We present an investigation on the onset of Darcy-Bénard instability in a two-dimensional porous medium saturated with a non-Newtonian fluid and heated from below in the presence of a uniform horizontal pressure gradient. The fluid is taken to be of power-law nature with constant rheological index and temperature-dependent consistency index. A two-dimensional linear stability analysis in the vertical plane yields the critical wavenumber and the generalised critical Rayleigh number as functions of dimensionless problem parameters, with a non-monotonic dependence from and with maxima/minima at given values of , a parameter representing the effects of consistency index variations due to temperature. A series of experiments are conducted in a Hele-Shaw cell of aspect ratio to provide a verification of the theory. Xanthan Gum mixtures (nominal concentration from 0.10 % to 0.20 %) are employed as working fluids with a parameter range and. The experimental critical wavenumber corresponding to incipient instability of the convective cells is derived via image analysis for different values of the imposed horizontal velocity. Theoretical results for critical wavenumber favourably compare with experiments, systematically underestimating their experimental counterparts by 10 % at most. The discrepancy between experiments and theory is more relevant for the critical Rayleigh number, with theory overestimating the experiments by a maximum factor less than two. Discrepancies are attributable to a combination of factors: nonlinear phenomena, possible subcritical bifurcations, and unaccounted-for disturbing effects such as approximations in the rheological model, wall slip, ageing and degradation of the fluid properties.

Petrolo D., Chiapponi L., Longo S., Celli M., Barletta A., Di Federico V. (2020). Onset of Darcy-Bénard convection under throughflow of a shear-thinning fluid. JOURNAL OF FLUID MECHANICS, 889, 1-12 [10.1017/jfm.2020.84].

Onset of Darcy-Bénard convection under throughflow of a shear-thinning fluid

Celli M.
Membro del Collaboration Group
;
Barletta A.
Membro del Collaboration Group
;
Di Federico V.
Membro del Collaboration Group
2020

Abstract

We present an investigation on the onset of Darcy-Bénard instability in a two-dimensional porous medium saturated with a non-Newtonian fluid and heated from below in the presence of a uniform horizontal pressure gradient. The fluid is taken to be of power-law nature with constant rheological index and temperature-dependent consistency index. A two-dimensional linear stability analysis in the vertical plane yields the critical wavenumber and the generalised critical Rayleigh number as functions of dimensionless problem parameters, with a non-monotonic dependence from and with maxima/minima at given values of , a parameter representing the effects of consistency index variations due to temperature. A series of experiments are conducted in a Hele-Shaw cell of aspect ratio to provide a verification of the theory. Xanthan Gum mixtures (nominal concentration from 0.10 % to 0.20 %) are employed as working fluids with a parameter range and. The experimental critical wavenumber corresponding to incipient instability of the convective cells is derived via image analysis for different values of the imposed horizontal velocity. Theoretical results for critical wavenumber favourably compare with experiments, systematically underestimating their experimental counterparts by 10 % at most. The discrepancy between experiments and theory is more relevant for the critical Rayleigh number, with theory overestimating the experiments by a maximum factor less than two. Discrepancies are attributable to a combination of factors: nonlinear phenomena, possible subcritical bifurcations, and unaccounted-for disturbing effects such as approximations in the rheological model, wall slip, ageing and degradation of the fluid properties.
2020
Petrolo D., Chiapponi L., Longo S., Celli M., Barletta A., Di Federico V. (2020). Onset of Darcy-Bénard convection under throughflow of a shear-thinning fluid. JOURNAL OF FLUID MECHANICS, 889, 1-12 [10.1017/jfm.2020.84].
Petrolo D.; Chiapponi L.; Longo S.; Celli M.; Barletta A.; Di Federico V.
File in questo prodotto:
File Dimensione Formato  
onset-of-darcybenard-convection-under-throughflow-of-a-shear-thinning-fluid(1).pdf

accesso aperto

Tipo: Versione (PDF) editoriale
Licenza: Licenza per Accesso Aperto. Creative Commons Attribuzione (CCBY)
Dimensione 1.27 MB
Formato Adobe PDF
1.27 MB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/785202
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 14
  • ???jsp.display-item.citation.isi??? 10
social impact