Flood propagation modelling with the Local Inertia Approximation: theoretical and numerical analysis of its physical limitations

Attention of the researchers has increased towards a simplification of the complete Shallow water Equations called the Local Inertia Approximation (LInA), which is obtained by neglecting the advection term in the momentum conservation equation. In the present paper it is demonstrated that a shock is always developed at moving wetting-drying frontiers, and this justifies the study of the Riemann problem on even and uneven beds. In particular, the general exact solution for the Riemann problem on horizontal frictionless bed is given, together with the exact solution of the non-breaking wave propagating on horizontal bed with friction, while some example solution is given for the Riemann problem on discontinuous bed. From this analysis, it follows that drying of the wet bed is forbidden in the LInA model, and that there are initial conditions for which the Riemann problem has no solution on smoothly varying bed. In addition, propagation of the flood on discontinuous sloping bed is impossible if the bed drops height have the same order of magnitude of the moving-frontier shock height. Finally, it is found that the conservation of the mechanical energy is violated. It is evident that all these findings pose a severe limit to the application of the model. The numerical analysis has proven that LInA numerical models may produce numerical solutions, which are unreliable because of mere algorithmic nature, also in the case that the LInA mathematical solutions do not exist. The applicability limits of the LInA model are discouragingly severe, even if the bed elevation varies continuously. More important, the non-existence of the LInA solution in the case of discontinuous topography and the non-existence of receding fronts radically question the viability of the LInA model in realistic cases. It is evident that classic SWE models should be preferred in the majority of the practical applications

Application of Buckingham π theorem for scaling-up oriented fast modelling of Proton Exchange Membrane Fuel Cell impedance

Abstract This work focuses on the development of a fast PEMFC impedance model, built starting from both physical and geometrical variables. Buckingham's π theorem is proposed to define non-dimensional parameters that allow suitably describing the relationships linking the physical variables involved in the process under-study to the fundamental dimensions. This approach is a useful solution for those problems, whose first principles-based models are not known, difficult to build or computationally unfeasible. The key contributions of the proposed similarity theory-based modelling approach are presented and discussed. The major advantage resides in its straightforward online applicability, thanks to very low computational burden, while preserving good level of accuracy. This makes the model suitable for several purposes, such as design, control, diagnostics, state of health monitoring and prognostics. Experimental data, collected in different operating conditions, have been analysed to demonstrate the capability of the model to reproduce PEMFC impedance at different loads and temperatures. This results in a reduction of the experimental effort for the FCS lab characterization. Moreover, it is highlighted the possibility to use the model with scaling-up purposes to reproduce the full stack impedance from single-cell one, thus supporting FC design and development from lab-to commercial system-scale

A Derivative Recovery Spectral Volume model for the analysis of constituents transport in one-dimensional flows

The treatment of advective fluxes in high-order finite volume models is well established, but this is not the case for diffusive fluxes, due to the conflict between the discontinuous representation of the solution and the continuous structure of analytic solutions. In this paper, a derivative reconstruction approach is proposed in the context of spectral volume methods, for the approximation of diffusive fluxes, aiming at the reconciliation of this conflict. Two different reconstructions are used for advective and diffusive fluxes: the advective reconstruction makes use of the information contained in a spectral cell, and allows the formation of discontinuities at the spectral cells boundaries; the diffusive reconstruction makes use of the information contained in contiguous spectral cells, imposing the continuity of the reconstruction at the spectral cells boundaries. The method is demonstrated by a number of numerical experiments, including the solution of shallow-water equations, complemented with the advective-diffusive transport equation of a conservative substance, showing the promising abilities of the numerical scheme proposed

Friction decoupling and loss of rotational invariance in flooding models

Friction decoupling, i.e. the computation of friction vector components making separate use of the corresponding velocity components, is common in staggered grid models of the SWE simplifications (Zero-Inertia and Local Inertia Approximation), due to the programming simplicity and to the consequent calculations speed-up. In the present paper, the effect of friction decoupling has been studied from the theoretical and numerical point of view. First, it has been found that friction vector decoupling causes the reduction of the computed friction force and the rotation of the friction force vector. Second, it has been demonstrated that decoupled-friction models lack of rotational invariance, i.e. model results depend on the alignment of the reference framework. These theoretical results have been confirmed by means of numerical experiments. On this basis, it is evident that the decoupling of the friction vector causes a major loss of credibility of the corresponding mathematical and numerical models. Despite the modest speed-up of decoupled-friction computations, classic coupled-friction models should be preferred in every case

Utility trenches: sinks or barriers? Modeling the fate of leaked water in a crowded subsurface

High permeability sand/gravel trenches surrounding utility pipes are deemed to create preferential pathways for water in the subsurface of urban environments. Although this can be true when both trench filling material and surrounding soils are fully water saturated, the same is not obvious in the unsaturated zone. This study explores the behavior of these anthropogenic features in the unsaturated zone and their role in the formation of the urban karst with specific interest to the fate of water leaked from utility pipelines and its potential to affect urban aquifers. A series of 3D steady state numerical simulations was performed assuming two groups of nearby utility trenches hosting a water pipeline, up to 6 concurrent leaks, different leak rates, native soil properties, slopes of the utility trenches, and initial water saturation profiles. The analysis showed that utility trenches in the unsaturated zone are more likely an obstacle to water flow originated from leaking water utilities. Indeed, they served as capillary barriers rather than sinks in the simulations, although with a limited diversion capacity. Nevertheless, a pronounced lateral spreading of leaked water within the trenches was predicted in some scenarios, which suggests that there is still potential for the urban karst effect to occur when native soil properties are not that far from those of the trench filling material, although high initial effective water saturations would be required in this case

Optimal Regulation of Pumping Station in Water Distribution Networks Using Constant and Variable Speed Pumps: A Technical and Economical Comparison

Greenhouse gas emission is one of the main environmental issues of today, and energy savings in all industries contribute to reducing energy demand, implying, in turn, less carbon emissions into the atmosphere. In this framework, water pumping systems are one of the most energy-consuming activities. The optimal regulation of pumping systems with the use of variable speed drives is gaining the attention of designers and managing authorities. However, optimal management and operation of pumping systems is often performed, employing variable speed drives without considering if the energy savings are enough to justify their purchasing and installation costs. In this paper, the authors compare two optimal pump scheduling techniques, optimal regulation of constant speed pumps by an optimal ON/OFF sequence and optimal regulation with a variable speed pump. Much of the attention is devoted to the analysis of the costs involved in a hypothetical managing authority for the water distribution system in order to determine whether the savings in operating costs is enough to justify the employment of variable speed drives

A Derivative Free Non-Linear Programming Method for the Optimal Setting of PATs to Be Used in a Hybrid Genetic Algorithm: A Preliminary Work

In recent years, recovering energy while managing excessive pressure in water distribution networks (WDNs) has gradually taken hold through the use of Pumps as Turbines (PATs). Therefore, algorithms commonly used for the optimizations of WDNs require modifications to incorporate these devices. Within this study, an intermediate step toward a new Hybrid Genetic Algorithm (HGA) for the optimal placement and setting of PATs within WDNs is proposed. The described methodology is based on a non‐linear optimization algorithm, the Powell Direction Set (PDS) method. For each WDN configuration with PATs, a non‐linear univariate function, namely the energy production subjected to pressure and technical constraints, is maximized by the PDS method. The promising capabilities of the algorithm are demonstrated with a case study

The Effect of Geological Heterogeneity and Groundwater Table Depth on the Hydraulic Performance of Stormwater Infiltration Facilities

Urbanization has led to a substantial change in the hydrological cycle of urban catchments. Increased runoff and urban flooding, decreased direct subsurface infiltration and groundwater recharge, deterioration of water quality are among the major effects of this alteration. To alleviate these effects, Low Impact Development (LID) practices have been frequently adopted for stormwater management. Among LID infrastructures, infiltration facilities are particularly challenging to design and model due to the considerable amount of uncertainties related to the hydrogeological configuration of installation sites. To date, analysis on how soil heterogeneity, groundwater table depth, and thickness of the unsaturated zone affect the hydraulic performance of infiltration facilities are lacking. To address this knowledge gap, a series of numerical experiments under transient variably water saturated conditions were performed for a hypothetical infiltration facility. Numerical simulations showed that i) infiltration rates increase considerably as the initial depth of the groundwater table increases, ii) the contribution of the bottom of the facility to the infiltration of water is generally higher than the sides, iii) the presence of a less conducting soil layer at a short depth from the bottom of the facility reduces infiltration rates dramatically, iv) the complete clogging of the bottom of the facility has a dramatic impact on the hydraulic performance, v) the stochastic heterogeneity of the soil controls the overall stormwater infiltration process through the facility, and the hydraulic performance may largely deviate from the case when heterogeneity is absent