10.1063/5.0061768.4

Introduction: Side weir structures are extensively used in hydraulic engineering, irrigation and environmental engineering, and it usually consists of a main weir and a lateral channel. Side weirs are also used as an emergency structure. This structure is installed on one side or both sides of the main channel to divert the flow from the main channel to the side channel. Lateral outflow takes place when the water surface in the main channel rises above the weir sill. Flow over a side weir is a typical case of spatially varied flow with decreasing discharge. There have been extensive studies on side weir overflows. Most of the previous theoretical analysis and experimental research works are related to the flow over rectangular side weirs in rectangular main channels. In the current study, the flow conditions over a trapezoidal side weir located in a rectangular main channel in subcritical flow regime is considered. Materials and Methods: The experiments were performed in a rectangular open channel having provisions for a side weir at one side of the channel. The main channel was horizontal with 12 m length, 0.25 m width, and 0.5 m height, and it was installed on a frame; lateral channel that has a length of 6 m, width of 0.25 m, and height of 1 m. It was set up parallel to the main channel; walls and its bed were made up of Plexiglas plates. The side weir was positioned at a distance of 6 m from the channel’s entrance. A total of 121 experiments on trapezoidal side weirs were carried out. Results and Discussion: For trapezoidal side weir, effective non-dimensionnal parameters were identified using dimensional analysis and Buckingham's Pi-Theorem. Finally, the following non-dimensional parameters were considered as the most effective ones on the discharge coefficient of the trapezoidal side weir flow. in which Fr1= upstream Froude number, P= hight of the trapezoidal side weir, y1= upstream water depth, z=side slope of the trapezoidal side weir and T=top flow width of the trapezoidal side weir. Water surface profiles were measured along the weir crest, the main channel centerline, and far from the weir section. Different elevations in water surface profile depend on the upstream Froude number in the main channel; depth differences in low Froude numbers are at minimum values, and in high Froude numbers are at maximum amounts. The water surface level along the crest drops at the entrance of the side weir to the first half of the side weir; and it has been attributed to the side weir entrance effect at the upstream. Afterwards, the water level rises towards the downstream of the weir. According to the experimental results, measurements of the water in the centerline of the main channel are reliable and water surface drop is negligible. According to the parameters affecting the discharge coefficient for each value of z, discharge coefficient equations were developed with acceptable accuracy such that the effects of this parameter were shown separately. Finally, the general equation was proposed. The general functional form for discharge coefficient is presented as follows where the effect of the side slope parameter, z, is also considered. The mean and maximum percentage errors of the discharge coefficient computed using the proposed equation are as 2.6% and 11.5% , respectively. Conclusion: In this study, the characteristics of trapezoidal side weir overflows in subcritical flow regime were discussed. For this purpose, experimental data related to the water surface profile of the side weir and discharge coefficient were collected and analyzed. The results showed that the most efficient section for measuring water surface profile is located at the center line of the main channel. It was found that for trapezoidal side weir, the discharge coefficient depends on the Froude number, the ratio of crest height to initial depth, the overflow length to initial depth, and the side slope of the weir. In this study, conventional trapezoidal weir theory has been used in order to evaluate the discharge coefficient and provide side weir discharge equation. For this purpose, three reference depths were considered for conventional weir, and for each depth an equation was developed for the discharge coefficient. Comparison between predicted values and experimental data showed that average flow depth results in accurate outcomes for assessing the discharge coefficient. The average value of error for discharge coefficient estimation by the proposed equation is 2.6%. Thus this equation is proposed for use in practice by water engineers. Keywords: Control structure, Conventional weir, Discharge coefficient, Spatially varied flow, Trapezoidal side weir, Water surface profile

Space–time variation of the free-surface roughness pattern, due to sub-surface turbulence, is one of the most important features of turbulent open-channel flows. Despite its importance, the free-surface dynamics is not fully understood, especially regarding the advection and propagation features of surface variations. In this study, a direct numerical simulation of a smooth-wall turbulent open-channel flow allowing free-surface deformation was performed to investigate the dependence of the free-surface features on Reynolds and Froude numbers. The results show that the key features of the free surface are due to surface waves and turbulence, and one or another may prevail depending on the Froude number. While the turbulence is dominant in subcritical flow at low Froude number, the surface waves propagating upstream become more dominant at high Froude number when flow becomes supercritical. Furthermore, it was found that the advection velocity of the roughness patterns becomes slower than the mean surface velocity in the flow where the surface waves become dominant.

This paper presents a few hydrodynamics analyses of two corvette hulls with different operational profiles (corvette 1 with maximum maintained speed of 25 knots and corvette 2 with 35 knots), which designs follow some Brazilian Navy high-level system requirements and are based on modern world military vessels. The total resistance coefficient and wave pattern were determined from computational fluid dynamics simulations using free surface models and ITTC procedures, and the form factors of both ships by Prohaska’s method and CFD simulations at low Froude numbers (to neglect the wave resistance). A preliminary numerical analysis of bulbous bow was carried out using CFD, and it was possible to notice that, at high Froude numbers, the ship resistance substantially decreased if compared to the bulbless hull and, with low Froude numbers, the resistance subtly increased. Moreover, the propulsive arrangements of both ships were predimensioned and it was possible to notice the differences due to the operational profiles. Corvette 1 has a combined diesel and diesel propulsion system with two controllable pitch propellers, which optimum pitch was defined using the OpenProp software and the wake field from CFD. Corvette 2, which has a broader range of speed, has a propulsive arrangement of two waterjets and a gas turbine at high speeds, and a CPP with diesel engines when operating at low speeds.

Numerical analysis of the street canyon thermal conductance to improve urban design and climate

This study investigates the ventilated cavities around a surface-piercing hydrofoil, aiming to extend previous studies by an in-depth understanding of the vaporous cavity behaviors and the flow-regime transition at high Froude numbers. An experiment is carried out in a constrained-launching water tank with a vertically cantilevered hydrofoil piercing a still water surface. The cavity is recorded using high-speed photography, and flow-regime maps are summarized over a broad range of Froude number and yaw angle at different immersed aspect ratios. In addition to the well-known steady flow regimes (i.e., fully wetted flow and fully ventilated flow), an unsteady vaporous cavitating flow is revealed at a very high Froude number with a small yaw angle, which exhibits cavitation shedding dynamics behaviors, including the cavity growth, destabilization, and collapse. The transition from the fully wetted flow to the fully ventilated flow is attributed to the vapor-cavitation-induced ventilation besides the tip-vortex-induced ventilation. Vaporous cavitation promotes ventilation formation, but it has to meet the criterion that air should enter the sub-atmospheric cavity through the tip-vortex path before the cavity length reaches the maximum. Moreover, an improved lifting-line model is developed with considering the effects of free surface and finite aspect ratio. Both analytical modeling and experimental measurements reveal that the vaporous cavity length follows a power relation against the cavitation parameter. Such knowledge lays a foundation for the design optimization and control strategy of high-speed hydrofoils.

Recent numerical simulations reveal remarkably different behavior in rotating stably stratified fluids at low Froude numbers for finite Rossby numbers as compared with the behavior at both low Froude and Rossby numbers. Here the reduced low Froude number limiting dynamics in both of these situations is developed with complete mathematical rigor by applying the theory for fast wave averaging for geophysical flows developed recently by the authors. The reduced dynamical equations include all resonant triad interactions for the slow (vortical) modes, the effect of the slow (vortical) modes on the fast (inertial gravity) modes, and also the general resonant triad interactions among the fast (internal gravity) waves. The nature of the reduced dynamics in these two situations is compared and contrasted here. For example, the reduced slow dynamics for the vortical modes in the low Froude number limit at finite Rossby numbers includes vertically sheared horizontal motion while the reduced slow dynamics in the low Froude number and low Rossby number limit yields the familiar quasigeostrophic equations where such vertically sheared motion is completely absent-in fact, such vertically sheared motions participate only in the fast dynamics in this quasigeostrophic limit. The use of Ertel's theorem on conservation of potential vorticity is utilized, for example, in studying the limiting behavior of the rotating Boussinesq equations with general slanted rotation and unbalanced initial data. Other interesting physical effects such as those of varying Prandtl number on the limiting dynamics are also developed and compared here.

Linear non-modal analyses are performed to study the mechanism of how deformable free surfaces influence very-large-scale motions (VLSMs) in turbulent open channel flows. The mean velocity and eddy viscosity profiles obtained from direct numerical simulations are used in the generalised Orr–Sommerfeld and Squire equations to represent background turbulence effects. Solutions of surface-wave eigenmodes and shear eigenmodes are obtained. The results indicate that at high Froude numbers, free surfaces enhance the maximum transient growth rate of VLSMs through surface-wave eigenmodes. We then analyse the energy budget equation to reveal the underlying mechanism. For streamwise-uniform motions, the energy growth rate is enhanced by an energy production term associated with the correlation between the streamwise velocity, which is generated by the lifting-up effect of streamwise vortices composed of shear eigenmodes, and the vertical velocity, which is induced by a spanwise standing wave composed of surface-wave eigenmodes. For streamwise-varying motions, the energy growth rate is enhanced by a standing wave moving with a pair of vortices that travel at a speed approximately equal to the projection of the mean surface velocity along the wavenumber vector direction. Finally, an analytical expression of the energy production term is derived to provide the initial conditions for the maximum transient growth and explain the weak free-surface effect observed at large spanwise wavenumbers and low Froude numbers. The results demonstrate a linear non-modal mechanism in interactions between free surfaces and VLSMs in open channel flows.

Effects of equatorially-confined shear flow on MRG and Rossby waves

Part 1 of this two-part paper presents results from a towing-tank experiment conducted in order to explicate the influence of wavemaking by a surface-piercing body on its boundary layer and wake and provide detailed documentation of the complete flow field appropriate for validating computational methods. Mean-velocity and pressure field measurements were performed for Froude numbers 0.16 and 0.316 for a 3.048 m Series 60 CB = 0.6 hull form at numerous stations from the bow to the stern and into the near wake. For Froude number = 0.316, free-surface effects are very significant, whereas for Froude number = 0.16, they are negligible, except near the bow, such that comparison of the results enables the identification of the salient features of the wave-induced effects. Wave profiles and local and global elevations were also measured. In addition, resistance tests were conducted. The experimental equipment and procedures are described and the results are discussed to point out the essential differences between the flows at low and high Froude number. On the forebody, the differences are primarily in the outer (inviscid) flow, except at the bow, whereas on the afterbody and in the near wake, both the inner (viscous) and outer flows are altered. The results are discussed to assess the nature of the interaction between wavemaking and the boundary layer and wake. Most of the interaction can be explicated as a result of the wave elevations, wave-induced pressure gradients, and the displacement effects of the boundary layer. Part 2 concerns scale effects on near-field wave patterns and comparisons between the experimental results and inviscid theory.

As basilisk lizards (Basiliscus basiliscus) and shore birds run along the water surface they support their body weight by slapping and stroking into the water with their feet. The foot motions exploit the hydrodynamic forces of low-speed water entry. To determine the forces that are produced during water entry at low speeds, we measured directly the impact and drag forces for disks dropped into water at low Froude numbers (u2/gr=1–80). Also, we measured the period during which the air cavity behind the disk remains open to atmospheric air. We found that the force impulse produced during the impact phase is due to the acceleration of the virtual mass of fluid associated with a disk at the water surface. A dimensionless virtual mass M, defined as M=mvirtual/(4/3)πρr3, has a value near 1/π for disks. After impact, as penetration depth of the disk increases, the drag force can rise by as much as 76% even though the downward velocity is steady. However, a dimensionless force which includes the contribution from hydrostatic pressure [CD*=Drag(t)/(ρSgh(t)+0.5ρSu2)] takes a constant value near 0.7 regardless of disk size, speed, or cavity depth. Over the entire range of disk sizes and velocities, the period between impact and cavity closure, Tseal, can be described by a single value of dimensionless time, τ=Tseal(g/r)0.5, near 2.3. We con- clude that the fundamental phenomena associated with the low-speed water entry of a disk can be characterized by three dimensionless numbers (M, CD*, and τ).

The habitat-scale ecohydraulics of rivers

The dynamic evolution of fluid strouhal number under flow fields around flexible vertical pipe groups

This paper presents simulations of flow past a circular cylinder within the subcritical Reynolds number (Re) range from 3900 to 2 × 105, utilizing the parameterized cumulant lattice Boltzmann model. In this study, a three-dimensional characteristic boundary condition for incompressible flow has been integrated into the lattice Boltzmann method at the outflow boundary to minimize spurious reflection. The flow field, wake statistics, hydrodynamic force, and power spectra results of Re = 3900 from the cumulant lattice Boltzmann model are exhaustively compared with the laboratory data and other numerical models. Relative to other numerical models employing turbulence closure, the cumulant lattice Boltzmann simulations demonstrate enhanced agreement with the experimental data even with relatively coarser grid resolution. The resolution-spanning feature for the cumulant lattice Boltzmann model in turbulent flows, without using explicit turbulence model, aligns with the previous benchmark case studies. The stability-preserving regularization process in the present model is analyzed. Results indicate that the influence of the regularization parameter is mitigated with improved grid resolution. A specific regularization parameter for flow around cylinder simulations is recommended. Variations in flow properties and hydrodynamic forces within the subcritical Reynolds number range of 3900 to 2 × 105 are analyzed. The results confirm that the parameterized cumulant lattice Boltzmann model can accurately simulate practical engineering flows, characterized by complex separation and recirculation, within the subcritical range. Moreover, the computational efficiency and parallel scalability are compared with other numerical methods.

High speed motion-picture studies were made of the dependence of air-water entry cavities on the relevant physical parameters—in particular, on the atmospheric pressure over the water surface. Experiments on the vertical entry of spheres ¼ in. to 1 in. in diameter, with entrance velocities between 15 ft./sec. and 100 ft./sec., and air pressures between 1/60 atmosphere and 3 atmospheres, show that surface sealing of the cavity is a major factor in controlling cavity formation, and is the factor most responsible for non-Froude scaling of cavity phenomena. Surface sealing is a function chiefly of the atmospheric density and projectile velocity, although surface tension is also important in its effect on splash formation. Froude's scaling is found to hold true in the region of low Froude's numbers and low atmospheric pressures. The measured average drag coefficient of the projectiles is independent of cavity size and shape. Jets are found to occur regularly and with great strength at both deep and surface closures of the cavity. The observed presence of jets in finite cavities is predicted by an extension of the Kirchhoff-Helmholtz theory of the infinite (two-dimensional) cavity to the case of finite cavities with finite cavitation numbers. Some of the results of this theory are mentioned.

Interactions between surface waves and underlying viscous wake are investigated for a turbulent flow past a free surface piercing circular cylinder at Reynolds number Re=2.7×104 using large eddy simulation (LES). The computations have been performed for three Froude numbers Fr=0.2, 0.5 and 0.8 in order to examine the influence of the Froude number. A second-order finite volume method coupled with a fractional step method is used for solving the grid-filtered incompressible Navier-Stokes equations. The computational results are found to be in good agreement with the available experimental data. At low Froude numbers Fr=0.2 and 0.5, the amplitude of generated surface wave is small and the influence on the wake is not evident. On the other hand, strong wave-wake interactions are present at Fr=0.8, when the generated free surface wave is very steep. It is shown that structures of the underlying vortical flow correlate closely with the configuration of the free surface. Computational results show presence of a recirculation zone starting at the point where the surface slope changes discontinuously. Above this zone the surface elevation fluctuates intensively. The computed intensity of the surface fluctuation is in good agreement with the measurements. It is also shown that the periodic vortex shedding is attenuated near the free surface at a high Froude number. The region in which the periodic vortex shedding is hampered extends to about one diameter from the mean water level. It is qualitatively shown that the separated shear layers are inclined outward near the free surface due to the generation of the surface waves. This change in the relation between two shear layers is suggested to be responsible for the attenuation of the periodic vortex shedding.