3,834 research outputs found
Effective Forchheimer Coefficient for Layered Porous Media
Inertial flow in porous media, governed by the Forchheimer equation, is affected by domain heterogeneity at the field scale. We propose a method to derive formulae of the effective Forchheimer coefficient with application to a perfectly stratified medium. Consider uniform flow under a constant pressure gradient Delta P/L in a layered permeability field with a given probability distribution. The local Forchheimer coefficient beta is related to the local permeability k via the relation beta = a/k(c), where a > 0 being a constant and c is an element of [0, 2]. Under ergodicity, an effective value of beta is derived for flow (i) perpendicular and (ii) parallel to layers. Expressions for effective Forchheimer coefficient, beta(e), generalize previous formulations for discrete permeability variations. Closed-form beta(e) expressions are derived for flow perpendicular to layers and under two limit cases, F << 1 and F >> 1, for flow parallel to layering, with F a Forchheimer number depending on the pressure gradient. For F of order unity, beta(e) is obtained numerically: when realistic values of Delta P/L and a are adopted, beta(e) approaches the results valid for the high Forchheimer approximation. Further, beta(e) increases with heterogeneity, with values always larger than those it would take if the beta - k relationship was applied to the mean permeability; it increases (decreases) with increasing (decreasing) exponent c for flow perpendicular (parallel) to layers. beta(e) is also moderately sensitive to the permeability distribution, and is larger for the gamma than for the lognormal distribution
Combined Management of Groundwater Resources and Water Supply Systems at Basin Scale Under Climate Change
Water stress conditions associated with population growth, climate change, and groundwater contamination, represent a significant challenge for all stakeholders in the water sector. Increasing the resilience of Water Supply Systems (WSSs) becomes of fundamental importance: along with an adequate level of service, sustainability targets must be ensured. A long-term management strategy is strictly connected to a holistic approach, based on analyses at different scales. To this end, both groundwater modeling tools and water management models, with different spatial and temporal scales, are routinely and independently employed. Here, we propose a coupled approach combining: i) groundwater models (MODFLOW) to investigate different stress scenarios, involving climate change and anthropic activities; ii) water management models (Aquator), to assess the water resources availability and the best long-term management strategy for large-scale WSS. The management models are implemented starting from input and output flows derived by groundwater models: this leads to establish a comprehensive framework usually not defined in management models and including a quantitative characterization of the aquifer. The proposed methodology, general and applicable to any study area, is here implemented to the WSS of Reggio Emilia Province, and its main groundwater resource, the Enza aquifer, considering three different stress scenarios for groundwater models (BAU, ST1, and ST2), and for management strategies (BAU, BAURV2, ST2). Among the key results, we observe that coupling the two model types: i) allows evaluating water resources availability in connection with management rules; ii) leads to examining more realistic operation choices; iii) permits planning of infrastructures at basin scale
Effective conductivity of inertial flows through porous media
We study two-dimensional incompressible inertial flows through porous media. At core (small) scale, we prove that the constitutive, nonlinear model can be rewritten into a linear one by means of a new parameter K* which encompasses all the inertial effects. In natural (large-scale) formations, K* is erratically changing, and we analytically compute its counterpart, which is coined generalized effective conductivity, by the self-consistent approach (SCA). In spite of its approximate nature, the SCA leads to simple results that are in good agreement with Monte Carlo simulations
Uncertainty quantification and global sensitivity analysis of seismic metabarriers
Seismic metabarriers consist of an array of locally resonant elements (i.e., mechanical resonators) installed over the soil surface, whose design is rationally engineered to reduce ground-induced vibrations and shield vulnerable structures against seismic surface waves. Successful design and implementation of seismic metabarriers require a comprehensive knowledge and characterization of the role played by the model parameters (and their associated uncertainty) governing soil-barrier dynamic interaction. In this context, sensitivity analysis techniques allow assessing the response of a given model through the quantification of the influence and action of model inputs (and model input uncertainties) concerning a target model output. This study relies on global sensitivity analysis techniques to investigate the influence that the uncertainty associated with three key mechanical parameters of a metabarrier (i.e., soil density, soil shear modulus, and mass of mechanical resonators) has on its seismic isolation performance. The latter is measured in terms of transmission coefficient (TC). We do so by employing a two-dimensional wave finite element model developed under the plane-strain conditions to evaluate the dispersion relation and transmission coefficient of a metabarrier interacting with Rayleigh waves in the low-frequency regime (i.e., frequencies between 2 Hz and 7 Hz). Our results suggest that the shear modulus is the uncertain parameter with the most significant influence on the transmission coefficient of the metabarrier across the entire frequency range of interest. Otherwise, the resonator mass plays a substantial role in the frequency range close to the metabarrier resonant frequency
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
The propagation of gravity currents in a circular cross-section channel: experiments and theory
High-Reynolds number gravity currents (GC) in a horizontal channel with
circular/semicircular side walls are investigated by comparing experimental data
and shallow-water (SW) theoretical results. We focus attention on a Boussinesq
system (salt water in fresh water): the denser fluid, occupying part of the depth or
the full depth of the ambient fluid which fills the remaining part of the channel, is
initially at rest in a lock separated by a gate from the downstream channel. Upon the
rapid removal of the gate (‘dam break’), the denser ‘current’ begins propagating into
the downstream channel, while a significant adjustment motion propagates upstream
in the lock as a bore or rarefaction wave. Using an experimental channel provided
by a tube of 19 cm diameter and up to 615 cm length, which could be filled to
various levels, we investigated both full-depth and part-depth releases, considered the
various stages of inertial-buoyancy propagation (in particular, the initial ‘slumping’
with constant speed, and the transition to the late self-similar propagation with time
to the power 3=4), and detected the transition to the viscous-buoyancy regime. A first
series of tests is focused on the motion in the lock while a second series of tests
is focused on the evolution of the downstream current. The speed of propagation of
the current in the slumping stage is overpredicted by the theory, by about the same
amount (typically 15 %) as observed in the classical flat bottom case. The length of
transition to viscous regime turns out to be TRe0.h0=x0/U (Re0 D .g0h0/1=2h0= c is
the initial Reynolds number, g0 is the reduced gravity, c is the kinematic viscosity
of the denser fluid, h0 and x0 are the height of the denser current and the length of
the lock, respectively), with the theoretical D3=8 and experimental 0:27
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
Onset of Darcy--Bénard convection under throughflow of a shear-thinning fluid
We present an investigation on the onset of Darcy--B'enard instability in a two--dimensional porous medium saturated with a non--Newtonian fluid and heated from below in 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 wave number 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 wave number 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 wave number favourably compare with experiments, systematically underestimating their experimental counterparts by 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.
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
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