Nitrous oxide self-pressurization feeding pressure prediction method considering boiling mass transfer

Abstract

The application provides a nitrous oxide self-pressurization supply pressure prediction method considering boiling mass transfer, an algebraic differential equation set describing a nitrous oxide self-pressurization tank is established by constructing a tank physical model, combining a mass conservation equation, an energy conservation equation, an actual fluid state equation, a heat transfer model, a mass transfer model and a constraint equation; and the tank pressure change condition is obtained by solving. The method considers the boiling vaporization rate of liquid nitrous oxide, conforms to the actual physical process, can predict the transient change of the tank pressure, has high prediction precision, has higher precision and can predict the transient change of the pressure. Through the method, the change condition of the tank pressure in the self-pressurization process can be obtained, and the change conditions of the supply flow rate, the vaporization rate, the mass of the gas-liquid two-phase, the temperature and other parameters can be obtained, so that the method can provide guidance for related research and application.

Description

Technical Field

[0001] This invention belongs to the field of solid-liquid hybrid engine technology, specifically relating to a method for predicting the self-pressurizing supply pressure of nitrous oxide considering boiling mass transfer. Background Technology

[0002] Nitrous oxide has advantages such as being able to be stored at room temperature, being non-toxic, having good safety, and possessing high saturated vapor pressure. Its saturated vapor pressure is 3.12 MPa at 0℃ and 5.65 MPa at 25℃. Utilizing this high saturated vapor pressure, nitrous oxide can achieve self-pressurization, meaning the compressed gas comes from the vapor produced by the continuous vaporization of nitrous oxide. This self-pressurization eliminates the need for high-pressure cylinders and associated pipelines, valves, and regulators, greatly simplifying the structure of solid-liquid hybrid engines, reducing negative weight and cost, and contributing to improved engine performance.

[0003] The thrust of a hybrid solid-liquid engine is related to the propellant mass flow rate, which primarily depends on the oxidizer supply flow rate. However, for a self-pressurized hybrid solid-liquid engine, the oxidizer supply flow rate is determined by the tank pressure. Therefore, obtaining information on the variation of the self-pressurized nitrous oxide supply pressure is a crucial indicator of engine performance.

[0004] In their paper "Modeling of Propellant Tank Pressurization" (41st AIAA / ASME / SAE / ASEE Joint Propulsion Conference & Exhibition. 2005:3549), Zilliac and Karabeyoglu proposed a three-zone model for predicting the pressurization performance of a propellant tank. This model divides the tank into three regions: a liquid phase region, a gas phase region, and a saturation region. The saturation region is the interface between the gas and liquid phases. Mass conservation equations and energy conservation equations are established for the gas and liquid phase regions respectively, and the mass and energy exchange between the gas / liquid phase region and the saturation region is considered. Cai Guobiao and Sun Wei, in their patent "A Prediction Method for the Self-Pressurization Process of a Nitrous Oxide Tank" (CN102116217A, 2011-07-06), disclosed a method for predicting the self-pressurization process of nitrous oxide applicable to the field of monocomponent micro-propulsion. This method is also based on the three-zone model proposed by Zilliac. However, the three-zone model used in the above method assumes that liquid vaporization only occurs at the interface between the gas and liquid phases. The mechanism of nitrous oxide self-pressurization, however, involves the tank pressure dropping below the liquid's saturated vapor pressure, causing internal boiling and vaporization to generate pressurized gas. Therefore, the above method does not consider the boiling vaporization caused by pressure below the liquid's saturated vapor pressure, making it difficult to accurately describe the transient characteristics of the nitrous oxide self-pressurization tank pressure and causing deviations in pressure prediction. Summary of the Invention

[0005] To overcome the shortcomings of existing tank pressure prediction methods that do not consider the boiling vaporization of nitrous oxide, resulting in large errors in describing the transient changes in the pressure of self-pressurized nitrous oxide tanks, this invention provides a method for predicting the self-pressurized nitrous oxide supply pressure that considers boiling mass transfer. This method can predict the transient characteristics of the self-pressurized tank pressure and improve the accuracy of pressure prediction.

[0006] To achieve the above objectives, the technical solution provided by this invention is:

[0007] A method for predicting the self-pressurized nitrous oxide supply pressure considering boiling mass transfer, characterized by the following steps:

[0008] Step 1: Construct a physical model of the nitrous oxide self-pressurization tank;

[0009] In the physical model, the tank is divided into a gas phase region and a liquid phase region, with a liquid surface layer between the gas phase region and the liquid phase region, and the thickness of the liquid surface layer is ignored.

[0010] The temperature and density parameters of the gas phase and liquid phase regions change only with time in space, and the pressures of the two regions are equal.

[0011] The physical properties of the liquid surface layer are taken as the saturation parameters under the tank pressure.

[0012] The volume of the storage tank is fixed, and there is no heat exchange between the storage tank and nitrous oxide;

[0013] Step 2: Construct the thermodynamic model of the tank described in Step 1, including the mass conservation equations and energy conservation equations for the gas phase region and the liquid phase region;

[0014] Step 3: Construct the heat transfer model of the tank described in Step 1 to obtain the heat transfer rate between the liquid surface layer and the gas phase region. and the heat transfer rate between the liquid surface layer and the liquid phase region

[0015] Step 4: Construct the mass transfer model of the tank described in Step 1 to obtain the evaporation rate of the liquid surface layer. Boiling vaporization rate in the liquid phase region

[0016] Step 5: Based on the model equations established in Steps 2-4, and combined with the actual fluid state equations and supplementary equations, establish a set of algebraic differential equations describing the nitrous oxide self-pressurization tank.

[0017] The supplementary equations are calculated based on the volume constraint equations and pressure constraint equations;

[0018] Step 6: Solve the system of algebraic differential equations describing the self-pressurized nitrous oxide tank to obtain the pressure inside the tank.

[0019] Furthermore, the mass conservation equation established in step 2 is as follows:

[0020]

[0021]

[0022] Define m g For gas phase mass, m l For liquid phase mass;

[0023] In the formula, Let be the derivative of the gas phase mass with respect to time. Let be the derivative of the liquid phase mass with respect to time. The mass flow rate of nitrous oxide flowing out of the storage tank. The evaporation rate of the liquid surface layer. The boiling vaporization rate in the liquid phase region;

[0024] The energy conservation equation is:

[0025]

[0026]

[0027] Definition: U g V g These represent the internal energy and volume of the gas phase, respectively; U l V l These are the internal energy and volume of the liquid phase region, respectively.

[0028] In the formula, These are the derivatives of the gas phase energy and the gas phase volume with respect to time, respectively. Let be the internal energy of the liquid phase and the derivative of the volume of the liquid phase with respect to time, respectively, and p be the tank pressure. The heat transfer rate between the liquid surface layer and the gas phase region. The heat transfer rate between the liquid surface layer and the liquid phase region;

[0029] h v The specific enthalpy of the evaporated nitrous oxide is taken as the specific enthalpy of saturated gaseous nitrous oxide under the tank pressure;

[0030] h b The specific enthalpy is taken as the specific enthalpy of boiling nitrous oxide, and is the specific enthalpy of saturated gaseous nitrous oxide at the liquid phase temperature;

[0031] h e The specific enthalpy of nitrous oxide flowing out of the storage tank is taken as the specific enthalpy of the liquid phase.

[0032] Furthermore, in step 3, the heat transfer rate between the liquid surface layer and the gas phase region is obtained. for:

[0033]

[0034]

[0035]

[0036]

[0037] In the formula, A sg α is the heat transfer area between the gas phase region and the liquid surface layer. sg T is the heat transfer coefficient between the gas phase region and the liquid surface layer. s T represents the temperature of the liquid surface layer. g The temperature represents the liquid phase region; the subscript sgf indicates that the qualitative temperature is taken as the arithmetic mean temperature of the boundary layer. (T) sgf =(T s +T g ) / 2, C sg and n sg L represents the coefficients and exponents in the natural convection experimental equations. sg For feature size, Gr sgf Pr is the Grashof number at the qualitative temperature. sgf Where β is the Prandtl number at the qualitative temperature, J is the acceleration of the tank, and β is the acceleration of the tank. sgf ν is the coefficient of volume expansion at the qualitative temperature. sgf Let μ be the kinematic viscosity at the qualitative temperature. sgf c is the dynamic viscosity at the qualitative temperature. p,sgf λ is the isobaric specific heat at the qualitative temperature. sgf The thermal conductivity at the qualitative temperature,

[0038] Heat transfer rate between the liquid surface layer and the liquid phase region for:

[0039]

[0040]

[0041]

[0042]

[0043] In the formula, A sl α is the heat transfer area between the liquid phase and the liquid surface layer. sl T is the heat transfer coefficient between the liquid phase and the liquid surface layer. l The temperature represents the liquid phase region. The subscript slf indicates that the qualitative temperature is taken as the arithmetic mean temperature of the boundary layer. (T) slf=(T s +T g ) / 2, C sl and n sl L represents the coefficients and exponents in the natural convection experimental equations. sl For feature size, Gr slf Pr is the Grashof number at the qualitative temperature. slf Where β is the Prandtl number at the qualitative temperature, J is the acceleration of the tank, and β is the acceleration of the tank. slf ν is the coefficient of volume expansion at the qualitative temperature. slf Let μ be the kinematic viscosity at the qualitative temperature. slf c is the dynamic viscosity at the qualitative temperature. p,slf λ is the isobaric specific heat at the qualitative temperature. slf is the thermal conductivity at the characteristic temperature.

[0044] Furthermore, in step 4, the evaporation rate of the liquid surface layer is obtained. for: In the formula, Δh v Latent heat of vaporization;

[0045] Boiling vaporization rate in the liquid phase for:

[0046] In the formula, Z g R is the compressibility factor in the gas phase region. g R is the gas constant in the gas phase region. g =188.91J / (kg·K), T l p is the temperature of the liquid phase region. s Let be the saturated vapor pressure of the liquid phase, and Δt be the integration step size.

[0047] Furthermore, in step 4, the integration step size Δt is obtained based on simulation calculations and experimental measurements;

[0048] The integration step size Δt minimizes the simulated pressure error of the tank. The simulated pressure error of the tank is:

[0049]

[0050] In the formula, t l Duration of self-pressurization supply; p sim The pressure obtained from the model simulation; p ex For the purpose of measuring pressure in the experiment.

[0051] Furthermore, the specific process of establishing the algebraic differential equation system describing the nitrous oxide self-pressurization tank in step 5 is as follows:

[0052] Step 5.1: Expand the internal energy derivative term in the energy conservation equation established in Step 1 to obtain the gas phase temperature T. g Liquid phase temperature T l The derivative with respect to time;

[0053]

[0054]

[0055] In the formula, u g u l These are the specific internal energy in the gas phase region and the specific internal energy in the liquid phase region, respectively.

[0056] Step 5.2: First, based on the constant tank volume and the equal pressures in the gas and liquid phases, the constraint equations are obtained as follows:

[0057] V g +V l =V0

[0058] p g -p l =0

[0059] In the formula, V0 is the volume of the storage tank;

[0060] Then, differentiating the constraint equations with respect to time yields the supplementary equations:

[0061]

[0062]

[0063] In the formula, This is the derivative of the gas phase volume with respect to time; Let be the derivative of the liquid phase volume with respect to time. Let be the derivative of gas phase pressure with respect to time. This is the derivative of the liquid phase pressure with respect to time.

[0064] Finally, expanding the derivative terms in the supplementary equation, we get...

[0065]

[0066]

[0067] In the formula, ρ g T g These are gas phase density and gas phase temperature, respectively. ρ are the derivatives of gas phase density and gas phase temperature with respect to time, respectively. l T l These are the liquid phase density and liquid phase temperature, respectively. These are the derivatives of the liquid phase density and liquid phase temperature with respect to time, respectively.

[0068] Step 5.3: Establish the actual fluid state equation and calculate the thermodynamic parameters of nitrous oxide;

[0069] The actual fluid state equation is:

[0070]

[0071]

[0072]

[0073] In the formula, f is the specific Helmholtz energy; δ is the dimensionless density, δ = ρ / ρ c , ρ c τ is the critical density; τ is the dimensionless temperature, τ = T c / T, T c α is the critical temperature; α is the dimensionless Helmholtz energy of the real gas; α 0 α is the dimensionless Helmholtz energy assuming the fluid is an ideal gas; r Let a1, a2, c0, c1, c2, υ be the dimensionless Helmholtz complement functions; k n k i k j k l k These are the coefficients of the actual fluid state equation;

[0074] The thermodynamic parameters of nitrous oxide calculated using the above formula are as follows:

[0075] Compression factor:

[0076] Internal energy:

[0077] Enthalpy:

[0078] Partial derivative of specific internal energy with respect to density:

[0079] The partial derivative of the specific internal energy with respect to temperature:

[0080] Partial derivative of pressure with respect to density:

[0081] Partial derivative of pressure with respect to temperature:

[0082] In the formula,

[0083] Step 5.4: Based on the energy conservation equation established in Step 1 and the results obtained in Steps 5.1-5.3, construct a set of algebraic differential equations describing the self-pressurized nitrous oxide tank:

[0084]

[0085] Furthermore, in step 5.3, the established actual fluid state equation is the Span-Wagner state equation, and the thermodynamic parameters of the nitrous oxide are calculated based on the partial derivatives of the Helmholtz energy.

[0086] Furthermore, in step 6, the method for solving the system of algebraic differential equations describing the self-pressurizing nitrous oxide tank is as follows:

[0087] Step 6.1: Calculate and obtain the initial parameters for the gas phase and liquid phase regions;

[0088] Assuming the tank is initially in equilibrium, and given the initial mass m0 of nitrous oxide and the initial temperature T0, the initial densities of the gas and liquid phases are as follows:

[0089] ρ g,0 =ρ g,sat (T0)

[0090] ρ l,0 =ρ l,sat (T0),

[0091] In the formula, ρ g,sat (T0) is the density of saturated nitrous oxide gas at the initial temperature T0; ρ l,sat (T0) is the density of the saturated nitrous oxide liquid at the initial temperature T0;

[0092] The initial masses of the gas phase and liquid phase regions were obtained as follows:

[0093]

[0094]

[0095] Step 6.2: Based on the initial parameters of the gas phase and liquid phase obtained in Step 6.1, integrate the algebraic differential equations describing the self-pressurizing nitrous oxide tank to obtain the tank pressure p = Z. g ρ g R g T g ,

[0096] In the formula, ρ g R is the gas phase density. g T is the gas constant in the gas phase region. gZ represents the temperature of the gas phase region. g It is the gas phase compressibility factor.

[0097] The advantages of this invention are:

[0098] 1. The present invention discloses a method for predicting the self-pressurized nitrous oxide supply pressure considering boiling mass transfer. When calculating the heat and mass transfer between the gas and liquid phases, an algebraic differential equation system describing the self-pressurized nitrous oxide tank is established by combining the mass conservation equation, energy conservation equation, actual fluid state equation, heat transfer model, mass transfer model and constraint equation. The boiling vaporization rate of liquid nitrous oxide is taken into account. The method of the present invention conforms to the actual physical process, has high prediction accuracy, and can more accurately simulate the working process of the self-pressurized tank.

[0099] 2. The present invention discloses a method for predicting the self-pressurization supply pressure of nitrous oxide considering boiling mass transfer. It can not only obtain the changes in tank pressure during the self-pressurization process, but also the changes in parameters such as supply flow rate, vaporization rate, mass of gas and liquid phases, and temperature. It can provide guidance for related research and application.

[0100] 3. The present invention discloses a method for predicting the self-pressurized supply pressure of nitrous oxide considering boiling mass transfer. When calculating the thermodynamic parameters of nitrous oxide, the actual fluid state equation is used, which can accurately calculate the relationship between parameters such as pressure, temperature and density of gaseous and liquid nitrous oxide, ensuring the accuracy of tank pressure prediction.

[0101] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0102] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0103] Figure 1 This is a flowchart of the method for predicting the pressure of a self-pressurizing nitrous oxide tank that takes boiling mass transfer into account, provided by the present invention.

[0104] Figure 2 This is a schematic diagram of the physical model of the nitrous oxide self-pressurizing tank in this invention;

[0105] Figure 3 This is a comparison chart of the tank pressure obtained by simulation using the method of this invention and the experimental results;

[0106] Figure 4 This is a comparison chart of the tank pressure obtained by the method of this invention and the simulation method using a three-zone model. Detailed Implementation

[0107] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments, so that the advantages and features of the present invention can be more easily understood by those skilled in the art, thereby providing a clearer and more explicit definition of the scope of protection of the present invention.

[0108] Reference Figure 1 A method for predicting the self-pressurizing supply pressure of nitrous oxide considering boiling mass transfer includes the following steps:

[0109] Step 1: Construct a physical model of a self-pressurizing nitrous oxide storage tank.

[0110] Reference Figure 2 In the physical model, the tank is divided into a gas phase region and a liquid phase region, and the interface between the gas phase region and the liquid phase region is the liquid surface layer.

[0111] When establishing the physical model of the storage tank, the following conditions are set:

[0112] (1) The temperature and density of the gas phase and liquid phase are spatially uniform and only change with time.

[0113] (2) The liquid surface layer is the interface between the gas phase region and the liquid phase region. Its thickness is ignored. Its physical property parameters are taken as the saturation parameters under the tank pressure. The heat transfer between the liquid surface layer and the gas phase region and the liquid phase region is natural convection.

[0114] (3) The storage tank is a rigid, insulated container, meaning that the volume of the storage tank remains constant and there is no heat exchange between the storage tank and nitrous oxide;

[0115] (4) Ignore the pressure difference caused by the gravity of the liquid, that is, the pressure in the liquid phase is equal to the pressure in the gas phase.

[0116] Step 2: Establish a thermodynamic model of the storage tank and analyze the mass and energy exchange processes in the gas phase and liquid phase regions, including the discharge of nitrous oxide from the liquid phase region, the boiling and vaporization of nitrous oxide in the liquid phase region, the evaporation and vaporization of nitrous oxide on the liquid surface layer, the heat transfer between the liquid phase region and the liquid surface layer, and the heat transfer between the gas phase region and the liquid surface layer. Establish the mass conservation equations and energy conservation equations for the gas phase and liquid phase regions.

[0117] The mass conservation equation is:

[0118]

[0119]

[0120] Define m g For gas phase mass, m l For liquid phase mass;

[0121] In the formula, Let be the derivative of the gas phase mass with respect to time. The derivative of the liquid phase mass with respect to time, The mass flow rate of nitrous oxide flowing out of the storage tank, The evaporation rate of the liquid surface layer. This represents the boiling vaporization rate in the liquid phase region.

[0122] The energy conservation equation is:

[0123]

[0124]

[0125] In the formula, U g V g These represent the internal energy and volume of the gas phase, respectively, U. l V l These are the internal energy and volume of the liquid phase region, respectively.

[0126] In the formula, These are the derivatives of the gas phase energy and the gas phase volume with respect to time, respectively. Let be the internal energy of the liquid phase and the derivative of the volume of the liquid phase with respect to time, respectively, and p be the tank pressure. The heat transfer rate between the liquid surface layer and the gas phase region. The heat transfer rate between the liquid surface layer and the liquid phase region;

[0127] h e To determine the specific enthalpy of nitrous oxide flowing out of the storage tank, the specific enthalpy of the liquid phase is taken.

[0128] h v The specific enthalpy of evaporated nitrous oxide is taken as the specific enthalpy of saturated gaseous nitrous oxide under the tank pressure.

[0129] h b The specific enthalpy is taken as the enthalpy of boiling nitrous oxide, and is the specific enthalpy of saturated gaseous nitrous oxide at the liquid phase temperature.

[0130] Step 3: Establish a heat transfer model and obtain the heat transfer rate between the liquid surface layer and the gas phase region based on the heat transfer model. and the heat transfer rate between the liquid phase region and the liquid phase region at the liquid surface layer

[0131] Heat transfer rate between the liquid surface layer and the gas phase region for:

[0132]

[0133]

[0134]

[0135]

[0136] In the formula, A sg α is the heat transfer area between the gas phase region and the liquid surface layer. sg T is the heat transfer coefficient between the gas phase region and the liquid surface layer. s T represents the temperature of the liquid surface layer. g The temperature represents the liquid phase region; the subscript 'sgf' indicates that the qualitative temperature is taken as the arithmetic mean temperature of the boundary layer. (T) sgf =(T s +T g ) / 2, C sg and n sg L represents the coefficients and exponents in the natural convection experimental relationship. sg For feature size, Gr sgf Pr is the Grashof number at the qualitative temperature. sgf Where β is the Prandtl number at the qualitative temperature, J is the acceleration of the tank, and β is the acceleration of the tank. sgf ν is the coefficient of volume expansion at the qualitative temperature. sgf Let μ be the kinematic viscosity at the qualitative temperature. sgf c is the dynamic viscosity at the qualitative temperature. p,sgf λ is the isobaric specific heat at the qualitative temperature. sgf The thermal conductivity at the characteristic temperature;

[0137] Heat transfer rate between the liquid surface layer and the liquid phase region for:

[0138]

[0139]

[0140]

[0141]

[0142] In the formula, A sl α is the heat transfer area between the liquid phase and the liquid surface layer. sl T is the heat transfer coefficient between the liquid phase and the liquid surface layer. l The temperature represents the liquid phase region. The subscript slf indicates that the qualitative temperature is taken as the arithmetic mean temperature of the boundary layer. (T) slf =(T s +T g ) / 2, C sl and n sl L represents the coefficients and exponents in the natural convection experimental relationship. sl For feature size, Gr slf Pr is the Grashof number at the qualitative temperature. slf Where β is the Prandtl number at the qualitative temperature, J is the acceleration of the tank, and β is the acceleration of the tank.slf ν is the coefficient of volume expansion at the qualitative temperature. slf Let μ be the kinematic viscosity at the qualitative temperature. slf c is the dynamic viscosity at the qualitative temperature. p,slf λ is the isobaric specific heat at the qualitative temperature. slf is the thermal conductivity at the characteristic temperature.

[0143] Step 4: Establish a mass transfer model to obtain the evaporation rate of the liquid surface layer. Boiling vaporization rate in the liquid phase region

[0144] The evaporation rate of the liquid surface layer is:

[0145]

[0146] In the formula, Δh v Latent heat of vaporization;

[0147] The boiling vaporization rate in the liquid phase region is:

[0148]

[0149] In the formula, Z g R is the compressibility factor in the gas phase region. g R is the gas constant in the gas phase region. g =188.91J / (kg·K), T l p is the temperature of the liquid phase region. s Let be the saturated vapor pressure of the liquid phase, and Δt be the integration step size.

[0150] The integration step size Δt can be determined based on self-pressurization simulation and experiments, that is, selecting the Δt that minimizes the simulation pressure error. The pressure error is calculated as follows:

[0151]

[0152] In the formula, t l Duration of self-pressurization supply; p sim The pressure obtained from the model simulation; p ex For the purpose of measuring pressure in the experiment.

[0153] Step 5: Establish a set of algebraic differential equations describing the self-pressurized nitrous oxide tank;

[0154] Step 5.1, select gas phase mass m g Liquid phase mass m l Gas phase density ρ g Vapor phase temperature T g Liquid phase density ρ l Liquid phase temperature T lAs an independent variable, the gas phase mass m g Liquid phase mass m l The derivative with respect to time has been given by the mass conservation equation in step 2, namely:

[0155]

[0156]

[0157] Step 5.2: Expand the internal energy derivative term in the energy conservation equation from Step 2 to obtain...

[0158]

[0159] From the above formula, we can obtain T g T l The derivative with respect to time:

[0160]

[0161]

[0162] In the formula, u g u l These are the specific internal energy in the gas phase and the specific internal energy in the liquid phase, respectively.

[0163] Step 5.3, based on the constant tank volume and the equal pressures in the gas and liquid phases, the constraint equations are obtained:

[0164] V g +V l =V0

[0165] p g -p l =0

[0166] In the formula, V0 is the volume of the storage tank.

[0167] Differentiating the constraint equations with respect to time yields two supplementary equations:

[0168]

[0169]

[0170] Expanding the derivative terms in the above supplementary equation, we get:

[0171]

[0172]

[0173] In the formula, ρ g T g These are gas phase density and gas phase temperature, respectively. ρ are the derivatives of gas phase density and gas phase temperature with respect to time, respectively. l T l These are the liquid phase density and liquid phase temperature, respectively. These are the derivatives of the liquid phase density and liquid phase temperature with respect to time, respectively.

[0174] Step 5.4: Establish the actual fluid state equation and calculate the thermodynamic parameters of nitrous oxide;

[0175] Using the Span-Wagner equations of state:

[0176]

[0177]

[0178]

[0179] In the formula, f is the specific Helmholtz energy; δ is the dimensionless density, δ = ρ / ρ c , ρ c τ is the critical density; τ is the dimensionless temperature, τ = T c / T, T c α is the critical temperature; α is the dimensionless Helmholtz energy of the real gas; α 0 α is the dimensionless Helmholtz energy assuming the fluid is an ideal gas; r Let a1, a2, c0, c1, c2, υ be the dimensionless Helmholtz complement functions; k n k i k j k l k These are the coefficients of the Span-Wagner equations of state.

[0180] The thermodynamic parameters of nitrous oxide are calculated based on the partial derivatives of the Helmholtz energy. These thermodynamic parameters include:

[0181] Compression factor:

[0182]

[0183] Internal energy:

[0184]

[0185] Enthalpy:

[0186]

[0187] Partial derivative of specific internal energy with respect to density:

[0188]

[0189] The partial derivative of the specific internal energy with respect to temperature:

[0190]

[0191] Partial derivative of pressure with respect to density:

[0192]

[0193] Partial derivative of pressure with respect to temperature:

[0194]

[0195] In the formula,

[0196] Step 5.5, based on the information about m in step 5.1 g m l The two differential equations, along with the results obtained in steps 5.2-5.4, constitute a set of algebraic differential equations describing the nitrous oxide self-pressurizing tank:

[0197]

[0198] Step 6: Solve the system of algebraic differential equations describing the self-pressurized nitrous oxide tank to obtain the internal pressure p of the tank;

[0199] Step 6.1: Calculate and obtain the initial parameters for the gas phase and liquid phase regions:

[0200] Assuming the tank is initially in equilibrium, and given the initial mass of nitrous oxide (m0) and the initial temperature (T0), the initial densities of the gas and liquid phases are respectively:

[0201] ρ g,0 =ρ g,sat (T0)

[0202] ρ l,0 =ρ l,sat (T0)

[0203] In the formula, ρ g,sat (T0) is the density of saturated nitrous oxide gas at the initial temperature T0; ρ l,sat (T0) is the density of the saturated nitrous oxide liquid at the initial temperature T0.

[0204] The initial masses of the gas phase and the liquid phase are as follows:

[0205]

[0206]

[0207] Step 6.2: Based on the initial parameters of the gas phase and liquid phase obtained in Step 6.1, integrate the algebraic differential equations describing the self-pressurizing nitrous oxide tank to obtain the instantaneous pressure change within the tank: p = Z g ρ g R g T g ,

[0208] In the formula, ρ g R is the gas phase density. g T is the gas constant in the gas phase region. g Z represents the temperature of the gas phase region. g This is the gas-phase compressibility factor, calculated from the actual equation of state.

[0209] By following the above steps, the pressure change of the nitrous oxide self-pressurizing tank over time can be obtained.

[0210] Reference Figure 3 The figure shows a comparison between the tank pressure obtained by simulation using the method of the present invention and the experimentally measured pressure. As can be seen from the figure, the predicted pressure of the nitrous oxide self-pressurizing tank obtained by the method of the present invention is consistent with the actual measurement.

[0211] Reference Figure 4 The figure shows a comparison between the tank pressure obtained by simulation using the method of the present invention and the pressure obtained by the three-zone model method. As can be seen from the figure, the pressure prediction result of the nitrous oxide self-pressurizing tank obtained by the method of the present invention can better reflect the dynamic change characteristics of the self-pressurizing tank. The relative error of the result obtained by the method of the present invention is only 0.54%, while the relative error of the pressure result obtained by the three-zone model method is 1.18%. This indicates that the pressure prediction method of the nitrous oxide self-pressurizing tank provided by the present invention has higher prediction accuracy than the three-zone model method.

[0212] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the scope of the technology disclosed in the present invention, and such modifications or substitutions should all be covered within the scope of protection of the present invention.

Claims

1. A method for predicting the self-pressurized nitrous oxide supply pressure considering boiling mass transfer, characterized in that, Includes the following steps: Step 1: Construct a physical model of the nitrous oxide self-pressurization tank; In the physical model, the tank is divided into a gas phase region and a liquid phase region, with a liquid surface layer between the gas phase region and the liquid phase region, and the thickness of the liquid surface layer is ignored. The temperature and density parameters of the gas phase and liquid phase regions change only with time in space, and the pressures of the two regions are equal. The physical properties of the liquid surface layer are taken as the saturation parameters under the tank pressure. The volume of the storage tank is fixed, and there is no heat exchange between the storage tank and nitrous oxide; Step 2: Construct the thermodynamic model of the tank described in Step 1, including the mass conservation equations and energy conservation equations for the gas phase region and the liquid phase region; Step 3: Construct the heat transfer model of the tank described in Step 1 to obtain the heat transfer rate between the liquid surface layer and the gas phase region. and the heat transfer rate between the liquid surface layer and the liquid phase region Step 4: Construct the mass transfer model of the tank described in Step 1 to obtain the evaporation rate of the liquid surface layer. Boiling vaporization rate in the liquid phase region Step 5: Based on the model equations established in Steps 2-4, and combined with the actual fluid state equations and supplementary equations, establish a set of algebraic differential equations describing the nitrous oxide self-pressurization tank. The supplementary equations are calculated based on the volume constraint equations and pressure constraint equations; Step 6: Solve the system of algebraic differential equations describing the self-pressurized nitrous oxide tank to obtain the pressure inside the tank.

2. The method for predicting the self-pressurized nitrous oxide supply pressure considering boiling mass transfer according to claim 1, characterized in that, The mass conservation equation established in step 2 is: Define m g For gas phase mass, m l For liquid phase mass; In the formula, Let be the derivative of the gas phase mass with respect to time. Let be the derivative of the liquid phase mass with respect to time. The mass flow rate of nitrous oxide flowing out of the storage tank. The evaporation rate of the liquid surface layer. The boiling vaporization rate in the liquid phase region; The energy conservation equation is: Definition: U g V g These represent the internal energy and volume of the gas phase, respectively; U l V l These are the internal energy and volume of the liquid phase region, respectively. In the formula, These are the derivatives of the gas phase energy and the gas phase volume with respect to time, respectively. Let be the internal energy of the liquid phase and the derivative of the volume of the liquid phase with respect to time, respectively, and p be the tank pressure. The heat transfer rate between the liquid surface layer and the gas phase region. The heat transfer rate between the liquid surface layer and the liquid phase region; h v The specific enthalpy of the evaporated nitrous oxide is taken as the specific enthalpy of saturated gaseous nitrous oxide under the tank pressure; h b The specific enthalpy is taken as the specific enthalpy of boiling nitrous oxide, and is the specific enthalpy of saturated gaseous nitrous oxide at the liquid phase temperature; h e The specific enthalpy of nitrous oxide flowing out of the storage tank is taken as the specific enthalpy of the liquid phase.

3. The method for predicting the self-pressurized nitrous oxide supply pressure considering boiling mass transfer according to claim 2, characterized in that, In step 3, the heat transfer rate between the liquid surface layer and the gas phase region is obtained. for: In the formula, A sg α is the heat transfer area between the gas phase region and the liquid surface layer. sg T is the heat transfer coefficient between the gas phase region and the liquid surface layer. s T represents the temperature of the liquid surface layer. g The temperature represents the liquid phase region; the subscript 'sgf' indicates that the qualitative temperature is taken as the arithmetic mean temperature of the boundary layer. (T) sgf =(T s +T g ) / 2, C sg and n sg L represents the coefficients and exponents in the natural convection experimental relationship. sg For feature size, Gr sgf Pr is the Grashof number at the qualitative temperature. sgf Where β is the Prandtl number at the qualitative temperature, J is the acceleration of the tank, and β is the acceleration of the tank. sgf ν is the coefficient of volume expansion at the qualitative temperature. sgf Let μ be the kinematic viscosity at the qualitative temperature. sgf c is the dynamic viscosity at the qualitative temperature. p,sgf λ is the isobaric specific heat at the qualitative temperature. sgf The thermal conductivity at the qualitative temperature, Heat transfer rate between the liquid surface layer and the liquid phase region for: In the formula, A sl α is the heat transfer area between the liquid phase and the liquid surface layer. sl T is the heat transfer coefficient between the liquid phase and the liquid surface layer. l The temperature represents the liquid phase region. The subscript slf indicates that the qualitative temperature is taken as the arithmetic mean temperature of the boundary layer. (T) slf =(T s +T g ) / 2, C sl and n sl L represents the coefficients and exponents in the natural convection experimental relationship. sl For feature size, Gr slf Pr is the Grashof number at the qualitative temperature. slf Where β is the Prandtl number at the qualitative temperature, J is the acceleration of the tank, and β is the acceleration of the tank. slf ν is the coefficient of volume expansion at the qualitative temperature. slf Let μ be the kinematic viscosity at the qualitative temperature. slf c is the dynamic viscosity at the qualitative temperature. p,slf λ is the isobaric specific heat at the qualitative temperature. slf is the thermal conductivity at the characteristic temperature.

4. The method for predicting the self-pressurized nitrous oxide supply pressure considering boiling mass transfer according to claim 3, characterized in that, In step 4, the evaporation rate of the liquid surface layer is obtained. for: In the formula, Δh v Latent heat of vaporization; Boiling vaporization rate in the liquid phase for: In the formula, Z g R is the compressibility factor in the gas phase region. g R is the gas constant in the gas phase region. g =188.91J / (kg·K), T l p is the temperature of the liquid phase region. s Let be the saturated vapor pressure of the liquid phase, and Δt be the integration step size.

5. The method for predicting the self-pressurized nitrous oxide supply pressure considering boiling mass transfer according to claim 4, characterized in that, In step 4, the integration step size Δt is obtained through simulation experiments to minimize the simulated pressure error of the storage tank. The simulated pressure error of the storage tank is... In the formula, t l Duration of self-pressurization supply; p sim The pressure obtained from the model simulation; p ex For the purpose of measuring pressure in the experiment.

6. The method for predicting the self-pressurized nitrous oxide supply pressure considering boiling mass transfer according to claim 5, characterized in that, The specific process of establishing the algebraic differential equation system describing the nitrous oxide self-pressurization tank in step 5 is as follows: Step 5.1: Expand the internal energy derivative term in the energy conservation equation established in Step 1 to obtain the gas phase temperature T. g Liquid phase temperature T l The derivative with respect to time; In the formula, u g u l These are the specific internal energy in the gas phase region and the specific internal energy in the liquid phase region, respectively. Step 5.2: First, based on the constant tank volume and the equal pressures in the gas and liquid phases, the constraint equations are obtained as follows: V g +V l =V0 p g -p l =0 In the formula, V0 is the volume of the storage tank; Then, differentiating the constraint equations with respect to time yields the supplementary equations: In the formula, This is the derivative of the gas phase volume with respect to time; Let be the derivative of the liquid phase volume with respect to time. Let be the derivative of gas phase pressure with respect to time. This is the derivative of the liquid phase pressure with respect to time; Finally, expanding the derivative terms in the supplementary equation, we get... In the formula, ρ g T g These are gas phase density and gas phase temperature, respectively. ρ are the derivatives of gas phase density and gas phase temperature with respect to time, respectively. l T l These are the liquid phase density and liquid phase temperature, respectively. These are the derivatives of the liquid phase density and liquid phase temperature with respect to time, respectively. Step 5.3: Establish the actual fluid state equation and calculate the thermodynamic parameters of nitrous oxide; The actual fluid state equation is: In the formula, f is the specific Helmholtz energy; δ is the dimensionless density, δ = ρ / ρ c , ρ c τ is the critical density; τ is the dimensionless temperature, τ = T c / T, T c α is the critical temperature; α is the dimensionless Helmholtz energy of the real gas; α 0 α is the dimensionless Helmholtz energy assuming the fluid is an ideal gas; r Let a1, a2, c0, c1, c2, υ be the dimensionless Helmholtz complement functions; k n k i k j k l k These are the coefficients of the actual fluid state equation; The thermodynamic parameters of nitrous oxide calculated using the above formula are as follows: Compression factor: Internal energy: Enthalpy: Partial derivative of specific internal energy with respect to density: The partial derivative of the specific internal energy with respect to temperature: Partial derivative of pressure with respect to density: Partial derivative of pressure with respect to temperature: In the formula, Step 5.4: Based on the energy conservation equation established in Step 1 and the results obtained in Steps 5.1-5.3, construct a set of algebraic differential equations describing the self-pressurized nitrous oxide tank:

7. The method for predicting the self-pressurized nitrous oxide supply pressure considering boiling mass transfer according to claim 6, characterized in that, In step 5.3, the established actual fluid state equation is the Span-Wagner state equation, and the thermodynamic parameters of the nitrous oxide are calculated based on the partial derivatives of the Helmholtz energy.

8. The method for predicting the self-pressurized nitrous oxide supply pressure considering boiling mass transfer according to claim 7, characterized in that, In step 6, the method for solving the system of algebraic differential equations describing the self-pressurized nitrous oxide tank is as follows: Step 6.1: Calculate and obtain the initial parameters for the gas phase and liquid phase regions; Assuming the tank is initially in equilibrium, and given the initial mass m0 of nitrous oxide and the initial temperature T0, the initial densities of the gas and liquid phases are as follows: r g,0 =ρ g,sat (T0) r l,0 =ρ l,sat (T0), In the formula, ρ g,sat (T0) is the density of saturated nitrous oxide gas at the initial temperature T0; ρ l,sat (T0) is the density of the saturated nitrous oxide liquid at the initial temperature T0; The initial masses of the gas phase and liquid phase regions were obtained as follows: Step 6.2: Based on the initial parameters of the gas phase and liquid phase obtained in Step 6.1, integrate the algebraic differential equations describing the self-pressurizing nitrous oxide tank to obtain the tank pressure p = Z. g ρ g R g T g , In the formula, ρ g R is the gas phase density. g T is the gas constant in the gas phase region. g Z represents the temperature of the gas phase region. g It is the gas phase compressibility factor.

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