Role of friction terms in two-dimensional modelling of dense snow avalanches

Voellmy–Salm friction model is one of the most extensively used theories for assessing the frictional terms of the equations that describe the motion of non-Newtonian flows such as snow avalanches. Based on the Coulomb- and turbulent-type friction, this model has been implemented in numerical tools for computation of snow avalanche dynamics based on the Shallow Water Equations (SWE). The range of the Voellmy parameters has been discussed widely, focusing mainly on the required values for achieving good results for the description of the moment and position of the avalanche when it stops. However, effects of parameters on the SWE terms, and their physical interpretation have not been investigated sufficiently. This work focuses on analysing the effects of the Voellmy–Salm parameters and cohesion on the avalanche characteristics and evolution of the new SWE-based numerical model Iber. In the numerical scheme, an upwind discretization was used for the solid friction and cohesion terms, while a centred one was used for the turbulent friction. Results show that the Voellmy–Salm model dominates the avalanche dynamics and the cohesion model allows the representation of long tails, whereas the friction and cohesion parameters may vary within a wide range.

Numerical Simulation on Interface Evolution and Impact of Flooding Flow

A numerical model based on Navier-Stokes equation is developed to simulate the interface evolution of flooding flows. The two-dimensional fluid domain is discretised by structured rectangular elements according to finite volume method (FVM). The interface between air and liquid is captured through compressive interface capturing scheme for arbitrary meshes (CICSAM) based on the idea of volume of fluid (VOF). semiimplicit method for pressure linked equations (SIMPLE) scheme is used for the pressure-velocity coupling. A second order upwind discretization scheme is applied for the momentum equations. Both laminar flow model and turbulent flow model have been studied and the results have been compared. Previous experiments and other numerical solutions are employed to verify the present results on a single flooding liquid body. Then the simulation is extended to two colliding flooding liquid bodies. The impacting force of the flooding flow on an obstacle has been also analyzed. The present results show a favourable agreement with those by previous simulations and experiments.

First-break traveltime tomography with the double-square-root eikonal equation

First-break traveltime tomography is based on the eikonal equation. Because the eikonal equation is solved at fixed-shot positions and only receiver positions can move along the raypath, the adjoint-state tomography relies on inversion to resolve possible contradicting information between independent shots. The double-square-root (DSR) eikonal equation allows not only the receivers but also the shots to change position, and thus describes the prestack survey as a whole. Consequently, its linearized tomographic operator naturally handles all shots together, in contrast with the shotwise approach in the traditional eikonal-based framework. The DSR eikonal equation is singular for the horizontal waves, which require special handling. Although it is possible to recover all branches of the solution through postprocessing, our current forward modeling and tomography focuses on the diving wave branch only. We consider two upwind discretizations of the DSR eikonal equation and show that the explicit scheme is only conditionally convergent and relies on nonphysical stability conditions. We then prove that an implicit upwind discretization is unconditionally convergent and monotonically causal. The latter property makes it possible to introduce a modified fast matching method thus obtaining first-break traveltimes efficiently and accurately. To compare the new DSR eikonal-based tomography and traditional eikonal-based tomography, we perform linearizations and apply the same adjoint-state formulation and upwind finite-differences implementation to both approaches. Synthetic model examples justify that the proposed approach converges faster and is more robust than the traditional one.

FLOW PHYSICS OF 3-BLADED STRAIGHT CHORD H-DARRIEUS WIND TURBINE

Steady-state two-dimensional Computational Fluid Dynamics (CFD) simulations were performed using Fluent 6.0 software to analyze the flow physics of 3-bladed straight chord H-Darrieus wind turbine having blade twist of 300 for 10% of its chord at the trailing ends. The flow was simulated using finite volume method coupled with moving mesh technique to solve mass and momentum conservation equations. The standard k-ε turbulence model with enhanced wall condition was used. Second-order upwind discretization scheme was adopted for pressure-velocity coupling of the flow. Flow physics of the turbine was analyzed with the help of pressure and velocity contours. It was found that velocity magnitude decreases from upstream to downstream side across the turbine, which will cause overall lift for the turbine. Further, blade twist at the trailing ends creates circulations that interact with the blades in a direction opposite to the direction of rotation of the turbine which would enhance power production for the three bladed turbine.

PERFORMANCE ANALYSIS OF A HELICAL SAVONIUS ROTOR WITHOUT SHAFT AT 45° TWIST ANGLE USING CFD

Helical Savonius rotor exhibits better performance characteristics at all the rotor angles compared to conventional Savonius rotor. However studies related to the performance measurement and flow physics of such rotor are very scarce. Keeping this in view, in this paper, a three dimensional Computational Fluid Dynamics analysis using commercial Fluent 6.2 software was done to predict the performance of a two-bucket helical Savonius rotor without shaft and with end plates in a complete cycle of rotation. A two-bucket helical Savonius rotor having height of 60 cm and diameter of 17 cm with 45° bucket twist angle was designed using Gambit. The buckets were connected at the top and bottom circular end plates, which are 1.1 times the rotor diameter. The k-ε turbulence model with second order upwind discretization scheme was adopted with standard wall condition. Power coefficients (Cp) and torque coefficients (Ct) at different tip speed ratios were evaluated at different rotor angles. From the investigation, it was observed that power coefficient increased with increase of tip speed ratio up to an optimum limit, but then decreased even further tip speed ratio was increased. Further investigation was done on the variations of Cp & Ct in a complete cycle of rotation from 0° to 360° in a step of 45° rotor corresponding to the optimum tip speed ratio. The value of Cp at all the rotor angles is positive. Moreover, velocity magnitude contours were analyzed for each rotor angle and it could be concluded that high aerodynamic torque and power can be expected when the rotor is positioned at 45º & 90º with respect to incoming flow.