An eight-valve solid-state attitude control engine interior ballistic design method

Abstract

The application provides an eight-valve solid attitude control engine interior ballistic design method, which provides effective guidance for the design method of the eight-valve solid attitude control engine interior ballistic. The idea of the application is to realize constant engine working pressure through the constraint conditions of grain burning surface and total throat area, to transform the valve number through rotational symmetry and mirror symmetry rules, to obtain the valve thrust calculation formula through sequentially deducing the zero thrust mode, single-valve effective thrust and adjacent 2-valve effective thrust and the like; under the condition of constant combustion chamber pressure, the working conditions of each needle valve nozzle are simplified, the efficiency of obtaining the corresponding thrust coefficient of the throat plug under different strokes is improved, and the valve total throat area calculation method for realizing constant combustion chamber pressure at any time is realized.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of variable-thrust solid rocket engine, in particular to an interior ballistic design method. BACKGROUND

[0002] The core task of solid rocket engine design is to determine the interior ballistic performance of the engine, i.e. the pressure and thrust curve of the engine. For a conventional solid rocket engine with a fixed throat diameter, the pressure and thrust curve is determined after the design. For a solid attitude control engine with eight needle valve nozzles, the interior ballistic design method is quite different. During stable operation of the engine, the size and direction of the combustion chamber pressure and the engine combined thrust can be changed in a large range by adjusting the throat area of each needle valve nozzle. At present, there is still a lack of design method for the interior ballistic of the eight-valve solid attitude control engine, which hinders the engineering application of the eight-valve solid attitude control engine. Therefore, it is urgent to propose a simple and reliable interior ballistic design method for the eight-valve solid attitude control engine. SUMMARY

[0003] In order to overcome the shortcomings of the prior art and provide effective guidance for the design method of the interior ballistic of the eight-valve solid attitude control engine, the present application provides an interior ballistic design method for an eight-valve solid attitude control engine.

[0004] An interior ballistic design method for an eight-valve solid attitude control engine, comprising the following steps:

[0005] Step S1: establishing a vector thrust model;

[0006] The vector thrust model includes a needle valve model, constraint conditions, single-valve thrust capacity, relative two-valve thrust capacity, and multi-valve circumferential transformation rules;

[0007] Step S1.1: establishing a needle valve model;

[0008] The needle valve model is that the vector thrust model includes Num needle valve nozzles, the Num needle valve nozzles are symmetrically and uniformly distributed along the circumference, 6≤Num≤14, and Num is an even number; the thrust line of the needle valve nozzle is located in the same plane; Valves k is the kth valve, where 1≤k≤Num;

[0009] Let the size of the vector combined thrust be F sum , the angle between the vector combined thrust and the x-axis be α, and the components of the vector combined thrust in the x and y axes be F sum-x and F sum-y , respectively, where F sum-x =F sum ·cosα, and F sum-y =F sumsinα; β is the smallest symmetry angle, β=360 / (Num×2);

[0010] Step S1.2: Determine the constraints;

[0011] The constraints are:

[0012] To maintain a constant pressure in the combustion chamber, the combustion surface A b and total throat area A t-tot satisfy const represents a fixed value;

[0013] The constraint condition that the combustion surface of the propellant grain must satisfy during stable engine operation is: Combustion surface A b and total throat area A t-tot Must meet In the formula A t-i-j p represents the total throat area corresponding to the maximum opening of valve i and the minimum opening of valve j; c ρ is the combustion chamber pressure; a is the burning rate coefficient; ρ is the propellant density; C * The characteristic velocity is n, and the pressure exponent is n.

[0014] Step S1.3: Multi-valve circumferential transformation rules;

[0015] The circumferential transformation rule for multiple valves is as follows:

[0016] (1) Rotational symmetry rule;

[0017] The initial range of α is 0°≤α<β. For every counterclockwise rotation of α by 2β, the original valve number is reduced by 1 to obtain the transformed valve number. If the valve number after subtraction is 0, it is changed to Num.

[0018] The general expression for the rotational symmetry rule is:

[0019] When 0°+2βn≤α<β+2βn, n=0,1,…,Num-1, the calculation steps for valve number ai are as follows:

[0020] ai = (i - n + Num) mod (Num);

[0021] If the valve number after subtracting ai is 0, then change the value of ai to Num;

[0022] Where i represents the valve number, i = 1, 2, ..., Num;

[0023] (2) Mirror symmetry + rotational symmetry rules;

[0024] The initial range of α is 0°≤α<β. When β≤α<2β, the original valve number and the transformed valve number are mirror-symmetric about the line 2×β. The transformed valve number is:

[0025]

[0026] Based on the numbering of β≤α<2β, α rotates 2β counterclockwise each time, and the transformed valve number is added by 1. If the value of ai after addition is Num+1, the value of ai is changed to 1;

[0027] The general expression of the mirror symmetry + rotation symmetry rule is:

[0028] When β+2βn≤α<2β+2βn, n=0,1,…,Num-1, the calculation formula of ai is:

[0029]

[0030] If the value of ai at this time is 0, the value of ai is updated to Num; i represents the valve number, i=1,2,…,Num;

[0031] Step S1.4: Calculate the single-valve thrust capacity and the relative two-valve thrust capacity;

[0032] Step S2: According to the vector thrust model of step S1, calculate the effective thrust mode of the system;

[0033] The effective thrust mode of the system includes zero thrust mode, adjacent 2-valve effective thrust mode and adjacent 3-valve effective thrust mode;

[0034] 1) Zero thrust F sum =0, there are many ways to achieve it, and the odd-numbered valve is selected to be fully open, and the even-numbered valve is fully closed, that is, the stroke L=0;

[0035] 2) When F sum ≠0, select the two valves adjacent to the direction of F sum from small to large, and provide effective thrust until the sum valves adjacent to the direction of F sum provide effective thrust, while meeting the constraint of constant pressure on total throat area.

[0036] Further, the step of calculating the single-valve thrust capacity is:

[0037] The combustion chamber pressure is a constant value p c , the single valve plug moves along the axial direction, and the corresponding nozzle throat area is A t when the stroke is L, and the thrust coefficient is C f , the thrust of a single valve F s is:

[0038] F s =p c ​A t C f ;

[0039] throat area A t The correspondence between the stroke L and the thrust coefficient C f is obtained through the profile design of the plug, the throat liner, or through flow field simulation or test, i.e. given the stroke L value, the throat area A t , the thrust coefficient C f and the thrust F s are all known quantities;

[0040] A t , C f , and F s are all monotonically increasing single-variable functions of L, given F s , the corresponding A t , C f and L are solved;

[0041] The value range of L is defined as [0, L max ];

[0042] When L = 0, the nozzle throat area takes the minimum value A t-min , the nozzle thrust coefficient takes the minimum value C f-min , and the thrust takes the minimum value F s-min ;

[0043] When L = L max , the nozzle throat area takes the maximum value A t-max , the nozzle thrust coefficient takes the maximum value C f-max , and the thrust takes the maximum value F s-max .

[0044] Further, the steps for calculating the relative two-valve thrust capacity are as follows:

[0045] Two valves on the same thrust line are called relative two-valves; the combined thrust of the relative two-valves is the difference between the thrust values of the two valves, and the direction of the combined thrust of the relative two-valves is the same as that of the valve with the largest thrust value among the two valves;

[0046] When the thrusts of the relative two-valves are the same, the combined thrust value is the smallest, which is 0;

[0047] When one of the relative two-valves outputs the maximum thrust F s-max and the other outputs the minimum thrust F s-min , the combined thrust value is the largest, which is defined as F max = F s-max - F s-min ;

[0048] In order to reduce the thrust loss, make Maximum, by the thrust formula F s = p c A t C f , in the valve structure design by the profile design makes Maximum;

[0049] Relative to the two valve thrust implementation [0, F max ] contains mode one and mode two.

[0050] Further, the mode one and mode two are:

[0051] Mode one: relative to one of the two valves thrust constant F s-min , the other valve thrust from F s-min To F s-max Change;

[0052] Mode two: relative to the two valve throat area and A t-min +A t-max Keep constant, when the two valve throat area is equal to 0, when the two valve throat area is A t-min , A t-max F max .

[0053] The beneficial effects of the present application are:

[0054] 1 the present application is proposed to realize the constant pressure combustion chamber need to the burning surface of the grain, the valve total throat area of the constraint condition, proposed at any time to realize the constant pressure combustion chamber valve total throat area calculation method;

[0055] 2 constant pressure combustion chamber can improve the play rate of engine structure material, reduce the engine structure mass, is beneficial to increase the effective payload of the aircraft, improve flight maneuverability;

[0056] 3 constant pressure combustion chamber, simplified each needle valve nozzle working condition, facilitate the corresponding thrust coefficient of the plug under different stroke; BRIEF DESCRIPTION OF DRAWINGS

[0057] Figure 1 For the needle valve nozzle structure schematic diagram;

[0058] Figure 2 For the needle valve nozzle structure schematic diagram;

[0059] Figure 3 For the eight valve numbering conversion schematic diagram;

[0060] Figure 4 For the flow chart;

[0061] In the figure, T1 is the gas outlet; T2 is the throat area changing with the action of the plug; T3 is the plug body; T4 is the gas inlet; and T5 is the thrust nozzle. DETAILED DESCRIPTION

[0062] A method for designing the interior ballistic of an eight-valve solid attitude control engine, comprising the following steps:

[0063] Step S1: establishing a vector thrust model;

[0064] The vector thrust model comprises a needle valve thrust model, constraint conditions of the needle valve thrust model, single-valve thrust capacity, relative two-valve thrust capacity, and eight-valve circumferential transformation rules;

[0065] Step S1.1: establishing an eight-needle valve thrust model;

[0066] The eight needle valve nozzles are uniformly distributed in the circumferential direction; the thrust lines are located in the same plane; and the valve numbers are 1, 2, 3, 4, 5, 6, 7, and 8;

[0067] Let the vector resultant thrust size be F sum , the included angle with the x-axis be α, and the components of the vector resultant thrust in the x and y axes be F sum-x and F sum-y , respectively, wherein F sum-x =F sum ·cosα, and F sum-y =F sum ·sinα; β is the minimum symmetry angle, β=360 / (8*2)=22.5 for eight valves; and 0°≤α<22.5°;

[0068] Step S1.2: determining the constraint conditions of the needle valve thrust model;

[0069] In order to realize constant combustion chamber pressure and continuous and accurate regulation of engine all-around thrust, the grain burning surface satisfies the constraint conditions during stable engine operation;

[0070] The engine pressure balance formula is:

[0071] p c is the combustion chamber pressure; after the selected propellant, the burning rate coefficient a, the propellant density ρ, the characteristic velocity C * , and the pressure exponent n are all known constants, the grain burning surface A b is a known array varying with the working time; in order to realize constant combustion chamber pressure p c , the burning surface A b and the total throat area A t-tot satisfy the conditions:

[0072]

[0073] The thrust distribution and calculation method requires the grain design to make the burning area A b Satisfy the following constraint conditions:

[0074]

[0075] Definition A t-3-5 The total throat area corresponding to the maximum opening of 3 valves and the minimum opening of 5 valves, that is, A t-3-5 = 3A t-max + 5A t-min ;

[0076] Definition A t-4-4 The total throat area corresponding to the maximum opening of 4 valves and the minimum opening of 4 valves, that is, A t-4-4 = 4A t-max + 4A t-min ;

[0077] Step S1.3: Calculate the single-valve thrust capacity and the relative two-valve thrust capacity;

[0078] According to the vector thrust model and the constraint conditions of the grain burning area, the single-valve thrust capacity and the relative two-valve thrust capacity are calculated as:

[0079] The steps for calculating the single-valve thrust capacity are:

[0080] The combustion chamber pressure is a constant value p c , the single valve plug moves along the axial direction, and the corresponding nozzle throat area is A t when the stroke is L, the thrust coefficient is C f , and the thrust of a single valve F s is:

[0081] F s = p c A t C f ;

[0082] The corresponding relationship between the throat area A t and the stroke L is obtained through the profile design of the plug and the throat liner; the corresponding relationship between the thrust coefficient C f and the stroke L is obtained through flow field simulation or test, that is, given the stroke L value, the throat area A t , the thrust coefficient C f and the thrust F s are all known quantities;

[0083] A t , C f , and F s are all monotonic increasing single-variable functions of L, and F sThe corresponding A can be solved. t C f and L;

[0084] The range of values ​​for L is defined as [0, L]. max ];

[0085] When L = 0, the nozzle throat area reaches its minimum value A. t-min The thrust coefficient of the nozzle reaches its minimum value C. f-min The thrust reaches its minimum value F s-min ;

[0086] When L = L max At that time, the nozzle throat area reaches its maximum value A. t-max The thrust coefficient of the nozzle reaches its maximum value C. f-max The thrust reaches its maximum value F s-max ;

[0087] The steps to calculate the relative thrust capacity of the two valves are as follows:

[0088] Two valves on the same thrust line are called opposite valves, for example Figure 2 Valve 1 and valve 5, valve 2 and valve 6, valve 3 and valve 7 are two opposing valves;

[0089] The combined thrust of two valves is the difference between their thrust values, and the direction of the combined thrust of the two valves is the same as the direction of the valve with the largest thrust value.

[0090] When the thrust of the two valves is the same, the combined thrust is the minimum, which is 0.

[0091] When one of the two valves outputs the maximum thrust F s-max The other valve outputs minimum thrust F s-min At this time, the combined thrust is at its maximum, defined as F. max =F s-max -F s-min ;

[0092] To reduce thrust loss, it should be made Maximum, according to the thrust formula F s =p c A t C f In valve structural design, the surface design is used to make... maximum;

[0093] The combined thrust of the two valves achieves [0, F] max Includes Mode 1 and Mode 2:

[0094] Mode 1: The thrust of one of the two valves is always F. s-min Another valve thrust can be generated from Fs-min to F s-max changes;

[0095] Mode two: relative throat area of two valves and A t-min +A t-max is constant, the combined thrust is 0 when the throat areas of the two valves are equal, and the combined thrust is F t-min , A t-max when the throat areas of the two valves are A max ;

[0096] Step S1.4: Eight-valve circumferential transformation rule:

[0097] Because the eight valves are evenly distributed circumferentially, there is a symmetry rule, and the direction of the vector combined thrust is extended from 0°≤α<22.5° to 0°≤α<360° through the transformation rule;

[0098] The transformation rule is:

[0099] The vector combined thrust may be in any direction in the real situation, and the value range of α is 0°≤α<360°. The original valve numbers are a1, a2, a3, a4, a5, a6, a7, and a8, respectively. In particular, when 0°≤α<22.5°, the valve numbers are 1, 2, 3, 4, 5, 6, 7, and 8. The purpose of transformation is to determine the corresponding relationship between valve numbers 1-8 and original valve changes a1-a8.

[0100] For the coordinate system shown in FIG. Figure 3 , because the eight valves are evenly distributed circumferentially, there is a symmetry rule, and the direction of the vector combined thrust can be transformed from 0°≤α<22.5° to 0°≤α<360° through transformation. In order to avoid confusion of valve numbers, it is assumed that the original valve numbers are a1, a2, a3, a4, a5, a6, a7, and a8, and the transformed valve numbers are 1, 2, 3, 4, 5, 6, 7, and 8. The transformation rule is as follows:

[0101] (1) Rotational symmetry rule;

[0102] Observe Figure 3 , the initial range of α is 0°≤α<22.5°, and the original valve number is reduced by 1 every 45° counterclockwise rotation to obtain the transformed valve number. If the number after subtraction is 0, it is changed to 8.

[0103] The general expression of the rotational symmetry rule is:

[0104] When 0°+45°×n≤α<22.5°+45°×n, n=0,1,…,7, ai=(i-n+8)mod8;

[0105] if ai=0,ai=8, where i represents the valve number, i=1,2,…,8;

[0106] (2) Mirror symmetry + rotational symmetry rule;

[0107] Observation Figure 3 The initial range of α is 0°≤α<22.5°, when 22.5°≤α<45°, the original valve number and the transformed valve number are mirror symmetric about the 45° straight line, and the transformed valve number is:

[0108]

[0109] Based on the number of 22.5°≤α<45°, α rotates 45° counterclockwise, and the transformed valve number is increased by 1. If the added number is 9, it is changed to 1;

[0110] The general expression of the mirror symmetry + rotational symmetry rule is:

[0111] When 22.5°+45°×n≤α<45°+45°×n, n=0,1,…,7:

[0112]

[0113] if ai=0,ai=8;

[0114] i represents the valve number, i=1,2,…,8;

[0115] Step S2: According to the vector thrust model of step S1, the effective thrust mode of the system is solved;

[0116] Because the transformation from 0°≤α<22.5° to 0°≤α<360° only needs to change the valve number, when calculating the valve thrust, only the case of 0°≤α<22.5° can be calculated;

[0117] The effective thrust mode of the system includes zero thrust mode, single valve effective thrust mode, adjacent 2-valve effective thrust mode, and adjacent 3-valve effective thrust mode;

[0118] Step S2.1: Zero thrust mode:

[0119] When the vector resultant thrust of the eight valves is zero, it is a zero thrust mode. There are many ways to realize F sum =0, here only one of the logic simple and easy to realize method is selected: valves 1, 3, 5, 7 are open, and valves 2, 4, 6, 8 are closed, i.e. the stroke L=0, all the following "valves are closed" means the stroke L=0;

[0120] By adjusting the total throat area A t-tot , the pressure is kept constant;

[0121] The throat area of each valve is:

[0122]

[0123] Single-valve effective thrust mode:

[0124] When α = 0°, 0 < F sum ≤ F max , the effective thrust provided by valve 1 can be achieved; the effective thrust of valve 1 is distributed in mode one, that is:

[0125] F s1 = F sum + F s-min , the throat area corresponding to valve 1 at this time can be solved as A t1 ;

[0126] F s5 = F s-min , the throat area corresponding to valve 5 at this time is A t-min .

[0127] In order to realize the constant pressure of the combustion chamber, valves 3 and 7 are selected to be closed, and valves 2, 4, 6 and 8 are adjusted by equal opening to make the total throat area adjustable in the range of A t-3-5 < A t-tot < A t-4-4 , and the specific total throat area value is determined according to the instantaneous combustion surface;

[0128] In summary, the throat area of each valve is:

[0129]

[0130] Step S2.2: Effective thrust mode of adjacent 2 valves;

[0131] When 0° < α < 22.5°, the two valves with the smallest angle with the resultant thrust vector, that is, valves 1 and 2, provide effective thrust, and the resultant thrust at this time is:

[0132] F sum = F1·cosα + F2·cos(45°-α)

[0133] The constraint should be satisfied:

[0134]

[0135] It can be solved that:

[0136]

[0137] It is noted that when α = 0°, F1 = F sum in the above formula, F2 = 0, which can include the case of single-valve providing effective thrust;

[0138] Define the maximum value of effective thrust F that can be taken by the adjacent 2 valves sum The maximum value that can be taken is F sum-2max At this time:

[0139]

[0140] In summary, when 0°≤α<22.5°, ,

[0141]

[0142] The effective thrust of the valves 1, 2 is realized in mode 1, in order to realize the constant pressure of the combustion chamber, the total throat area can be adjusted in the range of A t-3-5 A t-tot A t-4-4 The specific total throat area value is determined according to the instantaneous combustion surface; the thrust and throat area of each valve are:

[0143]

[0144] Step S2.3: Effective thrust mode of adjacent 3 valves

[0145] When 0°<α<22.5°, F sum >F sum-2max , the effective thrust provided by only valves 1, 2 cannot be realized, and the effective thrust needs to be provided by the three valves with the smallest angle between the vector resultant thrust, i.e. valves 1, 2, 8, and the resultant thrust is:

[0146] F sum =F1·cosα+F2·cos(45°-α)+F8·cos(45°+α)

[0147] The constraint should be satisfied:

[0148]

[0149] The solution is:

[0150]

[0151] Note that when α=0°, F1=F max in the above formula, The solution method is still correct, so the above formula can be extended to the case where α=0°.

[0152] Define the maximum value of effective thrust F that can be taken by the adjacent 3 valves sum-3max At this time:

[0153]

[0154] In summary, when 0°≤α<22.5°,

[0155]

[0156] In order to keep the pressure constant in the combustion chamber, the total throat area should be adjusted in the range of A t-3-5 <A t-tot <A t-4-4 The effective thrust of the valves 2, 8 is realized by mode two, and the throat area of the valves 1, 5, 2, 6, 4, 8 is 3(A t-min +A t-max ), and the equal opening valves 3, 7 can meet the constraint of A t-3-5 <A t-tot <A t-4-4 The thrust and throat area of each valve are as follows:

[0157] Step S2.4: Summary of the effective thrust calculation method;

[0158] Summarize the calculation methods of S2.1-S2.3,

[0159] In the case of 0°≤α<22.5°, according to the size of the resultant thrust F sum , it can be divided into three calculation methods:

[0160] Case one: F sum =0

[0161] At this time, the valves 1, 3, 5, 7 are open, and the valves 2, 4, 6, 8 are closed (i.e. the stroke L=0)

[0162] The throat area of each valve is:

[0163]

[0164] Case two:

[0165] At this time, the valves 1, 2 provide effective thrust, and the valves 3, 4, 7, 8 are closed-loop pressure regulating. The thrust of each valve is:

[0166] The throat area of each valve is:

[0167]

[0168] Case three:

[0169] ​At this time, the valves 1, 2 and 8 provide effective thrust, and the valves 3 and 7 are closed-loop pressure regulating. The thrust of each valve is:

[0170]

[0171] For the stroke L of each valve, the stroke L and the throat area A t of each valve are calculated according to the corresponding relationship, and L is solved after the throat area A ti of each valve is calculated.

[0172] 1 The present application proposes the constraint conditions of the burning surface of the grain and the total throat area of the valve for realizing the constant pressure of the combustion chamber, and proposes the calculation method of the total throat area of the valve for realizing the constant pressure of the combustion chamber at any time.

[0173] 2 The constant pressure of the combustion chamber can improve the play rate of the structural material of the engine, reduce the structural mass of the engine, and is beneficial to increase the effective load of the aircraft and improve the flight maneuverability.

[0174] 3 The constant pressure of the combustion chamber simplifies the working conditions of each needle valve nozzle, and facilitates the corresponding thrust coefficient of the plug at different strokes.

[0175]

[0176] The present application is further described below in combination with the drawings and embodiments.

[0177] The present application proposes a method for realizing the constant pressure of the combustion chamber during the stable operation of the engine and the full-range and continuous adjustable thrust. The stable operation of the engine refers to the removal of the rising section and the falling section in the pressure-time curve of the engine.

[0178] The schematic diagram of the typical needle valve nozzle structure is shown in Figure 1 Eight needle valve nozzles are uniformly distributed along the circumference, and the thrust line is located in the same plane, and the schematic diagram is shown in Figure 2 .

[0179] The realization method of the constant pressure of the combustion chamber is as follows: firstly, the burning surface A b of the grain and the total throat area A t-tot are designed to meet certain constraint conditions, and secondly, the total throat area A t-tot is calculated at each time during the stable operation, so that

[0180] According to the total thrust F sum and the angle α output by the overall requirements of the aircraft, the thrust distribution and solving method of each valve nozzle is as follows: under the premise that the total throat area A t-tot meets the constant pressure condition of the combustion chamber, firstly, the total thrust angle 0°≤α<360° is converted to the range of 0°≤α<22.5°, and then according to Fsum The thrust is divided into four cases: zero thrust mode, single valve providing effective thrust, two adjacent valves providing effective thrust, and three adjacent valves providing effective thrust. The valves are allocated and the thrust is calculated accordingly.

[0181] The constraints on the combustion surface and total throat area of ​​the propellant are as follows:

[0182] To achieve constant combustion chamber pressure and continuous, precise adjustment of engine thrust across all directions, the combustion surface of the propellant grain must meet certain constraints during stable engine operation. The engine pressure balance formula is as follows: After selecting the propellant, the burning rate coefficient a, propellant density ρ, and characteristic velocity C are... * The pressure exponent n is a known constant, and the burning surface A of the propellant column is... b It is a known array that changes with operating time, in order to achieve the combustion chamber pressure p c As a constant value, the burning surface A b and total throat area A t-tot Must meet The thrust distribution and calculation method involved in this invention requires the rational design of the propellant type to maximize the thrust distribution of the combustion surface A. b The following constraints must be met:

[0183]

[0184] Define A t-3-5 Let A be the total throat area corresponding to the maximum opening of 3 valves and the minimum opening of 5 valves. t-3-5 =3A t-max +5A t-min ;

[0185] Define A t-4-4 Let A be the total throat area corresponding to the four valves being at their maximum opening and the four valves being at their minimum opening. t-4-4 =4A t-max +4A t-min .

[0186] Under the condition that the combustion surface meets the above constraints, the pressure p must be maintained during engine operation. c To maintain a constant value, the total throat area A of the 8 valves needs to be adjusted. t-tot Adjustments are made. All the thrust distribution and calculation methods below satisfy the total throat area. In A t-3-5 t-tot t-4-4 Adjustable within a certain range.

[0187] Valve numbering change method:

[0188] for Figure 3 In the coordinate system shown, let the magnitude of the vector resultant thrust be F. sum ​​The angle between the vector thrust and the x-axis is α, where 0° ≤ α < 22.5°. The components of the vector thrust along the x and y axes are F and F, respectively. sum-x F sum-y (F sum-x =F sum ·cosα,F sum-y =F sum ·sinα).

[0189] Because the circumferential distribution of the eight valves exhibits symmetry, the vector resultant thrust direction (0°≤α<22.5°) can be extended to 0°≤α<360° through transformation. To avoid confusion in valve numbering, assume the original valve numbers are a1, a2, a3, a4, a5, a6, a7, and a8, and the transformed valve numbers are 1, 2, 3, 4, 5, 6, 7, and 8. The transformation rules are as follows:

[0190] (1) Rotational symmetry rule:

[0191] observe Figure 3 The initial range of α is 0° ≤ α < 22.5°. For every 45° counterclockwise rotation of α, the original valve number is subtracted by 1 to obtain the transformed valve number. If the subtraction result is 0, it is changed to 8. This can be expressed as a general expression:

[0192] When 0°+45°×n≤α<22.5°+45°×n, n=0,1,…,7:

[0193] ai = (i - n + 8) mod 8

[0194] if ai = 0, ai = 8

[0195] i represents the valve number, i = 1, 2, ..., 8

[0196] (2) Mirror symmetry + rotational symmetry rules:

[0197] observe Figure 3 The initial range of α is 0°≤α<22.5°. When 22.5°≤α<45°, the original valve number and the transformed valve number are mirror-symmetric about the 45° line. The transformed valve number is:

[0198]

[0199] Based on the numbering rule of 22.5° ≤ α < 45°, for every 45° counterclockwise rotation of α, the valve number is incremented by 1. If the resulting number is 9, it is changed to 1. This can be expressed as a general expression:

[0200] When 22.5°+45°×n≤α<45°+45°×n, n=0,1,…,7:

[0201]

[0202] if ai=0,ai=8i represents the valve number, i = 1, 2, …, 8

[0203]

[0204]

[0205] Valve thrust solving method:

[0206] The method of extending the vector resultant thrust direction 0°≤α<22.5° to 0°≤α<360° has been given in the foregoing, so only the thrust of the case needs to be solved. Figure 3

[0207] First, the single-valve thrust capacity and the relative two-valve thrust mode are defined, and then the thrust solving method of each valve is given according to the vector resultant thrust from small to large.

[0208] Single-valve thrust capacity:

[0209] The combustion chamber pressure is a constant value p c , the single valve plug moves along the axial direction, and the corresponding nozzle throat area is A t when the stroke is L, the thrust coefficient is C f , and the single valve thrust is F s =p c A t C f . The corresponding relationship between the throat area A t and the stroke L can be known through the profile design of the plug and the throat liner; the corresponding relationship between the thrust coefficient C f and the stroke L can be obtained through flow field simulation or test, that is, given the stroke L value, the throat area A t , the thrust coefficient C f and the thrust F s are all known quantities. It is easy to know that A t , C f , and F s are all monotonic increasing single variable functions of L, and given F s , A t , C f and L can be easily solved.

[0210] The range of defined L values is [0, L max ]. When L = 0, the nozzle throat area takes the minimum value A t-min , the thrust coefficient of the nozzle takes the minimum value C f-min , and the thrust takes the minimum value F s-min ; L = L max ​The throat area of the time jet pipe is taken to the maximum value A t-max , the thrust coefficient of the jet pipe is taken to the maximum value C f-max , and the thrust is taken to the maximum value F s-max .

[0211] Relative two-valve thrust mode:

[0212] Two valves on the same thrust line are called relative two-valves, for example Figure 2 valve 1 and valve 5, valve 2 and valve 6, valve 3 and valve 7, etc. are relative two-valves. Obviously, the combined thrust of relative two-valves is the difference between the thrust values of the two valves, and the direction is the same as the larger one. When the relative two-valve thrust is the same, the combined thrust value is the smallest, which is 0, and when one of the relative two-valve outputs the maximum thrust F s-max , and the other valve outputs the minimum thrust F s-min , the combined thrust value is the largest, defined as F max = F s-max -F s-min . In order to reduce the thrust loss, F should be as large as possible, and according to the thrust formula F s =p c A t C f , F should be as large as possible in the valve structure design by careful profile design.

[0213] In the present application, there are two modes for the combined thrust of relative two-valves to achieve [0, F max ]:

[0214] Mode one: the thrust of one of the relative two-valves is constant F s-min , and the thrust of the other valve can vary from F s-min to F s-max ;

[0215] Mode two: the throat areas of the relative two-valves are constant A t-min +A t-max , and when the throat areas of the two valves are equal, the combined thrust is 0, and when the throat areas of the two valves are A t-min and A t-max , the combined thrust is F max .

[0216] Valve thrust solving formula summary:

[0217] In the case of 0°≤α<22.5°, according to the size of the combined thrust F sum , there are three solving methods:

[0218] Case one: F sum = 0

[0219] At this time, valves 1, 3, 5, 7 are open, and valves 2, 4, 6, 8 are closed (i.e. stroke L = 0)

[0220] The throat area of each valve is:

[0221]

[0222] Case II:

[0223] At this time, valves 1, 2 provide effective thrust, and valves 3, 4, 7, 8 are closed-loop pressure regulating. The thrust of each valve is:

[0224]

[0225] The throat area of each valve is:

[0226]

[0227] Case III:

[0228] At this time, valves 1, 2, 8 provide effective thrust, and valves 3, 7 are closed-loop pressure regulating. The thrust of each valve is:

[0229]

[0230] For the stroke L of each valve, the corresponding relationship between the stroke L and the throat area A t is known, and the throat area A ti of each valve is calculated, and then L can be easily solved.

[0231] Valve thrust calculation formula derivation:

[0232] Zero thrust mode:

[0233] There are many ways to achieve F sum = 0 thrust mode, here only one method is selected: valves 1, 3, 5, 7 are open, and valves 2, 4, 6, 8 are closed (i.e. stroke L = 0, all "valves closed" below refers to stroke L = 0).

[0234] By adjusting the total throat area A t-tot corresponding to the opening of valves 1, 3, 5, 7, the pressure is kept constant.

[0235] The throat area of each valve is:

[0236]

[0237] Single valve provides effective thrust:

[0238] When α = 0°, 0 < F sum ≤ Fmax The effective thrust provided by valve 1 can be realized at this time. The effective thrust of valve 1 is distributed in mode 1, that is:

[0239] F s1 = F sum + F s-min The throat area corresponding to valve 1 at this time can be solved as A t1 ;

[0240] F s5 = F s-min The throat area corresponding to valve 5 at this time is A t-min .

[0241] In order to realize the constant pressure of the combustion chamber, valves 3 and 7 are selected to be closed, and valves 2, 4, 6 and 8 are adjusted by equal opening to make the total throat area adjustable in the range of A t-3-5 <A t-tot <A t-4-4 , and the specific total throat area value is determined according to the instantaneous combustion surface.

[0242] In summary, the throat areas of the valves are:

[0243]

[0244] The effective thrust provided by adjacent 2 valves is:

[0245] When 0° < α < 22.5°, only valves 1 and 2 provide effective thrust, and the combined thrust at this time is:

[0246] F sum = F1·cosα+F2·cos(45°-α)

[0247] The constraint should be satisfied:

[0248]

[0249] It can be solved that:

[0250]

[0251] It is noted that when α = 0°, F1 = F sum in the above formula, F2 = 0, which can include the case of single valve providing effective thrust.

[0252] Define the maximum value of the effective thrust F sum provided by adjacent 2 valves as F sum-2max , then at this time:

[0253]

[0254] In summary, when 0° ≤ α < 22.5°, hour,

[0255]

[0256] The effective thrust of valves 1 and 2 is achieved using mode one. To maintain constant combustion chamber pressure, valves 3, 4, 7, and 8 are used to ensure that the total throat area can be within the range of A. t-3-5 t-tot t-4-4 The adjustment range is determined based on the transient combustion surface, with the specific total throat area value set accordingly. The thrust and throat area of ​​each valve are as follows:

[0257]

[0258] Three adjacent valves provide effective thrust:

[0259] When 0° < α < 22.5°, F sum >F sum-2max At this point, effective thrust cannot be achieved solely through valves 1 and 2; effective thrust must be provided through valves 1, 2, and 8. The combined thrust is:

[0260] F sum =F1·cosα+F2·cos(45°-α)+F8·cos(45°+α)

[0261] Constraints must be met:

[0262]

[0263] The solution is:

[0264]

[0265] Note that when α = 0°, F1 = F in the above equation. max , The solution method is still correct, so the above formula can be extended to the case where α = 0°.

[0266] The maximum effective thrust that can be achieved by three adjacent valves is defined as F. sum-3max Then at this time:

[0267]

[0268] In summary, when 0° ≤ α < 22.5°, hour:

[0269]

[0270] To achieve constant combustion chamber pressure, the total throat area needs to be within A... t-3-5 t-tot t-4-4 ​​​​The range is adjusted. The effective thrust of the valve 2, 8 is realized by mode two, the throat area of the valve 1, 5, 2, 6, 4, 8 is 3 (A t-min +A t-max ), and the equal opening valve 3, 7 can meet the constraint of A t-3-5 <A t-tot <A t-4-4 The thrust and throat area of each valve are:

[0271]

[0272] The calculation process is:

[0273] The calculation process is Figure 4 .

[0274] Generalization:

[0275] The thrust distribution and solving method of the application can be extended to the case of 6 valves, 10 valves or more even number of valves. The main idea is still to realize the constant pressure of the engine working pressure through the constraint conditions of the grain burning surface and the total throat area, to transform the valve number through the rules of rotational symmetry and mirror symmetry, and to obtain the valve thrust solving formula through the derivation of the zero thrust mode, single valve providing effective thrust, adjacent 2 valves providing effective thrust and other cases.

[0276] For example, for the case of 6 valves, through reasonable grain design, the burning surface A b satisfies the following constraint conditions:

[0277]

[0278] According to the symmetry of 6 valves, only 1 / 12 of the vector combined thrust angle α, i.e. 0°≤α<30°, can be analyzed, and then the method of similar rotational symmetry and mirror symmetry+rotational symmetry is extended to the case of 0°≤α<360°.

[0279] The valve thrust solving formula is obtained by sequentially deriving the zero thrust mode, single valve providing effective thrust, adjacent 2 valves providing effective thrust.

[0280] The method described in the application can be extended to the case of 10 valves or more even number of valves, and the analysis method is the same.

[0281] Advantages:

[0282] 1. The application proposes the constraint conditions of the grain burning surface and the total throat area of the valve to realize the constant pressure of the combustion chamber, and proposes a valve total throat area calculation method to realize the constant pressure of the combustion chamber at any time.

[0283] 2 The constant pressure of combustion chamber can improve the performance of engine structure material, reduce the engine structure mass, and is beneficial to increase the effective load of the aircraft and improve the flight maneuverability.

[0284] 3 The constant pressure of combustion chamber simplifies the working condition of each needle valve nozzle, and facilitates the obtaining of the corresponding thrust coefficient of the nozzle plug at different strokes.

[0285] In the steady one-dimensional isentropic flow state of the nozzle, without considering the flow loss in the nozzle and the chemical reaction of the gas, the thrust coefficient formula of the nozzle is:

[0286]

[0287] According to the above formula, when the propellant is selected, the adiabatic index k and the coefficient Γ are both constants, and the main influencing factors of the thrust coefficient of the nozzle are the pressure ratio of the combustion chamber to the outlet environment and the area ratio of the nozzle outlet area to the throat area.

[0288] For the needle valve nozzle, the thrust coefficient is related to the pressure ratio, the area ratio and the flow state of the gas in the nozzle. When the throat plug actuation causes the throat area to be too small, and the area ratio of the nozzle outlet to the throat is too large, the shock wave will appear in the expansion section, which directly affects the pressure distribution of the inner wall of the nozzle, and further affects the thrust and the thrust coefficient. When the combustion chamber pressure is not constant, and the throat area changes due to the needle actuation, the change process of the engine thrust and the thrust coefficient will be very complex, which brings great challenges to the engine design. When the combustion chamber pressure is constant, and the needle actuation reaches a certain position, the throat area and the flow state of the gas in the nozzle are both determined, that is, the thrust coefficient is determined by only one variable, the needle position, and the corresponding thrust and thrust coefficient of the nozzle plug actuation to different positions can be easily obtained. In this way, the engine design process is greatly simplified.

[0289] 4 The engine full-range thrust continuous and accurate adjustment is realized. According to the symmetry of the eight valves uniformly distributed in the circumferential direction, the full-range thrust analysis of the engine in the range of 0°≤α<360° is converted into the analysis in the range of 0°≤α<22.5°, and then according to the total thrust size required by the overall aircraft, the four cases of zero thrust mode, single valve providing effective thrust, adjacent 2 valves providing effective thrust and adjacent 3 valves providing effective thrust are divided to allocate the valves and calculate the thrust, so as to obtain the thrust, throat area and plug stroke of each valve nozzle. The engine servo control system design is greatly simplified, and the accuracy of the engine output thrust is provided.

[0290] Nomenclature:

[0291] p c Combustion chamber pressure

[0292] a - Propellant burning rate coefficient

[0293] ρ — propellant density;

[0294] C* — Characteristic velocity;

[0295] n—Propellant pressure index;

[0296] A b —The powder column is burning;

[0297] A t (or A) ti — The throat area of ​​a single valve, where the subscript i represents the valve number, i = 1, 2, ... 8;

[0298] A t-min —Minimum throat area for a single valve;

[0299] A t-max —Maximum throat area of ​​a single valve;

[0300] A t-tot —Total throat area of ​​8 valves;

[0301] A t-3-5 —The total throat area corresponding to 3 valves at maximum opening and 5 valves at minimum opening;

[0302] A t-4-4 —The total throat area corresponding to the 4 valves being opened to their maximum and the 4 valves being opened to their minimum;

[0303] L (or L) i — The stroke of a single valve, where the subscript i represents the valve number, i = 1, 2, ... 8;

[0304] L max —Maximum stroke of a single valve;

[0305] F sum —The overall flight requirements require the combined thrust provided by the engine;

[0306] α — Rotate counterclockwise from the positive x-axis to the position opposite to F sum The minimum angle in the same direction, 0°≤α<360°;

[0307] F sum-x ——F sum Components on the x-axis;

[0308] F sum-y ——F sum Components on the y-axis;

[0309] F s (or F) si — The thrust output of a single valve, where the subscript i represents the valve number, i = 1, 2, ... 8;

[0310] F s-min - the minimum thrust output of a single valve;

[0311] F s-max - the maximum thrust output of a single valve;

[0312] F i - the effective thrust of a single valve, subscript i represents the valve number, i = 1, 2, …, 8. The effective thrust of the ith valve is defined as the difference between the thrust of the valve and the thrust of another valve on the same thrust line, for example, Fi = F s1 F s5 , F2 = F s2 F s6 ;

[0313] F max - the maximum effective thrust of a single valve, F max = F s-max F s-min ;

[0314] F sum-2max - the maximum combined thrust that can be achieved by the effective thrust of two adjacent valves;

[0315] F sum-3max - the maximum combined thrust that can be achieved by the effective thrust of three adjacent valves;

[0316] C f - the single valve thrust coefficient;

[0317] C f-min - the minimum single valve thrust coefficient;

[0318] C f-max - the maximum single valve thrust coefficient.

Claims

1. A method for designing the internal ballistics of an eight-valve solid rocket motor, characterized in that, Includes the following steps: Step S1: Establish a vector thrust model; The vector thrust model includes a needle valve model, constraints, single valve thrust capacity, relative two-valve thrust capacity, and multi-valve circumferential transformation rules. Step S1.1: Establish a needle-type valve model; Needle-type valve models include A needle-type valve nozzle The needle-type valve nozzles are symmetrically and evenly distributed circumferentially. ,and The number is even; the thrust lines of the needle-type valve nozzle lie in the same plane; For the first One valve, among which ; Let the magnitude of the vector resultant thrust be F. sum The angle between the vector resultant thrust and the x-axis is The components of the vector resultant thrust along the x and y axes are F and F, respectively. sum-x and F sum-y ,in , ; It is the smallest symmetric angle. ; Step S1.2: Determine the constraints; The constraints are: To maintain a constant pressure in the combustion chamber, the combustion surface... and total throat area satisfy ; Indicates a constant value; The constraints that the combustion surface of the propellant grain must satisfy during stable engine operation are: combustion surface and total throat area Must meet In the formula p represents the total throat area corresponding to the maximum opening of valve i and the minimum opening of valve j; c ρ is the combustion chamber pressure; a is the burning rate coefficient; ρ is the propellant density; C * The characteristic velocity is n, and the pressure exponent is n. Step S1.3: Multi-valve circumferential transformation rules; Because multiple valves are evenly distributed along the circumference and exhibit a symmetrical pattern, the direction of the vector resultant thrust is extended to 360 degrees through the circumferential transformation rule of multiple valves. Step S1.4: Calculate the thrust capacity of a single valve and the relative thrust capacity of two valves; Step S2: Based on the vector thrust model in Step S1, calculate the effective thrust mode of the system; The system's effective thrust modes include zero thrust mode, effective thrust mode with two adjacent valves, and effective thrust mode with three adjacent valves. 1) Zero thrust There are multiple ways to achieve this, such as using the method of opening odd-numbered valves and closing even-numbered valves, i.e., stroke L=0; 2) When At that time, with F sum Choose from small to large with F sum Two valves in adjacent directions provide effective thrust until they are in contact with F. sum Adjacent directions Each valve provides effective thrust while satisfying the constraint of constant pressure on the total throat area.

2. The internal ballistic design method for an eight-valve solid rocket motor according to claim 1, characterized in that, The steps for calculating the thrust capacity of a single valve are as follows: The combustion chamber pressure is a constant value p c When the throat plug of a single valve moves axially, the nozzle throat area corresponding to its stroke of L is A. t The thrust coefficient is C f The thrust of a single valve for: ； Laryngeal area A t The correspondence with the stroke L is obtained through the surface design of the laryngeal plug and laryngeal liner; thrust coefficient C f The correspondence between the stroke L and the throat area A is obtained through flow field simulation or experimental testing; that is, given a stroke L value, the throat area A is... t Thrust coefficient C f and thrust All are known quantities; A t C f ,and Both are monotonically increasing single-variable functions of L, given Solve for the corresponding A t C f and L; The range of values ​​for L is defined as [0, L]. max ]; When L=0, the nozzle throat area reaches its minimum value A. t-min The thrust coefficient of the nozzle reaches its minimum value C. f-min The thrust reaches its minimum value F s-min ; When L = L max At that time, the nozzle throat area reaches its maximum value A. t-max The thrust coefficient of the nozzle reaches its maximum value C. f-max The thrust reaches its maximum value F s-max .

3. The internal ballistic design method for an eight-valve solid rocket motor according to claim 1, characterized in that, The steps to calculate the relative thrust capacity of the two valves are as follows: Two valves on the same thrust line are called two opposing valves; the resultant thrust of two opposing valves is the difference between their thrust values, and the direction of the resultant thrust of two opposing valves is the same as the direction of the valve with the largest thrust value. When the thrust of the two valves is the same, the combined thrust is the minimum, which is 0. When one of the two valves outputs maximum thrust The other valve outputs minimum thrust. At this time, the combined thrust is at its maximum, defined as follows: ; To reduce thrust loss, Maximum, according to the thrust formula In valve structural design, the surface design is used to make... maximum; The combined thrust of the two valves achieves [0, F] max It includes Mode 1 and Mode 2.

4. The internal ballistic design method for an eight-valve solid rocket motor according to claim 3, characterized in that, The first and second modes are as follows: Mode 1 is when the thrust of one of the two valves is constant. Another valve thrust from arrive change; Mode 2 is the throat area of ​​the two valves and A. t-min +A t-max Keeping the thrust constant, the net thrust is 0 when the throat areas of the two valves are equal, and 0 when the throat areas of the two valves are respectively A t-min A t-max The combined thrust is F max .

5. The internal ballistic design method for an eight-valve solid rocket motor according to claim 1, characterized in that, The multi-valve circumferential transformation rule is as follows: (1) Rotational symmetry rule; The initial range of α is α rotates counterclockwise 2 times The original valve number is subtracted by 1 to obtain the transformed valve number. If the valve number after subtraction is 0, it is changed to... ; The general expression for the rotational symmetry rule is: when hour, =0,1,…, -1, valve number The calculation steps are as follows: ； If at this time If the valve number after subtraction is 0, then... The value changed ; Where i represents the valve number, i=1,2,… ; (2) Mirror symmetry + rotational symmetry rules; The initial range of α is ,when At that time, the original valve number and the transformed valve number were related to The valves are numbered according to the linear mirror symmetry. ； based on The numbering, α rotates 2 times counterclockwise. The valve number after the change is incremented by 1. If the sum is... value +1, then Change the value to 1; The general expression for the rules of mirror symmetry and rotational symmetry is: when , =0,1,…, At -1, The calculation formula is: ； If at this time If the value is 0, then... The value is updated to ; i represents the valve number, i=1,2,…, .

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