Interdisciplinary Applied Mathematics

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and transient time responses of the system is shown in Figure 6.11. In the simulations, the base pressure is 1900 Pa, and the reference gap width is 2 p,m. The transient time response to a step acceleration applied for 10 p,s


Pressure distribution

X


FIGURE 6.10. Simulated pressure distribution in the air gap of an accelerometer. In this example there is a hole in the middle of the rectangular plate, and the plate is tilting, which creates an asymmetric pressure distribution. (Courtesy of T. Veijola.)


is shown in the top figure. The case without holes experiences oscillations corresponding to the springlike response, and the 3-hole case gives an overshoot due to the lack of sufficient damping. However, the 2-hole case gives the optimum response, reaching steady conditions with in 300 p,s (Veijola et al., 1995b). The steady frequency response of the system presented in the bottom figure also shows drastic variations in the amplitude and phase of the system. The maximum amplitude is shifting toward the low frequencies with increased number of holes. The cut-off frequency indicating the phase shift of the system from a mostly dissipative gas film behavior toward the springlike gas response also decreases with the increased number of holes (Veijola et al., 1995b).

6.2 Separated Internal Flows


In this section we investigate rarefied internal flows subject to separation. Such conditions are encountered in complex networks of microchannels where the    flow is    forced to    turn or    expand (Lee    et    al.,    2000).    As    a    pro


totype geometry we consider the backward-facing step studied extensively in continuum fluid dynamics (see (Kaiktsis et al., 1996), and references therein). The objective here is to investigate the validity of slip models considered in Chapter 2. The sudden changes in the flow conditions in the backward-facing step result in significant variations of the mean free path of the gas molecules (А ж 1/P), with corresponding variations in the wall

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