Reverse design method for throat bolt molded surface of variable thrust solid rocket engine

Abstract

The invention provides a reverse design method for a throat bolt molded surface of a variable thrust solid rocket engine, which comprises the following steps of: when the throat bolt molded surface is designed, firstly, determining a given engine thrust change relation, namely a thrust-throat bolt stroke change relation or curve; each position of the pintle corresponds to one steady-state thrust of the engine; according to the working principle of a rocket engine, the change relation between the theoretical thrust and the equivalent throat area is obtained; the relation between the equivalent throat area and the throat bolt stroke S-l is immediately obtained by combining the relational expressions obtained in the previous two steps; and substituting S-l into the throat bolt profile control equation set, and solving to obtain the throat bolt profile. Carrying out numerical simulation or experimental verification on the obtained molded surface of the throat bolt; correcting the theoretical thrust in combination with a simulation or test result; and after correction, repeating to obtain a final throat bolt profile. According to the method, the molded surface of the pintle is reversely designed by solving the algebraic equation set, the method has the characteristics of high precision and high speed, and repeated iterative optimization is not needed.

Description

Technical Field

[0001] The present invention proposes a reverse design method for the throat plug profile of a variable thrust solid rocket engine, which can reversely design the throat plug profile by solving the proposed binary high-order equation group according to a given thrust control requirement, and belongs to the technical field of solid rocket engines. Background Art

[0002] Compared with other rocket propulsion methods, solid rocket engines have advantages such as simple structure, easy maintenance and long storage time, so they are widely used in missiles and launch vehicles. However, traditional solid rocket engines also have the problem that thrust is difficult to control and energy management is difficult. At present, a more mature thrust control scheme is to set a throat plug along the axis near the throat of the nozzle, and drive the throat plug forward and backward through a driving mechanism (such as a motor) to change the actual throat area of ​​the nozzle, thereby achieving a change in thrust. It can be seen that the key to adjusting the thrust of the throat plug type solid rocket engine is that the actuation of the throat plug changes the throat area, and the shape of the throat plug directly affects the change law of the throat area during the actuation process. Therefore, the shape design of the throat plug is crucial for the throat plug type solid rocket engine.

[0003] The throat plug is arranged on the axis of the nozzle, and the head of the throat plug is located near the nozzle throat. The high-temperature and high-pressure combustion gas generated by the combustion of the charge enters the nozzle convergence section from the upstream of the throat plug-nozzle system and accelerates. The cross-sectional area of ​​the gas flow channel is the smallest (less than or equal to the nozzle throat area) somewhere near the nozzle throat, referred to as the equivalent throat. The Mach number at the equivalent throat is 1 (Ma=1). When the nozzle outlet area is determined, the change in the equivalent throat area of ​​the throat plug-nozzle system directly determines the change in engine thrust.

[0004] The existing technical solutions for throat plug profile design are:

[0005] 1. Use cone, ellipsoid, hyperbolic, parabolic and polynomial equations to construct the plug surface, combine computational fluid dynamics to conduct numerical simulation, and compare various surfaces. At present, some parameters (such as angle, radius, length) of the control surface are manually adjusted, and finally the optimal design result is obtained by iteration;

[0006] 2. For an existing (such as a typical design) throat-nozzle system, perform surface optimization design and analyze the sensitivity of the nozzle and throat design parameters (i.e., the impact on the results), with the goal of improving the aerodynamic efficiency of the nozzle. Compared with the first solution, this solution introduces the idea of ​​optimization design and replaces manual parameter adjustment;

[0007] 3. Based on the zero-dimensional interior ballistic model of solid rocket motors, the position of the typical throat plug surface is corrected. The throat plug surface is discretized, and then the coordinates are corrected point by point to match the target value. This scheme introduces a zero-dimensional interior ballistic model instead of simply considering the change in throat area geometrically. Ideally, the design results of this scheme are more in line with expectations.

[0008] The disadvantages of the existing throat plug profile design are:

[0009] (1) It has great limitations and relies on the experience of designers. It requires repeated iterations and is relatively time-consuming. It is also difficult to obtain a throat plug profile that matches the design thrust change curve. It is a forward design process of "design-trial-error".

[0010] (2) Direct optimization of the profile requires a huge amount of calculation. Even if limited experimental design points are used for calculation and design, the efficiency is relatively low. It is a forward design process of "design-optimization".

[0011] (3) The coordinates of each discrete point on the throat plug surface are obtained by searching, which is a recursive matching design process. No mathematical model is established for the throat plug surface design problem, nor is the ideal zero-dimensional interior ballistic model corrected. Summary of the invention

[0012] In view of the above technical problems, the present invention provides a reverse design method for the throat plug profile of a variable thrust solid rocket engine, comprising the following steps:

[0013] S1. When designing the throat plug profile, first determine the given engine thrust change relationship, that is, the thrust-throat plug stroke change relationship or curve, which is required to be linear. Each position of the throat plug corresponds to a steady-state thrust of the engine.

[0014] S2. According to the working principle of rocket engines, the relationship between theoretical thrust and equivalent throat area is obtained. Solid rocket engine systems are divided into two cases: a multi-nozzle system with constant combustion chamber pressure and an engine system with variable combustion chamber pressure; for the former, the calculation formula for engine thrust is:

[0015] F=C F P c A t

[0016]

[0017] Where F is the engine thrust, P c is the combustion chamber pressure, A t is the equivalent throat area, A e is the nozzle exit area, C F is the thrust coefficient, k is the specific heat ratio, Γ is the function of the specific heat ratio, Pe is the nozzle outlet pressure, P a For external pressure; and Approximate to a parabolic relationship, use quadratic / linear fitting to reduce variables, such as:

[0018]

[0019] Where α k , b k 、c k is the fitting parameter.

[0020] For engines whose combustion chamber pressure cannot be considered constant, the zero-dimensional interior ballistic model of solid rocket engines is introduced:

[0021]

[0022] Where r is the charge burning rate, α is the burning rate coefficient, n is the pressure index, P ceq is the equilibrium pressure of the combustion chamber, ρ p is the propellant density, c* is the characteristic velocity, A b is the propellant burning surface area; for charges with equal surface burning, A b Considered to be a fixed value.

[0023] The thrust formula is:

[0024]

[0025] S3. Connect the relationship obtained in the first two steps to get the relationship between equivalent throat area and throat plug stroke S1. Substitute S1 into the throat plug profile control equation group and solve to get the throat plug profile.

[0026] Calculation method of equivalent throat area and control equations of throat plug profile:

[0027] S3.1 Calculation of equivalent throat area:

[0028] The intersection of the nozzle convergent section and the throat cylindrical section is taken as the coordinate origin, and the equivalent throat flow channel is considered to appear between the coordinate origin and a certain point on the throat plug surface. A dimensionless analysis is performed, and the dimensionless coordinates of any point on the throat plug surface are recorded as (ξ,η). The equivalent flow channel cross section is expressed by a straight line equation:

[0029]

[0030] Then the equivalent throat area is expressed as:

[0031]

[0032] Where ds is the length from the origin along the straight line to (ξ,η), S is the dimensionless area, the nozzle throat area is unit 1, 0≤S≤1. The throat plug body is considered to be a convex set with a smooth surface, and the corresponding function is differentiable at any order. If the throat plug surface is tangent to the contour line of the S field at a certain point, then the line connecting this point and the origin is the minimum flow channel cross-sectional area, that is, the equivalent throat area.

[0033] S3.2 Throat plug profile control equations:

[0034] l is used to represent the dimensionless distance of the throat plug actuation, the unit 1 is the radius of the nozzle throat, l = 1 means the nozzle is fully open, and l = 0 means the nozzle is fully closed. The control equations of the throat plug profile are:

[0035]

[0036] The subscript T represents the design target, S T is a given function, i.e. a given Sl relation. The above equation is a system of binary high-order equations, with 6 sets of roots and only one real root satisfying y∈[0,1]. Given any l value, the corresponding x and y coordinates can be obtained, for l in the range [0,1].

[0037] S4 performs numerical simulation or test verification on the obtained throat plug profile. The theoretical thrust is corrected in combination with the simulation or test results. After correction, steps S2-S3 are repeated to obtain the final throat plug profile.

[0038] The invention proposes a design method for a throat plug profile of a variable thrust solid rocket engine. The throat plug profile is inversely designed by solving a group of algebraic equations. The method has the characteristics of high precision and high speed, and does not require repeated iterative optimization.

[0039] The present invention is a reverse design method, which reversely designs the profile of the throat plug according to the engine thrust requirement, without repeated iterative trial and error, and the design speed is relatively fast. The throat plug profile obtained by the proposed design method is obtained by mathematical derivation and solving a set of equations, and has the characteristics of clear form and high accuracy. It has been proven to have a wide range of applicability and is applicable to different nozzle configurations, propellant types, and thrust requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 is a flow chart of the present invention;

[0041] Figure 2 Schematic diagram for calculating equivalent throat area;

[0042] Figure 3 The throat plug profile obtained in the embodiment

[0043] Figure 4 It is the relationship curve between thrust and throat plug stroke;

[0044] Figure 5 The thrust formula is used to check the engine thrust for the embodiment. DETAILED DESCRIPTION

[0045] The technical solution of the present invention proposes a reverse design method for the throat plug profile. The design process of the throat plug profile is as follows: Figure 1 As shown, the details are as follows:

[0046] The reverse design method of the throat plug profile of a variable thrust solid rocket motor comprises the following steps:

[0047] S1. When designing the throat plug profile, first determine the given engine thrust change relationship, that is, the thrust-throat plug stroke change relationship (or curve), which is usually required to be linear. Each position of the throat plug corresponds to a steady-state thrust of the engine. When the engine thrust needs to change during actual operation, drive the throat plug to the corresponding position.

[0048] S2. According to the working principle of rocket engines, the relationship between theoretical thrust and equivalent throat area is obtained. Common solid rocket engine systems can be divided into two cases: multi-nozzle systems where the combustion chamber pressure can be considered constant (such as solid attitude and orbit control engines) and engine systems where the combustion chamber pressure varies (such as one combustion chamber corresponding to one nozzle). For the former, the calculation formula for engine thrust is:

[0049] F=C F P c A t

[0050]

[0051] Where F is the engine thrust, P c is the combustion chamber pressure, A t is the equivalent throat area, A e is the nozzle exit area, C F is the thrust coefficient, k is the specific heat ratio, Γ is the function of the specific heat ratio, P e is the nozzle outlet pressure, P a For external pressure; and Approximate to a parabolic relationship, use quadratic / linear fitting to reduce variables, such as:

[0052]

[0053] Where α k , b k 、c k is the fitting parameter.

[0054] For engines whose combustion chamber pressure cannot be considered constant, the zero-dimensional interior ballistic model of solid rocket engines is introduced:

[0055]

[0056] Where r is the charge burning rate, α is the burning rate coefficient, n is the pressure index, P ceq is the equilibrium pressure of the combustion chamber, ρ p is the propellant density, c* is the characteristic velocity, A b is the propellant burning surface area; for charges with equal surface burning, A b It can be considered as a fixed value.

[0057] Therefore, the thrust formula is:

[0058]

[0059] S3. The relationship between the equivalent throat area and the throat plug stroke (Sl) can be obtained by linking the relationship obtained in the first two steps. Substitute Sl into the throat plug profile control equations and solve them to obtain the throat plug profile. The following introduces the calculation method of the equivalent throat area and the throat plug profile control equations:

[0060] S3.1 Calculation of equivalent throat area

[0061] like Figure 2 As shown in the figure, the intersection of the nozzle convergent section and the throat cylindrical section is taken as the coordinate origin, and the equivalent throat flow channel (equivalent flow channel section) is considered to appear between the coordinate origin and a certain point on the throat plug surface. Dimensionless analysis is performed, and the dimensionless coordinates of any point on the throat plug surface are recorded as (ξ,η) (taking the unit of the nozzle throat radius as 1), and the equivalent flow channel section can be expressed by a straight line equation:

[0062]

[0063] The equivalent throat area can be expressed as

[0064]

[0065] Where ds is the length from the origin along the straight line to (ξ,η), S is the dimensionless area (the nozzle throat area is unit 1), 0≤S≤1. The throat plug body is considered to be a convex set with a smooth surface, and the corresponding function is differentiable at any order. If the throat plug surface is tangent to the contour line of the S field at a certain point, then the line connecting this point and the origin is the minimum flow channel cross-sectional area, that is, the equivalent throat area.

[0066] S3.2 Laryngeal plug profile control equations

[0067] l is used to represent the dimensionless distance of the throat plug actuation (unit 1 is the radius of the nozzle throat), l = 1 means the nozzle is fully open, and l = 0 means the nozzle is fully closed. The control equations of the throat plug profile are:

[0068]

[0069] The subscript T represents the design target, S T is a given function, i.e. a given Sl relation. The above formula is a system of binary high-order equations with 6 sets of roots, and only one real root that satisfies y∈[0,1]. Therefore, for any given l value, the corresponding x and y coordinates can be obtained. For l in the range [0,1]

[0070] When the nozzle configuration is a conical nozzle (no fillet at the throat), this method can ensure that the obtained profile is extremely accurate, and the Sl curve can be considered to have no deviation; when there is a fillet at the nozzle throat, the throat plug can be designed according to the conical nozzle of the corresponding size, the Sl relationship of the designed profile can be verified, the Sl relationship can be corrected by fitting with the theoretical value, and the equation group can be solved again to obtain the throat plug profile with a higher Sl relationship accuracy. In addition, if the throat plug profile is non-convex, it may not strictly meet the given Sl curve, but the design result is still of reference value.

[0071] S4 performs numerical simulation or test verification on the obtained throat plug profile. There is inevitably an error between the theoretical thrust of the engine and the actual situation, so the theoretical thrust can be corrected in combination with the simulation or test results. After correction, repeat steps S2-S3 to obtain the final throat plug profile.

[0072] For a certain attitude and orbit control power system, which consists of multiple orbit control and attitude control nozzles, the opening and closing degree of different nozzles can be controlled to keep the total nozzle throat area unchanged during operation, so the combustion chamber pressure can be considered unchanged. The operating parameters of the attitude and orbit control engine are shown in Table 1:

[0073] Table 1 Attitude and orbit control engine operating parameters

[0074]

[0075] The nozzle configuration is a conical nozzle, the design thrust changes from 1593.6N to 0N, the throat bolt stroke is 15.9025mm, which is 3 times the nozzle throat radius, and the thrust is required to change linearly within the stroke. In the initial design, the thrust coefficient is temporarily taken as a constant. From the thrust formula, it can be seen that the engine thrust is only related to the equivalent throat area at this time. Requiring a linear change in thrust is to require a linear change in the equivalent throat area. Non-dimensionalization is performed to determine the relationship between the equivalent throat area and the throat bolt stroke:

[0076] Will Substitute the control equations of the throat plug surface into the equations and solve for l in the range [0,1] to obtain the throat plug surface as follows: Figure 3 The thrust formula is used to check the engine thrust, and the result is as follows: Figure 5 As shown in the figure, the error is caused by taking the thrust coefficient as a constant when designing the throat plug profile. Introducing the influence of the actual expansion ratio change on the thrust coefficient will eliminate this part of the error. At this time, the Sl relationship can be given by an algebraic expression. The curve is Figure 4 Basically consistent.

Claims

1. A reverse design method for the throat plug profile of a variable thrust solid rocket engine, characterized in that: The following steps are involved: S1. When designing the throat plug profile, first determine the given engine thrust change relationship, that is, the thrust-throat plug stroke change relationship or curve; each position of the throat plug corresponds to a steady-state thrust of the engine; S2. According to the working principle of rocket engine, the relationship between theoretical thrust and equivalent throat area is obtained; S3. The relationship obtained in the first two steps is immediately connected to obtain the equivalent throat area - throat plug stroke Sl relationship; Substitute Sl into the throat plug profile control equations and solve to obtain the throat plug profile; S4 performs numerical simulation or test verification on the obtained throat plug profile; corrects the theoretical thrust in combination with the simulation or test results; after correction, repeats steps S2-S3 to obtain the final throat plug profile.

2. The reverse design method of the throat plug profile of the variable thrust solid rocket engine according to claim 1 is characterized in that: In S2, the solid rocket engine system is divided into two cases: a multi-nozzle system with constant combustion chamber pressure and an engine system with variable combustion chamber pressure; for the former, the engine thrust calculation formula is: F=C F P c A t Where F is the engine thrust, P c is the combustion chamber pressure, A t is the equivalent throat area, A e is the nozzle exit area, C F is the thrust coefficient, k is the specific heat ratio, Γ is the function of the specific heat ratio, P e is the nozzle outlet pressure, P a For external pressure; and Approximate to a parabolic relationship, use quadratic / linear fitting to reduce variables, such as: Where α k , b k 、c k is the fitting parameter; For engines whose combustion chamber pressure cannot be considered constant, the zero-dimensional interior ballistic model of solid rocket engines is introduced: Where r is the charge burning rate, α is the burning rate coefficient, n is the pressure index, P ceq is the equilibrium pressure of the combustion chamber, ρ p is the propellant density, c* is the characteristic velocity, A b is the propellant burning surface area; for charges with equal surface burning, A b Considered to be a fixed value; The thrust formula is:

3. The reverse design method of the variable thrust solid rocket engine throat plug profile according to claim 1, characterized in that: S3 includes the calculation of the equivalent throat area and the governing equations for the throat plug profile: (1) Calculation of equivalent throat area: The intersection of the nozzle convergent section and the throat cylindrical section is taken as the coordinate origin, and the equivalent throat flow channel is considered to appear between the coordinate origin and a certain point on the throat plug surface; a dimensionless analysis is performed, and the dimensionless coordinates of any point on the throat plug surface are recorded as (ξ,η), and the equivalent flow channel cross section is expressed by a straight line equation: Then the equivalent throat area is expressed as: Where ds is the length from the origin along the straight line to (ξ,η), S is the dimensionless area, the nozzle throat area is unit 1, 0≤S≤1; the throat plug body is considered to be a convex set with a smooth surface, and the corresponding function can be differentiated at any order. If the throat plug surface is tangent to the contour line of the S field at a certain point, then the line connecting this point and the origin is the minimum flow channel cross-sectional area, that is, the equivalent throat area; (2) Laryngeal plug profile control equations: l is used to represent the dimensionless distance of the throat plug actuation, the unit 1 is the radius of the nozzle throat, l = 1 means the nozzle is fully open, and l = 0 means the nozzle is fully closed; the control equations of the throat plug profile are: The subscript T represents the design target, S T is a given function, that is, a given Sl relationship; the above formula is a system of high-order equations in two variables, with 6 sets of roots and only 1 real root satisfying y∈[0,1]; for any given l value, the corresponding x and y coordinates can be obtained, and l is in the range of [0,1].

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