Cavitation risk estimation at orifice spillway based on UVP and dynamic pressure measurements
Orifice spillways might be affected by cavitation if the profile of the inlet structure includes a relevant curvature. At one of the world’s largest dams, such damages were observed on the profiled slab. To limit their progression, an adapted operation regime of the gates had to be defined using physical model tests. The risk estimation was based on dynamic pressure and velocity measurements, indicating that a maximum gate opening ratio of 0.8 should be respected until the damage is repaired and the profile re-shaped. Beside this, the data set allowed to compare the flow characteristics at the profile surface in terms of turbulence intensity and dominant frequencies. The Ultrasonic Velocity Profiler (UVP) provides comparable characteristic values as the dynamic pressure transmitter (DPS).
Influence of air entrainment on rock scour development and block stability in plunge pools
Rock scour occurring near dam foundations due to high-velocity jets of spillways impinging into the plunge pool is a major concern regarding dam safety. Scour in fractured rock resulting from high-velocity jet impact is a complex phenomenon, which involves the three phases: water, air and rock. Since 1998, the Laboratory of Hydraulic Constructions (LCH) of the Ecole Polytechnique Federale de Lausanne (EPFL) is conducting research in order to better understand the physical processes that contribute to rock scour. An innovative experimental facility, which can reproduce prototype jet velocities, was built and continuously improved. With the help of this experimental set-up, a new, completely physically based engineering model has been developed for the prediction of the ultimate scour depth of jointed rock, called Comprehensive Scour Method (CSM). The impact of high-velocity plunging jets produce highly dynamic pressures at the pool bottom, which are transferred into rock joints by transient flow governed by the propagation of pressure waves. The latter is strongly influenced by the air content in the plunge pool and the underlying rock fissures. Dr. Rafael Duarte studied for the first time the effect of active jet aeration on the scour process in fractured rock. Systematic experiments allowed assessing the response of a block in a plunge pool impacted by high-velocity jets having different amount of active aeration. He could show that the air entrained by the jet influences the pressures on the bottom by two opposed effects. On one hand, the air-water mixture reduces the apparent density of the jet and thus its momentum. The kinetic energy per unit volume reaching the pool bottom is lower and consequently the pressures are also lower compared to similar clear-water jet. On the other hand, the air bubbles reduce the shear stress of the diffusing jet in the plunge pool. The velocity decay of aerated jets is therefore less resulting in higher velocities reaching the bottom, and thus higher pressures. Which of the two effects will be stronger depends above all on the pool depth. Based on the experimental study and a comprehensive analysis of the results Dr. Duarte could enhance the Comprehensive Scour Method CSM in order to include active air entrainment at jet issuance.
Asymptotic Properties of Solutions to Second-Order Difference Equations of Volterra Type
<jats:p>We consider the discrete Volterra type equation of the form <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>b</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mrow><mml:msubsup><mml:mo stretchy="false">∑</mml:mo><mml:mrow><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msubsup><mml:mrow><mml:mi>K</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>n</mml:mi><mml:mo>,</mml:mo><mml:mi>k</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:math>. We present sufficient conditions for the existence of solutions with prescribed asymptotic behavior. Moreover, we study the asymptotic behavior of solutions. We use <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mi mathvariant="normal">o</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msup><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msup><mml:mo stretchy="false">)</mml:mo></mml:math>, for given nonpositive real <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:math>, as a measure of approximation.</jats:p>