CN104777183B - Satellite electric propulsion system xenon fills thermodynamic behaviour method for numerical simulation - Google Patents
Satellite electric propulsion system xenon fills thermodynamic behaviour method for numerical simulation Download PDFInfo
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Abstract
Thermodynamic behaviour method for numerical simulation is filled the present invention relates to a kind of satellite electric propulsion system xenon, including：Step S101, sets up xenon fluid state equation, including：The RK equations, BWR equation and Helmholtz equations for setting up xenon thermodynamic behaviour, the different types of empirical parameter equation of three kinds of comparative analysis are fitted with least square method numerical interpolation；Step S102, according to xenon in particular state or regional extent thermodynamic parameter come the one or more of the RK equations, BWR equation and the different types of empirical parameter equation of three kinds of Helmholtz equations that select the xenon thermodynamic behaviour；Step S103, characteristics numerical simulation is filled by setting analog parameter to carry out xenon.The present invention can fill characteristic to satellite electric propulsion system xenon and simulate, and total temperature and total pressure range values simulated test are filled to xenon and is estimated, has the advantages that strong adaptability, precision are high and easy to use.
Description
Technical field
The present invention relates to numerical simulation method for testing, more particularly to satellite electric propulsion system xenon fill and filling process in
Thermodynamic behaviour method for numerical simulation.
Background technology
Satellite electric propulsion system working medium is xenon, due to the spy such as xenon molecular weight is big, fusing point is high, boiling point is high and critical point is high
Different physical property, electric propulsion system working medium xenon is filled, launching site filling and in-orbit storage use etc. exist it is numerous it is unknown because
Element, security risk is high, and the storage of xenon ground, test, filling and in-orbit storage are also larger using technical difficulty, without corresponding basis
Test data, and satellite electric propulsion system xenon is wide in ground test and filling process parameters distribution scope, current nothing both at home and abroad
Method carries out the xenon thermodynamic behaviour physical test of overall process scope, and can not also obtain xenon overall process scope fills thermodynamics
Attribute testing data, and satellite is filled and launching site filling is pre- to satellite electric propulsion system xenon gas cylinder internal thermodynamic state parameters
Estimate claimed range wide, pressure limit：0~17MPa, temperature range：- 20 DEG C~100 DEG C, density range 0kg/l~2.3kg/l,
And to fill thermodynamic behaviour parameter prediction precision also require that it is higher, it is desirable to estimate accuracy control deviation be better than 0.5%.At present
The state equation of characteristic is filled without special description xenon, existing thermodynamic equation of state estimates generation to xenon fluid calculation very
Big error, general requirement works out the real fluid state equation for meeting xenon essence to gas phase, liquid phase and supercritical region,
It is required that pressure and density calculate and is better than 0.5% with measurement error, therefore, research electric propulsion system xenon is filled and filling process number
It is worth analogy method significant.
The content of the invention
The mesh of the present invention is to provide a kind of satellite electric propulsion system xenon and fills thermodynamic behaviour method for numerical simulation, so as to
Simulation calculation go out satellite electric propulsion system xenon fill and filling process xenon gas cylinder internal thermodynamic state parameters.
The satellite electric propulsion system xenon of the present invention, which fills thermodynamic behaviour method for numerical simulation, to be included：Step S101, builds
Vertical xenon fluid state equation, including：With least square method numerical interpolation be fitted set up xenon thermodynamic behaviour RK equations,
BWR equation and Helmholtz equations, the different types of empirical parameter equation of three kinds of comparative analysis；
Step S102, selects the xenon thermodynamics special according to xenon in particular state or regional extent thermodynamic parameter
The one or more of the RK equations of property, BWR equation and the different types of empirical parameter equation of three kinds of Helmholtz equations；Step
S103, characteristics numerical simulation is filled by setting analog parameter to carry out xenon.
Further, in step S101, based on saturated vapour pressure experimental data, saturation liquid density experimental data and gas-liquid
Phase PVT experimental datas, to be fitted the RK equations for setting up xenon thermodynamic behaviour, BWR equation and Helmholtz equations.
Further, in step s 102, in high-temperature low-pressure area, RK equations, BWR equation and Helmholtz side can be selected
One kind in journey.
Further, in step s 102, for monophase field, the supercritical region of gas-liquid two-phase and gas phase zone, selection
Helmholtz equations；It is interior for high-temperature low-pressure area, select RK equations.
Further, in step s 103, the analog parameter includes：Temperature, pressure, specific volume, quality, wherein, to temperature,
Any two parameter is configured in pressure and density.
Further, analog result is shown with visual means, including：Step 1)：The unit of analog parameter, simulation are set
Parameter includes：Temperature, pressure, specific volume, quality, density, wherein, analog parameter default setting is the SI International Systems of Units, and temperature can
Selection is set to SI uses degree Celsius；Step 2)：The number range of temperature, pressure and any two parameter in density is set,
Pressure, the scope of temperature includes origin temp, outlet temperature, step-length；Step 3：X-coordinate axle, drafting accuracy are set, whether drawn
Saturated line, obtains corresponding calculated value or visualization view, and parameter output includes being used under specified pressure, temperature and density conditions
The a certain Parameters Calculation table of xenon and progress gamut xenon fill thermodynamic behaviour Chinese visualization datagram description.
The characteristics of technical solution of the present invention, includes:
1. the present invention not only includes domestic experimental data, in addition to each research institution both at home and abroad in choice experiment data
The authoritative experimental data of announcement, it is ensured that the accuracy of test data and the accuracy for setting up equation model.
2. the high-precision theoretical equation that the equation model that the present invention is set up is xenon macroscopic property is characterized, pass through a most young waiter in a wineshop or an inn
Multiplication numerical interpolation the Fitting Calculation equation model parameter, and by equation model numerical simulation software, according to three kinds of calculating of xenon
The hot physical property numerical simulation software of xenon of model application JAVA development platforms establishment calculates particular state or regional extent thermodynamics
Parameter, establishes total temperature and the numerical Analysis software of pressure limit.
The present invention is that satellite electric propulsion system xenon fills the important method that experiment is realized, possesses satellite electric propulsion system xenon
Gas fills total temperature and simulated with total pressure range values with testing, and has the advantages that strong adaptability, precision are high and easy to use.
Brief description of the drawings
Fig. 1 is the flow chart of the analogy method of the present invention；
The xenon experimental data that Fig. 2 uses for the analogy method of the present invention；
Fig. 3 is an example for calculating obtained xenon pressure-density curve；
Fig. 4 calculates an example of obtained xenon pressure-temperature curve.
Embodiment
Introduced below is the embodiment as content of the present invention, below by embodiment to this
The content of invention is made further to illustrate.Certainly, the not Tongfang of description following detailed description only for the example present invention
The content in face, and should not be construed as limiting the scope of the invention.
As shown in figure 1, the inventive method mainly includes below scheme：
1) xenon fluid state establishing equation
In step S101, xenon fluid state equation is set up, including：Xenon is set up with the fitting of least square method numerical interpolation
RK equations, BWR equation and the Helmholtz equations of gas thermodynamic behaviour, three kinds of different types of empirical parameter sides of comparative analysis
Journey.
RK equations are a kind of less empirical equations of classical parameter, and the form of equation is simple, regular strong, user
Just, in the general presence for considering intermolecular attraction and volume of gas molecular co-volume factor, for thermodynamic state side
Journey is modified resulting.
BWR equation (Benedict-Webb-Rubin equations) and Helmholtz equations are multi-parameter equation, multi-parameter shape
State equation is also one kind of empirical equation.Helmholtz equations preferably describe a kind of equation of material property, and it considers
The difference of polar molecule and nonpolar molecule, and intermolecular interaction influence, fluid has been fitted with 12 coefficients
Equation, employ at the same fitting method, obtain the high fitting precision of comparison.
The experimental data that the present invention is used has saturated vapour pressure experimental data, saturation liquid density experimental data, liquid phase
PVT experimental datas, PVT represents pressure, volume and temperature respectively.Wherein, the PVT experimental datas of research are in pressure-temperature curve
On distribution it is as shown in Figure 2.
Shown in classical RK equations such as formula (1).
In formula 1, P is pressure, and R is volume, and T is absolute temperature (unit is K), and a, b are the peculiar parameter of material, actually should
In, general critical parameters are by critical-temperature TcWith critical pressure pcTo represent.It is input parameter, experiment by pressure P and temperature T
Data are as shown in Fig. 2 using each constant term a, b of least square method numerical interpolation the Fitting Calculation, the critical parameters of xenon are pc=
5836.336kPa, Tc=289.733K.
BWR equation form such as formula (2) is represented：
In formula 2, ρ represents density (unit is mol/m3), and T is temperature (unit is K), and P is pressure (unit is Pa), and R is
Gas constant (unit is J/ (K.mol)).
Pressure P, temperature T and density p are input parameter in experimental data, using least square method numerical interpolation the Fitting Calculation
Each term coefficient of obtained BWR equation, experimental data are as shown in Fig. 2 each term coefficient of BWR equation is as shown in table 1.
Each term coefficient of table 1BWR equations
Another multi-parameter state equation Helmholtz functional equation is expressed as follows：
α=α0+αr (3)
In formula 3, α0The part Helmholtz function items contributed for perfect gas, αrFor the intermolecular phase interaction of real fluid
With the part Helmholtz function items of contribution.This two can be further expressed as：
In formula 4 and formula 5, ui、vi、a1、a2、c0、c1、c2、NkFor each term coefficient, TcIt is critical-temperature, δ is nondimensionalization
Density, τ is the temperature of nondimensionalization, ik, jk, lkIt is the number of times of corresponding entry.Xenon is nonpolar molecule, Helmholtz function shapes
The equation of formula can be expressed as formula (6)：
N in the formula of the above twokIt is each term coefficient, is input parameter by pressure P, temperature T and density p in experimental data,
The contrast density of states δ and reduced state temperature τ under relevant pressure P are calculated, experimental data is as shown in Fig. 2 using least square method number
It is worth each term coefficient N of interpolation fitting accounting equationk, each term coefficient of Helmholtz equations is as shown in table 2.
Each term coefficient of table 2Helmholtz equations
In summary, method of the invention is based on PVT experimental datas and sets up xenon by the fitting of least square method numerical interpolation
RK equations, BWR equation and the different types of empirical parameter equation of three kinds of Helmholtz equations of gas thermodynamic behaviour are simultaneously compared
Relatively analyze, fit the coefficient of corresponding equation, the xenon for obtaining a set of high-precision gamut pressure limit fills thermodynamic behaviour
Calculating simulation equation.
2) xenon fluid state equation is selected
In step S102, the xenon thermodynamics is selected in particular state or regional extent thermodynamic parameter according to xenon
The one or more of the RK equations of characteristic, BWR equation and the different types of empirical parameter equation of three kinds of Helmholtz equations.
As it was previously stated, employing various forms of state equations realizes xenon related macroscopic property in region-wide scope
High-precision theoretical characterization and by theoretical model, RK equations, BWR equation and the Helmholtz equations of classics have been fitted respectively
Three kinds of empirical parameter equations.
In high-temperature low-pressure area, RK equations can preferably describe the PVT properties of xenon, and experimental data deviation 10% with
Interior, below critical-temperature, the deviation of data point is larger.In the region close to two-phase section, RK equations and experimental data density are inclined
Difference reaches that the calculating of more than 70%, RK equations can not reach required precision.
BWR equation calculates pressure, compares with experimental data and can reach the deviation within 5% in most of region, but
Close-to-critical range and experimental data deviation close to 15%, BWR equation, which is calculated, can not reach required precision.
Helmholtz equations characterize saturated vapour pressure, are less than 0.2% in the deviation of more than 230K and experimental data,
The result of calculation of Helmholtz equation saturation liquid densities is within the temperature range of 160K to 220K and experimental data deviation
0.2%, in 220K to 253K temperature ranges and experimental data deviation be less than 0.2%.Helmholtz equations calculate liquid phase region
Density, and experiment value deviation are less than 0.1%.Helmholtz equations calculate the pressure of gas phase and supercritical region, in 273K to 358K
It is interior, it is about 0.1% with external data deviation.In 289K to 373K, and the deviation of experimental data is about 0.05%.
No matter Helmholtz equations are attained by higher fitting precision in monophase field, the supercritical region of gas-liquid two-phase and gas phase zone, complete
Xenon all can be met and fill thermodynamic behaviour numerical simulation and forecast demand.
In the simulation of high-temperature low-pressure subfield value, it can be selected in classical RK equations, BWR equation and Helmholtz equations
Select, if liquid phase region, supercritical region carry out pressure, density numerical simulation, it is preferred to use Helmholtz equation simulations.
3) parameters for numerical simulation is set and simulated
In step s 103, characteristics numerical simulation is filled by setting analog parameter to carry out xenon.
Comprise the following steps that：
Step 1：The unit of analog parameter is set, and analog parameter includes：Temperature, pressure (pressure), specific volume, quality, density
Deng.Wherein, analog parameter default setting is the SI International Systems of Units, and temperature may be selected to be set to SI uses degree Celsius.
Step 2：The number range of temperature, pressure and any two parameter in density, pressure (pressure) are set.Temperature
Scope includes origin temp, outlet temperature, step-length.
Step 3：Setting includes X-coordinate axle, drafting accuracy, whether draws saturated line, obtains corresponding calculated value or visualization
View, parameter output includes for a certain Parameters Calculation table of xenon under specified pressure, temperature and density conditions and carries out gamut
Xenon fills thermodynamic behaviour Chinese visualization datagram description etc..
Fig. 3 is an example for calculating obtained xenon pressure-density curve, and Fig. 4 shows the xenon pressure that calculating is obtained
One example of power-temperature curve.
Three kinds of models are respectively in saturation liquid density, liquid phase region equation density and gas phase and supercritical region pressure and experiment number
Be shown in Table 3, table 4 and table 5 respectively according to relative deviation, from test data compare as can be seen that three kinds of computation models all reached it is higher
Simulation precision, wherein Helmholtz equation models precision highest, no matter in monophase field or in gas phase and overcritical
The deviation of area, pressure and density values simulation is controlled within 0.1%, is entirely capable of meeting satellite electric propulsion system working medium xenon and is filled
Fill characteristics numerical simulation experiment and forecast demand.
Each equation relative deviation of the saturation liquid density of table 3 compares
Each equation density relative deviation in the liquid phase region of table 4 compares
The gas phase of table 5 and supercritical region each side stroke pressure relative deviation compare
From the foregoing, it will be observed that the present invention solves satellite electric propulsion system xenon working medium and fills thermodynamic behaviour Numerical-Mode well
Intend experiment and forecast demand.
Although the embodiment to the present invention gives detailed description and illustrated above, it should be noted that
We can carry out various equivalent changes and modification according to the conception of the present invention to above-mentioned embodiment, and the function produced by it is made
, all should be within protection scope of the present invention during with the spirit still covered without departing from specification and accompanying drawing.
Claims (6)
1. a kind of satellite electric propulsion system xenon fills thermodynamic behaviour method for numerical simulation, it is characterised in that including：
Step S101, sets up xenon fluid state equation, including：Xenon thermodynamics is set up with the fitting of least square method numerical interpolation
RK equations, BWR equation and the Helmholtz equations of characteristic, the different types of empirical parameter equation of three kinds of comparative analysis；
Step S102, the xenon thermodynamic behaviour is selected according to xenon in particular state or regional extent thermodynamic parameter
The one or more of RK equations, BWR equation and the different types of empirical parameter equation of three kinds of Helmholtz equations；
Step S103, characteristics numerical simulation is filled by setting analog parameter to carry out xenon.
2. satellite electric propulsion system xenon according to claim 1 fills thermodynamic behaviour method for numerical simulation, its feature
It is, in step S101, based on saturated vapour pressure experimental data, the gentle liquid phase P VT experiments of saturation liquid density experimental data
Data, to be fitted the RK equations for setting up xenon thermodynamic behaviour, BWR equation and Helmholtz equations.
3. satellite electric propulsion system xenon according to claim 1 fills thermodynamic behaviour method for numerical simulation, its feature
It is, in step s 102, one kind in high-temperature low-pressure area, selection RK equations, BWR equation and Helmholtz equations.
4. satellite electric propulsion system xenon according to claim 1 fills thermodynamic behaviour method for numerical simulation, its feature
It is, in step s 102, for high-temperature low-pressure area, selects RK equations；For monophase field, the supercritical region of gas-liquid two-phase, choosing
Select Helmholtz equations.
5. satellite electric propulsion system xenon according to claim 1 fills thermodynamic behaviour method for numerical simulation, its feature
It is, in step s 103, the analog parameter includes：Temperature, pressure, specific volume, quality, density, wherein, to temperature, pressure
And any two parameter is configured in density.
6. satellite electric propulsion system xenon according to claim 5 fills thermodynamic behaviour method for numerical simulation, its feature
It is, analog result is shown with visual means, including：
Step 1)：The unit of analog parameter is set, and analog parameter includes：Temperature, pressure, specific volume, quality, density, wherein, simulation
Parameter default setting is the SI International Systems of Units, and temperature selection is set to SI Celsius temperatures；
Step 2)：The number range of temperature, pressure and any two parameter in density is set, and the number range of temperature includes
Point temperature, outlet temperature, step-length；
Step 3：X-coordinate axle, drafting accuracy are set, whether saturated line is drawn, corresponding calculated value or visualization view is obtained, joined
Number output includes filling for a certain Parameters Calculation table of xenon under specified pressure, temperature and density conditions and progress gamut xenon
Thermodynamic behaviour Chinese visualization datagram description.
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