Binary gas mixtures expansion into vacuum. Dimitris Valougeorgis, Manuel Vargas, Steryios Naris

Transcription

1 Binary gas mixtures expansion into vacuum Dimitris Valougeorgis, Manuel Vargas, Steryios Naris University of Thessaly Department of Mechanical Engineering Laboratory of Transport Phenomena Pedion reos, Volos, Greece presented at the Workshop on Vacuum Metrology for Industry PTB Berlin, June 5 7, 04

2 . Introduction Rarefied gas mixture flows through tubes connecting two vessels are very common in industrial applications related to vacuum technology. The characteristics and properties of these flows are different than the corresponding ones for single gas flows (Varoutis et al. JVST 008; 009). The different velocities of the species result to gas flow separation, which greatly influences the overall flow description (Sharipov JVST 00; Phys. Fluids 005; Naris et al. Phys. Fluids 005). The basic parameter characterizing vacuum flows is the Knudsen number: Kn L 0 kt0 / m RT0 P 0 We are also using the gas rarefaction parameter: LP 0 Kn

3 To have a valid solution in the whole range of the Knudsen number kinetic modeling is needed. It requires the direct solution of a suitable kinetic model equation or the implementation of the DSMC method. The simulation of gas mixture flows in the whole range of the Knudsen number is a complicated task due to the large number of parameters involved. In the present work, o representative binary gas mixture flows are solved, o the issues of gas separation, conductance and equivalent single gas are analyzed and o practical guidelines which may be useful in industrial applications are deduced. 3

4 . Flow configuration with input parameters and output quantities Consider the steady state binary gas mixture flow through a tube connecting two vessels: 4

5 Input parameters: The molar masses m and m of the components of the binary gas mixture The upstream and downstream concentrations C and The upstream and downstream pressures and temperatures P, T and P B, T B The tube length L and radius R The accommodation coefficients and between the tube walls and the species Based on the above the reference molar mass of the mixture and the reference Knudsen number ( Kn ) are defined. Here, is assumed that PB 0, T TB, L/ R and. C B m C m C m 5

6 We focus on the flow dependency on o the Knudsen number ( Kn ), o the mixture composition ( m, m ) and o its concentration ( C ). The steady state flow of the mixtures of He Ne, He r and He Kr has been simulated for Kn 0, C 0,. and Gas He Ne r Kr m (g/mol) at 95K (m/s) The main output quantities of practical interest are o the dimensionless flow rates of each species J, J and the total flow rate of the mixture J J J as well as o the conductance of each species defined as Qi Ji R, i, and the total conductance is Q Q Q. 6

7 3. Results and discussion The flow rates J and J are provided for all three mixtures for 0, 0., 0.5,, 5, 0, 50, 00 and C 0, 0.5, 0.5, 0.375, 0.5, 0.675, 0.750, 0.875,. The values of this database (Vargas et al. Vacuum 04) support: o the analysis on the intensity of the gas separation phenomenon o the computation of the conductance o the examination of the range of validity of the equivalent single gas approach 7

8 3. Gas separation (characterized by the ratio J/ J ) J o Viscous limit ( ): J C ; Free molecular limit ( 0 C J C o For 0 the quantity varies as m / m J C J C m ): J C m Variation of Z in terms of for He Ne, He r, He Kr with various C 8

9 3. Conductance (Q ) The conductance of the single species are connected as Q Q m / m. m m The conductance of the mixture varies as Q Q Q or m m m m Q. Q m Variation of conductance Q in terms of for He Ne, He r, He Kr with various C 9

10 3.3 Equivalent single gas approach (no separation effect) The binary gas mixture is replaced by a single gas with m m C m C m. eq It is readily deduced that Q Q m m and m / / m Q Q. / eq m eq eq eq Comparison between Q of He Ne, He r, He Kr (empty symbols) and the corresponding Q (filled symbols) with various C eq 0

11 The error is decreased as o the difference m m m is reduced and o the rarefaction parameter is increased. With regard to C there is a maximum at 0.5,0.75 C. Introduced error / Q Q Q vs for He r with various eq C

12 4. Practical guidelines General Kn 0.05: the mixture flow may be substituted by the corresponding single gas m C m C m. flow with Kn 0: the flow of each component may be considered independently and the binary gas mixture flow rate is the weighted sum of the flow rates of each species Kn 0: a detailed analysis is required. / m : is of major importance and as approaches one, the binary gas mixture flow is gradually deduced to the corresponding single gas flow. m

13 Gas separation The ratio J/ J is characteristic of the intensity of gas separation. For 0 Kn the ratio J/ J varies between the limiting values of C / C m / m in the free molecular limit (maximum separation) and o o C / C in the viscous limit (no separation). 3

14 Conductance Q at fixed Kn, is monotonically increased with C and varies as Q Q Q. m m Q at fixed C, is monotonically increased with decreasing Kn when m / m is relatively small (He Ne, He r), while for large m / m (He Kr) a conductance minimum appears around Kn 0. at values of C between 0.5 and

15 Equivalent single gas approach The equivalent single gas approach introduces a relative error which depends on m, m, C and it varies as m / / m Q Q. The error is decreased as o m m m is reduced and eq eq o Kn is decreased (diminishes at Kn 0.05 and takes its maximum value at Kn ). 5

16 5. Concluding remarks The flow characteristics and properties of rarefied binary gas mixture flows into vacuum have been examined in terms of o the mixture composition, o its concentration and o the reference vacuum conditions. The conductance of He Ne, He r, He Kr with their concentration varying from zero to one in a wide range of the Knudsen number are reported. The gas separation phenomenon has been analysed and the range of validity of the equivalent single gas approach has been examined in terms of the binary gas mixture flow rates. Practical guidelines characterizing binary gas flows, which may be useful in technological applications and experimental work, are deduced. 6

17 Future work may include o Study the effect of the tube ratio L/ R and the pressure ratio P / B P o Mixture flows of polyatomic gases o Temperature and concentration driven flows in gas mixtures o Experimental work in binary gas mixtures (very limited) 7

18 cknowledgments This work has been performed in close collaboration with PTB (S. Pantazis and K. Jousten) Support through the one year EMRP IND/REG project is gratefully acknowledged. The EMRP is jointly funded by the EMRP participating countries within EURMET and the European Union. 8