[Kinetic theory and boundary conditions for flows of highly inelastic spheres: Applications to gravity driven granular flows down bumpy inclines]
We studied the effects of isotropic boundary vibrations on unconfined granular materials that are compressed by gravity and dilated by the agitation of horizontal, vibrating boundaries. Because the vibrations are isotropic, the assemblies experience no mean motion. Consequently, the resulting boundary value problem is simpler than the boundary value problem that results when the vibrating surface is inclined. However, in both cases, we confront difficulties associated the occurrence of a free surface, and must implement recently derived boundary conditions for vibrating boundaries. We calculate the steady state solid fraction and granular temperature profiles throughout assemblies of identical, smooth, inelastic spheres that are unconfined from above and thermalized from below by bumpy, horizontal surfaces that randomly vibrate about zero mean velocity. The analysis is based upon a kinetic constitutive theory and conditions that account for the effects of boundary vibrations on the momentum and energy transferred to the spheres. In presenting the results, we pay special attention to the thermalized states of fixed masses subjected to varying boundary vibrations and varying masses subjected to fixed vibrations. In the first study, we find that as the vibration of the boundary intensifies, the assemblies of fixed mass become deeper, more dilute, and more thermalized. In the second, we find that as the assemblies become more massive, fixed boundary vibrations effectively thermalize decreasing fractions of the total mass.
- Research Organization:
- Worcester Polytechnic Inst., MA (United States)
- Sponsoring Organization:
- DOE; USDOE, Washington, DC (United States)
- DOE Contract Number:
- AC22-91PC90185
- OSTI ID:
- 6904787
- Report Number(s):
- DOE/PC/90185-T5; ON: DE93004935
- Country of Publication:
- United States
- Language:
- English
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[Kinetic theory and boundary conditions for flows of high inelastic spheres: Application to gravity driven granular flows down bumpy inclines]
[Kinetic theory and boundary conditions for flows of high inelastic spheres: Application to gravity driven granular flows down bumpy inclines]. Quarterly progress report, July 1, 1992--September 30, 1992