A method for calculating the one-dimensional internal ballistics of multiple propellants that considers differences in gas combustion properties

Abstract

This invention discloses a one-dimensional internal ballistic calculation method for multi-propellant rocket engines that considers differences in gas properties. The method includes: establishing a physical model of a solid rocket motor; establishing a transient control equation set to calculate the density of the mixed gas, combustion chamber temperature, gas velocity, and combustion chamber pressure at the next time step; obtaining the remaining gas volume of different propellants at the next time step; updating the weighted average of physical property parameters; calculating the burning rate and burning surface area at the next time step; repeating the above operations until the propellant grain is completely burned out, thus completing the one-dimensional internal ballistic calculation. This invention considers the mixing process of gases generated by different propellants during the combustion of a mixed-charge solid rocket engine, resulting in accurate calculation results.

Description

Technical Field

[0001] The invention relates to the field of solid rocket engine design technology, specifically to a one-dimensional internal ballistic calculation method for multiple propellants that takes into account differences in gas properties. Background Technology

[0002] Solid rocket motors are the power source for solid rocket weapons, widely used due to their simple structure and ease of use and maintenance. The geometry and composition of the propellant charge in a solid rocket motor determine the dynamic process of propellant combustion, ultimately shaping the time-thrust curve of the solid rocket weapon. By using techniques such as interface bonding to create integral propellant charge combinations with propellant grains of different burning rates and energies, missile engines can achieve flexible and reliable output and conversion of complex thrust across multiple stages, including launch, acceleration, endurance, and terminal acceleration. This approach offers advantages such as simple engine structure, convenient thrust adjustment, and flexible energy output, significantly improving the overall performance of the engine.

[0003] For the calculation of the internal trajectory of solid rocket motors with multiple propellant combinations, most existing methods only consider the difference in burning rate, while ignoring the differences in other physical properties, resulting in certain errors in the calculation results. Summary of the Invention

[0004] To address the aforementioned shortcomings in the prior art, the invention provides a one-dimensional internal ballistic calculation method for multiple propellants that considers differences in gas properties, solving the problem of the difficulty in accurately quantifying one-dimensional internal ballistic calculations in the prior art.

[0005] To achieve the aforementioned objectives, the technical solution adopted by the invention is as follows:

[0006] A method for calculating the one-dimensional internal ballistics of multiple propellants that considers differences in gas properties is provided, comprising the following steps:

[0007] S1. Establish a physical model of the solid rocket motor and obtain the initial physical model parameters;

[0008] S2. Based on the initial physical model parameters and conservation relationships, establish a set of transient control equations to calculate the density of the mixed gas, combustion chamber temperature, gas flow rate and combustion chamber pressure at the next moment.

[0009] S3. Calculate the remaining amount of gas produced by different propellants at the next moment based on the density of the mixed gas and the gas flow rate.

[0010] S4. Update the weighted average of physical property parameters based on the remaining amount of gas produced by different propellants at the next moment;

[0011] S5. Calculate the combustion rate at the next moment based on the combustion chamber pressure at the next moment, and calculate the burning surface area at the next moment.

[0012] S6. Repeat steps S1 to S5 until the propellant grain is completely burned up, thus completing the one-dimensional internal ballistic calculation.

[0013] Furthermore, the physical model parameters in step S1 include: propellant burning surface perimeter, combustion chamber area curve, combustion chamber pressure, propellant combustion temperature, combustion chamber temperature, gas density, gas flow rate, propellant density, and propellant burning rate.

[0014] Furthermore, the transient control equations in step S2 are as follows:

[0015]

[0016] Where ρ g,k+1 T represents the density of the gas mixture at the next moment; k+1 V represents the combustion chamber temperature at the next moment. k+1 P represents the gas flow rate at the next moment. c,k+1 V represents the combustion chamber pressure at the next moment. x,k+1 A represents the component of the gas flow velocity along the x-direction at the next moment; k C is the channel area at the current moment; i,k ρ is the circumference of the burning surface of the i-th propellant at the current moment; pi r is the density of the i-th propellant; i,k T is the burning rate of the i-th propellant at the current moment; i Let be the combustion temperature of the i-th propellant; be the specific heat ratio at constant volume of the i-th propellant; and c. vi Let i be the specific heat ratio at constant volume for the i-th propellant. For c vi The weighted average of the physical properties of the gas quality at the current moment; D and E are intermediate parameters.

[0017] Furthermore, the specific process of step S3 is as follows:

[0018] According to the formula:

[0019] m i,k+1 =m i,k +m bi,k -m outi,k

[0020]

[0021]

[0022] Obtain the remaining gas volume m of different propellants at the next moment. i,k+1 ; where m i,k m is the mass of propellant i at the current moment; bi,km is the mass of the combustion gas produced by propellant i in the previous time step; outi,k A represents the outflow mass of the combustion gas produced by propellant i in the previous time step. bi,k Δx represents the burning surface area of ​​propellant i at the current moment. j The length of the j-th spatial grid is used to solve the transient control equations; Δt is the time step.

[0023] Furthermore, the specific process of step S4 is as follows:

[0024] According to the formula:

[0025]

[0026] Update the weighted average of the physical property parameters to obtain the weighted average of the physical property parameters at the next time step. Where n is the total number of propellant types.

[0027] Furthermore, the specific process for calculating the burning rate at the next moment in step S5 is as follows:

[0028] According to the formula:

[0029]

[0030] Calculate the burning rate at the next moment; where a i n is the combustion rate coefficient; i This is the pressure index.

[0031] Furthermore, the specific method for calculating the burning surface area at the next moment in step S5 is as follows:

[0032] Based on the burning rate at the next moment, calculate the thickness of the burn within one time step, and obtain the burn area at the next moment by using the burn surface regression algorithm or by interpolating the known burn surface thickness curve.

[0033] The beneficial effects of the invention are as follows: The one-dimensional internal ballistic calculation method provided by the invention takes into account the mixing process of gas produced by different propellants in the combustion process of a solid rocket engine with mixed propellant. Based on the mass ratio of the gas, the physical property parameters of the existing gas are weighted and averaged in real time, and the obtained physical property parameters are used as the physical property parameters of the mixed gas. The calculation parameters have a large range and the calculation results are accurate. It can accurately simulate the actual working situation of the engine and facilitate the subsequent optimization of various parameters of the rocket engine. Attached Figure Description

[0034] Figure 1 This is a flowchart of the present invention;

[0035] Figure 2 The curve showing the circumference of the burning surface of the propellant;

[0036] Figure 3 This is the channel area curve of the combustion chamber;

[0037] Figure 4 The combustion rate curve at the head of the combustion chamber;

[0038] Figure 5 The combustion rate curve at the tail end of the combustion chamber;

[0039] Figure 6 The pressure curve at the head of the combustion chamber;

[0040] Figure 7 This is the pressure curve at the head of the combustion chamber. Detailed Implementation

[0041] The specific embodiments of the invention are described below to enable those skilled in the art to understand the invention. However, it should be understood that the invention is not limited to the scope of the specific embodiments. For those skilled in the art, any changes that are within the spirit and scope of the invention as defined and determined by the appended claims are obvious. All inventions utilizing the inventive concept are protected.

[0042] like Figure 1 As shown, the multi-propellant one-dimensional internal ballistic calculation method considering differences in gas properties includes the following steps:

[0043] S1. Establish a physical model of the solid rocket motor and obtain the initial physical model parameters;

[0044] S2. Based on the initial physical model parameters and conservation relationships, establish a set of transient control equations to calculate the density of the mixed gas, combustion chamber temperature, gas flow rate and combustion chamber pressure at the next moment.

[0045] S3. Calculate the remaining amount of gas produced by different propellants at the next moment based on the density of the mixed gas and the gas flow rate.

[0046] S4. Update the weighted average of physical property parameters based on the remaining amount of gas produced by different propellants at the next moment;

[0047] S5. Calculate the combustion rate at the next moment based on the combustion chamber pressure at the next moment, and calculate the burning surface area at the next moment.

[0048] S6. Repeat steps S1 to S5 until the propellant grain is completely burned up, thus completing the one-dimensional internal ballistic calculation.

[0049] In practical implementation, when solving the transient control equations, the transient control equations can be dimensionless and transformed into the following conservation scheme:

[0050]

[0051] in

[0052] The governing equations under the above conservation scheme can be written in matrix form as follows:

[0053]

[0054] in:

[0055]

[0056]

[0057]

[0058] For the above matrix, the MacCormack scheme can be used to discretize the equation. Assuming the spatial step size is Δx′ and the time step size is Δt′, the subscript j represents the j-th node in space, and the subscript k represents the k-th time node in the current calculation. The specific steps are as follows:

[0059] The prediction step uses forward differencing to approximate the spatial derivative, and then uses a first-order Taylor expansion to approximate the prediction value:

[0060]

[0061]

[0062] Next, the calculated estimated values ​​are substituted into the formulas for calculating F and J to obtain the estimated values ​​of F and J. and

[0063] The correction step then approximates the time derivative using the average of the forward difference and the backward difference with the predicted value, and then approximates the corrected value using a first-order Taylor expansion:

[0064]

[0065]

[0066]

[0067] Calculate the value of U at the (k+1)th time node using the following formula, and then calculate the flow parameters at the (k+1)th time node based on U:

[0068]

[0069]

[0070] That is, to obtain the density of the gas mixture, the combustion chamber temperature, and the gas flow rate at the next moment, and then according to P c,k+1 =ρ g,k+1 T k+1 The combustion chamber pressure at the next moment can then be obtained. The subscript av represents the average of the predicted value and the corrected value.

[0071] In practical implementation, initial values ​​for the flow parameters need to be provided when calculating from the initial moment. Any knowledge related to the problem under consideration can be utilized when determining the initial values ​​of the flow parameters, as long as a suitable initial condition can be given. For example, for the problem studied in this invention, when the gas flows through the nozzle, ρ and T decrease, while V increases. Therefore, initial values ​​consistent with this trend should be selected. In this case, it can be assumed that the flow field variables are linear functions of x, given by the following formula:

[0072]

[0073] In one embodiment of the present invention, it is assumed that the propellant of the solid rocket motor consists of two propellants, A and B, wherein propellant A has high energy and a fast burning rate, while propellant B has low energy and a slow burning rate. The burning surfaces of the two propellants are as follows: Figure 2 As shown, the passage area of ​​the combustion chamber is as follows: Figure 3 As shown in the figure. This embodiment calculates the internal ballistic curves considering only propellant A, only propellant B, and both propellants. The burning rate curves at the head and tail of the combustion chamber in the three cases are shown in the figure. Figure 4 and Figure 5 As shown in the figure, the burning rate is fastest when only propellant A is considered, slowest when only propellant B is considered, and falls somewhere in between when considering a combined propellant charge of propellant A and propellant B. The pressure curves at the head and tail of the combustion chamber are shown in the figure. Figure 6 and Figure 7 As shown, at the head of the combustion chamber, the pressure is highest when only propellant A is considered, lowest when only propellant B is considered, and intermediate when considering a combination of propellants A and B. At the tail of the combustion chamber, the pressure corresponding to the combination of propellant A and B is slightly higher than that of propellant A alone. This is because the first half of the propellant charge consists of propellant A, which has a faster burning rate and higher burning temperature, resulting in a higher gas flow rate than propellant B, thus causing some gas to accumulate in the rear half of the combustion chamber. As can be seen from the embodiments, the one-dimensional internal ballistic calculation method provided by this invention can effectively simulate the combustion process of a mixed-propellant solid rocket engine, consistent with the actual operation of the engine.

[0074] The one-dimensional internal ballistic calculation method provided by this invention considers the mixing process of gas produced by different propellants in the combustion process of a solid rocket engine with mixed propellant. Based on the mass ratio of the gas, the physical property parameters of the existing gas are weighted and averaged in real time, and the obtained physical property parameters are used as the physical property parameters of the mixed gas. The calculation parameters have a large range and the calculation results are accurate. It can accurately simulate the actual working scenario of the engine and facilitate the subsequent optimization of various parameters of the rocket engine.

Claims

1. A multi-propellant one-dimensional interior ballistic calculation method considering differences in gas properties, characterized by, The method comprises the following steps: S1, establishing a physical model of the solid rocket engine and obtaining initial physical model parameters; S2, establishing a transient control equation set according to the initial physical model parameters and conservation relations, and calculating the density of mixed gas, the combustion chamber temperature, the gas flow rate and the combustion chamber pressure at the next time; S3, calculating the gas residual amount of different propellants at the next time according to the density of mixed gas and the gas flow rate; S4, updating the weighted average value of physical property parameters according to the gas residual amount of different propellants at the next time; S5, calculating the burning rate at the next time according to the combustion chamber pressure at the next time, and calculating the burning area at the next time; S6, repeating steps S1 to S5 until the propellant grain is completely burned out, and completing one-dimensional interior ballistic calculation.

2. The multi-propellant one-dimensional interior ballistic calculation method considering the difference in gas properties according to claim 1, characterized in that, The physical model parameters in step S1 include: propellant burning perimeter, area curve of the combustion chamber, combustion chamber pressure, propellant combustion temperature, combustion chamber temperature, gas density, gas flow rate, propellant density, and propellant burning rate.

3. The multi-propellant one-dimensional interior ballistic calculation method considering the difference in gas properties according to claim 1, characterized by, The transient control equation set in step S2 is: where p g,k+1 is the density of the mixture at the next time; T k+1 is the combustion chamber temperature at the next time; V k+1 is the flow rate of the gas at the next time; P c,k+1 is the pressure of the combustion chamber at the next time; V x,k+1 is the component of the flow rate of the gas at the next time in the x direction; A k is the channel area at the current time; C i,k is the burning surface perimeter of the i-th propellant at the current time; p pi is the density of the i-th propellant; r i,k is the burning rate of the i-th propellant at the current time; T i is the combustion temperature of the i-th propellant; c vi is the specific heat ratio at constant volume of the i-th propellant, is the specific heat ratio at constant volume of the i-th propellant, vi is the weighted average of the physical property parameters of the gas mass at the current time; D and E are both intermediate parameters.

4. The multi-propellant one-dimensional interior ballistic calculation method considering the difference in gas properties according to claim 3, characterized by, The specific process of step S3 is: According to the formula: m i,k+1 = m i,k + m bi,k - m outi,k m is the remaining mass of the gas produced by the different propellants at the next time instant i,k+1 ; where m i,k is the mass of the gas produced by the propellant i at the current time instant; m bi,k is the mass of the gas produced by the propellant i at the previous time step; m outi,k is the outflow mass of the gas produced by the propellant i at the previous time step; A bi,k is the burning area of the propellant i at the current time instant; Δx j is the length of the jth spatial grid divided when solving the transient control equations; and Δt is the time step.

5. The multi-propellant zero-dimensional interior ballistic calculation method considering the difference of gas properties according to claim 3, wherein, The specific process of step S4 is: According to the formula: Updating the weighted average of the physical property parameters to obtain the weighted average of the physical property parameters at the next time where n is the total number of propellants.

6. The multi-propellant one-dimensional interior ballistic calculation method considering the difference in gas properties according to claim 3, characterized in that, The specific process of calculating the burning rate at the next time in step S5 is: According to the formula: calculating the burning rate of the next time; wherein a i is the burning rate coefficient; n i is the pressure exponent.

7. The method of claim 1, wherein the method is a one-dimensional internal ballistic calculation method for multiple propellants considering differences in gas properties. The specific method of calculating the burning area at the next time in step S5 is: Based on the burning rate at the next time, the thickness of the meat burned in a time step is calculated, and the burning area at the next time is obtained according to the burning surface retreat algorithm or interpolation of the known burning surface thickness curve.

Images