on the second data table.

[0036] Step S104, obtaining the preset parameters of the solid rocket motor, where the preset parameters include but are not limited to the free volume including the initial free volume of the combustion chamber, the specific heat ratio of the gas, the characteristic velocity of the charge, and the charge density;

[0037] Step S106, determining the pressure-burning rate curve corresponding to the propellant of the solid rocket motor according to the burning surface thickness curve, the preset parameters, and the pressure-time curve;

[0038] Step S108, performing a fitting process on the pressure-burning rate curve to obtain a pressure-burning rate fitting curve;

[0039] Step S110, obtaining the burning rate relationship parameters corresponding to the propellant of the solid rocket motor based on the pressure-burning rate fitting curve; the above burning rate relationship parameters are the coefficients of the Vielle formula regarding the burning rate formula, and specifically may include the burning rate coefficient and the pressure exponent.

[0040] Optionally, the above burning rate relationship parameters include but are not limited to the burning rate coefficients and pressure exponents under different pressure ranges; the burning rate coefficients and pressure exponents of the first-stage pressure under different nozzle throat diameters; the burning rate coefficients and pressure exponents of the second-stage pressure under different nozzle throat diameters; the burning rate coefficients and pressure exponents of the third-stage pressure under different nozzle throat diameters.

[0041] Step S112, determining the time-pressure comparison curve corresponding to the propellant of the solid rocket motor according to the burning surface thickness curve, the preset parameters, and the burning rate relationship parameters.

[0042] It should be noted that based on the zero-dimensional interior ballistic differential equation, using the burning rate coefficients and pressure exponents of the high-pressure transient dynamic burning rate of solid rocket motors under different nozzle throat diameters and charging conditions to estimate the interior ballistic performance of solid rocket motors has a wide range of applicability, and can achieve dynamic identification of the burning rate and estimation of the interior ballistic performance of solid rocket motors for different propellant types and different charge shapes.

[0043] In an embodiment of the present invention, a pressure-time curve and a burning surface thickness curve corresponding to the propellant of a solid rocket motor are obtained, wherein the solid rocket motor has different nozzle throat diameters and charging conditions; preset parameters of the solid rocket motor are obtained, wherein the preset parameters include the free volume including the initial free volume of the combustion chamber, the specific heat ratio of the gas, the characteristic velocity of the charge, and the charge density; according to the burning surface thickness curve, the preset parameters, and the pressure-time curve, a pressure-burning rate curve corresponding to the propellant of the solid rocket motor is determined; the pressure-burning rate curve is fitted to obtain a pressure-burning rate fitting curve; based on the pressure-burning rate fitting curve, burning rate relationship parameters corresponding to the propellant of the solid rocket motor are obtained; according to the burning surface thickness curve, the preset parameters, and the burning rate relationship parameters, a time-pressure comparison curve corresponding to the propellant of the solid rocket motor is determined. That is to say, in the embodiment of the present invention, complex burning rate measurement methods such as the supersonic method do not need to be used. Instead, by conducting ignition experiments on solid rocket motors with different throat diameters under different charging conditions and analyzing the test data, burning rate relationship parameters within different pressure ranges of the propellant are obtained. Then, using the burning surface thickness curve, the preset parameters, and the burning rate relationship parameters, a time-pressure comparison curve corresponding to the propellant of the solid rocket motor is calculated. This time-pressure comparison curve can reflect the interior ballistic performance of the solid rocket motor, thereby predicting the interior ballistic performance of the solid rocket motor, and further solving the technical problems of complex process and unsatisfactory calculation effect in predicting the interior ballistic performance of solid rocket motors in the related art, achieving the technical effect of improving the accuracy of predicting the interior ballistic performance of solid rocket motors.

[0044] In an alternative embodiment, determining a pressure-burning rate curve corresponding to the propellant of a solid rocket motor according to the burning surface thickness curve, the preset parameters, and the pressure-time curve includes: obtaining the thickness, burning surface, and free volume of the propellant of the solid rocket motor at different times according to the burning surface thickness curve and the preset parameters; calculating the burning rate of the propellant of the solid rocket motor at different times according to the thickness at different times; and obtaining the pressure-burning rate curve according to the pressure-time curve and the burning rate at different times.

[0045] In the above embodiment of the present invention, the thickness, burning surface, and free volume of the propellant of the solid rocket motor at different times can be calculated using the burning surface thickness curve and the preset parameters, and the burning rate of the propellant of the solid rocket motor at different times can be calculated using the thickness at different times, so as to accurately obtain the pressure-burning rate curve corresponding to the propellant of the solid rocket motor according to the pressure at different times and the burning rate at different times in the pressure-time curve.

[0046] In an alternative embodiment, a pressure burning rate curve is fitted to obtain a pressure burning rate fitting curve, including: screening out a plurality of line segments to be fitted from the pressure burning rate curve, where the line segments to be fitted include a fitting start point and a fitting end point. The fitting start point is the point on the pressure burning rate curve that has an obvious linear feature and starts to decline, and the fitting end point is the point on the pressure burning rate curve that has an obvious linear feature and ends the decline trend; fitting each of the plurality of line segments to be fitted to obtain the pressure burning rate fitting curve.

[0047] In the above embodiment of the present invention, by fitting each of the plurality of line segments to be fitted screened out from the pressure burning rate curve, the pressure burning rate fitting curve is accurately fitted.

[0048] In an alternative embodiment, according to the burning surface meat thickness curve, preset parameters, and burning rate relationship parameters, a time-pressure comparison curve corresponding to the propellant of a solid rocket engine is determined, including: calculating the pressures of the propellant of the solid rocket engine at different times according to the burning surface meat thickness curve, preset parameters, and burning rate relationship parameters; generating a time-pressure comparison curve based on the pressures at different times.

[0049] In the above embodiment of the present invention, the pressures of the propellant of the solid rocket engine at different times can be calculated using the burning surface meat thickness curve, preset parameters, and burning rate relationship parameters, and a time-pressure comparison curve can be generated using the pressures at different times.

[0050] In an alternative embodiment, calculating the pressures of the propellant of the solid rocket engine at different times according to the burning surface meat thickness curve, preset parameters, and burning rate relationship parameters includes: calculating the generated gas amount and discharged gas amount of the propellant of the solid rocket engine at different times according to the burning surface meat thickness curve, preset parameters, and burning rate relationship parameters; calculating the pressure change rate of the propellant of the solid rocket engine at different times based on the generated gas amount and discharged gas amount at different times; calculating the pressure change amount of the propellant of the solid rocket engine at different times based on the pressure change rate at different times; calculating the pressures of the propellant of the solid rocket engine at different times based on the pressure change amount at different times.

[0051] In the above embodiments of the present invention, in order to more accurately calculate the pressure of the propellant of the solid rocket engine at different times, it is necessary to calculate the generated gas volume and the discharged gas volume of the propellant of the solid rocket engine at different times through the burning surface thickness curve, preset parameters and burning rate relational parameters, and then calculate the pressure change rate of the propellant of the solid rocket engine at different times according to the generated gas volume and the discharged gas volume at different times, and then use the pressure change rate at different times to calculate the pressure change amount of the propellant of the solid rocket engine at different times. Finally, use the pressure change amount at different times to calculate the pressure of the propellant of the solid rocket engine at different times in turn.

[0052] It should be noted that according to the law of conservation of mass, the rate of change of the gas mass m in the combustion chamber g with time should be equal to the gas generation rate in the combustion chamber minus the mass flow rate of the gas discharged from the nozzle , that is:

[0053]

[0054] From

[0055]

[0056] where is the burning rate in the combustion chamber, χRT 0 is the powder force considering the heat loss coefficient; p 0 is the stagnation pressure in the nozzle or the total pressure at the nozzle inlet.

[0057] The gas mass m in the combustion chamber g is:

[0058] m g = ρV g

[0059] where ρ is the average density of the gas; V g is the volume occupied by the gas, called the free volume of the combustion chamber. Differentiate m g = ρV g :

[0060]

[0061] represents the gas mass filled due to the increase in the free volume of the combustion chamber per unit time, called the gas filling amount. In fact, the increase in the free volume is equal to the volume burned by the propellant:

[0062]

[0063]

[0064] Indicates the mass of the gas required due to the change in gas density per unit time. If during the propellant combustion, the gas temperature T 0 is a constant, the ideal gas composition and the gas constant remain unchanged, and the heat loss correction coefficient is regarded as a constant, then:

[0065]

[0066] Substitute into to obtain:

[0067]

[0068] Also, because

[0069] Γ 2 *C *2 = χRT 0

[0070] Among them, k is defined as the specific heat ratio of the gas.

[0071] If erosion combustion and the heat loss correction coefficient are not considered, a simplified form of the zero-dimensional interior ballistic differential equation can be obtained:

[0072]

[0073] The above equation can also be rewritten in the following form:

[0074]

[0075] Combined with the burning rate relationship:

[0076]

[0077] Furthermore, from

[0078] A b ·de = dV

[0079]

[0080] If the sampling time T is a uniform time interval, for example, in this calculation, the measurement interval of the pressure curve is T = 0.0005 s.

[0081] Then the one-dimensional interior ballistic differential equation is transformed into:

[0082]

[0083] Among them, the pressure corresponding to each time is known, the time interval is known, and the throat area equivalent is a constant, which will become a linear equation of one variable about the free volume. From the assembly drawing of the combustion chamber, the initial free volume can be calculated. Using the combustion chamber, the initial free volume V 1 = 0.0001. Then, the free volume V 2 corresponding to the next time point can be calculated. Then, taking V 2 as V 1 and substituting it into the above formula, the free volume of the next point can be calculated, and so on.

[0084] After obtaining the free volume, using the interpolation method, insert the free volume data into the original free volume table, and the meat thickness corresponding to each free volume can be calculated. Then, take the derivative of it with respect to time to obtain the burning rate corresponding to each throat diameter.

[0085] From Combined with the Vieille formula (i.e., the burning rate relationship), we have

[0086]

[0087] Among them, the Vieille formula defines the burning rate, and the burning rate is a function of time and meat thickness. Therefore, as long as the burning rate in the previous time period is obtained, the meat thickness burned during this time can be calculated. Then, through the geometric relationship between the meat thickness, the burning surface, and the free volume, the burning surface and the free volume at the next moment can be calculated using the interpolation method. The specific process is as follows:

[0088] r = ap n

[0089]

[0090] e 1 = e 0 + de

[0091]

[0092]

[0093] Then, the unknown quantity in each step is only P 2 , and this equation can be solved.

[0094] It should be noted that V g is the free volume of the combustion chamber, e is the meat thickness that has been burned by the charge, Ab is the burning surface area of the propellant grain, P is the combustion chamber pressure, T is the calculation step length, that is, the time interval between two adjacent pressure points, ρ is the charge density, a is the burning rate coefficient in the Vieille formula, n is the pressure exponent, C * is the characteristic velocity of the charge, and A t is the throat area of the nozzle.

[0095] Taking the nozzle throat diameter of 11.5 as an example, the present invention will be described in detail below.

[0096] The propellant (also known as the grain) used in this calculation is a modified double-base propellant containing high-energy metal particles, which is a stepped charge. Since the burning rate of this grain type is significantly affected by pressure and has different burning rate coefficients and pressure exponents in different pressure ranges, the mass flow rate method can be used to calculate its burning rate, and the pressure coefficient in different pressure ranges can be solved by non-linear fitting.

[0097] Furthermore, programming calculations are carried out using Matlab, and the implementation code is as follows:

[0098]

[0099]

[0100]

[0101]

[0102] Figure 2 It is a schematic diagram of the pressure-time curve under the nozzle throat diameter of 11.5 provided by an optional embodiment of the present invention. As Figure 2 shown, the pressure changes in a stepped manner over time.

[0103] Figure 3 It is a schematic diagram of the pressure-burning rate curve under the nozzle throat diameter of 11.5 provided by an optional embodiment of the present invention. As Figure 3 shown, the burning rate changes continuously with the increase of pressure. From the change trend of the burning rate, it can be seen that there will be relatively stable stages and fluctuating stages. The line segment formed by the point with obvious linear characteristics and the starting downward trend in the pressure-burning rate curve and the point with obvious linear characteristics and the ending downward trend in the pressure-burning rate curve is the object of fitting processing. The object of fitting processing includes but is not limited to the first-step pressure, the second-step pressure, and the third-step pressure in the pressure-burning rate curve.

[0104] Figure 4 It is a schematic diagram of the pressure-burning rate fitting curve under the nozzle throat diameter of 11.5 provided by an optional embodiment of the present invention. As Figure 4 shown, * represents the fitting result, the line segment represents the original curve, and the fitting gives a = 0.004587 and n = 0.4946. In addition, after calculating the pressure-time curves of different nozzle throat diameters and different pressure ranges, it can be found that in the same pressure interval, the burning rates corresponding to each nozzle throat diameter are basically the same. Then, after processing the obtained pressure-time curves of each nozzle throat diameter and each pressure range, the burning rate coefficients and pressure exponents in different pressure ranges are finally sorted out, as shown in Table 1:

[0105] Table 1 Burning rate coefficients and pressure exponents under different pressure ranges

[0106] Pressure range Burning rate coefficient Pressure exponent 3.93232-5.09487 0.00425 0.56235 5.33111-6.72926 0.0053 0.45506 6.86937-8.0794 0.00452 0.50137 8.35529-9.35691 0.00876 0.19388 10.17648-11.246 0.00949 0.15584 11.76144-13.09679 0.00734 0.27214 14.4-17.08828 0.00368 0.54803 23.32915-26.9543 0.00161 0.8565 80-114 0.0002674 1.277

[0107] If calculated separately according to the throat diameters of each nozzle and the pressures of each step, the burning rate coefficients and pressure exponents of the first-step pressure under different nozzle throat diameters, the burning rate coefficients and pressure exponents of the second-step pressure under different nozzle throat diameters, and the burning rate coefficients and pressure exponents of the third-step pressure under different nozzle throat diameters can be obtained. Specifically, as shown in Tables 2, 3, and 4:

[0108] Table 2 Burning rate coefficients and pressure exponents of the first-step pressure under different nozzle throat diameters

[0109] Nozzle throat diameter Burning rate coefficient Pressure exponent 11.5 0.00949 0.15584 10.98 0.00734 0.27214 10.45 0.00368 0.54803 10.15 0.00161 0.8565 9.5 0.0002674 1.277

[0110] Table 3 Burning rate coefficients and pressure exponents of the second-step pressure under different nozzle throat diameters

[0111] Nozzle throat diameter Burning rate coefficient Pressure exponent 11.5 0.00452 0.50137 10.98 0.00876 0.19388 10.45 0.00882 0.18978 10.15 0.00684 0.30542 9.5 0.00201 0.7848

[0112] Table 4 Burning rate coefficients and pressure exponents of the third-step pressure under different nozzle throat diameters

[0113] Nozzle throat diameter Burning rate coefficient Pressure exponent 11.5 0.00425 0.56235 10.98 0.0053 0.45506 10.45 0.00568 0.40342 10.15 0.00637 0.35468 9.5 0.00744 0.25753

[0114] Furthermore, based on the burning rate coefficients and pressure exponents of each throat diameter and each step given above, if any throat diameter is given, the interpolation method is as follows:

[0115]

[0116]

[0117] The burning rate coefficient and pressure exponent of the propellant at any throat diameter can be calculated.

[0118] Then using The pressure can be calculated and the time-pressure comparison curve can be plotted. The implementation code is as follows:

[0119]

[0120]

[0121]

[0122] Figure 5 Schematic diagram of selecting characteristic points from the burning surface meat thickness curve provided by an optional embodiment of the present invention, as Figure 5As shown, after the program runs, it is necessary to first select 2 step end points of the stepped charge, that is, the characteristic points (X, Y); optionally, the first characteristic point is X1 = 0.00351, Y1 = 0.0247013; the second characteristic point is X2 = 0.00603, Y2 = 0.0189892.

[0123] Figure 6 It is a schematic diagram of the calculated pressure-time comparison curve provided by an optional embodiment of the present invention. As Figure 6 shown, after the characteristic points are selected, the computer will automatically calculate the pressure-time comparison curve of a certain burning surface thickness relationship under the nozzle throat diameter of the nozzle, and compare it with the pressure-time curve. It can be seen that the calculated pressure-time comparison curve is basically consistent with the pressure-time curve, which proves that the method has certain practicability. The pressure-time comparison curve is the calculated curve under the nozzle throat diameter of 11.5. The nozzle throat diameter can also be changed to any value between 10.15 and 11.5, and good results can be obtained.

[0124] According to another aspect of the embodiments of the present invention, there is also provided a device for predicting the internal ballistic performance of a solid rocket motor. Figure 7 It is a schematic diagram of the device for predicting the internal ballistic performance of a solid rocket motor provided by an embodiment of the present invention. As Figure 7 shown, the device for predicting the internal ballistic performance of the solid rocket motor includes: a first acquisition module 702, a second acquisition module 704, a first determination module 706, a fitting processing module 708, a third acquisition module 710, and a second determination module 712. The device for predicting the internal ballistic performance of the solid rocket motor will be described in detail below.

[0125] The first acquisition module 702 is configured to acquire the pressure-time curve and the burning surface thickness curve corresponding to the propellant of the solid rocket motor, where the solid rocket motor has different nozzle throat diameters and charging conditions;

[0126] The second acquisition module 704 is connected to the first acquisition module 702 and is configured to acquire the preset parameters of the solid rocket motor, where the preset parameters include but are not limited to the free volume including the initial free volume of the combustion chamber, the specific heat ratio of the gas, the characteristic velocity of the charge, and the charge density;

[0127] The first determination module 706 is connected to the second acquisition module 704 and is configured to determine the pressure-burning rate curve corresponding to the propellant of the solid rocket motor according to the burning surface thickness curve, the preset parameters, and the pressure-time curve;

[0128] The fitting processing module 708 is connected to the first determination module 706 and is configured to perform fitting processing on the pressure-burning rate curve to obtain a pressure-burning rate fitting curve;

[0129] The third acquisition module 710 is connected to the above-mentioned fitting processing module 708, and is configured to obtain the burning rate relational expression parameters corresponding to the propellant of the solid rocket motor based on the pressure-burning rate fitting curve;

[0130] The second determination module 712 is connected to the above-mentioned third acquisition module 710, and is configured to determine the time-pressure comparison curve corresponding to the propellant of the solid rocket motor according to the burning surface-to-thickness curve, preset parameters, and burning rate relational expression parameters.

[0131] It should be noted here that the above-mentioned first acquisition module 702, second acquisition module 704, first determination module 706, fitting processing module 708, third acquisition module 710, and second determination module 712 correspond to steps S102 to S112 in the method embodiment. The examples and application scenarios implemented by the above-mentioned modules and the corresponding steps are the same, but are not limited to the content disclosed in the above-mentioned method embodiment.

[0132] In the embodiment of the present invention, the device for predicting the internal ballistic performance of the solid rocket motor can obtain the pressure-time curve and the burning surface-to-thickness curve corresponding to the propellant of the solid rocket motor, wherein the solid rocket motor has different nozzle throat diameters and charging conditions; obtain the preset parameters of the solid rocket motor, wherein the preset parameters include the free volume including the initial free volume of the combustion chamber, the specific heat ratio of the gas, the charging characteristic velocity, and the charging density; determine the pressure-burning rate curve corresponding to the propellant of the solid rocket motor according to the burning surface-to-thickness curve, preset parameters, and pressure-time curve; perform fitting processing on the pressure-burning rate curve to obtain a pressure-burning rate fitting curve; based on the pressure-burning rate fitting curve, obtain the burning rate relational expression parameters corresponding to the propellant of the solid rocket motor; determine the time-pressure comparison curve corresponding to the propellant of the solid rocket motor according to the burning surface-to-thickness curve, preset parameters, and burning rate relational expression parameters. That is to say, in the embodiment of the present invention, it is not necessary to use complex burning rate measurement methods such as the supersonic method. Instead, by conducting ignition experiments on solid rocket motors with different throat diameters under different charging conditions and analyzing the test data, the burning rate relational expression parameters within different pressure ranges of the propellant are obtained. Then, using the burning surface-to-thickness curve, preset parameters, and burning rate relational expression parameters, the time-pressure comparison curve corresponding to the propellant of the solid rocket motor is calculated. This time-pressure comparison curve can reflect the internal ballistic performance of the solid rocket motor, thereby predicting the internal ballistic performance of the solid rocket motor, and further solving the technical problems of complex process and unsatisfactory calculation effect in predicting the internal ballistic performance of solid rocket motors in related technologies, achieving the technical effect of improving the accuracy of predicting the internal ballistic performance of solid rocket motors.

[0133] In an alternative embodiment, the above-mentioned first determination module 706 includes: a first calculation unit for obtaining the web thickness, burning surface, and free volume of the propellant of the solid rocket motor at different times according to the burning surface-web thickness curve and preset parameters; a second calculation unit for calculating the burning rate of the propellant of the solid rocket motor at different times according to the web thickness at different times; and a first processing unit for obtaining the pressure-burning rate curve according to the pressure-time curve and the burning rate at different times.

[0134] In an alternative embodiment, the above-mentioned fitting processing module 708 includes: a screening unit for screening out a plurality of line segments to be fitted from the pressure-burning rate curve, where the line segments to be fitted include a fitting start point and a fitting end point, the fitting start point is a point on the pressure-burning rate curve with an obvious linear feature and a starting downward trend, and the fitting end point is a point on the pressure-burning rate curve with an obvious linear feature and an ending downward trend; and a fitting processing unit for performing fitting processing on the plurality of line segments to be fitted respectively to obtain a pressure-burning rate fitting curve.

[0135] In an alternative embodiment, the above-mentioned burning rate relationship parameters include at least one of the following: burning rate coefficients and pressure exponents in different pressure ranges; burning rate coefficients and pressure exponents of the first step pressure under different nozzle throat diameters; burning rate coefficients and pressure exponents of the second step pressure under different nozzle throat diameters; burning rate coefficients and pressure exponents of the third step pressure under different nozzle throat diameters.

[0136] In an alternative embodiment, the above-mentioned second determination module 712 includes: a third calculation unit for calculating the pressure of the propellant of the solid rocket motor at different times according to the burning surface-web thickness curve, preset parameters, and burning rate relationship parameters; and a generation unit for generating a time-pressure comparison curve according to the pressure at different times.

[0137] In an alternative embodiment, the above-mentioned third calculation unit includes: a first calculation subunit for calculating the generated gas amount and discharged gas amount of the propellant of the solid rocket motor at different times according to the burning surface-web thickness curve, preset parameters, and burning rate relationship parameters; a second calculation subunit for calculating the pressure change rate of the propellant of the solid rocket motor at different times according to the generated gas amount and discharged gas amount at different times; a third calculation subunit for calculating the pressure change amount of the propellant of the solid rocket motor at different times according to the pressure change rate at different times; and a fourth calculation subunit for calculating the pressure of the propellant of the solid rocket motor at different times according to the pressure change amount at different times.

[0138] In an alternative embodiment, the above-mentioned first acquisition module 702 includes: a second processing unit configured to conduct ignition experiments on solid rocket engines under different nozzle throat diameters and propellant loading conditions, obtain experimental data, and record the experimental data into a first data table and a second data table respectively, where the first data table includes different pressures and the corresponding times for different pressures, and the first data table includes the web thicknesses of different propellants and the burning surfaces and free volumes respectively corresponding to the web thicknesses; a third processing unit configured to acquire the first data table and generate a pressure-time curve based on the first data table; and a fourth processing unit configured to acquire the second data table and generate a burning surface-web thickness curve based on the second data table.

[0139] According to another aspect of the embodiments of the present invention, there is also provided a computer-readable storage medium, which includes a stored program. When the program runs, it controls the device where the computer-readable storage medium is located to execute the method for predicting the internal ballistic performance of a solid rocket engine as described in any one of the above.

[0140] According to another aspect of the embodiments of the present invention, there is also provided a processor for running a program. When the program runs, it executes the method for predicting the internal ballistic performance of a solid rocket engine as described in any one of the above.

[0141] The above is only a preferred embodiment of the present invention and is not intended to limit the protection scope of the present invention.

Claims

1. A method for predicting the internal ballistic performance of a solid rocket motor, characterized in that, it includes: Obtain the pressure-time curve and the burning surface thickness curve corresponding to the propellant of the solid rocket motor, wherein the solid rocket motor has different nozzle throat diameters and charging conditions; Obtain the preset parameters of the solid rocket motor, wherein the preset parameters include the free volume including the initial free volume of the combustion chamber, the specific heat ratio of the gas, the characteristic velocity of the charge, and the charge density; According to the burning surface thickness curve, the preset parameters, and the pressure-time curve, determine the pressure-burning rate curve corresponding to the propellant of the solid rocket motor; including: According to the burning surface thickness curve and the preset parameters, obtain the thickness, burning surface, and free volume of the propellant of the solid rocket motor at different times; According to the thickness at different times, calculate the burning rate of the propellant of the solid rocket motor at different times; According to the pressure-time curve and the burning rate at different times, obtain the pressure-burning rate curve; Perform fitting processing on the pressure-burning rate curve to obtain a pressure-burning rate fitting curve; including: Select multiple segments to be fitted from the pressure-burning rate curve, wherein the segments to be fitted include a fitting starting point and a fitting ending point, the fitting starting point is the point on the pressure-burning rate curve with an obvious linear feature and a starting downward trend, and the fitting ending point is the point on the pressure-burning rate curve with an obvious linear feature and an ending downward trend; Perform fitting processing on multiple segments to be fitted respectively to obtain the pressure-burning rate fitting curve; Based on the pressure-burning rate fitting curve, obtain the burning rate relationship parameters corresponding to the propellant of the solid rocket motor; the burning rate relationship parameters include at least one of the following: The burning rate coefficient and pressure exponent in different pressure ranges; The burning rate coefficient and pressure exponent of the first step pressure under different nozzle throat diameters; The burning rate coefficient and pressure exponent of the second step pressure under different nozzle throat diameters; The burning rate coefficient and pressure exponent of the third step pressure under different nozzle throat diameters; According to the burning surface thickness curve, the preset parameters, and the burning rate relationship parameters, determine the time-pressure comparison curve corresponding to the propellant of the solid rocket motor; including: According to the burning surface thickness curve, the preset parameters, and the burning rate relationship parameters, calculate the pressure of the propellant of the solid rocket motor at different times; Generate the time-pressure comparison curve according to the pressure at different times.

2. The method according to claim 1, characterized in that, According to the burning surface thickness curve, the preset parameters, and the burning rate relationship parameters, calculating the pressure of the propellant of the solid rocket motor at different times includes: According to the burning surface thickness curve, the preset parameters, and the burning rate relationship parameters, calculate the generated gas volume and the discharged gas volume of the propellant of the solid rocket motor at different times; According to the generated gas volume and the discharged gas volume at different times, calculate the pressure change rate of the propellant of the solid rocket motor at different times; Calculate the pressure change amount of the propellant of the solid rocket motor at different times according to the pressure change rate at different times; Calculate the pressure of the propellant of the solid rocket motor at different times according to the pressure change amount at different times.

3. The method according to any one of claims 1 to 2, characterized in that obtain the pressure-time curve and the burning surface thickness curve corresponding to the propellant of the solid rocket motor, including: Conduct ignition experiments on solid rocket motors under different nozzle throat diameters and charging conditions to obtain experimental data, and record the experimental data into a first data table and a second data table respectively. Among them, the first data table includes different pressures and the corresponding times of different pressures, and the first data table includes the thickness of the propellant and the burning surface and free volume corresponding to the thickness respectively; Obtain the first data table and generate the pressure-time curve based on the first data table; Obtain the second data table and generate the burning surface thickness curve based on the second data table.

4. An apparatus for implementing the method for predicting the interior ballistic performance of the solid rocket motor described in claim 1, characterized in that comprising: A first acquisition module for acquiring the pressure-time curve and the burning surface thickness curve corresponding to the propellant of the solid rocket motor, wherein the solid rocket motor has different nozzle throat diameters and charging conditions; A second acquisition module for acquiring the preset parameters of the solid rocket motor, wherein the preset parameters include the free volume including the initial free volume of the combustion chamber, the specific heat ratio of the gas, the characteristic velocity of the charge, and the charge density; A first determination module for determining the pressure-burning rate curve corresponding to the propellant of the solid rocket motor according to the burning surface thickness curve, the preset parameters, and the pressure-time curve; A fitting processing module for performing fitting processing on the pressure-burning rate curve to obtain a pressure-burning rate fitting curve; A third acquisition module for acquiring the burning rate relationship parameters corresponding to the propellant of the solid rocket motor based on the pressure-burning rate fitting curve; A second determination module for determining the time-pressure comparison curve corresponding to the propellant of the solid rocket motor according to the burning surface thickness curve, the preset parameters, and the burning rate relationship parameters.

5. A computer-readable storage medium, characterized in that The computer-readable storage medium includes a stored program, wherein when the program runs, it controls the device where the computer-readable storage medium is located to execute the method for predicting the interior ballistic performance of the solid rocket motor according to any one of claims 1 to 3.

6. A processor, characterized in that The processor is used to run a program, wherein when the program runs, it executes the method for predicting the interior ballistic performance of the solid rocket motor according to any one of claims 1 to 3.

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