Experimental verification of theoretical approaches for radial gravity currents draining from an edge

We present an experimental study of inertial gravity currents (GCs) propagating in a cylindrical wedge under different drainage directions (inward/outward), lock-release (full/partial gate width) and geometry (annulus/full cylinder). We investigate the following combinations representative of operational conditions for dam-break flows: (i) inward drainage, annular reservoir, full gate; (ii) outward drainage, full reservoir, full gate; and (iii) outward drainage, full reservoir, partial gate. A single-layer shallow-water (SW) model is used for modelling the first two cases, while a box model interprets the third case; the results of these approximations are referred to as “theoretical”. We performed a first series of experiments with water as ambient fluid and brine as intruding fluid, measuring the time evolution of the volume in the reservoir and the velocity profiles in several sections; in a second series, air was the ambient and water was the intruding fluid. Careful measurements, accompanied by comparisons with the theoretical predictions, were performed for the behaviour of the interface, radial velocity and, most important, the volume decay V(t) / V(0). In general, there is good agreement: the theoretical volume decay is more rapid than the measured one, but the discrepancies are a few percent and the agreement improves as the Reynolds number increases. Velocity measurements show a trend correctly reproduced by the SW model, although often a delay is observed and an over- or under-estimation of the peak values. Some experiments were conducted to verify the role of inconsistencies between experimental set-up and model assumptions, considering, for example, the presence or absence of a top lid, wedge angle much less than 2 π, suppression of the viscous corner at the centre, reduction of disturbances in the dynamics of the ambient fluid: all these effects resulted in negligible impacts on the overall error. These experiments provide corroboration to the simple models used for capturing radial drainage flows, and also elucidate some effects (like oscillations of the radial flux) that are beyond the resolution of the models. This holds also for partial width lock-release, where axial symmetry is lost

Experimental verification of theoretical approaches for radial gravity currents draining from an edge

We present an experimental study of inertial gravity currents (GCs) propagating in a cylindrical wedge under different drainage directions (inward/outward), lock-release (full/partial gatewidth) and geometry (annulus/full cylinder). We investigate the following combinations representative of operational conditions for dam-break flows: (i) inward drainage, annular reservoir, full gate; (ii) outward drainage, full reservoir, full gate; and (iii) outward drainage, full reservoir, partial gate. A single-layer shallow-water (SW) model is used for modelling the first two cases, while a box model interprets the third case; the results of these approximations are referred to as "theoretical". We performed a first series of experiments with water as ambient fluid and brine as intruding fluid, measuring the time evolution of the volume in the reservoir and the velocity profiles in several sections; in a second series, airwas the ambient andwaterwas the intruding fluid. Careful measurements, accompanied by comparisons with the theoretical predictions, were performed for the behaviour of the interface, radial velocity and, most important, the volume decay V(t)/V(0). In general, there is good agreement: the theoretical volume decay is more rapid than the measured one, but the discrepancies are a few percent and the agreement improves as the Reynolds number increases. Velocity measurements show a trend correctly reproduced by the SWmodel, although often a delay is observed and an over- or under-estimation of the peak values. Some experiments were conducted to verify the role of inconsistencies between experimental set-up and model assumptions, considering, for example, the presence or absence of a top lid, wedge angle much less than 2p, suppression of the viscous corner at the centre, reduction of disturbances in the dynamics of the ambient fluid: all these effects resulted in negligible impacts on the overall error. These experiments provide corroboration to the simple models used for capturing radial drainage flows, and also elucidate some effects (like oscillations of the radial flux) that are beyond the resolution of the models. This holds also for partial width lock-release, where axial symmetry is lost

Evaluation of transverse shear stresses in layered beams/plates/shells via stress recovery accounting for various CUF-based theories

This paper exploits the stress recovery technique to evaluate the out-of-plane stress components in the static analysis of composite beams, plates and shells. This technique is implemented in the framework of the Carrera Unified Formulation, an approach allowing the implementation of the theories of structures in a compact way. This work uses Taylor, Legendre and Jacobi polynomials with equivalent single-layer and layer-wise approaches. The finite element method is applied to provide numerical solutions. Multi-layered beams, plates and shells subjected to different loading and boundary conditions are studied to validate and assess the proposed technique. The results are compared with those from the literature and show that the stress recovery technique provides reasonable accuracy for the shear stresses, even with lower-order models. Furthermore, results confirm that, when dealing with thick structures, the adoption of layer-wise models is mandatory to obtain accurate results

Ascending non-Newtonian long drops in vertical tubes

We report on theoretical and experimental studies describing the buoyancy-driven ascent of a Taylor long drop in a circular vertical pipe where the descending fluid is Newtonian, and the ascending fluid is non-Newtonian yield shear thinning and described by the three-parameter Herschel–Bulkley model, including the Ostwald–de Waele model as a special case for zero yield. Results for the Ellis model are included to provide a more realistic description of purely shear-thinning behaviour. In all cases, lubrication theory allows us to obtain the velocity profiles and the corresponding integral variables in closed form, for lock-exchange flow with a zero net flow rate. The energy balance allows us to derive the asymptotic radius of the inner current, corresponding to a stable node of the differential equation describing the time evolution of the core radius. We carried out a series of experiments measuring the rheological properties of the fluids, the speed and the radius of the ascending long drop. For some tests, we measured the velocity profile with the ultrasound velocimetry technique. The measured radius of the ascending current compares fairly well with the asymptotic radius as derived through the energy balance, and the measured ascent speed shows a good agreement with the theoretical model. The measured velocity profiles also agree with their theoretical counterparts. We have also developed dynamic similarity conditions to establish whether laboratory physical models, limited by the availability of real fluids with defined rheological characteristics, can be representative of real phenomena on a large scale, such as exchanges in volcanic conduits. Appendix B contains scaling rules for the approximated dynamic similarity of the physical process analysed; these rules serve as a guide for the design of experiments reproducing real phenomena

Ascending non-Newtonian long drops in vertical tubes

We report on theoretical and experimental studies describing the buoyancy-driven ascent of a Taylor long drop in a circular vertical pipe where the descending uid is Newtonian, and the ascending uid is non-Newtonian yield-shear-thinning and described by the threeparameter Herschel-Bulkley model, including the Ostwald-deWaele (OdW) model as a special case for zero yield. Results for the Ellis model are included to provide a more realistic description of purely shear-thinning behaviour. In all cases, lubrication theory allows obtaining the velocity pro les and the corresponding integral variables in closed form, for lock-exchange ow with a zero net ow rate. The energy balance allows deriving the asymptotic radius of the inner current, corresponding to a stable node of the di erential equation describing the time evolution of the core radius. We carried out a series of experiments measuring the rheological properties of the uids, the speed and the radius of the ascending long drop. For some tests, we measured the velocity pro le with Ultrasound velocimetry technique. The measured radius of the ascending current compares fairly well with the asymptotic radius as derived through the energy balance, and the measured ascent speed shows a good agreement with the theoretical model. The measured velocity pro les also agree with their theoretical counterparts. We have also developed dynamic similarity conditions to establish whether laboratory physical models, limited by availability of real uids with de ned rheological characteristics, can be representative of real phenomena on a large scale, such as exchanges in volcanic conduits. The Appendix contains scaling rules for the approximated dynamic similarity of the physical process analysed; these rules serve as a guide for the design of experiments reproducing real phenomena

Onset of Darcy-B\ue9nard convection under throughflow of a shear-thinning fluid

We present an investigation on the onset of Darcy-B\ue9nard 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