A method for calculating engine interior ballistics at any temperature

Abstract

The present invention discloses a method for calculating engine internal ballistics at any temperature, comprising the following steps: 1. obtaining engine internal ballistics data at a typical temperature; 2. selecting two typical temperatures and their data as calculation basis according to the required temperature value; 3. interpolating the longest running time of the data obtained at the typical temperature to solve the longest running time of the required temperature value; 4. dividing the data into N equal parts based on the value of the longest running time; 5. dividing the engine internal ballistics data at the typical temperature into N equal parts respectively; 6. using the interpolation method to calculate the corresponding internal ballistic parameters at the required temperature. The method solves the problem of inconsistent time scales through the equal division method, making the calculation results more accurate; performing calculations based on existing data saves calculation time, and verifying the effectiveness of the newly proposed calculation method through examples.

Description

Technical Field

[0001] The invention belongs to the technical field of solid rocket engines, and in particular relates to a method for calculating engine internal ballistics applicable to any temperature. Background Art

[0002] For solid rocket engines, internal ballistics is actually the gas dynamics in the engine combustion chamber. Its basic task is to calculate the change of engine thrust, pressure, mass, center of mass, moment of inertia and other data over time and space under various working conditions. The calculation of engine internal ballistics is an important indicator in the engine development process and an important basis for guiding the demonstration of aircraft systems and the calculation of aircraft flight trajectory.

[0003] The calculation of the flight trajectory of an aircraft requires the prediction of the flight trajectory based on the ambient temperature during flight. Researchers usually measure the internal ballistic parameters of the engine under different temperature conditions. Obtaining the internal ballistic data of the engine under different temperature conditions through manual experiments involves a huge workload, is difficult to achieve accurately, and is time-consuming and expensive. Therefore, it is urgent to establish a method for calculating the internal ballistics of the engine at any temperature, which can effectively solve the above problems and accurately and quickly calculate the ballistic parameters, thereby reducing the number of experiments, improving calculation efficiency, and saving calculation costs. Summary of the invention

[0004] To solve the above problems, the present invention provides a fast calculation method for engine internal ballistics at any temperature, so as to solve the problems of complex operation, high cost and low efficiency of existing calculation methods. The method uses the accurate value of internal ballistics under typical temperature state as a reference to calculate the reference value of internal ballistics at any temperature within the engine working range.

[0005] The present invention is achieved through the following technical solutions.

[0006] The present invention provides a method for calculating engine interior ballistics applicable to any temperature, comprising the following steps:

[0007] ① Obtain the data F(t) of the engine internal ballistic parameters changing with the working time at typical temperature;

[0008] ②According to the required temperature value T x , select the required temperature T x The two closest typical temperatures T1 and T2 and the data of their corresponding ballistic parameters changing with running time F1(t) and F2(t) are used as the basis for calculation;

[0009] ③The longest operating time t1 based on the data obtained at typical temperatures T1 and T2 max ,

[0010] t2max , use the interpolation method to calculate the required temperature value T x The maximum running time of tx max ;

[0011] ④Based on t1 max , t2 max ,tx max The value is divided into N equal parts, and the time series b1 is obtained after N equal parts i , b2 i , bx i ;

[0012] ⑤ Use the interpolation method to divide the data of the trajectory parameters in F1(t) and F2(t) with the running time into N equal parts, and obtain b1 for each time division i 、b2 i The data of the trajectory parameters n1 i ′、n2 i ′, its data sets are C1 and C2;

[0013] ⑥Based on n1 i ′、n2 i ′, use the interpolation method to calculate each time division bx i The data of the trajectory parameters nx i , combined with step ④, tx max The data bx obtained by dividing the value N into equal parts i , get the required temperature value T x The data Fx′(t) showing the variation of trajectory parameters with running time.

[0014] In the step ①, the data of the variation of the ballistic parameter n with the working time t at a representative temperature obtained by theoretical calculation or experimental measurement is expressed as F(t)={(t1,n1), (t2,n2), ..., (t max ,n max )}, at least two typical temperatures should be selected, generally no less than three (such as low temperature, normal temperature, high temperature), and the boundaries of the engine operating temperature should be included as much as possible.

[0015] In step ②, F1(t)={(t11,n11),(t12,n12),...,(t1 max ,n1 max )}, F2(t)={(t21,n21), (t22,n22),..., (t2 max ,n2 max )}, where t1 is the running time, n1 is the value of the internal ballistic parameter at t1, t2 is the running time, and n2 is the value of the internal ballistic parameter at t2.

[0016] In step ③, the longest operating time t1 obtained by theoretical calculation or experimental measurement at temperature T1 max The maximum operating time t2 obtained by theoretical calculation or experimental measurement at temperature T2 max , for the required temperature value T x The maximum running time of tx max Perform interpolation calculation, the tx max It is expressed by the following formula:

[0017]

[0018] Where: tx max is the required temperature value T x The maximum running time, t1 max is the maximum operating time obtained by theoretical calculation or experimental measurement at the required temperature value T1, t2 max It is the maximum operating time obtained based on theoretical calculation or experimental measurement at the required temperature value T2.

[0019] In the step ④, The N value can be selected according to demand. The larger the N value, the higher the calculation accuracy.

[0020] In step ⑤, C1={n11′, n12′, ..., n1 N ′}, C2={n21′, n22′,..., n2 N ′}, the cyclic algorithm is used to calculate the data of the trajectory parameters changing with time under N equally divided time periods: let i = {1, 2, ..., N-1, N}, j = {2, 3, ..., t1 n-1 , t1 n}, where t 1n is the number of operating times obtained at temperature T1 based on theoretical calculation or experimental measurement. For each element in i, each element in j needs to be calculated once using the following formula ② to obtain n1 i ′、n2 i ', when the value of the i-th equally divided time is between the j-1th running time and the jth running time, the n1 i ′、n2 i ' is expressed by the following formula:

[0021]

[0022] Where: i is the set of {1, 2, ..., N-1, N}, j is the set of {2, 3, ..., t1 n-1 , t1 n}, t1 jis the jth operating time at temperature T1, t1 (j-1) is the j-1th running time at temperature T1, F1(j) is the ballistic parameter data of the j-1th running time at temperature T1, F1(j-1) is the ballistic parameter data of the j-1th running time at temperature T1, n1 i ′ is the ballistic parameter data of the i-th equal-division time at temperature T1;

[0023] When the value of the i-th divided time is equal to the j-th running time, n1 i The value of ′ is F1(j);

[0024] Use the same method to obtain n2 i ′.

[0025] In step ⑥, Fx′(t) is the value bx of each time interval divided into N equal parts. i The corresponding ballistic parameter nx i The set of , denoted as Fx′(t)={(bx1,nx1),(bx2,nx2),...,(bx i ,nx i )}, where bx i The value of tx max The value of the i-th time interval after N equal divisions;

[0026] The nx i It is expressed by the following formula:

[0027]

[0028] Where: i is the set of {1,2,...,N-1,N}, n1 i ′ is the ballistic parameter data of the ith equal-division time at temperature T1, n2 i ′ is the ballistic parameter data of the ith equal time division at temperature T2, b1 i b2 is the value of each time interval after the maximum operating time at temperature T1 is divided into N equal parts, i 、bx i Same, nx i It is T x Ballistic parameter data of the i-th equal-division time at temperature.

[0029] The beneficial effects of the present invention are:

[0030] 1. The problem of inconsistent time scales is solved by the equal division method, making the calculation results more accurate;

[0031] 2. Calculations are performed based on existing data, saving calculation time. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 It is a principle block diagram of the present invention.

[0033] Figure 2 It is the graph of interior ballistic parameters changing with time.

[0034] Figure 3 It is a comparison diagram between the calculation results of the present invention and the theoretical values. DETAILED DESCRIPTION

[0035] The contents of the present invention are further described in detail below in the form of embodiments, but it should not be understood that the scope of the subject matter described in the present invention is limited to the following embodiments. Without departing from the above-mentioned technical ideas of the present invention, various modifications, substitutions and changes made according to the common technical knowledge and customary means in the field are included in the scope of the present invention without substantially changing the technical content.

[0036] The present invention comprises the following steps:

[0037] ① Obtain the data F(t) of the variation of the ballistic parameters of the engine at a typical temperature with the working time. The data of the variation of the ballistic parameter n at a representative temperature with the working time t obtained by theoretical calculation or experimental measurement is expressed as F(t) = {(t1,n1), (t2,n2), ..., (t max ,n max )}, the typical temperature should be at least two representative temperatures, generally not less than three (such as low temperature, normal temperature, high temperature), and should include the boundary of the engine operating temperature as much as possible;

[0038] ②According to the required temperature value T x , select the required temperature T x The two closest typical temperatures T1 and T2 and their corresponding data of ballistic parameters changing with running time F1(t) and F2(t) are used as the basis for calculation. F1(t) = {(t11, n11), (t12, n12), ..., (t1 max ,n1 max )}, F2(t)={(t21,n21), (t22,n22),..., (t2 max ,n2 max )}, where t1 is the running time, n1 is the value of the internal ballistic parameter at t1, t2 is the running time, n2 is the value of the internal ballistic parameter at t2;

[0039] ③The longest operating time t1 based on the data obtained at typical temperatures T1 and T2 max , t2 max , use the interpolation method to calculate the required temperature value T x The maximum running time of tx maxBased on the maximum operating time t1 obtained by theoretical calculation or experimental measurement at temperature T1. max The maximum operating time t2 obtained by theoretical calculation or experimental measurement at temperature T2 max , for the required temperature value T x The maximum running time of tx max Perform interpolation calculation, the tx max It is expressed by the following formula:

[0040]

[0041] Where: tx max is the required temperature value T x Maximum running time; t1 max It is the maximum operating time obtained by theoretical calculation or experimental measurement under the required temperature value T1; t2 max It is the maximum operating time obtained by theoretical calculation or experimental measurement under the required temperature value T2;

[0042] ④Based on t1 max , t2 max ,tx max The value is divided into N equal parts, and the time series b1 is obtained after N equal parts i , b2 i , bx i . The N value can be selected according to demand. The larger the N value, the higher the calculation accuracy.

[0043] ⑤ Use the interpolation method to divide the data of the trajectory parameters in F1(t) and F2(t) with the running time into N equal parts, and obtain b1 for each time division i 、b2 i The data of the trajectory parameters n1 i ′、n2 i ′, its data set is C1={n11′,n12′,...,n1 N ′}, C2={n21′, n22′,..., n2 N ′}. Let i={1, 2,..., N-1, N}, j={2, 3,..., t1 n-1 , t1 n}, where t 1n is the number of running times obtained by theoretical calculation or experimental measurement at temperature T1. The continuous data of ballistic parameters changing with time under N equally divided time is calculated by the cyclic algorithm. For each element in i, each element in j needs to be calculated once by the following formula ② to obtain n1 i ′、n2 i ′;

[0044] When the value of the i-th equal-division time is between the j-1th running time and the jth running time, the n1 i ′、n2 i ' is expressed by the following formula:

[0045]

[0046] Where: i is the set of {1, 2, ..., N-1, N}, j is the set of {2, 3, ..., t1 n-1 , t1 n}, t1 j is the jth operating time at temperature T1, t1 (j-1) is the j-1th running time at temperature T1, F1(j) is the ballistic parameter data of the j-1th running time at temperature T1, F1(j-1) is the ballistic parameter data of the j-1th running time at temperature T1, n1 i ′ is the ballistic parameter data of the i-th equal-division time at temperature T1;

[0047] When the value of the i-th divided time is equal to the j-th running time, n1 i The value of ′ is F1(j);

[0048] Use the same method to obtain n2 i ′.

[0049] ⑥Based on n1 i ′、n2 i ′, use the interpolation method to calculate the data nx of the trajectory parameters in each time division i , combined with step ④, tx max The data bx obtained by dividing the value of N into equal parts i , get the required temperature value T x The data Fx′(t) of the trajectory parameters changing with the running time. Fx′(t) is the value bx of each time interval divided into N equal parts. i The corresponding ballistic parameter nx i The set of , denoted as Fx′(t)={(bx1,nx1),(bx2,nx2),...,(bx i ,nx i )}, where bx i The value of tx max The value of the i-th time interval after N equal divisions. i It is expressed by the following formula:

[0050]

[0051] Where: i is the set of {1,2,...,N-1,N}, n1i ′ is the ballistic parameter data of the ith equal-division time at temperature T1, n2 i ′ is the ballistic parameter data of the ith equal time division at temperature T2, b1 i b2 is the value of each time interval after the maximum operating time at temperature T1 is divided into N equal parts, i is the value of each time interval after the maximum operating time at temperature T2 is divided into N equal parts, bx i It is T x The value of each time interval after the maximum operating time at the temperature is divided into N equal parts, nx i It is T x Ballistic parameter data of the i-th equal-division time at temperature.

[0052] This embodiment is based on the internal ballistic data of a certain type of engine at +50℃ and -40℃, taking the center of mass calculation as an example, and calculating the center of mass data at +20℃. In this embodiment, the N value is selected as 1000, and the change of the engine center of mass distance over time at typical temperatures of +50℃ and -40℃ is calculated as follows Figure 2 Under this condition, the data of the change of the center of mass at +20℃ with time were calculated according to the above method, and compared with the theoretical value of the change of the center of mass at +20℃ with time. The comparison results are shown in Figure 3 As shown in the figure, it can be seen that, as predicted, this method is close to the results obtained by theoretical calculations.

Claims

1. A method for calculating engine interior ballistics at any temperature, characterized in that: The following steps are involved: ① Obtain the data F(t) of the engine internal ballistic parameters changing with the working time at typical temperature; ②According to the required temperature value T x , select the required temperature T x The two closest typical temperatures T1 and T2 and the data of their corresponding ballistic parameters changing with running time F1(t) and F2(t) are used as the basis for calculation; ③The longest operating time t1 based on the data obtained at typical temperatures T1 and T2 max , t2 max , use the interpolation method to calculate the required temperature value T x The maximum running time of tx max ; ④Based on t1 max , t2 max ,tx max The value is divided into N equal parts, and the time series b1 is obtained after N equal parts i , b2 i , bx i ; ⑤ Use the interpolation method to divide the data of the trajectory parameters in F1(t) and F2(t) with the running time into N equal parts, and obtain b1 for each time division i 、b2 i The data of the trajectory parameters n1 i ′、n2 i ′; ⑥Based on n1 i ′、n2 i ′, use interpolation to calculate each time division bx i The data of the trajectory parameters nx i , get the required temperature value T x The data Fx′(t) showing the variation of trajectory parameters with running time.

2. The method for calculating engine interior ballistics applicable to any temperature as claimed in claim 1, characterized in that: In the step ①, at least two representative temperatures are selected as typical temperatures.

3. The method for calculating engine interior ballistics applicable to any temperature as claimed in claim 1, characterized in that: In the step ①, the data of the ballistic parameter n changing with the working time t at a representative temperature obtained by theoretical calculation or experimental measurement is expressed as F(t)={(t1, n1), (t2, n2), ..., (t max , n max )}.

4. The method for calculating engine interior ballistics applicable to any temperature as claimed in claim 1, characterized in that: In step ③, the required temperature value T x The maximum running time of tx max The calculation formula is: Where: tx max is the required temperature value T x Maximum running time; t1 max It is the maximum operating time obtained by theoretical calculation or experimental measurement under the required temperature value T1; t2 max It is the maximum operating time obtained based on theoretical calculation or experimental measurement at the required temperature value T2.

5. The method for calculating engine interior ballistics applicable to any temperature as claimed in claim 1, characterized in that: In step ④, the value of N can be selected as required.

6. The method for calculating engine interior ballistics applicable to any temperature as claimed in claim 1, characterized in that: In step ⑤, for each b1 i First, determine whether there is the same time value in F1(t): If so, directly get the b1 i The corresponding n1 i ′; if not, then select the two closest time points in F1(t) and perform interpolation to get n1 i '; Obtain n2 in the same way i ′.

7. The method for calculating engine interior ballistics applicable to any temperature as claimed in claim 1, characterized in that: In step ⑥, Fx′(t) is the time bx i The corresponding ballistic parameter nx i The set of is represented by Fx′(t)={(bx1,nx1),(bx2,nx2),...,(bx i , nx i )}, where bx i The value of tx max The value of the i-th time interval after N equal divisions. The nx i It is expressed by the following formula: Where: i is the set of {1, 2, ..., N-1, N}, n1 i ′ is the ballistic parameter data of the ith equal-division time at temperature T1, n2 i ′ is the ballistic parameter data of the ith equal-division time at temperature T2, b1 i b2 is the value of each time interval after the maximum operating time at temperature T1 is divided into N equal parts, i 、bx i Same, nx i It is T x Ballistic parameter data of the i-th equal-division time at temperature.

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