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Article Dans Une Revue Journal of Non-Newtonian Fluid Mechanics Année : 2017

Compressibility regularizes the μ(I)-rheology for dense granular flows

Joris Heyman
  • Fonction : Auteur correspondant
Alexandre Valance
Renaud Delannay
Herve Tabuteau

Résumé

The μ(I)-rheology was recently proposed as a potential candidate to model the incompressible flow of frictional grains in the dense inertial regime. However, this rheology was shown to be ill-posed in the mathematical sense for a large range of parameters, notably in the low and large inertial number limits (Barker et al., J. Fluid Mech., vol. 779, 2015, pp. 794–818). In this rapid communication, we extend the stability analysis of Barker et al. (J. Fluid Mech., vol. 779, 2015, pp. 794–818) to compressible flows. We show that compressibility regularizes the equations, making the problem well-posed for all parameters, with the condition that sufficient dissipation be associated with volume changes. In addition to the usual Coulomb shear friction coefficient μ, we introduce a bulk friction coefficient μb , associated with volume changes and show that the problem is well-posed if μb > 1 − 7μ/6. Moreover, we show that the ill-posed domain defined by Barker et al. (J. Fluid Mech., vol. 779, 2015, pp. 794–818) transforms into a domain where the flow is unstable but remains well-posed when compressibility is taken into account. These results suggest the importance of taking into account dynamic compressibility for the modelling of dense granular flows and open new perspectives to investigate the emission and propagation of acoustic waves inside these flows.

Dates et versions

hal-01623518 , version 1 (25-10-2017)

Identifiants

Citer

Joris Heyman, Alexandre Valance, Renaud Delannay, Herve Tabuteau. Compressibility regularizes the μ(I)-rheology for dense granular flows. Journal of Non-Newtonian Fluid Mechanics, 2017, 830, pp.553-568. ⟨10.1017/jfm.2017.612⟩. ⟨hal-01623518⟩
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