The influence of pool geometry and induced flow patterns in rock scour by high-velocity plunging jets

The dissipation of energy of flood discharges from water releasing structures of dams is often done by plunging jets diffusing in water and impacting on the riverbed downstream. The construction of expensive concrete structures for energy dissipation can be avoided but the assessment of the scour evolution is mandatory for dam safety. The scour growth rate and shape depend on the riverbed geology. The geometry of scour may influence the turbulent flow pattern in the pool, the dynamic loadings acting on the rock interface, and the pressures propagating inside rock joints. Up to present, dynamic impact pressures at the pool bottom have been investigated mainly in pools with flat bottom and are therefore described as function of the pool depth and the characteristics of the jets only. To approach the conditions found in practice, non-flat plunge pools and turbulent two-phase jets are investigated in this research work. This fundamental investigation focuses on the interaction between the development of plunging jets in the water and the geometry of the plunge pool. The influence of laterally confining jet diffusion is investigated by means of experimental work in near prototype conditions, in terms of jet velocities and air entrainment in the pool. Different pool geometries typical of prototype conditions are tested and compared with a reference pool with flat bottom. Pressure measurements at the jet outlet, at the pool bottom and inside a closed-end fissure are presented. The main emphasis of the text is on the analysis and the description of physical processes. The integration of the findings in existing scour estimation models is discussed. The thickening of the water cushion downstream, artificially or by scour, is investigated for fully controlled jet issuance conditions. The dissipation of jet energy is estimated based on measurements of mean impact pressures and is compared with results from an analytical model. The developed model features jet diffusion in limited-depth pools and is tentatively applied to turbulent two-phase jets. Agreement is good in the early stages of scour and in deep flat pools. For pool depths about the jet core development length (i.e. transitional pools), analytical estimates are quite sensitive to the initial assumptions on the centreline velocity decay, dimensions of the impinging zone and pool aeration. The findings highlight the limitations of existing empirical laws in representing the diffusion of turbulent two-phase jets in pools with flat bottom. Turbulent impact pressures are also investigated for increasing pool depths. Based on an evaluation of high-order statistical moments and autocorrelation functions of pressure fluctuations at stagnation, jet development conditions at impact are distinguished in core and developed impact conditions. Core impact conditions are typical of shallow pools and generate negatively asymmetric distributions at stagnation. The end of core development is associated with highly intermittent flow conditions, with important pressure fluctuations (high kurtosis). For developed impact conditions, pressure fluctuations at stagnation are positively asymmetric. A Gaussian distribution fits satisfactorily the data, save for extreme high and low (cumulated) probabilities. Air-water measurements are carried out at selected points in pools with at bottom. They allow describing the behaviour of air bubbles before, at, and aside stagnation. Void fraction estimates close to the entry of rock fissures show that air bubbles reduce in size under the influence of the high-pressure gradient at stagnation. The characteristic dimensions of the air bubbles close to the bottom are small compared to typical entry dimensions of rock fissures. The investigations conducted in pools with flat bottom are used as a reference scenario in the investigation of plunge pools with more realistic geometries. The experimental results show that mean impact pressures at the pool bottom are lower in laterally confined pools than in equivalent pools with flat bottom. The length of core development can be reduced, depending on the degree of confinement and pool depth. Enhanced pool turbulence is described by power spectra density and probabilistic distribution functions of impact pressures. It is concluded that the flow currents created by deflection of the jet on the lateral boundaries of the pool may interfere with the development of the jet, generate additional dissipation in the water column and hinder the propagation in depth of air bubbles in the pool. For shallow and transitional laterally confined pools, pressure fluctuations may have more energy than in corresponding pools with flat bottom. Power spectra of pressure fluctuations have higher energy content in the intermediate frequency range (e.g. 10 a 100 Hz). Extreme positive pressures increase. In terms of scour, there is a trade-off relatively to flat pools: there is hardly core impact and persistent hydro-fracturing (because mean impact pressures are lower), but fracturing may occur if high low-persistence pressure peaks are generated inside rock fissures (by transients due to enhanced impact pressure fluctuations). For deep laterally confined pools, the energy of pressure fluctuations is lower than in pools with flat bottom. Extreme positive pressures are similar, but increase in relative terms to the total energy of pressure fluctuations. Negative extreme pressures are lower. The most relevant flow features in laterally confined pools are identified using direct observations of flow patterns and in-depth analysis of the characteristics of turbulent pressures at impact. Large-scale pool flow features like surface oscillations, shear eddies and air-water ejections are described. The evolution of geometry-induced flow patterns and dynamic loading with scour development, for variable width of confinement and pool depth, are presented for four typical scour scenarios. The role of the deflected upward currents and shear eddies in the dissipation process depends on the degree of confinement, jet velocity and pool depth. The closer they are to the plunging jet, the higher is the dissipation of energy before impact. Recirculation currents may enhance jet development by either pushing upward currents into the jet. The dynamic pressure measurements performed inside closed-end fissures allow concluding that the dynamic response of rock fissures varies with the turbulent character of impact pressures at the rock interface. It is shown that the dimensions of the entry of the fissure play an important role in filtering turbulent pressure fluctuations in the transition from the pool into the fissure: the larger the dimensions, the lower are the frequencies filtered out. It is observed that the energy of pressure fluctuations inside the fissure is always higher than at the entry, for all pool configurations tested. The energy of pressure fluctuations inside rock fissures is lower in narrow confined pools for transition and deep pools, but higher in shallow pools, compared with equivalent pools with flat bottom. This is also valid for positive extreme pressures. Negative extreme pressures are generally lower. Amplification of pressure peaks is observed inside a closed-end fissure for both shallow and deep pools; it depends of the degree of jet development, i.e. of relative pool depth, pool geometry and jet turbulent characteristics (and, indirectly, of the amount of entrained air reaching the bottom of the pool). Therefore, transient pressure peaks generated inside fissures are a potential agent of scour in laterally confined pools, from shallow to deep. Amplification occurs due to the development of transient flows inside the fissure, that may include column separation. The occurrence of resonance inside fissures is investigated numerically. Multiple resonant harmonics are replicated solving numerically the waterhammer equations inside the fissure with the hydraulic impedance method. A probabilistic-based event analysis is developed to correlate the probability, persistence, duration and energy content of extreme pressure pulses. It is shown that pulses with high extreme (cumulated) probabilities have low persistence and high energy content. The concept of relevant probability is outlined, allowing for the selection of pressure events that should effectively be considered for the propagation of rock fissures or for the dynamic uplift of rock blocks. The role of extreme pressure events in the scouring processes of crack propagation and block displacement is discussed. In conclusion, the experimental investigation of jet diffusion in pools with flat bottom and laterally confined pools shows the importance of pool flow patterns in the definition of impact pressures and transient pressures inside rock fissures. It provides detailed information on hydrodynamic processes involved in rock scour, as well as several contributions to engineering practice, in terms of jet issuance conditions, empirical relationships for impact pressures and recommendations for the design of pre-excavated pools.