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Publication# Modelling Small-Scale Drifting Snow with a Lagrangian Stochastic Model Based on Large-Eddy Simulations

Marc Diebold, Michael Lehning, Gian-Duri Lieberherr, Jan Overney, Marc Parlange

*Springer Verlag, *2014

Article

Article

Résumé

Observations of drifting snow on small scales have shown that, in spite of nearly steady winds, the snow mass flux can strongly fluctuate in time and space. Most drifting snow models, however, are not able to describe drifting snow accurately over short time periods or on small spatial scales as they rely on mean flow fields and assume equilibrium saltation. In an attempt to gain understanding of the temporal and spatial variability of drifting snow on small scales, we propose to use a model combination of flow fields from large-eddy simulations (LES) and a Lagrangian stochastic model to calculate snow particle trajectories and so infer snow mass fluxes. Model results show that, if particle aerodynamic entrainment is driven by the shear stress retrieved from the LES, we can obtain a snow mass flux varying in space and time. The obtained fluctuating snow mass flux is qualitatively compared to field and wind-tunnel measurements. The comparison shows that the model results capture the intermittent behaviour of observed drifting snow mass flux yet differences between modelled turbulent structures and those likely to be found in the field complicate quantitative comparisons. Results of a model experiment show that the surface shear-stress distribution and its influence on aerodynamic entrainment appear to be key factors in explaining the intermittency of drifting snow.

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Uncontrolled overtopping during flood events can endanger embankment dams. Erosion of the downstream slope and scouring of its base caused by the high velocity and energy of the overflow can indeed lead to breach formation until complete failure. In this context and faced with the important number of overtopped embankment dams to be rehabilitated, since the early eighties, researchers have investigated surface protection solutions for downstream slope. Overlays against erosion such as seeded goetextile or cable-tied cellular concrete blocks, are not sufficient. In fact, they can resist only short events with low discharge and velocity. Solution to overcome more severe overflow lies in overlays which dissipate flow energy along the downstream embankment slope. Conventional steps resulting from Roller Compacted Concrete (RCC) techniques fulfill efficiently this challenge. However, flows over steep stepped chutes are quite complex, characterizing by great aeration, high turbulence and confused wavy free surface. Then, most of hydraulic studies of such flows are performed on physical model. Yet, understanding and definition of flow behaviour and accurate approach to estimate energy dissipation are still lacking. General guidelines of hydraulics of aerated flows over stepped macro-roughness chutes and for optimal design of protection overlay remain confusing. To contribute to reduce these uncertainties, experimental study of flow over stepped chutes equipped with macro-roughness elements is performed in a laboratory gated flume for mild (~ 1:7H : 1V ) and weak (~ 3H : 1V ) chutes. Thus, they are representative of the range of embankment dams and spillways slopes. Three types of stepped macro-roughness overlays are assessed, namely rectangular conventional steps, steps equipped with endsills fixed on their nose over all the flume width and steps equipped with rectangular spaced blocks. Endsills overlays were characterized with different longitudinal distributions whereas blocks overlays consisted in different transverse patterns. Tests were conducted for the three nappe, transition and skimming flow regimes. Results can be extrapolated to 1/5 to 1/15 scaled prototypes using the Froude similarity with negligible scale effects. Flow depth, local air concentration and longitudinal velocities are measured with a double fiber-optical probe. Pressures at macro-roughness faces are taken with piezo-resistive sensors. Sequent depths of the hydraulic jump forced in the stilling basin at the flume base are measured with ultrasound sensors. Thus, this experimental phase of the thesis has allowed: to define flow parameters (regimes, depths, velocity and air concentration distributions, hydrodynamic forces) for tested overlays, to highlight that air-water flow depth is divided into: a rough boundary layer influenced by shear stress and by drag form (macro-turbulence) caused by macro-roughness, a homogeneous aerated layer which represents the main portion of flow involved in energy dissipation mechanism, a free surface layer which must be considered in the side walls design, to stress that energy dissipation is mainly a question of drag losses, to validate indirect method of hydraulic jump for energy dissipation estimation, to estimate relative energy loss for several stepped macro-roughness overlays. Tests finally show that an optimal alternative to dissipate the overflow energy during an overtopping event consists in spaced blocks, with transverse space larger than the width of block and fixed alternately on conventional steps. However, experimental results remain related and limited to their tested domains. Then, in order to provide more general governing equations of aerated flows over macro-roughness stepped chutes, a numerical modeling of two phase flows over conventional stepped flume was performed in collaboration with the Laboratory of Applied Hydrodynamics and Hydraulic Constructions at University of Liège. A quasi-2D numerical model based on the finite volume method was developed. It consists in applying the classical depth-averaged simplified Navier-Stokes equations (viscosity and Coriolis terms neglected) to a 1D incompressible air-water mixture flow over mild and steep slopes with a stepped topography. Self-aeration process is modeled by a transport equation of depth-averaged air concentration whereas turbulent structures are indirectly implemented through the Boussinesq coefficient. This first 1D-approach of semi-theoretical description of aerated flow over steps is tested for a 30o gated stepped flume and a 52° crested spillway laboratory model. This numerical model leads to realistic results regarding mixture depth, mean flow velocity, air concentration and wave amplitudes of the flow free surface. Finally, on the basis of existing protections of embankment dams and previous studies, the present experimental and numerical results contribute to extend the knowledge of high velocity aerated flows over macro-roughness and to provide elements of guidelines to optimize stepped macro-roughness overlays for embankment dams safety.

Michael Lehning, Benjamin Andreas Walter

Particle-laden boundary flows occur in many geophysical and industrial environments yet are difficult to understand and quantitatively describe because the interactions of an often turbulent boundary layer flow with surface and particle dynamics are complex. The SLF wind tunnel allows the investigation of snow and sand particle laden boundary layer flows over their natural surfaces with and without the presence of a grass canopy.The experimental results are used to investigate the two possible approaches in describing the surface dynamics: (i) Models of particle transport, which assume a stationary flow situation and predict a mass flux for an hypothetical equilibrium; (ii) Models that take the temporal variability of the mass flux explicitly into account such as Lagrangian Stochastic particle tracking Models (LSM) on the basis of large eddy simulation (LES) or direct numerical simulation (DNS) of flow and turbulence. This presentation shows that wind tunnel data support the form of semi-empirical equilibrium models, which predict mass flux, q, as a function of the mean wind speed or the friction velocity, u, and a threshold velocity, uth: q=a(u-uth)x. For the exponent "x", a value of approximately 3, as based on theoretical considerations, is consistent with the data. This simple form of equilibrium models as well as more complicated equilibrium models are all based on the hypothesis that the surface shear stress induced by a fluid on the ground during sediment saltation is constant, i.e. independent of the magnitude of the particle mass flux (Owen's second hypothesis). Our surface shear stress measurements in a drifting-sand wind tunnel show a constant value of the fluid shear stress for saltation layers of various mass-flux magnitudes, directly validating Owen’s second hypothesis for the first time. The equilibrium models, however, only insufficiently describe the full dynamics of particle-laden flows. The second part of the presentation therefore discusses non-equilibrium features such as a high variability of the particle mass flux caused by flow turbulence and surface heterogeneity. Mass flux intermittency is primarily observed around the threshold value uth. Using a combination of LES and LSM models, we show how the simulation of individual feed-back processes leads to a more complete understanding of the mechanisms behind the flux variability.

2013In this thesis, we develop a new large-eddy simulation (LES) framework to simulate atmospheric boundary layer (ABL) flows through wind turbines and wind farms. A Lagrangian scale-dependent dynamic model is used to compute the Smagorinsky model coefficient dynamically based on the local dynamics of the resolved velocity field. The turbine-generated power outputs and the turbine-induced forces (e.g., thrust, lift, drag) are parameterized using two actuator-disk models: (a) the traditional actuator-disk model without rotation (ADM-NR), which uses 1D momentum theory to relate the power output and the uniform thrust force distribution with an incoming velocity; and (b) the actuator-disk model with rotation (ADM-R), which adopts blade element theory to calculate the lift and drag forces (that produce thrust, rotor shaft torque, and power) based on the local blade and flow characteristics. The performance of the LES framework is first evaluated through comparisons with high-resolution velocity measurements collected in the wind-tunnel experiments with the single wake of a stand-alone miniature wind turbine [Chamorro and Porté-Agel, 2010a] as well as the multiple turbine wakes in a model aligned wind farm [Chamorro and Porté-Agel, 2011]. Emphasis is placed on the structure and characteristics of the simulated turbine wakes using the ADM-NR and the ADM-R. In general, the ADM-R yields improved predictions compared with the ADM-NR in the wake regions, where the ADM-NR tends to underestimate the velocity deficit and the enhancement of turbulence intensity in the wakes. Next, the LES framework is used to model multiple turbine wakes and associated power losses in a large wind farm. Here, we propose a new dynamic procedure coupled with the ADM-R to predict turbine power output based on a turbine-model-specific relationship between the shaft torque and the blade angular speed. The Horns Rev offshore wind farm is chosen as a case study since both power data from eighty Vestas V80 wind turbines and flow data from three nearby meteorological masts were available [Barthelmie et al., 2009]. The torque-speed relationship for the V80 turbine is obtained from a series of stand-alone turbine simulations. In the wind farm simulations, the ADM-R gives the best power prediction. Finally, the validated LES framework is used to study atmospheric turbulence effects on wind-turbine wakes in neutrally-stratified ABL over homogeneous flat surfaces with four different aerodynamic roughness lengths. In this study, the simulation result shows that the different turbulence intensity levels of the incoming flow lead to considerable influence on the spatial distribution of the mean velocity deficit, turbulence intensity, and turbulent shear stress in the wake region. In particular, when the turbulence intensity level of the incoming flow is higher, the turbine-induced wake (velocity deficit) recovers faster, and the locations of the maximum turbulence intensity and turbulent stress are closer to the turbine.