Virgilio Fiorotto

The importance of the forces acting on particles in turbulent flows

The analysis of the importance of the forces that act over an ensemble of particles in a turbulent field has been carried out by using direct numerical simulation for a wide range of density ratios (2.65<ρ<2650). It has been observed that, compared to the Stokes drag, the added mass is always negligible, the pressure drag is relevant for density ratios O(1), and the Basset force is appreciable for the whole range investigated. However, the effect of these forces on the particle dispersion is about 1% for ρ∼1 as well as for large density ratios.

Effect of the subgrid scales on particle motion

In this study, the effects of small-scale velocity fluctuations on the motion of tracer particles is investigated by releasing particles in a turbulent channel flow at Reτ=175, and following their motion in time. Two types of numerical experiments were carried out: first, the Eulerian velocity field was evaluated by the direct numerical simulation (DNS) and the particles were advanced in time using the resolved and several filtered velocity fields to study the effect of the subgrid-scale velocity fluctuations on particle motion without the influence of modeling errors. In the second stage, the particle-motion study was performed using independent DNS and large-eddy simulations (LES), thus including the effect of interpolation and subgrid-scale stress modeling errors on the dispersion statistics. At this Reynolds number the small scales were found to have a limited effect on the statistics examined (one-particle dispersion, one-particle velocity autocorrelation, Lagrangian integral time scale, turbulent di...

SOLUTE TRANSPORT IN HIGHLY HETEROGENEOUS AQUIFERS

The paper deals with the transport of nonreactive solute in heterogeneous formations with prescribed statistical properties of the hydraulic log conductivity Y=ln K. Available solutions obtained from perturbation methods are limited to first- and second-order solutions, valid only for small values of the log conductivity variance σ2Y. Published numerical investigations give comparative results with finite values of σ2Y, but some discrepancies among the results generate doubts about the capability of numerical methods to capture high-order effects for media with large variance values. When these large σ2Y values are encountered in natural formations, the related nonlinear effects could be significant in the velocity statistics and in the overall dispersion process. The nonlinearity consequences are here investigated in two-dimensional isotropic porous media by the Monte Carlo technique coupled with a finite element analysis. The analysis includes σ2Y values from 0.05 to 4 enhancing the relevance of the nonlinear effects in the dispersion tensor solution. To dissipate the doubts related to the numerical approach, the accuracy of the solutions was defined by checking the influence of the factors which can affect the solution and by giving an estimation of the related errors. The numerical results confirm the validity of the first-order and second-order analyses when σ2Y → 0; the second-order solution captures the nonlinear effects in a small range of log conductivity variance close to zero. The nonlinear terms neglected in the first-order formulation for higher σ2Y values give (1) late travel time longitudinal dispersion values greater than the linear solution, (2) notably non-Gaussian distribution of the Lagrangian velocity and particle displacements, and (3) travel times to approach the asymptotic Fickian regime longer than those obtained using the linear solution.

Solute Concentration Statistics in Heterogeneous Aquifers for Finite Péclet Values

A Lagrangian framework is used for analysing the concentration fields associated with transport of nonreactive solutes in heterogeneous aquifers. This is related to two components: advection by the random velocity field v(x) and pore-scale dispersion, characterized by the dispersion tensor Dd; the relative effect of the two components is quantified by the Péclet number. The principal aim of this paper is to define the probability density function (pdf) of a nonreactive solute concentration and its relevant moments >C< and σ2c as sampled on finite detection volumes. This problem could be relevant in technical applications such as risk analysis, field monitoring and pollution control. A method to compute the concentration statistical moments and pdf is developed in the paper on the basis of the reverse formulation widely adopted to study solute dispersion in turbulent flows. The main advantages of this approach are: (i) a closed form solution for concentration mean and variance is attained, in case of small size of the sampling volume; (ii) a numerically efficient estimate of the concentration pdf can be derived. The relative effects of injection and sampling volume size and Péclet number on concentration statistics are assessed. The analysis points out that the concentration pdf can be reasonably fitted by the beta function. These results are suitable to be employed in practical applications, when the estimate of probability related to concentration thresholds is required.

Turbulent Pressure-Fluctuations under Hydraulic Jumps

New experimental evidence on the statistical structure of turbulent pressure fluctuations at the bottom of hydraulic jumps is brought in this paper in view of its relevance on stability of the linings in stilling basins. Maximum values and the structures of temporal and spatial correlation of the anisotropic field of fluctuating pressures are described. Pressures are measured in the zones of the jump where the uplift load produced on the slabs is maximum for a 5÷10 range of Froude numbers. The results define a novel design criterion for hydraulic engineering practice. It is concluded, upon comparison with analogous results from extensive although seemingly incomplete literature, that the systematic experimentation described herein completes the information needed to characterize the statistical structure of pressure fields past hydraulic jumps.

Stability Analysis of Plunge Pool Linings

AbstractIn the paper, the stability of a plunge pool bottom under the impact of an impinging jet is theoretically analyzed, with reference to the mean characteristics of the flow field: pressure and velocity. In cases when the mean components are relevant in respect to the fluctuating ones, this analysis is exhausting. In other cases, a separate evaluation of the fluctuation effects in lining design is treated by means of experimental evidence. The mean dynamic pressure at the bottom depends strongly on the impingement angle, which assumes a relevant role in the design of floor protections. In plunge pools, which are confined upstream by the presence of the drop structure, the impingement angle is theoretically determined by mass balance and momentum conservation, resulting independent of the jet entrance angle at the plunge pool water surface. The theoretical results are compared with literature, experimental evidence, and numerical simulations. This highlights the capability of the proposed theoretical ...

Dispersion tensor evaluation in heterogeneous media for finite Peclet values.

In natural formations the transport process at the local scale is characterized by the spatial heterogeneity of hydraulic conductivity and by the pore-scale dispersion. Usually, theoretical investigations consider only the effect due to the spatial variation of hydraulic conductivity, because the first prevails over the latter by some order of magnitude. Nevertheless, the pore-scale dispersion has a noteworthy impact on the concentration variance evaluation and on the ergodicity condition, so that its influence on the overall dispersion processes may be relevant. The note illustrates a theoretical procedure that allows one to define the global dispersion tensor at the local scale by taking into account the pore-scale effects as evaluated in laboratory columns. To reach this goal, the pore-scale and the local-scale velocity fluctuations are coupled via a rigorous analytical procedure in the three-dimensional (3-D) domain, and it is demonstrated that the porous media heterogeneity modifies the pore-scale dispersion effects as measured in laboratory columns. The impact of the hydraulic conductivity heterogeneity on the pore-scale dispersion at the local scale is due to (1) the path line sinuosity and (2) the module of the local velocity variation. A quantitative evaluation of these effects is made according to a first-order analysis, i.e., assuming that the spatial fluctuations of the hydraulic conductivity are small, and, in the 2-D case, a comparison with nonlinear results is made also. The results demonstrate that the only path line sinuosity coupled with the pore-scale anisotropy enhances the transversal mixing and reduces the longitudinal one, but the global heterogeneity effect, considering also the velocity module fluctuations, gives a generalized increase of the local dispersion tensor components.

Unsteady Seepage Applied to Lining Design in Stilling Basins

AbstractCases of damages experienced in stilling basins and on the toe of chute spillways are recognized to be due to global instantaneous uplift force resulting from imbalance between the instantaneous pressure distribution both above and below slabs. The latter is due to pressure fluctuation propagation forced though unsealed slab joints. In the past, several theoretical approaches were developed to estimate the uplift contribution due to pressure transmission underneath the slabs. In the paper, a model is presented, based on unsteady flow analysis of seepage through porous media, that shows that the propagation models proposed in literature are particular cases of this more comprehensive formulation. In addition, the use of the unsteady seepage model makes it possible to account for finite thickness foundation layers, typical in the cases of earth dams, rock-fill dams, and in other dam types, whenever the slabs are posed on alluvial substrates. Experimental results obtained in laboratory facilities, as...

A new approach to master recession curve analysis

Abstract The analysis of drought discharge is of utmost relevance in the design of water intake structures, management of water resources, and in coping with environmental issues. In this context, the master recession curve represents a tool in hydrological analysis, giving integrated information on long period drought flow rates. In this paper, a technique is developed for deriving a master recession curve directly from daily discharge series that takes into account the high variability in the behaviour of individual recession segments. The statistical framework developed allows us to explicitly represent uncertainty, and hence a novel interpretation of the master recession curve is derived. The method is successfully applied to three important Italian basins draining the southern slopes of the eastern Alps. Citation Fiorotto, V. and Caroni, E., 2013. A new approach to master recession curve analysis. Hydrological Sciences Journal, 58 (5), 966–975.

Spillway Stilling Basins Lining Design via Taylor Hypothesis

AbstractThe paper presents the results from detailed experiments of the statistical structure of turbulence pressure fluctuations at the bottom of hydraulic jumps, with special reference to the spillway stilling basins lining design. Here, the whole spatial correlation structure of the fluctuating pressure field is required in order to evaluate slab stability. This is computed via simultaneous acquisition of the point pressure fluctuations on a dense grid in the hydraulic jump region, requiring a severe experimental work. As an alternative, one can evaluate the pressure spatial correlation structure via autocorrelation using one point pressure acquisition and applying the Taylor hypothesis. To adopt the Taylor hypothesis, one must know the pressure propagation celerity in space that can be obtained by comparing the whole spatial pressure correlation with the pivot point pressure autocorrelation. The experiments were performed by simultaneous pressure acquisitions at the bottom of a hydraulic jump for Frou...