Design method for inner trajectory of eight-valve solid attitude control engine

Abstract

The invention provides a design method for an inner trajectory of an eight-valve solid attitude control engine, and provides effective guidance for the design method for the inner trajectory of the eight-valve solid attitude control engine. According to the thought of the method, constant working pressure of an engine is achieved through constraint conditions of a grain combustion surface and a total throat area, valve numbers are converted through rotational symmetry and mirror symmetry rules, and a valve thrust resolving formula is obtained by sequentially deducing conditions of a zero thrust mode, effective thrust provided by a single valve, effective thrust provided by two adjacent valves and the like; under the condition that the pressure intensity of a combustion chamber is constant, the working condition of each pintle type valve spray pipe is simplified, the efficiency of obtaining corresponding thrust coefficients of the pintle under different strokes is improved, and the valve total throat area calculation method for achieving the constant pressure intensity of the combustion chamber at any time is achieved.

Description

Technical Field

[0001] The invention relates to the field of variable thrust solid rocket engines, and in particular to an interior ballistic design method. Background Art

[0002] The core task of solid rocket engine design is to determine the engine's internal ballistic performance, that is, the engine's pressure and thrust curves. For conventional solid rocket engines with a fixed throat diameter, the pressure and thrust curves are determined after the design is completed. For solid attitude control engines using eight pintle valve nozzles, there are great differences in the internal ballistic design methods. During the stable operation of the engine, by adjusting the throat area of ​​each pintle valve nozzle, the size and direction of the combustion chamber pressure and the engine's combined thrust can be varied over a wide range. At present, there is a lack of internal ballistic design methods for eight-valve solid attitude control engines, which hinders the engineering application of eight-valve solid attitude control engines. Therefore, it is urgent to propose a simple and reliable internal ballistic design method for eight-valve solid attitude control engines. Summary of the invention

[0003] In order to overcome the deficiencies of the prior art and provide effective guidance for the design method of the internal ballistics of an eight-valve solid attitude control engine, the present invention provides a design method of the internal ballistics of an eight-valve solid attitude control engine.

[0004] A method for designing interior ballistics of an eight-valve solid attitude control engine comprises the following steps:

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

[0006] The vector thrust model includes the pintle valve model, constraints, single valve thrust capacity, relative two-valve thrust capacity and multi-valve circumferential transformation rules;

[0007] Step S1.1: Establishing a pintle valve model;

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

[0009] The magnitude of the vector force is F sum , the angle between the vector force and the x-axis is α, and the components of the vector force on the x-axis and y-axis are F sum-x 、F sum-y , where F sum-x =F sum ·cosα, F sum-y =F sumsinα; β is the minimum symmetry angle, β = 360 / (Num×2);

[0010] Step S1.2: Determine constraints;

[0011] The constraints are:

[0012] In order to keep the combustion chamber pressure constant, the combustion surface A b and total throat area A t-tot satisfy const means a fixed value;

[0013] The constraints that the burning surface of the grain meets during the stable operation of the engine are: b and total throat area A t-tot Need to meet Where A t-i-j It is expressed as the total throat area corresponding to the maximum opening of valve i and the minimum opening of valve j; p c is the combustion chamber pressure; a is the burning rate coefficient, ρ is the propellant density, C * is the characteristic velocity, n is the pressure index;

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

[0015] The rules for circumferential transformation of multiple valves are:

[0016] (1) Rotational symmetry rules;

[0017] The initial range of α is 0°≤α<β. Every time α rotates counterclockwise 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 of the rotational symmetry rule is:

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

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

[0021] If the valve number after subtracting ai is 0, 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 2×β line. The transformed valve number is:

[0025]

[0026] Based on the numbering of β≤α<2β, every time α rotates counterclockwise by 2β, the transformed valve number is increased 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 + rotational 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 is 0 at this time, then the value of ai is updated to Num; i represents the valve number, i = 1, 2, ..., Num;

[0031] Step S1.4: Calculate the thrust capacity of a single valve and the thrust capacity of two valves relative to each other;

[0032] Step S2: Calculate the effective thrust mode of the system according to the vector thrust model of step S1;

[0033] The effective thrust modes of the system include zero thrust mode, two adjacent valves effective thrust mode and three adjacent valves effective thrust mode;

[0034] 1) Zero thrust F sum =0, there are many ways to achieve it, choose the method of odd-numbered valves opening equally and even-numbered valves fully closing, that is, stroke L = 0;

[0035] 2) When F sum ≠0, as F sum Choose from small to large and F sum The two adjacent valves provide effective thrust until they meet F sum Directionally adjacent The valve provides effective thrust while satisfying the constraint of constant pressure on the total throat area.

[0036] Furthermore, the steps to solve the thrust capacity of a single valve are:

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

[0038] F s =p cA t C f ;

[0039] Throat area A t The corresponding relationship with the stroke L is obtained through the surface design of the throat plug and throat liner; thrust coefficient C f The corresponding relationship with the stroke L is obtained through flow field simulation or experimental test, that is, given the stroke L value, the throat area A t , thrust coefficient C f and thrust F s All are known quantities;

[0040] A t , C f , and F s are all monotonically increasing univariate functions of L. Given that F s , solve the corresponding A t , C f and L;

[0041] Define the value range of L to be [0,L max ];

[0042] 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 , the thrust takes the minimum value F s-min ;

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

[0044] Furthermore, the steps to solve the relative thrust capacity of the two valves are:

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

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

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

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

[0049] The relative thrust of the two valves is [0,F max ] Includes mode 1 and mode 2.

[0050] Furthermore, the mode 1 and mode 2 are:

[0051] Mode 1: The thrust force relative to one of the two valves is constant at F s-min , the other valve thrust from F s-min to F s-max change;

[0052] Mode 2: Relative throat area of ​​the two valves and A t-min +A t-max Keep constant. When the throat areas of the two valves are equal, the total thrust is 0. When the throat areas of the two valves are A t-min , A t-max The total thrust is F max .

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

[0054] 1 The present invention proposes the constraints on the burning surface of the charge and the total throat area of ​​the valve to achieve a constant pressure in the combustion chamber, and proposes a method for calculating the total throat area of ​​the valve to achieve a constant pressure in the combustion chamber at any time;

[0055] 2. Constant combustion chamber pressure can improve the utilization rate of engine structural materials, reduce the weight of engine structure, increase the payload of aircraft, and improve flight maneuverability;

[0056] 3. The combustion chamber pressure is constant, which simplifies the working conditions of each pintle valve nozzle and facilitates the acquisition of the thrust coefficient corresponding to the throat plug at different strokes; BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 It is a schematic diagram of the pintle valve nozzle structure;

[0058] Figure 2 It is a schematic diagram of the pintle-type eight-valve nozzle being evenly distributed along the circumference and the thrust lines being located in the same plane;

[0059] Figure 3 This is a schematic diagram of the eight valve numbering transformation;

[0060] Figure 4 is a flow chart;

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

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

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

[0064] The vector thrust model includes a pintle valve thrust model, constraints of the pintle 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-pin plug valve thrust model;

[0066] The eight pintle valve nozzles are evenly and symmetrically distributed along the circumference; the thrust lines are located in the same plane; the valves are numbered 1, 2, 3, 4, 5, 6, 7, 8;

[0067] The magnitude of the vector force is F sum , the angle between the vector force and the x-axis is α, and the components of the vector force on the x-axis and y-axis are F sum-x 、F sum-y , where F sum-x =F sum ·cosα, F sum-y =F sum ·sinα; β is the minimum symmetry angle, for eight valves β=360 / (8*2)=22.5; 0°≤α<22.5°;

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

[0069] In order to achieve constant combustion chamber pressure and continuous and precise adjustment of engine thrust in all directions, the burning surface of the grain must meet the constraints during stable engine operation.

[0070] The engine pressure balance formula is:

[0071] p c is the combustion chamber pressure; after the propellant is selected, the burning rate coefficient a, the propellant density ρ, and the characteristic velocity C * , pressure index n are known constants, and the burning surface A of the grain b is a known array that changes with working time. In order to achieve the combustion chamber pressure p c is a constant value, the combustion surface A b and total throat area A t-tot Requirements:

[0072]

[0073] Thrust distribution and solution method require that the charge design make the combustion surface A b The following constraints are met:

[0074]

[0075] Definition A t-3-5 The total throat area corresponding to 3 valves opening to the maximum and 5 valves opening to the minimum, 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 the four valves and the minimum opening of the four valves, that is, A t-4-4 =4A t-max +4A t-min ;

[0077] Step S1.3: Calculate the thrust capacity of a single valve and the thrust capacity of two valves relative to each other;

[0078] According to the vector thrust model and the constraints of the grain burning surface, the thrust capacity of a single valve and the thrust capacity of two valves are calculated as follows:

[0079] The steps to solve the thrust capacity of a single valve are:

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

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

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

[0083] A t , C f , and F s are all monotonically increasing univariate functions of L. Given that F sThe corresponding A can be solved t , C f and L;

[0084] Define the value range of L to be [0,L max ];

[0085] 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 , the thrust takes the minimum value F s-min ;

[0086] When L = L max When the nozzle throat area reaches the maximum value A t-max , the thrust coefficient of the nozzle takes the maximum value C f-max , the thrust reaches the maximum value F s-max ;

[0087] The steps to solve the relative thrust capacity of the two valves are:

[0088] Two valves on the same thrust line are called opposite valves, for example Figure 2 Among them, valve 1 and valve 5, valve 2 and valve 6, valve 3 and valve 7, etc. are two relative valves;

[0089] The combined thrust relative to the two valves is the difference between the thrust values ​​of the two valves, and the direction of the combined thrust relative to the two valves is the same as the direction of the valve with the largest thrust value among the two valves;

[0090] When the thrusts of the two valves are the same, the combined thrust is the smallest, which is 0;

[0091] When one of the two valves outputs the maximum thrust F s-max , the other valve outputs the minimum thrust F s-min When the combined thrust is the largest, it is defined as F max =F s-max -F s-min ;

[0092] In order to reduce thrust loss, Maximum, according to the thrust formula F s =p c A t C f In the valve structure design, the profile design is used to make maximum;

[0093] The relative thrust of the two valves is [0,F max ] Includes mode 1 and mode 2:

[0094] Mode 1: The thrust force relative to one of the two valves is constant at F s-min , another valve thrust can be from Fs-min to F s-max change;

[0095] Mode 2: Relative throat area of ​​the two valves and A t-min +A t-max Keep constant. When the throat areas of the two valves are equal, the total thrust is 0. When the throat areas of the two valves are A t-min , A t-max The total thrust is F max ;

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

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

[0098] The transformation rules are:

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

[0100] for Figure 3 In the coordinate system shown, since the eight valves are evenly distributed around the circumference and there is a symmetry law, the vector thrust direction 0°≤α<22.5° can be transformed to 0°≤α<360° by 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, a8, and the transformed valve numbers are 1, 2, 3, 4, 5, 6, 7, 8. The transformation rules are as follows:

[0101] (1) Rotational symmetry rules;

[0102] observe Figure 3 , the initial range of α is 0°≤α<22.5°. Every time α rotates 45° counterclockwise, the original valve number is reduced by 1 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 rules;

[0107] 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:

[0108]

[0109] Based on the numbering of 22.5°≤α<45°, the valve number after transformation increases by 1 for every 45° counterclockwise rotation of α. 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: Calculate the effective thrust mode of the system according to the vector thrust model of step S1;

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

[0117] The effective thrust modes of the system include zero thrust mode, single valve effective thrust mode, adjacent 2 valves effective thrust mode and adjacent 3 valves effective thrust mode;

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

[0119] When the vector thrust of the eight valves is zero, it is zero thrust mode. There are many ways to achieve F sum = 0 thrust mode, here only one of the methods with simple logic and easy implementation is selected: valves 1, 3, 5, 7 are open, valves 2, 4, 6, 8 are fully closed, that is, stroke L = 0, all the following "valve fully closed" refers to stroke L = 0;

[0120] By adjusting the valves 1, 3, 5, 7, etc., the corresponding total throat area A t-tot Keep the pressure 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 When the valve 1 provides effective thrust, it can be realized; the effective thrust of valve 1 adopts mode 1 distribution, that is:

[0125] F s1 =F sum +F s-min , we can solve that the throat area of ​​valve 1 is A t1 ;

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

[0127] In order to achieve a constant pressure in the combustion chamber, valves 3 and 7 are closed, and valves 2, 4, 6, and 8 are opened equally so that the total throat area can be kept at A. t-3-5 t-tot t-4-4 The specific value of total throat area is determined according to the transient combustion surface.

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

[0129]

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

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

[0132] F sum =F1·cosα+F2·cos(45°-α)

[0133] The constraints should be satisfied:

[0134]

[0135] It can be solved as:

[0136]

[0137] Note that when α = 0°, F1 = F sum , F2 = 0, which can include the situation where a single valve provides effective thrust;​​

[0138] Define the effective thrust F provided by two adjacent valves sum The maximum value that can be obtained is F sum-2max , then at this time:

[0139]

[0140] In summary, when 0°≤α<22.5°, hour,

[0141]

[0142] The effective thrust of valves 1 and 2 is realized by mode 1. In order to achieve a constant pressure in the combustion chamber, the total throat area can be kept at A by opening valves 3, 4, 7, and 8 equally. t-3-5 t-tot t-4-4 The specific total throat area is determined according to the transient combustion surface; the thrust and throat area of ​​each valve are:

[0143]

[0144] Step S2.3: effective thrust mode of three adjacent valves;

[0145] When 0°<α<22.5°, F sum >F sum-2max When the thrust is greater than 0.05, it is no longer possible for valves 1 and 2 to provide effective thrust. The three valves with the smallest angle with the vector thrust, namely valves 1, 2, and 8, need to provide effective thrust. The combined thrust is:

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

[0147] The constraints should be satisfied:

[0148]

[0149] The solution is:

[0150]

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

[0152] Define the maximum value of effective thrust provided by three adjacent valves as F sum-3max , then at this time:

[0153] ​​

[0154] In summary, when 0°≤α<22.5°, hour:

[0155]

[0156] In order to achieve a constant pressure in the combustion chamber, the total throat area needs to be kept within A. t-3-5 t-tot t-4-4 The effective thrust of valves 2 and 8 is achieved through mode 2, and the sum of the throat areas of valves 1, 5, 2, 6, 4, and 8 is 3 (A t-min +A t-max ), and opening valves 3 and 7 can satisfy A t-3-5 t-tot t-4-4 Constraints; the thrust and throat area of ​​each valve are:

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

[0158] Summarize the solution methods of S2.1~S2.3.

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

[0160] Case 1: F sum =0

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

[0162] The throat area of ​​each valve is:

[0163]

[0164] Case 2:

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

[0166] The throat area of ​​each valve is:

[0167]

[0168] Case 3:

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

[0170]

[0171] For each valve stroke L, the stroke L and throat area A are known. t The corresponding relationship is used to calculate the throat area A of each valve. ti Then solve for L.

[0172] 1 The present invention proposes the constraints on the burning surface of the grain and the total throat area of ​​the valve to achieve a constant pressure in the combustion chamber, and proposes a method for calculating the total throat area of ​​the valve to achieve a constant pressure in the combustion chamber at any time.

[0173] 2 Constant combustion chamber pressure can improve the utilization rate of engine structural materials, reduce the weight of engine structure, and help increase the payload of the aircraft and improve flight maneuverability.

[0174] 3. The combustion chamber pressure is constant, which simplifies the working conditions of each pintle valve nozzle and makes it easier to obtain the thrust coefficient corresponding to the throat plug at different strokes.

[0175]

[0176] The present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0177] The present invention proposes a method for achieving constant combustion chamber pressure and all-round, continuously adjustable thrust during stable engine operation. The stable engine operation refers to removing the rising and falling sections in the engine pressure-time curve.

[0178] A typical pintle valve nozzle structure diagram is shown in Figure 1 The eight pintle valve nozzles are evenly distributed along the circumference, and their thrust lines are located in the same plane. See the schematic diagram Figure 2 .

[0179] The method to achieve constant combustion chamber pressure is: first, ensure that the combustion surface A of the grain column is b and total throat area A t-tot Satisfy certain constraints, and then at each moment during stable operation, the total throat area A t-tot Calculate so that

[0180] The total thrust F output according to the overall requirements of the aircraft sum and angle α, the thrust distribution and solution method of each valve nozzle is: in the total throat area A t-tot Under the premise of meeting the constant pressure condition of the combustion chamber, the combined thrust angle 0°≤α<360° is first converted to the range of 0°≤α<22.5°, and then according to F sumThe size of the valve is divided into zero thrust mode, single valve providing effective thrust, two adjacent valves providing effective thrust, and three adjacent valves providing effective thrust, and the valves are allocated and the thrust is calculated respectively.

[0181] The constraints of the burning surface and total throat area of ​​the grain are:

[0182] In order to achieve constant combustion chamber pressure and continuous and precise adjustment of engine thrust in all directions, the combustion surface of the grain needs to meet certain constraints during the stable operation of the engine. The engine pressure balance formula is: After the propellant is selected, the burning rate coefficient a, propellant density ρ, characteristic velocity C * , pressure index n are known constants, and the burning surface A of the grain b is a known array that changes with working time. In order to achieve the combustion chamber pressure p c is a constant value, the combustion surface A b and total throat area A t-tot Need to meet The thrust distribution and solution method involved in the present invention requires that the combustion surface A b The following constraints are met:

[0183]

[0184] Definition A t-3-5 The total throat area corresponding to 3 valves opening to the maximum and 5 valves opening to the minimum, that is, A t-3-5 =3A t-max +5A t-min ;

[0185] Definition A t-4-4 The total throat area corresponding to the maximum opening of the four valves and the minimum opening of the four valves, that is, A t-4-4 =4A t-max +4A t-min .

[0186] When the combustion surface meets the above constraints, the pressure p during engine operation should be maintained at c To be a constant value, the total throat area A of the 8 valves needs to be t-tot All the following thrust distribution and solution methods meet the total throat area In A t-3-5 t-tot t-4-4 Adjustable within the range.

[0187] Valve number conversion method:

[0188] for Figure 3 The coordinate system shown, the magnitude of the vector thrust is F sum ​​, the angle with the x-axis is α, 0°≤α<22.5°, the components of the vector thrust on the x-axis and y-axis are F sum-x 、F sum-y (F sum-x =F sum ·cosα, F sum-y =F sum ·sinα).

[0189] Since the eight valves are evenly distributed around the circumference and there is a symmetry rule, the vector thrust direction of 0°≤α<22.5° can be extended to 0°≤α<360° through transformation. In order to avoid confusion in valve numbers, it is assumed that the original valve numbers are a1, a2, a3, a4, a5, a6, a7, a8, and the transformed valve numbers are 1, 2, 3, 4, 5, 6, 7, 8. The transformation rules are as follows:

[0190] (1) Rotational symmetry rules:

[0191] observe Figure 3 , the initial range of α is 0°≤α<22.5°. Every time α rotates 45° counterclockwise, the original valve number is reduced by 1 to obtain the transformed valve number. If the number after subtraction is 0, it is changed to 8. The general expression is:

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

[0193] ai=(i-n+8)mod8

[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 of 22.5°≤α<45°, the valve number after transformation increases by 1 for every 45° counterclockwise rotation of α. If the added number is 9, it is changed to 1. The general expression is:

[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 In summary, the valve number after transformation is:

[0203]

[0204]

[0205] Valve thrust calculation method:

[0206] The method of generalizing the vector thrust direction from 0°≤α<22.5° to 0°≤α<360° has been given in the previous article, so we only need to solve Figure 3 The thrust of the situation is enough.

[0207] Firstly, the thrust capacity of a single valve and the thrust mode of two valves are defined. Then, the thrust calculation methods of each valve are given from small to large according to the vector thrust.

[0208] Single valve thrust capacity:

[0209] The combustion chamber pressure is a constant value p c The throat plug of a single valve moves axially, and when its stroke is L, the corresponding nozzle throat area is A. t , thrust coefficient is C f , the thrust of a single valve is F s =p c A t C f The throat area A can be known through the surface design of the throat plug and throat liner. t The corresponding relationship with the stroke L; the thrust coefficient C can be obtained through flow field simulation or experimental testing f The corresponding relationship with the stroke L, that is, for a given stroke L value, the throat area A t , thrust coefficient C f and thrust F s All are known quantities. t , C f , and F s are all monotonically increasing univariate functions of L. Given that F s The corresponding A can be easily solved t , C f and L.

[0210] The range of L values ​​is defined as [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 , the thrust takes the minimum value F s-min ; L = L maxWhen the nozzle throat area reaches the maximum value A t-max , the thrust coefficient of the nozzle takes the maximum value C f-max , the thrust reaches the maximum value F s-max .

[0211] Relative two valve thrust modes:

[0212] 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, etc. are two relative valves. Obviously, the combined thrust of the two relative valves is the difference between the thrust values ​​of the two valves, and the direction is the same as the thrust value of the larger valve. When the thrusts of the two relative valves are the same, the combined thrust value is the smallest, which is 0. When one of the two relative valves outputs the maximum thrust F s-max , the other valve outputs the minimum thrust F s-min When the combined thrust is the largest, it is defined as F max =F s-max -F s-min In order to reduce thrust loss, As large as possible, according to the thrust formula F s =p c A t C f In the valve structure design, careful surface design should be used to make As big as possible.

[0213] The present invention realizes [0,F max ]There are two modes:

[0214] Mode 1: The thrust force relative to one of the two valves is constant at F s-min , another valve thrust can be from F s-min to F s-max change;

[0215] Mode 2: Relative throat area of ​​the two valves and A t-min +A t-max Keep constant. When the throat areas of the two valves are equal, the total thrust is 0. When the throat areas of the two valves are A t-min , A t-max The total thrust is F max .

[0216] Summary of valve thrust calculation formulas:

[0217] In the case of 0°≤α<22.5°, according to the combined thrust F sum The size of can be divided into three solution methods:

[0218] Case 1: F sum =0

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

[0220] The throat area of ​​each valve is:

[0221]

[0222] Case 2:

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

[0224]

[0225] The throat area of ​​each valve is:

[0226]

[0227] Case 3:

[0228] At this time, valves 1, 2, and 8 provide effective thrust, and valves 3 and 7 close the loop to regulate pressure. The thrust of each valve is:

[0229]

[0230] For each valve stroke L, the stroke L and throat area A are known. t The corresponding relationship is used to calculate the throat area A of each valve. ti Then L can be easily solved.

[0231] Derivation of valve thrust calculation formula:

[0232] Zero thrust mode:

[0233] There are several ways to implement F sum = 0 thrust mode, only one of the methods is selected here: valves 1, 3, 5, 7 are open, and valves 2, 4, 6, 8 are fully closed (i.e., stroke L = 0, all "valves fully closed" below refer to stroke L = 0).

[0234] By adjusting the valves 1, 3, 5, 7, etc., the corresponding total throat area A t-tot Keep the pressure constant.

[0235] The throat area of ​​each valve is:

[0236]

[0237] Single valve provides effective thrust:

[0238] When α=0°, 0<F sum ≤Fmax When the valve 1 provides effective thrust, it can be realized. The effective thrust of valve 1 is distributed in mode 1, that is:

[0239] F s1 =F sum +F s-min , we can solve that the throat area of ​​valve 1 is A t1 ;

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

[0241] In order to achieve a constant pressure in the combustion chamber, valves 3 and 7 are closed, and valves 2, 4, 6, and 8 are opened equally so that the total throat area can be kept at A. t-3-5 t-tot t-4-4 The total throat area can be adjusted within a certain range, and the specific value of the total throat area is determined according to the transient combustion surface.

[0242] In summary, the throat area of ​​each valve is:

[0243]

[0244] Two adjacent valves provide effective thrust:

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

[0246] F sum =F1·cosα+F2·cos(45°-α)

[0247] The constraints should be satisfied:

[0248]

[0249] It can be solved as:

[0250]

[0251] Note that when α = 0°, F1 = F sum , F2=0, which can include the situation where a single valve provides effective thrust.

[0252] Define the effective thrust F provided by two adjacent valves sum The maximum value that can be obtained is 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 realized by mode 1. In order to achieve a constant pressure in the combustion chamber, the total throat area can be kept at A by opening valves 3, 4, 7, and 8 equally. t-3-5 t-tot t-4-4 The specific total throat area is determined according to the transient combustion surface. The thrust and throat area of ​​each valve are:

[0257]

[0258] Three adjacent valves provide effective thrust:

[0259] When 0°<α<22.5°, F sum >F sum-2max When the effective thrust provided by valves 1 and 2 is insufficient, valves 1, 2, and 8 are required to provide effective thrust. The combined thrust is:

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

[0261] The constraints should be satisfied:

[0262]

[0263] It can be solved as:

[0264]

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

[0266] Define the maximum value of effective thrust provided by three adjacent valves as F sum-3max , then at this time:

[0267]

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

[0269]

[0270] In order to achieve a constant pressure in the combustion chamber, the total throat area needs to be kept within A. t-3-5 t-tot t-4-4 ​​​​The effective thrust of valves 2 and 8 is achieved through mode 2. The sum of the throat areas of valves 1, 5, 2, 6, 4, and 8 is 3 (A t-min +A t-max ), and opening valves 3 and 7 can satisfy A t-3-5 t-tot t-4-4 The thrust and throat area of ​​each valve are:

[0271]

[0272] Calculation process:

[0273] The calculation process is shown in Figure 4 .

[0274] Promotion:

[0275] The thrust distribution and solution method of the present invention can be extended to the case where 6 valves are evenly distributed, 10 valves are evenly distributed or more even-numbered valves are evenly distributed. The main idea is still to achieve constant engine working pressure through the constraints of the grain combustion surface and the total throat area, transform the valve numbering through the rotational symmetry and mirror symmetry rules, and obtain the valve thrust solution formula by successively deriving the zero thrust mode, the single valve providing effective thrust, and the adjacent two valves providing effective thrust.

[0276] For example, in the case of 6 valves evenly distributed, reasonable design of the medicine type can make the combustion surface A b The following constraints are met:

[0277]

[0278] According to the symmetry of the evenly distributed six valves, only 1 / 12 of the vector thrust angle α can be analyzed, that is, 0°≤α<30°, and then extended to the case of 0°≤α<360° through similar rotational symmetry and mirror symmetry + rotational symmetry methods.

[0279] The valve thrust calculation formula is derived in turn for the zero thrust mode, the single valve providing effective thrust, and the two adjacent valves providing effective thrust.

[0280] The method of the present invention is extended to the case where 10 valves are evenly distributed or a greater even number of valves are evenly distributed, and the analysis method is the same.

[0281] Beneficial effects:

[0282] 1 The present invention proposes the constraints on the burning surface of the grain and the total throat area of ​​the valve to achieve a constant pressure in the combustion chamber, and proposes a method for calculating the total throat area of ​​the valve to achieve a constant pressure in the combustion chamber at any time.

[0283] ​​2 Constant combustion chamber pressure can improve the utilization rate of engine structural materials, reduce the weight of engine structure, and help increase the payload of the aircraft and improve flight maneuverability.

[0284] 3. The combustion chamber pressure is constant, which simplifies the working conditions of each pintle valve nozzle and makes it easier to obtain the thrust coefficient corresponding to the throat plug at different strokes.

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

[0286]

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

[0288] For the pintle valve nozzle, the thrust coefficient is related not only to the pressure ratio and area ratio, but also to the flow state of the gas in the nozzle. When the throat area is too small due to the actuation of the throat plug, and the area ratio between the nozzle outlet and the throat is too large, a shock wave will appear in the expansion section. The shock wave directly affects the pressure distribution on the inner wall of the nozzle, and then affects the thrust and thrust coefficient. When the combustion chamber pressure is not constant and the throat area changes due to the actuation of the pintle, the change process of the engine's thrust and thrust coefficient will be very complicated, which brings great challenges to the engine design. When the combustion chamber pressure is constant and the pintle is actuated to 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 only by the single variable of the pintle position, and the thrust and thrust coefficient corresponding to the actuation of the throat plug to different positions can be easily obtained. This greatly simplifies the engine design process.

[0289] 4 The present invention realizes continuous and precise adjustment of the engine's omnidirectional thrust. According to the symmetry of the eight valves uniformly distributed around the circumference, the engine's 0°≤α<360° omnidirectional thrust analysis is converted into an analysis within the range of 0°≤α<22.5°, and then the total thrust required by the aircraft is divided into four situations: 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 respectively to obtain the thrust, throat area, and throat bolt stroke of each valve nozzle. The design of the engine servo control system is greatly simplified, and the accuracy of the engine output thrust is improved.

[0290] Glossary:

[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 burning surface of the charge;

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

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

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

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

[0301] A t-3-5 ——Total throat area corresponding to 3 valves opened to the maximum and 5 valves opened to the minimum;

[0302] A t-4-4 ——Total throat area corresponding to 4 valves opened to the maximum and 4 valves opened to the minimum;

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

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

[0305] F sum ——The total thrust provided by the engines required for the overall flight;

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

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

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

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

[0310] F s-min ——Minimum thrust output by a single valve;

[0311] F s-max ——The maximum thrust output by a single valve;

[0312] F i ——Effective thrust of a single valve, the subscript i represents the valve number, i = 1, 2, ... 8. The effective thrust of the i-th 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, F1 = 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 two adjacent valves providing effective thrust;

[0315] F sum-3max ——The maximum combined thrust that can be achieved by providing effective thrust from three adjacent valves;

[0316] C f ——single valve thrust coefficient;

[0317] C f-min ——Minimum value of single valve thrust coefficient;

[0318] C f-max ——Maximum value of single valve thrust coefficient.

Claims

1. A method for designing interior ballistics of an eight-valve solid attitude control engine, characterized in that: The steps include: Step S1: establishing a vector thrust model; The vector thrust model includes the pintle valve model, constraints, single valve thrust capacity, relative two-valve thrust capacity and multi-valve circumferential transformation rules; Step S1.1: Establishing a pintle valve model; The pintle valve model includes Num pintle valve nozzles, which are evenly distributed symmetrically along the circumference, 6≤Num≤14, and Num is an even number; the thrust lines of the pintle valve nozzles are located in the same plane; Valves k is the kth valve, where 1≤k≤Num; The magnitude of the vector force is F sum , the angle between the vector force and the x-axis is α, and the components of the vector force on the x-axis and y-axis are F sum-x and F sum-y , where F sum-x =F sum ·cosα, F sum-y =F sum sinα; β is the minimum symmetry angle, β = 360 / (Num×2); Step S1.2: Determine constraints; The constraints are: In order to keep the combustion chamber pressure constant, the combustion surface Ab and the total throat area At-tot meet const means a fixed value; The constraints that the burning surface of the grain meets during the stable operation of the engine are: b and total throat area A t-tot Need to meet Where A t-i-j It is expressed as the total throat area corresponding to the maximum opening of valve i and the minimum opening of valve j; p c is the combustion chamber pressure; a is the burning rate coefficient, ρ is the propellant density, C * is the characteristic velocity, n is the pressure index; Step S1.3: multi-valve circumferential transformation rules; Since multiple valves are evenly distributed along the circumference and there is a symmetry rule, 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 thrust capacity of two valves relative to each other; Step S2: Calculate the effective thrust mode of the system according to the vector thrust model of step S1; The effective thrust modes of the system include zero thrust mode, two adjacent valves effective thrust mode and three adjacent valves effective thrust mode; 1) Zero thrust F sum =0, there are many ways to achieve it, choose the method of odd-numbered valves opening equally and even-numbered valves fully closing, that is, stroke L = 0; 2) When F sum ≠0, as F sum Choose from small to large and F sum The two adjacent valves provide effective thrust until they meet F sum Directionally adjacent The valve provides effective thrust while satisfying the constraint of constant pressure on the total throat area.

2. The interior ballistic design method of an eight-valve solid attitude control engine according to claim 1, characterized in that: The steps for calculating the thrust capacity of a single valve are: The combustion chamber pressure is a constant value p c The throat plug of a single valve moves axially, and when its stroke is L, the corresponding nozzle throat area is A. t , thrust coefficient is C f , thrust F of a single valve s for: F s =p c A t C f ; Throat area A t The corresponding relationship with the stroke L is obtained through the surface design of the throat plug and throat liner; thrust coefficient C f The corresponding relationship with the stroke L is obtained through flow field simulation or experimental test, that is, given the stroke L value, the throat area A t , thrust coefficient C f and thrust F s All are known quantities; A t , C f , and F s are all monotonically increasing univariate functions of L. Given that F s , solve the corresponding A t , C f and L; Define the value range of L to be [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 , the thrust takes the minimum value F s-min ; When L = L max When the nozzle throat area reaches the maximum value A t-max , the thrust coefficient of the nozzle takes the maximum value C f-max , the thrust reaches the maximum value F s-max .

3. The interior ballistic design method of an eight-valve solid attitude control engine according to claim 1, characterized in that: The steps to solve the relative thrust capacity of the two valves are: Two valves on the same thrust line are called relative valves; the combined thrust of the relative valves is the difference between the two thrust values, and the direction of the combined thrust of the relative valves is the same as the direction of the valve with the largest thrust value among the two valves; When the thrusts of the two valves are the same, the combined thrust is the smallest, which is 0. When one of the two valves outputs the maximum thrust F s-max , the other valve outputs the minimum thrust F s-min When the combined thrust is the largest, it is defined as F max =F s-max -F s-min ; In order to reduce thrust loss, Maximum, according to the thrust formula F s =p c A t C f In the valve structure design, the profile design is used to make maximum; The relative thrust of the two valves is [0,F max ] Includes mode 1 and mode 2.

4. The interior ballistic design method of an eight-valve solid attitude control engine according to claim 3, characterized in that: The mode 1 and mode 2 are: Mode 1: The thrust of one valve relative to the two valves is constant at F s-min , the other valve thrust from F s-min to F s-max change; Mode 2 is the relative throat area of ​​the two valves and A t-min +A t-max Keep constant. When the throat areas of the two valves are equal, the total thrust is 0. When the throat areas of the two valves are A t-min , A t-max The total thrust is F max .

5. The method for designing interior ballistics of an eight-valve solid attitude control engine according to claim 1, characterized in that: The multi-valve circumferential transformation rule is: (1) Rotational symmetry rules; The initial range of α is 0°≤α<β. Every time α rotates counterclockwise 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. The general expression of the rotational symmetry rule is: When 0°+2βn≤α<β+2βn, n=0,1,…,Num-1, the calculation steps of valve number ai are: ai=(i-n+Num)mod(Num); If the valve number after subtracting ai is 0, change the value of ai to Num; Where i represents the valve number, i=1,2,…,Num; (2) Mirror symmetry + rotational symmetry rules; 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 2×β line. The transformed valve number is: Based on the numbering of β≤α<2β, every time α rotates 2β counterclockwise, the transformed valve number is increased by 1. If the value of ai after addition is Num+1, the value of ai is changed to 1; The general expression of the mirror symmetry + rotational symmetry rule is: When β+2βn≤α<2β+2βn, n=0,1,…,Num-1, the calculation formula of ai is: If the value of ai is 0 at this time, the value of ai is updated to Num; i represents the valve number, i=1, 2,…, Num.

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