Experimental and numerical investigation on the hydraulic design criteria for a step-pool nature-like fishway

Abstract

Hydraulic considerations specific for the design of step-pool nature-like fishways (NLFs) are limited to the body dimensions of the target species. Additional hydraulic criteria for flow depth, maximum values for each of pool depth, velocity, and turbulent kinetic energy in terms of the weir opening width and discharge can help design an optimum step-pool NLF. The present study developed design charts and rating curves based on numerical modeling using the computational fluid dynamics software FLOW-3D^® HYDRO. Instantaneous velocity measurements on a 1:4 scaled physical model of a step-pool nature-like fishway designed as per the available design guidelines have been used to validate the numerical model. The hydrodynamics of the fishway with respect to the weir opening ratio b_r (0.10, 0.25, 0.45, 0.65, and 1.00) and discharge Q (0.1–1.5 m³/s) was analyzed through numerical simulations on a prototype scale. The simulation results showed that the maximum flow velocity and the averaged velocity over the crest at b_r = 0.10 and 0.25 are considerably lower than at b_r > 0.25. The maximum turbulent kinetic energy and energy dissipation factors for the tested range of discharges were within recommended limits for b_r = 0.10 and 0.25. The present study outcome in terms of the design charts and rating curves that illustrate the relationship between different variables can be used for an optimum design and ease in field implementation. In addition, the bed structure of the step-pool NLF presented in this study can be used to recreate full-scale or pilot models.

Keywords

Fishway numerical modeling hydraulics step-pool turbulence

1. Introduction

Anthropogenic activities as part of socio-economic development produce lasting effects on the ecological and morphological characteristics of the river network. On a global scale, only 23% of the world’s rivers run uninterrupted into the oceans (Grill et al., 2019). One of the immediate effects of damming the river system is the disruption of upstream migration of aquatic species for spawning, dispersal, or seeking refuge from predators. Diadromous fishes that undertake regular migration between freshwater and seawater are the most affected by the cross-stream infrastructures. The provision of environmental flows and fishways across high- and low-head dams are vital aspects that must be incorporated into dam constructions.

The traditional technical fishways in practice are rigid structures that often fail to cater to the requirements of diverse fish species. A more inclusive environment similar to nature-like fishways (NLFs) and ideal flow conditions at the fishway entrance is capable of attracting diverse fish species and increasing the passage efficiency of the fishway (Eberstaller et al., 1998; Schmutz et al., 1998; Katopodis et al., 2001; Landsman et al., 2018). In recent years, NLFs have gained popularity as an efficient means for re-connecting river networks. They are structures designed to resemble the natural riverine ecosystem and enable the passage and inhabitation of diverse aquatic organisms in the most efficient manner (Mooney et al., 2007). Recently, with increased demands to implement and maintain environmental flow schemes, cost-effective and eco-friendly structures like NLFs provide a promising tool to facilitate economic development alongside ecological conservation.

The NLFs are divided into three types: (i) bottom ramps and slopes, (ii) bypass channels, and (iii) fish ramps. The construction styles for bottom ramps and slopes are further classified into three: (i) set or embedded boulder construction, (ii) rockfill constructions, and (iii) dispersed or cascaded constructions (step-pool type)) (DVWK, 2002). They are generally constructed at low-head barriers with full or partial channel widths. Franklin et al. (2012) studied the passage efficiency of adult alewives in field settings of two NLFs. A perturbation boulder rock ramp at a bed slope of 4.2% showed 94% passage efficiency, while a step-pool bypass channel at 7.1% bed slope passed only 40% of the fish that reached the fishway entrance. It was observed that passage efficiency was generally high at stretches with bed slopes between 1.01% and 5.43%. This supports the recommendation by DVWK (2002) that limits the usage of NLFs beyond a 5% bed slope. More recently, Landsman et al. (2018) compared the performance of the NLF bypass channel (2.4% bed slope) to the technical pool and weir fishway for the passage of Rainbow Smelt Osmerus mordax and Brook Trout Salvelinus fontinalis on the Glenfinnan River, Canada. The NLFs passed rainbow smelt at a modest rate of 28.6%, while the pool and weir fishway passed none, and as for brook trout, both fishways performed well with 90–100% passage for both the years tested. It was also observed that NLFs served as spawning habitat for rainbow smelt, enhancing its performance in providing efficient migration and inhabitation environment. Baki et al. (2019) studied the hydraulic characteristics of vortex weirs with notches and developed fishway coefficients and velocity reduction factors. The study also considered the different flow modes (Ruttenberg, 2007) that occur due to the notches of varied dimensions.

Fishway characteristics such as turbulence kinetic energy and energy dissipation factor are indicators of the local and global turbulence levels, respectively (Tarrade et al., 2008). Lacey et al. (2012) postulated an IPOS Framework to characterize the suitability of a fishway for the target species. IPOS stands for Intensity (turbulence intensity, turbulent kinetic energy, Reynolds shear stress, and vorticity), Periodicity (predictability and energy spectra), Orientation (axis of eddy rotation and direction of dominant fluctuation), and Scale (eddy length scale, eddy diameter, and Reynolds number). Researchers have begun to understand the importance of studying the turbulence in fishways and have initiated a ripple of model studies in the recent past (Bretón et al., 2013; Tran et al., 2016; Kucukali and Hassinger, 2018).

While general design guidelines addressing the dimensions of flow pathways and bed slopes for various nature-like fishways are available (DVWK, 2002; Turek et al., 2016), performance evaluation of designed step-pool NLFs in terms of turbulence parameters is still lacking. The minimum of pool depth, weir opening width, and its depth (Figure 1) have been recommended as a function of the body depth and total length of the largest target species, such that it is habitable for the entire target species in the area. It was also recommended that the width of the channel should be as wide as possible (DVWK, 2002). However, it is worth noting that increase in channel width for a particular weir opening width will lead to decrease in the available water head over the crest and nonfulfillment of the minimum weir opening depth. Therefore, it is beneficial to know the dependence of flow characteristics on the bed dimensions, to arrive at an optimum design that satisfies the hydraulic criteria at all ranges of flow.

Figure 1.

Illustration of (a) body measurements of a fish and (b) design parameters as per existing guidelines (modified from Turek et al., 2016).

The present study incorporates both experimental investigations and numerical simulations to generate hydraulic criteria for the design of step-pool NLFs for different ranges of weir opening widths and discharges. In addition, it is also sought to compare the flow equations developed for the step-pool NLF with that of the existing rock weirs, for both overtopping and non-overtopping cases. The study commences with the design of a typical step-pool NLF (SP-NLF) designed as per guidelines issued by the Federal Interagency (Turek et al., 2016) and target species data collected from Rema Devi et al. (2007). Experimental data obtained from the scaled down model of SP-NLF were used to validate the numerical model (validation model). The validation model was subjected to tests of boundary convergence and mesh size convergence, prior to the verification of simulation results. After that, the bed topography of a distinct step-pool unit was adopted to create a series of step-pool units with varying weir opening widths (simulation model). The experimental methodology and features of numerical simulation are discussed in the following section. The output from the simulation model was then used to generate data for a broader range of bed and flow conditions to develop design charts and rating curves. Further, the characteristics of the step-pool NLF so developed is also compared with the existing rock weir equations for better insights.

2. Materials and methods

The Federal Interagency has developed specific guidelines for the design of step-pool nature-like fishways (NLFs) under the collaboration of The National Marine Fisheries Service (NMFS), the U. S. Geological Survey (USGS), and the U. S. Fish and Wildlife Service (USFWS) (Turek et al., 2016). These guidelines were developed after evaluating published journal articles, reports, gray literature, recent data from laboratory experiments, and performance feedback from constructed fishways. The guidelines are reported to be generic and not to replace site-specific recommendations, limitations, and protocols.

The fish fauna of southern Western Ghats has been selected as the target species. A list of freshwater fauna and their body measurements were collected from Rema Devi et al. (2007). The longest fish in terms of the standard length (SL) was Ompok bimaculatus, with a value of 474 mm SL. The body depth (BD) and total length (TL) measured using ImageJ from a scaled photograph of the fish were approximately 23.98% SL and 113.36% SL, respectively. Therefore, corresponding to a SL of 474 mm, BD = 0.2398 * 474 = 113.67 mm, and TL = 1.1336 * 474 = 537.33 mm. According to these dimensions, the design values calculated as per guidelines (Turek et al., 2016) are given below. An illustration of the body measurements of the fish and design parameters are given in Figure 1.

• Minimum pool depth d_P = 1 ft + 4BD = 760 mm.

• Minimum weir opening width W_N = 2TL = 1075 mm.

• Minimum weir opening depth d_N = 3BD = 341 mm.

2.1 Laboratory experiments

The experimental setup consists of a rectangular flume of 11 m in length, 1 m in width, and 1 m in height. A 30 Hp centrifugal pump was used to re-circulate flow, while a SCADA system and electromagnetic flow meter (accurate to ±0.5% of the measured value) helped regulate the flow. Three discharges (Q) of 0.02, 0.03, and 0.04 m³/s were tested in the present study. The flow velocity was measured using Nortek Vectrino Acoustic Doppler Velocimeter (ADV) at a sampling frequency of 25 Hz. The instrument is accurate to ±1% of the measured value ±1 mm/s. The data was filtered using Win-ADV software for correlation coefficient greater than 40%, subjected to a minimum of 70% retainment of data (Martin et al., 2002; Cea et al., 2007; Kalathil and Chandra, 2021) and sound to noise ratio (SNR) greater than 15 dB. The data was thereafter processed applying the phase-space threshold de-spiking method of Goring and Nikora (2002). Data replacement has not been done to avoid introduction of additional spikes. For Q = 0.02 m³/s, 91.4% of the measurement points retained more than 70% of the time-series data. For Q = 0.03 and 0.04 m³/s, the retained data points amounted to 75.14% and 56.19%, respectively.

The average bed slope (S) has been chosen as 5%, which lies within the range of bed slopes (3−5%) recommended for NLFs (DVWK, 2002). The pool length and crest height of successive steps have been checked and altered so that S_f ≤ S, and a quasi-uniform flow is created in the fishway. A model scale of 1:4 has been chosen to scale the design parameters into the laboratory framework. The bed structure consists of small to medium-sized stones (2–40 mm) embedded in the base plain bed or interlocked with adjacent members without cementitious materials. The steps or rock weirs were created by arranging large granite stones (170–250 mm). The weir opening height and the height of the weir opening crest from the downstream bed level have been arbitrarily fixed at 0.14 m and 0.18 m, respectively. The average weir opening width and weir opening height were measured to be 0.25 m and 0.14 m, respectively. The pools were created by the uniform placement of bed materials (D₈₄ = 2.45 mm) with light compaction. The pool bed surface was expected to deform naturally under the action of flowing water. The stability of the structure was tested and verified by visual observation under a high discharge of 0.070 m³/s. A photograph of the experimental setup and the longitudinal profile of the final equilibrium bed surface along the flume centerline are shown in Figure 2(a) and (b), respectively. The longitudinal, cross-stream, and vertical axes of the setup are denoted with the notations X, Y, and Z, respectively. The distinct units of the step-pool NLF are denoted as SP-NLF-1, SP-NLF-2, and SP-NLF-3, respectively. The fall height (ΔH), pool length (L_P), ratio of step opening width to the channel width (b_r), bed slope(S), and details of each step-pool NLF are given in Table 1.

Figure 2.

Experimental setup: (a) Photograph showing the experimental setup of the artificial step-pool system depicting a nature-like step-pool fishway (Q = 0.02 m³/s), (b) longitudinal profile of the constructed step-pool systems through the step opening at Y = 0.5 m, and (c) the bed structure of the step-pool NLFs considered for study, SP-NLF-2 and SP-NLF-3.

Table 1.

The hydraulic drop and bed dimensions in the laboratory experimental model (1:4 scale) of step-pool NLF.

Unit no.	ΔH (m)	L_P (m)	S (%)	b_r (m)
SP-NLF-1	0.047	1.05	4.5	0.24
SP-NLF-2	0.040	1.05	3.8	0.25
SP-NLF-3	0.034	0.80	4.3	0.27

On visual inspection of the flow regime and the bed topography in the experimental setup, it was found that the incoming flow energy resulted in high self-aeration rates and undue toe scour in SP-NLF-1, even for the lowest discharge (0.020 m³/s) tested. However, due to a sufficient pool length of 1.05 m in SP-NLF-1, the flow energy greatly diminished, and the outgoing flow into SP-NLF-2 was relatively calm and tranquil. The presence of sufficient pool volume in SP-NLF-2 and tranquil incoming flow resulted in minimal modifications to the bed topography. However, the reduced pool length in SP-NLF-3 caused a local scour at the pool bottom downstream of the step weir. The hydraulic study of the setup was limited to SP-NLF-2 and SP-NLF-3 since the conditions in SP-NLF-1 do not agree with the fishway requirements. The three-dimensional bed structure of the step-pool systems under study is shown in Figure 2(c). Velocity measurements were taken at 17 verticals spanning SP-NLF-2 and SP-NLF-3 each for discharges 0.020 m³/s, 0.030 m³/s, and 0.040 m³/s, respectively.

The derived quantities used for results analysis are velocity magnitude, turbulent kinetic energy, and energy dissipation factor of the pools. The velocity magnitude of flow is calculated as $V = \sqrt{u^{2} + v^{2} + w^{2}}$ , where u, v, and w are the velocity components in the streamwise, cross-stream, and vertical directions, respectively. The turbulent kinetic energy (TKE) is obtained as $T K E = \frac{1}{2} ({u_{r m s}^{'}}^{2} + {v_{r m s}^{'}}^{2} + {w_{r m s}^{'}}^{2})$ , where u’_rms, v’_rms, and w’_rms are the root mean square of the fluctuating velocity components. The energy dissipation factor is derived as EDF=γQΔH/⩝, where γ is the specific weight of water, Q is the flow rate, ΔH is the hydraulic drop between the pools, and ⩝ is the pool volume.

2.2 Model setup for validation

The computational fluid dynamics (CFD) software package used for numerical simulations is FLOW-3D^® HYDRO which caters primarily to the needs of civil and environmental engineers. Various researchers have successfully employed FLOW-3D^® to simulate fishway flows and it has been found to be capable to simulate complex flow phenomena occurring in fishways efficiently (Abdelaziz et al., 2013; Afshar and Hoseini, 2013; Duguay and Lacey, 2016; Quaresma and Pinheiro, 2021). The numerical algorithm of FLOW-3D^® HYDRO is based on the finite volume method derived directly from the integral form of the conservation equations of mass and momentum. It solves the equations of motion for a given problem in each computation cell and undergoes algebraic approximations to arrive at a numerical solution as close to that of the original problem. The Cartesian form of the general mass continuity equation is given in equation (1), where V_F is the fractional flow volume, ρ is the density, (u, v, w) are the velocities in (x, y, z) directions, and (A_x, A_y, A_z) are the fractional flow area in the respective directions. The Navier–Stokes equations representing the conservation of momentum in x, y, and z directions are given in equations (2a)–(2c), where (G_x, G_y, G_z) and (f_x, f_y, f_z) represent the body acceleration and viscous accelerations, respectively.

V_{F} \frac{\partial ρ}{\partial t} + \frac{\partial}{\partial x} (ρ u A_{x}) + \frac{\partial}{\partial y} (ρ v A_{y}) + \frac{\partial}{\partial z} (ρ w A_{z}) = 0

(1)

\frac{\partial u}{\partial t} + \frac{1}{V_{F}} [u A_{x} \frac{\partial u}{\partial x} + v A_{y} \frac{\partial u}{\partial y} + w A_{z} \frac{\partial u}{\partial z}] = - \frac{1}{ρ} \frac{\partial p}{\partial x} + G_{x} + f_{x}

(2a)

\frac{\partial v}{\partial t} + \frac{1}{V_{F}} [u A_{x} \frac{\partial v}{\partial x} + v A_{y} \frac{\partial v}{\partial y} + w A_{z} \frac{\partial v}{\partial z}] = - \frac{1}{ρ} \frac{\partial p}{\partial y} + G_{y} + f_{y}

(2b)

\frac{\partial w}{\partial t} + \frac{1}{V_{F}} [u A_{x} \frac{\partial w}{\partial x} + v A_{y} \frac{\partial w}{\partial y} + w A_{z} \frac{\partial w}{\partial z}] = - \frac{1}{ρ} \frac{\partial p}{\partial z} + G_{z} + f_{z}

(2c)

The software uses structured rectangular grids numbered consecutively with the indices i, j, and k, where i represents the x-direction, j the y-direction, and k the z-direction. A computational grid discretizes the physical space of the model. For single-phase free surface flows, the free surface behaves as one of the model’s external boundaries. A volume of fluid (VOF) method is employed to identify the free surface. The method entails solving the VOF function F, where F = 1 denotes a fluid volume while F = 0 represents a void space. The geometry is incorporated into the computational domain through Fraction Area/Volume Obstacle Representation (FAVOR^TM) mechanism (FLOW-3D®, 2008). The curved edges are approximated at the intersections of geometry and computational grid. Numerical approximations are carried out in each grid, which approaches the correct solution as the grid sizes reduce. However, with the reduction in the computational grid size, the size of the numerical model increases and results in unrealistic computational time. Therefore, model developers must determine the optimal grid size that delivers numerical solutions of acceptable accuracy.

The model domain size was restricted to 3.9 x 1.0 x 0.9 m. The inlet and outlet boundaries were set as discharge (Q) and pressure (P), respectively. The outlet pressure value was obtained from the experimental measurement of the flow depths. The left and right boundaries were set as non-slip wall (W) boundaries. The nested mesh block boundary is set as a symmetry (S) boundary signifying a mirror surface. Reynolds-averaged Navier–Stokes (RANS) equations are solved through the RNG turbulence closure model chosen following past literature of similar nature (Abdelaziz et al., 2013; Plymesser, 2014; Stamou et al., 2018). Second-order monotonicity preserving method was opted for momentum equation approximation based on technical guidelines and checks (CFD Project Workflow Guide, 2017). The roughness coefficient was 2.8 times D₈₄ (= 0.0686 m) of the pool bed materials (López and Barragan, 2008). The model setup is illustrated in Figure 3(a). To determine an optimum grid size and mesh block arrangements that would give accurate results, boundary convergence analysis and grid convergence analysis were performed.

Figure 3.

Validation model: (a) Model geometry and (b) illustration of the distance from the nested mesh-block boundary.

2.2.1 Boundary convergence

The model is set up as a nested mesh block of finer mesh size within a containing mesh block of the coarser mesh size. To determine the optimum distance of the nested mesh block boundary from the point of interest, simulations were performed at a constant discharge of 0.02 m³/s by varying the boundary distance by an even multiple of the mesh size (CFD Project Workflow Guide, 2017) as shown in Figure 3(b). For all such simulations, the coarse mesh size m and fine mesh size n were maintained as 0.03 m and 0.015 m, respectively. From the analysis of the velocity profile at a representative point for different boundary locations, it was found that the results converged at a distance of 60n with less than 3% error (Figure 4(a)). Henceforth, the nested mesh blocks were set up at a distance of 60n from the farthermost point of interest.

Figure 4.

Variation of velocity magnitude with depth at a representative point for (a) different boundary distances and (b) different mesh sizes.

2.2.2 Mesh size convergence

To determine an optimum mesh size, simulations were run for five different mesh sizes –0.04, 0.03, 0.02, 0.015, and 0.0075 m, where 0.02, 0.015, and 0.0075 m were provided as nested mesh blocks. The computational times for each of the simulations are given in Table 2. The results converged at a mesh size of 0.015 m as shown in Figure 4(b). Therefore, the simulations to validate the model were run with a coarse mesh block of 0.03 m and a nested fine mesh block of 0.015 m.

Table 2.

Computational time for different mesh sizes (system configuration: Intel ® Core ™ i7-4770 CPU @ 3.40 GHz, 32 GB RAM, 2 GB NVIDIA Graphics Card).

Mesh size (m)	Time for 10s simulation (hh:mm:ss)
0.04	00:02:12
0.03	00:02:26
0.02	00:06:05
0.015	00:13:25
0.0075	00:38:23

2.3 Performance evaluation of the validation model

Simulations were run for all three discharges (0.02, 0.03, and 0.04 m³/s) considered for the experimental study. Simulation results corresponding to the 17 vertical profiles were extracted to compare with the experimental data. The variables used for comparison are flow depth, velocity magnitude, and turbulent kinetic energy.

The water surface elevations obtained through laboratory measurements and numerical simulations are shown in Figure 5. The average differences in the elevation levels for 0.02 m³/s, 0.03 m³/s, and 0.04 m³/s are 1.8 cm, 2.1 cm, and 0.7 cm, respectively. Experimental data for the full flow depth range is unavailable due to instrumental limitations and data loss after filtration. Therefore, numerical data was also restricted to the range that coincides with the experimental data for comparison purposes. The velocity distribution pattern has been analyzed at each point to ensure no marked difference between the datasets. Depth-averaged values of u, v, w, and V were used to apply statistical indices for validating the numerical model. The respective values of MAE and RMSE for each parameter are given in Table 3. The mean of the measured time-series instantaneous velocities varied between ±0.01 and ±0.19 m/s for u, ±0.00 and ±0.14 m/s for v, and ±0.04 and ±0.26 m/s for w, respectively. The numerical and experimental error falls within the estimated error in the experimental data measurements.

Figure 5.

Longitudinal profile of the bed and water surface for both experimental and numerical simulations at Y = 0.50 for different discharges.

Table 3.

The statistical error between the experimental and simulated results for the validation model.

	Count	H	u	v	w	V	TKE
	(No.)	(m)	(m/s)	(m/s)	(m/s)	(m/s)	(m²/s²)
MAE	51	0.021	0.099	0.063	0.052	0.079	0.018
RMSE	51	0.011	0.053	0.037	0.028	0.046	0.01

Similar to the velocity profiles, the vertical profiles of turbulent kinetic energy were also analyzed to verify the similarity in the distribution. It was found that the depth-averaged values of the vertical profile of the turbulent kinetic energy obtained from the numerical data varied from the experimental with a mean absolute error (MAE) and root mean square error (RMSE) of 0.015 and 0.018 m²/s² for 0.02 m³/s, 0.020 and 0.024 m²/s² for 0.03 m³/s, and 0.019 and 0.022 m²/s² for 0.04 m³/s.

The energy dissipation factor for the experimental data has been calculated with the values of hydraulic drop and volume measurements. The volume of the pool was calculated by applying the centerline water surface levels to the entire pool surface. For the numerical data, the volume was calculated by applying the water surface levels at the respective grid points. The trapezoidal rule of volume calculation was used in both cases. The average difference (MAE) of EDF between the experimental and numerical results is 10 W/m³ which amounts to a mean absolute percentage error (MAPE) of 8.6%. The statistical error between the experimental and numerical results of EDF is less than 10% which is acceptable. Therefore, the numerical model is adequate for simulating the flow characteristics in the fishway structure.

2.4 Model domain and design parameters

The pool length and pool volume of SP-NLF-2 was sufficient to prevent scour hole formation, in contrast to SP-NLF-3 (Figure 2(b)). Therefore, the bed geometry of SP-NLF-2 was replicated to create a series of seven step-pool units forming a step-pool NLF. The boundary conditions are the same as the validation model. The model scale 1:4 was used to translate the mesh size and boundary distance estimated for the validation model into prototype dimensions. Therefore, the mesh sizes used for the simulations in the prototype scale were 0.12 m for the containing mesh block and 0.06 m for the nested mesh block. The domain size of the containing mesh block was 26.75 x 3.96 x 3.96 m, and that of the nested mesh block was 13.20 x 3.96 x 3.96 m. The origin of the longitudinal axis X, cross-stream axis Y, and vertical axis Z lies at the upstream bottom point as denoted in Figure 6(a). The bed materials in the pool with sizes ranging from 2 mm to 40 mm are not scaled up in the prototype. Therefore, the bed roughness height was kept as 0.0686 m itself.

Figure 6.

Simulation model: (a) Model geometry for b_r = 0.25, (b) model geometry for b_r = 0.65, and (c) longitudinal section through a step-pool NLF unit.

Five geometries with weir opening ratios b_r varying as 0.10, 0.25, 0.45, 0.65, and 1.00 were studied for 15 discharges varying from 0.1 to 1.5 m³/s, where b_r is the ratio of weir opening width b to the channel width B. The geometries of b_r = 0.25 and 0.65 are illustrated in Figure 6(a) and (b), respectively. The hydraulic parameters, such as head over the step crest h₀ (Figure 6(c)), depth-averaged velocity magnitude over the step V₀, maximum velocity magnitude V_max in the step-pool unit, maximum turbulent kinetic energy TKE_max in the step-pool unit, pool volume ⩝, and energy dissipation factor EDF of the pools, were estimated for the middle step-pool unit (extending between X = 10–14.25 m). The values of h₀ and V₀ were estimated at X = 9.15 m (0.84 m upstream of the step crest).

3. Results and discussion

The simulation results are presented in terms of rating curves that relate the dimensionless form of h₀, h_p, and V₀ and with the study parameters (b_r and Q). Empirical equations are developed for EDF as a function of Q. In addition, simulations have been performed for the step-pool NLF model with an elevated pool bed level to study the effect of reduced pool depth on the fishway hydraulics. In addition, the characteristics of the developed step-pool NLF is compared with the existing rock weir equations to assess performance.

3.1 Effect of weir opening ratio

The initial design of the step-pool NLF corresponding to the target species required a minimum weir opening width of 1075 mm (269 mm in model scale). An average 250 mm (b) weir opening was provided in a 1 m (B) flume, giving a weir opening ratio (b_r) = 0.25. While implementing the step-pool NLF in actual field conditions, b depends on the target species in the region, and B depends on the field conditions. Therefore, it is beneficial to analyze the dependence of b_r on the flow characteristics such as flow depth, velocity, turbulent kinetic energy, and energy dissipation factor, each of which are discussed below.

3.1.1 Flow depth and flow velocity

By the law of conservation of mass, the flow depth increases with an increase in flow contraction. Therefore, the maximum flow depths are obtained for b_r = 0.10. However, analyzing the flow variation with discharge enabled a better understanding of the increased percentages. There is a wider drift between the flow depths from b_r = 0.45 to 0.25, showing an average increase of 37%. However, the data for b_r = 0.25 differed by only 11% from that of b_r = 0.1 (Figure 7(a)). The dimensionless flow depth h₀ ^* (= h₀/B) and dimensionless maximum pool depth h_p^* (= h_p/B) share a linear relation with b_r for all discharges. Linear regression analysis obtained equations of the form $h_{0}^{*} = \bar{a} + \bar{b} b_{r}$ (R² varies between 0.83 and 0.96) and $h_{p}^{*} = \bar{c} + \bar{d} b_{r}$ (R² varies between 0.76 and 0.92). The mean values of the coefficients a, b, c, and d at each discharge are plotted as a function of discharge in Figure 7(b). The x-axis is represented by dimensionless discharge Q^*, where Q^* = Q/(gSB⁵)^0.5. These curves can arrive at approximate coefficient values for step-pool NLFs for varied bed and flow parameters or structures of similar bedforms.

Figure 7.

Variation of flow depths with discharge for the different step-pool NLFs (a) plot of dimensionless Q versus dimensionless h₀, (b)variation of coefficient values in the empirical equations with respect to dimensionless Q; the coefficients a and b are related to h₀^*, while c and d are related to h_p^*.

The influence of b_r on the flow velocity is analyzed through (i) velocity contour plots, (ii) depth-averaged velocity magnitude, and (iii) flow region with a velocity greater than 2 m/s. The fishway design guidelines recommend a velocity lower than 2 m/s for the unhindered migration of aquatic species (DVWK, 2002). The dominance of plunging flow reduces with an increase in discharge, and beyond a point, streaming flows completely dominate the flows. At Q = 0.1 m³/s, transitional flow can be observed for b_r = 0.10 and 0.25, while its plunging flow for b_r = 0.45, 0.65, and 1.00. At Q = 0.5 m³/s, for b_r = 0.10, 0.25, 0.45, and 0.65, transitional flow regime is observed while it is plunging flow regime in b_r = 1.00 as shown in Figure 8.

Figure 8.

Velocity contour and streamlines for a step-pool unit at Q = 0.5 m³/s for b_r: (a) 0.10, (b) 0.25, (c) 0.45, (d) 0.65, and (e) 1.00. The velocity range has been limited to 2 m/s since that is the maximum permissible velocity recommended for fishways.

The variation of dimensionless depth-averaged velocity with dimensionless flow depth is plotted in Figure 9(a). The figure shows that as b_r reduces to 0.10 and 0.25, there is a marked shift in the velocity values establishing greater flow depth with lower velocity ranges. Also, b_r = 0.45 produces the maximum values of velocity values due to the critical contraction conditions of the step-pool NLF. While this representation helps to identify an optimum b_r, the percentage of flow volume carrying velocities greater than 2 m/s would help differentiate between the flow characteristics at b_r = 0.10 and 0.25. Figure 9(b) shows the percentage of the flow volume with velocities greater than 2 m/s. Although V₀ at b_r = 0.10 has the lowest values, the volume percentage depicted reveals a greater value due to the high flow contraction for b_r = 0.10. The volume percentages are 2.65% and 0.21% respectively for b_r = 0.10 and 0.25. Therefore, b_r = 0.25 gives the best flow and depth conditions in the step-pool NLF.

Figure 9.

Scatter plot of datapoints belonging to different b_r values displaying: (a) dimensionless h₀ versus dimensionless V₀ and (b) Q versus percentage volume of flow with a velocity greater than 2 m/s (Ɐ_{Vmax >2}).

However, the choice for an optimum b_r cannot be warranted in the field scenarios due to site restrictions. Therefore, rating curves that include the full range of tested parameters can aid to determine the fundamental flow variables. Polynomial curve fitting to Figure 7(a) and 9(a) produces a generic design curve for step-pool NLF as a function of the weir opening ratios (Figure 10). Depending on known values of B and Q, and a desired value of b_r, the available ranges of flow depth and velocity can be ascertained. The weir opening height also influences the net flow depth above crest. In the present case, in prototype dimensions, the weir opening height is 0.56 m. This value when analyzed with respect to h₀^* in Figure 10 can guide in limiting the weir opening height in accordance with the design h₀. Also, like a typical weir rating curve, the field measurement of head over the crest can be used to obtain the discharge value.

Figure 10.

Rating curves in terms of h₀^*,Q^* and V^* for design purpose. The value of weir opening ratio is shown across each curve.

3.1.2 Turbulent kinetic energy and energy dissipation factor

Turbulent kinetic energy is a measure of the turbulent fluctuations in the flow. The maximum values are observed near-bed and near-surface (Figure 11). For plunging flow regimes, the maximum TKE is along the bed surface. For transitional and streaming flow regimes, higher values of TKE are distributed across the high-velocity zones. The turbulent kinetic energy is higher at lower discharges for b_r = 0.45, 0.65, and 1.00. Therefore, it can be understood that TKE has an inverse dependence on the available flow depth. Moreover, an increase in h₀ resulted from a reduction in b_r from 0.25 to 0.10 did not produce a considerable reduction in the TKE. An average increase of 1% in flow depth showed only an average decrease of 1% in TKE_max, when b_r reduced from 0.25 to 0.10, as compared to a 4.67% decrease in TKE_max when b_r reduced from 0.45 to 0.25. It leads to an inference that there exists an optimum weir opening ratio (b_r = 0.25) that produces optimum levels of turbulent kinetic energy while restricting Ɐ_{Vmax > 2 m/s} to the minimum (Figure 9(b)).

Figure 11.

Contour plots of turbulent kinetic energy for a step-pool unit at Q = 0.5 m³/s for b_r: (a) 0.10, (b) 0.25, (c) 0.45, (d) 0.65, and (e) 1.00.

The zones complimentary to the jet zones act as recirculation zones where the species rest amid the migration for a few minutes to several days (DVWK, 2002; Haro et al., 2008; Silva et al., 2020; Baharvand and Lashkar-Ara, 2021). With an increase in b_r, the volume of low-velocity regions reduces. The change in the resting zone volume is reflected in the calculations of the energy dissipation factor. The EDF is analyzed as a function of TKE and Q for all weir opening ratios. Generally, for a pool-weir type fishway, the pool volume is considered below the crest elevation and not the flow volume (DVWK, 2002; Silva et al., 2020). A similar methodology is applied here, neglecting the passage volume (h₀*b_r*B*L_p) from the total pool volume. The average increase in EDF due to the reduction in pool volume is 1.9%, 6.2%, 8.2%, 9.3%, and 10.6% for b_r = 0.10, 0.25, 0.45, 0.65, and 1.00, respectively. The linear equations relating EDF and Q are given in Table 4.

Table 4.

Linear equations to calculate energy dissipation factor EDF in the step-pool NLF as a function of discharge Q for different weir opening ratios b_r.

b _r	Equation	R ²
0.10	EDF=15.343+82.821Q	0.98
0.25	EDF=28.152+80.643Q	0.93
0.45	EDF=25.867+158Q	0.95
0.65	EDF=15.733+189.25Q	0.99
1.00	EDF=5.419+158.893Q	0.97

Figure 12 shows the variation of EDF with TKE_max. The dependence of TKE_max with both Q and EDF follows a similar trend since EDF shares a linear relation with Q and h₀. Yet again, b_r = 0.10 and 0.25 carries the lowest EDF values. The maximum EDF values obtained for the range of discharges tested with b_r = 0.10 and 0.25 are 136 and 145 W/m³, respectively. A maximum EDF value of 150 W/m³ was recommended for flows as low as 0.2 m³/s (Larinier, 2002); however, Armstrong et al. (2010) restricted 150 W/m³ for flows up to 1 m³/s (Towler et al., 2015). Due to sediment accumulation, the pool volume is bound to reduce with time in field scenarios. Therefore, the range of EDF also will increase accordingly. However, considering just the weir design aspect, lower b_r values will deliver maximum energy dissipation through sufficient pool depth and pool volume.

Figure 12.

Variation of maximum turbulent kinetic energy TKE_max with energy dissipation factor EDF for different b_r values.

3.2. Effect of pool depth

The pool depth in the initial experimental setup was fixed through trial runs to develop flow depth in line with the design guidelines. The upscaled value of the same (= 0.70 m) had been carried forward for all the numerical simulations. The implications of a reduced pool depth on the desired hydraulic characteristics will be additional information that would aid the practitioners while implementing the designs in the field. This section discusses the results of a 0.20 m uniform increase in the pool bed elevation of the step-pool NLF with b_r = 0.25. The particular b_r has been chosen since it was identified as an optimum design in the earlier discussion.

In specific terms, the change in pool depth means the change in the elevation between the step crest and the downstream pool bed. The set of simulations corresponding to the reduced pool depth is termed h_pr. Figure 13 shows the variation of V_max with h₀ for h_p and h_pr. The value of V_max in the step-pool unit and V₀ over the step crest increased by 6.2% and 5.3%, with an increase of 0.20 m in the pool bed elevation. The turbulent kinetic energy for both cases did not vary significantly. However, EDF increased by 35% on average due to the decrease in the resultant pool volume.

Figure 13.

Variation of maximum velocity magnitude V_max with flow depth over step crest h₀ for initial maximum pool depth h_p and maximum reduced pool depth h_pr.

3.3. Rock weir equations

The characteristics of the present step-pool NLFs are compared with the rock weir equations developed for submerged weir conditions, to evaluate the study results in conjunction with the existing literature. Ruttenberg (2007) postulated four modes of flow over vortex weirs for fish passage, namely, orifice flow, gap flow, weir flow, and drowned flow depending on the relative positions of water surface and weir elevations. When the water surface elevation is lower than the step crest elevation, flow occurs through the orifices between the bed materials and is termed orifice flow. Gap flow occurs for unsubmerged weir flows where the flow is confined to the weir notches or weir openings. Weir flow occurs when the flow submerges the entire weir section, while drowned flow is when the relative roughness is greater than 3–5. In the present study, relative roughness was calculated as h₀/y_c, and its values ranged from 0.08 to 1.26, negating any drowned flow conditions, where y_c is the weir opening crest elevation. Although cracks in the bed materials generating orifice flows existed in the experimental setup, the weir sections in the numerical model were modeled impervious using only the bed surface elevations. Therefore, only gap and weir flows are considered for analysis in the present study. Step-pool NLF configurations with 0.25 ≤ b_r < 1.00 produced non-overtopping weir flows through the weir openings for the tested range of discharges.

The configuration with b_r = 0.10 and Q ≥0.7 m³/s produced submerged overtopping weir flow conditions along the weir section, which was analyzed by splitting the combined discharge into gap flow discharge and weir flow discharge. Hereafter, the flow depth above the crest represented by h₀ so far for all configurations has been split into h_sub and h_w depending on the submerged conditions of flow (Figure 14). The gap flow discharge is calculated as Q_gap = V_weir x A_gap, and weir flow discharge Q_weir = Q_total – Q_gap. The weir coefficient, in this case, is estimated through a modified form of Poleni’s equation (Chow, 1959) with considerations for the plan angle of the weir section and the effective weir length (Ruttenberg, 2007).

Figure 14.

Illustration of a submerged overtopping flow over a rock weir (a) cross-section and (b) longitudinal section through the centerline.

The submerged weir conditions in the present study (b_r = 0.10) are compared with the vortex rock weirs studied by Baki et al. (2019). Vortex weirs (model scale of 1:4) consisted of notches in the weir crest. The flow analysis followed the considerations of Ruttenberg (2007), wherein the weir coefficient μ is a calibration parameter that depends on the geometry of the weir. The variation of μ for the vortex weirs (W = 0 and θ = 70°), and the trapezoidal weir (W = 0.4 and θ = 66°) of the present study are presented in Figure 15, where W is the weir crest length perpendicular to the flow direction and θ is the weir angle. Since the present study produced only a limited dataset (Q = 1–1.5 m³/s) of overtopping flows under submergence conditions, the analysis lacks solid conclusions. However, the coefficient μ follows an exponential relation with the submergence ratio (h_w/y_w) similar to the vortex weirs. The best fit curve is of the form μ = 2.131 exp(-4.621h_w/y_w) having R² = 0.97. The μ values in the present study vary between 0.93 and 1.29, which lies within the range reported for vortex weirs (0.74 and 1.43). Nevertheless, the variation in the constants of the exponential fit between the two studies owes to the lower submergence ratios in the present study. In addition, the notches in Baki et al. (2019) were located on either side or both sides of the vortex arm, while the present study had the weir opening at the center of the weir. To summarize the flow analysis on submerged overtopping weir flows, further research is required to ascertain the effect of notch location and weir geometry on the weir flows.

Figure 15.

Variation of weir coefficient μ with h_w/y_w for the vortex weirs (Baki et al., 2019) and the trapezoidal weir (b_r = 0.10) of the present study.

For the submerged non-overtopping weir flow configurations, a modified form of the fundamental Poleni’s equation (Chow, 1959) of weir flow has been used to calculate the weir coefficient (equation (8)). The drowned flow reduction factor σ is introduced into the equation to account for the influence of the downstream tailwater depth for h₂/h₁ > 0.614 (DWVK, 2002), where h₁ and h₂ are the flow heads upstream and downstream of the weir crest. The equation is limited to an intermediate level of submergence with h₂/h₁ < 0.9 (Larinier, 2002).

Q = \frac{2}{3} C_{d} L σ h_{1}^{3 / 2} \sqrt{2 g}

(8)

where

C_d – discharge coefficient

L – bottom length of weir crest

σ – drowned flow reduction factor

Villemonte’s submerged weir (non-overtopping) equation (Villemonte, 1947: equations 9 and 10) relates the free-flowing discharge Q₁ under unsubmerged conditions (Figure 16) with head h₁ to the backflow Q₂ due to the submergence with head h₂ through the coefficient of discharge C_d (estimated using equation (8)). The coefficients β₀ and β₁ depend on the geometry of the weir and pool dimensions. However, a constant value of β₁ = 0.385 holds suitable for all submerged weir conditions.

C_{d} = β_{0} {(1 - \frac{Q_{2}}{Q_{1}})}^{β_{1}}

(9)

C_{d} = β_{0} {(1 - {(\frac{h_{2}}{h_{1}})}^{1.5})}^{β_{1}}

(10)

Figure 16.

Illustration of a submerged non-overtopping flow over a rock weir (a) cross-section and (b) longitudinal section through the centerline.

Estimation of discharge coefficients for step-pools was first attempted by Fuentes-Pérez et al. (2017) on a field arrangement of a step-pool nature-like fishway consisting of four cross-walls along a bypass channel 2.712 m wide and 2.9% bed slope constructed for a design discharge of 0.4 m³/s. The cross-wall has two notch openings of mean width of 0.207 m and a 0.208 m wide slot. The ratio of combined weir opening to the channel width (b_r) is 0.23. The experiments covered multiple scenarios at discharges 0.329 and 0.455 m³/s, amounting to 45 datasets. The best fit curve that satisfies equation (10) produced β₀ = 0.812 and β₁ = 0.335 at R² = 0.755 (Fuentes-Pérez et al., 2017). However, maintaining a constant value of β₁ = 0.385 (Villemonte, 1947; Hegberg et al., 2001) produced β₀ = 0.843 with R² = 0.72 and RMSE = 0.070.

The present study data comprising 45 data points are plotted in Figure 17(a) to illustrate the distribution of C_d with respect to varying h₂/h₁ for flows with h₂ > 0 indicating submerged weir opening crest conditions (non-overtopping weir). While b_r ≥ 0.45 followed an inverse power relation similar to the pattern observed by Fuentes-Pérez et al. (2017) for step-pool nature-like fishways and by DVWK (2002) for broad crested weir, b_r = 0.10 and 0.25 shows an upward trend due to high flow as a result of the increased flow contractions. However, lower discharges of b_r = 0.10 and 0.25 gave similar ranges of C_d as for the other cases of b_r. Therefore, the limits of validity of this modified weir equation were checked by analyzing the variation of h₂/h₁ with specific discharge q, as illustrated in Figure 17(b). The Villemonte’s equation holds good for the present study data with q < 1 m³/s/m.

Figure 17.

Data used for fitting Villemonte’s submerged weir equation (a) variation of C_d with the flow head ratio h₂/h₁ for the entire dataset, (b) flow head ratio as a function of q, and (c) curve fitting for present study data for q < 1 m³/s/m and Fuentes-Pérez et al. (2017).

A set of 43 field data points were digitized from the graphical plot presented in Fuentes-Pérez et al. (2017). The present study data with q < 1 m³/s/m were considered for curve fitting (Figure 17(c)). Adding the present study data to the results of Fuentes-Pérez et al. (2017) produced more diversity in the dataset by incorporating different weir opening widths and higher discharge scenarios. The modified values obtained are β₀ = 0.809 and β₁ = 0.326 with an R² of 0.73 and RMSE of 0.05. Applying a constant value of β₁ = 0.385, β₀ was obtained as 0.850 with an R² of 0.71 and RMSE of 0.05. The plots reveal that the numerical simulations of step-pool NLFs generates similar flow characteristics as the field observations of the step-pool bypass channel, within the extents of applicability. The C_d values in the present study for submerged non-overtopping weir flows varies between 0.56 and 0.97, while DVWK (2002) quotes values between 0.6 and 0.8 for round stones and between 0.5 and 0.6 for vortex weirs.

4. Conclusions

Nature-like Fishways (NLFs) are cost-effective and eco-friendly structures that facilitate economic development and ecological conservation. The present study highlighted the benefits of nature-like fishways (NLFs) in the migration and inhabitation of aquatic species. Implementation of locally available bed materials into natural pathways across low-head obstructions can improve the ecological well-being in the vicinity. Since the advent of nature-like fishways has been relatively recent compared to technical fishways, knowledge gaps exist regarding their design and performance. The available design criteria for the step-pool

NLFs specify the minimum values for each of weir opening width, depth of flow over the weir crest, and the pool depth as a factor of the body dimensions of the largest target species. These parameters are site and species-specific, such that field implementations would require elaborate trials to ensure the limiting conditions. Therefore, additional hydraulic criteria for flow depth and maximum values for pool depth, velocity, and turbulent kinetic energy in terms of weir opening width and discharge can help design an optimum step-pool NLF. The present study addressed this gap by analyzing the relationship between these variables and developing rating curves and design charts to ease field implementation. The two parameters of the study were b_r = 0.10, 0.25, 0.45, 0.65, and 1.00 and Q = 0.1–1.5 m3/s, where b_r is the ratio of the weir opening width to the channel width. The performance of the developed NLFs was tested by comparing them with Villemonte’s submerged weir equations for non-overtopping (Fuentes-Pérez et al., 2017) and with Baki et al. (2019) for overtopping cases.

The findings from the numerical modeling of step-pool NLF produced an optimum weir opening width of 0.25 times the channel width. There is less probability of incorporating this value in small streams. However, this can be incorporated in artificial bypass channels constructed around the riverine obstructions while adhering to the minimum width constraints. The actual performance of the fishway, with respect to fish passage efficiency, attraction rates, and fish locomotion, can be assessed only through pilot studies in the field or experiments in eco-hydraulic laboratories through the inclusion of live fish species.

Nevertheless, the bed structure of the step-pool NLF presented in this study can be used to recreate full-scale or pilot models. The rock weir step-pool NLF was designed with a weir opening height of 0.57 m and the height of the weir opening crest from the downstream bed level as 0.70 m (in prototype scale). These dimensions have been arbitrarily fixed in the experimental setup. However, they can be restricted depending on the design flow depth requirements with the aid of design curves presented in this study.

Footnotes

Acknowledgments

The authors thank Flow Science, Inc. for FLOW-3D^® HYDRO software made available through the FLOW-3D Academic Program.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Ministry of Shipping, Government of India (Sanction Order No. S2-25021/2/2017 dated 12/03/2018; Project No. CIE/18-19/269/MOSH/VENU).

ORCID iDs

Sruthi Thazhathe Kalathil

Venu Chandra

Data Availability Statement

The data given in this article are the numerical modeling data used for analysis in the study and are available at HydroShare via

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