Carbon dioxide phase change ejection attitude prediction method considering rigid-flexible coupling

Abstract

The invention discloses a carbon dioxide phase change ejection attitude prediction method considering rigid-flexible coupling, and belongs to the technical field of cold ejection. The implementation method comprises the following steps: describing thermodynamic parameters of carbon dioxide by adopting an S-R-K state equation, and deducing an analytical expression of key thermodynamic parameters through a deviation function method; establishing a closed state equation set of the inner ballistic model according to the law of conservation of mass, the law of conservation of energy, the gas flow equation and the S-R-K real gas state equation; in Abaqus, a cold ejection model considering rigid-flexible coupling is established; gravity is applied to the whole cold ejection model, a low-pressure chamber pressure-time curve obtained through calculation of the closed state equation set serves as a thrust load, reverse pressure is applied to the bottom of the launch canister, and the counter-acting force of thrust on the launch canister when the aircraft leaves the canister is simulated; setting a lower reference point of a tire in the frame as a fixed constraint; and setting a kinetic analysis step and submitting operation to realize attitude prediction of the aircraft ejection process considering rigid-flexible coupling.

Description

Technical Field

[0001] The present invention belongs to the technical field of cold ejection, and in particular relates to a posture prediction method for carbon dioxide phase change ejection considering rigid-flexible coupling. Background Art

[0002] The vehicle-mounted mobile launch of aircraft is one of the main forms of rapid launch and the main development direction of aircraft land launch. At present, the launch methods of aircraft are mainly divided into hot launch and cold ejection. The hot launch technology is relatively mature, with a simple structure and high reliability, but the high-temperature and high-speed tail jet generated during launch may cause damage to the launch device and surrounding personnel. Therefore, it is not suitable for vehicle-mounted mobile launch, while the cold ejection method is more friendly to the mobile launch of aircraft. At present, the common cold ejection methods are: compressed air ejection, gas generator ejection, gas-steam ejection and supercritical carbon dioxide phase change ejection. Compared with the traditional gas-type and gas-steam ejection methods, the compressed air ejection and supercritical carbon dioxide phase change ejection do not have the problem of gas ablation of the aircraft, no need to set up heat insulation devices, no ablation pollution of the launch tube, good reusability, no high-temperature gas flow, high infrared concealment, and good environmental adaptability. Further comparison of compressed air ejection and carbon dioxide phase change ejection shows that within a given temperature and pressure range, the specific internal energy of supercritical carbon dioxide is greater than that of air. The compressed air ejection method requires more fluid to eject the same mass of aircraft, which will cause the ejection device to be relatively large and bulky. Therefore, in order to solve the problems of low pressure of traditional gas medium as a power source, large device volume and high energy consumption of air compressor, it is necessary to study supercritical carbon dioxide phase change ejection. The research focus of supercritical carbon dioxide phase change ejection is on the attitude prediction of the aircraft during the ejection process. The most important attitude is the speed of the aircraft when it leaves the barrel and the acceleration of the aircraft during the ejection process. Among them, the aircraft's exit speed is related to whether the current working fluid can meet the ejection requirements of the aircraft. Too small exit speed will cause the GNC control strategy of the aircraft after exiting the barrel to fail, resulting in the ejection failure of the aircraft; and the acceleration of the aircraft during the ejection process is related to whether the overload of the aircraft during the ejection process meets the design requirements of the aircraft. Too large overload acceleration will cause the structural failure of the aircraft, and then cause the launch failure.

[0003] The existing methods for predicting the attitude of aircraft using supercritical carbon dioxide phase change ejection are as follows: 1) Designing a supercritical carbon dioxide ejection device for physical testing, using supercritical carbon dioxide with different initial masses for ejection testing, and using velocity sensors and acceleration sensors to record the attitude parameters of the aircraft during the ejection process, and comparing the aircraft's exit velocity from the cylinder and the acceleration during the ejection process in the test data to obtain a suitable initial working fluid. 2) Treating the entire ejection system as a rigid body, using an internal ballistic model to predict the attitude of the aircraft during the ejection process through numerical simulation. The problems and defects of the existing technology are as follows: 1) The cost of using an experimental method to study the attitude prediction method of aircraft using supercritical carbon dioxide phase change ejection is too high, and a complete ejection system needs to be developed. 2) The existing internal ballistic model, which studies the attitude prediction of aircraft using supercritical carbon dioxide ejection through numerical simulation, focuses on aircraft masses below 2000kg, and there is a lack of research on large-mass aircraft, which cannot fully reflect the advantages of supercritical carbon dioxide as an ejection working fluid. 3) Most existing internal ballistic models treat the ejection fluid as an ideal gas, but the supercritical carbon dioxide pressure is relatively high, and the classic ideal gas assumption is no longer applicable. Using ideal gas for numerical simulation will lead to large deviations in thermal properties. 4) Existing internal ballistic models treat the entire ejection system as a rigid body during modeling, ignoring the rigid-flexible coupling characteristics of the aircraft-launch tube-launch vehicle during the ejection process, resulting in errors between the attitude prediction of the aircraft during the ejection process and the actual situation. Summary of the invention

[0004] The purpose of the present invention is to provide a posture prediction method for carbon dioxide phase change ejection considering rigid-flexible coupling. By considering the ejection working medium as a real gas, the Soave-Redlich-Kwong (SRK) state equation is used to describe the thermodynamic parameters of carbon dioxide, so as to improve the calculation accuracy of carbon dioxide when the state changes; on the basis of the SRK state equation, the analytical expressions of key thermodynamic parameters are derived by the deviation function method; the flow of high-pressure gas from a high-pressure chamber to a low-pressure chamber is regarded as an isentropic flow, and the viscosity is ignored and the flow equation is obtained by introducing the Noorli method; according to the law of conservation of mass, the law of conservation of energy, the gas flow equation and the SRK real gas state equation, the expressions of the internal ballistic equations of the high-pressure chamber and the low-pressure chamber are obtained, and the high-pressure chamber, the low-pressure chamber and the low-pressure chamber are combined. The closed state equation group of the internal ballistic model is obtained by obtaining the expression of the internal ballistic equation in the chamber; the initial conditions are set for the closed state equation group of the internal ballistic model, and the closed state equation group of the internal ballistic model is solved by the fourth-order Runge-Kutta method to obtain the attitude parameters and thermodynamic parameters of the aircraft during the ejection process, wherein the thermodynamic parameters include the pressure-time curve of the low-pressure chamber; by changing the initial mass of the aircraft in the initial conditions, the ejection simulation prediction of a large-mass aircraft with supercritical carbon dioxide as the ejection working fluid can be realized, thereby reducing the experimental cost; in Abaqus, the actual physical model of the transport vehicle is modeled and meshed according to the initial conditions, the aircraft is set as a rigid body, and a cold ejection model considering rigid-flexible coupling is established; a -9.8 m / s is applied to the entire cold ejection model 2 The gravity of the low-pressure chamber is calculated by the closed state equation group and the pressure-time curve of the low-pressure chamber is applied as the thrust load to the bottom of the aircraft. The reverse pressure is applied to the bottom of the launch tube to simulate the reaction force of the thrust on the launch tube when the aircraft leaves the tube. The lower reference point of the tire in the frame is set as a fixed constraint. The dynamic analysis step is set and the operation is submitted to realize the attitude prediction of the aircraft ejection process considering rigid-flexible coupling. The attitude parameters include velocity and acceleration. Thermodynamic parameters include high-pressure chamber thermodynamic parameters and low-pressure chamber thermodynamic parameters.

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

[0006] The present invention discloses a method for predicting the posture of carbon dioxide phase change ejection considering rigid-flexible coupling, comprising the following steps:

[0007] Step 1: Use the Soave-Redlich-Kwong (SRK) state equation to describe the thermodynamic parameters of carbon dioxide, improve the calculation accuracy of carbon dioxide when the state changes, derive the analytical expressions of key thermodynamic parameters through the deviation function method, and equate the thermodynamic parameters of real gas to two parts consisting of deviation terms and ideal gas values. Derived the deviation terms and ideal gas values ​​separately, the deviation terms and ideal gas values ​​are added to obtain the analytical expressions of the thermodynamic parameters of real gas.

[0008] Step 1.1, establish the real gas equation of supercritical carbon dioxide, that is, the SRK (Soave-Redlich-Kwong) state equation, which is expressed as follows:

[0009]

[0010] Where p is pressure, T is temperature, v is gas molar volume, R is universal gas constant, ω is material factor, α(T,ω) is correction function related to working fluid temperature, a and b are specific material coefficients;

[0011] The “deviation function method” is used to model the thermodynamic parameters of real gas, that is, the thermodynamic parameters of real gas are regarded as consisting of two parts: ideal gas value and deviation term, and the expression is:

[0012] χ(p,T)=χ i +△χ(p,T) (2)

[0013] Among them, χ is the real gas thermodynamic parameter, χ i is the ideal gas thermodynamic parameter, △χ is the deviation term;

[0014] Step 1.2: Obtain the deviation terms of thermodynamic parameters according to the laws of thermodynamics and the SRK equation of state.

[0015] From the first equation of thermodynamics, we know:

[0016]

[0017] Among them, c v is the constant volume specific heat capacity, V is the specific volume, keeping the temperature constant, the above formula is integrated with the specific volume to obtain:

[0018]

[0019] When the specific volume approaches infinity, the specific internal energy is only related to the temperature. Therefore, the first term in the above formula is the specific internal energy of the ideal gas, and the second term is the deviation term of the specific internal energy. The specific expression is:

[0020]

[0021] Taking partial differential of the SRK equation with respect to temperature, we get:

[0022]

[0023] Among them, S is the coefficient related to the material properties, T c is the critical temperature, T r For comparison of temperature;

[0024] The relationship between specific volume and molar volume is:

[0025] v=MV (7)

[0026] Where M is the molar mass;

[0027] Substituting formula (6) into formula (5) yields:

[0028]

[0029] In order to convert the formula into a form related to temperature and pressure, the compression factor Z is introduced, and the expression is:

[0030]

[0031] According to the SRK state equation, the compression factor satisfies the following relationship:

[0032] Z 3 -Z 2 +(ABB 2 )Z-AB=0 (10)

[0033] Among them, A and B are variables related to pressure and temperature:

[0034]

[0035] Substituting equations (9) and (11) into equation (8) yields the deviation term of the specific internal energy:

[0036]

[0037] Similarly, the deviation term of specific enthalpy is:

[0038]

[0039] Among them, R g is the specific gas constant;

[0040] The deviation term of the constant volume specific heat capacity is:

[0041]

[0042] Step 1.3: Use NASA polynomials to fit the ideal values ​​of thermodynamic parameters as polynomials of temperature.

[0043] The specific heat capacity of an ideal gas at constant pressure is expressed as:

[0044]

[0045] The relationship between the specific heat capacity at constant volume and the specific heat capacity at constant pressure of an ideal gas is:

[0046]

[0047] The ideal value of specific heat capacity at constant volume is:

[0048]

[0049] According to the relationship between the specific enthalpy of an ideal gas and its specific heat capacity at constant pressure, the specific enthalpy of an ideal gas is:

[0050]

[0051] According to the relationship between the ideal gas specific internal energy and the specific heat capacity at constant volume, the ideal gas specific internal energy is:

[0052]

[0053] The ideal values ​​of thermodynamic parameters include the ideal gas specific heat capacity at constant pressure, the ideal gas specific heat capacity at constant volume, the ideal gas specific enthalpy, and the ideal gas specific internal energy, as shown in equations (15), (17), (18), and (19), respectively.

[0054] Step 1.4: Add the deviation terms derived in step 1.2 and the ideal gas values ​​derived in step 1.3 to obtain the analytical expressions of the thermodynamic parameters of the real gas.

[0055] Step 2: The flow of high-pressure gas from the high-pressure chamber to the low-pressure chamber is regarded as isentropic flow, and the flow equation is obtained by ignoring the viscosity and using the Noorli method. The expression of the flow equation is:

[0056]

[0057] Among them: the subscript "1" represents the parameters corresponding to the high-pressure chamber, and the subscript "2" represents the gas parameters corresponding to the low-pressure chamber (the subsequent representation method remains unchanged); μ x is the flow correction factor, S c is the flow area (control valve size), and k is the air adiabatic index.

[0058] Step 3: According to the law of conservation of mass, the law of conservation of energy, the gas flow equation and the SRK real gas state equation, the interior ballistic equation of the high-pressure chamber is obtained; according to the law of conservation of mass, the law of conservation of energy, the gas flow equation and the SRK real gas state equation, the expression of the interior ballistic equation of the low-pressure chamber is obtained; the expression of the ballistic equation of the high-pressure chamber and the expression of the ballistic equation of the low-pressure chamber are combined to obtain the closed state equation group of the interior ballistic model.

[0059] Step 3.1, according to the law of conservation of mass, the law of conservation of energy, the gas flow equation and the SRK real gas state equation, the internal ballistic equation of the high pressure chamber is obtained as follows:

[0060]

[0061] Among them, V H is the volume of the high pressure chamber;

[0062] Step 3.2, according to the law of conservation of mass, the law of conservation of energy, the gas flow equation and the SRK real gas state equation, the internal ballistic equation of the low-pressure chamber is obtained as follows:

[0063]

[0064] Among them, m e is the mass of the aircraft, L is the distance traveled by the aircraft, S t is the cross-sectional area of ​​the launch tube, v e is the speed of the projectile exiting the tube, p a is atmospheric pressure;

[0065] Step 3.3: Combine the internal ballistic equations of the high and low pressure chambers in step 3.1 and step 3.2 to obtain the closed state equations of the internal ballistic model, expressed as:

[0066]

[0067] Step 4: Set initial conditions for the closed state equation group of the interior ballistic model, and solve the closed state equation group of the interior ballistic model in step 3 by the fourth-order Runge-Kutta method to obtain the attitude parameters and thermodynamic parameters of the aircraft during the ejection process, where the thermodynamic parameters include the pressure-time curve of the low-pressure chamber.

[0068] Step 4.1: The initial conditions set for the closed state equations of the interior ballistic model include the cross-sectional area S of the launch tube t 、Aircraft mass m e , the initial temperature of the high pressure chamber T 1,0 , the initial pressure of the high pressure chamber p 1,0 、The volume of the high pressure chamber V H , Control valve size S c , the initial temperature of the low pressure chamber T 2,0 , the initial pressure of the low pressure chamber p 2,0 , the initial chamber volume V of the low pressure chamber L,0 .

[0069] Step 4.2: Using the initial conditions in step 4.1, solve the closed state equations in step 3.3 to obtain the attitude parameters and thermodynamic parameters of the aircraft during the ejection process. The attitude parameters include the speed and acceleration of the aircraft; the thermodynamic parameters include the pressure-time curve of the low-pressure chamber.

[0070] Step 5: In Abaqus, the actual physical model of the transport vehicle is modeled according to the initial conditions in step 4. The frame, launch tube, aircraft and adapter are modeled and meshed respectively. The aircraft is set as a rigid body using rigid body constraints, and the inner surface of the adapter is bound to the corresponding outer surface of the aircraft using binding constraints. A cold ejection model considering rigid-flexible coupling is established. A -9.8 m / s force is applied to the entire cold ejection model. 2 The low-pressure chamber pressure-time curve obtained in step 4 is applied to the bottom of the aircraft as a thrust load, and a reverse pressure is applied to the bottom of the launch tube to simulate the reaction force of the thrust on the launch tube when the aircraft leaves the tube; the lower reference point of the tire in the frame is set as a fixed constraint; the dynamic analysis step is set and the operation is submitted, and the attitude parameters in the ejection process considering the rigid-flexible coupling effect are obtained in the post-processing module, that is, the attitude prediction of the carbon dioxide phase change ejection considering the rigid-flexible coupling is realized.

[0071] Step 5.1. In order to consider the rigid-flexible coupling effect, a cold ejection model considering rigid-flexible coupling is established in Abaqus; the adapter is modeled using C3D8R solid elements, the frame, launch tube and aircraft are modeled using S4R shell elements, and the adapter, frame, launch tube and aircraft are meshed;

[0072] Step 5.2, establish a binding constraint between the inner surface of the adapter and the corresponding outer surface of the aircraft, and set a rigid body constraint on the aircraft;

[0073] Step 5.3: Apply -9.8m / s to the entire cold ejection model 2 The gravity of the vehicle is applied, and the low-pressure chamber pressure-time curve obtained in step 4.2 is used as the thrust load to the bottom of the vehicle; reverse pressure is applied to the bottom of the launch tube to simulate the reaction force of the thrust on the launch tube when the vehicle leaves the tube; the lower reference point of the tire in the frame is set as a fixed constraint; set the dynamic analysis step and submit the calculation;

[0074] Step 5.4: After the calculation is completed, the attitude parameters of the aircraft during the ejection process are extracted in the post-processing of Abaqus, including the speed and acceleration of the aircraft during the ejection process, and then the attitude prediction results of the carbon dioxide phase change ejection considering the rigid-flexible coupling are obtained, so as to realize the attitude prediction of the aircraft ejection process considering the rigid-flexible coupling.

[0075] Step 5.5: Modify the aircraft mass m in step 4.1 e By repeating the above operations, the ejection simulation prediction of a large-mass aircraft using supercritical carbon dioxide as the ejection fluid can be realized.

[0076] Beneficial effects:

[0077] 1. The present invention discloses a posture prediction method for carbon dioxide phase change ejection considering rigid-flexible coupling. By applying the low-pressure chamber pressure-time curve obtained by calculating the closed state equation of the internal ballistic model to the bottom of the aircraft of the rigid-flexible coupling integrated dynamic model established in Abaqus, the posture prediction of the aircraft ejection process considering rigid-flexible coupling can be realized. The result is different from the aircraft posture calculated only by using the internal ballistic model. By considering the coupling relationship between the aircraft and the launch tube and the launch vehicle, the prediction accuracy of the aircraft ejection posture can be improved.

[0078] 2. The present invention discloses a posture prediction method for carbon dioxide phase change ejection considering rigid-flexible coupling, which adopts the Soave-Redlich-Kwong (SRK) state equation to describe the gas state change of the thermodynamic parameters of carbon dioxide, which has higher accuracy than the ideal gas model. The analytical expressions of the key thermodynamic parameters of the high and low pressure chambers are derived by the SRK real gas state equation, and the thermodynamic parameters of the real gas are equivalent to two parts consisting of a deviation term and an ideal gas value. The deviation term and the ideal gas value are derived respectively, and the deviation term and the ideal gas value are added to obtain the analytical expressions of the thermodynamic parameters of the real gas; the analytical expressions of the thermodynamic parameters are used to make the established interior ballistic model have higher accuracy under high temperature and high pressure environments.

[0079] 3. The present invention discloses a posture prediction method for carbon dioxide phase change ejection considering rigid-flexible coupling. The expressions of the internal ballistic equations of the high and low pressure chambers are obtained according to the law of conservation of mass, the law of conservation of energy, the gas flow equation and the SRK real gas state equation; the closed state equation group of the internal ballistic model is obtained by combining the expressions of the internal ballistic equations of the high and low pressure chambers. The closed state equation of the internal ballistic model is solved by the fourth-order Runge-Kutta method to obtain the attitude parameters of the aircraft during the ejection process and the thermodynamic parameters of the high and low pressure chambers; by changing the initial value of the simulation, not only can the ejection simulation prediction of a large-mass aircraft using supercritical carbon dioxide as the ejection fluid be realized, but also the attitude parameters of the aircraft under different initial state ejection fluids can be obtained. The attitude results of the aircraft under different initial ejection fluids can be used to optimize the aircraft vehicle-mounted ejection device and reduce the experimental cost. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the prior art descriptions are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention, and for ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0081] Figure 1A flow chart of a posture prediction method for carbon dioxide phase change ejection considering rigid-flexible coupling disclosed in the present invention;

[0082] Figure 2 It is a schematic diagram of the ejection device structure and state parameters;

[0083] Figure 3 Plot of vehicle velocity versus time calculated for the interior ballistic model;

[0084] Figure 4 Plot of low-pressure chamber pressure versus time calculated for the interior ballistic model;

[0085] Figure 5 The mesh division of each component of the rigid-flexible coupling model is shown in Figure 2. Figure 5 (a) shows the grid division of the frame. Figure 5 (b) The grid division of the launch tube is as follows Figure 5 (c) and the aircraft grid division as shown in Figure 5 (d)

[0086] Figure 6 Schematic diagram of the rigid-flexible coupling integrated dynamic model established for Abaqus;

[0087] Figure 7 The velocity-time curve obtained by considering the rigid-flexible coupling ejection model;

[0088] Figure 8 This is the acceleration time curve obtained considering the rigid-flexible coupling ejection model. DETAILED DESCRIPTION

[0089] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0090] The following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention. In order to better illustrate the objects and advantages of the present invention, the present invention is described in detail below in conjunction with the accompanying drawings and embodiments.

[0091] Example

[0092] This example discloses a method for predicting the attitude of carbon dioxide phase change ejection considering rigid-flexible coupling, the purpose of which is to analyze the supercritical carbon dioxide phase change cold ejection technology of vehicle-mounted aircraft, specifically to predict the attitude of the aircraft during the ejection process considering the rigid-flexible coupling effect. t =3.142m 2 、Projectile mass m e =40t, initial temperature of high pressure chamber T 1,0 =423K, initial pressure of high pressure chamber p 1,0 =12MPa, the chamber volume of the high pressure chamber is V H =2.4m 3 , the diameter of the control valve is S c =0.0057m 2 , the initial temperature of the low pressure chamber is T 2,0 =323K, initial pressure of low pressure chamber p 2,0 =0.1013MPa, the initial chamber volume of the low pressure chamber V L,0 =2.5m 3 , whether the aircraft's exit speed from the tube can be greater than 20m / s, and whether the overload of the aircraft during the ejection process can be less than 5g, so as to meet the basic requirements for successful ejection.

[0093] like Figure 1 As shown, this example discloses a posture prediction method for carbon dioxide phase change ejection considering rigid-flexible coupling, and the specific implementation steps are as follows:

[0094] Step 1: Use the Soave-Redlich-Kwong (SRK) state equation to describe the thermodynamic parameters of carbon dioxide, improve the calculation accuracy of carbon dioxide when the state changes, derive the analytical expressions of key thermodynamic parameters through the deviation function method, and equate the thermodynamic parameters of real gas to two parts consisting of deviation terms and ideal gas values. Derived the deviation terms and ideal gas values ​​separately, the deviation terms and ideal gas values ​​are added to obtain the analytical expressions of the thermodynamic parameters of real gas.

[0095] Step 1.1, establish the Soave-Redlich-Kwong (SRK) state equation of supercritical carbon dioxide, the specific expression is:

[0096]

[0097] Where p is pressure, T is temperature, v is gas molar volume, R is universal gas constant, ω is material factor, α(T,ω) is correction function related to working fluid temperature, a and b are specific material coefficients;

[0098] The expressions of specific material coefficients a and b are:

[0099]

[0100] The critical temperature and critical pressure of supercritical carbon dioxide are T c =304.18K and p c =7.38MPa;

[0101] The expression of the correction function α(T,ω) is:

[0102]

[0103] Among them, T r To compare temperatures:

[0104]

[0105] S is a coefficient related to the properties of the material, and its expression is:

[0106] S=0.48508+1.5517ω-0.15613ω 2 (28)

[0107] Material factor ω = 0.239;

[0108] The “deviation function method” is used to model the thermodynamic parameters of real gas, that is, the thermodynamic parameters of real gas are regarded as consisting of two parts: ideal gas value and deviation term, and the expression is:

[0109] χ(p,T)=χ i +△χ(p,T) (29)

[0110] Among them, χ is the real gas thermodynamic parameter, χ i is the ideal gas thermodynamic parameter, △χ is the deviation term;

[0111] Step 1.2: Obtain the deviation terms of thermodynamic parameters according to the laws of thermodynamics and the SRK equation of state.

[0112] From the first equation of thermodynamics:

[0113]

[0114] Keeping the temperature constant, integrating the above formula over the volume yields:

[0115]

[0116] When the specific volume approaches infinity, the specific internal energy is only related to the temperature. Therefore, the first term in the above formula is the specific internal energy of the ideal gas, and the second term is the deviation term of the specific internal energy. The specific expression is:

[0117]

[0118] Taking partial differential of the SRK equation with respect to temperature, we get:

[0119]

[0120] The relationship between specific volume and molar volume is:

[0121] v=MV (34)

[0122] The molar mass of carbon dioxide is M = 44.01 g·mol -1 ;

[0123] Substituting formula (33) into formula (32), we get:

[0124]

[0125] In order to convert the formula into a form related to temperature and pressure, the compression factor Z is introduced, and the expression is:

[0126]

[0127] According to the SRK state equation, the compression factor satisfies the following relationship:

[0128] Z 3 -Z 2 +(ABB 2 )Z-AB=0 (37)

[0129] Among them, A and B are variables related to pressure and temperature:

[0130]

[0131] Substituting equations (36) and (38) into equation (35) yields the deviation term of the specific internal energy:

[0132]

[0133] Similarly, the deviation term of specific enthalpy is:

[0134]

[0135] Among them, R g is the carbon dioxide gas constant, expressed as:

[0136] R g =R / M=188.96J·(kg·K) -1 (41)

[0137] Similarly, the deviation term of the constant volume specific heat capacity is:

[0138]

[0139] Step 1.3: Use NASA polynomials to fit the ideal values ​​of thermodynamic parameters as polynomials of temperature.

[0140] The specific heat capacity of an ideal gas at constant pressure is expressed as:

[0141]

[0142] In the formula, the fitting parameters are:

[0143] a0=2.5356,a1=8.1×10 -3 ,a2=-5.7061×10 -6 ,a3=1.7939×10 -9 ,a4=-1.5282×10 -13 (44)

[0144] The relationship between the specific heat capacity at constant volume and the specific heat capacity at constant pressure of an ideal gas is:

[0145]

[0146] Therefore, the ideal value of specific heat capacity at constant volume is:

[0147]

[0148] According to the relationship between the specific enthalpy of an ideal gas and its specific heat capacity at constant pressure, the specific enthalpy of an ideal gas is:

[0149]

[0150] Among them, the value of the polynomial coefficient a5 is 58.8179;

[0151] According to the relationship between the ideal gas specific internal energy and the specific heat capacity at constant volume, the ideal gas specific internal energy is:

[0152]

[0153] The ideal values ​​of thermodynamic parameters include the ideal gas specific heat capacity at constant pressure, the ideal gas specific heat capacity at constant volume, the ideal gas specific enthalpy, and the ideal gas specific internal energy as shown in equations (43), (46), (47), and (48), respectively.

[0154] Step 1.4: Add the deviation terms derived in step 1.2 and the ideal gas values ​​derived in step 1.3 to obtain the analytical expressions of the thermodynamic parameters of real gas, namely, specific heat capacity at constant volume, specific enthalpy and specific internal energy.

[0155] Step 2: The flow of high-pressure gas from the high-pressure chamber to the low-pressure chamber is regarded as isentropic flow, and the flow equation is obtained by ignoring the viscosity and using the Noorli method. The expression of the flow equation is:

[0156]

[0157] Among them: the subscript "1" represents the parameters corresponding to the high-pressure chamber, and the subscript "2" represents the gas parameters corresponding to the low-pressure chamber (the subsequent representation method remains unchanged); μ x is the flow correction factor, S c is the flow area (control valve size), and k is the air adiabatic index.

[0158] Step 3: According to the law of conservation of mass, the law of conservation of energy, the gas flow equation and the SRK real gas state equation, the interior ballistic equation of the high-pressure chamber is obtained; according to the law of conservation of mass, the law of conservation of energy, the gas flow equation and the SRK real gas state equation, the expression of the interior ballistic equation of the low-pressure chamber is obtained; the expression of the ballistic equation of the high-pressure chamber and the expression of the ballistic equation of the low-pressure chamber are combined to obtain the closed state equation group of the interior ballistic model.

[0159] Step 3.1, according to the law of conservation of mass, the law of conservation of energy, the gas flow equation and the SRK real gas state equation, the internal ballistic equation of the high pressure chamber is obtained as follows:

[0160] According to the law of conservation of mass, the mass change of S-CO2 per unit time in the high-pressure chamber is equal to the flow rate out of the control valve, that is:

[0161]

[0162] Among them, V H is the cavity volume of the high pressure chamber;

[0163] According to the law of conservation of energy, we have:

[0164]

[0165] The S-CO2 in the high pressure chamber uses the SRK real gas state equation:

[0166]

[0167] The fourth-order Runge-Kutta method is used to solve the internal ballistic equations. Therefore, it is necessary to obtain the first-order derivative form of the variables with respect to time, and then the specific expression of the internal ballistic equation of the high-pressure chamber is:

[0168]

[0169] Among them, V H is the volume of the high pressure chamber;

[0170] Step 3.2: Obtain the internal ballistic equations of the low-pressure chamber. The specific method is:

[0171] The mass flowing into the low-pressure chamber is the mass flowing out of the high-pressure chamber:

[0172]

[0173] The volume of the low-pressure chamber will change with the change of the projectile:

[0174]

[0175] Among them, V L is the volume of the low pressure chamber, S t is the cross-sectional area of ​​the launch tube, v e is the speed of the aircraft;

[0176] After the pressure in the low-pressure chamber is greater than the starting pressure, the projectile starts to move and is launched vertically. The resistance during the movement is simplified to 1.2m e g, the projectile motion equation is as follows:

[0177]

[0178] Among them, m e is the mass of the aircraft, L is the distance traveled by the aircraft, S t is the cross-sectional area of ​​the launch tube, v e is the speed of the projectile exiting the tube, p a is atmospheric pressure;

[0179] Part of the energy contained in the S-CO2 flowing from the high-pressure chamber into the low-pressure chamber becomes the energy contained in the gas in the low-pressure chamber, and the rest does work externally. According to the energy conservation equation, we get:

[0180]

[0181] Wherein, L is the projectile travel;

[0182] The velocity of the projectile is:

[0183]

[0184] The gas in the low-pressure chamber adopts the SRK real gas state equation:

[0185]

[0186] The internal ballistic equation is written as the first-order derivative form of the variable with respect to time. The specific expression of the internal ballistic equation of the low-pressure chamber is:

[0187]

[0188] Step 3.3: Combine the internal ballistic equations of the high and low pressure chambers in step 3.1 and step 3.2 to obtain the closed state equations of the internal ballistic model, expressed as:

[0189]

[0190] Step 4: Set initial conditions for the closed state equation group of the interior ballistic model, and solve the closed state equation group of the interior ballistic model in step 3 by the fourth-order Runge-Kutta method to obtain the attitude parameters and thermodynamic parameters of the aircraft during the ejection process, where the thermodynamic parameters include the pressure-time curve of the low-pressure chamber.

[0191] Step 4.1. Set initial conditions: launch tube cross-sectional area S t =3.142m 2 、Projectile mass m e =40t, initial temperature of high pressure chamber T 1,0 =423K, initial pressure of high pressure chamber p 1,0 =12MPa, the chamber volume of the high pressure chamber is V H =2.4m 3 , the diameter of the control valve is S c =0.0057m 2 , the initial temperature of the low pressure chamber is T 2,0 =323K, initial pressure of low pressure chamber p 2,0 =0.1013MPa, the initial chamber volume of the low pressure chamber V L,0 =2.5m 3 , the schematic diagram of the ejection device structure and state parameters is as follows Figure 2 shown.

[0192] Step 4.2: Using the initial conditions in step 4.1, solve the closed state equations in step 3.3 to obtain the attitude parameters and thermodynamic parameters of the aircraft during the ejection process. The attitude parameters include the speed and acceleration of the aircraft; the thermodynamic parameters include the pressure-time curve of the low-pressure chamber. Among them, the time required for the aircraft to leave the tube is 1.296s, and the speed when leaving the tube is 20.936m / s. The speed-time curve of the aircraft during the ejection process is as follows: Figure 3 As shown, the pressure-time curve of the low-pressure chamber is as follows Figure 4 As shown;

[0193] Step 5: In Abaqus, the actual physical model of the transport vehicle is modeled according to the initial conditions in 4. The frame, launch tube, aircraft and adapter are modeled and meshed respectively. The aircraft is set as a rigid body using rigid body constraints, and the inner surface of the adapter is bound to the corresponding outer surface of the aircraft using binding constraints. A cold ejection model considering rigid-flexible coupling is established. A -9.8 m / s load is applied to the entire model. 2The low-pressure chamber pressure-time curve obtained in 4 is applied to the bottom of the aircraft as the thrust load, and a reverse pressure is applied to the bottom of the launch tube to simulate the reaction force of the thrust on the launch tube when the aircraft leaves the tube; the lower reference point of the tire in the frame is set as a fixed constraint; the dynamic analysis step is set and the calculation is submitted, and finally the attitude parameters in the ejection process considering the rigid-flexible coupling effect are obtained in the post-processing module.

[0194] Step 5.1. In order to consider the rigid-flexible coupling effect, a cold ejection model considering rigid-flexible coupling is established in Abaqus. The adapter is modeled using C3D8R solid elements, and the frame, launch tube and aircraft are modeled using S4R shell elements. The adapter, frame, launch tube and aircraft are meshed. The mesh division of each component of the adapter, frame, launch tube and aircraft is shown in the figure. Figure 5 (a), 5(b), 5(c) and 5(d).

[0195] Step 5.2: Assemble the adapter, frame, launch tube and aircraft components, establish binding constraints between the inner surface of the adapter and the corresponding outer surface of the aircraft, set rigid body constraints on the aircraft, and establish a cold ejection model that considers rigid-flexible coupling, such as Figure 6 As shown;

[0196] Step 5.3: Apply -9.8 m / s to the entire model 2 The gravity of the vehicle is applied, and the low-pressure chamber pressure-time curve obtained in step 4.2 is used as the thrust load to the bottom of the vehicle; reverse pressure is applied to the bottom of the launch tube to simulate the reaction force of the thrust on the launch tube when the vehicle leaves the tube; the lower reference point of the tire in the frame is set as a fixed constraint; set the dynamic analysis step and submit the calculation;

[0197] Step 5.4: After the calculation is completed, the attitude parameters of the aircraft during the ejection process are extracted in the post-processing of Abaqus, including the velocity and acceleration of the aircraft during the ejection process, and then the attitude prediction results of the carbon dioxide phase change ejection considering the rigid-flexible coupling are obtained, so as to realize the attitude prediction of the aircraft ejection process considering the rigid-flexible coupling, such as Figure 7 and Figure 8 The results show that the time required for the aircraft to leave the tube is 1.329s, the speed when leaving the tube is 20.35m / s, the speed is greater than 20m / s, and the overload during the entire ejection process is less than 5g, which meets the basic requirements for successful ejection.

[0198] Step 5.5: Modify the aircraft mass m in step 4.1 e By repeating the above operations, the ejection simulation prediction of a large-mass aircraft using supercritical carbon dioxide as the ejection fluid can be realized.

[0199] In the above embodiment, the analytical expression of the thermodynamic parameters derived by the SRK real gas state equation is obtained by step 1, which improves the calculation accuracy of carbon dioxide when the state changes; the pressure-time curve of the low-pressure chamber is obtained by step 4, and it is applied as a load to the bottom of the aircraft of the rigid-flexible coupling integrated dynamic model established in step 5, and the attitude prediction result of carbon dioxide phase change ejection considering rigid-flexible coupling can be obtained. Compared with the attitude prediction result calculated by the existing internal ballistic model, the result has higher accuracy than the internal ballistic model calculated by pure rigid body because the rigid-flexible coupling characteristics of the aircraft-launch tube-launch vehicle during the ejection process are considered. In addition, changing the setting of the initial conditions in step 4.1 can not only realize the ejection simulation prediction of a large-mass aircraft with supercritical carbon dioxide as the ejection working fluid, but also obtain the attitude parameters of the aircraft under different initial state ejection working fluids. The attitude results of the aircraft under different initial ejection working fluids can optimize the aircraft vehicle-mounted ejection device and reduce the experimental cost.

[0200] The specific description above further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A posture prediction method for carbon dioxide phase change ejection considering rigid-flexible coupling, characterized by: The following steps are included: Step 1: Use the SRK state equation to describe the thermodynamic parameters of carbon dioxide, improve the calculation accuracy of carbon dioxide when the state changes, derive the analytical expressions of key thermodynamic parameters through the deviation function method, and equate the thermodynamic parameters of real gas to two parts consisting of deviation terms and ideal gas values. Derived the deviation terms and ideal gas values ​​respectively, and added the deviation terms and ideal gas values ​​to obtain the analytical expressions of the thermodynamic parameters of real gas; Step 2: The flow of high-pressure gas from the high-pressure chamber to the low-pressure chamber is regarded as isentropic flow, and the flow equation is obtained by ignoring viscosity and substituting it into the Noorli method; Step 3: According to the law of conservation of mass, the law of conservation of energy, the gas flow equation and the SRK real gas state equation, the internal ballistic equation of the high-pressure chamber is obtained; according to the law of conservation of mass, the law of conservation of energy, the gas flow equation and the SRK real gas state equation, the expression of the internal ballistic equation of the low-pressure chamber is obtained; the expression of the ballistic equation of the high-pressure chamber and the expression of the ballistic equation of the low-pressure chamber are combined to obtain the closed state equation group of the internal ballistic model; Step 4: Set initial conditions for the closed state equation group of the interior ballistic model, and solve the closed state equation group of the interior ballistic model in step 3 by the fourth-order Runge-Kutta method to obtain the attitude parameters and thermodynamic parameters of the aircraft during the ejection process, wherein the thermodynamic parameters include the pressure-time curve of the low-pressure chamber; Step 5: In Abaqus, the actual physical model of the transport vehicle is modeled according to the initial conditions in step 4. The frame, launch tube, aircraft and adapter are modeled and meshed respectively. The aircraft is set as a rigid body using rigid body constraints, and the inner surface of the adapter is bound to the corresponding outer surface of the aircraft using binding constraints. A cold ejection model considering rigid-flexible coupling is established. A -9.8 m / s force is applied to the entire cold ejection model. 2 The low-pressure chamber pressure-time curve obtained in step 4 is applied to the bottom of the aircraft as a thrust load, and a reverse pressure is applied to the bottom of the launch tube to simulate the reaction force of the thrust on the launch tube when the aircraft leaves the tube; the lower reference point of the tire in the frame is set as a fixed constraint; the dynamic analysis step is set and the operation is submitted, and the attitude parameters in the ejection process considering the rigid-flexible coupling effect are obtained in the post-processing module, that is, the attitude prediction of the carbon dioxide phase change ejection considering the rigid-flexible coupling is realized.

2. The method for predicting the posture of carbon dioxide phase change ejection considering rigid-flexible coupling as claimed in claim 1, characterized in that: Step 1 is implemented as follows: Step 1.1, establish the real gas equation of supercritical carbon dioxide, that is, the SRK state equation, which is expressed as follows: Where p is pressure, T is temperature, v is gas molar volume, R is universal gas constant, ω is material factor, α(T,ω) is correction function related to working fluid temperature, a and b are specific material coefficients; The "deviation function method" is used to model the thermodynamic parameters of real gas, that is, the thermodynamic parameters of real gas are regarded as consisting of two parts: ideal gas value and deviation term. The expression is: x(p,T)=x i +△χ(p,T) (2) Among them, χ is the real gas thermodynamic parameter, χ i is the ideal gas thermodynamic parameter, △χ is the deviation term; Step 1.2, obtain the deviation term of thermodynamic parameters according to the thermodynamic laws and SRK state equation; From the first equation of thermodynamics, we know: Among them, c v is the constant volume specific heat capacity, V is the specific volume, keeping the temperature constant, the above formula is integrated with the specific volume to obtain: When the specific volume approaches infinity, the specific internal energy is only related to the temperature. Therefore, the first term in the above formula is the specific internal energy of the ideal gas, and the second term is the deviation term of the specific internal energy. The specific expression is: Taking partial differential of the SRK equation with respect to temperature, we get: Among them, S is the coefficient related to the material properties, T c is the critical temperature, T r To compare the temperature, substitute equation (6) into equation (5) to obtain: Where M is the molar mass; In order to convert the formula into a form related to temperature and pressure, the compression factor Z is introduced, and the expression is: According to the SRK state equation, the compression factor satisfies the following relationship: Z 3 -Z 2 +(A-B-B 2 )Z-AB=0 (9) Among them, A and B are variables related to pressure and temperature: Substituting equations (8) and (10) into equation (7) yields the deviation term of the specific internal energy: Similarly, the deviation term of specific enthalpy is: Among them, R g is the specific gas constant; The deviation term of the constant volume specific heat capacity is: Step 1.3, using NASA polynomials to fit the ideal values ​​of thermodynamic parameters as polynomials of temperature; The specific heat capacity of an ideal gas at constant pressure is expressed as: The relationship between the specific heat capacity at constant volume and the specific heat capacity at constant pressure of an ideal gas is: The ideal value of specific heat capacity at constant volume is: According to the relationship between the specific enthalpy of an ideal gas and its specific heat capacity at constant pressure, the specific enthalpy of an ideal gas is: According to the relationship between the ideal gas specific internal energy and the specific heat capacity at constant volume, the ideal gas specific internal energy is: The ideal values ​​of thermodynamic parameters include the ideal gas specific heat capacity at constant pressure, the ideal gas specific heat capacity at constant volume, the ideal gas specific enthalpy, and the ideal gas specific internal energy as shown in equations (14), (16), (17), and (18), respectively; Step 1.4: Add the deviation terms derived in step 1.2 and the ideal gas values ​​derived in step 1.3 to obtain the analytical expressions of the thermodynamic parameters of the real gas.

3. The method for predicting the posture of carbon dioxide phase change ejection considering rigid-flexible coupling as claimed in claim 2, characterized in that: In step 2, the expression of the flow equation is: Among them: the subscript "1" indicates the parameters corresponding to the high-pressure chamber, and the subscript "2" indicates the gas parameters corresponding to the low-pressure chamber; μ x is the flow correction factor, S c is the flow area and k is the air adiabatic index.

4. The method for predicting the posture of carbon dioxide phase change ejection considering rigid-flexible coupling as claimed in claim 3, characterized in that: Step 3 is implemented as follows: Step 3.1, according to the law of conservation of mass, the law of conservation of energy, the gas flow equation and the SRK real gas state equation, the internal ballistic equation of the high pressure chamber is obtained as follows: Among them, V H is the volume of the high pressure chamber; Step 3.2, according to the law of conservation of mass, the law of conservation of energy, the gas flow equation and the SRK real gas state equation, the internal ballistic equation of the low-pressure chamber is obtained as follows: Among them, m e is the mass of the aircraft, L is the distance traveled by the aircraft, S t is the cross-sectional area of ​​the launch tube, v e is the speed of the projectile exiting the tube, p a is atmospheric pressure; Step 3.3: Combine the internal ballistic equations of the high and low pressure chambers in step 3.1 and step 3.2 to obtain the closed state equations of the internal ballistic model, expressed as:

5. The method for predicting the posture of carbon dioxide phase change ejection considering rigid-flexible coupling as claimed in claim 4, characterized in that: Step 4 is implemented as follows: Step 4.1: The initial conditions set for the closed state equations of the interior ballistic model include the cross-sectional area S of the launch tube t 、Aircraft mass m e , the initial temperature of the high pressure chamber T 1,0 , the initial pressure of the high pressure chamber p 1,0 、The volume of the high pressure chamber V H , Control valve size S c , the initial temperature of the low pressure chamber T 2,0 , the initial pressure of the low pressure chamber p 2,0 , the initial chamber volume V of the low pressure chamber L,0 ; Step 4.2: Using the initial conditions in step 4.1, solve the closed state equations in step 3.3 to obtain the attitude parameters and thermodynamic parameters of the aircraft during the ejection process; the attitude parameters include the speed and acceleration of the aircraft; the thermodynamic parameters include the pressure-time curve of the low-pressure chamber.

6. The method for predicting the posture of carbon dioxide phase change ejection considering rigid-flexible coupling as claimed in claim 5, characterized in that: Step 5 is implemented as follows: Step 5.

1. In order to consider the rigid-flexible coupling effect, a cold ejection model considering rigid-flexible coupling is established in Abaqus; the adapter is modeled using C3D8R solid elements, the frame, launch tube and aircraft are modeled using S4R shell elements, and the adapter, frame, launch tube and aircraft are meshed; Step 5.2, establish a binding constraint between the inner surface of the adapter and the corresponding outer surface of the aircraft, and set a rigid body constraint on the aircraft; Step 5.3, apply gravity to the entire cold ejection model, and apply the low-pressure chamber pressure-time curve obtained in step 4.2 as a thrust load to the bottom of the aircraft; apply reverse pressure to the bottom of the launch tube to simulate the reaction force of the thrust on the launch tube when the aircraft leaves the tube; set the lower reference point of the tire in the frame as a fixed constraint; set the dynamic analysis step and submit the calculation; Step 5.4: After the calculation is completed, the attitude parameters of the aircraft during the ejection process are extracted in the post-processing of Abaqus, including the speed and acceleration of the aircraft during the ejection process, and then the attitude prediction results of the carbon dioxide phase change ejection considering the rigid-flexible coupling are obtained, so as to realize the attitude prediction of the aircraft ejection process considering the rigid-flexible coupling.

7. The method for predicting the posture of carbon dioxide phase change ejection considering rigid-flexible coupling as claimed in claim 6, characterized in that: Also includes step 5.5, modifying the aircraft mass m in step 4.1 e , repeat the above operations to realize the ejection simulation prediction of a large-mass aircraft using supercritical carbon dioxide as the ejection working fluid.

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