Closure to “Discussion of ‘Free Molecule Flow Through a Vacuum Seal’” (1970, ASME J. Basic Eng., 92, p. 410)

1970 ◽  
Vol 92 (3) ◽  
pp. 410-410
Author(s):  
H. S. Yu ◽  
E. M. Sparrow
Keyword(s):  
Free Molecule ◽  
Flow Through ◽  
Molecule Flow

Orifice flow at high Knudsen numbers

1961 ◽  
Vol 10 (3) ◽  
pp. 371-384 ◽  
Author(s):  
Roddam Narasimha
Keyword(s):  
Flow Field ◽  
Three Dimensional ◽  
Mean Free Path ◽  
Free Molecule ◽  
First Order ◽  
Orifice Flow ◽  
Flow Through ◽  
The Mean ◽  
Molecule Flow ◽  
Inverse Knudsen Number

Several interesting features of the flow field in free-molecule flow through an orifice are discussed. An estimate is then made of the deviation of the mass flow $\dot{m}$ through the orifice from its limiting free-molecule value $\dot{m}$ for small departures from the limit. Using an iteration method proposed by Willis, it is shown that this deviation is of the first order in ε, the inverse Knudsen number, defined as the ratio of the radius of the hole to the mean free path in the gas at upstream infinity. An estimate of the coefficient is obtained making some reasonable assumptions about the three-dimensional nature of the flow, and the value so derived, giving $\dot{m}=\dot{m}(1+0.25\epsi)$, shows fair agreement with the measurements of Liepmann. It appears that ‘nearly’ free-molecular conditions prevail up to ε ∼ 1.0.

Free Molecule Flow Through Slit and Annular Orifices in the Presence of Participating Bounding Walls

1969 ◽  
Vol 36 (4) ◽  
pp. 715-722
Author(s):  
E. M. Sparrow ◽  
H. S. Yu ◽  
T. S. Lundgren
Keyword(s):  
Integral Equations ◽  
Approximate Model ◽  
Geometrical Parameters ◽  
Free Molecule ◽  
Closed Form Solutions ◽  
Wide Range ◽  
Flow Through ◽  
Bounding Surfaces ◽  
Molecule Flow ◽  
Range Of Values

The effect of actively participating bounding surfaces on the free molecule flow through a slit or an annular orifice situated in a wall separating two regions of different pressure is analyzed. The flow through the slit or orifice depends on the distributions of the flux of mass leaving the bounding surfaces. These distributions are found by formulating and solving pairs of integral equations. In the case of the slit, the integral equations are formulated by employing kinetic theory methods, while for the annular orifice it was found advantageous to use the techniques of radiative transfer. In addition to exact solutions, closed-form solutions based on an approximate model are derived. Results are presented for a wide range of values of the relevant geometrical parameters.

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