A multi-propellant zero-dimensional interior ballistic calculation method considering the difference of gas properties

Abstract

The application discloses a kind of multi-propellant zero-dimensional interior ballistic calculation methods considering the difference of gas properties, which includes establishing the physical model of solid rocket engine, obtaining the initial parameters of physical model;According to the initial parameters of physical model and the conservation relation, the transient control equation is established, and the combustion chamber pressure at the current time is obtained;The gas balance of different propellants producing gas at the next time is calculated;Obtain the physical property parameters of mixed gas at the next time;The burning rate and burning area at the next time are calculated;Repeat the above steps until the burning area is 0, and the zero-dimensional interior ballistic calculation is completed.The application considers the mixing process of different propellants producing gas during the combustion process of mixed charge solid rocket engine, and the calculation result is accurate.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of solid rocket engine design, and particularly relates to a multi-propellant zero-dimensional interior ballistic calculation method considering differences in gas properties. BACKGROUND

[0002] Solid rocket engines are the power source of solid rocket weapons, and are widely used due to their simple structure, convenient use and maintenance, etc. The geometric structure and composition of the propellant charge of a solid rocket engine determine the dynamic process of propellant combustion, and ultimately determine the time-thrust curve of the solid rocket weapon. By using interface bonding technology, propellant grain columns with different burning rates and different energies are combined into a whole-stage propellant combined grain column, so that the missile engine can realize flexible output and reliable conversion of multi-stage complex thrust such as launching, speed increasing, cruising and terminal acceleration, and has the characteristics of simple engine structure, convenient thrust adjustment and flexible energy output, which can significantly improve the comprehensive performance of the engine.

[0003] For the calculation of the interior ballistic of a multi-propellant combined charge solid rocket engine, the existing methods mostly only consider the difference in burning rate, and ignore the difference in other physical properties, so there is a certain error in the calculation results. SUMMARY

[0004] In view of the above problems in the prior art, the multi-propellant zero-dimensional interior ballistic calculation method considering differences in gas properties provided by the present application solves the problem that the prior art zero-dimensional interior ballistic calculation is difficult to accurately quantify.

[0005] In order to achieve the above-mentioned application purposes, the technical scheme adopted by the present application is as follows:

[0006] The present application provides a multi-propellant zero-dimensional interior ballistic calculation method considering differences in gas properties, which comprises the following steps:

[0007] S1, a physical model of a solid rocket engine is established, and initial parameters of the physical model are obtained;

[0008] S2, a transient control equation is established according to the initial parameters of the physical model and the conservation relationship, and the combustion chamber pressure at the current time is obtained;

[0009] S3, the gas residue of the gas generated by different propellants at the next time is calculated according to the combustion chamber pressure at the current time;

[0010] S4, the physical property parameters of the mixed gas at the next time are obtained according to the gas residue of the gas generated by different propellants at the next time;

[0011] S5, the burning rate at the next time is calculated according to the current combustion chamber pressure, and the burning area at the next time is calculated;

[0012] S6, repeat steps S1 to S5 until the burning area is 0, and complete the zero-dimensional interior ballistic calculation;

[0013] The transient control equation in step S2 is:

[0014]

[0015]

[0016] Wherein: represents the change of the combustion chamber pressure; P c,x is the combustion chamber pressure at the current time; is the average characteristic velocity of the propellant at the current time; subscript i represents the i-th propellant; is the property parameter of the mixed gas at the current time, Γ i represents the property parameter of the gas produced by the combustion of propellant i; V c is the free volume; p pi is the density of propellant i; r i,x is the burning rate of propellant i at the current time; A bi,x is the burning area of propellant i at the current time; p gi is the gas density of the gas produced by the combustion of propellant i; A t is the nozzle throat area; k i is the specific heat ratio of the gas.

[0017] Further, the physical model parameters in step S1 include: gas density, free volume, propellant density, propellant burning rate, propellant burning area, propellant characteristic velocity, propellant combustion flame temperature, gas gas constant, combustion chamber temperature, combustion chamber pressure, nozzle throat area, and specific heat ratio of the gas.

[0018] Further, the specific process of calculating the gas residual amount m i of the gas produced by different propellants at the next time in step S3 is as follows:

[0019] According to the formula:

[0020] m i,x+1 = m i,x + m bi,x - m outi,x

[0021] m bi,x = Δt p pi A bi,x r i,x

[0022]

[0023] Get the gas residual amount mi,x+1 ; where m i,x m is the mass of propellant i at the current moment; bi,x m is the mass of the combustion gas produced by propellant i in the previous time step; outi,x Δt represents the mass of the gas produced by propellant i in the previous time step; Δt represents the time step.

[0024] Furthermore, the specific process of step S4 is as follows:

[0025] S4-1, the remaining gas volume m generated by different propellants at the next moment. i,x+1 According to the formula:

[0026]

[0027]

[0028]

[0029]

[0030] The combustion flame temperature T of propellant i was respectively... i The gas constant R of propellant i i and the average characteristic velocity c of propellant i i Weighted averages based on weight composition and energy composition are performed to obtain the weighted average combustion flame temperature. Gas constant after weighted average and the average characteristic velocity at the next moment Where n represents the total number of propellant types; q i c represents the mass percentage of the i-th propellant. pi The specific heat ratio at constant pressure for the i-th propellant;

[0031] S4-2, According to the formula:

[0032]

[0033] Calculate the physical properties of the mixed gas at the next moment.

[0034] Furthermore, the specific process for calculating the burning rate at the next moment in step S5 is as follows:

[0035] The combustion chamber pressure P at the next moment is obtained based on the change in combustion chamber pressure. c,x+1 And according to the formula:

[0036]

[0037] Calculate the burning rate r at the next moment. i,x+1; wherein a i is the burning rate coefficient; n i is the pressure exponent.

[0038] Further, the specific method for calculating the burning area at the next moment in step S5 is as follows:

[0039] Based on the burning rate at the next moment, the thickness of the meat burned in a time step is calculated, and the burning area at the next moment is obtained according to the burning surface retreat algorithm or interpolation of the known burning surface thickness curve.

[0040] The beneficial effects of the present application are as follows: the zero-dimensional interior ballistic calculation method provided by the present application considers the mixing process of the gases generated by different propellants during the combustion process of the hybrid charge solid rocket engine, performs real-time weighted average on the physical property parameters of the stock gas based on the mass proportion of the gas, and obtains the physical property parameters of the mixed gas after mixing, which is more in line with the physical process of the actual combustion of the hybrid charge solid rocket engine; the calculation parameters have a large generalization range, and more accurate interior ballistic curves and time-thrust curves can be obtained, which facilitates subsequent optimization of various parameters of the rocket engine. BRIEF DESCRIPTION OF DRAWINGS

[0041] Figure 1 is the flowchart of the present application;

[0042] Figure 2 is the burning surface-thickness curve of the propellant in the embodiment;

[0043] Figure 3 is the time-burning surface curve of the propellant in the embodiment;

[0044] Figure 4 is the calculated interior ballistic curve. DETAILED DESCRIPTION

[0045] The specific embodiments of the present application are described below to facilitate understanding of the present application by those skilled in the art, but it should be clear that the present application is not limited to the scope of the specific embodiments, and for those skilled in the art, it is obvious that various changes are within the spirit and scope of the present application defined and determined by the appended claims, and all applications utilizing the concept of the present application are within the scope of protection.

[0046] As Figure 1 shown, the multi-propellant zero-dimensional interior ballistic calculation method considering the difference in gas properties includes the following steps:

[0047] S1, a physical model of the solid rocket engine is established, and initial parameters of the physical model are obtained;

[0048] S2, establishing transient control equation according to physical model initial parameter and conservation relation, obtaining combustion chamber pressure at current time;

[0049] S3, calculating gas surplus of different propellant generated gas at next time according to combustion chamber pressure at current time;

[0050] S4, obtaining physical property parameter of mixed gas at next time according to gas surplus of different propellant generated gas at next time;

[0051] S5, calculating burning rate at next time according to current combustion chamber pressure, and calculating burning area at next time;

[0052] S6, repeating step S1 to step S5 until burning area is 0, completing zero-dimensional interior ballistic calculation;

[0053] Wherein, transient control equation in step S2 is:

[0054]

[0055]

[0056] Wherein: represents combustion chamber pressure change; P c,x is combustion chamber pressure at current time; is average characteristic velocity of propellant at current time; subscript i represents the i-th propellant; is physical property parameter of mixed gas at current time, Γ i represents physical property parameter of propellant i combustion generated gas; V c is free volume; ρ pi is density of propellant i; r i,x is burning rate of propellant i at current time; A bi,x is burning area of propellant i at current time; ρ gi is gas density of propellant i combustion generated gas; A t is nozzle throat area; k i is specific heat ratio of gas.

[0057] Preferably, in step S2, when solving combustion chamber pressure, 4-order 5-step Rung Kutta format is adopted, and specific steps are as follows:

[0058] Wherein, subscript 0 represents flow parameter at previous time, and subscript k (k=1, 2, …, 5) represents flow parameter at k-th step in Rung Kutta format, then

[0059]

[0060]

[0061]

[0062]

[0063]

[0064]

[0065] Where α kj β k γ k The coefficients are in RungKutta format.

[0066] In step S3, the remaining gas volume m of different propellants at the next time step is calculated. i The specific process is as follows: According to the formula:

[0067] m i,x+1 =m i,x +m bi,x -m outi,x

[0068] m bi,x =Δtρ pi A bi,x r i,x

[0069]

[0070] Obtain the remaining gas volume m of different propellants at the next moment. i,x+1 ; where m i,x m is the mass of propellant i at the current moment; bi,x m is the mass of the combustion gas produced by propellant i in the previous time step; outi,x Δt represents the mass of the gas produced by propellant i in the previous time step; Δt represents the time step.

[0071] The specific process of step S4 is as follows:

[0072] S4-1, the remaining gas volume m generated by different propellants at the next moment. i,x+1 According to the formula:

[0073]

[0074]

[0075]

[0076]

[0077] The combustion flame temperature T of propellant i was respectively... i The gas constant R of propellant i i and the average characteristic velocity c of propellant i i Weighted averages based on weight composition and energy composition are performed to obtain the weighted average combustion flame temperature. Gas constant after weighted average and the average characteristic velocity at the next moment Where n represents the total number of propellant types; q i c represents the mass percentage of the i-th propellant. pi The specific heat ratio at constant pressure for the i-th propellant;

[0078] S4-2, According to the formula:

[0079]

[0080] Calculate the physical properties of the mixed gas at the next moment.

[0081] The specific process for calculating the combustion rate at the next moment in step S5 is as follows: obtain the combustion chamber pressure P at the next moment based on the change in combustion chamber pressure. c,x+1 And according to the formula:

[0082]

[0083] Calculate the burning rate r at the next moment. i,x+1 ;where a i n is the combustion rate coefficient; i This is the pressure index.

[0084] In step S5, when calculating the burning surface area at the next moment, the burning surface area at the next moment can be calculated using the burning surface retreat method. Since the burning surface retreat calculation involves more complex geometric operations and a larger computational load compared to the internal ballistics calculation, in actual calculations, a larger time step can be used for the burning surface retreat calculation, while a smaller time step can be used for the internal ballistics calculation. During the internal ballistics calculation, the burning surface retreat result is interpolated to obtain the burning surface area at the next moment, until the next burning surface retreat operation is performed.

[0085] In the specific implementation of this method, the derivation process of the transient control equation is as follows:

[0086] The first step is to establish the formula for the rate of change of gas volume in the combustion chamber based on the law of conservation of mass:

[0087]

[0088] Where m r The amount of gas in the combustion chamber. This indicates that the variable is differentiated over time. For gas generation rate, This refers to the gas outflow rate;

[0089] The second step is to measure the gas volume m in the combustion chamber. r =ρ g V c Substituting into the formula for the rate of change, we get:

[0090]

[0091] Where ρ g V is the density of the gas. c Free volume;

[0092] The third step is to combine the formulas to obtain a combined formula, and then express the following:

[0093]

[0094]

[0095]

[0096] Substituting these equations into the combination formula yields the transient control equations proposed in this method:

[0097]

[0098] In one embodiment of the present invention, it is assumed that the propellant grain is composed of two propellants, propellant A and propellant B, and the two propellants have different physical properties. It is assumed that the burn surface-to-wall thickness curves of the two propellants are known as follows: Figure 2 As shown, the time-burning surface curves for the two propellants are obtained by interpolating the burnout-wall thickness curves, as follows: Figure 3 As shown. The internal trajectory was calculated using both the balanced pressure method and a multi-propellant zero-dimensional internal trajectory calculation method considering gas combustion differences. Figure 4 As can be seen, compared to the curve obtained by the equilibrium pressure method, the pressure also changes drastically when the combustion surface changes. The curve obtained by the multi-propellant zero-dimensional internal ballistic calculation method, which considers the difference in combustion gases, is smoother and more consistent with the fact that it takes a period of time for the change in combustion surface to be reflected in the change in pressure.

[0099] In summary, the zero-dimensional internal ballistic calculation method provided by this invention considers the mixing process of gas produced by different propellants in a solid rocket engine with mixed propellant combustion. Based on the mass and energy proportions 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 wide range and the calculation results are accurate, which facilitates the subsequent optimization of various parameters of the rocket engine.

Claims

1. A multi-propellant zero-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 parameters of the physical model; S2, establishing a transient control equation according to the initial parameters of the physical model and a conservation relation, and obtaining a combustion chamber pressure at a current time; S3, calculating a gas residue of gas generated by different propellants at a next time according to the combustion chamber pressure at the current time; S4, obtaining physical property parameters of mixed gas at the next time according to the gas residue of gas generated by different propellants at the next time; S5, calculating a burning rate at the next time according to the current combustion chamber pressure, and calculating a burning surface area at the next time; S6, repeating the steps S1 to S5 until the burning surface area is 0, and completing zero-dimensional interior ballistic calculation; The transient control equation in the step S2 is: where: represents the change in combustion chamber pressure; P c,x is the current time combustion chamber pressure; is the current time average characteristic velocity of the propellant; subscript i represents the i-th propellant; Γ is the property parameter of the mixed gas at the current time; i V represents the property parameter of the gas produced by the combustion of the propellant i; c V is the free volume; ρ pi ρ is the density of the propellant i; r i,x r is the burning rate of the propellant i at the current time; A bi,x A is the burning surface area of the propellant i at the current time; ρ gi ρ is the gas density produced by the combustion of the propellant i; A t A is the nozzle throat area; k i k is the specific heat ratio of the gas.

2. The multi-propellant zero-dimensional interior ballistic calculation method considering the difference of gas properties according to claim 1, characterized in that, The physical model parameters in the step S1 include: gas density, free volume, propellant density, propellant burning rate, propellant burning surface area, propellant characteristic velocity, propellant combustion flame temperature, gas gas constant, combustion chamber temperature, combustion chamber pressure, nozzle throat area, and gas specific heat ratio.

3. The multi-propellant zero-dimensional interior ballistic calculation method considering the difference of gas properties according to claim 1, characterized in that, The gas balance m of the next time at which the different propellants produce gas is calculated in step S3 i The specific process is as follows: According to the formula: m i,x+1 = m i,x + m bi,x - m outi,x m bi,x = Δtρ pi A bi,x r i,x m = m + m - m - m i,x+1 ; where m i,x is the mass of gas produced by propellant i at the current time step; m bi,x is the mass of gas produced by propellant i at the previous time step; m outi,x is the outflow mass of gas produced by propellant i at the previous time step; and Δt is the time step.

4. The multi-propellant zero-dimensional interior ballistic calculation method considering the difference in gas properties according to claim 1, characterized by, The specific process of the step S4 is: S4-1, the gas remaining amount m generated by the different propellant at the next time i,x+1 , according to the formula: i i i wherein n represents the total number of propellants; q i is the mass proportion of the i-th propellant; c pi is the specific heat ratio at constant pressure of the i-th propellant.​​​​​​ S4-2, according to the formula: calculating the physical property parameters of the mixed fuel gas at the next time 5. The method of claim 1, wherein the method is a multi-propellant zero-dimensional interior ballistic calculation method considering a difference in gas properties, characterized by, The specific process of calculating the burning rate at the next time in the step S5 is: According to the pressure change of the combustion chamber, the pressure P of the next moment of the combustion chamber is obtained c,x+1 and according to the formula: calculating the burning rate r for the next time i,x+1 ; where a i is the burning rate coefficient; n i is the pressure exponent.

6. The method of claim 1, wherein the method is a multi-propellant zero-dimensional interior ballistic calculation method considering a difference in gas properties, characterized by, The specific method of calculating the burning surface area at the next time in the step S5 is: Based on the burning rate at the next time, a thickness of the meat within a time step is calculated, and the burning surface area at the next time is obtained according to a burning surface recession algorithm or interpolation of a known burning surface thickness curve.

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