A Comparative Assessment of Various Turbulence Models Applied for Simulation of Air-Water Flow Over Chute Spillway

Chute aerators have been largely used to reduce cavitation hazard in high head spillways. There is no definite turbulence model for simulating these devices in smooth spillways in spite of its importance in critical conditions. A simulation in two-phase air-water chute flow and its aerator with five different turbulence models (RNG, Standard and Realizable k–ε Models, SST and Standards k–ω Models) has been numerically investigated by Fluent software. Finite Volume and VOF methods were used for discretization of flow equations and free surface modeling. Flow depth, velocity and bottom pressure comparison were made along with the air cavity length determination by numerical, experimental and reference equations. The best model with the minimum value of error percentage for flow depth and velocity was RNG k–ε turbulence model. The realizable and RNG k–ε turbulence models showed better results for the pressure head at the bottom of the chute. The RNG k–ε model results for the jet length have a very slight difference with the experimental results. The length of the cavity is closely associated with the flow emergence angle θ’ over aerators. The bottom air concentration of spillway chute simulated by all the turbulence models, except for the RNG k–ε model, can be overestimated and therefore may affect the designing of aerator geometry.

Air Diffusion and Velocity Characteristics of Self-Aerated Developing Region in Flat Chute Flows

Self-aerated flows in flat chutes are encountered downstream of the bottom outlet, in spillways with a small slope and in storm waterways. In the present study, the development of self-aeration in flat chute flow is described and new experiments are performed in a long flat chute with a pressure outlet for different flow discharge rates. The distribution of air concentration, time mean velocity and velocity fluctuation in flow direction in the self-aerated developing region—where air bubbles do not diffuse next to the channel bottom—were measured and analyzed. The region of self-aeration from free surface was about 27.16% to 51.85% of the water depth in the present study. The analysis results revealed that the maximum distance of air bubble diffusion to the channel bottom increased with the development of self-aeration along the flow direction. This indicates that for flat chute flow, the process of air bubble diffusion from free surface to channel bottom was relatively long. Cross-section velocities increased along the flow direction in the self-aerated developing region, and this trend was much more remarkable in the area near water free surface. The velocity fluctuations in flow direction in cross-sections flattened and increased with the development of self-aerated flow. Higher velocity fluctuations in flow direction corresponded to the presence of much stronger turbulence, which enhanced air bubble diffusion from the water free surface to channel bottom along the flow direction.

A dynamical systems view of granular flow: from monoclinal flood waves to roll waves

On the basis of the Saint-Venant equations for flowing granular matter, we study the various travelling waveforms that are encountered in chute flow for growing Froude number. Generally, for $Fr<2/3$ one finds either a uniform flow of constant thickness or a monoclinal flood wave, i.e. a shock structure monotonically connecting a thick region upstream to a shallower region downstream. For $Fr>2/3$ both the uniform flow and the monoclinal wave cease to be stable; the flow now organizes itself in the form of a train of roll waves. From the governing Saint-Venant equations we derive a dynamical system that elucidates the transition from monoclinal waves to roll waves. It is found that this transition involves several intermediate stages, including an undular bore that had hitherto not been reported for granular flows.

The kinematics of bidisperse granular roll waves

Small perturbations to a steady uniform granular chute flow can grow as the material moves downslope and develop into a series of surface waves that travel faster than the bulk flow. This roll wave instability has important implications for the mitigation of hazards due to geophysical mass flows, such as snow avalanches, debris flows and landslides, because the resulting waves tend to merge and become much deeper and more destructive than the uniform flow from which they form. Natural flows are usually highly polydisperse and their dynamics is significantly complicated by the particle size segregation that occurs within them. This study investigates the kinematics of such flows theoretically and through small-scale experiments that use a mixture of large and small glass spheres. It is shown that large particles, which segregate to the surface of the flow, are always concentrated near the crests of roll waves. There are different mechanisms for this depending on the relative speed of the waves, compared to the speed of particles at the free surface, as well as on the particle concentration. If all particles at the surface travel more slowly than the waves, the large particles become concentrated as the shock-like wavefronts pass them. This is due to a concertina-like effect in the frame of the moving wave, in which large particles move slowly backwards through the crest, but travel quickly in the troughs between the crests. If, instead, some particles on the surface travel more quickly than the wave and some move slower, then, at low concentrations, large particles can move towards the wave crest from both the forward and rearward sides. This results in isolated regions of large particles that are trapped at the crest of each wave, separated by regions where the flow is thinner and free of large particles. There is also a third regime arising when all surface particles travel faster than the waves, which has large particles present everywhere but with a sharp increase in their concentration towards the wave fronts. In all cases, the significantly enhanced large particle concentration at wave crests means that such flows in nature can be especially destructive and thus particularly hazardous.