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Publication# Direct numberical simulation of turbulent slope flows up to Grash of number Gr=2.1 x 10(11)

Jiannong Fang, Marco Giovanni Giometto, Gabriel George Katul, Marc Parlange

*Cambridge Univ Press, *2017

Article

Article

Résumé

Stably stratified turbulent flows over an unbounded, smooth, planar sloping surface at high Grashof numbers are examined using direct numerical simulations ( DNS). Four sloping angles ( alpha = 15 degrees; 30 degrees; 60 degrees and 90 degrees) and three Grashof numbers (Gr = 5 X 10(10); 1 X 10(11) and 2 : 1 X 10(11)) are considered. Variations in mean flow, second- order statistics and budgets of mean- ( MKE) and turbulent- kinetic energy ( TKE) are evaluated as a function of ff and Gr at fixed molecular Prandtl number. Pr = 1 . Dynamic and energy identities are highlighted, which diagnose the convergence of the averaging operation applied to the DNS results. Turbulent anabatic ( upward moving warm fluid along the slope) and katabatic ( downward moving cold fluid along the slope) regimes are identical for the vertical wall set- up ( up to the sign of the along- slope velocity), but undergo a different transition in the mechanisms sustaining turbulence as the sloping angle decreases, resulting in stark differences at low ff. In addition, budget equations show how MKE is fed into the system through the imposed surface buoyancy, and turbulent fluctuations redistribute it from the low- level jet ( LLJ) nose towards the boundary and outer flow regions. Analysis of the TKE budget equation suggests a subdivision of the boundary layer of anabatic and katabatic flows into four distinct thermodynamical regions: ( i) an outer layer, corresponding approximately to the return flow region, where turbulent transport is the main source of TKE and balances dissipation; ( ii) an intermediate layer, bounded below by the LLJ and capped above by the outer layer, where the sum of shear and buoyant production overcomes dissipation, and where turbulent and pressure transport terms are a sink of TKE; ( iii) a buffer layer, located at 5 / z C / 30, where TKE is provided by turbulent and pressure transport terms, to balance viscous diffusion and dissipation; and ( iv) a laminar sublayer, corresponding to z C / 5, where the influence of viscosity is significant.. / C denotes a quantity rescaled in inner units. Interestingly, a zone of global backscatter ( energy transfer from the turbulent eddies to the mean flow) is consistently found in a thin layer below the LLJ in both anabatic and katabatic regimes.

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Turbulence

vignette|Léonard de Vinci s'est notamment passionné pour l'étude de la turbulence.
La turbulence désigne l'état de l'écoulement d'un fluide, liquide ou gaz, dans lequel la vitesse présente en tout poi

Couche limite

vignette|redresse=2|Couches limites laminaires et turbulentes d'un écoulement sur une plaque plane (avec profil des vitesses moyennes).
La couche limite est la zone d'interface entre un corps et le fl

Direct numerical simulation

A direct numerical simulation (DNS) is a simulation in computational fluid dynamics (CFD) in which the Navier–Stokes equations are numerically solved without any turbulence model. This means that the

Centrifugal pumps are required to sustain a stable operation of the system they support under all operating conditions. Minor modifications of the surfaces defining the pump's water passage can influence the tendency to unstable system operation significantly. The action of such modifications on the flow are yet not fully understood, leading to costly trial and error approaches in the solution of instability problems. The part-load flow in centrifugal pumps is inherently time-dependent due to the interaction of the rotating impeller with the stationary diffuser (Rotor-Stator Interaction, RSI). Furthermore, adverse pressure gradients in the pump diffuser may cause flow separation, potentially inducing symmetry-breaking non-uniformities, either spatially stationary or rotating and either steady or intermittent. Rotating stall, characterized by the presence of distinct cells of flow separation on the circumference, rotating at a fraction of the impeller revolution rate, has been observed in thermal and hydraulic turbomachines. Due to its complexity, the part-load flow in radial centrifugal pumps is a major challenge for numerical flow simulation methods. The present study investigates the part-load flow in radial centrifugal pumps and pump-turbines by experimental and numerical methods, the latter using a finite volume discretization of the Reynolds-averaged Navier-Stokes (RANS) equation. Physical phenomena of part load flow are evidenced based on three case studies, and the ability of numerical simulation methods to reproduce part-load flow in radial centrifugal pumps qualitatively and quantitatively is assessed. A numerical study of the flow in a high specific speed radial pump-turbine using steady approaches and the hypothesis of angular periodicity between neighboring blade channels evidences the relation of sudden flow topology changes with an increase of viscous losses, impacting on the energy-discharge characteristic, and thus increasing the risk of unstable operation. When the flow rate drops below a critical threshold, the straight through-flow with flow separation zones attached to the guide vanes changes to an asymmetrical flow. Energy is drawn off the mean flow and dissipated in a large vortex-like structure. Besides flow separation in some diffuser channels, time-dependent numerical simulations of the flow in a double suction pump evidence a flow rate imbalance between both impeller sides interacting with asymmetric flow separation in the diffuser. Viscous losses increase substantially as this imbalance occurs, the resulting segment of positive slope in the energy-discharge characteristic is found for a flow rate sensibly different from measurements. Different modes of rotating stall are identified by transient pressure measurements in a low-specific-speed pump-turbine, showing 3 to 5 zones of separated flow, rotating at 0.016 to 0.028 times impeller rotation rate, depending on discharge. For operating conditions where stall with 4 cells is most pronounced, velocity is measured by Laser-Doppler methods at locations of interest. The velocity field is reconstructed with respect to the passage of stall cells by definition of a stall phase obtained from simultaneous transient pressure measurements. Time-dependent numerical simulation predicting rotating stall with 4 cells shows velocity fields that are in reasonable agreement with the measured velocity fields, but occurring at a sensibly higher flow rate than found from experiments. In consideration of the quantitative shortcomings of the numerical simulation, a novel modelling approach is proposed: Replacing the costly 3-dimensional simulation of the major part of the impeller channels by a 1-dimensional model allows a significant economy in computational resources, allowing an improved modeling for the remainder of the domain at constant computational cost. The model is validated with the challenging cases of rotating stall and impeller side flow rate imbalance. The satisfying coherence of the results with the simulation including the entire impeller channels qualifies this approach for numerous turbomachinery applications. It could also provide improved, time-dependent boundary conditions for draft tube vortex rope simulations at reasonable computational cost. Parameter studies modifying deliberately some quantities of mean flow and turbulence at the modeled boundary surfaces can be implemented in the framework of the method.

Holly Jayne Oldroyd, Eric Richard Pardyjak, Marc Parlange

Generally, the more an underlying terrain deviates from being flat, uniform and homogeneous, the less that classical theories and models of the atmospheric boundary layer hold. At times this leads to high uncertainties in turbulent flux predictions, and at other times the models completely break down. Hence, to better understand, model and subsequently predict surface turbulent exchanges over non-idealized terrain, an important objective of many recent field campaigns has been to investigate the near-surface turbulence structure. We present observations of momentum fluxes in nocturnal slope flows over steep (35.5 degree), alpine terrain in Val Ferret, Switzerland. Under clear-sky conditions, we observe two distinct flow regimes with mean winds directed down the slope: (1) buoyancy-driven, ‘katabatic flow', for which an elevated velocity maximum (katabatic jet peak) is observed and (2) ‘downslope winds', for which larger-scale forcing prevents formation of a katabatic jet. In downslope wind cases, the velocity profile is quite similar to a logarithmic profile often observed over flat terrain, and the corresponding momentum fluxes roughly resemble a constant-flux surface-layer. In stark contrast, the velocity profiles in the katabatic regime exhibit a jet-like shape. The katabatic jet strongly modulates the corresponding momentum fluxes, which show steep gradients over the shallow katabatic layer and typically change sign near the jet peak as the velocity gradients change sign. However, frequently a counter-gradient momentum flux is observed near the jet peak (and at times at higher levels), suggesting significant non-local turbulent transport within the katabatic jet layer. We compare and contrast this behavior with katabatic flow theories and observational studies over shallow-angle slopes, and use budget and co-spectral analyses to better understand the non-local transport dynamics. In addition, we show that as a consequence of the counter-gradient momentum fluxes, even local stability can be difficult to characterize because a counter-gradient momentum flux represent a sink in the shear term of turbulence kinetic energy budget equation. These results have broad implications for stability-based modeling of katabatic flows.

2016Uncontrolled 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.