Development of roll-waves in power-law fluids with non-uniform initial conditions

Campomaggiore, Francesca; Cristo, Cristiana Di; Iervolino, Michele; Vacca, Andrea

doi:10.1080/00221686.2016.1140684

Cited by 12 publications

(20 citation statements)

References 57 publications

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“…In particular, it has been found that a hypocritical accelerated profile may improve the instability and, conversely, a hypocritical decelerated one may inhibit it. Campomaggiore et al (2016a) confirmed this effect even for power-law fluids, for both shear-thinning and shear-thickening behaviors. Moreover, in hypercritical conditions it has been shown that an accelerated profile reduces the growth of the disturbance while a decelerated one promotes the instability.…”

Section: Introductionsupporting

confidence: 53%

“…The present Appendix describes some details about the near wave-front expansion analysis applied for studying the stability of a gradually varying profile. Present developments extend the stability analysis of Campomaggiore et al (2016a) to the case of a discontinuity on spatial derivatives of order larger than one. The technique considers that for any hyperbolic system a discontinuity of the unknown derivatives propagates in the (x,t) plane along the characteristic line with slope  0  .…”

Section: Appendixmentioning

confidence: 94%

“…In particular, the former has been evaluated superposing to the initial value a small random timedependent perturbation, while the latter has been assumed constant in time and equal to the initial value. At the channel outlet, in order to account for the possible occurrence of instantaneous hypocritical conditions caused by the roll-waves crests, absorbing boundary condition have been imposed (Campomaggiore et al, 2016a).…”

Section: Methodsmentioning

confidence: 99%

“…Following the procedure developed in Campomaggiore et al (2016a), the unknown vector, the matrix A and the source terms are expanded in powers of around = 0, whose substitution in (A2) leads tothe following system:…”

Section: Appendixmentioning

confidence: 99%

“…For small h1 values the non-linear term in Eq. (A11) may be neglected and its solution is (Campomaggiore et al, 2016a):…”

Section: Appendixmentioning

confidence: 99%

See 4 more Smart Citations

A Strategy for Passive Control of Natural Roll-Waves in Power-Law Fluids through Inlet Boundary Conditions

Cristo

Iervolino

Vacca

2017

JAFM

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The paper investigates the influence of the inlet boundary condition on the spatial evolution of natural rollwaves in a power-law fluid flowing in steep slope channels. The analysis is carried out numerically, by solving the von Kármán depth-integrated mass and momentum conservation equations, in the long-wave approximation. A second-order accurate scheme is adopted and a small random white-noise is superposed to the discharge at the channel inlet to generate the natural roll-waves train. Both shear-thinning and shearthickening power-law fluids are investigated, considering uniform, accelerated and decelerated hypercritical profiles as the unperturbed condition. Independently of the unperturbed profile and of the fluid rheology, numerical simulations clearly enlighten the presence of coalescence, coarsening and overtaking processes, as experimentally observed. All the considered statistical parameters indicate that the natural roll-waves spatial evolution is strongly affected by the unperturbed profile. Compared with the uniform condition, at the beginning of roll-waves development an accelerated profile reduces the growth of the roll-waves with a downstream shift of the non-linear wave interaction. The opposite behavior is observed if the roll wave train develops over a decelerated profile. The comparison with the theoretical outcomes of the linearized near wave-front analysis allows the interpretation of this result in terms of stability of the base flow. It is shown that once the coarsening process starts to take place, the roll-waves spatial growth rate is independent of the unperturbed profile. Present results suggest that an appropriate selection of the flow depth at the channel inlet may contribute to control, either enhancing or inhibiting, the formation of a roll-waves train in power-law fluids.

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Section: Introductionsupporting

confidence: 53%

Section: Appendixmentioning

confidence: 94%

Section: Methodsmentioning

confidence: 99%

Section: Appendixmentioning

confidence: 99%

“…For small h1 values the non-linear term in Eq. (A11) may be neglected and its solution is (Campomaggiore et al, 2016a):…”

Section: Appendixmentioning

confidence: 99%