Pfeiffer Vacuum A Passion for Perfection

1.2.6 Types of flow

A distinction is made between three types of flow in a vacuum. The types of flows described below will occur as a function of pressure, mean free path and component dimensions d.

 Types of flow in a vacuumzoom figure
Figure 1.5: Types of flow in a vacuum
Source: Jousten (publisher) Wutz, Handbuch Vakuumtechnik, Vieweg Verlag

Continuous flow in low vacuum, p = 103 – 100 mbar, where l << d

What characterizes continuous flow, as well as viscous flow, is frequent contact between gas molecules, yet less frequent contact with the walls of the vessel. In this case, the mean free path of the gas molecules is significantly shorter than the dimensions d of the vacuum equipment.

The dimensionless Knudsen number Kn is defined as the ratio between mean free path and component diameter

Formula 1-9:

Knudsen number

In this case, Kn is < 0.01. In addition, the term viscous flow is used if the product of pressure p and diameter d of the components through which gas is flowing is p · d ≥ 6 · 10-1 mbar · cm for air.

In the case of viscous flow, a distinction is made between laminar and turbulent flow. Laminar flow prevails at low flow speeds. At higher flow speeds, this changes to a turbulent flow [2]. The occurrence of turbulent flow is contingent upon the Reynolds number

Formula 1-10:

Reynolds number

Where is:

ρ=density [kg / m3]
η=viscosity [Pas]
v=flow velocity [m / s]
d=tube diameter [m]

Up to values of Re < 2,300 the flow will be laminar, and where Re > 4,000 the flow will be turbulent. In vacuum systems, the lines are dimensioned in such a manner that turbulent flow occurs only briefly at relatively high pressures, as the high flow resistance that occurs in this process necessitates that the pumps produce higher volume flow rates.

Knudsen flow in medium vacuum, p = 100 – 10-3 mbar, mit l d

If the Knudsen number is between 0.01 and 0.5, this is termed Knudsen flow. Because many process pressures are in the medium vacuum range, this type of flow occurs with corresponding frequency. Since this is a transitional flow, this range is transited relatively quickly when pumping down vacuum chambers. This means that the influence of this conductivity on pump-down times is correspondingly low. It is a complicated endeavor to perform a precise calculation of conductivity where the flow range is still laminar and yet already molecular, and this will not be discussed here. A simple approximation for the Knudsen range can be obtained by adding the laminar and molecular conductivities. Figure 1.7 shows the conductivities of round, one meter long tubes of differing diameters in all three flow ranges.

Molecular flow in high vacuum, (p = 10-3 – 10-7 mbar), where l > d and in ultra high vacuum (p < 10-7 mbar), mit l >> d

At Knudsen numbers of Kn > 0.5 molecular interaction virtually no longer occurs. What prevails is molecular flow. In this case, the product of pressure p and component diameter d is p · d ≤ 1.3 · 10-2 mbar · cm.

Figure 1.6: Flow ranges in vacuum

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