CN104777183A - Satellite electric propulsion system xenon filling thermodynamic characteristic numerical simulation method - Google Patents

Abstract

The invention relates to a satellite electric propulsion system xenon filling thermodynamic characteristic numerical simulation method which includes the following steps: step S101, xenon fluid state equations are established, the xenon fluid state equations include Redlich-Kwong equation, BWR equation and Helmholtz equation for using least square method numerical interpolation fitting to establish thermodynamic properties, the three different types of empirical parameter equations are compared and analyzed; step S102, according to thermodynamic parameters of xenon in a particular state or region range, one or more of the three different types of empirical parameter equations of the RK equation, the BWR equation and the Helmholtz equation is/ are selected; and step S103, xenon filling thermodynamic characteristic numerical simulation can be performed by setting of the simulation parameters. The satellite electric propulsion system xenon filling characteristic numerical simulation method can simulate satellite electric propulsion system xenon filling characteristics, test and estimate xenon filling total temperature and total pressure range numerical simulation, and has the advantages of strong adaptability, high precision and easiness in use.

Description

Satellite electric propulsion system xenon fills thermodynamic behaviour method for numerical simulation

Technical field

The present invention relates to numerical simulation method for testing, particularly relate to satellite electric propulsion system xenon and fill and thermodynamic behaviour method for numerical simulation in filling process.

Background technology

Satellite electric propulsion system working medium is xenon, because xenon molecular weight is large, fusing point is high, the special physical property such as the high and critical point of boiling point is high, electric propulsion system working medium xenon fills, there is numerous X factor in launching site filling and in-orbit storage use etc., security risk is high, xenon ground stores, test, filling and in-orbit storage operation technique difficulty are also larger, without corresponding basic test data, and satellite electric propulsion system xenon ground test and filling process parameters distribution scope wide, the xenon thermodynamic behaviour physical test of overall process scope cannot be carried out at present both at home and abroad, what also cannot obtain xenon overall process scope fills thermodynamic behaviour test figure, and satellite fills and launching site filling is wide to satellite electric propulsion system xenon bottle internal heat mechanical state parameter prediction claimed range, pressure limit: 0 ~ 17MPa, temperature range :-20 DEG C ~ 100 DEG C, density range 0kg/l ~ 2.3kg/l, and also require higher to filling thermodynamic behaviour parameter prediction precision, require that estimate accuracy control deviation is better than 0.5%.Current nothing describes the state equation that xenon fills characteristic specially, existing thermodynamic equation of state estimates the very large error of generation to xenon fluid calculation, general requirement works out the real fluid state equation meeting xenon essence. to gas phase, liquid phase and supercritical region, require that pressure and density calculation and measurement error are better than 0.5%, therefore, study electric propulsion system xenon fill and filling process method for numerical simulation significant.

Summary of the invention

Order of the present invention is to provide a kind of satellite electric propulsion system xenon and fills thermodynamic behaviour method for numerical simulation, fills and the thermodynamic state parameters of filling process xenon gas cylinder internal so that simulation calculation goes out satellite electric propulsion system xenon.

Satellite electric propulsion system xenon of the present invention fills thermodynamic behaviour method for numerical simulation and comprises: step S101, set up xenon fluid state equation, comprise: set up the RK equation of xenon thermodynamic behaviour, BWR equation and Helmholtz equation with the matching of least square method numerical interpolation, the empirical parameter equation that comparative analysis three kinds is dissimilar;

Step S102, one or more of the empirical parameter equation selecting the RK equation of described xenon thermodynamic behaviour, BWR equation and Helmholtz equation three kinds dissimilar in particular state or regional extent thermodynamic parameter according to xenon; Step S103, carries out xenon fill characteristics numerical simulation by arranging analog parameter.

Further, in step S101, based on saturated vapour pressure experimental data, the gentle liquid phase P VT experimental data of saturation liquid density experimental data, carry out matching and set up the RK equation of xenon thermodynamic behaviour, BWR equation and Helmholtz equation.

Further, in step s 102, in high-temperature low-pressure district, the one in RK equation, BWR equation and Helmholtz equation can be selected.

Further, in step s 102, for supercritical region and the gas phase zone of monophase field, gas-liquid two-phase, Helmholtz equation is selected; Interior for high-temperature low-pressure district, select RK equation.

Further, in step s 103, described analog parameter comprises: temperature, pressure, specific volume, quality, wherein, arranges two parameters any in temperature, pressure and density.

Further, analog result is shown by visual means, comprise: step 1): the unit that analog parameter is set, analog parameter comprises: temperature, pressure, specific volume, quality, density, wherein, analog parameter default setting is SI International System of Units, and temperature can be selected to be set to SI use degree Celsius; Step 2): the numerical range of any two parameters in set temperature, pressure and density, pressure, the scope of temperature comprises origin temp, terminal temperature, step-length; Step 3: X-coordinate axle, draughting accuracy are set, whether draw saturated line, obtain corresponding calculated value or visualization view, parameter exports and comprises for a certain Parameters Calculation table of xenon under specified pressure, temperature and density conditions and carry out gamut xenon and fill thermodynamic behaviour Chinese visualized data figure and describe.

The feature of technical solution of the present invention comprises:

1. the present invention not only comprises domestic experimental data in choice experiment data, also comprises the authoritative experimental data that domestic and international each research institution announces, and ensures the accuracy of test data and sets up the accuracy of equation model.

2. the equation model that the present invention sets up is that the high precision theoretical equation of xenon macroscopic property characterizes, by least square method numerical interpolation the Fitting Calculation equation model parameter, and by equation model numerical simulation software, the hot physical property numerical simulation software of xenon according to xenon three kinds of computation model application JAVA development platform establishments calculates particular state or regional extent thermodynamic parameter, establishes the numerical Analysis software of total temperature and pressure limit.

The present invention is the important method that satellite electric propulsion system xenon fills test and realizes, and possesses satellite electric propulsion system xenon and fills total temperature and total pressure range values and simulate and test, and has the advantages such as strong adaptability, precision are high and easy to use.

Accompanying drawing explanation

Fig. 1 is the process flow diagram of analogy method of the present invention;

Fig. 2 is the xenon experimental data that analogy method of the present invention adopts;

Fig. 3 visualization view is arranged;

An example of xenon pressure-densimetric curve that Fig. 4 calculates.

Embodiment

What below introduce is embodiment as content of the present invention, further illustrates described content of the present invention below by embodiment.Certainly, describe the content that following detailed description is only example different aspect of the present invention, and should not be construed as the restriction scope of the invention.

As shown in Figure 1, the inventive method mainly comprises following flow process:

1) xenon fluid state establishing equation

In step S101, set up xenon fluid state equation, comprising: set up the RK equation of xenon thermodynamic behaviour, BWR equation and Helmholtz equation with the matching of least square method numerical interpolation, the empirical parameter equation that comparative analysis three kinds is dissimilar.

RK equation is the less empirical equation of a kind of parameter of classics, the form of equation is simple, regular strong, easy to use, the existence of general consideration intermolecular attraction and the factor of the volume of volume of gas Middle molecule own, carry out revising obtained for thermodynamic equation of state.

BWR equation (Benedict-Webb-Rubin equation) and Helmholtz equation are multiparameter equations, and multiparameter state equation is also the one of empirical equation.Helmholtz equation describes a kind of equation of material property preferably, it considers the difference of polar molecule and non-polar molecule, and the impact of intermolecular interaction, convection cell matching has the equation of 12 coefficients, have employed the method for matching simultaneously, obtain higher fitting precision.

The experimental data that the present invention adopts has saturated vapour pressure experimental data, saturation liquid density experimental data, liquid phase PVT experimental data, and PVT represents pressure, volume and temperature respectively.Wherein, the distribution of the PVT experimental data of research on pressure-temperature curve as shown in Figure 1.

Classical RK equation is as shown in formula (1).

$P=\frac{\mathrm{RT}}{V-b}-\frac{a}{T^{0.5}V(V+b)}---\left(1\right)$

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, and in actual applications, general critical parameters are by critical temperature T _cwith emergent pressure p _crepresent.Be input parameter by pressure P and temperature T, as shown in Figure 1, adopt each constant term a of least square method numerical interpolation the Fitting Calculation, b, the critical parameters of xenon are p to experimental data _c=5836.336kPa, T _c=289.733K.

BWR equation form such as formula (2) represents:

$\begin{array}{c}P=\mathrm{RT\ρ}+(B_0\mathrm{RT}-A_0-\frac{C_0}{T^2}){\mathrm{\ρ}}^2+(\mathrm{BRT}-A){\mathrm{\ρ}}^3\\ +\mathrm{A\α}{\mathrm{\ρ}}^6+C\frac{{\mathrm{\ρ}}^3}{T^2}(1+\mathrm{\γ}{\mathrm{\ρ}}^2)e^{-\mathrm{\γ}{\mathrm{\ρ}}^2}\end{array}---\left(2\right)$

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 law constant (unit is J/ (K.mol)).

In experimental data, pressure P, temperature T and density p are input parameter, and each term coefficient of the BWR equation adopting least square method numerical interpolation the Fitting Calculation to obtain, as shown in Figure 1, each term coefficient of BWR equation is as shown in table 1 for experimental data.

The each term coefficient of table 1BWR equation

Another multiparameter state equation Helmholtz functional equation is expressed as follows:

α＝α ⁰+α ^r(3)

In formula 3, α ⁰for the part Helmholtz function item of ideal gas contribution, α ^rfor the part Helmholtz function item that the intermolecular interaction of real fluid is contributed.These two can be expressed as further:

${\mathrm{\α}}^0=a_1+a_2\mathrm{\τ}+\ln \mathrm{\δ}+(c_0-1)\ln \mathrm{\τ}-\frac{c_1{(T_c/K)}^{c_2}}{c_2(c_2+1)}{\mathrm{\τ}}^{-c_2}+\underset{k=1}{\overset{5}{\mathrm{\Σ}}}{v}_k\ln [1-e^{-u_k\mathrm{\τ}/T_c}]---\left(4\right)$

${\mathrm{\α}}^r(\mathrm{\δ},\mathrm{\τ})=\mathrm{\Σ}{N}_k{\mathrm{\δ}}^{j_k}{\mathrm{\τ}}^{j_k}+\mathrm{\Σ}{N}_k{\mathrm{\δ}}^{i_k}{\mathrm{\τ}}^{i_k}{e}^{-{\mathrm{\δ}}^k}---\left(5\right)$

In formula 4 and formula 5, u _i, v _i, a ₁, a ₂, c ₀, c ₁, c ₂, N _kfor each term coefficient, T _cbe critical temperature, δ is the density of nondimensionalization, and τ is the temperature of nondimensionalization, i ^k, j ^k, l ^kit is the number of times of corresponding entry.Xenon is non-polar molecule, and the equation of Helmholtz functional form can be expressed as formula (6):

$\begin{array}{c}{\mathrm{\α}}^r(\mathrm{\δ},\mathrm{\τ})=n_1\mathrm{\δ}{\mathrm{\τ}}^{0.25}+n_2\mathrm{\δ}{\mathrm{\τ}}^{1.25}+n_3\mathrm{\δ}{\mathrm{\τ}}^{1.5}+n_4{\mathrm{\δ}}^3{\mathrm{\τ}}^{0.25}+n_5{\mathrm{\δ}}^7{\mathrm{\τ}}^{0.875}+\\ n_6\mathrm{\δ}{\mathrm{\τ}}^{2.375}{e}^{-\mathrm{\δ}}+n_7{\mathrm{\δ}}^2{\mathrm{\τ}}^{2.0}{e}^{-\mathrm{\δ}}+n_8{\mathrm{\δ}}^5{\mathrm{\τ}}^{2.125}{e}^{-\mathrm{\δ}}+n_9\mathrm{\δ}{\mathrm{\τ}}^{3.5}{e}^{-{\mathrm{\δ}}^2}+\\ n_{10}\mathrm{\δ}{\mathrm{\τ}}^{6.5}{e}^{-{\mathrm{\δ}}^2}+n_{11}{\mathrm{\δ}}^4{\mathrm{\τ}}^{4.75}{e}^{-{\mathrm{\δ}}^2}+n_{12}{\mathrm{\δ}}^2{\mathrm{\τ}}^{12.5}{e}^{-{\mathrm{\δ}}^3}\end{array}---\left(6\right)$

N in above two formulas _kit is each term coefficient, in data, pressure P, temperature T and density p are input parameter by experiment, calculate the reduced state density δ under relevant pressure P and reduced state temperature τ, experimental data as shown in Figure 1, adopts each term coefficient N of least square method numerical interpolation the Fitting Calculation equation _k, each term coefficient of Helmholtz equation is as shown in table 2.

The each term coefficient of table 2Helmholtz equation

In sum, method of the present invention is set up the dissimilar empirical parameter equation of the RK equation of xenon thermodynamic behaviour, BWR equation and Helmholtz equation three kinds based on PVT experimental data by the matching of least square method numerical interpolation and is carried out comparative analysis, simulate the coefficient of corresponding equation, the xenon 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, one or more of the empirical parameter equation selecting the RK equation of described xenon thermodynamic behaviour, BWR equation and Helmholtz equation three kinds dissimilar in particular state or regional extent thermodynamic parameter according to xenon.

As previously mentioned, have employed multi-form state equation realize the high precision theoretical characterization of xenon associated hot mechanical property in region-wide scope and by theoretical model, distinguish matching classical RK equation, BWR equation and Helmholtz equation three kinds of empirical parameter equations.

In high-temperature low-pressure district, RK equation can describe the PVT character of xenon preferably, and with experimental data deviation within 10%, below critical temperature, the deviation of data point is larger.In the region close to two-phase region, the calculating that RK equation and experimental data density variation reach more than 70%, RK equation can not reach required precision.

BWR equation calculating pressure, can reach the deviation within 5% compared with experimental data in most of region, but in the deviation of close-to-critical range and experimental data close to 15%, BWR equation calculates can not reach required precision.

Helmholtz equation characterizes saturated vapour pressure, 0.2% is less than at more than 230K and the deviation of experimental data, the result of calculation of Helmholtz equation saturation liquid density in the temperature range of 160K to 220K with experimental data deviation 0.2%, in 220K to 253K temperature range, be less than 0.2% with experimental data deviation.Helmholtz equation calculates the density of liquid phase region, is less than 0.1% with experiment value deviation.Helmholtz equation calculates the pressure of gas phase and supercritical region, in 273K to 358K, is about 0.1% with external data deviation.In 289K to 373K, be about 0.05% with the deviation of experimental data.Helmholtz equation no matter in monophase field, the supercritical region of gas-liquid two-phase and gas phase zone can reach higher fitting precision, xenon can be met completely and fill thermodynamic behaviour numerical simulation and forecast demand.

In the simulation of high-temperature low-pressure subfield value, can select in the RK equation of classics, BWR equation and Helmholtz equation, if in liquid phase region, supercritical region carries out the numerical simulation of pressure, density, preferably adopts Helmholtz equation simulation.

3) parameters for numerical simulation is set and simulates

In step s 103, carry out xenon fill characteristics numerical simulation by arranging analog parameter.

Concrete steps are as follows:

Step 1: the unit arranging analog parameter, analog parameter comprises: temperature, pressure (pressure), specific volume, quality, density etc.Wherein, analog parameter default setting is SI International System of Units, and temperature can be selected to be set to SI use degree Celsius.

Step 2: the numerical range of any two parameters in set temperature, pressure and density, pressure (pressure).The scope of temperature comprises origin temp, terminal temperature, step-length.

Step 3: arrange and draw together X-coordinate axle, draughting accuracy, whether draw saturated line, obtain corresponding calculated value or visualization view, parameter exports and comprises for a certain Parameters Calculation table of xenon under specified pressure, temperature and density conditions and carry out gamut xenon and fill thermodynamic behaviour Chinese visualized data figure description etc.

Fig. 3 shows an example of the xenon pressure densimetric curve calculated, and Fig. 4 shows an example of the pressure temperature curve calculated.

Three kinds of models respectively at saturation liquid density, liquid phase region equation density and gas phase and supercritical region pressure and test figure relative deviation respectively in table 3, table 4 and table 5, as can be seen from test figure relatively, three kinds of computation models all reach higher simulation precision, wherein Helmholtz equation model precision is the highest, no matter in monophase field or in gas phase and supercritical region, the deviation of pressure and density values simulation controls within 0.1%, can meet satellite electric propulsion system working medium xenon completely and fill characteristics numerical simulation test and forecast demand.

The each equation relative deviation of table 3 saturation liquid density compares

Table 4 liquid phase region each equation density relative deviation compares

Table 5 gas phase and supercritical region each side stroke pressure relative deviation compare

As from the foregoing, the present invention solves satellite electric propulsion system xenon working medium well and fills thermodynamic behaviour numerical experiments and forecast demand.

Although give detailed description and explanation to the specific embodiment of the present invention above; but what should indicate is; we can carry out various equivalence according to conception of the present invention to above-mentioned embodiment and change and amendment; its function produced do not exceed that instructions and accompanying drawing contain yet spiritual time, all should within protection scope of the present invention.

Claims (6)

1. satellite electric propulsion system xenon fills a thermodynamic behaviour method for numerical simulation, it is characterized in that, comprising:

Step S101, sets up xenon fluid state equation, comprising: set up the RK equation of xenon thermodynamic behaviour, BWR equation and Helmholtz equation with the matching of least square method numerical interpolation, the empirical parameter equation that comparative analysis three kinds is dissimilar;

Step S102, one or more of the empirical parameter equation selecting the RK equation of described xenon thermodynamic behaviour, BWR equation and Helmholtz equation three kinds dissimilar in particular state or regional extent thermodynamic parameter according to xenon;

Step S103, carries out xenon fill characteristics numerical simulation by arranging analog parameter.

2. satellite electric propulsion system xenon according to claim 1 fills thermodynamic behaviour method for numerical simulation, it is characterized in that, in step S101, based on saturated vapour pressure experimental data, the gentle liquid phase P VT experimental data of saturation liquid density experimental data, carry out matching and set up the RK equation of xenon thermodynamic behaviour, BWR equation and Helmholtz equation.

3. satellite electric propulsion system xenon according to claim 1 fills thermodynamic behaviour method for numerical simulation, it is characterized in that, in step s 102, in high-temperature low-pressure district, can select the one in RK equation, BWR equation and Helmholtz equation.

4. satellite electric propulsion system xenon according to claim 1 fills thermodynamic behaviour method for numerical simulation, it is characterized in that, in step s 102, for high-temperature low-pressure district, selects RK equation; For supercritical region and the gas phase zone of monophase field, gas-liquid two-phase, select Helmholtz equation.

5. satellite electric propulsion system xenon according to claim 1 fills thermodynamic behaviour method for numerical simulation, it is characterized in that, in step s 103, described analog parameter comprises: temperature, pressure, specific volume, quality, wherein, two parameters any in temperature, pressure and density are arranged.

6. satellite electric propulsion system xenon according to claim 5 fills thermodynamic behaviour method for numerical simulation, it is characterized in that, shows analog result by visual means, comprising:

Step 1): the unit that analog parameter is set, analog parameter comprises: temperature, pressure, specific volume, quality, density, and wherein, analog parameter default setting is SI International System of Units, and temperature can be selected to be set to SI use degree Celsius;

Step 2): the numerical range of any two parameters in set temperature, pressure and density, pressure, the scope of temperature comprises origin temp, terminal temperature, step-length;

Step 3: X-coordinate axle, draughting accuracy are set, whether draw saturated line, obtain corresponding calculated value or visualization view, parameter exports and comprises for a certain Parameters Calculation table of xenon under specified pressure, temperature and density conditions and carry out gamut xenon and fill thermodynamic behaviour Chinese visualized data figure and describe.