Fig. 1 Pump down factor curve chart. Published in most editions of Edwards Vacuum product catalogs.

By Howard Tring

Resistance to gas flow through components that make up a vacuum system has a considerable effect on the pumping speed and pressure obtainable within the system.

Any pipe or component that gas has to flow through is a hindrance to the flow of that gas, i.e. it offers resistance to the flow. It occurs in the roughing line, the foreline and the high vacuum piping and affects the amount of time taken to evacuate a vacuum chamber to its required base or process pressure.

For example, if a large vacuum chamber is connected to its vacuum pump using a long small bore pipe the gas flow down the pipe will be difficult and the gas will be removed from the chamber very slowly. There is a high resistance to gas flow and the conductance of that small bore pipe is low.

Let’s first look at a simple vacuum system, using a single mechanical vacuum pump, the vacuum chamber if often mounted right above the inlet to the vacuum pump.

In this case calculating the time needed to evacuate the chamber is a simple matter, using the equation

T  =  FV / S

Fig. 2 Typical vacuum furnace vacuum pumps. Photo courtesy of “Modern Vacuum Practice” p. 223, written by Nigel Harris and reprinted with permission from the author.

In North America the units used in this equation for simple vacuum systems are usually T = time in minutes, V = volume of chamber in cubic feet, and S = pumping speed of the vacuum pump in cubic feet per minute (cfm). The units used must be consistent. F is a factor taken from the curve shown in Fig. 1 and is a correction used to allow for the reduction in pump speed as the pressure drops.

Often, the designer needs to select the correct size of vacuum pump to suit a certain pump down time. For selecting a pump size the equation becomes S  =  FV / T

In Fig. 1, at a pressure of about 6 x 10^-1 mbar, the curve splits into one curve for a one-stage pump and another curve for a two-stage pump. If the process is one where an oil diffusion pump is used to evacuate the chamber into the high vacuum range, the mechanical vacuum pump is generally a two-stage pump. A single-stage rotary piston pump with a Roots blower (or vacuum booster) is considered the equivalent of a two-stage pump. This is due to the fact that the Roots blower reduces the pressure by about one decade from the one-stage pump ultimate vacuum as well as adding a much higher pumping speed to the system once it is at full pumping speed.

Assuming the chamber has a volume (V) of 120 cu ft, (about 5 feet diameter and 6 feet long) the vacuum pump connection is no more than 1 ft. long where conductance is not taken into consideration, and the vacuum required is 6 x 10^-2 torr (60 microns). From the chart (Fig. 1) the factor F is close to 11. This chart shows mbar on the pressure scale and the conversion is 8 x 10^-2 mbar (a 3/4 ratio). The designer wants to reach the pressure in 10 minutes. (This chart is from Europe and mbar is used as the pressure unit)

So the formula becomes S = 11 x 120 / 10   which becomes  1320 / 10     =    132 cfm

To allow for outgassing in the system and other unknowns a vacuum pump with 150 cfm pumping speed would appear to be a good selection.

Putting the selected pump size into the pump down time version of the equation gives us:

T  =  FV / S   and   T  =  11 x 120 / 150          which becomes 1302 / 150    and    T =  8.8 minutes

Fig. 3 Vacuum furnace roughing line length. Photograph supplied by VAC AERO.

This gives a small safety factor to allow for process outgassing, but some processes may need a larger pump if the outgassing from the furnace and product surfaces is large, i.e. when using cellular insulation or if the plant is in a very humid area.    

Now let’s compare that result for the same chamber volume with a more normal pipeline arrangement for that large volume.

In vacuum systems the term conductance is used rather than resistance. Conductance is the direct value of how much gas will flow, per meter of pipe, at a specific pressure (or average pressure) in that pipe.

Conductance is the reciprocal of Resistance     C = 1 / R

An informal definition of conductance is the capacity of a pipe to allow a volume of gas (at any pressure) flow from one end to the other in unit time. Units are generally liters per second (l/s or l.sec^-1) but can be shown in any unit of volume per unit of time.

(In this discussion I will use the format l/s for units as sometimes using the scientific notation x^-n can be confusing when pressures are shown in the same format)

The definition is the equation C (conductance) = Q (throughput) / P₁ – P₂      where P₁ is greater than P₂     

This equation can be manipulated (by substituting Q / S for P) to give   S_eff   =    S_p x C / S_p + C
(Throughput Q = P x S)

Fig. 4 Pump Speed conversion table. Recreated from the original in “Vacuum System Design”.

With these equations we can now compare the “actual” pump speed and the “effective” pump speed to see how piping length and diameter affects the roughing stage pump down time.

In a typical vacuum furnace the chamber would also have an oil diffusion pump mounted on it and other pipelines and valves are used to allow the furnace to be evacuated by the pumps in the correct sequence. A popular design would be similar to that shown in Fig. 2, where the oil diffusion pump is connected to the high vacuum valve. The piping from the main pump set also connects to the exhaust of the diffusion pump and a holding pump is included in the backing line of the diffusion pump to be used during the roughing stage of the cycle.

A real-life piping layout is shown in Fig. 3 which is a typical pump set for a vacuum furnace. For this discussion we will concentrate on the length of the roughing line. This roughing line, from the mechanical pump inlet up to the connection at the high vacuum valve appears to be at least 6 feet. Just to confuse the reader, most available curves and charts are from Europe and show mbar and meters so this is about 2 meters. For the sake of the discussion the piping size is 6” (close to 152mm).

The last conversion needed is to convert the selected pump speed of 150 cfm to l/s units. From Fig.4 we see cfm x 0.472  =  l/s, so 150 cfm  =  70.8 l/s.

To determine the “effective” pumping speed of the selected vacuum pump, at the closest point of the roughing line to the chamber, the last parameter needed is the conductance of the roughing line at pressure required of 6 x 10^-2 torr. This can be taken from Fig. 5 that shows conductance “per meter” of various diameter pipes at different pressures.

Note on the chart, or off the top of the chart, that at pressures approaching atmospheric pressure conductance is high and little or no restriction on pump speed is seen. As the pressure drops the conductance value drops by a factor of about ten for each decade of pressure drop. For the chosen 100 mm pipe the conductance curve flattens out between 1 x 10^-1 and 2 x 10^-3 torr and is constant at about 100 l/s below that pressure.

At 6 x 10^-2 torr, conductance C = 1000 l/s (per meter)

Fig. 5 Conductance in 1 m long pipes. Photo courtesy of “Modern Vacuum Practice” p. 320. as above.

As the pipe is 2 meters long the actual conductance C = 500 l/sec

In the area where the curve is about 45° the gas is in viscous or continuum flow. Where the curve flattens to a horizontal line the gas is in transitional flow, and once the curve is horizontal gas flow is in molecular flow. A pictorial analogy of different flow regimes is shown on Fig. 6. Transitional flow will be a changing mix of laminar and molecular flows.

Now let us see what the effective pumping speed will be at the chamber end of the roughing line at the required pressure of 6 x 10^-2 torr.

S_eff   =  S_p x C / S_p + C                    S_eff  =  70.8 x 500  / 70.8 + 500      S_eff  =  35400  /  570.8

The effective pump speed at the chamber end of the roughing line S_eff  =  62 l/s

Converting 62 l/s back to cfm we see 62 x 2.12  =  131 cfm
In this example, with an effective pumping speed of 131 cfm, there is no excess pump speed to take care of outgassing as the pressure drops. The pump size (S_p)  may have to be increased to about 200 cfm.     

If the roughing line was 3 meters long, for the same pump the effective speed would be 124 cfm at that pressure. That represents about a 17% loss of pumping speed, which would extend the pump down time past the 10 minute specification.

Fig. 6 Gas flow diagrams. Photo courtesy of “Modern Vacuum Practice” p. 320. as above.

If you check back to Fig. 5 and look at the conductance for a 70 mm bore pipe (about 3” bore) at the required pressure of 6 x 10^-2 torr, you will see the conductance has dropped to about 300 l/s per meter of pipe or only 150 l/s for the 2 meter pipe we used in this example. That would indicate that the 100 mm (4”) pipe is a much better pipeline size for this example than a 70 mm (3”) pipe.

Conductance does change as the pressure changes, so a designer may calculate the effective speed for each decade of pressure. For mechanical piston and vane pumps this would really only be necessary from where the specific pipe size starts on the conductance chart. This is because the pump speed is fairly constant at higher pressures.

Calculating effective pump speed is more important when a Roots blower is used because its pump speed is in the shape of a bell curve. To estimate pump down time the average pump speed for each decade of pressure would be used as S_p to calculate the pump down time for each decade of pressure and then add up the times to find the total time.

There are other factors that should be taken into account when calculating pump down times; the two main considerations are the gas being pumped and the gas temperature. The number of bends in the piping, surface finish inside the pipe and conductance through the valves will all affect the calculations.
If the pipeline has two different diameters of pipe, the conductance for each length is calculated and used to determine the overall conductance of the pipeline.

This comparison of conductance in vacuum lines shows that it is an important consideration when designing a process chamber and selecting the mechanical vacuum pumps.

(When preparing a technical article containing equations and numbers there is always the chance that an error has been made converting from one unit to another and back again even with the numbers having been double checked. I trust that at least one reader will check the numbers and let me know if there is an error.)

References:

Part of this Vacuum Pump Practice article was abridged from the student notes of an Edwards Vacuum training course titled “Vacuum System Design” from 2001.

Howard Tring / Tel: (610) 792-3505 / E-mail: HowardT@VacuumAndLowPressure.com / Web: www.vacuumandlowpressure.com

Howard Tring is the owner of Vacuum and Low Pressure Consulting, a company that supplies vacuum pump accessories such as reconditioned inlet traps and exhaust filters and new replacement elements for exhaust filters. Howard also offers on-site vacuum technology and oil sealed vacuum pump repair training and consulting services, customized to the needs of the client. Howard is a member of ASM International and the Heat Treat Society, the AVS, the SME, the SVC and the American Society for Training and Development.

Comments and suggestions on this article are always welcome, and even a note about your own experience on any of the subjects written about. I do not profess to know everything about any specific vacuum related subject. However, I have worked in the vacuum pump industry a long time and have seen good, bad and ugly. Please contact me with any comment or question. All messages related to the content of the article will be answered.

Copyright December 2013, Tring Enterprises LLC