CN104133969A - Method for calculating adsorption capture area of liquid helium cryogenic pump of vacuum plume experimental system - Google Patents

Abstract

The invention provides a method for calculating the adsorption capture area of a liquid helium cryogenic pump of a vacuum plume experimental system. A brand new adsorption capture area model, based on a vacuum plume efficient and high-precision numerical simulation method, of the liquid helium cryogenic pump solves the problem that the cold plate area worked out through a traditional method is too large, and accurate calculation of the area of a helium plate with a built-in cryogenic pump is achieved. According to the method, correction is conducted on the ideal pumping speed calculation formula of the unit area in the Maxwell heat balance theory, a macroscopic movement speed item is added, and the objective movement rule of plume high-speed jet flow is conformed to; according to plume flow field similarity characteristics, the method for segmenting and averaging a liquid helium cryogenic pump cold plate structure along the axis is provided, and the difficulty of integral computation in total pumping speed calculation is avoided. The method is clear in theory, ingenious in through and good in area calculation accuracy and conforms to engineering application, the risk that the development cost is too high due to the fact that the cold plate area obtained through the traditional design method is too large is avoided, and the design efficiency of the vacuum plume effect experimental system is improved.

Description

Area computation method is caught in a kind of Vacuum Plume experimental system liquid helium cryogenic pump absorption

Technical field

The invention belongs to vacuum science technical field, the present invention relates to a kind of Vacuum Plume experimental system liquid helium cryogenic pump absorption and catch area computation method, be mainly used in the corresponding experimental system scheme design of rail control engine Vacuum Plume.

Background technology

Vacuum Plume effect experiment system is mainly used in space flight appearance, control thruster plume experimental study, can carry out simulated experiment to the Vacuum Plume effect of electric propulsion engine or chemical propulsion engine, for the duty of effective simulated engine in vacuum cryogenic environment, during engine plume test, indoor environment vacuum is required very harsh, as extremely low background environment temperature (subzero 260 degree are following), the large speed of evacuation (10 ⁷l/s), the environment vacuum tightness (10 of superelevation ^-6pa).For meeting the experiment demand of the large pumping speed of above-mentioned vacuum deep cooling, need in cabin, arrange liquid helium cyropump---built-in liquid helium cyropump.

Traditional built-in cryogenic pump design is based on all pressing the maxwell theory formula of distribution theory to calculate.According to Maxwell's kinetic molecular theory, the Distribution and Maxwell's Velocity function under thermal equilibrium state within the scope of free molecule flow (X speed component):

$f\left({\mathrm{\υ}}_x\right)=\sqrt{\frac{m}{2\mathrm{\πkT}}}{e}^{-{\mathrm{m\υ}}_x^2/2\mathrm{kT}}---\left(1\right)$

Wherein: v _xfor gas is at X-velocity component, f (v _x) be that molecule is in (v _x, v _x+ dv _x) probability of speed interval, m is gas molecule quality, and k is Boltzmann constant, and T is gas temperature.Because thermal equilibrium macroscopic velocity is zero, can ignore the impact of two other direction speed, the theoretical maximum gas pumping speed of unit area S _mfor formula:

$S_m={\∫}_0^{\∞}{\mathrm{\υ}}_{x}f\left({\mathrm{\υ}}_x\right){\mathrm{d\υ}}_x=\sqrt{\frac{\mathrm{kT}}{2\mathrm{\πm}}}=\sqrt{\frac{R_{m}T}{2\mathrm{\π}}}---\left(2\right)$

Cold drawing pumping speed:

S＝S _mF _bG (3)

Wherein, F _bfor cold drawing area, G is adsorption coefficient.Simultaneous formula (1), (2) and (3), obtain cold drawing area computing formula:

$F_b=\frac{\stackrel{\·}{m}}{\mathrm{PG}}\sqrt{{2\mathrm{\πR}}_{m}T}---\left(4\right)$

Above-mentioned calculating is based on thermal equilibrium hypothesis, and the gas macroscopic velocity under this hypothesis is zero, is applicable to quasi-static density, pressure is uniformly distributed situation.And vacuum plume is high speed Non-uniform Currents, in cabin, can produce inhomogeneous density and pressure distribution.We are only concerned about the plume distribution situation in limited area, as long as not being backflowed by cold drawing, plume density, pressure distribution in limited area do not affect and satisfied test demand, therefore actual required helium plate area is much smaller than formula (4) calculated value, cannot adopt formula (4) to carry out the design of liquid helium cold drawing area in Vacuum Plume effect experiment system, be badly in need of the new cold drawing area Capturing Models of development.

Summary of the invention

In order to address the above problem, the present invention proposes a kind of Vacuum Plume experimental system liquid helium cryogenic pump absorption and catches area computation method, has solved classic method and cannot accurately calculate a built-in liquid helium cyropump cold drawing area difficult problem.

An area computation method is caught in the absorption of Vacuum Plume experimental system liquid helium cryogenic pump, comprises following step:

Step 1: the feature based on gas macroscopic velocity similarity on helium plate in cryogenic pump, helium board space structure is carried out to segmentation vertically, be divided into a～e Wu Ge district, comprise respectively the impact zone a that backflows, impact zone b backflows, expanding flow impact zone c, main flow side collision district d and main flow head-on crash district e, helium plate is cylindrical structural, two circular end surface, be respectively the impact zone a that backflows, main flow head-on crash district e, flexible shape side is respectively the impact zone b that backflows, expanding flow impact zone c, main flow side collision district d, wherein, c district and b section length are 0.4L, d section length is 0.2L, L is the axial overall length of helium plate, D is the diameter of helium plate,

Step 2: adopt DSMC numerical value emulation method, obtain the mean value of plume gas macroscopic velocity each district of a～e in, and the plume gas macroscopic velocity after on average processes as constant, obtain respectively u _{0, a}, u _{0, b}, u _{0, c}, u _{0, d}, u _{0, e}, wherein: u _{0, a}represent to backflow the average macroscopic velocity of impact zone plume gas, u _{0, b}represent to backflow the average macroscopic velocity of impact zone plume gas, u _{0, c}represent the average macroscopic velocity of expanding flow collision plume gas, u _{0, d}represent the average macroscopic velocity of the trivial plume gas of main flow side collision, u _{0, e}represent the average macroscopic velocity of main flow head-on crash district plume gas;

Step 3: by the total pumping speed S of given target, obtain the required helium plate area based on cryogenic pump.

Advantage of the present invention and good effect are:

1, solved and traditional based on Maxwell, all pressed theoretical mathematics computing model cannot accurately calculate the defect of built-in liquid helium cyropump cold drawing area in Vacuum Plume effect experiment system;

2, by the desirable Calculation of Pumping formula to unit area in Maxwell's heat balance theory, revise, added macroscopic motion speed term, meet the objective characteristics of motion of plume high speed jet;

3, by the plume aerodynamic characteristic corresponding to built-in cryogenic pump of high-accuracy high-efficiency rate Vacuum Plume DSMC software for calculation assistant analysis different spaces structure, the parameters such as plume gas macroscopic velocity that proposed first under different cyropump structures have similarity feature;

4, according to plume flow field similarity feature, proposed liquid helium cyropump cold drawing structure to prolong axis segmental averaging way, avoided the difficulty of quadraturing and calculating in total Calculation of Pumping;

5, area computation method is caught in a kind of Vacuum Plume experimental system liquid helium cryogenic pump absorption of the present invention, principle is distinct, thinking is ingenious, it is good that area calculates accuracy, meet engineering application, avoid the too high equivalent risk of the excessive development cost causing of cold drawing area that adopts traditional method for designing to draw, improved Vacuum Plume effect experiment system efficiency.

Accompanying drawing explanation

Fig. 1 is gas parameter segmental averaging signal on cyropump provided by the invention;

Fig. 2 is the cold drawing position signal of engine free plume density simulation result provided by the invention and different supposition areas;

Fig. 3 is the front that different cold drawing area provided by the invention is corresponding, the flow field velocity contrast of cold drawing position, side.

In figure:

L-built-in cryogenic pump total length; D-built-in cryogenic pump diameter.

Embodiment

Below in conjunction with drawings and Examples, the present invention is described in further detail.

Area computation method is caught in a kind of Vacuum Plume experimental system liquid helium cryogenic pump absorption that the present invention proposes, that Area Model is caught in brand-new liquid helium cyropump absorption based on Vacuum Plume high-efficiency high-accuracy method for numerical simulation, solve the cold drawing area that conventional approach calculates and crossed hang-up, realized the accurate Calculation of built-in cyropump helium plate area.

Area computation method is caught in a kind of Vacuum Plume experimental system liquid helium cryogenic pump absorption of the present invention, comprises following step:

Step 1: the feature based on gas macroscopic velocity similarity on helium plate in cryogenic pump, helium board space structure is carried out to segmentation vertically, be divided into a～e Wu Ge district, comprise respectively the impact zone a that backflows, impact zone b backflows, expanding flow impact zone c, main flow side collision district d and main flow head-on crash district e, helium plate is cylindrical structural, two circular end surface, be respectively the impact zone a that backflows, main flow head-on crash district e, flexible shape side is respectively the impact zone b that backflows, expanding flow impact zone c, main flow side collision district d, wherein, c district and b section length are 0.4L, d section length is 0.2L, L is the axial overall length of helium plate, D is the diameter of helium plate, as shown in Figure 1.

Step 2: adopt DSMC numerical value emulation method, obtain the mean value of plume gas macroscopic velocity each district of a～e in, and the plume gas macroscopic velocity after on average processes as constant, obtain respectively u _{0, a}, u _{0, b}, u _{0, c}, u _{0, d}, u _{0, e}, wherein: u _{0, a}represent to backflow the average macroscopic velocity of impact zone plume gas, u _{0, b}represent to backflow the average macroscopic velocity of impact zone plume gas, u _{0, c}represent the average macroscopic velocity of expanding flow collision plume gas, u _{0, d}represent the average macroscopic velocity of the trivial plume gas of main flow side collision, u _{0, e}represent the average macroscopic velocity of main flow head-on crash district plume gas.

Step 3: by the total pumping speed S of given target (constant), obtain the required helium plate area based on cryogenic pump, be specially:

1, the desirable Calculation of Pumping formula of unit area in Maxwell's heat balance theory is modified to:

$S_m={\∫}_0^{\∞}{\mathrm{uf}}_{\mathrm{Maxwell}}\left(u\right)\mathrm{du}---\left(5\right)$

Wherein u is molecular velocity, by macroscopic velocity u ₀form with microcosmic heat movement speed u', i.e. u=u ₀+ u'; S _mfor the theoretical maximum gas pumping speed of unit area S _m, f _maxwell(u) be Distribution and Maxwell's Velocity function.

2, by u=u ₀+ u' brings in above formula (5), and to above formula integral transformation, obtains meeting the desirable pumping speed formula of unit area of plume characteristic:

$S_m={\∫}_{-u_0}^{\∞}(u_0+u^{\′})f_{\mathrm{Maxwell}}\left(u^{\′}\right){\mathrm{du}}^{\′}=\sqrt{\frac{\mathrm{RT}}{2\mathrm{\π}}}\{\exp (-s)+\sqrt{\mathrm{\π}}s[1+\mathrm{erf}\left(s\right)\left]\right\}---\left(6\right)$

In formula, R is gas law constant, and T is gas temperature, and s is molecular speed ratio:

$s=\frac{u_0}{v_m}---\left(7\right)$

V _mfor most probable heat movement speed, be defined as

$v_m=\sqrt{2\mathrm{RT}}---\left(8\right)$

S is called molecular speed ratio, can find out that it is relevant with the macroscopic velocity of air-flow.Erf (s) is error function, is defined as:

$\mathrm{erf}\left(s\right)=\frac{2}{\sqrt{\mathrm{\π}}}{\∫}_0^s\exp \left({-x}^2\right)\mathrm{dx}---\left(9\right)$

Can find out, all press the desirable Calculation of Pumping formula (2) of distribution theory unit area to be actually the special shape of formula (6) when s=0.When the pumping speed when s ≠ 0 is s=0 doubly.Obviously when macroscopic velocity is larger, this multiple cannot be ignored.

3, utilize formula (6) to calculate respectively the desirable pumping speed S of a-eGe district unit area _m,a, S _m,b, S _m,c, S _m,d, S _m,e, obtaining cryogenic pump absorption, to catch area computing formula as follows:

$F_b=\frac{S}{G(S_{m,a}+S_{m,b}+S_{m,c}+S_{m,d}+S_{m,e})}---\left(7\right)$

Area computation method is caught in a kind of Vacuum Plume experimental system liquid helium cryogenic pump absorption that the present invention proposes, Area Model is caught in the brand-new liquid helium cyropump absorption having proposed based on Vacuum Plume high-efficiency high-accuracy method for numerical simulation, solve the difficult problem that the polycomponent that rail control engine Vacuum Plume is tested, final relief amount, condition of high vacuum degree keep, realized the accurate Calculation of built-in cyropump helium plate area.

Embodiment:

Suppose that area is 100m ², 200m ²and 300m ²three kinds of cold drawing structures, analyze the normal velocity on cold drawing surface respectively, and Density Distribution and cold drawing position are as shown in Figure 2.

When analysis shows different cold drawing area there is similarity in the parameters such as plume gas macroscopic velocity of cold drawing position within the specific limits, as shown in Figure 3.

Then according to flow field characteristic, the cold drawing space structure that will design is carried out to segmental averaging vertically, can to cold drawing, carry out subregion processing by mode as shown in Figure 3, be divided into a～e Wu Ge district, comprise the impact zone a that backflows, the impact zone b that backflows, expanding flow impact zone c, main flow side collision district d and main flow head-on crash district e.Wherein c district and b section length are 0.4L, and d section length is 0.2L.Ge averages macroscopic velocity in district, and while calculating total pumping speed to realize, flow field parameter and cold drawing position are processed in decoupling zero.Through segmentation, be averaging, can obtain each section of speed u _{0, a}=1740m/s, u _{0, b}=540m/s, u _{0, c}=1020m/s, u _{0, d}=564m/s, u _{0, e}=-60m/s.Avoided the calculating of quadraturing in total Calculation of Pumping.

Finally based on "current" model, can obtain required cold drawing area and be about 264m ².For guaranteeing to realize development target, consider certain design margin, cold drawing area is set as to 300m ².By the adsorption area Capturing Models that is suitable for the experiment of engine Vacuum Plume proposing, improved the precision of cold drawing area design, calculate the 300m obtaining ²cold drawing area can realize.

Claims (1)

1. an area computation method is caught in the absorption of Vacuum Plume experimental system liquid helium cryogenic pump, comprises following step:

Step 1: the feature based on gas macroscopic velocity similarity on helium plate in cryogenic pump, helium board space structure is carried out to segmentation vertically, be divided into a～e Wu Ge district, comprise respectively the impact zone a that backflows, impact zone b backflows, expanding flow impact zone c, main flow side collision district d and main flow head-on crash district e, helium plate is cylindrical structural, two circular end surface, be respectively the impact zone a that backflows, main flow head-on crash district e, flexible shape side is respectively the impact zone b that backflows, expanding flow impact zone c, main flow side collision district d, wherein, c district and b section length are 0.4L, d section length is 0.2L, L is the axial overall length of helium plate, D is the diameter of helium plate,

Step 2: adopt DSMC numerical value emulation method, obtain the mean value of plume gas macroscopic velocity each district of a～e in, and the plume gas macroscopic velocity after on average processes as constant, obtain respectively u _{0, a}, u _{0, b}, u _{0, c}, u _{0, d}, u _{0, e}, wherein: u _{0, a}represent to backflow the average macroscopic velocity of impact zone plume gas, u _{0, b}represent to backflow the average macroscopic velocity of impact zone plume gas, u _{0, c}represent the average macroscopic velocity of expanding flow collision plume gas, u _{0, d}represent the average macroscopic velocity of the trivial plume gas of main flow side collision, u _{0, e}represent the average macroscopic velocity of main flow head-on crash district plume gas;

Step 3: by the total pumping speed S of given target, obtain the required helium plate area based on cryogenic pump, be specially:

(1), the desirable Calculation of Pumping formula of unit area in Maxwell's heat balance theory is modified to:

Wherein u is molecular velocity, by macroscopic velocity u ₀form with microcosmic heat movement speed u', i.e. u=u ₀+ u'; S _mfor the theoretical maximum gas pumping speed of unit area S _m, f _maxwell(u) be Distribution and Maxwell's Velocity function;

(2), by u=u ₀+ u' brings in above formula (5), and to above formula integral transformation, obtains meeting the desirable pumping speed formula of unit area of plume characteristic:

In formula, R is gas law constant, and T is gas temperature, and s is molecular speed ratio:

V _mfor most probable heat movement speed, be defined as

Erf (s) is error function, is defined as:

(3), utilize formula (6) to calculate respectively the desirable pumping speed S of a-eGe district unit area _m,a, S _m,b, S _m,c, S _m,d, S _m,e, obtaining cryogenic pump absorption, to catch area computing formula as follows:

。