Interdisciplinary Applied Mathematics

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For the continuum description presented in Chapter 2, we did not need the scattering kernel but rather an equivalent lumped accommodation coefficient, which was determined empirically depending on the gas and the wall type. For    example,    for    light    gases,    such    as    helium    and    neon,    the    tan

gential accommodation coefficient may be much less than unity, but for heavy gases, e.g., xenon and krypton, the tangential accommodation coefficient is close to one. For typical surfaces in microsystems and argon or nitrogen the value obtained in (Arkilic, 1997), is around 0.8.

In    general,    the    cleaner the surface,    the    smaller    the    value    of    the    tan

gential accommodation coefficient.

Also, the position-dependent accommodation coefficient is a matrix, the elements of which depend on the distribution function of the impinging molecules.

A comparison of the Maxwell scattering kernel and the Cercignani-Lampis kernel for micronozzle flows was presented in (Ketsdever et al., 2000b). In particular, the free molecule microresistojet (FMMR) discussed in Section 6.6 was considered with argon as propellant. Two forms of the Cercignani-Lampis-Lord (CLL) model were employed in the simulations (Lord, 1991; Lord, 1995): the original model as well as a generalized form permitting diffuse reflection at a surface with incomplete energy accommodation. A comparison of the normalized specific impulse at the exit of the FMMR is shown in Figure 15.14. For the same value of the accommodation

h 1.0

Maxwell, a=1.0

CLL(diffuse), a=0.5

CLL(ongmal), a=0.5

transverse distance y/w

FIGURE 15.14. Gas-surface interaction in micronozzle flows. The normalized specific impulse is plotted across the expansion slot of a free molecule microre-sistojet (Ketsdever et al., 2000b). (a denotes accommodation coefficient, same as av in this book). (Courtesy of A. Ketsdever.) coefficient (symbol a in the figure) the models differ by about 5%, whereas varying the accommodation coefficient from specular (av = a = 0) to diffuse (av = a =1) leads to about 20% variation in the value of the predicted specific impulse Isp. It was shown in (Ketsdever et al., 2000b), that other quantities, such as axial velocity distribution functions, are more sensitive to the scattering model assumption.

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