Invited Paper VT-MoA3
Modeling and Simulation of Fast Flows in the Vacuum Regime

Monday, October 28, 2013, 2:40 pm, Room 202 C

It is well known that the Navier-Stokes-Fourier formulation may provide inaccurate solutions for low pressure gas flows. On the other hand, the numerical solution of the Boltzmann equation poses up to date great challenges in problems of engineering interest. Several modeling techniques have been developed to provide results in corresponding ranges of the vacuum regime. Among them is the Direct Simulation Monte Carlo (DSMC) method, which is usually the method of choice for the simulation of fast flows due to its simplicity and the fact that it can accurately reproduce solutions of the Boltzmann equation in the whole range of the Knudsen number. Problems arise when the density levels increase, as the computational effort may reach prohibitively high levels. For the simulation of such flows, a method able to deal with locally rarefied flows may be required if the problem is not susceptible to modeling simplifications without significant sacrifices in accuracy. Hybrid particle-continuum algorithms are often used as viable alternatives for this purpose. The flow domain is decomposed in different regions based on appropriate criteria, such as the local Knudsen number, and treated either by a continuum or a particle method. However, such methods are less frequently encountered in problems of unsteady nature due to modeling difficulties.

An efficient implementation of a hybrid simulation algorithm is presented. The characteristics of such algorithms, such as the coupling at the interface between the two methods, as well as computational features, such as parallel computing capabilities and arbitrary geometry handling, are explained. The main differences with other works in the literature are highlighted. The validation is performed through comparison with simplified but relevant cases of fast flows in the vacuum regime, such as shock tube and orifice flow, and the benefits of the approach as opposed to pure DSMC are commented. Furthermore, a challenging application of the code on a practical problem is discussed. A dynamic vacuum expansion calibration facility is studied, constructed in PTB to study the response time of vacuum gauges to rapid pressure changes, such as in the control of load locks in industrial applications. The pressure may change from 100 kPa to 100 Pa in less than 1 s by expansion to a vessel with a larger volume through a fast opening gate DN40 valve. Experiments have been performed with capacitance diaphragm gauges with improved electronics, leading to an update time of 0.7 ms. The modeling approximations are explained and measurements are compared with simulation results.