Last year we presented a new method to model moving surfaces in DSMC. The method was validated by modelling a single rotor of a turbomolecular pump and comparison with experimental results. We have now applied the method to model the gas dynamics inside a 25 stage turbomolecular pump (13 rotors and 12 stators) under various discharge pressures and for various gases and gas mixtures. The turbo pump consists of two sections with different number of blades and different angles. The compression of the turbopump is about 6 orders of magnitude and the flow regime insode the pump goes from free molecular conditions at the inlet side to transitional flow on the discharge side. Interesting phenomena inside the pump are shown, such as a non-linear pressure profile inside he pump, with the non-linearity taking place at a position that would not be expected based on the geometry. Details of the gas flow inside the turbopump are visualized such as the concentration profile of gas mixtures inside the pump, temperature effects and the pressure contours inside the pump. All of these things can also be visualized as a function of time showing the pressure increase at the blade edges ahen a rotor passes a stator and the pressure decrease when the rotor has passed the stator, followed by the backflow of molecules in the wake of the blade.

The method allows a completely new look inside the turbopump and offers possibilities for simulation of new prototypes, optimisation of blade geometry, spacing etc. The current algorithm that calculates the interactions between molecules and rotors is limited to linear blade motions. The rotational motion of the blade is therefore linearized to a straight motion, but the method itself is general. The algorithm can easily be replaced for non-linear velocities although the calculation of collisions between blade and molecules becomes more tedious.

By running the calculations a large cluster of dedicated computers (up to 100 parallel nodes) the calculation time for discharge pressures around 1 Pa is still reasonably small (around 1 day).

The attached document shows an example of the results of a calculation for nitrogen.

The current turbo-drag pumps commercially available for high vacuum systems are based on either Gaede or Holweck molecular drag stages technology, used in series downstream axial bladed stages to extend the maximum compression ratio up to the 10 mbar foreline pressure range.

Modern Gaede molecular drag stages use a disk shaped impeller, allowing a very compact design, but their maximum compression ratio is limited by the leakage effect to about 10 per stage.

Holweck stages use a less compact drum-shaped impeller, but are able to supply a higher compression ratio per stage and can easily be designed to supply a higher pumping speed thanks to the presence of many channels in parallel.

In this paper a new spiral molecular drag stage design is presented, with the advantages of both high compression ratio and pumping speed per stage and very compact design: a stage occupying the very tiny axial room of a Gaede, can compress as much as two or three Gaede stages in series, and supply the same compression ratio and pumping speed of a Holweck stage of the same diameter and peripheral speed, in a much smaller axial room.

The new spiral drag stage allows the design of very compact, high compression ratio turbo-drag pumps. The comparison of new design turbo-drag pump in the size of 700 l/s with existing Gaede and Holweck based products of the same size is presented, showing the technology advantages of the new design.

A rarefied gas flow through a short channel into a vacuum presents a complex task due to significant non-equilibrium. Therefore, it is possible to find a good number of empirical formulas in open literature for calculating flow rate in this case. Correct approach to solving this problem should be based on the Boltzmann equation [1]. The difficulties of numerical solutions for this equation, caused by a large number of independent variables and a complex structure of a non-linear collision integral, are well-known. In our opinion, direct simulation Monte Carlo (DSMC) method [2], which is customarily viewed as a stochastic solution for Boltzmann equation, is preferable for use in tasks with strong non-equilibrium. DSMC method is an effective tool to solve problems of rarefied gas dynamics from free molecular to viscous regimes. An approach based on using DSMC method allows to take into account several factors, such as strong non-equilibrium, as well as to use various models of the gas-surface scattering and the gas molecule-molecule interactions. Therefore, it is appropriate to use DSMC method to study the rarefied gas flow through a short channel into a vacuum.

Practical application of the results of such research can be in the development and creation of such devices as micro- and nanoseparators, micropumps, microshutters, microgyroscopes, micro- and nanosatellites, and other micro- and nanoelectromechanical systems (MEMS/NEMS) [3]. The flow of gas in MEMS/NEMS, depending on device size and gas pressure, can be viscous, transitional or free molecular.

In this study, the mass flow rate through the channel into a vacuum is calculated over the wide range of gas rarefaction as function of channel’s length. To study the gas molecule–molecule interaction influence, we used the variable hard sphere and variable soft sphere models defined for inverse–power–law potential and also the generalized hard sphere model defined for the Lennard–Jones potential. Maxwell, Cercignani–Lampis and Epstein models were used to simulate the gas–surface scattering. This study demonstrates that the gas molecule–molecule interaction and the gas–surface scattering can have a significant influence on the rarefied gas flow through a short channel into a vacuum. The analysis of the flow field, both within the channel as well as in upstream and downstream containers, is presented.

REFERENCES

1. C. Cercignani, The Boltzmann Equation and its Application, Springer, New York (1988).

2. G.A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flow, Oxford University Press, Oxford (1994).

3. Encyclopedia of Microfluidics and Nanofluidics, ed. by Dongqing Li, Springer, New York (2008).

For precise calculations of conductance and pressure distribution in vacuum chamber at molecular flow, it is important to know a degree of realization of diffuse reflection (also called cosine law) at surface. The conductance of an experimental channel changing the surface material and roughness was measured and compared with the results using Monte Carlo calculation assuming diffuse reflection.

The experimental channel consisted of two parallel disks was equipped with the vacuum chamber with an inner volume of 8.42x10-2 m3.The lower disk made from polished stainless steel (SS) has a diameter of 40 mm and a hole of 10 mm in diamter at the center. The upper disk with 51 mm in diameter is located as facing parallel to the lower one. The space between the upper and the lower disks was determined from 0.3 mm to 0.7 mm using gauge blocks as a spacer. After the vacuum chamber was filled with N2, Ar, or He gas at approximately 100 Pa, it was evacuated from the hole of lower disk by turbo molecular pump (0.22 m3/s) through the space between two parallel disks. The conductance of the channel was obtained from the pressure decrease rate in the vacuum chamber.

Eleven upper disks with different material and surface were prepared: polished SS, unpolished SS, quartz, Ti, Cu, Al, alumina with smooth surface, alumina with rough surface, SS with Au coating, SS with Pt coating, and SS with DLC coating. The effect of surface material and roughness on conductance was estimated from the measurement of the conductance of the channel by replacing the upper disk.