Fabián A. Bombardelli

Numerical modeling of large-scale bubble plumes accounting for mass transfer effects

Abstract A mathematical model for dilute bubble plumes is derived from the two-fluid model equations. This is coupled to a mass transfer model to get a closed CFD formulation. The mass transfer equations used are the same as those implemented in the 1D model proposed, so as to get a CFD formulation and a 1D integral formulation that are fully consistent. In fact, the 1D model can be rigorously derived from the CFD one. The mathematical derivation is detailed pointing out the approximations involved. Results of both models for typical conditions of isolated aeration plumes in deep wastewater reservoirs are presented. Good agreement is reported between them, emphasizing on the most relevant variables such as gas dissolution rates, gas holdup, liquid’s velocity and bubbles’ radius. Furthermore, entrainment rates evaluated from the CFD results are shown to lie within the experimental range. Finally, CFD-based assessment of the approximations involved in the 1D model proves them to hold within a few percents of relative accuracy. A solid basis for applying CFD models to aeration plumes, as natural extensions of the popular integral models, emerges from the investigation.

A biogeochemical model of contaminant fate and transport in river waters and sediments

A quasi-two-dimensional model is presented for simulating transport and transformation of contaminant species in river waters and sediments, taking into account the effect of both biotic and abiotic geochemical reactions on the contaminant fate and mobility. The model considers the downstream transport of dissolved and sediment-associated species, and the mass transfer with bed sediments due to erosion and resuspension, using linked advection-dispersion-reaction equations. The model also couples both equations to the reactive transport within bed sediment phases. This is done by the use of a set of vertical one-dimensional columns representing sediment layers that take into account the reactive transport of chemicals, burial, sorption/desorption to/from the solid phase, and the diffusive transport of aqueous species. Kinetically-controlled reversible solid-water mass exchange models are adopted to simulate interactions between suspended sediments and bulk water, as well as the mass exchange between bed sediments and pore water. An innovative multi-time step approach is used to model the fully kinetic nonlinear reaction terms using a non-iterative explicit method. This approach enables the model to handle fast and near-equilibrium reactions without a significant increase in computational burden. At the end, two demonstration cases are simulated using the model, including transport of a sorbing, non-reactive trace metal and nitrogen cycling, both in the Colusa Basin Drain in the Central Valley of California.

3D numerical simulation of particle-particle collisions in saltation mode near stream beds

The importance of particle-particle collisions in sediment saltation in the bed-load layer is analyzed herein by means of numerical simulation. The particle saltation theoretical/numerical model follows a Lagrangian approach, and addresses the motion of sediment particles in an open channel flow described by a logarithmic velocity profile. The model is validated with experimental data obtained from the literature. In order to evaluate the importance of the phenomenon, simulations with and without particle-particle collisions were carried out. Results for two different sediment concentrations are presented, namely 0.13% and 2.33%. For each concentration of particles, three different flow intensities were considered, and trajectories of two different particle sizes, within the sand range were computed. Changes in particle rotation, particle velocity, and angle of trajectory before and after particle-particle collisions appear to be relatively important at lower shear stresses, whereas they decrease in significance with increasing flow intensities. Analyses of the evolution in time of the second order moment of particle location suggest that inter-particle collisions introduce transverse diffusion in saltating particles in the span-wise direction.

Scouring of granular beds by jet-driven axisymmetric turbulent cauldrons

We study a sustained, jet-driven, axisymmetric turbulent cauldron that scours a pothole in a cohesionless granular bed. We focus on the energetics of the turbulent cauldron and use dimensional analysis and similarity methods to derive (up to a multiplicative constant) a formula for the equilibrium depth of the pothole. To that end, we assume that the power of the jet is stationary and that under equilibrium conditions no air or granular material from the bed is entrained in the cauldron. The resulting formula contains a single similarity exponent, which we show can be determined via the phenomenological theory of turbulence. Our method of analysis may prove useful in developing a theoretical understanding of mine burial, bridge pier-induced erosion, and other applications in which a localized turbulent flow interacts with a granular bed.

Air entrainment onset in skimming flows on steep stepped spillways: an analysis

ABSTRACT We discuss, apply and validate several physics-based criteria for air entrainment into flows on steep stepped spillways, using laboratory observations and numerical results published elsewhere. To the best of our knowledge, this is the first time a validation of these criteria is undertaken for any chute flow in general, and for the skimming flow in steep stepped spillways in particular. To undertake the validation, we employed experimental and numerical data covering a considerable range of volume flow rates and step heights. We observed an overall good performance of most of the criteria, especially taking into account the intrinsic difficulties in defining the time-averaged location and depth of the inception point of air entrainment experimentally. Finally, we present two novel non-dimensional numbers designed to facilitate the physical interpretation of the location of the inception point of air entrainment.

Analytical solutions of nonlinear and variable-parameter transport equations for verification of numerical solvers

All numerical codes developed to solve the advection–diffusion-reaction (ADR) equation need to be verified before they are moved to the operational phase. In this paper, we initially provide four new one-dimensional analytical solutions designed to help code verification; these solutions are able to handle the challenges of the scalar transport equation including nonlinearity and spatiotemporal variability of the velocity and dispersion coefficient, and of the source term. Then, we present a solution of Burgers’ equation in a novel setup. Proposed solutions satisfy the continuity of mass for the ambient flow, which is a crucial factor for coupled hydrodynamics-transport solvers. By the end of the paper, we solve hypothetical test problems for each of the solutions numerically, and we use the derived analytical solutions for code verification. Finally, we provide assessments of results accuracy based on well-known model skill metrics.

Numerical aspects of the simulation of discontinuous saline underflows: the lock-exchange problem

Issues associated with the adequate representation of flow instabilities of saline, discontinuous density currents in two and three dimensions are discussed. First, simulations of the experiments by Alahyari and Longmire (1996) developed with an advanced commercial code are presented, and they are compared with results obtained through Direct Numerical Simulation of the problem. Various meshes and turbulence models are then tested with the commercial code, including a Large Eddy Simulation. The features of the density current that are not reproduced well by the simulations with the commercial code are further analyzed. Then, two-dimensional numerical simulations of an unpublished set of experiments are presented. The response of commercial and open-source codes to different grids is addressed. Important conclusions on the risks of using inadequate resolution with codes in which not all variables are controlled are obtained, and the nature of these two-dimensional, “mathematical” numerical solutions is discussed.

Parallel Computations of the Dynamic Behavior of Bubble Plumes

This paper discusses numerical results obtained with different strategies for modeling air-water flows. Mathematical models for dilute mixtures, derived from the two-fluid model equations, are presented. These models include diverse degrees of complexity, and they handle turbulence via a k-e model and a Large-Eddy Simulation (LES) approach, in a consistent way. The models are implemented in a parallel code, which is then used to numerically simulate the dynamic behavior of bubble columns in two and three dimensions. The results of the simulations are employed to study the interplay between the turbulence of the carrier and the scales of the wandering motion, and to compare the capability of different models to capture the physics behind the phenomenon.Copyright

Wind‐driven nearshore sediment resuspension in a deep lake during winter

Ongoing public concern over declining water quality at Lake Tahoe, California-Nevada (USA) led to an investigation of wind-driven nearshore sediment resuspension that combined field measurements and modeling. Field data included: wind speed and direction, vertical profiles of water temperature and currents, nearbed velocity, lakebed sediment characteristics, and suspended sediment concentration and particle size distribution. Bottom shear stress was computed from ADV-measured nearbed velocity data, adapting a turbulent kinetic energy method to lakes, and partitioned according to its contributions attributed to wind-waves, mean currents, and random motions. When the total shear stress exceeded the critical shear stress, the contribution to overall shear stress was about 80% from wind-waves and 10% each from mean currents and random motions. Therefore, wind-waves were the dominant mechanism resulting in sediment resuspension as corroborated by simultaneous increases in shear stress and total measured sediment concentration. The wind-wave model STWAVE was successfully modified to simulate wind-wave-induced sediment resuspension for viscous-dominated flow typical in lakes. Previous lake applications of STWAVE have been limited to special instances of fully turbulent flow. To address the validity of expressions for sediment resuspension in lakes, sediment entrainment rates were found to be well represented by a modified 1991 Garcia and Parker formula. Last, in situ measurements of suspended sediment concentration and particle size distribution revealed that the predominance of fine particles (by particle count) that most negatively impact clarity was unchanged by wind-related sediment resuspension. Therefore, we cannot assume that wind-driven sediment resuspension contributes to Lake Tahoes declining nearshore clarity.

Computation of the Basset force: recent advances and environmental flow applications

Abstract When numerically integrating the equation describing the motion of a particle in a carrier fluid, the computation of the Basset (history) force becomes by far the most expensive and cumbersome, as opposed to forces such as drag, virtual mass, lift, buoyancy and Magnus. The expression representing the Basset force constitutes an integro-differential term whose standard integrand is singular when the upper integration limit is enforced. These shortcomings have led some researchers to either disregard or outright neglect the contribution of the Basset force to the total force, even in those cases where it may yield to important errors in the determination of particle trajectories in the computation of sediment transport and other environmental flows. This work is devoted to review four recent contributions associated with the computation of the Basset force, and to compare their proposals to diminish the inherent problems of the term integration. All papers, except one, use variants of a window-based approach; the most recent contribution, in turn, employs a specialized quadrature to increase the accuracy of the computation. An analysis was carried out to compare CPU computation times, rates of convergence and accuracy of the approximations versus a known analytical solution. All methods provide sound solutions to the issues associated with the computation of the Basset force; further, a road map to select the best solution for each given problem is provided. Finally, we discuss the implications of the techniques for the simulation of sediment transport processes and other environmental flows.