| Description: |
International audience ; Turbulence being an ubiquitous flow behavior, the transition to this state is one of the most studiedfields in fluid mechanics, yet it is not entirely understood. Turbulence, in addition to its academicsappeal, is also a key element for the fluid transport optimization in many industrial processes. Amongthem, wastewater treatment processes require to control the transition to turbulence in the pipe with theadded complexity of an Herschel-Bulkley fluid [1]. The transition to turbulence is realised through nonlinear amplifications of finite-size amplitudes perturbations [2]. The practical interest of modelling theintermittency is to optimize the sludge transport in pipe. For this reason the present work investigatesthe non-linear physics in the momentum equation that are essential to explain the intermittency and thenon-linear interaction between turbulent and laminar regions leading to transition.A one-dimensional model characterizing the transition to turbulence in Newtonian fluid has beendeveloped by Barkley [3]. We generalized this model [4] to include power-law fluids, a particular case ofan Herschel-Bulkley fluid without yield-stress, in a heated pipe. Recently, the model has further beenextended [5] to study the radial receptivity to finite-size perturbations for an Herschel-Bulkley fluid. Theobjective of this work is to integrate the interaction between temperature and rheology to the modeldeveloped in previous works. We aim here to be capable to describe the receptivity to perturbations inpipe flow for different thermo-rheological properties and different heating conditions.Références1. P.T. Slatter, Water SA, 30, 5 (2005).2. B. Hof, C. W. H. van Doorne, J. Westerweel, F. T. M. Nieuwstadt et al., Science, 302, 1594-1598 (2004).3. D. Barkley, Theoretical perspective on the route to turbulence in a pipe, J. of Fluid Mech., 803, P1 (2016).4. F. Romanò, A. Charles, F. Dottori, S. A. Bahrani., Phys. Fluids, 33, 091702 (2021).5. A. Charles, F. Romanò, T. Ribeiro, S. Azimi, V. Rocher, ... |