Stability analysis of unbounded uniform dense granular shear flows
Date Issued
2009
Date
2009
Author(s)
Lai, Jeng-You
Abstract
This thesis presents a linear stability analysis of unbounded uniform dense granular shear flows. The analysis is based on the revised constitutive equations of the kinetic theory (Savage 2008) for dry, identical spherical, smooth and inelastic particles in the dense state. In the present work, the purely kinetic model in dense state has been studied by asymptotic and transient stability analyses. Transient phenomena can provide a viable way to trigger finite amplitude effects. The solution of the linear perturbed system is obtained by the Kelvin-mode which means that the wavenumber vector of the disturbances is turned by the mean shear flow. The result of spatially uniform mode is unstable when time proceeds. Disturbances of zero streamwise wavenumber are always stable by the asymptotic results and the marginal stability curve has proved that it does not exist. As the solids volume fraction and coefficient of restitution are increased, the initial transient growth rate and the maximum transient growth are both enhanced. As the initial transversal wavenumber is increased, the initial transient growth rate is also enhanced but the maximum transient growth is reduced. Disturbances of nonzero streamwise wavenumber can produce multiple and significant peaks as the initial transversal wavenumber are small. Since the matrix of our linear system is the non-normality matrix, the initial growth rate can be a positive value at initial period. The transient growth function may cause a significant transient growth value and the oscillatory peaks. The temporal evolution of each component from the initial condition is presented in this thesis, the dominated component can be observed. The case of adding the quasi-static stresses is discussed in the end. Because the results are disorderly, we propose a suggestion to the model (Savage 2008).
Subjects
dense granular flows
purely kinetic model
asymptotic stability
transient stability
layering modes
non-layering modes
Type
thesis
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