Calculation method for ballistic trajectory in paste engine based on differential cone angle method

Abstract

The invention provides a pasty fluid engine inner trajectory calculation method based on a differential cone angle method, which comprises the following steps of: 1, setting parameters of a simulation program, and performing parameter modeling on an engine needing to be simulated according to various index parameters of the engine; 2, inputting parameters into a calculation algorithm to serve as an algorithm preset value, and forwards outputting a calculation result of current corresponding physical time according to a time step sequence; and step 3, completing calculation of all set time step lengths by an algorithm, and obtaining a pressure / thrust / flow curve of the whole working process of the engine according to a stored calculation result. According to the inner ballistic dynamic algorithm, differential cone angle assumption is used, the thixotropic propellant rocket engine with constant hydraulic supply can be calculated, the defect that hydraulic supply cannot be calculated through a traditional algorithm is overcome, and the applicability of the algorithm is greatly improved.

Description

Technical Field

[0001] The invention belongs to the field of rocket engine simulation, relates to a paste propellant rocket engine system and the combustion performance of the paste propellant, and specifically relates to a method for calculating the internal combustion surface and internal ballistics of a paste engine based on a differential cone angle. Background Art

[0002] The variable thrust multi-pulse rocket engine based on paste propellant has the advantages of high energy density, good ignition performance, good storage performance, good material compatibility, high thrust adjustment ratio, good modular performance, etc., and can realize intelligent and controllable thrust. Therefore, it has a wide range of potential application prospects in military and civilian fields such as air-to-air missiles, ballistic missiles and spacecraft, and is one of the important development directions of future solid rocket engines.

[0003] At present, the research on thixotropic propellant rocket engines is still insufficient, and its design ideas and simulation verification methods are not yet mature. The existing internal ballistic dynamic algorithm of paste thixotropic propellant rocket engines is only applicable to the calculation under the condition of constant propellant flow rate supply. There are a lot of assumptions and simplifications in the algorithm, which cannot reflect the actual working state of the rocket engine. Therefore, it is necessary to develop a set of internal ballistic dynamic calculation methods based on the basic combustion principle of paste thixotropic propellant.

[0004] [1] Xiao Jinwu, Zhang Wengang. Research on PEPA / AP Paste Propellant Formula [J]. Solid Rocket Technology, 2001(04):46-49. (This paper mainly introduces the PEPA / AP-based paste propellant formula and its physicochemical properties.)

[0005] [2] Shi Jian. Performance characteristics and application prospects of paste propellant rocket engines [J]. Cruise Missile, 2008(10):61-63. (This paper mainly introduces the main advantages and application directions of current paste propellant rocket engines.)

[0006] [3]YOON C.Injection dynamics of gelled propellants.[D]:Purdue University,2011.(This paper mainly introduces the dynamic characteristics of paste propellants under extrusion supply, including the changes in its flow characteristics under high pressure extrusion.)

[0007] [4] Qin Zhenyang. Research on the working characteristics of multi-pulse paste rocket engine [D]: Nanjing University of Science and Technology, 2019. (This paper mainly realizes the pulse operation of paste propellant rocket engine through single / multiple pulse devices, and compiles a feasible paste propellant rocket engine internal ballistic simulation algorithm)

[0008] [5] ANDERSON DJ, JOHN D, et al. NASA In-Space advanced chemical propulsion development in recent years [C] / / . 2010 IEEE Aerospace Conference, 2010: 1-20. (NASA's review paper on advanced chemical propulsion technology in recent years, which involves paste propellant rocket engines)

[0009] [6] Yang Hai. Experimental and simulation study on working characteristics of paste propellant rocket engine [D]: Nanjing University of Science and Technology, 2016. (Research literature on the working characteristics of paste propellant rocket engine system from Nanjing University of Science and Technology, in which the working process of paste propellant rocket engine is divided into three main stages, namely the initial combustion stage, the stable combustion stage and the residual combustion stage) Summary of the invention

[0010] The present invention models the designed thixotropic propellant rocket engine thrust chamber system, laying the foundation for simulating the propellant flow characteristics and the internal combustion characteristics of the engine. Since the common combustion mode of the paste propellant rocket engine involved in the present invention is conical surface combustion, its main feature is that the combustion surface changes dynamically with the propellant supply hydraulic pressure and the combustion chamber pressure, so the simulation of its combustion characteristics cannot use the general zero-dimensional internal ballistic model. To this end, the present invention proposes a differential dynamic model of conical surface combustion of the thrust chamber system of a paste thixotropic propellant rocket engine, and introduces its basic mathematical expression and its Matlab algorithm implementation ideas, laying a theoretical foundation for the simulation of the working characteristics of the whole system of future paste propellant rocket engines.

[0011] The internal ballistic dynamic algorithm involved in the present invention uses the differential cone angle assumption to calculate the thixotropic propellant rocket engine with constant hydraulic supply, which solves the defect that the traditional algorithm cannot calculate the hydraulic supply and greatly improves the applicability of the algorithm. The algorithm successfully simulates the dynamic characteristics of the engine combustion surface, flow rate and chamber pressure under constant hydraulic supply, obtains relevant data, and finds the law of the change of the internal ballistic pressure peak characteristics of the paste thixotropic propellant cone surface combustion with the change of hydraulic supply, which greatly improves the reliability of the paste propellant engine design.

[0012] The common combustion mode of the paste propellant rocket engine simulated by this simulation system is conical combustion, and its main feature is that the combustion surface changes dynamically with the propellant supply hydraulic pressure and the combustion chamber pressure, so the general zero-dimensional interior ballistic model cannot be used to simulate its combustion characteristics. The existing paste propellant rocket engine interior ballistic simulation model generally simply sets the combustion surface of the paste propellant rocket engine when it burns inside the combustion chamber as a conical surface, so it cannot effectively simulate the dynamic characteristics of the paste propellant rocket engine during combustion. For this reason, this software uses the cone combustion differential dynamic model and the differential cone angle assumption to calculate the working states of the thixotropic propellant rocket engine with different supplies such as constant pressure, variable pressure, and variable flow, which solves the defect that the traditional algorithm cannot calculate the dynamic working characteristics of the engine and greatly improves the applicability of the algorithm.

[0013] This algorithm can realize high-precision calculation of paste propellant rocket engine parameters. Given the engine parameters, it can automatically calculate the key parameters of the paste propellant rocket engine in working state, including the engine's propellant burning surface, combustion chamber pressure, propellant flow rate, etc. The algorithm automatically solves the shape of the burning surface formed by the propellant inside the combustion chamber and displays it in the form of animation during the calculation process.

[0014] The internal ballistic dynamic simulation algorithm of the present invention mainly includes the following main parts: calculation function, main program and result output program. The calculation function includes the main parameter calculation and produces various results including chamber pressure, fuel flow rate and combustion surface morphology. The main component block diagram of the algorithm is shown in the figure. Figure 1 shown.

[0015] Based on this algorithm, the dynamic calculation simulation of the internal ballistic characteristics of the engine is realized. The main modules included can output the following main results: engine chamber pressure, combustion surface data, output as time domain image. The dynamic change process of the cone surface of the engine, and the dynamic image of the combustion surface are output as the algorithm is executed.

[0016] The software for implementing the present invention is a paste propellant rocket engine interior ballistics simulation software system based on the differential cone angle method developed under Matlab R2022b. The GUI interface is developed using Matlab R2022b's App Designer, and the simulation parameters are set and adjusted, as well as the simulation results are returned using a full GUI method. At the same time, users can adjust the simulation content and simulation method according to their needs, and even add new simulation algorithms.

[0017] To this end, the present invention proposes a method for calculating the internal ballistics of a paste engine based on a differential cone angle method, the steps of which are as follows:

[0018] Step 1: Set the parameters of the simulation program and perform parameter modeling on the engine to be simulated according to the various index parameters of the engine.

[0019] Step 2: Input parameters into the calculation algorithm as the algorithm preset value, and output the calculation results of the current corresponding physical time in the order of time steps.

[0020] Step 3: The algorithm completes the calculation of all the set time steps and obtains the pressure / thrust / flow curve of the entire engine operation process based on the stored calculation results.

[0021] In step 2, the engine combustion surface and combustion structure characteristics are finely simulated by the differential cone angle method. This step protects the method of calculating and simulating the paste rocket engine using the differential cone angle method. This method mainly includes three main steps, see the calculation method in the specific implementation method.

[0022] The main innovative features of the present invention are:

[0023] (1) The common combustion mode of the paste propellant rocket engine simulated by this simulation system is cone combustion. The simulated object has complex dynamic characteristics and difficult parameter input. This system allows users to efficiently simulate the combustion characteristics of the entire engine process under different input conditions, as well as the changes in parameters such as the engine combustion surface and chamber pressure, and quickly determine whether the engine design is reasonable and whether the engine test parameters will cause the engine to produce adverse combustion phenomena such as backfire. It has reference value for engine design and test process.

[0024] (2) The half-section of the engine combustion surface can be displayed in real time, allowing the user to observe the engine working status and simulation operation status in real time and discover problems during operation in a timely manner.

[0025] (3) The simulation software has a small number of input parameters, mainly covering the main parameters of the engine and propellant, and has a complete user interface, so that ordinary users can also adjust the engine parameters and perform simulations by themselves. It is easy to use and does not require users to modify the program.

[0026] (4) This algorithm makes up for the deficiency of the existing algorithm for the cone combustion of thixotropic paste propellants that cannot calculate the pressure supply, and can obtain the rotationally symmetric three-dimensional model of the combustion surface at each working moment of the engine through calculation. In the future, it can be used for applications such as the comparison of X-ray fluoroscopy data of the cone combustion of thixotropic paste propellants and the digital twin of thixotropic paste propellant engines. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 The figure is a flowchart of the steps of the main process of the operation process of the present invention.

[0028] Figure 2It is a schematic diagram of differential cone angle iteration during the operation of the present invention.

[0029] Figure 3 Schematic diagram of the physical meaning of each parameter in the differential cone angle iteration.

[0030] Figure 4 The half-section diagram of the burning surface at different times (0.1s, 0.2s, 0.4s) calculated by the differential cone angle algorithm (unit: mm).

[0031] Figure 5 Comparison between the differential cone angle algorithm results and the experimental results. DETAILED DESCRIPTION

[0032] The present invention provides a method for calculating the internal ballistics of a paste engine based on the differential cone angle method, and is based on a cone combustion thixotropic propellant rocket engine with a given supply pressure. Therefore, the first step is to establish a paste thixotropic propellant flow model under a constant pressure supply. This model mainly includes a mathematical relationship between the propellant flow loss and the change of the propellant supply pressure / supply flow rate. In establishing this series of models, based on experience, the flow loss in the propellant supply process can be divided into two parts, that is, based on the high viscosity and low flow rate characteristics of the paste propellant, the propellant mainly flows in the pipeline in a laminar form, and the Bernoulli formula (Formula 1) is used for thrust calculation. The resistance effect in the flow process is manifested as pressure loss. This time, a pressure loss coefficient is added, which is proportional to the flow velocity. The second flow loss is directly manifested as a flow velocity loss, that is, there is a loss coefficient between the flow velocity calculated according to the Bernoulli formula and the actual flow velocity. According to these two coefficients and test data, the propellant flow performance can be calibrated with the help of a cold flow calibration test. ,

[0033] The second step is to construct a transient combustion model of the engine along the surface based on the differential quasi-steady state assumption. This assumption assumes that at every moment, the propellant can stably enter a stable state of combustion along the surface, so the two processes can be separated - the process of the propellant entering the combustion chamber to form a combustion surface, and the process of the propellant combustion building up pressure in the combustion chamber, and then the two processes can be modeled and calculated separately. First, the transient combustion surface model of the engine is constructed. For the combustion of the paste propellant in the combustion chamber, it is generally believed that it forms a stable combustion surface in a cone shape under steady-state conditions, and the cone angle of the combustion surface is related to the extrusion speed and the burning rate. In order to simulate its dynamic characteristics, it is necessary to consider the dynamic changes of the fuel inside the combustion chamber. Here, the present invention assumes that the fuel forms a differential conical combustion surface at the moment of entering the combustion chamber. Considering that the burning rate and flow rate are basically unchanged at the moment of entry, the cone angle of this combustion surface is only related to the burning rate and flow rate at the moment of entry. After this differential combustion surface leaves the inlet, it should only burn through the surface, and the equal surface combustion will not change the cone angle of this differential conical combustion surface until it is completely burned out. This sequence process is as follows Figure 2 As shown,

[0034] In the third step, the gas parameters generated by the transient combustion model are input into the combustion chamber equation to generate a new transient combustion chamber pressure. The calculation formula is as shown in Equation 13. After the chamber pressure calculation is completed, iterate to the next step.

[0035] The mathematical form of the first step was established. Given that the paste propellant has extremely strong viscosity, a slow flow rate in the engine, and an extremely low Reynolds number, it can be regarded as laminar flow, and the Bernoulli equation can better reflect its flow characteristics. Therefore, for the paste thixotropic propellant, the calculation of its flow characteristics can refer to the Bernoulli equation, which is:

[0036]

[0037] Among them, k is the velocity loss caused by the viscosity of the paste fuel, which reflects the non-ideal fluid characteristics of the propellant flow process. b Supply hydraulic pressure to the propellant, p c is the combustion chamber pressure, p loss It is the sum of the local pressure losses of the propellant in the pipe and the grid hole due to non-laminar flow, and ρ is the density of the propellant.

[0038] For the local pressure loss of the propellant, the local loss is proportional to the square of the flow rate of the propellant in the pipeline, and the following formula is obtained. loss is the local loss coefficient.

[0039] p loss =k loss υ 2 (2)

[0040] Therefore, the flow rate can be used to iteratively calculate the flow of propellant from the tank to the combustion chamber. The basic calculation process is:

[0041] The flow rate of the propellant inside the pipeline is calculated according to the pressure difference between the combustion chamber and the tank according to formula (1), and then the pressure loss of the propellant in the local pipeline is calculated according to formula (2). Then, according to the pressure loss value, the new propellant flow rate is calculated by substituting it into formula (1). This iterative calculation process generally converges after 3 to 5 times, so that the new pressure loss and flow rate values ​​generated by each iteration are no more than 1% different from the results of the previous iteration. At this time, the iteration is considered to have converged, and the result is taken as the input value for the next calculation.

[0042] The relationship between the combustion rate and chamber pressure inside the combustion chamber is:

[0043]

[0044] The burning rate formula of the PEAP / nano-Al paste propellant selected in the present invention from the Xi'an Institute of Modern Chemistry is as follows; wherein p is the chamber pressure, in MPa, and the others are constants related to the characteristics of the propellant itself. Substituting into formula (3) yields the following specific calculation formula:

[0045]

[0046] Therefore, the combustion rate can be calculated using the chamber pressure parameters.

[0047] Regarding the combustion of paste propellant in the combustion chamber, it is generally believed that under steady-state conditions, a stable combustion surface is formed in a cone shape, and the cone angle of the combustion surface is related to the extrusion velocity and the burning rate. In order to simulate its dynamic characteristics, it is necessary to consider the dynamic changes of the fuel inside the combustion chamber. Here, the present invention assumes that the fuel forms a differential conical combustion surface upon entering the combustion chamber. Considering that the burning rate and flow rate are basically unchanged at the moment of entry, the cone angle of this combustion surface is only related to the burning rate and flow rate at the moment of entry. After this differential combustion surface leaves the inlet, it should only burn through the surface, and isosurface combustion will not change the cone angle of this differential conical combustion surface until it is completely burned out, so the combustion surface formula can be obtained:

[0048] A b =∑{[πl i (r i +r i+1 )]+πr 2} (5)

[0049] In the formula, the physical meaning of the main size parameters can be found in Figure 3 , li is the cone chord length calculated by formula (6), ri, ri+1 are the upper and lower radii of the cone, and r is the top radius. For the above burning surface formula, A b Characterize the total combustion surface. Obviously, this formula can be obtained through calculus to obtain an analytical formula, but in view of the fact that the propellant differential layers enter the combustion chamber in chronological order during the actual test, the summation form is used here to facilitate the future joint deployment with the engine measurement and control device as an engine digital twin calculation program.

[0050] The combustion surface area formed by the propellant inside the engine can be obtained by summing up formula (4). Note that although each differential table surface is calculated using the cone side area formula, the cone angles of each differential cone surface are different, so the overall combustion surface shape formed by the combination is not a simple cone. In fact, according to the simulation results, the combustion surface is a curved surface that changes with time, and its shape is similar to a spindle surface.

[0051]

[0052] Among them, r iis the base radius of the micro-layer. For the layer that first enters the combustion chamber, its base radius is the grid hole radius. tanβ is the cone angle of the micro-layer. Since the cone surface is burning along the surface, the cone angle will no longer change after entering the combustion chamber. When this cone burns along the surface, only the cone radius changes.

[0053]

[0054] in, represents the propellant burning rate at the time of input, and υ i Characterizes the flow rate of the fuel at this moment. This formula characterizes that when the differential layer enters the combustion chamber, the tangent value of the cone angle of the propellant cone surface is only related to the flow rate when the propellant enters the combustion chamber and the burning rate of the propellant at the current moment, and has nothing to do with other parameters. It can be found that the differential cone angle of the propellant is determined when it enters the combustion chamber, and it does not change in the subsequent combustion process. From this, we can find that when the engine starts to work, the burning rate is close to 0, the tangent value is close to infinity, and the propellant shape is similar to a cylinder, which is consistent with the phenomenon observed in the experiment. When the propellant flow rate is stable and the combustion enters a steady state, the pressure inside the combustion chamber can be regarded as basically unchanged. In order to maintain this steady state, the propellant shape (burning surface) should be basically unchanged. Obviously, at this time, the burning rate of the propellant is basically stable at each moment, the flow rate is basically stable, the tangent value is basically unchanged, and the propellant combustion shape should be similar to a cone, which is also consistent with the phenomenon observed in the experiment.

[0055] To calculate the pressure from the combustion surface to the chamber, the differential form of the rocket engine chamber pressure formula can be used. For rocket engines, the gas mass flow rate is approximately equal to the input fuel flow rate. The gas mass change rate inside the combustion chamber is Equal to the input fuel mass flow rate and the mass flow rate leaving through the throat Difference:

[0056]

[0057] The fuel volume flow rate of the present invention is equal to the burning surface area multiplied by the burning speed From this, we can get the formula of the current gas quality change rate with the burning surface area, where ρ p Refers to the propellant density:

[0058]

[0059] The throat exhaust rate in the present invention can be calculated using the standard Laval nozzle formula, which is:

[0060]

[0061] Among them, A tis the throat area, in m 2 , C * is the nozzle efficiency, which is generally between 1.4 and 1.5.

[0062] In addition, according to the third law of thermodynamics, there is a differential relationship between the quality of the gas inside the combustion chamber and time, where V g is the combustion chamber volume, ρ g is the gas density:

[0063]

[0064] Through the ideal gas relationship, we can get the relationship between pressure, gas density and temperature:

[0065] p=ρ g RT (12)

[0066] Replace the original formula (10) with a form expressed using volume, pressure and temperature T, and substitute the gas quality change rate The formula can be used to obtain the differential equation of the internal ballistics of the engine. The main independent variables of this formula are the current burning surface and burning rate, and the main dependent variable is the internal pressure of the combustion chamber. In order to facilitate iteration and further reflect physical reality, the chamber pressure calculated from the burning surface at the previous moment is used as the input value for calculating the engine burning rate at the next moment. This completes the closed loop of the algorithm and can be solved iteratively.

[0067]

[0068] Based on this algorithm, during actual operation, new differential cone layers will be added forward layer by layer according to the set time step, thereby forming the propellant shape (curved cone) burning inside the paste engine layer by layer. As the engine works, the shape of the curved cone will change, from which the performance evolution and other changes during the engine operation process can be seen.

[0069] Here, the parameters of a certain type of engine are used as input parameters to estimate the thrust and engine dynamic working process performance. The specific parameters of the engine are shown in the following table:

[0070]

[0071]

[0072] The engine parameters are input into the calculation algorithm, and the relationship between the engine predicted thrust curve and the actual ignition thrust curve is obtained through iterative calculation. Figure 5As shown in the figure, the engine working process curve before the engine is shut down shows that the engine thrust prediction accuracy is high, and the prediction accuracy is within 5%, which has reached the engineering usable accuracy. At the same time, the prediction function predicts the thrust peaks in the front and rear sections of the engine working process, which can be regarded as predicting the characteristics of the engine working to a certain extent.

Claims

1. A method for calculating the interior ballistics of a paste engine based on the differential cone angle method, characterized in that: Here are the steps: Step 1: Set the parameters of the simulation program and perform parameter modeling on the engine to be simulated according to the various index parameters of the engine; Step 2: Input parameters into the calculation algorithm as the algorithm preset value, and output the calculation result of the current corresponding physical time in the order of time steps; Step 3: The algorithm completes the calculation of all the set time steps and obtains the pressure / thrust / flow curve of the entire engine operation process based on the stored calculation results.

2. The method for calculating interior ballistics of a paste engine based on the differential cone angle method according to claim 1, characterized in that: The differential cone angle method is used to perform detailed simulation of the engine combustion surface and combustion structure characteristics; the differential cone angle method is used to perform computational simulation of the paste rocket engine.

3. The method for calculating interior ballistics of a paste engine based on the differential cone angle method according to claim 2, characterized in that: Based on the cone combustion thixotropic propellant rocket engine with a given supply pressure, it is necessary to first establish a paste thixotropic propellant flow model under a constant pressure supply, including the mathematical relationship between the propellant flow loss and the propellant supply pressure / supply flow rate; the flow loss in the propellant supply process is divided into two parts, namely, according to the high viscosity and low flow velocity characteristics of the paste propellant, the propellant flows in the pipeline in a laminar form, and the thrust is calculated using the Bernoulli formula. The influence of resistance in the flow process is manifested as pressure loss. This time, a pressure loss coefficient is added, which is proportional to the flow velocity; the second flow loss is directly manifested as a flow velocity loss, that is, there is a loss coefficient between the flow velocity calculated according to the Bernoulli formula and the actual flow velocity. Based on these two coefficients and test data, the propellant flow performance is calibrated with the help of a cold flow calibration test.

4. The method for calculating interior ballistics of a paste engine based on the differential cone angle method according to claim 2 or 3, characterized in that: Based on the differential quasi-steady-state assumption, a transient combustion model of the engine is constructed; assuming that the propellant can stably enter a stable state of combustion along the surface at every moment, the two processes are separated, namely the process of the propellant entering the combustion chamber to form a combustion surface and the process of the propellant combustion building up pressure in the combustion chamber, and then the two processes are modeled and calculated separately; the transient combustion surface model of the engine is constructed, and for the combustion of the paste propellant in the combustion chamber, it is assumed that it forms a stable combustion surface in a cone shape under steady-state conditions, and the cone angle of the combustion surface is related to the extrusion speed and the burning rate; assuming that the fuel forms a differential conical combustion surface at the moment of entering the combustion chamber, considering that the burning rate and flow rate at the moment of entry are basically unchanged, the cone angle of this combustion surface is only related to the burning rate and flow rate at the moment of entry; after this differential combustion surface leaves the inlet, it should only burn through the surface, and the equal surface combustion will not change the cone angle of this differential conical combustion surface until it is completely burned out.

5. The method for calculating interior ballistics of a paste engine based on the differential cone angle method according to claim 4, characterized in that: The gas parameters generated by the transient combustion model are input into the combustion chamber equation to generate a new transient combustion chamber pressure. After the chamber pressure calculation is completed, the next step is iterated.

6. The method for calculating interior ballistics of a paste engine based on the differential cone angle method according to claim 3, characterized in that: For paste thixotropic propellants, the flow characteristics are calculated by referring to the Bernoulli equation: Where k is the velocity loss caused by the viscosity of the paste fuel, p b Supply hydraulic pressure to the propellant, p c is the combustion chamber pressure, p loss is the sum of the local pressure losses of the propellant in the pipe and the grid hole due to non-laminar flow, and ρ is the density of the propellant; For the local pressure loss of the propellant, the local loss is proportional to the square of the flow rate of the propellant in the pipeline, and the following formula is obtained; where k loss is the local loss coefficient; p loss =k loss u 2 (2) The flow rate of the propellant inside the pipeline is calculated according to the pressure difference between the combustion chamber and the tank according to formula (1), and then the pressure loss of the propellant in the local pipeline is calculated according to formula (2). Then, according to the pressure loss value, the new propellant flow rate is calculated by formula (1). After 3 to 5 times, convergence begins, so that the new pressure loss and flow rate values ​​generated by each iteration are less than 1% different from the results of the previous iteration. At this time, the iteration is considered to have converged, and the result is taken as the input value for the next calculation.

7. The method for calculating interior ballistics of a paste engine based on the differential cone angle method according to claim 4, characterized in that: The relationship between the combustion rate and chamber pressure inside the combustion chamber is: Where p is the room pressure in MPa.

8. The method for calculating interior ballistics of a paste engine based on the differential cone angle method according to claim 4, characterized in that: Assuming that the fuel forms a differential conical combustion surface when it enters the combustion chamber, and considering that the combustion rate and flow rate are basically unchanged at the time of entry, the cone angle of this combustion surface is only related to the combustion rate and flow rate at the moment of entry; after this differential combustion surface leaves the entrance, it should only burn through the surface, and the equal surface combustion will not change the cone angle of this differential conical combustion surface until it is completely burned, so there is a combustion surface formula: A b ＝∑{[πl i (r i +r i+1 )]+πr 2} (5) Where li is the chord length of the cone, ri, ri+1 are the upper and lower radii of the cone, and r is the top radius; A b Characterize the total burning surface; The burning surface test is a surface that changes with time, and its shape is similar to a spindle surface; Among them, r i is the bottom radius of the micro-layer. For the layer that first enters the combustion chamber, its bottom radius is the grid hole radius. tanβ is the cone angle of the micro-layer. Since the cone surface burns along the surface, the cone angle will not change after entering the combustion chamber. When the cone burns along the surface, only the cone radius changes. in, represents the propellant burning rate at the time of input, and υ i Characterizes the fuel flow rate at this moment.

9. The method for calculating interior ballistics of a paste engine based on the differential cone angle method according to claim 8, characterized in that:To calculate the pressure from the combustion surface to the chamber, the differential form of the rocket engine chamber pressure formula is used; for rocket engines, the gas mass flow rate is equal to the input fuel flow rate; and the rate of change of the gas mass retained in the combustion chamber is Equal to the input fuel mass flow rate and the mass flow rate leaving through the throat Difference: The fuel volume flow rate is equal to the burning surface area multiplied by the burning rate From this, we can get the formula of the current gas quality change rate with the burning surface area, where ρ p Refers to the propellant density: The throat exhaust velocity is calculated using the standard Laval nozzle formula as: Among them, A t is the throat area, in m 2 , C * is the nozzle efficiency, which is generally between 1.4 and 1.5; In addition, according to the third law of thermodynamics, there is a differential relationship between the quality of the gas inside the combustion chamber and time, where V g is the combustion chamber volume, ρ g is the gas density: Through the ideal gas relationship, we can get the relationship between pressure, gas density and temperature: p=ρ g RT (12).

10. The method for calculating interior ballistics of a paste engine based on the differential cone angle method according to claim 9, characterized in that: Replace the original formula (10) with a form expressed using volume, pressure and temperature T, and substitute the gas quality change rate Formula, the engine internal ballistic differential equation is obtained, the independent variables are the current burning surface and burning rate, and the dependent variable is the internal pressure of the combustion chamber; the chamber pressure calculated by the burning surface at the previous moment is used as the input value for calculating the engine burning rate at the next moment, completing the closed loop of the algorithm and performing iterative solution;

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