A zero-dimensional interior ballistics calculation method for solid attitude and orbit control rocket considering ablation-deposition

Abstract

The present invention discloses a method for calculating the zero-dimensional internal ballistics of a solid attitude and orbit control engine considering ablation-deposition, including establishing a zero-dimensional internal ballistics calculation model of a solid attitude and orbit control engine considering the influence of ablation / deposition, and solving the zero-dimensional internal ballistics calculation model of a solid attitude and orbit control engine to obtain the pressure of a combustion chamber; wherein, the total equivalent throat area of ​​the engine is obtained based on the spray ablation / deposition rate. The present invention is applied to the field of internal ballistics calculation of attitude and orbit control engines, taking the influence of ablation / deposition on the size of the equivalent throat area into consideration, and calculating the zero-dimensional internal ballistics of attitude and orbit control engines after the ablation / deposition law is known, so as to obtain a combustion chamber pressure that is closer to the actual engineering situation, reduce the thrust calculation error caused by the inaccurate zero-dimensional internal ballistic calculation, facilitate the precise control of the thrust by the control mechanism, facilitate the performance assessment and numerical simulation of the engine in the later stage, and solve the problem of accurate and fast calculation of the zero-dimensional internal ballistics of the engine.

Description

Technical Field

[0001] The invention relates to the field of attitude and orbit control engine performance guidelines, and in particular to a zero-dimensional interior ballistic calculation method for a solid attitude and orbit control engine taking ablation-deposition into consideration. Background Art

[0002] Solid attitude and trajectory control engines are direct force control systems for modern kinetic weapons and are also one of the key technologies for improving the combat performance of tactical missile weapon systems in the future. Solid attitude and trajectory control engines usually work by coupling multiple nozzles to change the size and direction of the thrust vector, achieving high-thrust rapid trajectory change and attitude adjustment of the missile. The engine thrust changes in real time according to the movement of the regulating valve. By adjusting the relative position of the throat plug and the nozzle, it directly affects the equivalent throat area of ​​the engine, thereby affecting the nozzle mass flow rate and thrust size. The engine combustion chamber pressure is an extremely important design parameter and a necessary condition to ensure the stable operation of the engine. Its change law directly determines the thrust and working time of the engine.

[0003] At present, conventional zero-dimensional interior ballistics is usually used to calculate the combustion chamber pressure, without considering the deviation of the equivalent throat area due to ablation / deposition. According to the known throat plug generatrix, nozzle generatrix and the throat plug position at the initial moment, the relationship between throat plug displacement and equivalent throat area change can be calculated. By interpolating the known throat plug displacement-equivalent throat area relationship, the current throat plug displacement of each valve and the corresponding equivalent throat area are obtained. The sum of the equivalent throat areas of each nozzle at different times can be obtained by superimposing them. Substituting them into the basic equation of zero-dimensional interior ballistics can obtain the combustion chamber pressure under the working state.

[0004] The existing zero-dimensional internal ballistics solution method for solid attitude and orbit control engines is mainly derived from the zero-dimensional internal ballistics solution method for solid engines, which calculates the variation of the combustion chamber pressure with time and space under various working conditions of the engine. Under ideal conditions, the equivalent throat area of ​​the solid attitude and orbit control engine can be simply regarded as the sum of the equivalent throat areas of each valve, but in actual working process, the airflow in the throat of the engine nozzle is complex, and the problems of heat transfer, deposition and ablation are serious. The conventional zero-dimensional internal ballistics is used to solve the combustion chamber pressure of the solid attitude and orbit control engine, which can only obtain the combustion chamber pressure under ideal conditions, which will cause a large deviation between the theoretical pressure of the combustion chamber and the actual pressure, and inaccurate thrust control. Summary of the invention

[0005] In view of the problem that in the above-mentioned prior art, due to the high combustion temperature of the engine, impure fuel, and the internal material being not resistant to high temperature, ablation and deposition effects occur at the throat plug head and the throat of the nozzle, causing the engine nozzle profile to change, the actual equivalent throat area deviates from the ideal value, affecting the engine thrust performance, and causing inaccurate thrust control of the solid attitude and orbit control engine. The present invention provides a zero-dimensional internal ballistic calculation method for a solid attitude and orbit control engine considering ablation-deposition, which can perform zero-dimensional internal ballistic calculation of the solid attitude and orbit control engine after the ablation / deposition law is known, obtain a combustion chamber pressure that is closer to the actual engineering situation, reduce the thrust calculation error caused by the inaccurate zero-dimensional internal ballistic calculation, facilitate the precise control of the thrust by the control mechanism, and facilitate the performance assessment and numerical simulation of the engine in the later stage.

[0006] To achieve the above object, the present invention provides a zero-dimensional interior ballistics calculation method for a solid attitude and trajectory control engine considering ablation-deposition, comprising the following steps:

[0007] Establish a zero-dimensional interior ballistic calculation model for solid attitude and orbit control engines after considering the effects of ablation / deposition;

[0008] The Longo Kutta method is used to iteratively solve the zero-dimensional interior ballistic calculation model of the solid attitude and orbit control engine, and the corresponding combustion chamber pressure is obtained after considering the influence of ablation / deposition.

[0009] Before each iteration of the Runge-Kutta method, the equivalent throat area of ​​each valve is obtained based on the throat plug displacement and the ablation / deposition rate of the nozzle and throat plug, and the total equivalent throat area of ​​the engine is accumulated.

[0010] In another embodiment, the zero-dimensional interior ballistic calculation model of the solid attitude and trajectory control engine after considering the influence of ablation / deposition is:

[0011]

[0012] In the formula, p c is the combustion chamber pressure, t is the time, Γ is the function of the specific heat ratio k, c * is the characteristic velocity, V c is the free volume of the combustion chamber, ρ p is the propellant density, A b is the burning surface area of ​​the charge, a is the burning rate coefficient, n is the pressure index, A t is the sum of the equivalent throat areas of all valves, e is the thickness of the powder column, R is the gas constant of the fuel gas, T f is the constant pressure combustion temperature, k is the specific heat ratio, A ti is the single valve equivalent throat area, x i is the displacement of the laryngeal plug, r t 、r p are the ablation / deposition amounts of the nozzle throat and throat plug, respectively.

[0013] In another embodiment, a nested binary search is used to obtain the equivalent throat area of ​​each current valve, and the single equivalent throat area solution process is divided into an outer circulation layer and an inner circulation layer, wherein the outer circulation layer performs a binary search on the throat plug profile curve, and the inner circulation layer performs a binary search on the nozzle profile curve.

[0014] In another embodiment, the process of the outer circulation layer is:

[0015] Step 1.1, obtaining the current displacement position of the throat plug, and updating the throat plug profile curve after considering the ablation / deposition effect according to the ablation / deposition model to obtain the first search interval;

[0016] Step 1.2, selecting any two points near the left and right endpoints and the midpoint of the first search interval as first control points, and obtaining the equivalent throat area corresponding to each first control point based on the inner loop layer;

[0017] Step 1.3, selecting the first control point with the smallest equivalent throat area in step 1.2, and updating the first search interval, using the two first control points adjacent to the left and right of the first control point corresponding to the minimum equivalent throat area as the left and right endpoints of the first search interval after update;

[0018] Step 1.4, determine whether the first search interval reaches the convergence condition, if so, output the minimum equivalent throat area in step 1.2 as the equivalent throat area of ​​the corresponding valve, otherwise return to step 1.2.

[0019] In another embodiment, in step 1.3, the equivalent throat area corresponding to each first control point is obtained based on the inner circulation layer, specifically:

[0020] For each first control point, we have:

[0021] Step 2.1, updating the nozzle profile curve after considering the ablation / deposition effect according to the ablation / deposition model to obtain a second search interval;

[0022] Step 2.2, selecting any two points near the left and right endpoints and the midpoint of the second search interval as second control points, and obtaining the equivalent throat area between the first control point and each second control point;

[0023] Step 2.3, screening out the second control point with the smallest equivalent throat area in step 2.2, and updating the second search interval, using the two second control points adjacent to the left and right of the second control point corresponding to the minimum equivalent throat area as the left and right endpoints of the updated second search interval;

[0024] Step 2.4, determine whether the second search interval reaches the convergence condition, if so, output the minimum equivalent throat area in step 2.2 as the equivalent throat area corresponding to the first control point, otherwise return to step 2.2.

[0025] In another embodiment, in step 2.2, obtaining the equivalent throat area between the first control point and each second control point is specifically:

[0026]

[0027] In the formula, A ti is the equivalent throat area, f 1 (m,h t ) and f 2 (n,x i ,h p ) are respectively the nozzle generatrix equation and the throat plug generatrix equation after considering ablation / deposition, m is the horizontal coordinate of the second control point on the nozzle, h t is the ablation / deposition thickness on the nozzle throat surface, n is the horizontal coordinate of the first control point on the throat plug, x i is the current displacement of the throat plug vertex, h p is the thickness of laryngeal plug surface ablation / deposition.

[0028] Compared with the prior art, the zero-dimensional interior ballistic calculation method of a solid attitude and trajectory control engine considering ablation-deposition provided by the present invention has the following beneficial technical effects:

[0029] 1. Considering the change of equivalent throat area caused by ablation / deposition effect during engine combustion, accurate and rapid calculation of combustion chamber pressure during the working process of solid attitude and orbit control engine is achieved;

[0030] 2. Considering the ablation / deposition rates of the throat plug and the nozzle separately can realize the zero-dimensional internal ballistic calculation under different deposition characteristics of the two parts, laying a technical foundation for the accurate calculation of engine thrust. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the structures shown in these drawings without paying creative work.

[0032] Figure 1 This is a flow chart of a zero-dimensional interior ballistic calculation method considering ablation / deposition effects in an embodiment of the present invention;

[0033] Figure 2This is a flow chart of searching for equivalent throat area using a nested binary search method in an embodiment of the present invention;

[0034] Figure 3 Schematic diagram of a coordinate system for calculating an equivalent throat area in an embodiment of the present invention;

[0035] Figure 4 It is a schematic diagram of the layout of a track control engine according to an example of an embodiment of the present invention;

[0036] Figure 5 Schematic diagram of the nozzle throat plug profile structure according to an example of an embodiment of the present invention;

[0037] Figure 6 It is a displacement change curve diagram of throat plugs of various valves in the embodiment of the present invention;

[0038] Figure 7 is a curve diagram of the change of the ideal equivalent throat area of ​​each valve exemplified in the embodiment of the present invention;

[0039] Figure 8 It is a curve diagram of equivalent throat area variation of each valve after considering the deposition effect in the embodiment of the present invention;

[0040] Fig. 9 4 is a combustion chamber pressure curve diagram exemplified in an embodiment of the present invention.

[0041] The realization of the purpose, functional features and advantages of the present invention will be further explained in conjunction with embodiments and with reference to the accompanying drawings. DETAILED DESCRIPTION

[0042] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0043] It should be noted that all directional indications in the embodiments of the present invention (such as up, down, left, right, front, back, etc.) are only used to explain the relative position relationship, movement status, etc. between the components under a certain specific posture (as shown in the accompanying drawings). If the specific posture changes, the directional indication will also change accordingly.

[0044] In addition, in the present invention, descriptions such as "first", "second", etc. are only used for descriptive purposes and cannot be understood as indicating or implying their relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" or "second" may explicitly or implicitly include at least one of the features. In the description of the present invention, the meaning of "plurality" is at least two, such as two, three, etc., unless otherwise clearly and specifically defined.

[0045] In the present invention, unless otherwise clearly specified and limited, the terms "connection", "fixation", etc. should be understood in a broad sense. For example, "fixation" can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection, an electrical connection, a physical connection, or a wireless communication connection; it can be a direct connection, or an indirect connection through an intermediate medium, or it can be the internal connection of two elements or the interaction relationship between two elements, unless otherwise clearly defined. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0046] In addition, the technical solutions between the various embodiments of the present invention can be combined with each other, but it must be based on the fact that ordinary technicians in the field can implement it. When the combination of technical solutions is contradictory or cannot be implemented, it should be deemed that such combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0047] During the operation of the solid attitude and orbit control engine, due to factors such as high engine combustion temperature, impure fuel, and high temperature resistance of internal materials, ablation and deposition effects will occur at the throat plug head and nozzle throat, causing the engine nozzle profile to change, and the actual equivalent throat area deviates from the ideal value, affecting the engine thrust performance, causing the problem of inaccurate thrust control of the solid attitude and orbit control engine. Based on this, this embodiment is based on solid engine interior ballistics and discloses an efficient and fast zero-dimensional interior ballistic calculation method for solid attitude and orbit control engines considering ablation-deposition. After considering the influence of ablation and deposition on the equivalent throat area, this method uses a nested dichotomy method to quickly and accurately update the actual equivalent throat area according to the time step, realizing the solution of the engine combustion chamber pressure after the known configuration, the known solid attitude and orbit control engine valve ablation / deposition law, and the known throat plug motion scheme. By using this method to calculate the zero-dimensional internal ballistics of a solid attitude and orbit control engine with known ablation / deposition laws, a combustion chamber pressure that is closer to the actual engineering situation can be obtained, which reduces the thrust calculation error caused by the inaccurate calculation of the zero-dimensional internal ballistics, facilitates the precise control of the thrust by the control mechanism, and facilitates the performance assessment and numerical simulation of the engine in the later stage, solving the problem of accurate and rapid calculation of the zero-dimensional internal ballistics of the engine. Compared with the conventional zero-dimensional internal ballistics method, this method can be used to calculate the combustion chamber pressure, which can obtain results that are closer to the actual working process and more accurate, laying a technical foundation for the precise control of the thrust of solid attitude and orbit control engines.

[0048] This embodiment first defines the ablation / deposition efficiency of the throat and nozzle of a solid attitude and orbit control engine of known configuration to obtain an ablation / deposition model. Secondly, after the throat motion scheme is known, the busbar after considering the ablation / deposition effect is parameterized. Then, the nested dichotomy method is used to quickly and accurately solve the equivalent throat area of ​​different valves at each moment, and the actual sum of the equivalent throat area after considering ablation / deposition at the current moment is obtained, and it is substituted into the zero-dimensional interior ballistic calculation model for iterative calculation. Finally, the zero-dimensional interior ballistic calculation after ablation / deposition is iterated according to the time step from the initial moment to the final moment.

[0049] In this embodiment, the specific implementation process of the zero-dimensional interior ballistic calculation method of the solid attitude and trajectory control engine considering ablation-deposition is as follows:

[0050] First, the given attitude and orbit control engine configuration parameters, material physical property parameters and calculation setting parameters are obtained. Among them, the attitude and orbit control engine configuration parameters include the variation law of charge burning surface and mass characteristics with burning thickness, nozzle and throat plug surface parameters; material physical property parameters include propellant parameters, nozzle ablation / deposition model and throat plug ablation / deposition model; calculation setting parameters include internal ballistic calculation time step and throat plug motion scheme.

[0051] Then, the zero-dimensional interior ballistic calculation model of the solid attitude and orbit control engine considering the influence of ablation / deposition is established as follows:

[0052]

[0053] In the formula, p c is the combustion chamber pressure, t is the time, Γ is the function of the specific heat ratio k, c * is the characteristic velocity, V c is the free volume of the combustion chamber, ρ p is the propellant density, A b is the burning surface area of ​​the charge, a is the burning rate coefficient, n is the pressure index, A t is the sum of the equivalent throat areas of all valves, e is the thickness of the powder column, R is the gas constant of the fuel gas, T f is the constant pressure combustion temperature, k is the specific heat ratio, A ti is the single valve equivalent throat area, x i is the displacement of the laryngeal plug, r t 、r p They are the ablation / deposition of the nozzle throat and throat plug, respectively. When calculating the equivalent throat, the throat plug displacement and the ablation / deposition rate of the nozzle and throat plug should be comprehensively considered to perform a single-step equivalent throat area calculation. When ablation occurs, the actual equivalent throat area is greater than the theoretical equivalent throat area; when deposition occurs, the actual equivalent throat area is less than the theoretical equivalent throat area.

[0054] According to the zero-dimensional interior ballistic calculation model of the solid attitude and orbit control engine after considering the influence of ablation / deposition, refer to Figure 1 , the zero-dimensional interior ballistic calculation process of the solid attitude and orbit control engine is:

[0055] Step 1: Input engine and nozzle parameters, propellant performance parameters, combustion surface parameters and throat plug movement plan;

[0056] Step 2: Give the initial values ​​and constants required for calculation;

[0057] Step 3: Determine the burning time division (give the time step);

[0058] Step 4: Calculation of initial combustion chamber pressure;

[0059] Step 5: Determine the current throat plug and nozzle ablation / deposition amount, and calculate the equivalent throat area;

[0060] Step 6: Burning rate calculation;

[0061] Step 7: Calculation of burn-off thickness;

[0062] Step 8: Interpolate the existing burning surface data to obtain the corresponding burning surface size;

[0063] Step 9: Calculate the corresponding combustion chamber pressure after considering the ablation-deposition effect of the current throat plug movement scheme;

[0064] Step 10: Determine whether the combustion has reached the end of the propellant column. If so, end the process; otherwise, return to step 5.

[0065] In this embodiment, the fourth-order Longo Kutta method is used to iteratively solve the zero-dimensional interior ballistic calculation model of the solid attitude and orbit control engine to obtain the corresponding combustion chamber pressure after considering the influence of ablation / deposition. Among them, the initial pressure of the combustion chamber is obtained by calculating the setting parameters, and the charge combustion area A b (e) and the free volume V of the combustion chamber c (e) The combustion surface area and free volume under different combustion thicknesses e are directly calculated by the combustion surface calculation program, and the valve and nozzle ablation / deposition rates h(p) under different pressures and equivalent throat areas are obtained by interpolation. c ,A ti ) and g(p c ,A ti )According to the experimental data, the equivalent throat area of ​​each valve is A ti =f(x i ,r t ,r p ) is obtained by the nested binary search method shown in step (4). Before each iteration of the Runge-Kutta method, the equivalent throat area of ​​each valve is obtained based on the throat plug displacement and the ablation / deposition rate of the nozzle and the throat plug, and the total equivalent throat area of ​​the engine is accumulated.

[0066] The nested binary search method is used to obtain the displacement of the throat plug of different valves at any time, and the corresponding sum of equivalent throat areas after ablation / deposition. Since there is a unique extreme point in the equivalent throat area of ​​the throat plug during the movement of the nozzle, the binary search method is used to search for the minimum channel area between the throat plug and the throat, which can greatly improve the solution efficiency and reduce the calculation consumption. In the problem of solving the equivalent throat area, since the minimum channel area between the throat plug and the nozzle busbar is calculated, the solution intervals of the two should be considered separately. Therefore, this embodiment adopts a double-layer nested binary search method for cyclic search and solution. When solving the single equivalent throat area, it is divided into an outer circulation layer and an inner circulation layer, wherein the outer circulation layer performs a binary search on the throat plug profile curve, and the inner circulation layer performs a binary search on the nozzle profile curve.

[0067] refer to Figure 2 , the process of the outer loop layer is:

[0068] Step 1.1, obtaining the current displacement position of the throat plug, and updating the throat plug profile curve after considering the ablation / deposition effect according to the ablation / deposition model to obtain the first search interval;

[0069] Step 1.2, selecting any two points near the left and right endpoints and the midpoint of the first search interval as first control points, and obtaining the equivalent throat area corresponding to each first control point based on the inner loop layer;

[0070] Step 1.3, selecting the first control point with the smallest equivalent throat area in step 1.2, and updating the first search interval, using the two first control points adjacent to the left and right of the first control point corresponding to the minimum equivalent throat area as the left and right endpoints of the first search interval after update;

[0071] Step 1.4, determine whether the first search interval has reached the convergence condition, if so, output the minimum equivalent throat area in step 1.2 as the equivalent throat area of ​​the corresponding valve, otherwise return to step 1.2. Wherein, the manner of determining whether the first search interval has reached the convergence condition is that the maximum number of outer loop iterations is reached or the current length of the first search interval is less than the preset judgment accuracy.

[0072] In step 1.3, the equivalent throat area corresponding to each first control point is obtained based on the inner circulation layer. For each first control point, there is:

[0073] Step 2.1, read the first control point of the current throat plug profile curve in the outer circulation layer, update the nozzle profile curve after considering the ablation / deposition effect according to the ablation / deposition model, and obtain the second search interval;

[0074] Step 2.2, select any two points near the left and right endpoints and the midpoint of the second search interval as the second control points, and obtain the equivalent throat area between the first control point and each second control point. The implementation process is:

[0075] Given the profile parameters of the throat plug and the nozzle, assuming that the profile functions of the throat plug and the nozzle after considering their ablation / deposition laws are:

[0076]

[0077] In the formula, y 1 =f 1 (m,h t ) and y 2 =f 2 (n,x i ,h p ) are respectively the nozzle generatrix equation and the throat plug generatrix equation after considering ablation / deposition; m is the horizontal coordinate of any point on the nozzle, h t is the ablation / deposition thickness on the nozzle throat surface, m L 、m R are the left and right endpoints of the nozzle busbar, i.e., the initial left and right endpoints of the first search interval; n is the horizontal coordinate of any point on the throat plug, h p is the thickness of laryngeal plug surface ablation / deposition, n L 、x i are the left and right endpoints of the throat plug busbar, i.e., the initial left and right endpoints of the second search interval, x iIt is also the current displacement of the throat plug vertex.

[0078] The coordinate system for calculating the effective travel range of the throat plug and the equivalent throat area corresponding to different movement positions of the throat plug is as follows: Figure 3 The relationship between the thickness of the deposits on the nozzle throat and throat plug surface and the deposition rate is:

[0079] h t =r t Δt

[0080] h p =r p Δt

[0081] In the formula, r t is the nozzle throat surface ablation / deposition rate, r p is the ablation / deposition rate of the laryngeal plug surface, and Δt is the time step.

[0082] For a single valve, as the throat plug moves from left to right, the equivalent throat area gradually decreases with the movement of the throat plug, and reaches the minimum value when the throat plug and the throat are completely closed. i Calculate the throat area A ti Usually, take any point (m,y 1 ), select any point on the throat plug (n,y 2 ) and then calculate the equivalent throat area, traverse all points, and the minimum area solved in the process is the equivalent throat area of ​​the valve. Traverse the valve displacement x i After the effective movement range, all displacement values ​​in the process and the corresponding equivalent throat area solved are the relationship between the displacement of the single valve throat plug and the change of the equivalent throat area. In this embodiment, the equivalent throat area search is performed by binary search, which can greatly improve the solution efficiency and reduce the calculation consumption. The equivalent throat area calculation process is:

[0083]

[0084] In the formula, A ti is the equivalent throat area, m in the above formula is the horizontal coordinate of the second control point on the nozzle, and n is the horizontal coordinate of the first control point on the throat plug;

[0085] Step 2.3, screening out the second control point with the smallest equivalent throat area in step 2.2, and updating the second search interval, using the two second control points adjacent to the left and right of the second control point corresponding to the minimum equivalent throat area as the left and right endpoints of the updated second search interval;

[0086] Step 2.4, determine whether the second search interval has reached the convergence condition, if so, output the minimum equivalent throat area in step 2.2 as the equivalent throat area corresponding to the first control point, otherwise return to step 2.2. Wherein, the manner of determining whether the second search interval has reached the convergence condition is to reach the maximum number of inner loop iterations or the current length of the second search interval is less than the preset judgment accuracy.

[0087] The following takes the timing experiment design of a four-nozzle orbit control engine as an example to give a specific case to verify the method, and further illustrate the zero-dimensional interior ballistic calculation method of the solid attitude and orbit control engine considering ablation-deposition in this embodiment.

[0088] The layout of the orbit control engine in this experimental design is as follows Figure 4 As shown in the figure, the orbit control engine can generate orbit control force along the Oy axis and Oz axis of the body. The valves are numbered as valves 1, 2, 3, and 4 in the clockwise direction. Figure 5 As shown, its configuration parameters are shown in Table 1, and the engine operating parameters are set as shown in Table 2.

[0089] Table 1 Nozzle throat configuration parameters

[0090]

[0091]

[0092] Table 2 Engine operating parameters

[0093]

[0094] The purpose of this calculation method is to realize the rapid and accurate calculation of the combustion chamber pressure after considering the ablation / deposition effect during the operation of the solid attitude and orbit control engine, and to reduce the error between the theoretical calculated value and the actual value of the combustion chamber pressure. For this case, the zero-dimensional interior ballistic calculation method of the solid attitude and orbit control engine considering the ablation / deposition effect is applied to calculate the combustion chamber pressure during the operation. The specific steps are as follows:

[0095] Step 1: Give Figure 6 The laryngeal plug movement scheme shown in the figure corresponds to the ideal equivalent laryngeal area change as shown in the figure Figure 7 As shown. Set the ablation / deposition model as shown in the formula, consider the valve throat plug and throat deposition law separately, and update the current generatrix equation with the formula for calculating the deposition thickness on the throat plug surface and the formula for calculating the deposition thickness on the nozzle surface. Perform a loop solution according to the time step within the defined working time. Knowing that the time 0s is the initial time, superimpose it according to the time step of 0.01s and calculate until the final time of 10s.

[0096] h d =rΔt=aA t (t) mΔt

[0097] Among them, h d is the thickness of the ablation / deposition, r is the ablation / deposition rate, Δt is the time step, A t is the ideal equivalent throat area, a is the ablation / deposition term coefficient, and m is the exponent of the ablation / deposition term change affected by the change in equivalent throat area.

[0098]

[0099]

[0100] Among them, h pi_d is the thickness of the deposits attached to the surface of each throat plug, h ti_d is the thickness of the deposits attached to the surface of each nozzle, r pi_d is the laryngeal plug deposition rate, r ti_d is the nozzle deposition rate, Δt is the time step, A ti is the ideal equivalent throat area of ​​each valve, P c is the ideal pressure in the combustion chamber, a 1 ,a 2 are respectively the throat plug deposition coefficient and the nozzle deposition coefficient, m 1 ,m 2 They are respectively the index of change of throat plug deposition item affected by change of equivalent throat area and the index of change of nozzle deposition item affected by change of equivalent throat area.

[0101] Step 2: Use the nested dichotomy method to calculate the equivalent throat area of ​​the nozzle after considering the ablation / deposition effect, and obtain the equivalent throat area change curve considering the deposition effect, such as Figure 8 As shown. Figure 7 , Figure 8 It can be seen that due to the consumption of the effective range of throat area change due to sediment blockage, the range of equivalent throat area change after considering the deposition effect gradually decreases, while the range of equivalent throat area change under ideal conditions remains unchanged. The change of equivalent throat area considering the ablation / deposition effect is more in line with actual engineering experience.

[0102] Step 3: Calculate the zero-dimensional internal ballistics based on the equivalent throat area after considering the ablation / deposition effect, and obtain the combustion chamber pressure after considering the deposition. The ideal pressure is the combustion chamber pressure calculated without considering the influence of the ablation / deposition effect on the equivalent throat area, such as Fig. 9 As shown. Fig. 9 It can be clearly seen that there is a large difference between the ideal pressure and the combustion chamber pressure after considering the deposition effect. If the conventional zero-dimensional interior ballistic calculation method is used, it will be quite different from the actual situation of the engine. The combustion chamber pressure calculated by the method of this embodiment can better support the later research on engine performance.

[0103] The above description is only a preferred embodiment of the present invention, and does not limit the patent scope of the present invention. All equivalent structural changes made by using the contents of the present invention specification and drawings under the inventive concept of the present invention, or directly / indirectly applied in other related technical fields are included in the patent protection scope of the present invention.

Claims

1. A zero-dimensional interior ballistic calculation method for a solid attitude and orbit control engine considering ablation-deposition, characterized in that: The steps include: The zero-dimensional interior ballistic calculation model of the solid attitude and orbit control engine considering the influence of ablation / deposition is established as follows: ； In the formula, is the combustion chamber pressure, It's time. is the specific heat ratio The function of is the characteristic velocity, is the free volume of the combustion chamber, is the propellant density, is the burning surface area of ​​the charge, is the burning rate coefficient, is the pressure index, is the sum of the equivalent throat areas of all valves, The medicine column is thick. is the gas constant of the fuel gas, is the constant pressure combustion temperature, is the specific heat ratio, is the single valve equivalent throat area, It is the displacement of the laryngeal plug. , are the ablation / deposition amounts of the nozzle throat and throat plug, respectively; The Runge-Kutta method is used to iteratively solve the zero-dimensional interior ballistic calculation model of the solid attitude and orbit control engine, and the corresponding combustion chamber pressure is obtained after considering the ablation / deposition effect. Before each iteration of the Runge-Kutta method, the equivalent throat area of ​​each valve is obtained based on the throat plug displacement and the ablation / deposition rate of the nozzle and throat plug, and the total equivalent throat area of ​​the engine is accumulated.

2. The zero-dimensional interior ballistics calculation method of a solid attitude and orbit control engine considering ablation-deposition according to claim 1 is characterized in that: The nested binary search method is used to obtain the equivalent throat area of ​​each valve. The single equivalent throat area solution process is divided into an outer circulation layer and an inner circulation layer. The outer circulation layer performs a binary search on the throat plug profile curve, and the inner circulation layer performs a binary search on the nozzle profile curve.

3. The zero-dimensional interior ballistic calculation method of a solid attitude and orbit control engine considering ablation-deposition according to claim 2 is characterized in that: The process of the outer circulation layer is: Step 1.1, obtaining the current displacement position of the throat plug, and updating the throat plug profile curve after considering the ablation / deposition effect according to the ablation / deposition model to obtain the first search interval; Step 1.2, selecting any two points near the left and right endpoints and the midpoint of the first search interval as first control points, and obtaining the equivalent throat area corresponding to each first control point based on the inner loop layer; Step 1.3, selecting the first control point with the smallest equivalent throat area in step 1.2, and updating the first search interval, using the two first control points adjacent to the left and right of the first control point corresponding to the minimum equivalent throat area as the left and right endpoints of the first search interval after update; Step 1.4, determine whether the first search interval reaches the convergence condition, if so, output the minimum equivalent throat area in step 1.2 as the equivalent throat area of ​​the corresponding valve, otherwise return to step 1.

2.

4. The zero-dimensional interior ballistic calculation method of a solid attitude and orbit control engine considering ablation-deposition according to claim 3 is characterized in that: In step 1.3, the equivalent throat area corresponding to each first control point is obtained based on the inner circulation layer, specifically: For each first control point, we have: Step 2.1, updating the nozzle profile curve after considering the ablation / deposition effect according to the ablation / deposition model to obtain a second search interval; Step 2.2, selecting any two points near the left and right endpoints and the midpoint of the second search interval as second control points, and obtaining the equivalent throat area between the first control point and each second control point; Step 2.3, screening out the second control point with the smallest equivalent throat area in step 2.2, and updating the second search interval, using the two second control points adjacent to the left and right of the second control point corresponding to the minimum equivalent throat area as the left and right endpoints of the updated second search interval; Step 2.4, determine whether the second search interval reaches the convergence condition, if so, output the minimum equivalent throat area in step 2.2 as the equivalent throat area corresponding to the first control point, otherwise return to step 2.

2.

5. The zero-dimensional interior ballistic calculation method of a solid attitude and orbit control engine considering ablation-deposition according to claim 4 is characterized in that: In step 2.2, the equivalent throat area between the first control point and each second control point is obtained, specifically: ; In the formula, is the equivalent throat area, and They are respectively the nozzle generatrix equation and the throat plug generatrix equation after considering ablation / deposition, is the horizontal coordinate of the second control point on the nozzle, is the ablation / deposition thickness on the nozzle throat surface, is the horizontal coordinate of the first control point on the throat plug, is the current displacement of the throat plug vertex, is the thickness of the laryngeal plug surface ablation / deposition.

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