Vertical gates were used in the past decade to regularize seasonal variations in streams under a broad range of operational conditions. A submerged hydraulic jump (SHJ) occurs downstream of the gate when the tail water depth exceeds the conjugate subcritical depth of the free jump and a reverse flow occurs above the wall jet. Typically, upstream flow that passes below the gate strongly interacts with the reverse flow (Figure 1
) in the roller region, and this interaction creates spatially and temporally varying vortex structures around the gate. Vortex-induced hydrodynamic effects acting on the gate may lead to the oscillation and breakdown of the gate structure depending on flow conditions. Thus, a clear understanding of the three-dimensional features of the vortex structure around the gate is necessary to develop novel designs that would reduce the hydrodynamic effects that act on the gate, which is the main aim of the present study.
A large number of experimental studies were carried out to investigate the flow features in the SHJ. Long et al. [1
] examined the turbulent flow structure of the SHJ in terms of surface profiles, mean velocity components, and Reynolds stresses for various Froude numbers and submergence ratios. Vertical distribution of the velocity measurements at different spanwise locations revealed that the flow structure in the SHJ is three-dimensional due to vortex motions near the gate. Demirel [2
] conducted series of experimental studies for the investigation of SHJ under different flow conditions and concluded that the interaction of mean and reverse flows caused the formation of two corner vortices downstream of the gate. Vortex induced free-surface fluctuations observed in the vicinity of the structure were found to play an important role in creating hydrodynamic forces on the gate. Liu et al. [3
] experimentally investigated the turbulence structure of the hydraulic jump at low Froude numbers and the dominant frequency was found to be in the range 0 to 4 Hz for both horizontal and vertical velocity components. Dynamics of vortices in the SHJ were experimentally investigated by Dios et al. [4
] using acoustic doppler velocimetry (ADV) and particle tracking velocimetry (PTV) in terms of mean flow and turbulence statistics at different vertical planes. The relationship between the length scales of the roller and the vortices revealed the strong coherent motion of vortex structure in the SHJ. Characteristics of the submerged wall jet on the rough bed were extensively investigated, and it was shown that the rate of jet decay in submerged jump increased with increase in bed roughness [5
]. Although experimental studies emphasized the strong motion of vortices near the gate, the three-dimensional features of the vortex field around the gate remain to be thoroughly investigated due to the inherent limitations of experimental measurements.
The flow around the gate is three-dimensional and unsteady due to the interaction of the vortices with the mean flow, which produces counter-rotating vortices at the upstream and forms a roller region at the downstream of the gate (Figure 1
). The reverse flow in the roller region interacts with the vortex-induced flow and creates two counter-rotating vortices downstream of the gate (Figure 1
b). Several researchers conducted experimental studies in an attempt to evaluate the vortex-induced hydrodynamic pressures acting on the gate. Bhargava et al. [7
] conducted experimental studies in a laboratory flume to investigate the hydrodynamic pressures on the gate lip in terms of mean and fluctuating pressure coefficients. Thang and Naudascher [8
] studied the vortex-excited vibration of underflow lift gates experimental. They observed that the dynamic interaction between the gate and unstable shear layer may produce periodic vortex shedding that oscillates the gate. Turbulent flow-induced multiple mode vibration of the submerged gate was experimentally investigated by Billeter and Staubli [9
] based on simultaneous measurements of velocity and pressure. Transition to galloping flow structure was found to play a significant role in the production of instability-induced excitation for the reduced velocities ranging from 0.8 to 14 (dimensionless). Cross-flow vibrations of underflow gates were experimentally investigated by Erdbrink et al. [10
] using resistance-type water level and force meter equipment. Studies identified that the vortex flow around the submerged gate may play a critical role in the onset of vibration of the structure due to hydrodynamic effects. The present study focuses on the formation of vortices around the submerged gate and the hydrodynamic forces acting on the structure, which are critical issues for the design of vortex damping structures that may eliminate damage to gate structures.
Numerical simulations of complex flows around submerged structures made it possible to evaluate the internal flow features of turbulent flows. Two-dimensional Reynolds-averaged Navier–Stokes (RANS)-based numerical models were first attempted in the literature to simulate turbulent flows in the SHJ [11
]. While these studies provided insights into the turbulence structure of low- and high-Froude-number flows, the two-dimensional numerical models could not predict the formation of vortex structure around the submerged gate. An assessment of the literature on the numerical simulation of the SHJ clearly shows that the RANS-based numerical models may suffer from inaccurate simulation of vortex structures that form both at the upstream and at the downstream of the gate due to strong coherent motions and energetic eddies. Eddy resolving computational models are alternatively used to simulate unsteady dynamics of coherent structures that are present near the gate. In order to overcome this limitation of RANS-based numerical models, Jesudhas et al. [15
] performed a detached eddy simulation (DES) of the SHJ with an incident Froude number of 8.2 to examine the coherent structure of the three-dimensional turbulent flow field in the developing and developed zones. The limitation of this numerical study is that they focused on the flow downstream of the gate while imposing an inlet velocity field below the gate and the flow upstream of the gate was not simulated, which may play an important role in the formation of vortex structures around the gate. A large number of numerical studies were conducted in the literature to understand the flow features downstream of the gate, but the three-dimensional features of the vortex formation around the submerged gate were not reported.
The present experimental and numerical study considers turbulent flow underneath the submerged vertical gate in a flat-bed channel as schematically shown in Figure 1
. Constant flow rate Q
enters the channel at the inlet and emerges from the outlet of the domain to maintain constant water depths of
at the upstream and downstream of the channel, respectively. The Froude number of the flow is defined based on the gate opening
and average flow velocity
below the gate as F1
is the gravitational acceleration. The corresponding Reynolds number of the flow is defined based on the hydraulic radius (R) below the gate as R =
is the kinematic viscosity. Here for submerged flow conditions, the tail water depth
is greater than the water depth
, which is the subcritical conjugate depth of the
as obtained from the Belanger equation. The corresponding submergence factor can be calculated as
The aim of this study is to gain a deeper understanding of flow and turbulence structures, as well as vortex generation around a submerged gate using experimental and numerical analysis, with the goal of developing vortex damping structures downstream of the gate. Experimental studies were conducted in a laboratory flume to evaluate and validate the numerical model. Time-averaged flow velocities and turbulence stresses were measured using ADV at different locations downstream of the gate. Recognizing that the coherent motions of vortices may result in hydrodynamic effects on the gate, LES studies were performed to analyze hydrodynamic effects acting on the submerged vertical gate for different inlet Froude numbers and submergence ratios. The first objective of the present study is to reveal the three-dimensional flow structure and vortex formations at both upstream and downstream of the gate. Achievement of this goal will allow us to understand the connection between upstream and downstream flows since the incident vortex flow strongly interacts with the recirculating flow downstream of the gate. The second objective is to analyze vortex-induced hydrodynamic forces acting the submerged gate using high-resolution numerical simulations. The third objective is to develop a vortex breaker to mitigate the adverse hydrodynamic effects acting on the gate. Performance of the proposed vortex breaker was evaluated for different flow conditions in terms of mean and instantaneous flow fields, as well as hydrodynamic forces acting on the gate body.
2. Flume Experiments
Experimental studies were conducted in a laboratory flume, which was 10 m long, 40 cm wide, and 60 cm high with plexiglass sidewalls and a stainless-steel bottom. Water was supplied from a large water tank using a pump with 100 L/s maximum flow rate capacity. Flow discharge at the inlet of the flume was controlled by a valve manually and measured using the ultrasonic flow meter mounted on the feeding pipe. Supercritical depth was produced using a vertical gate located at the upstream of the flume, and the tail water depth was provided using a tilting gate located at the downstream end of the flume to adjust for the desirable incident Froude number and submergence factor, which are the key parameters to characterize the flow through the submerged gate.
A downward-looking 200-Hz Nortek ADV was used to measure velocity components instantaneously at a cylindrical sampling volume of 5 cm below the ADV probe. Velocity components were spatially averaged in the sampling volume to collect enough data near the sampling point. The use of a relatively larger sampling volume in the near bed region may cause unrealistic velocity measurements since the sampling volume may not be representative of the main flow region. Thus, a smaller sampling volume was used near the channel bed to satisfy the signal-to-noise ratio (SNR) being greater than 20, which is recommended by the manufacturer of the ADV [16
]. Other critical parameters of the ADV measurements were nominal velocity range (NVR), transmit length (TL), and power level (PL), to adjust the range of flow velocities, the length of the transmitted wave from the ADV probe, and the power level of the electricity to be generated by the ADV, respectively. Details of the experimental set-up can be found in Demirel [2
]. Optimum parameters of the ADV were adjusted such that the SNR > 20 in both near-wall and roller regions. ADV measurements were conducted in the laboratory for the flow conditions given in Table 1
The flow in the flume was recirculated about 2 h with a constant flow rate before the velocity measurements commenced to exclude initial conditions, as well as to satisfy mass conservation in the roller region. Velocity at a point was measured for 180 s in order to collect adequate data and to obtain time-averaged flow quantities. Velocity data may contain spikes due to noise effects with the reflection of transmitted acoustic waves near the bed. In this study, the raw data were filtered using WinADV software [17
]. A snapshot of the experimental study is given in Figure 2
. The ADV was attached to a mobile traverse table in order to fix the ADV probes to a specific measurement point.
ADV measurements were conducted at different spanwise locations in order to determine at which stations the three-dimensional effects were significant. Vertical distributions of time-averaged streamwise velocity component at x/y1
= 5 are depicted for different spanwise locations in Figure 3
a. Dimensionless jet velocity below the gate is about 1.2 and almost independent of the backward effects since the flow with high momentum is strongly in the downstream direction in this region. However, recirculation effects tend to increase near the free surface due to the fact that the baroclinic torque caused by the high gradient of fluid density along the air–water interface generates vortex motion [18
]. As seen in Figure 3
b, the maximum spanwise velocity is observed at z/b = 0.4, at which station the vorticity effects are expected to be considerable. While normalized Reynolds stresses in horizontal
directions seem to be identical, the vertical distributions of Reynolds stress in the spanwise direction
are variable, and the maximum value is observed at z/b = 0.4, which is consistent with the previous observations in the literature [1
]. While the normal components of Reynolds stresses in horizontal and vertical directions are identical at each measurement station, the spanwise component of Reynolds stress exhibits a significant variation due to the energetic vortex structures observed on the free surface.