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.

Commercial low temperature cofired ceramic (LTCC) technology is established in microelectronics and microsystems packaging, multichip and radio frequency (RF) modules, and sensors. The ability to combine structural considerations with embedded traces and components using laminated glass-ceramic tapes has created solutions to unconventional packaging requirements of micro-electro-mechanical systems (MEMS) devices. Many MEMS devices such as resonators are very sensitive to pressure and require packaging in a vacuum environment. Attaining and maintaining desirable pressure levels in sealed vacuum packages requires knowledge of the permeation characteristics of the vacuum envelope and the sealing materials.

An experimental system to measure the time dependent gas permeation through LTCC at temperatures from room temperature to 500°C has been developed. This system utilizes a membrane technique in which a gas is allowed to permeate through a test sample, held at a constant temperature, into a high vacuum chamber where it is detected using a mass spectrometer. The gas permeation value is determined from the steady state gas flux through the sample. The gas diffusivity and solubility in the material were calculated using data from the time dependent approach to the steady state condition. The gas-solid permeation data for helium and hydrogen through DuPont 951 and 9K7 LTCC will be presented and compared to the permeation through other common vacuum envelope materials such as glasses and high-purity alumina ceramics. Application of the permeation data to the prediction of vacuum levels inside hermetic LTCC packaged devices will be discussed. This data can further be utilized in designs to create LTCC packages that meet specific pressure/time operating requirements.

Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000