Vapor-Liquid Phase Separation of Superfluid Helium (He II)

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Vapor Liquid Phase Separation of Superfluid Helium (He II, Superfluidity)

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Liquid helium dewars used for the cooling of instruments in space requires both a fill and a vent line. Due to the low-g environment, bulk liquid tends to escapes through the vent line and reduces the life time of the mission. A device known as the vapor-liquid phase separator (VLPS), consisting a porous medium, is installed between the dewar and the vent line, allowing the heat load from the instrument to be rejected, while retaining liquid in the dewar.

Figure 1 shows how the VLPS works. With finite evaporation of liquid helium from the downstream of the VLPS, a temperature gradient is set up across the porous plug. Normal fluid, behaving as a Newtonian fluid carries heat from high to low temperature. Superfluid, on the other hand tend to travel in the opposite direction, retaining fluid in the dewar. This transport mode is very similar to that of the Zero Net Mass Flow (ZNMF).

From the two fluid model

......................Eq (1)

The superfluid mass flux component can be written in terms of the normal and superfluid relative velocity, w=v_n-v_s, and the heat flux density written as for a finite mass flow system, q=r_swST. Equation 1 thus becomes

......................Eq (2)

The mass flux, rv, can be eliminated by applying the first law to the helium evaporating on the downstream side of the porous plug, q=lrv (where l is the latent heat). Substituting and rearranging the equation gives

......................Eq (3)

With this, one can arrive at the relationship between ZNMF and VLPS.

......................Eq (4)

On the right hand side of the above equation, rSTv_n is the heat flux density at ZNMF by the temperature dependence of (l/l + ST). Because l << ST, the magnitude of (l/l + ST) is quite close to unity, ranging from 0.872 at T_l to 0.999 at 1K. Subsequently, the Vapor Liquid Phase Separation mode approaches an asymptotic limit to ZNMF at low temperatures.

Based on Eq 4, the laminar and turbulent transport of He II in a phase separator can be written as, (we deliberately use mass flow in Eq 5 and heat flow in Eq 6, the two are related by Q = l m)

......................Eq (5)

And

......................Eq (6)

Choked Flow

Choked flow in He II was first explored experimentally by Murakami et al. DiPirro offered a simplified model for choked flow, hypothesizing that the vapor-liquid interface recedes into the porous plug, resulting in excessive temperature drop. Lages et al. postulated a more complete theory for choked flow based on the Gibbs free energy analysis, which boils down to DiPirro's equation, for pore sizes on the order seen in VLPS. In DiPirro's model, the temperature difference is given by

......................Eq (7)

where s is the surface tension, h is the height of the liquid and D_c is the equivalent capillary diameter. In combining Equations 5 and 7, one can predict the onset of choked flow. Since choked flow begins at the largest pores and the bubble-point-pressure-test measures the diameter of the largest pores near the surface of the plug, we propose to substitute the equivalent capillary diameter in Equation 7 with the bubble point,

......................Eq (8)

where DP is the bubble point pressure.

The actual VLPS data of IRAS, COBE and SIRTF are compared with the theory (Eq 5 to 8) in Figures 2 to 4. Excellent agreement was found between the two. Important parameters used in the analysis are summarized in Table 1. The experimental and predicted critical mass flux (where choked flow begins) for COBE is listed in Table 2.

Figure 2a- IRAS Test Data	Figure 2b- Predicted IRAS Performance
Figure 3a- COBE Test Data	Figure 3b- Predicted COBE Performance
Figure 4a- SIRTF Test Data	Figure 4b- Predicted SIRTF Performance

Table 1. Important VLPS parameters used in the study

	Diameter (cm)	Thickness (cm)	Permeability (cm²)	Porosity	Bubble Pt. Pore Size (mm)
IRAS	1.95	0.635	1E-9	0.380	3.9
COBE	3.30	0.635	1E-9	0.380	3.9
SIRTF (JPL)	7.74	0.635	5.4E-10	0.380	4.7

Table 2. Critical mass flow of the COBE plug

Temperature (K)	Experimental Mc (mg/s)	Predicted Mc (mg/s)
1.45	3.2	3.2
1.50	4.1	4.0
1.60	6.0	6.4

References

"Vapor-Liquid Phase Separation of He-II", Cryogenices, Vol. 38, Number 9, P921, 1998. (with A.R. Urbach, S.M. Volz, J.H.Lee) Abstract Download

"The Dependence of Choked Flow and Breakthrough on Pore Size Distribution in Vapor-Liquid Phase Separation of He II Using Porous Media", in Proc. of Advances in Cryogenic Engineering, 1996, Vol. 41B, P1189-1194 (with D.J. Frank & Chris Lages).

"Space Cryogenics Components Based on the Thermomechanical Effect", Journal of Thermophysics & Heat Transfer, 1990, vol. 3, No. 406-415. (With T.H.K. Frederking.) (With I.E. Spradley.) Abstract Download

"Non-Linear Vapor-Liquid Phase Separation Including Microgravity Effects", Cryogenics, 1987, vol. 27, p. 27. (With T.H.K. Frederking.) (With I.E. Spradley.) Abstract Download

"Heat and Mass Transfer in Porous Media Phase Separation at Temperatures Below the Lambda-Point of He-4", in the Proceedings of the 8th International Heat Transfer Conference, San Francisco, August 17-22, 1986, vol. 5, p. 2683. (With T.H.K. Frederking.)

"Equations for Heat and Mass Flow of Non-Newtonian Fluid Through Porous Media: Liquid He II - Helium - 4 Vapor Separation", in the Proceedings of the National Heat Transfer Conference (ASME), Denver, Colorado, August 1985, Paper 85-HT-5. (With Jeffrey M. Lee, W.A. Hepler and T.H.K. Frederking.) (With I.E. Spradley.) Abstract Download

"Sintered Plug Flow Modulation of a Vapor-Liquid Phase Separator for a Helium II Vessel", Proc. Advances in Cryogenic Engineering, 1984, vol. 29, p. 687. (With T.H.K. Frederking, C. Chuang, Y. Kamioka and J.M. Lee.) (With I.E. Spradley.) Abstract Download

"Darcy Law of Thermo-Osmosis for Zero Net Mass Flow at Low Temperatures", in Proc. of ASME-JSME Thermal Engineering Joint Conference, Honolulu, Hawaii, March 1983, vol. 2, p. 191. (With T.H.K. Frederking.) Abstract Download

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About the author- Dr. Sidney Yuan is a consultant in the field of Low Temperature Physics and Cryogenics, and has written a Book on Cryogenics and published extensively in the field. E-Mail.

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