Standard test engine pressure index calculation method

Abstract

The invention relates to the technical field of solid rocket engine performance testing, in particular to a standard test engine pressure index calculation method. The standard test engine pressure index calculation method is provided for the first time, and under the conditions that a standard engine does not meet the pressure neutrality requirement that NP is larger than or equal to 0.90 and smaller than or equal to 1.10 and the actually-measured pressure neutrality is higher than 1.10, the engine pressure index can still be calculated. Meanwhile, based on actually-measured pressure intensity-time data of three standard engines, the relation between the burning speed and the pressure intensity is deduced through the thickness of the standard engines and the actually-measured pressure intensity-time data, and then the corresponding burning speed is calculated according to the working pressure intensity range of the whole engine to be evaluated. The pressure index is obtained through fitting by adopting the Shengbert-Vieyersi formula, and important technical support is provided for rapid evaluation of the combustion performance of the solid rocket engine.

Description

Technical Field

[0001] The invention relates to the technical field of solid rocket engine performance testing, and in particular to a method for calculating a pressure index of a standard test engine. Background Art

[0002] The most commonly used relationship between the burning rate and pressure of solid rocket motor propellants is the Saint-Robert-Viery formula, which is applicable to a wide range of pressures.

[0003] r=a1p n

[0004] Where: a1——engine combustion rate coefficient, generally a constant;

[0005] p——combustion chamber pressure, MPa;

[0006] r——propellant burning rate, mm / s;

[0007] n——pressure exponent, is a dimensionless value, its size indicates the degree of influence of pressure change on burning rate. The smaller the value, the smaller the influence of pressure on burning rate.

[0008] In the prior art solution, the logarithm of both sides of the Saint Robert-Vieri formula is first taken to obtain

[0009] lnr=lna1+nlnp

[0010] The exponential relationship between r and p is converted into a linear relationship between lnr and lnp, and the slope of the straight line is the pressure exponent n. Then, through the measured values ​​of the average pressure and burning rate of five standard engines, five sets of combustion chamber pressure-propellant burning rate values ​​are obtained, and the linear relationship between lnr and lnp is fitted, and then the pressure exponent n is obtained.

[0011] "GJB 97A-2020 Standard Test Engine Technical Requirements and Data Processing" defines: Pressure neutrality (N P ) is the stability of the stable section of the pressure-time curve of the standard test engine, which is numerically expressed by the ratio of the pressure value with the largest difference from the average pressure during the combustion time in the stable section to the average pressure during the combustion time:

[0012]

[0013] Where: N P ——pressure neutrality in the “stable” section of the pressure curve;

[0014] p c ——Combustion chamber pressure, MPa;

[0015] P b ——Average pressure during combustion time, MPa.

[0016] GJB 97A clearly states that except for the BSFΦ75 standard test engine specified in GJB 96, other standard test engines with a neutrality of N P Should meet:

[0017] 0.90≤N P ≤1.10

[0018] In the prior art, the measured pressure-time curves of the five standard engines must meet the above conditions. However, the neutrality of the high-pressure standard engine is usually greater than 1.10, which does not meet the above conditions. Summary of the invention

[0019] The present invention proposes for the first time a method for calculating the pressure index of a standard test engine, and performs a method for calculating the pressure index of a standard test engine when the pressure neutrality of a high-pressure standard test engine is greater than 1.10. The unit price of a single standard test engine is 5,000 yuan to 6,000 yuan, and the overall cost is relatively high. In order to meet the actual demand for cost reduction, the present invention is based only on the measured pressure-time data of three standard engines, and the relationship between the burning rate and the pressure is derived through the standard engine thickness and the measured pressure-time data. The corresponding burning rate is calculated according to the working pressure range of the engine to be evaluated, and the pressure index is obtained by fitting the Saint-Robert-Vieri formula, which provides important technical support for the rapid evaluation of the combustion performance of solid rocket engines.

[0020] In order to achieve the above object, the present invention solves the above technical problems through the following technical solutions:

[0021] A method for calculating a standard test engine pressure index comprises the following steps:

[0022] S1: The relationship between burning rate and pressure under set high pressure conditions;

[0023] S2: Based on the definition of wall thickness, the relationship between wall thickness and propellant burning rate is obtained;

[0024] S3: Find the relationship between the thickness and the pressure;

[0025] S4: measured combustion chamber pressure-time data of three standard engines;

[0026] S5: Find the relationship between burning rate and pressure, and find the corresponding burning rate value;

[0027] S6: The pressure index is obtained by fitting using the Saint-Robert-Vieri formula.

[0028] According to the power series expansion of the function in S1, the St. Robert-Vieri formula satisfies the sufficient conditions for expansion into a Taylor series. The St. Robert-Vieri formula is expanded into the form of a Taylor series and simplified, with each coefficient represented by a parameter and high-order terms removed. Therefore, the relationship between the burning rate and pressure under high pressure conditions is set as follows:

[0029] r = ap 2 +bp+c (1)

[0030] Where: p——combustion chamber pressure, MPa;

[0031] r——propellant burning rate, mm / s;

[0032] a, b, c——are constant terms.

[0033] According to the definition of meat thickness in S2:

[0034]

[0035] In the formula: w——meat thickness, mm.

[0036] In S3, the formulas in S1 and S2 are combined to obtain the relationship between the thickness and pressure:

[0037]

[0038] Where: t b ——Burning time, seconds.

[0039] In S4, a program is used to process the measured combustion chamber pressure-combustion time data of three standard engines, and the combustion time t b , the integral of the square of the measured pressure over time during the combustion time, and the measured combustion chamber pressure impulse during the combustion time are substituted into the formula of S3 to obtain a group of equations containing three unknowns a, b, and c. The three unknowns a, b, and c are solved by MATLAB, and then the relationship between the burning rate and the pressure is obtained.

[0040] According to the values ​​of a, b, and c obtained in S4, they are substituted into the formula of S1 to obtain the relationship between the burning rate and pressure in S5: r = -0.0134 × P 2 +0.5129×P+4.8208.

[0041] Select the pressure values ​​of at least 5 representative characteristic points, substitute them into the formula in S5, and calculate the corresponding burning rate value.

[0042] Using the Saint Robert-Vieri formula r = a1p n , use EXCEL or LINEST function to solve the engine burning rate coefficient a1 and pressure index n.

[0043] Based on the implementation of the above technical solution, the present invention can achieve the following technical effects:

[0044] 1. The present invention provides a method for calculating the pressure index of a standard test engine, and proposes a method for calculating the pressure index of a high-pressure standard test engine, which is suitable for the case where the pressure neutrality of the standard test engine is greater than 1.10.

[0045] 2. The present invention provides a method for calculating the pressure index of a standard test engine. When the standard engine does not meet the pressure neutrality requirement of 0.90≤NP≤1.10 and the measured pressure neutrality is higher than 1.10, the engine pressure index can still be calculated.

[0046] 3. The present invention provides a method for calculating the pressure index of a standard test engine, which can accurately fit the propellant pressure index, further reduce the number of standard test engines used to fit the pressure index, reduce the processing and testing costs of standard testers, and the pressure index calculation method is simple.

[0047] 4. The present invention provides a method for calculating the pressure index of a standard test engine. The relationship between the burning rate and the pressure can be determined by only the measured data of three standard engines, and then the pressure index can be obtained by fitting. The pressure index can be obtained under high pressure conditions while reducing the test cost. DETAILED DESCRIPTION

[0048] The following examples are used to illustrate the present invention, but they are not intended to limit the scope of the present invention.

[0050] In the description of the embodiments of the present invention, it should be noted that, unless otherwise clearly specified and limited, the terms "connected" and "connection" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium. For ordinary technicians in this field, the specific meanings of the above terms in the embodiments of the present invention can be understood according to specific circumstances.

[0051] In the embodiments of the present invention, unless otherwise clearly specified and limited, a first feature being "above" or "below" a second feature may mean that the first and second features are in direct contact, or the first and second features are in indirect contact through an intermediate medium. Moreover, a first feature being "above", "above" or "above" a second feature may mean that the first feature is directly above or obliquely above the second feature, or simply means that the first feature is higher in level than the second feature. A first feature being "below", "below" or "below" a second feature may mean that the first feature is directly below or obliquely below the second feature, or simply means that the first feature is lower in level than the second feature.

[0052] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the embodiment of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, without contradiction.

[0053] The following is a detailed description of a method for calculating the pressure index of a standard test engine provided by the present invention:

[0054] The first step is to expand the St. Robert-Vieri formula into the form of a Taylor series according to the power series expansion of the function. The St. Robert-Vieri formula satisfies the sufficient conditions for expansion into a Taylor series, and is simplified, with each coefficient represented by a parameter and high-order terms removed. Therefore, the relationship between the burning rate and pressure under high pressure conditions is as follows:

[0055] r = ap 2 +bp+c (1)

[0056] Where: p——combustion chamber pressure, MPa;

[0057] r——propellant burning rate, mm / s;

[0058] a, b, c——are constant terms.

[0059] The second step is based on the definition of meat thickness:

[0060]

[0061] In the formula: w——meat thickness, mm.

[0062] The third step is to combine formulas (1) and (2) to obtain the relationship between the thickness and pressure:

[0063]

[0064] Where: t b ——Burning time, seconds.

[0065] The fourth step is to process the measured combustion chamber pressure-time data of the three standard engines using a program and convert the combustion time t b , the integral of the square of the measured pressure over time during the combustion time, and the measured combustion chamber pressure during the combustion time are entered into formula (3), and a system of equations containing three unknowns a, b, and c (containing 3 equations) is obtained. The three unknowns a, b, and c are solved by MATLA, and then the relationship between the burning rate and the pressure is obtained.

[0066] The implementation code is as follows:

[0067] clc

[0068] clear

[0069] syms abc% defines three unknown numbers a, b, and c to be solved

[0070] tb1=3.9;%First standard engine combustion time

[0071] tb2=3.3;% Second standard engine combustion time

[0072] tb3=3; % The third standard engine combustion time

[0073] w=28;% standard engine thickness

[0074] p12=118.14;%Integral of the square of the measured pressure of the first standard engine over time

[0075] p22=314.55;%Integral of the square of the measured pressure of the second standard engine over time

[0076] p32 = 624.64; % The integral of the square of the measured pressure of the third standard engine over time

[0077] Ip1=21.02;%The measured pressure impulse of the first standard engine

[0078] Ip2=31.79; % Actual pressure impulse of the second standard engine

[0079] Ip3=42.71;% Actual pressure impulse of the third standard engine

[0080] eq1=p12*a+Ip1*b+tb1*cw;%The first equation in the equation group

[0081] eq2=p22*a+Ip2*b+tb2*cw;%The second equation in the system of equations

[0082] eq3=p32*a+Ip3*b+tb3*cw;%The third equation in the equation group

[0083] [a,b,c]=vpasolve(eq1==0,eq2==0,eq3==0,[a,b,c]); % Solve the equation system

[0084] disp(a)%Display parameter a

[0085] disp(b)% Display parameter b

[0086] disp(c)% Display parameter c

[0087] Step 5: Substitute the values ​​of a, b, and c obtained in step 4 into formula (1) to obtain the relationship between burning rate and pressure: r = -0.0134 × P 2 +0.5129×P+4.8208

[0088] Combined with the operating pressure range of the evaluated engine, a set of burning rate and pressure data are calculated respectively: for example, the operating pressure range of the full-size engine is 0-20MPa. In order to reduce the amount of calculation without affecting the calculation accuracy, 5 characteristic points are selected, and the corresponding burning rates r(4MPa), r(8MPa), r(12MPa), r(16MPa), and r(20MPa) are calculated using five pressure points of 4MPa, 8MPa, 12MPa, 16MPa, and 20MPa. The specific data are shown in Table 1.

[0089] Table 1 Burning rate and pressure data

[0090] Serial number Pressure / MPa Burning rate / mm / s 1 4 r(4MPa) 2 8 r(8MPa) 3 12 r(12MPa) 4 16 r(16MPa) 5 20 r(20MPa)

[0091] Step 6: Use the Saint Robert-Vieri formula r = a1p n Based on the data in Table 1, use EXCEL or LINEST function to solve the engine combustion rate coefficient a1 and pressure index n.

[0092] The specific implementation code is:

[0093] a1=EXP(INDEX(LINEST(LN(r(4MPa):r(20MPa)),LN(4:20)),1,2))

[0094] n=INDEX(LINEST(LN(r(4MPa):r(20MPa)),LN(4:20)),1)

[0095] The engine combustion rate coefficient a1 is solved to be 4.528672, the pressure index n is 0.276953, and R 2 The value is 0.9981, indicating that the power equation currently obtained has a high degree of fit to the burning rate pressure data and the solution is effective.

[0096] Example:

[0097] In order to verify the calculation method of the present invention, the measured data of three other different standard engines of the same engine as the one in the implementation code are selected, and the three unknowns a, b, and c are solved according to the fourth step to obtain the relationship between the combustion rate and the pressure as follows:

[0098] r=-0.0269r 2 +0.7844r+3.7664

[0099] According to the working pressure range of the high-pressure engine of 0-18 MPa, 5 pressure points are selected and substituted into the above formula to calculate the corresponding burning rate values, as shown in Table 2 for details.

[0100] Table 2 Burning rate and pressure data

[0101] Serial number Pressure / MPa Burning rate / mm / s 1 6 7.504659464 2 8 8.320342891 3 10 8.920830202 4 12 9.306121396 5 14 9.476216474

[0102] Based on the above data, the engine burning rate coefficient a1 = 4.4169 and the pressure index n = 0.2989 are solved using EXCEL or LINEST functions. 2 The value is 0.981, indicating that the power formula currently obtained has a high degree of fit to the burning rate pressure data. The relative deviation from the pressure index calculated by the case used in the implementation code is 7.34%, which is small and has good consistency.

[0103] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for calculating the pressure index of a standard test engine, characterized in that: The steps include: S1: The relationship between burning rate and pressure under set high pressure conditions; S2: Based on the definition of wall thickness, the relationship between wall thickness and propellant burning rate is obtained; S3: Find the relationship between the thickness and the pressure; S4: measured combustion chamber pressure-time data of three standard engines; S5: Find the relationship between burning rate and pressure, and find the corresponding burning rate value; S6: The pressure index is obtained by fitting using the Saint-Robert-Vieri formula.

2. The method for calculating the standard test engine pressure index according to claim 1, characterized in that: According to the power series expansion of the function in S1, the St. Robert-Vieri formula satisfies the sufficient conditions for expansion into a Taylor series. The St. Robert-Vieri formula is expanded into the form of a Taylor series and simplified, with each coefficient represented by a parameter and high-order terms removed. Therefore, the relationship between the burning rate and pressure under high pressure conditions is set as follows: r=ap 2 +bp+c (1) Where: p——combustion chamber pressure, MPa; r——propellant burning rate, mm / s; a, b, c——are constant terms.

3. The method for calculating the standard test engine pressure index according to claim 2, characterized in that: According to the definition of meat thickness in S2: In the formula: w——meat thickness, mm.

4. The method for calculating the standard test engine pressure index according to claim 3, characterized in that: In S3, the formulas in S1 and S2 are combined to obtain the relationship between the thickness and pressure: Where: t b ——Burning time, seconds.

5. The method for calculating the standard test engine pressure index according to claim 4, characterized in that: In S4, a program is used to process the measured combustion chamber pressure-combustion time data of three standard engines, and the combustion time t b , the integral of the square of the measured pressure over time during the combustion time, and the measured combustion chamber pressure impulse during the combustion time are substituted into the formula of S3 to obtain a group of equations containing three unknowns a, b, and c. The three unknowns a, b, and c are solved by MATLAB, and then the relationship between the burning rate and the pressure is obtained.

6. The method for calculating the standard test engine pressure index according to claim 5, characterized in that: According to the values ​​of a, b, and c obtained in S4, they are substituted into the formula of S1 to obtain the relationship between the burning rate and pressure in S5: r = -0.0134 × P 2 +0.5129×P+4.8208.

7. The method for calculating the standard test engine pressure index according to claim 6, characterized in that: Select the pressure values ​​of at least 5 representative characteristic points, substitute them into the formula in S5, and calculate the corresponding burning rate value.

8. The method for calculating the standard test engine pressure index according to claim 7, characterized in that: Using the Saint Robert-Vieri formula r = a1p n , use EXCEL or LINEST function to solve the engine burning rate coefficient a1 and pressure index n.

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