A postural prediction method considering rigid-flexible coupling of carbon dioxide phase change ejection

Abstract

The application discloses a posture prediction method for carbon dioxide phase change ejection considering rigid-flexible coupling, and belongs to the technical field of cold ejection. The application realizes the method as follows: a S-R-K state equation is used to describe thermodynamic parameters of carbon dioxide, and an analytic expression of key thermodynamic parameters is derived through a deviation function method; a closed state equation group of an interior ballistic model is established according to a mass conservation law, an energy conservation law, a gas flow equation and the S-R-K real gas state equation; a cold ejection model considering rigid-flexible coupling is established in Abaqus; gravity is applied to the whole cold ejection model, a pressure-time curve of a low-pressure chamber calculated by the closed state equation group is taken as a thrust load, and a reverse pressure is applied to the bottom of a launching cylinder to simulate the reaction force of the thrust on the launching cylinder when the aircraft exits the cylinder; a lower reference point of a tire in the vehicle frame is set as a fixed constraint; a dynamic analysis step is set and calculation is submitted, and posture prediction of an aircraft ejection process considering rigid-flexible coupling is realized.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of cold ejection, and particularly relates to a posture prediction method for carbon dioxide phase change ejection considering rigid-flexible coupling. BACKGROUND

[0002] Vehicle-mounted mobile launch of a spacecraft is one of the main forms of rapid launch and is the main development direction of land launch of the spacecraft. At present, launch modes of the spacecraft mainly include hot launch and cold ejection. The hot launch technology is relatively mature, simple in structure and high in reliability, but high-temperature and high-speed exhaust flow generated during the launch may cause damage to the launch device and surrounding personnel, and therefore the hot launch is not suitable for vehicle-mounted mobile launch. The cold ejection mode is more friendly to mobile launch of the spacecraft. Common cold ejection modes include compressed air ejection, gas generator ejection, gas-steam ejection and supercritical carbon dioxide phase change ejection. Compared with traditional gas ejection and gas-steam ejection modes, the compressed air ejection and the supercritical carbon dioxide phase change ejection do not have the problem of ablation of gas to the spacecraft, do not need to set a heat insulation device, do not have the problem of ablation pollution to the launch cylinder, have good reusability, do not have high-temperature gas flow, are high in infrared concealment and good in environmental adaptability. Further comparison between the compressed air ejection and the carbon dioxide phase change ejection shows that existing researches show that the specific internal energy of supercritical carbon dioxide is greater than that of air in a given temperature and pressure range, and more working medium is needed for the compressed air ejection mode to eject the same mass of the spacecraft, which will cause the size of the ejection device to be relatively large and heavy. Therefore, in order to solve the problems of low pressure of traditional gas medium as a power source, large size of the device and high energy consumption of the air compressor, it is necessary to study the supercritical carbon dioxide phase change ejection. The research focus of the supercritical carbon dioxide phase change ejection is the posture prediction of the spacecraft during the ejection process, and the most important postures are the speed of the spacecraft when leaving the cylinder and the acceleration of the spacecraft during the ejection process. The speed of the spacecraft when leaving the cylinder is related to whether the current working medium can meet the ejection demand of the spacecraft, too small speed of the spacecraft when leaving the cylinder will cause the GNC control strategy of the spacecraft after leaving the cylinder to be invalid, resulting in failure of the ejection of the spacecraft, and the acceleration of the spacecraft during the ejection process is related to whether the overload of the spacecraft during the ejection process meets the design requirement of the spacecraft, and too large overload acceleration of the spacecraft will cause the structure of the spacecraft to be invalid, and further cause the launch to fail.

[0003] The existing supercritical carbon dioxide phase transition ejection aircraft attitude prediction method has: 1) design supercritical carbon dioxide ejection device to carry out physical test, use different initial mass of supercritical carbon dioxide to carry out ejection test, and use speed sensor and acceleration sensor to record the attitude parameters of the aircraft in the ejection process, compare the off-cylinder speed of the aircraft in the test data and the acceleration in the ejection process, and get the appropriate initial working medium. 2) The whole ejection system is regarded as a rigid body, and the attitude of the aircraft in the ejection process is predicted by using the interior ballistic model through numerical simulation. The problems and defects of the prior art are: 1) the cost of using the test method to study the aircraft attitude prediction method of supercritical carbon dioxide phase transition ejection is too high, and a complete ejection system needs to be developed. 2) The existing interior ballistic model, through numerical simulation, studies the aircraft attitude prediction of supercritical carbon dioxide ejection, and the mass of the aircraft is concentrated below 2000kg, and the research of large mass aircraft is still lacking, which cannot fully reflect the advantages of supercritical carbon dioxide as ejection working medium. 3) Most of the existing interior ballistic models regard the ejection working medium as an ideal gas, but the pressure of supercritical carbon dioxide is high, and the classical ideal gas assumption is no longer applicable, and the ideal gas numerical simulation will lead to large deviation of thermophysical properties. 4) The existing interior ballistic model regards the whole ejection system as a rigid body when modeling, ignores the rigid-flexible coupling characteristics of the aircraft-launching cylinder-launching vehicle in the ejection process, and leads to errors in the prediction of the attitude of the aircraft in the ejection process. SUMMARY

[0004] The application aims to provide a posture prediction method for carbon dioxide phase change ejection considering rigid-flexible coupling, which improves the calculation accuracy of carbon dioxide in state change by regarding the ejection working medium as a real gas, and describing the thermodynamic parameters of carbon dioxide by using a Soave-Redlich-Kwong (S-R-K) equation of state; the analytical expression of the key thermodynamic parameters is derived by using a deviation function method on the basis of the S-R-K equation of state; the flow of high-pressure gas from a high-pressure chamber to a low-pressure chamber is regarded as isentropic flow, and the flow equation is obtained by ignoring viscosity and bringing in the Nuliy mode; the interior ballistic equation expressions of the high-pressure chamber and the low-pressure chamber are obtained according to the mass conservation law, the energy conservation law, the gas flow equation and the S-R-K real gas equation of state, and the closed state equation set of the interior ballistic model is obtained by combining the interior ballistic equation expressions of the high-pressure chamber and the low-pressure chamber; the initial conditions are set for the closed state equation set of the interior ballistic model, and the posture parameters of the aircraft in the ejection process and the thermodynamic parameters are obtained by solving the closed state equation set of the interior ballistic model by using a fourth-order Runge-Kutta method, wherein the thermodynamic parameters include the pressure-time curve of the low-pressure chamber; the ejection simulation prediction of a large-mass aircraft using supercritical carbon dioxide as the ejection working medium can be realized by changing the initial mass of the aircraft in the initial conditions, thereby reducing the experimental cost; the actual physical model of the transport vehicle is modeled and meshed in Abaqus according to the initial conditions, the aircraft is set as a rigid body, and a cold ejection model considering rigid-flexible coupling is established; the gravity of-9.8 m / s 2 is applied to the whole cold ejection model, the pressure-time curve of the low-pressure chamber calculated by the closed state equation set is used as the thrust load applied to the bottom of the aircraft, 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 exits the tube; the lower reference point of the tire in the vehicle frame is set as a fixed constraint; the dynamic analysis step is set and submitted for operation, and the posture prediction of the ejection process of the aircraft considering rigid-flexible coupling can be realized. The posture parameters include velocity and acceleration. The thermodynamic parameters include high-pressure chamber thermodynamic parameters and low-pressure chamber thermodynamic parameters.

[0005] The application aims to achieve the above-mentioned technical effects by the following technical scheme.

[0006] The application discloses a posture prediction method for carbon dioxide phase change ejection considering rigid-flexible coupling, which comprises the following steps:

[0007] Step 1: the thermodynamic parameters of carbon dioxide are described by using a Soave-Redlich-Kwong (S-R-K) equation of state, the calculation accuracy of carbon dioxide in state change is improved, the analytical expression of the key thermodynamic parameters is derived by using a deviation function method, the thermodynamic parameters of the real gas are equivalent to two parts of a deviation term and an ideal gas value, the deviation term and the ideal gas value are derived respectively, and the analytical expression of the thermodynamic parameters of the real gas is obtained by adding the deviation term and the ideal gas value.

[0008] Step 1.1, establish the real gas equation of supercritical carbon dioxide, that is, S-R-K (Soave-Redlich-Kwong) state equation, the expression of which is:

[0009]

[0010] Wherein, p is pressure, T is temperature, v is gas molar volume, R is general gas constant, ω is material factor, α(T, ω) is correction function related to working medium 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 considered to be composed of two parts, namely, ideal gas value and deviation term, the expression of which is:

[0012] χ(p, T) = χ i +△χ(p, T) (2)

[0013] Wherein, χ is the thermodynamic parameter of real gas, χ i is the thermodynamic parameter of ideal gas, and △χ is the deviation term;

[0014] Step 1.2, obtain the deviation term of thermodynamic parameters according to the thermodynamic law and S-R-K state equation.

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

[0016]

[0017] Wherein, c v is the specific heat capacity at constant volume, V is the specific volume, the temperature is kept constant, and the above formula is integrated with respect to specific volume:

[0018]

[0019] When the specific volume tends to infinity, the specific internal energy is only related to temperature, so the first term of the above formula is the specific internal energy of ideal gas, and the second term is the deviation term of specific internal energy, the specific expression of which is:

[0020]

[0021] The partial derivative of S-R-K equation with respect to temperature is obtained as:

[0022]

[0023] Wherein, S is a coefficient related to the properties of the material, T c is the critical temperature, and T r is the reduced temperature;

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

[0025] v = MV (7)

[0026] where M is the molar mass;

[0027] Substituting equation (6) into equation (5) gives:

[0028]

[0029] In order to convert the formula to the form about temperature and pressure, the compressibility factor Z is introduced, and the expression is:

[0030]

[0031] According to the S-R-K state equation, the compressibility factor satisfies the following relationship:

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

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

[0034]

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

[0036]

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

[0038]

[0039] where R g is the specific gas constant;

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

[0041]

[0042] Step 1.3, use NASA polynomial to fit the ideal value of thermodynamic parameters as a polynomial of temperature.

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

[0044]

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

[0046]

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

[0048]

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

[0050]

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

[0052]

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

[0054] Step 1.4: The deviation term derived in step 1.2 and the ideal gas value derived in step 1.3 are added to obtain the analytical expression 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 considered as isentropic flow, and the viscosity is ignored to obtain the flow equation in the Nulie way, and the expression of the flow equation is:

[0056]

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

[0058] Step 3: According to the mass conservation law, the energy conservation law, the gas flow equation, and the S-R-K real gas state equation, the interior ballistic equation of the high-pressure chamber is obtained; according to the mass conservation law, the energy conservation law, the gas flow equation, and the S-R-K real gas state equation, the interior ballistic equation of the low-pressure chamber is obtained; the closed state equation set of the interior ballistic model is obtained by combining the interior ballistic equation expression of the high-pressure chamber and the interior ballistic equation expression of the low-pressure chamber.

[0059] Step 3.1, according to the mass conservation law, the energy conservation law, the gas flow equation, and the S-R-K real gas state equation, the interior ballistic equation expression of the high-pressure chamber is:

[0060]

[0061] wherein, 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 S-R-K real gas state equation, the interior ballistic equation expression of the low pressure chamber is obtained as:

[0063]

[0064] wherein, m e is the mass of the vehicle, L is the vehicle travel, S t is the launch tube cross-sectional area, v e is the projectile muzzle velocity, p a is the atmospheric pressure;

[0065] Step 3.3, the closed state equation set of the interior ballistic model is obtained by combining the interior ballistic equations of the high and low pressure chambers in step 3.1 and step 3.2, and the expression is:

[0066]

[0067] Step 4: initial conditions are set for the closed state equation set of the interior ballistic model, and the attitude parameters of the vehicle and the thermodynamic parameters in the launching process are obtained by solving the closed state equation set of the interior ballistic model in step 3 through the fourth-order Runge-Kutta method, wherein 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 equation set of the interior ballistic model include the launch tube cross-sectional area S t , the mass of the vehicle 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 chamber volume of the high pressure chamber V H , the size of the control valve 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 of the low pressure chamber V L,0 .

[0069] Step 4.2, using the initial conditions in step 4.1, the closed state equation set in step 3.3 is solved to obtain the attitude parameters of the vehicle and the thermodynamic parameters in the launching process. The attitude parameters include the speed and acceleration of the vehicle; the thermodynamic parameters include the pressure-time curve of the low pressure chamber.

[0070] Step 5: Model the actual physical model of the transport vehicle according to the initial conditions in step 4 in Abaqus, model and mesh the parts of the vehicle frame, launch tube, aircraft and adapter respectively, set the aircraft as a rigid body using rigid body constraints, and bind the inner surface of the adapter to the corresponding surface on the outside of the aircraft using binding constraints, to establish a cold launch model considering rigid-flexible coupling; apply a gravity of-9.8m / s 2 to the entire cold launch model, apply the low-pressure chamber pressure-time curve obtained in step 4 as a thrust load to the bottom of the aircraft, and apply a reverse pressure at the bottom of the launch tube to simulate the reaction force of the thrust on the launch tube when the aircraft exits the tube; set the lower reference point of the tire in the vehicle frame as a fixed constraint; set the dynamic analysis step and submit the operation, and obtain the attitude parameters during the launch process considering rigid-flexible coupling in the post-processing module, i.e. realize the attitude prediction of the carbon dioxide phase change launch considering rigid-flexible coupling.

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

[0072] Step 5.2, a binding constraint is established between the inner surface of the adapter and the corresponding surface on the outside of the aircraft, and a rigid body constraint is set for the aircraft;

[0073] Step 5.3, apply a gravity of-9.8m / s 2 to the entire cold launch 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 a reverse pressure at the bottom of the launch tube to simulate the reaction force of the thrust on the launch tube when the aircraft exits the tube; set the lower reference point of the tire in the vehicle frame as a fixed constraint; set the dynamic analysis step and submit the operation;

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

[0075] Step 5.5, modify the mass m e of the aircraft in step 4.1, and repeat the above operations to realize the launch simulation and prediction of a large mass aircraft using supercritical carbon dioxide as the launch working medium.

[0076] Advantages:

[0077] 1.The attitude prediction method of the carbon dioxide phase-change ejection considering rigid-flexible coupling, which applies the low-pressure chamber pressure-time curve calculated by the closed state equation of the interior ballistic model to the bottom of the rigid-flexible coupling integrated dynamic model established in Abaqus, can realize the attitude prediction of the ejection process of the aircraft considering rigid-flexible coupling, which is different from the aircraft attitude calculated by only using the interior ballistic model, and can improve the prediction accuracy of the ejection attitude of the aircraft by considering the coupling relationship between the aircraft and the launch cylinder and the launch vehicle.

[0078] 2.The attitude prediction method of the carbon dioxide phase-change ejection considering rigid-flexible coupling, which uses the Soave-Redlich-Kwong (S-R-K) state equation to describe the thermodynamic parameters of carbon dioxide for gas state change, has higher accuracy compared with the ideal gas model, derives the analytical expressions of the key thermodynamic parameters of the high and low pressure chambers through the S-R-K real gas state equation, and equivalently obtains the thermodynamic parameters of the real gas from the deviation term and the ideal gas value, respectively derives the deviation term and the ideal gas value, and adds the deviation term and the ideal gas value to obtain the analytical expression of the thermodynamic parameters of the real gas; the analytical expression of the thermodynamic parameters makes the established interior ballistic model have higher accuracy in high temperature and high pressure environment.

[0079] 3.The attitude prediction method of the carbon dioxide phase-change ejection considering rigid-flexible coupling, which obtains the interior ballistic equation expressions of the high and low pressure chambers 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; obtains the closed state equation set of the interior ballistic model by simultaneously solving the interior ballistic equation expressions of the high and low pressure chambers. The closed state equation of the interior ballistic model is solved by the fourth-order Runge-Kutta method to obtain the attitude parameters of the aircraft and the thermodynamic parameters of the high and low pressure chambers in the ejection process; by changing the initial value of the simulation, not only the ejection simulation prediction of the large mass aircraft using supercritical carbon dioxide as the ejection working medium can be realized, but also the attitude parameters of the aircraft under different initial state ejection working medium can be obtained, and the attitude results of the aircraft under different initial ejection working medium can be used to optimize the vehicle-mounted ejection device of the aircraft and reduce the experimental cost. BRIEF DESCRIPTION OF DRAWINGS

[0080] In order to more clearly illustrate the technical solutions of the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or prior art description will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present application, and those skilled in the art can obtain other drawings according to these drawings without creating any inventive labor.

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

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

[0083] Figure 3 A diagram of the time-varying speed of the vehicle calculated by the interior ballistic model;

[0084] Figure 4 A diagram of the time-varying pressure in the low-pressure chamber calculated by the interior ballistic model;

[0085] Figure 5 A mesh division condition of each component of the rigid-flexible coupling model, wherein the mesh division condition of the adapter is as shown in Figure 5 (a), the mesh division condition of the vehicle frame is as shown in Figure 5 (b), the mesh division condition of the launch tube is as shown in Figure 5 (c), and the mesh division condition of the vehicle is as shown in Figure 5 (d);

[0086] Figure 6 A schematic diagram of the rigid-flexible coupling integrated dynamic model established by Abaqus;

[0087] Figure 7 A time curve of the speed obtained by the rigid-flexible coupling ejection model;

[0088] Figure 8 A time curve of the acceleration obtained by the rigid-flexible coupling ejection model. DETAILED DESCRIPTION

[0089] To make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are some but not all of the embodiments of the present application. Based on the embodiments in the present application, all the other embodiments obtained by a person of ordinary skill in the art without creative work fall within the protection scope of the present application.

[0090] The following embodiments are used to illustrate the present application, but not to limit the scope of the present application. In order to better illustrate the objects and advantages of the present application, the present application will be described in detail below with reference to the drawings and embodiments.

[0091] EMBODIMENT

[0092] The example discloses a posture prediction method of carbon dioxide phase change ejection considering rigid-flexible coupling, and aims to analyze supercritical carbon dioxide phase change cold ejection technology of a vehicle-mounted aircraft, and specifically predicts the posture of the aircraft in the ejection process by considering rigid-flexible coupling. t = 3.142 m 2 , the mass m e = 40 t of the projectile body, the initial temperature T 1,0 = 423 K of the high-pressure chamber, the initial pressure p 1,0 = 12 MPa of the high-pressure chamber, the chamber volume V H = 2.4 m 3 of the high-pressure chamber, the diameter S c = 0.0057 m 2 of the control valve, the initial temperature T 2,0 = 323 K of the low-pressure chamber, the initial pressure p 2,0 = 0.1013 MPa of the low-pressure chamber, the initial chamber volume V L,0 = 2.5 m 3 of the low-pressure chamber, whether the ejection speed of the aircraft can be greater than 20 m / s, and whether the overload of the aircraft in the ejection process can be less than 5 g, so as to achieve the basic requirements for successful ejection.

[0093] As shown in Figure 1 , the posture prediction method of carbon dioxide phase change ejection considering rigid-flexible coupling disclosed by the example specifically implements the following steps:

[0094] Step 1: The Soave-Redlich-Kwong (S-R-K) equation of state is used to describe the thermodynamic parameters of carbon dioxide, so as to improve the calculation accuracy of carbon dioxide in the state change, and the analytical expression of the key thermodynamic parameters is derived by the deviation function method. The thermodynamic parameters of the real gas are equivalent to two parts of the deviation term and the ideal gas value, and the deviation term and the ideal gas value are derived respectively. The deviation term and the ideal gas value are added to obtain the analytical expression of the thermodynamic parameters of the real gas.

[0095] Step 1.1, the Soave-Redlich-Kwong (S-R-K) equation of state of supercritical carbon dioxide is established, and the specific expression is as follows:

[0096]

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

[0098] The expression of the specific material coefficients a and b is:

[0099]

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

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

[0102]

[0103] wherein T r is the reduced temperature:

[0104]

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

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

[0107] The substance factor ω = 0.239;

[0108] The thermodynamic parameters of real gas are modeled by using the "deviation function method", that is, the thermodynamic parameters of real gas are considered to be composed of two parts of ideal gas value and deviation term, and the expression is:

[0109] χ(p, T) = χ i +△χ(p, T) (29)

[0110] wherein χ is the thermodynamic parameter of real gas, χ i is the thermodynamic parameter of ideal gas, and△χ is the deviation term;

[0111] Step 1.2, the deviation term of the thermodynamic parameter is obtained according to the thermodynamic law and the S-R-K state equation.

[0112] According to the first du equation of thermodynamics:

[0113]

[0114] Integrating the above formula with respect to the specific volume under the condition of constant temperature, we have:

[0115]

[0116] When the specific volume tends to infinity, the specific internal energy is only related to the temperature, so the first term of 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, and the specific expression is:

[0117]

[0118] The partial derivative of temperature with respect to S-R-K equation is obtained:

[0119]

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

[0121] v=MV (34)

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

[0123] The formula (33) is brought into formula (32):

[0124]

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

[0126]

[0127] According to S-R-K state equation, the compression factor satisfies the following relationship:

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

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

[0130]

[0131] The formula (36) and (38) are brought into formula (35) to obtain the deviation term of specific internal energy:

[0132]

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

[0134]

[0135] Wherein, R g is the constant of carbon dioxide gas, and the expression is:

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

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

[0138]

[0139] Step 1.3: The ideal values of thermodynamic parameters are fitted as polynomials of temperature by using NASA polynomials.

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

[0141]

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

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

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

[0145]

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

[0147]

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

[0149]

[0150] In which, the value of the polynomial coefficient a5 is 58.8179;

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

[0152]

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

[0154] Step 1.4: The deviation term derived in step 1.2 and the ideal gas value derived in step 1.3 are correspondingly added to obtain the analytical expressions of the thermodynamic parameters of real gas, including the constant volume specific heat capacity, the specific enthalpy, and the specific internal energy.

[0155] Step 2: The flow of high-pressure gas from the high-pressure chamber to the low-pressure chamber is considered as an isentropic flow, and the viscous afterflow is ignored. The flow equation is obtained in the Nulie way, and the expression of the flow equation is:

[0156]

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

[0158] Step 3: 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 S-R-K real gas state equation; the interior ballistic equation of the low-pressure chamber is obtained 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; and the closed state equation set of the interior ballistic model is obtained by combining the interior ballistic equation expression of the high-pressure chamber and the interior ballistic equation expression of the low-pressure chamber.

[0159] Step 3.1: The interior ballistic equation expression 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 S-R-K real gas state equation, and is as follows:

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

[0161]

[0162] wherein V H is the volume of the cavity of the high-pressure chamber;

[0163] According to the law of conservation of energy, there is:

[0164]

[0165] The S-CO2 in the high-pressure chamber adopts the S-R-K real gas state equation:

[0166]

[0167] The fourth-order Runge-Kutta method is used to solve the interior ballistic equation set, and therefore the first-order derivative form of the variable with respect to time is required, and the specific expression of the interior ballistic equation of the high-pressure chamber is:

[0168]

[0169] wherein V H is the volume of the high-pressure chamber;

[0170] Step 3.2, obtain the interior ballistic equations of the low pressure chamber, the specific method is:

[0171] The mass of the low pressure chamber inflow is the mass of the high pressure chamber outflow:

[0172]

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

[0174]

[0175] Where, 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 vehicle;

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

[0177]

[0178] Where, m e is the mass of the vehicle, L is the travel of the vehicle, S t is the cross-sectional area of the launch tube, v e is the speed of the projectile out of the tube, p a is the atmospheric pressure;

[0179] The energy contained in the S-CO2 flowing from the high pressure chamber into the low pressure chamber, part of which becomes the energy contained in the low pressure chamber gas, and the rest does work on the outside, which is obtained from the energy conservation equation:

[0180]

[0181] Where, L is the travel of the projectile;

[0182] The speed of the projectile is:

[0183]

[0184] The low pressure chamber gas adopts S-R-K real gas state equation:

[0185]

[0186] Write the interior ballistic equation as the first derivative of the variable with respect to time, and the specific expression of the interior ballistic equation of the low pressure chamber is:

[0187]

[0188] Step 3.3, the closed state equations of the interior ballistic model are obtained by using the interior ballistic equations of the high pressure chamber and the low pressure chamber in step 3.1 and step 3.2, and the expression is:

[0189]

[0190] Step 4: set initial conditions for the closed state equations of the interior ballistic model, and solve the closed state equations of the interior ballistic model in step 3 by using the fourth order Runge-Kutta method to obtain the attitude parameters of the vehicle and the thermodynamic parameters in the ejection process, wherein the thermodynamic parameters include the pressure-time curve of the low pressure chamber.

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

[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 of the vehicle and the thermodynamic parameters in the ejection process. The attitude parameters include the speed and acceleration of the vehicle; the thermodynamic parameters include the pressure-time curve of the low pressure chamber. Among them, the time required for the vehicle to leave the tube is 1.296 s, the speed when leaving the tube is 20.936 m / s, the speed-time curve of the vehicle in the ejection process is shown in Figure 3 , and the pressure-time curve of the low pressure chamber is shown in Figure 4 ;

[0193] Step 5: model the actual physical model of the transport vehicle in Abaqus according to the initial conditions in step 4, model and mesh the components of the vehicle frame, the launch tube, the vehicle and the adapter, set the vehicle as a rigid body using rigid body constraints, and bind the inner surface of the adapter to the corresponding surface on the outside of the vehicle using binding constraints, and establish a cold ejection model considering rigid-flexible coupling; apply-9.8 m / s 2The low-pressure chamber pressure-time curve obtained in step 4 is applied as a thrust load to the bottom of the aircraft, 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. Finally, the attitude parameters during 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 meshing of the adapter, frame, launch tube and aircraft components is shown in the figure below. 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, as shown in the following example: 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 a thrust load to the bottom of the vehicle. A reverse pressure is applied to the bottom of the launch tube to simulate the thrust reaction force 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 canister is 1.329s, the speed when leaving the canister 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 a 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 using the S-R-K real gas equation of state is obtained by step 1, which improves the calculation accuracy of carbon dioxide during state change; the pressure-time curve of the low-pressure chamber is obtained by step 4, which is applied as a load to the bottom of the vehicle in the rigid-flexible coupling integrated dynamic model established in step 5, and the attitude prediction result of the carbon dioxide phase change ejection considering rigid-flexible coupling can be obtained. Compared with the existing attitude prediction result calculated by using the interior ballistic model, since the rigid-flexible coupling characteristics of the vehicle-launching cylinder-launching vehicle during the ejection process are considered, compared with the pure rigid body calculation of the interior ballistic model, the attitude prediction result has higher accuracy. In addition, by changing the setting of the initial condition in step 4.1, not only can the ejection simulation prediction of the large-mass vehicle using supercritical carbon dioxide as the ejection working medium be realized, but also the attitude parameters of the vehicle under different initial state ejection working medium can be obtained. The attitude results of the vehicle under different initial ejection working medium can be used to optimize the vehicle-mounted ejection device of the vehicle, and the experimental cost can be reduced.

[0200] The above specific description further details the purpose, technical solutions and beneficial effects of the application. It should be understood that the above description is only a specific embodiment of the application and is not used to limit the protection scope of the application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the application should be included in the protection scope of the application.

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 equation of state to describe the thermodynamic parameters of carbon dioxide to improve the calculation accuracy of carbon dioxide during state changes. Use the deviation function method to derive analytical expressions for key thermodynamic parameters. Equivalently, the thermodynamic parameters of real gas are composed of deviation terms and ideal gas values. The deviation terms and ideal gas values ​​are derived separately, and the deviation terms and ideal gas values ​​are added together to obtain the analytical expressions for the thermodynamic parameters of real gas. Step 2: Consider the flow of high-pressure gas from the high-pressure chamber to the low-pressure chamber as isentropic flow, ignore viscosity, and use the Noorli method to obtain the flow equation; Step 3: Obtain the interior ballistic equation of the high-pressure chamber based on the law of conservation of mass, the law of conservation of energy, the gas flow equation, and the SRK true gas state equation; obtain the expression of the interior ballistic equation of the low-pressure chamber based on the law of conservation of mass, the law of conservation of energy, the gas flow equation, and the SRK true gas state equation; combine the expressions of the ballistic equation of the high-pressure chamber and the ballistic equation of the low-pressure chamber to obtain the closed state equation system of the interior ballistic model; Step 4: Set initial conditions for the closed state equations of the interior ballistic model and solve the closed state equations of the interior ballistic model in step 3 using the fourth-order Runge-Kutta method to obtain the attitude parameters and thermodynamic parameters of the aircraft during the ejection process, including 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 velocity 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 calculation is submitted. The attitude parameters of 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 a carbon dioxide phase change ejection considering rigid-flexible coupling according to 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 gases. That is, the thermodynamic parameters of real gases are considered to consist of two parts: ideal gas values ​​and deviation terms. The expression is: x(p,T)=x i +Δχ(p,T) (2) Among them, χ is the real gas thermodynamic parameter, χ i is the ideal gas thermodynamic parameter, Δχ is the deviation term; Step 1.2, obtain the deviation terms of thermodynamic parameters according to the thermodynamic laws and the SRK equation of state; 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 over the specific volume to get: 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 compressibility 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: Use 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 ideal gas and the specific heat capacity at constant pressure, the specific enthalpy of 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 for the thermodynamic parameters of the real gas.

3. The method for predicting the posture of a carbon dioxide phase change ejection considering rigid-flexible coupling according to claim 2, characterized in that: In step 2, the flow equation is expressed as: Among them: subscript "1" represents the parameters corresponding to the high pressure chamber, and the following table "2" represents 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 a carbon dioxide phase change ejection considering rigid-flexible coupling according to claim 3, characterized in that: Step 3 is implemented as follows: Step 3.1: Based on 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: Based on 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 aircraft travel, 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 interior ballistic equations of the high-pressure and low-pressure chambers in steps 3.1 and 3.2 to obtain the closed-loop state equations of the interior ballistic model, expressed as:

5. The method for predicting the posture of a carbon dioxide phase change ejection considering rigid-flexible coupling according to claim 4, characterized in that: Step 4 is implemented as follows: Step 4.1: Set the initial conditions for the closed state equations of the interior ballistic model, including the cross-sectional area of ​​the launch tube S t , aircraft mass m e , the initial temperature of the high pressure chamber T 1,0 , the initial pressure p of the high-pressure chamber 1,0 , the chamber volume V of the high pressure chamber H , size S of control valve 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 a carbon dioxide phase change ejection considering rigid-flexible coupling according to claim 5, characterized in that: Step 5 is implemented as follows: Step 5.

1. To account for 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. Step 5.2: Create 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 use the low-pressure chamber pressure-time curve obtained in step 4.2 as a thrust load to the bottom of the vehicle. Apply reverse pressure to the bottom of the launch tube to simulate the thrust reaction force on the launch tube when the vehicle 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 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, thus realizing the attitude prediction of the aircraft ejection process considering the rigid-flexible coupling.

7. The method for predicting the posture of a carbon dioxide phase change ejection considering rigid-flexible coupling according to 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 fluid.

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