CN113051849B - Method for predicting pressurization performance of low-temperature propellant storage tank by considering gas component change - Google Patents
Method for predicting pressurization performance of low-temperature propellant storage tank by considering gas component change Download PDFInfo
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- 239000000306 component Substances 0.000 description 151
- MYMOFIZGZYHOMD-UHFFFAOYSA-N Dioxygen Chemical compound O=O MYMOFIZGZYHOMD-UHFFFAOYSA-N 0.000 description 28
- 238000013517 stratification Methods 0.000 description 12
- 239000001307 helium Substances 0.000 description 7
- 229910052734 helium Inorganic materials 0.000 description 7
- SWQJXJOGLNCZEY-UHFFFAOYSA-N helium atom Chemical compound [He] SWQJXJOGLNCZEY-UHFFFAOYSA-N 0.000 description 7
- 238000011160 research Methods 0.000 description 6
- UFHFLCQGNIYNRP-UHFFFAOYSA-N Hydrogen Chemical compound [H][H] UFHFLCQGNIYNRP-UHFFFAOYSA-N 0.000 description 5
- 239000001257 hydrogen Substances 0.000 description 5
- 229910052739 hydrogen Inorganic materials 0.000 description 5
- 238000010586 diagram Methods 0.000 description 3
- IJGRMHOSHXDMSA-UHFFFAOYSA-N Atomic nitrogen Chemical compound N#N IJGRMHOSHXDMSA-UHFFFAOYSA-N 0.000 description 2
- 238000004458 analytical method Methods 0.000 description 2
- QVGXLLKOCUKJST-UHFFFAOYSA-N atomic oxygen Chemical compound [O] QVGXLLKOCUKJST-UHFFFAOYSA-N 0.000 description 2
- 230000005486 microgravity Effects 0.000 description 2
- 239000001301 oxygen Substances 0.000 description 2
- 229910052760 oxygen Inorganic materials 0.000 description 2
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Abstract
The invention relates to a low-temperature propellant storage tank supercharging performance prediction method, in particular to a low-temperature propellant storage tank supercharging performance prediction method considering gas component change. The invention aims to solve the technical problem that the pressurizing performance of a propellant storage tank cannot be accurately predicted due to the lack of a low-temperature propellant storage tank model considering the gas composition change in the storage tank in the prior art. Firstly, establishing an energy equation and a continuous equation of a gas phase region and a liquid phase region of a low-temperature propellant storage tank respectively, and a state equation of actual mixed gas in the gas phase region and an additional equation in the low-temperature propellant storage tank to form a basic equation of a mathematical model of the low-temperature propellant storage tank; and then respectively establishing a heat transfer model, a mass transfer model and a mixed gas model to finally obtain a complete low-temperature propellant storage tank simulation model which can be used for predicting the supercharging performance of the low-temperature propellant storage tank.
Description
Technical Field
The invention relates to a low-temperature propellant storage tank supercharging performance prediction method, in particular to a low-temperature propellant storage tank supercharging performance prediction method considering phase change and gas composition change.
Background
The low-temperature propellant storage tank is a core component of a pressurizing conveying system, and in the pressurizing process of the storage tank, complex fluid-solid, gas-liquid two-phase coupling heat and mass transfer phenomena exist, the thermal stratification phenomenon of the propellant storage tank caused by heat leakage of the storage tank exists, and meanwhile, the influence of surface tension in a low gravity environment on the flow of liquid in the storage tank also exists. Thus, the low temperature propellant reservoir is the most difficult component of the low temperature pressurized delivery system to study.
The advent of numerical modeling has provided tremendous convenience to propellant tank research, and many students have conducted detailed studies of tank pressurization processes by building propellant tank models and have reached a number of valuable conclusions. The method comprises the steps that a learner fully researches thermodynamic properties, heat transfer, mass transfer phenomena and the like of fluid in the pressurizing process of a storage tank, establishes a thermodynamic model of the pressurizing system of the storage tank, simulates the autogenous pressurizing process of an oxidant storage tank, compares simulation results with experimental measurement results, and verifies the effectiveness of the model; in order to study the pressure control problem in the autogenous pressurizing process of the liquid hydrogen storage tank, a scholars establishes a mathematical model of the fluid flow and the gas-liquid phase change process in the storage tank, wherein a gas pillow area and a liquid phase area of the storage tank are modeled by adopting a lumped parameter method, and the processes of external heat leakage, natural convection between gas and liquid phases, phase change and the like are considered; aiming at the problem of controlling the evaporation capacity of a low-temperature propellant on-orbit storage tank, a learner establishes a self-pressurization and pressure control simulation model of a low Wen Zhuxiang thermodynamic exhaust system, and comprehensively considers a plurality of modules such as a heat insulation material heat leakage model, a gas-liquid interface heat and mass transfer model, a gas pillow and storage tank wall heat exchange model and the like; a learner researches the autogenous pressurizing process of the liquid nitrogen storage tank by utilizing a low-temperature propellant storage tank multi-node model, models the heat transfer and mass transfer of a gas-liquid interface in the pressurizing process, and also considers the heat transfer between the storage tank wall and the pressurizing gas and the heat leakage phenomenon through the storage tank wall and the heat preservation layer; the self-generated pressurizing process of the liquid hydrogen storage tank is numerically simulated by a learner, the changes of parameters such as gas quality, temperature and pressure of the gas pillow are analyzed, the phase change and turbulence model in the pressurizing process are considered by a simulation model, and the phase change is found to mainly occur near a gas-liquid interface.
With the development of aerodynamic thermodynamics, hydrodynamics, heat and mass transfer science and other subjects and aerospace technology, the propellant storage tank modeling has more and more influencing factors. A learner performs numerical study on the pressure of the liquid hydrogen storage tank, the quality of propellant and pressurized gas, the fluid temperature and the thermal stratification change under shaking excitation by adopting a numerical simulation method; aiming at the problem that the temperature and the pressure of the air pillow are obviously reduced due to the increase of the evaporation amount of the propellant caused by shaking waves, a new method for predicting the distribution of liquid drops generated by a propellant storage tank in the maneuvering process by using a numerical tool is proposed by a learner, and the evaporation of the liquid drops and the change of the temperature and the pressure of the storage tank caused by the evaporation of the liquid drops are calculated by using an analytical model. The heat and mass transfer of the gas-liquid interface and the thermal stratification of the fluid are always research hot spots for modeling the propellant storage tank, a learner mainly researches the heat and mass transfer of the gas-liquid interface of the storage tank, establishes a mathematical model of the low-temperature propellant storage tank comprising a heat and mass transfer model of the gas-liquid interface, and verifies the effectiveness of the model by comparing the model with the settlement result of an engineering example and measured data; the method comprises the steps that a learner develops a one-dimensional flow field model of a propellant storage tank, establishes a simulation model of helium pressurization and autogenous pressurization, and mainly researches thermal stratification of a liquid hydrogen storage tank and a liquid oxygen storage tank, and simulation results show that the thermal stratification of a gas part of the storage tank is obvious, and the thermal stratification of a liquid part is not obvious; the problem of large evaporation loss of low-temperature propellant under microgravity environment is considered by a learner, the evaporation of liquid and the influence of the evaporation on vapor pressure under the microgravity condition are studied by adopting a numerical method, and simulation results show that a tiny vapor zone generated in the evaporation process can influence the pressure rise of a storage tank; the learner carries out numerical simulation on the convection flow phenomenon and the thermal stratification phenomenon of the liquid in the low-temperature storage tank by adopting a gas-liquid mixing model, and the result shows that the thermal stratification degree along the axial direction of the storage tank becomes weak along with the extension of the evaporation time of the liquid, and the thermal stratification degree of a liquid area becomes larger along with the time; the liquid oxygen storage tank CFD model which considers the phase change of the gas-liquid interface and the external forced convection heat exchange is established by a learner to study the pressurizing performance and the temperature distribution of the low-temperature propellant storage tank in the ground parking and ground pre-pressurizing stage, and the numerical simulation result shows that the thermal stratification is thickened along with the increase of time under the influence of the heat transfer of the gas pillow and the heat leakage of the wall of the storage tank. The scholars establish a CFD model of the liquid hydrogen storage tank, wherein a phase change model is established based on the Hertz-Knudsen equation, and mass transfer time relaxation factors are determined according to experimental data of NASA, and simulation results show that temperature stratification exists on the surface area of the propellant and the air pillow along the axial direction, the phase change mainly occurs near a gas-liquid interface, and mass transfer expressed in a condensation or vaporization mode is mainly determined by heat convection and molecular concentration near the gas-liquid interface.
However, these models mostly put the focus on temperature stratification and phase change in the tank (i.e., complicated heat and mass transfer process in the tank), and rarely consider the case that the gas composition in the gas pillow (i.e., the gas in the tank) changes with the pressurizing process, and usually consider the gas in the gas pillow as a single gas and rarely consider it as a mixed gas. Therefore, when the components of the air pillow gas are changed along with the pressurizing process, some deviation exists more or less when the simulation study is carried out by using the propellant storage tank models, and the pressurizing performance of the propellant storage tank is difficult to accurately predict.
Therefore, a method for predicting the supercharging performance of a low-temperature propellant tank in consideration of the change of the gas composition is to be proposed.
Disclosure of Invention
The invention aims to solve the technical problem that the low-temperature propellant storage tank model considering the gas component change in the storage tank is lacking in the prior art, so that the pressurizing performance of the propellant storage tank cannot be accurately predicted.
In order to solve the technical problems, the technical solution provided by the invention is as follows:
The low-temperature propellant storage tank pressurizing performance prediction method considering the gas composition change is characterized by comprising the following steps of:
1) Dividing the low-temperature propellant storage tank into a gas phase region and a liquid phase region, and establishing an energy equation and a continuous equation of the gas phase region and the liquid phase region respectively, and a state equation of actual mixed gas in the gas phase region and an additional equation in the low-temperature propellant storage tank to form a basic equation of a mathematical model of the low-temperature propellant storage tank;
the additional equations comprise a temperature equation of a gas-liquid interface of the storage tank, a volume change rate equation of a gas phase and a liquid phase, a density change rate equation of the gas phase and the liquid phase, a wall temperature equation of the storage tank contacted with the gas pillow gas and a wall temperature equation of the storage tank contacted with the propellant;
2) Analyzing main heat transfer and mass transfer processes in the storage tank, and establishing a heat transfer model and a mass transfer model in the storage tank according to the main heat transfer and mass transfer processes;
3) Establishing an actual mixed gas model;
4) And (3) establishing a simulation model of the low-temperature propellant storage tank according to the results obtained in the steps 1, 2) and 3), and predicting the supercharging performance of the low-temperature propellant storage tank.
Further, in the step 2), the heat transfer model and the mass transfer model in the storage tank are established according to the main heat transfer and mass transfer processes specifically include:
A) Taking the heat transfer process inside the storage tank as a main part, and establishing a natural convection heat transfer model;
the heat transfer process inside the storage tank comprises the heat convection between the storage tank wall and the pressurized gas, the heat convection between the storage tank wall and the propellant, the heat convection between the pressurized gas and the gas-liquid interface and the heat convection between the propellant and the gas-liquid interface;
b) The evaporation of the propellant is taken as the main part, and a mass transfer model is obtained by establishing an energy balance equation of a gas-liquid interface.
Further, the step 3) specifically includes the following steps:
3.1 Respectively establishing thermodynamic properties, mole fractions and mass fraction calculation equations of all components in the actual mixed gas, and calculating thermodynamic parameters, mole fractions and mass fractions of all the components by using the thermodynamic properties, mole fractions and mass fractions;
3.2 And (3) establishing a calculation equation of each thermodynamic parameter of the actual mixed gas as an actual mixed gas model by using the result obtained in the step 3.1).
Further, in step 4), the modeling simulation model of the low-temperature propellant storage tank adopts a secondary development tool AMESet of modeling simulation software AMESim, and specifically includes the following steps:
4.1 Designing an icon of the tank according to the structure of the low-temperature propellant tank, and defining a port type according to the fluid property of each port;
4.2 Defining external variables, internal variables, integer parameters and real parameters of the low-temperature propellant storage tank according to the structure, input, output and the to-be-observed quantity of the model;
4.3 Writing source codes of all functional modules of the low-temperature propellant storage tank according to the results obtained in the steps 1) to 3);
4.4 A debugging program for completing the establishment of the simulation model of the low-temperature propellant storage tank.
Further, in step 1), the energy equation and the continuous equation of the gas phase region constitute a control equation of the gas phase region, and the energy equation and the continuous equation of the liquid phase region constitute a control equation of the liquid phase region;
a) Control equation
Control equation for gas phase region:
energy equation:
wherein ,
the continuous equation:
control equation for liquid phase region:
energy equation:
wherein ,
the continuous equation:
wherein ,Tg 、P g 、ρ g 、V g 、m g The temperature, pressure, density, volume and mass of the air pillow gas are respectively;the derivatives of temperature, pressure, density, volume and mass of the air pillow gas with respect to time are respectively obtained; />A mass flow rate of pressurized gas into the tank; />Mass flow rate for propellant evaporation; u (u) g The internal energy of the gas per unit mass; f is u g P g Is a partial derivative of (2); c (C) vg The specific heat capacity is the constant capacity of the gas; h is a pg Specific enthalpy for the pressurized gas; h is a v Specific enthalpy for the propellant vapor; t (T) l 、P l 、ρ l 、V l 、m l The temperature, pressure, density, volume and mass of the propellant are respectively; />Respectively the temperature and pressure of the propellantStrong, density, volume, and mass derivatives with respect to time; />For the mass flow of propellant out of the reservoir; u (u) l The internal energy of the propellant per unit mass; f (F) 1 Is u l For T l Is a partial derivative of (2); f (F) 2 Is u l P l Is a partial derivative of (2); c (C) vl Specific heat capacity for the propellant; h is a prop Specific enthalpy for the propellant flowing out of the tank; h is a l Specific enthalpy for the surface layer of the propellant; r is a general gas constant, A, B, T r Are all F 1 and F2 Variables involved in the calculation equations of (2); z is the compression factor of the fluid, and a, b, alpha and kappa are coefficients involved in the state equation; t (T) c Is the critical temperature of the fluid; />Heat exchange amount between the pressurized gas and the storage tank wall contacted with the pressurized gas; />Heat exchange capacity between the pressurized gas and the gas-liquid interface; />Heat exchange between the propellant and the wall of the tank in contact with the propellant; />Heat exchange capacity of the propellant surface layer and the gas-liquid interface; />Mass flow rate for propellant evaporation; />For the mass flow of propellant out of the reservoir;
b) The method for acquiring the state equation is as follows:
the mixing rule is introduced for the actual pure gas state equation to correct the actual pure gas state equation so as to be suitable for mixed gas:
Wherein r= 8.3144J/mol/K; v g ＝M g V g /m g ；M g Is the relative molecular mass of the fluid; a and b are coefficients of a Peng-Robinson state equation; i. j is a subscript for distinguishing between different gases; t (T) g Is the temperature of the fluid; x is x i B is the mole fraction of component i i For the coefficients of the component i state equation, a i Coefficients for the component i state equation; a, a j Coefficients for the component j state equation; a, a ij Correcting parameters in an equation for a state equation coefficient a; k (k) ij Is a binary interaction parameter;
c) Additional equations include:
the temperature of the gas-liquid interface of the storage tank is equal to the saturation temperature T corresponding to the pressure of the air pillow of the storage tank Sat The equation is:
T i ＝T l,Sat (P g )
volume change rate equation for gas and liquid phases:
density change rate equation for gas and liquid phases:
tank wall temperature equation for gas contact with air pillow:
tank wall temperature equation for contact with propellant:
wherein ,Ti Is the temperature of the gas-liquid interface; t (T) l,Sat As a function for calculating the saturation temperature of the liquid;the derivative of tank wall temperature with time for contact with the air pillow gas; />A specific heat capacity at constant pressure for a reservoir wall in contact with the propellant; t (T) wl A tank wall temperature that is in contact with the propellant; t (T) wg The wall temperature of the storage tank which is in contact with the air pillow gas; />The inverse of tank wall temperature versus time for contact with the propellant; / >An increase in the mass of the reservoir wall in contact with the gas pillow gas per unit time; />The constant pressure specific heat capacity of the wall of the storage tank contacted with the air pillow gas; m is m wg The total mass of the tank wall in contact with the air pillow gas; m is m wl Is the total mass of the reservoir walls in contact with the propellant; />The heat exchange quantity between the wall of the storage tank contacted with the air pillow gas and the external environment; />Heat exchange between the reservoir wall in contact with the propellant and the external environment;
further, in step A) of step 2), the convective heat transfer between the reservoir wall and the pressurized gas is
wherein ,hgw An average convective heat transfer coefficient between the reservoir wall and the pressurized gas; a is that gw A convective heat transfer area between the reservoir wall and the pressurized gas; t (T) wg The wall temperature of the storage tank which is in contact with the air pillow gas; ra (Ra) gw The Rayleigh number involved in natural convection heat exchange between the storage tank wall and the pressurized gas; c (C) gw and ngw A constant involved in an empirical formula for average convective heat transfer coefficient; k (k) gwf The thermal conductivity coefficient of the air pillow gas at the physical property reference temperature; l (L) gw Characteristic lengths of a storage tank wall and a pressurized gas heat exchange surface are provided; a is the acceleration of the aircraft; ρ wg Is the density of the air pillow gas at the wall temperature of the storage tank in contact with the air pillow gas; mu (mu) gwf Absolute viscosity of the air pillow gas at physical property reference temperature; alpha gwf The thermal diffusivity of the air pillow gas at the physical property reference temperature;
the physical property reference temperature is:
the convection heat exchange between the wall of the storage tank and the propellant is that
wherein ,an average convective heat transfer coefficient between the reservoir wall and the propellant; a is that lw A convective heat transfer area between the reservoir wall and the propellant; ra (Ra) lw The Rayleigh number involved in natural convective heat transfer between the tank wall and the propellant; c (C) lw 、n lw A constant involved in an empirical formula for average convective heat transfer coefficient; k (k) l Is the heat conductivity coefficient of the propellant; l (L) lw Is the characteristic length of the heat exchange surface of the storage tank wall and the propellant; ρ wl Is the density of the propellant at the wall temperature of the tank with which it is in contact; alpha l Is the thermal diffusivity of the propellant; mu (mu) l Is the absolute viscosity of the propellant;
the convection heat exchange between the pressurized gas and the gas-liquid interface is that
wherein ,hgi The average convective heat transfer coefficient between the gas pillow gas and the gas-liquid interface; a is that gi The heat exchange area between the gas pillow gas and the gas-liquid interface is used; t (T) i Is the temperature of the gas-liquid interface; ra (Ra) gi The Rayleigh number is related to natural convection heat exchange between the gas pillow gas and the gas-liquid interface; c (C) gi 、n gi A constant involved in an empirical formula for average convective heat transfer coefficient; k (k) gif The thermal conductivity coefficient of the air pillow gas at the physical property reference temperature; l (L) gi Is the characteristic length of the heat exchange surface of the gas pillow gas and the gas-liquid interface; ρ i Is the density of the gas pillow gas at the gas-liquid interface temperature; mu (mu) gif Absolute viscosity of the air pillow gas at physical property reference temperature; alpha gif The thermal diffusivity of the air pillow gas at the physical property reference temperature; the physical property reference temperature is:
convective heat transfer between the propellant and the gas-liquid interface is
wherein ,hli Is the average convective heat transfer coefficient between the propellant and the gas-liquid interface; a is that li Is the heat exchange area between the propellant and the gas-liquid interface; t (T) i Is the temperature of the gas-liquid interface; k (k) gi The heat conductivity coefficient of saturated steam of the propellant; mu (mu) gi Saturated steam absolute viscosity for propellant; ρ li Saturation of the density of the liquid for the propellant; ρ gi Saturation of the density of the vapor for the propellant;equivalent latent heat for film boiling of the propellant; h is a lv Is the vaporization latent heat of the propellant; c (C) Pg The constant pressure specific heat capacity of the air pillow gas is obtained; sigma is the surface tension of the propellant;
in step B) of step 2), the energy equation of the gas-liquid interface is as follows:
further takes the following form:
under steady state conditions, considerThen there are:
and has h s -h i ＝h lv ，h i -h u ＝C pl (T i -T l )，
Then:
h fg ＝h lv +C pl (T i -T l )
thus:
wherein ,is the mass flow of fluid at interface u; h is a u Specific enthalpy for the fluid at interface u; />Is the mass flow of fluid at the interface S; h is a s Is the specific enthalpy of the fluid at the interface S; />Mass flow rate for propellant evaporation; h is a i Specific enthalpy for the gas-liquid interface fluid; c (C) pl The constant pressure specific heat capacity of the propellant; h is a fg The heat required to vaporize the propellant is a unit mass flow.
Further, in the actual mixed gas model of step 3.2):
a) The specific enthalpy of the actual mixed gas is:
wherein ,hm Specific enthalpy of the actual mixed gas;specific enthalpy which is ideal mixed gas; a, a ci Constant a in the Peng-Robinson equation of state for component i c ；a cj Constant a in the Peng-Robinson equation of state for component j c ；α i A coefficient α involved in the Peng-Robinson state equation for component i; alpha j A coefficient α involved in the Peng-Robinson state equation for component j; k (k) i A coefficient k related to a Peng-Robinson state equation of the component i; k (k) j A coefficient k related to a Peng-Robinson state equation of the component j; k (k) ij Is a binary interaction parameter; t (T) ci The critical temperature for component i; t (T) cj Is the critical temperature of component j; x is x i A mole fraction of component i; x is x j A mole fraction of component j; y is i The mass fraction of the component i; />Ideal specific enthalpy of gas for component i; a, a m 、b m Coefficients of the mixed gas Peng-Robinson state equation; m is M m Is the molar mass of the mixed gas;
b) The internal energy of the actual mixed gas is as follows:
wherein ,um The internal energy of the actual mixed gas in unit mass;the internal energy of the ideal mixed gas in unit mass;the ideal gas internal energy of the component i in unit mass;
c) The density of the mixed gas is as follows:
d) The constant pressure specific heat capacity of the mixed gas is as follows:
wherein ,Cpm The constant pressure specific heat capacity of the actual mixed gas; c (C) vm The specific heat capacity is fixed for the actual mixed gas;the specific heat capacity is the constant heat capacity of ideal mixed gas; />The specific heat capacity is fixed for the ideal gas of the component i; alpha i 、α j The coefficients α involved in the Peng-Robinson state equation for component i, component j, respectively; a, a ci 、a cj Constant a involved in the Peng-Robinson equation of state for component i, component j, respectively c ；k i 、k j The coefficients k involved in the Peng-Robinson state equation for component i, component j, respectively; t (T) ci 、T cj Critical temperatures for component i and component j, respectively;
e) The absolute viscosity of the mixed gas is:
η rij ＝(η ri η rj ) 1/2
wherein ,μm Absolute viscosity of the mixed gas; h ij As a function of the absolute viscosity, the contrast temperature and the contrast dipole moment of component i, component j; h ik As a function of the absolute viscosity, the contrast temperature and the contrast dipole moment of component i, component k; k (K) i Component properties for component i; k (K) j Is the component property of component j; k (K) k Component properties for component k; m is M k Is the molar mass of component k; m is M i Is the molar mass of component i; m is M j Molar mass of component j; c (C) i As a function of the absolute viscosity, the contrast temperature and the contrast dipole moment of component i; c (C) j As a function of the absolute viscosity, the contrast temperature and the contrast dipole moment of component i; mu (mu) i Absolute viscosity as component i; u (U) i As a function of the contrast temperature and the contrast dipole moment of component i; t (T) rij As a function of the temperature of the components i and j versus each other; f (F) Rij As a function of the contrast temperature and the contrast dipole moment of component i and component j; t (T) ri The comparative temperature for component i; f (F) Ri Is a polarity correction for component i; η (eta) ri A comparative dipole moment for component i; η (eta) rj A comparative dipole moment for component j; η (eta) i An electric dipole moment of component i; p (P) ci The critical temperature for component i; t (T) ci The critical temperature for component i; t (T) cj Is the critical temperature of component j; η (eta) rij As a function of the comparative dipole moments of component i and component j;
f) The heat conductivity of the mixed gas is as follows:
wherein ,Aij As a function of the comparative temperature of component i, component j;translational thermal conductivity coefficients of component i and component j respectively; Γ -shaped structure i Reciprocal of the comparative thermal conductivity of component i; Γ -shaped structure j Reciprocal of the comparative thermal conductivity of component j; t (T) ri The comparative temperature for component i; t (T) rj The comparative temperature for component j; k (k) i Is the thermal conductivity of component i; epsilon is a constant close to 1, here epsilon=1; t (T) ci The critical temperature for component i; p (P) ci Is the critical pressure of component i.
Compared with the prior art, the invention has the following beneficial effects:
1. the invention provides a method for predicting the pressurizing performance of a low-temperature propellant storage tank by considering the change of gas components, which comprises the steps of firstly establishing an energy equation and a continuous equation of a gas phase region and a liquid phase region of the low-temperature propellant storage tank respectively, and a state equation of actual mixed gas in the gas phase region and an additional equation in the low-temperature propellant storage tank to form a basic equation of a mathematical model of the low-temperature propellant storage tank; and then respectively establishing a heat transfer model, a mass transfer model and an actual mixed gas model to finally obtain a complete low-temperature propellant storage tank simulation model which can be used for predicting the supercharging performance of the low-temperature propellant storage tank. The practical gas is adopted in the basic equation of the mathematical model of the low-temperature propellant storage tank, and the practical mixed gas model is added into the simulation model, so that the simulation model of the storage tank is closer to the actual situation, therefore, the prediction of the supercharging performance of the storage tank has higher precision, and can be used for the prediction of the supercharging performance of the low-temperature propellant storage tank, the design of the low-temperature propellant storage tank and the like.
2. The method for predicting the supercharging performance of the low-temperature propellant storage tank taking the gas component change into consideration can simulate main heat transfer and mass transfer processes in the storage tank, can effectively calculate various thermodynamic parameters of mixed gas when the gas component in the storage tank changes, and can simulate the working process of the low-temperature propellant storage tank more accurately.
Drawings
FIG. 1 is a general flow chart of a method of predicting pressurization performance of a low temperature propellant tank in consideration of gas composition variation in accordance with the present invention;
FIG. 2 is a schematic illustration of a cryogenic propellant reservoir in an embodiment of the present invention;
FIG. 3 is a schematic diagram of the gas-liquid interface energy balance of a mass transfer model in an embodiment of the invention;
FIG. 4 is a graph showing the change of tank pressure with time with or without an actual gas mixture model in an embodiment of the present invention;
FIG. 5 shows the change of the temperature of the tank air pillow with time with or without the actual gas mixture model in an embodiment of the invention;
FIG. 6 is a graph showing the change in tank propellant temperature over time with or without an actual gas mixture model in an embodiment of the present invention;
FIG. 7 is a graph showing the change of the wall temperature of the tank in contact with the gas of the gas pillow with or without the actual gas mixture model according to the embodiment of the present invention;
FIG. 8 is a graph showing the change in reservoir wall temperature over time with propellant in the presence and absence of an actual gas mixture model in an embodiment of the present invention;
In FIGS. 4 to 8, y-1 to y-3 are set to 0.01kg/s, 0.05kg/s, 0.1kg/s, respectively, for the evaporation rate of liquid oxygen in the case of the actual mixed gas model, respectively; n-1 to n-3 are set to 0.01kg/s, 0.05kg/s and 0.1kg/s, respectively, for the evaporation rate of liquid oxygen without the actual mixed gas model.
Detailed Description
The invention is further described below with reference to the drawings and examples.
A method for predicting pressurization performance of a low-temperature propellant storage tank taking into account gas composition changes, as shown in fig. 1, comprising the following steps:
1) Dividing the low-temperature propellant storage tank into a gas phase region and a liquid phase region, and establishing an energy equation and a continuous equation (of an opening system) of the gas phase region and the liquid phase region respectively, and a state equation of actual mixed gas in the gas phase region and an additional equation in the low-temperature propellant storage tank to form a basic equation of a mathematical model of the low-temperature propellant storage tank; the energy equation and the continuous equation of the gas phase region form a control equation of the gas phase region, and the energy equation and the continuous equation of the liquid phase region form a control equation of the liquid phase region;
a) Control equation
Control equation for gas phase region:
energy equation:
wherein ,
the continuous equation:
control equation for liquid phase region:
Energy equation:
wherein ,
the continuous equation:
/>
wherein ,
T g 、P g 、ρ g 、V g 、m g the temperature, pressure, density, volume and mass of the air pillow gas are respectively;
the derivatives of temperature, pressure, density, volume and mass of the air pillow gas with respect to time are respectively obtained;
a mass flow rate of pressurized gas into the tank;
mass flow rate for propellant evaporation;
u g the internal energy of the gas per unit mass;
f is u g P g Is a partial derivative of (2);
C vg the specific heat capacity is the constant capacity of the gas;
h pg is pressurized airSpecific enthalpy of the body;
h v specific enthalpy for the propellant vapor;
T l 、P l 、ρ l 、V l 、m l the temperature, pressure, density, volume and mass of the propellant are respectively;
the derivatives of the temperature, pressure, density, volume, and mass of the propellant with respect to time, respectively;
for the mass flow of propellant out of the reservoir;
u l the internal energy of the propellant per unit mass;
F 1 is u l For T l Is a partial derivative of (2);
F 2 is u l P l Is a partial derivative of (2);
C vl specific heat capacity for the propellant;
h prop specific enthalpy for the propellant flowing out of the tank;
h l specific enthalpy for the surface layer of the propellant;
r is a general gas constant, A, B, T r Are all F 1 and F2 Variables involved in the calculation equations of (2);
z is the compression factor of the fluid, and a, b, alpha and k are coefficients involved in the state equation;
T c is the critical temperature of the fluid;
Heat exchange amount between the pressurized gas and the storage tank wall contacted with the pressurized gas;
heat exchange capacity between the pressurized gas and the gas-liquid interface;
heat exchange between the propellant and the wall of the tank in contact with the propellant;
heat exchange capacity of the propellant surface layer and the gas-liquid interface;
mass flow rate for propellant evaporation;
for the mass flow of propellant out of the reservoir;
b) Equation of state
Actual clean gas equation of state (Peng-Robinson equation of state):
/>
k＝0.37464+1.54226ω-0.26992ω 2
for the actual mixture (i.e. the mixture rules are modified to be suitable for the mixture by introducing them into the Peng-Robinson state equation):
wherein ,
R＝8.3144J/mol/K；
v g ＝M g V g /m g ；
M g is the relative molecular mass of the fluid;
a and b are coefficients of a Peng-Robinson state equation;
a c is a constant determined by the critical temperature and critical pressure of the fluid in the Peng-Robinson state equation;
i. j is a subscript for distinguishing between different gases;
T g is the temperature of the fluid;
k is a function of the eccentricity factor ω;
alpha is a function of k;
x i b is the mole fraction of component i i For the coefficients of the component i state equation, a i Coefficients for the component i state equation; a, a j Coefficients for the component j state equation; a, a ij Correcting parameters in an equation for a state equation coefficient a;
k ij is a binary interaction parameter;
c) Additional equations include:
the temperature of the gas-liquid interface of the storage tank is equal to the saturation temperature T corresponding to the pressure of the air pillow of the storage tank Sat The equation is:
T i ＝T l,Sat (P g )
volume change rate equation for gas and liquid phases:
density change rate equation for gas and liquid phases:
tank wall temperature equation for gas contact with air pillow:
tank wall temperature equation for contact with propellant:
wherein ,
T i is the temperature of the gas-liquid interface;
T l,Sat as a function for calculating the saturation temperature of the liquid;
the derivative of tank wall temperature with time for contact with the air pillow gas;
a specific heat capacity at constant pressure for a reservoir wall in contact with the propellant;
T wl is in combination withThe wall temperature of the storage tank contacted by the propellant;
T wg the wall temperature of the storage tank which is in contact with the air pillow gas;
the inverse of tank wall temperature versus time for contact with the propellant;
an increase in the mass of the reservoir wall in contact with the gas pillow gas per unit time;
the constant pressure specific heat capacity of the wall of the storage tank contacted with the air pillow gas;
m wg the total mass of the tank wall in contact with the air pillow gas;
m wl is the total mass of the reservoir walls in contact with the propellant;
the heat exchange quantity between the wall of the storage tank contacted with the air pillow gas and the external environment;
heat exchange between the reservoir wall in contact with the propellant and the external environment;
2) Analyzing main heat and mass transfer process in the storage tank, and building a heat transfer model and a mass transfer model in the storage tank according to the main heat and mass transfer process, specifically
A) The heat transfer between the storage tank and the external environment is not considered, only the heat transfer process inside the storage tank is considered, namely the storage tank is considered to be insulated from the environment, the heat transfer process inside the storage tank is mainly used, the flow velocity of fluid in the storage tank is small, and a natural convection heat transfer model is established;
the heat transfer process inside the storage tank comprises the following steps:
convective heat transfer between a reservoir wall and a pressurized gas
wherein ,
h gw an average convective heat transfer coefficient between the reservoir wall and the pressurized gas;
A gw a convective heat transfer area between the reservoir wall and the pressurized gas;
T wg the wall temperature of the storage tank which is in contact with the air pillow gas;
Ra gw the Rayleigh number involved in natural convection heat exchange between the storage tank wall and the pressurized gas;
C gw and ngw A constant involved in an empirical formula for average convective heat transfer coefficient;
k gwf the thermal conductivity coefficient of the air pillow gas at the physical property reference temperature;
L gw characteristic lengths of a storage tank wall and a pressurized gas heat exchange surface are provided;
a is the acceleration of the aircraft;
ρ wg is the density of the air pillow gas at the wall temperature of the storage tank in contact with the air pillow gas;
μ gwf absolute viscosity of the air pillow gas at physical property reference temperature;
α gwf the thermal diffusivity of the air pillow gas at the physical property reference temperature;
physical property reference temperatureThe degree is:
convective heat transfer between the reservoir wall and the propellant
wherein ,
h lw An average convective heat transfer coefficient between the reservoir wall and the propellant;
A lw a convective heat transfer area between the reservoir wall and the propellant;
Ra lw the Rayleigh number involved in natural convective heat transfer between the tank wall and the propellant;
C lw 、n lw a constant involved in an empirical formula for average convective heat transfer coefficient;
k l is the heat conductivity coefficient of the propellant;
L lw is the characteristic length of the heat exchange surface of the storage tank wall and the propellant;
ρ wl is the density of the propellant at the wall temperature of the tank with which it is in contact;
α l is the thermal diffusivity of the propellant;
μ l is the absolute viscosity of the propellant;
convective heat transfer between a pressurized gas and a gas-liquid interface
wherein ,
h gi the average convective heat transfer coefficient between the gas pillow gas and the gas-liquid interface;
A gi the heat exchange area between the gas pillow gas and the gas-liquid interface is used;
T i is the temperature of the gas-liquid interface;
Ra gi the Rayleigh number is related to natural convection heat exchange between the gas pillow gas and the gas-liquid interface;
C gi 、n gi a constant involved in an empirical formula for average convective heat transfer coefficient;
k gif the thermal conductivity coefficient of the air pillow gas at the physical property reference temperature;
L gi is the characteristic length of the heat exchange surface of the gas pillow gas and the gas-liquid interface;
ρ i is the density of the gas pillow gas at the gas-liquid interface temperature;
μ gif absolute viscosity of the air pillow gas at physical property reference temperature;
α gif The thermal diffusivity of the air pillow gas at the physical property reference temperature;
the physical property reference temperature is:
convective heat transfer between a propellant and a gas-liquid interface
wherein ,
h li is the average convective heat transfer coefficient between the propellant and the gas-liquid interface;
A li is the heat exchange area between the propellant and the gas-liquid interface;
T i is the temperature of the gas-liquid interface;
k gi the heat conductivity coefficient of saturated steam of the propellant;
μ gi saturated steam absolute viscosity for propellant;
ρ li saturation of the density of the liquid for the propellant;
ρ gi saturation of the density of the vapor for the propellant;
equivalent latent heat for film boiling of the propellant;
h lv is the vaporization latent heat of the propellant;
C Pg the constant pressure specific heat capacity of the air pillow gas is obtained;
sigma is the surface tension of the propellant;
b) Because the mass transfer process mainly occurs near the gas-liquid interface of the storage tank and the evaporation of the propellant is mainly performed, other mass transfer effects are ignored, and the mass transfer and the heat transfer of the gas-liquid interface are considered to be dense and inseparable, the evaporation amount of the propellant can be determined by establishing an energy balance equation of the gas-liquid interface to obtain a mass transfer model;
the energy equation for the gas-liquid interface can be written as follows:
further writeable into the following form:
under steady state conditions, considerThen there are:
/>
and has h s -h i ＝h lv ，h i -h u ＝C pl (T i -T l )，
Then:
h fg ＝h lv +C pl (T i -T l )
Thus:
wherein ,
is the mass flow of fluid at interface u;
h u specific enthalpy for the fluid at interface u;
is the mass flow of fluid at the interface S;
h s is the specific enthalpy of the fluid at the interface S;
mass flow rate for propellant evaporation;
h i specific enthalpy for the gas-liquid interface fluid;
C pl the constant pressure specific heat capacity of the propellant;
h fg the heat required to evaporate the propellant for a unit mass flow;
3) Taking the condition that the components of the gas pillow gas change along with the pressurizing process into consideration, establishing an actual mixed gas model based on thermodynamic properties of each component in the mixed gas and proportions (mole fraction and mass fraction) thereof, and calculating each thermodynamic parameter of the mixed gas;
the method comprises the following specific steps:
3.1 Respectively establishing thermodynamic properties, mole fractions and mass fraction calculation equations of all the components, and calculating thermodynamic parameters, mole fractions and mass fractions of all the components by using the thermodynamic properties, mole fractions and mass fraction calculation equations;
3.2 Using the result obtained in the step 3.1) to establish a calculation equation of each thermodynamic parameter of the actual mixed gas as an actual mixed gas model;
in the actual mixed gas model:
a) The specific enthalpy of an actual mixed gas is expressed as the sum of the specific enthalpy of an ideal mixed gas and a deviation function:
wherein ,
h m specific enthalpy of the actual mixed gas;
Specific enthalpy which is ideal mixed gas; />
a ci Constant a in the Peng-Robinson equation of state for component i c ；
a cj Constant a in the Peng-Robinson equation of state for component j c ；
α i A coefficient α involved in the Peng-Robinson state equation for component i;
α j a coefficient α involved in the Peng-Robinson state equation for component j;
k i a coefficient k related to a Peng-Robinson state equation of the component i;
k j a coefficient k related to a Peng-Robinson state equation of the component j;
k ij is a binary interaction parameter;
T ci the critical temperature for component i;
T cj is the critical temperature of component j;
x i a mole fraction of component i;
x j a mole fraction of component j;
y i the mass fraction of the component i;ideal specific enthalpy of gas for component i;
a m 、b m coefficients of the mixed gas Peng-Robinson state equation;
M m is the molar mass of the mixed gas;
b) The internal energy of the actual mixed gas is as follows:
wherein ,
u m the internal energy of the actual mixed gas in unit mass;
the internal energy of the ideal mixed gas in unit mass;
the ideal gas internal energy of the component i in unit mass;
c) The density of the mixed gas is equal to the sum of the densities of the components at the current temperature and partial pressure, expressed as:
d) The constant pressure specific heat capacity of the mixed gas is expressed as follows:
/>
wherein ,
C pm The constant pressure specific heat capacity of the actual mixed gas;
C vm the specific heat capacity is fixed for the actual mixed gas;
the specific heat capacity is the constant heat capacity of ideal mixed gas;
the specific heat capacity is fixed for the ideal gas of the component i;
α i 、α j the coefficients α involved in the Peng-Robinson state equation for component i, component j, respectively;
a ci 、a cj constant a involved in the Peng-Robinson equation of state for component i, component j, respectively c ；
k i 、k j The coefficients k involved in the Peng-Robinson state equation for component i, component j, respectively;
T ci 、T cj critical temperatures for component i and component j, respectively;
e) The absolute viscosity of the mixed gas is expressed as:
/>
η rij ＝(η ri η rj ) 1/2
wherein ,
μ m absolute viscosity of the mixed gas;
H ij as a function of the absolute viscosity, the contrast temperature and the contrast dipole moment of component i, component j;
H ik as a function of the absolute viscosity, the contrast temperature and the contrast dipole moment of component i, component k;
K i component properties for component i;
K j is the component property of component j;
K k component properties for component k;
M k is the molar mass of component k;
M i is the molar mass of component i;
M j molar mass of component j;
C i as a function of the absolute viscosity, the contrast temperature and the contrast dipole moment of component i;
C j as a function of the absolute viscosity, the contrast temperature and the contrast dipole moment of component i;
μ i absolute viscosity as component i;
U i as a function of the contrast temperature and the contrast dipole moment of component i;
T rij As a function of the temperature of the components i and j versus each other;
F Rij as a function of the contrast temperature and the contrast dipole moment of component i and component j;
T ri the comparative temperature for component i;
F Ri is a polarity correction for component i;
η ri a comparative dipole moment for component i;
η rj a comparative dipole moment for component j;
η i an electric dipole moment of component i;
P ci the critical temperature for component i;
T ci the critical temperature for component i;
T cj is the critical temperature of component j;
η rij as a function of the comparative dipole moments of component i and component j;
f) And the thermal conductivity of the mixed gas is expressed as:
/>
wherein ,
A ij as a function of the comparative temperature of component i, component j;
translational thermal conductivity coefficients of component i and component j respectively;
Γ i reciprocal of the comparative thermal conductivity of component i;
Γ j reciprocal of the comparative thermal conductivity of component j;
T ri the comparative temperature for component i;
T rj the comparative temperature for component j;
k i is the thermal conductivity of component i;
epsilon is a constant close to 1, here epsilon=1;
T ci the critical temperature for component i;
P ci is the critical pressure of component i;
4) According to the results obtained in the steps 1, 2) and 3), a secondary development tool AMESet adopting modeling simulation software AMESim is utilized to establish a simulation model of the low-temperature propellant storage tank, and the supercharging performance of the low-temperature propellant storage tank is predicted;
The method comprises the following steps:
4.1 Designing an icon of the tank according to the structure of the low-temperature propellant tank, and defining a port type according to the fluid property of each port;
4.2 Defining external variables, internal variables, integer parameters and real parameters of the low-temperature propellant storage tank according to the structure, input, output and the to-be-observed quantity of the model;
4.3 Writing source codes of all functional modules of the low-temperature propellant storage tank according to the results obtained in the steps 1) to 3);
4.4 A debugging program for completing the establishment of the simulation model of the low-temperature propellant storage tank;
5) And 4) performing calculation by using the low-temperature propellant storage tank simulation model established in the step 4.4), and verifying the effectiveness of the model, wherein the method specifically comprises the following steps of:
5.1 Simulation calculation
5.1A) setting different evaporation rates of the low-temperature propellant, and performing simulation calculation by using the low-temperature propellant storage tank simulation model which is built in the step 4.4) and comprises an actual mixed gas model;
5.1B) establishing a low-temperature propellant storage tank simulation model which does not contain an actual mixed gas model, setting the evaporation rate of the low-temperature propellant which is the same as that of the step 5.1A), and performing simulation calculation by using the low-temperature propellant storage tank simulation model which does not contain the actual mixed gas model;
5.2 Comparison of (d)
Comparing the simulation results obtained in the step 5.1A) and the step 5.1B) to verify the validity of the model.
Examples
Taking a helium pressurized liquid oxygen storage tank as an example, after the structural parameters of the liquid oxygen storage tank and the initial conditions and performance indexes of the helium pressurization process are obtained, modeling work of the liquid oxygen storage tank is started.
1) Comprehensive and systematic analysis is carried out on the pressurizing process of the liquid oxygen storage tank, and the main heat and mass transfer process in the storage tank is determined, wherein the schematic diagram of the low-temperature propellant storage tank is shown in fig. 2; dividing the low-temperature propellant storage tank into a gas phase region and a liquid phase region, and establishing an energy equation and a continuous equation of the gas phase region and the liquid phase region respectively, and a state equation of actual mixed gas in the gas phase region and an additional equation in the low-temperature propellant storage tank to form a basic equation of a mathematical model of the low-temperature propellant storage tank;
2) Analyzing main heat transfer and mass transfer processes in the storage tank, and establishing a heat transfer model and a mass transfer model in the storage tank according to the main heat transfer and mass transfer processes;
a) Establishing a liquid oxygen storage tank heat transfer model
According to analysis, the heat transfer process inside the liquid oxygen storage tank mainly considers four heat transfer processes, namely the heat convection between the storage tank wall and the pressurized gas, the heat convection between the storage tank wall and the liquid oxygen, the heat convection between the pressurized gas and the gas-liquid interface and the heat convection between the liquid oxygen and the gas-liquid interface, and the flow velocity of fluid in the storage tank is small, so that the heat transfer process in the liquid oxygen storage tank adopts a natural convection heat transfer model, and on the basis, parameters required by each convection heat transfer process in the storage tank are obtained, namely the establishment of the heat transfer model of the liquid oxygen storage tank is completed;
B) Establishing a mass transfer model in a liquid oxygen storage tank
The mass transfer process in the liquid oxygen storage tank mainly occurs near the gas-liquid interface of the storage tank, the evaporation of liquid oxygen is dominant, the dissolution amount of helium in the liquid oxygen is very small and negligible, and considering that the mass transfer and the heat transfer of the gas-liquid interface are dense and inseparable, the evaporation amount of the liquid oxygen is determined by establishing an energy balance relation of the gas-liquid interface to obtain a mass transfer model, and the energy balance diagram of the gas-liquid interface of the mass transfer model is shown in fig. 3;
3) For a liquid oxygen storage tank pressurized by helium, due to the evaporation of liquid oxygen, a gas pillow of the storage tank simultaneously contains two gases of helium and oxygen, the gas proportion changes with time, and a mixed gas model is required to be established according to thermodynamic parameters, mole fraction and mass fraction of the helium and the oxygen, and the specific method comprises the following steps:
3.1 Respectively establishing thermodynamic properties, mole fractions and mass fraction calculation equations of all the components, and calculating thermodynamic parameters, mole fractions and mass fractions of all the components by using the thermodynamic properties, mole fractions and mass fraction calculation equations;
3.2 Using the result obtained in the step 3.1) to establish a calculation equation of each thermodynamic parameter of the actual mixed gas as an actual mixed gas model;
4) Establishing a simulation model of the liquid oxygen storage tank by using a secondary development tool AMESet of modeling simulation software AMESim
4.1 Designing an icon of the tank according to the structure of the low-temperature propellant tank, and defining a port type according to the fluid property of each port;
4.2 Defining external variables, internal variables, integer parameters and real parameters of the low-temperature propellant storage tank according to the structure, input, output and the to-be-observed quantity of the model;
4.3 Writing source codes of all functional modules of the low-temperature propellant storage tank according to the results obtained in the steps 1) to 3);
4.4 A debugging program for completing the establishment of the simulation model of the low-temperature propellant storage tank;
5) Verifying validity of simulation model
The evaporation rate of liquid oxygen is respectively set to be 0.01kg/s, 0.05kg/s and 0.1kg/s, simulation calculation is respectively carried out by using a liquid oxygen storage tank simulation model comprising an actual mixed gas model and a liquid oxygen storage tank simulation model not comprising an actual mixed gas model, simulation results are shown in fig. 4-8, and the change of the storage tank pressure with time when the actual mixed gas model exists or does not exist is shown in fig. 4; FIG. 5 is a graph showing the change in reservoir air pillow temperature over time with and without an actual mixed gas model; FIG. 6 is a graph showing the change in tank propellant temperature over time with and without an actual gas mixture model; FIG. 7 is a graph showing the change in reservoir wall temperature over time with and without an actual mixed gas model in contact with the gas pillow gas; FIG. 8 shows the change in reservoir wall temperature over time with and without an actual gas mixture model in contact with the propellant.
Comparing the simulation results, the simulation results of the liquid oxygen storage tank model which does not contain the actual mixed gas model are larger than those of the liquid oxygen storage tank model which contains the actual mixed gas model, and the deviation is larger as the liquid oxygen evaporation rate is increased.
The method for predicting the pressurizing performance of the low-temperature propellant storage tank has higher precision, and can be used for predicting the pressurizing performance of the low-temperature propellant storage tank and designing and researching the low-temperature propellant storage tank, especially for predicting the pressurizing performance of the low-temperature propellant storage tank, wherein the components of the air pillow gas can change along with the pressurizing process.
Finally, it should be noted that: the foregoing embodiments are merely for illustrating the technical solutions of the present invention, and not for limiting the same, and it will be apparent to those skilled in the art that modifications may be made to the specific technical solutions described in the foregoing embodiments, or equivalents may be substituted for some of the technical features thereof, without departing from the spirit of the technical solutions protected by the present invention.
Claims (7)
1. A method for predicting pressurization performance of a low-temperature propellant storage tank in consideration of gas composition change, comprising the steps of:
1) Dividing the low-temperature propellant storage tank into a gas phase region and a liquid phase region, and establishing an energy equation and a continuous equation of the gas phase region and the liquid phase region respectively, and a state equation of actual mixed gas in the gas phase region and an additional equation in the low-temperature propellant storage tank to form a basic equation of a mathematical model of the low-temperature propellant storage tank;
the additional equations comprise a temperature equation of a gas-liquid interface of the storage tank, a volume change rate equation of a gas phase and a liquid phase, a density change rate equation of the gas phase and the liquid phase, a wall temperature equation of the storage tank contacted with the gas pillow gas and a wall temperature equation of the storage tank contacted with the propellant;
2) Analyzing main heat transfer and mass transfer processes in the storage tank, and establishing a heat transfer model and a mass transfer model in the storage tank according to the main heat transfer and mass transfer processes;
3) Establishing an actual mixed gas model;
4) And (3) establishing a simulation model of the low-temperature propellant storage tank according to the results obtained in the steps 1, 2) and 3), and predicting the supercharging performance of the low-temperature propellant storage tank.
2. The method for predicting pressurization performance of a low-temperature propellant tank taking into account gas composition changes as recited in claim 1, wherein:
in the step 2), the heat transfer model and the mass transfer model in the storage tank are established according to the main heat transfer and mass transfer processes, and specifically:
A) Taking the heat transfer process inside the storage tank as a main part, and establishing a natural convection heat transfer model;
the heat transfer process inside the storage tank comprises the heat convection between the storage tank wall and the pressurized gas, the heat convection between the storage tank wall and the propellant, the heat convection between the pressurized gas and the gas-liquid interface and the heat convection between the propellant and the gas-liquid interface;
b) The evaporation of the propellant is taken as the main part, and a mass transfer model is obtained by establishing an energy balance equation of a gas-liquid interface.
3. The method for predicting pressurization performance of a low-temperature propellant tank taking into account gas composition changes as recited in claim 2, wherein the step 3) specifically comprises the steps of:
3.1 Respectively establishing thermodynamic properties, mole fractions and mass fraction calculation equations of all components in the actual mixed gas, and calculating thermodynamic parameters, mole fractions and mass fractions of all the components by using the thermodynamic properties, mole fractions and mass fractions;
3.2 And (3) establishing a calculation equation of each thermodynamic parameter of the actual mixed gas as an actual mixed gas model by using the result obtained in the step 3.1).
4. A method of predicting the pressurization performance of a low temperature propellant tank taking into account a change in gas composition according to any one of claims 1 to 3, wherein:
in step 4), the simulation model of the low-temperature propellant storage tank is built by adopting a secondary development tool AMESet of modeling simulation software AMESim, and the method specifically comprises the following steps:
4.1 Designing an icon of the tank according to the structure of the low-temperature propellant tank, and defining a port type according to the fluid property of each port;
4.2 Defining external variables, internal variables, integer parameters and real parameters of the low-temperature propellant storage tank according to the structure, input, output and the to-be-observed quantity of the model;
4.3 Writing source codes of all functional modules of the low-temperature propellant storage tank according to the results obtained in the steps 1) to 3);
4.4 A debugging program for completing the establishment of the simulation model of the low-temperature propellant storage tank.
5. The method for predicting pressurization performance of a low-temperature propellant tank taking into account gas composition changes as recited in claim 1, wherein:
in the step 1), an energy equation and a continuous equation of the gas phase region form a control equation of the gas phase region, and an energy equation and a continuous equation of the liquid phase region form a control equation of the liquid phase region;
a) Control equation
Control equation for gas phase region:
energy equation:
wherein ,
the continuous equation:
control equation for liquid phase region:
energy equation:
wherein ,
the continuous equation:
wherein ,
T g 、P g 、ρ g 、V g 、m g the temperature, pressure, density, volume and mass of the air pillow gas are respectively;
the derivatives of temperature, pressure, density, volume and mass of the air pillow gas with respect to time are respectively obtained;
A mass flow rate of pressurized gas into the tank;
mass flow rate for propellant evaporation;
u g the internal energy of the gas per unit mass;
f is u g P g Is a partial derivative of (2);
C vg the specific heat capacity is the constant capacity of the gas;
h pg specific enthalpy for the pressurized gas;
h v specific enthalpy for the propellant vapor;
T l 、P l 、ρ l 、V l 、m l the temperature, pressure, density, volume and mass of the propellant are respectively;
respectively propellantsTemperature, pressure, density, volume, and mass derivatives with respect to time;
for the mass flow of propellant out of the reservoir;
u l the internal energy of the propellant per unit mass;
F 1 is u l For T l Is a partial derivative of (2);
F 2 is u l P l Is a partial derivative of (2);
C vl specific heat capacity for the propellant;
h prop specific enthalpy for the propellant flowing out of the tank;
h l specific enthalpy for the surface layer of the propellant;
r is a general gas constant, A, B, T r Are all F 1 and F2 Variables involved in the calculation equations of (2);
z is the compression factor of the fluid, and a, b, alpha and k are coefficients involved in the state equation;
T c is the critical temperature of the fluid;
heat exchange amount between the pressurized gas and the storage tank wall contacted with the pressurized gas;
heat exchange capacity between the pressurized gas and the gas-liquid interface;
heat exchange between the propellant and the wall of the tank in contact with the propellant;
heat exchange capacity of the propellant surface layer and the gas-liquid interface;
Mass flow rate for propellant evaporation;
for the mass flow of propellant out of the reservoir;
b) The method for acquiring the state equation is as follows:
the mixing rule is introduced for the actual pure gas state equation to correct the actual pure gas state equation so as to be suitable for mixed gas:
wherein ,
R＝8.3144J/mol/K；
v g ＝M g V g /m g ；
M g is the relative molecular mass of the fluid;
a and b are coefficients of a Peng-Robinson state equation;
i. j is a subscript for distinguishing between different gases;
T g is the temperature of the fluid;
x i b is the mole fraction of component i i For the coefficients of the component i state equation, a i Coefficients for the component i state equation; a, a j Coefficients for the component j state equation; a, a ij Correcting parameters in an equation for a state equation coefficient a;
k ij is a binary interaction parameter;
c) Additional equations include:
the temperature of the gas-liquid interface of the storage tank is equal to the saturation temperature T corresponding to the pressure of the air pillow of the storage tank Sat The equation is:
T i ＝T l,Sat (P g )
volume change rate equation for gas and liquid phases:
density change rate equation for gas and liquid phases:
tank wall temperature equation for gas contact with air pillow:
tank wall temperature equation for contact with propellant:
wherein ,
T i is the temperature of the gas-liquid interface;
T l,Sat as a function for calculating the saturation temperature of the liquid;
the derivative of tank wall temperature with time for contact with the air pillow gas;
C pwl A specific heat capacity at constant pressure for a reservoir wall in contact with the propellant;
T wl a tank wall temperature that is in contact with the propellant;
T wg the wall temperature of the storage tank which is in contact with the air pillow gas;
the inverse of tank wall temperature versus time for contact with the propellant;
an increase in the mass of the reservoir wall in contact with the gas pillow gas per unit time;
C pwg the constant pressure specific heat capacity of the wall of the storage tank contacted with the air pillow gas;
m wg the total mass of the tank wall in contact with the air pillow gas;
m wl is the total mass of the reservoir walls in contact with the propellant;
the heat exchange quantity between the wall of the storage tank contacted with the air pillow gas and the external environment;
is the amount of heat exchange between the reservoir wall in contact with the propellant and the external environment.
6. The method for predicting pressurization performance of a low-temperature propellant tank taking into account gas composition changes as recited in claim 2, wherein:
in step A) of step 2), the convective heat transfer between the reservoir wall and the pressurized gas is
wherein ,
h gw an average convective heat transfer coefficient between the reservoir wall and the pressurized gas;
A gw a convective heat transfer area between the reservoir wall and the pressurized gas;
T wg the wall temperature of the storage tank which is in contact with the air pillow gas;
Ra gw the Rayleigh number involved in natural convection heat exchange between the storage tank wall and the pressurized gas;
C gw and ngw A constant involved in an empirical formula for average convective heat transfer coefficient;
k gwf the thermal conductivity coefficient of the air pillow gas at the physical property reference temperature;
L gw is a storage tankCharacteristic length of wall and pressurized gas heat exchange surface;
a is the acceleration of the aircraft;
ρ wg is the density of the air pillow gas at the wall temperature of the storage tank in contact with the air pillow gas;
μ gwf absolute viscosity of the air pillow gas at physical property reference temperature;
α gwf the thermal diffusivity of the air pillow gas at the physical property reference temperature;
the physical property reference temperature is:
the convection heat exchange between the wall of the storage tank and the propellant is that
wherein ,
h lw an average convective heat transfer coefficient between the reservoir wall and the propellant;
A lw a convective heat transfer area between the reservoir wall and the propellant;
Ra lw the Rayleigh number involved in natural convective heat transfer between the tank wall and the propellant;
C lw 、n lw a constant involved in an empirical formula for average convective heat transfer coefficient;
k l heat conducting system for propellantA number;
L lw is the characteristic length of the heat exchange surface of the storage tank wall and the propellant;
ρ wl is the density of the propellant at the wall temperature of the tank with which it is in contact;
α l is the thermal diffusivity of the propellant;
μ l is the absolute viscosity of the propellant;
the convection heat exchange between the pressurized gas and the gas-liquid interface is that
wherein ,
h gi the average convective heat transfer coefficient between the gas pillow gas and the gas-liquid interface;
A gi The heat exchange area between the gas pillow gas and the gas-liquid interface is used;
T i is the temperature of the gas-liquid interface;
Ra gi the Rayleigh number is related to natural convection heat exchange between the gas pillow gas and the gas-liquid interface;
C gi 、n gi a constant involved in an empirical formula for average convective heat transfer coefficient;
k gif the thermal conductivity coefficient of the air pillow gas at the physical property reference temperature;
L gi is the characteristic length of the heat exchange surface of the gas pillow gas and the gas-liquid interface;
ρ i is the density of the gas pillow gas at the gas-liquid interface temperature;
μ gif absolute viscosity of the air pillow gas at physical property reference temperature;
α gif the thermal diffusivity of the air pillow gas at the physical property reference temperature;
the physical property reference temperature is:
convective heat transfer between the propellant and the gas-liquid interface is
wherein ,
h li is the average convective heat transfer coefficient between the propellant and the gas-liquid interface;
A li is the heat exchange area between the propellant and the gas-liquid interface;
T i is the temperature of the gas-liquid interface;
k gi the heat conductivity coefficient of saturated steam of the propellant;
μ gi saturated steam absolute viscosity for propellant;
ρ li saturation of the density of the liquid for the propellant;
ρ gi saturation of the density of the vapor for the propellant;
equivalent latent heat for film boiling of the propellant;
h lv is the vaporization latent heat of the propellant;
C Pg the constant pressure specific heat capacity of the air pillow gas is obtained;
sigma is the surface tension of the propellant;
In step B) of step 2), the energy equation of the gas-liquid interface is as follows:
further takes the following form:
under steady state conditions, considerThen there are:
and has h s -h i ＝h lv ，h i -h u ＝C pl (T i -T l )，
Then:
h fg ＝h lv +C pl (T i -T l )
thus:
wherein ,
is the mass flow of fluid at interface u;
h u specific enthalpy for the fluid at interface u;
is the mass flow of fluid at the interface S;
h s is the specific enthalpy of the fluid at the interface S;
mass flow rate for propellant evaporation;
h i specific enthalpy for the gas-liquid interface fluid;
C pl the constant pressure specific heat capacity of the propellant;
h fg the heat required to vaporize the propellant is a unit mass flow.
7. A method of predicting the pressurization performance of a low temperature propellant tank in consideration of a change in gas composition as claimed in claim 3, wherein:
in the actual mixed gas model of step 3.2):
a) The specific enthalpy of the actual mixed gas is:
wherein ,
h m specific enthalpy of the actual mixed gas;
specific enthalpy which is ideal mixed gas;
a ci constant a in the Peng-Robinson equation of state for component i c ；
a cj Constant a in the Peng-Robinson equation of state for component j c ；
α i A coefficient α involved in the Peng-Robinson state equation for component i;
α j a coefficient α involved in the Peng-Robinson state equation for component j;
k i a coefficient k related to a Peng-Robinson state equation of the component i;
k j A coefficient k related to a Peng-Robinson state equation of the component j;
k ij is a binary interaction parameter;
T ci the critical temperature for component i;
T cj is the critical temperature of component j;
x i a mole fraction of component i;
x j a mole fraction of component j;
y i the mass fraction of the component i;ideal specific enthalpy of gas for component i;
a m 、b m coefficients of the mixed gas Peng-Robinson state equation;
M m is the molar mass of the mixed gas;
b) The internal energy of the actual mixed gas is as follows:
wherein ,
u m the internal energy of the actual mixed gas in unit mass;
the internal energy of the ideal mixed gas in unit mass;
an ideal gas internal energy per unit mass of the composition;
c) The density of the mixed gas is as follows:
d) The constant pressure specific heat capacity of the mixed gas is as follows:
wherein ,
C pm the constant pressure specific heat capacity of the actual mixed gas;
C vm the specific heat capacity is fixed for the actual mixed gas;
the specific heat capacity is the constant heat capacity of ideal mixed gas;
the specific heat capacity is fixed for the ideal gas of the component i;
α i 、α j the coefficients α involved in the Peng-Robinson state equation for component i, component j, respectively;
a ci 、a cj constant a involved in the Peng-Robinson equation of state for component i, component j, respectively c ；
k i 、k j The coefficients k involved in the Peng-Robinson state equation for component i, component j, respectively;
T ci 、T cj critical temperatures for component i and component j, respectively;
e) The absolute viscosity of the mixed gas is:
η rij ＝(η ri η rj ) 1/2
wherein ,
μ m absolute viscosity of the mixed gas;
H ij as a function of the absolute viscosity, the contrast temperature and the contrast dipole moment of component i, component j;
H ik as a function of the absolute viscosity, the contrast temperature and the contrast dipole moment of component i, component k;
K i is composed ofComponent properties of i;
K j is the component property of component j;
K k component properties for component k;
M k is the molar mass of component k;
M i is the molar mass of component i;
M j molar mass of component j;
C i as a function of the absolute viscosity, the contrast temperature and the contrast dipole moment of component i;
C j as a function of the absolute viscosity, the contrast temperature and the contrast dipole moment of component i;
μ i absolute viscosity as component i;
U i as a function of the contrast temperature and the contrast dipole moment of component i;
T rij as a function of the temperature of the components i and j versus each other;
F Rij as a function of the contrast temperature and the contrast dipole moment of component i and component j;
T ri the comparative temperature for component i;
F Ri is a polarity correction for component i;
η ri a comparative dipole moment for component i;
η rj a comparative dipole moment for component j;
η i an electric dipole moment of component i;
P ci the critical temperature for component i;
T ci the critical temperature for component i;
T cj is the critical temperature of component j;
η rij as a function of the comparative dipole moments of component i and component j;
f) The heat conductivity of the mixed gas is as follows:
/>
wherein ,
A ij as a function of the comparative temperature of component i, component j;
translational thermal conductivity coefficients of component i and component j respectively;
Γ i reciprocal of the comparative thermal conductivity of component i;
Γ j reciprocal of the comparative thermal conductivity of component j;
T ri the comparative temperature for component i;
T rj the comparative temperature for component j;
k i is the thermal conductivity of component i;
epsilon is a constant close to 1, here epsilon=1;
T ci the critical temperature for component i;
P ci is the critical pressure of component i.
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| EP1462605A1 (en) * | 2003-03-28 | 2004-09-29 | Institut Francais Du Petrole | Method of modelling a hydrocarbon mixture by subdividing it in pseudocomponents |
| CN103017852A (en) * | 2012-12-28 | 2013-04-03 | 中国人民解放军国防科学技术大学 | Method for measuring quantity of liquid propellant in storage tank |
| CN107871046A (en) * | 2017-11-20 | 2018-04-03 | 北京宇航系统工程研究所 | A kind of emulation mode of cryogenic propellant tank internal spraying blending |
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| EP1462605A1 (en) * | 2003-03-28 | 2004-09-29 | Institut Francais Du Petrole | Method of modelling a hydrocarbon mixture by subdividing it in pseudocomponents |
| CN103017852A (en) * | 2012-12-28 | 2013-04-03 | 中国人民解放军国防科学技术大学 | Method for measuring quantity of liquid propellant in storage tank |
| CN107871046A (en) * | 2017-11-20 | 2018-04-03 | 北京宇航系统工程研究所 | A kind of emulation mode of cryogenic propellant tank internal spraying blending |
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