Numerical Simulation of the Unsteady 3D Flow in Vertical Slot Fishway—The Impact of Macro-Roughness

Abstract

Vertical slot fishways (VSFs) are crossing devices that are built on rivers or streams. They were initially designed to help salmons to complete their migratory cycle by crossing permanent obstructions. In order to favor the passage of smaller or benthic species, stones or concrete cylinders, called macro-roughnesses, are often inserted at the bottom of the fishway. To study the effects of macro-roughnesses on the flow inside a VSF, three-dimensional unsteady simulations were carried out using the volume of fluid method to model the free surface. In this paper, kinematic quantities obtained by CFD are used to detail the flow inside a VSF with and without macro-roughnesses. It can provide valuable information about the flow characteristics, especially in areas where the experimental measurements are difficult to implement.

1. Introduction

To restore ecological continuity and allow fish species to cross structures that hinder their migration (dams, weirs), crossing devices are built on rivers and streams. Among these devices, the vertical slot fishway (VSF) is the most common kind of fishway in France. It is almost insensitive to changes in upstream and downstream water levels, allowing it to be functional for a wide range of flows. Originally designed for highly migratory species such as salmons, sea trouts or lampreys, this type of device must be adapted to small species with limited swimming capacities in order to restore biological connectivity. To this end, numerous studies have been conducted in recent years to characterize the flow in VSFs according to their main geometric features and to better understand the effect of mean and turbulent flow variables on fish behavior [1,2,3,4,5]. To modify the characteristics of the flow and adapt it to the swimming capacities of small species, the addition of obstacles in the flow has been proposed and studied [6,7,8]. An increasingly common solution to facilitate the passage of small or benthic species is to insert macro-roughnesses (blocks of cylindrical shape or rocks) at the bottom of the fishway [9,10,11]. In this type of configuration, experimental measurements are difficult to obtain because of the complex geometry. Numerical simulations are therefore a valuable alternative. Numerous authors [12] have studied the flows in VSFs through numerical simulation using RANS steady-state modeling, in 2D [13], 2D depth-averaged [11] [14,15,16,17,18,19,20] and in 3D [21,22,23,24,25,26,27,28,29,30,31,32]. However, the flow in VSFs is highly unsteady [5,33] and the presence of macro-roughness makes it strongly three-dimensional [10]. Consequently, steady 2D or 2D depth-averaged models are therefore insufficient. Moreover, it is essential to account for non-uniform and unsteady flows when adapting fishway hydrodynamics to the needs of target species. Therefore, the use of 3D unsteady models such as URANS, LES [24,34,35,36] or DES then becomes necessary to correctly model these flows and, in particular, to access the flow fluctuations in statistical turbulent quantities such as Reynolds stresses or turbulent kinetic energy.

This paper aims to complement the work of Fuentes-Pérez [31] on unsteady numerical flow modeling. For unsteady and 3D flows inside a VSF with macro-roughnesses, URANS and LES models are compared with experimental data to assess their ability to accurately predict the complex flow pattern. In addition, this numerical study highlights the influence of macro-roughness uniformly distributed on the bottom of a vertical slot fishway on the characteristics of the 3D flow.

2. Materials and Methods

2.1. VSF Geometry

This paper investigates a VSF design with a pool geometry similar to the design studied by Calluaud et al. [7] (Figure 1). The length of the pools is L = 0.75 m, and the width of the vertical slots is b = 0.075 m, giving a ratio of L/b equal to 10. The width of the pool is B = 0.675 m, i.e., B/b = 9.

The slope of the VSF was set to s = 7.5%. The average flow depth measured at the center of the pools is equal to 0.30 m. The discharge is fixed to Q = 0.023 m³/s. The macro-roughnesses arranged on the bottom of the VSF model are equally spaced cylindrical studs with a diameter of 0.035 m and a height h_r = 0.05 m.

The density d_r is defined as the ratio of the elementary surface covered by three elements of macro-roughnesses (S_r) to the total surface of the patch of cylinders (S_t) (Figure 2). In the studied configuration, the density is set to d_r = S_r/S_t = 15%.

2.2. Numerical Simulations

The VSF was simulated using Star CCM+ for two methods: URANS and LES. The URANS method (Unsteady Reynolds-Averaged Navier–Stokes) is based on the same principle as Reynolds decomposition, which divides the instantaneous quantities into a sum of a mean and a fluctuating value. Since the averaging process leads to a loss of information, closure models are required to complete the system of equations. Here, the low Reynolds number k–ε model is used. The URANS method takes the unsteady nature of the flow into account, while the RANS method does not.

The LES method (Large Eddy Simulation), however, takes a different approach. It uses a spatial filter to resolve large eddies (resulting from the domain geometry) while modeling only the smaller ones. The Smagorinsky model was used in this simulation. In both numerical simulations, the volume of fluid (VOF) method was implemented to emulate the free surface, which assigns volume fractions of both air and water to each computational cell. For the unsteady simulations, an implicit temporal discretization scheme is used for both methods. A system of two nested loops is employed. The first corresponds to the physical simulation time and captures the unsteady behavior of the flow. The second is nested within the first and aims to reach a provisional steady state. To exit the inner loop and proceed to the next time step, velocity convergence criteria at several monitoring points are applied.

Boundary conditions are schematized in Figure 3. The water levels are imposed at the inlet and outlet. Hydrostatic pressure and the volume fractions of each phase (water and air) are specified at the inlet and outlet of the computational domain. For all solid walls, no-slip wall boundary conditions are applied. The computational domain is extended above the fishway to move the upper boundary away from the region of the free surface. A symmetry condition is imposed on the boundaries of this domain.

The size of the cells (T*) in the various parts of the mesh was defined based on the width of the slot (T*/b). A mesh sensitivity analysis was performed for three different mesh sizes, from the coarsest to the finest: T*/b = 1/2, 1/4, and 1/8 [10]. To estimate the errors due to spatial discretization, the Grid Convergence Index (GCI) method was used [37]. For the URANS method, the T*/b ratio was set to 1/4 (Figure 4), which provides both a good geometric definition and a reduced spatial discretization error. The mean position of the free surface in each of the basins was estimated from the experimentally determined water level. The mesh was refined (T*/b = 1/8) in the region around this surface position (+/− 20%). The part of the domain containing only air (above the free surface) was meshed with T*/b = 1. To simulate the VSF flow near macro-roughnesses, a refinement (T*/b = 1/8) was applied in a region bounded by the height of the cylinders. For the LES simulation, the mesh size used for the URANS simulations was retained for all pools except the third one, which served as the reference pool. In this pool, the core mesh size is T*/b = 1/8 (Figure 4).

The k-ε turbulence model used for URANS simulations is valid down to the wall (low Reynolds turbulence model). Thus, the first inner node of the boundary layer mesh should be located within the viscous sub-layer, at y⁺ = 1, where y⁺ is the non-dimensional wall distance [38], defined as follows:

$$y^{+}={\displaystyle \frac{y_w.u_{\tau }}{\nu }}$$

(1)

where y⁺ is the non-dimensional wall distance, y_ω is the normal distance from the wall (m), u_τ is the wall friction velocity (m/s) and ν is the kinematic viscosity (m²/s).

In URANS simulation, u_τ is estimated from the friction coefficient given by the Schultz-Grunow expression:

$$C_f={\displaystyle \frac{0.37}{{\mathit{log}\left(\frac{U_{\infty }x}{\nu }\right)}^{2.584}}}$$

(2)

where C_f is the friction coefficient (-), U_∞ is the velocity of the flow (m/s), x is the distance in the flow direction (m) and ν is the kinematic viscosity (m²/s).

The same condition must be met in LES to correctly resolve the near-wall region. However, the wall shear velocity was approximated using the URANS results.

The boundary layer mesh thickness δ(x) was estimated to 0.03 m, based on the equation describing the evolution of the turbulent boundary layer thickness over a flat plate [39]:

$${\displaystyle \frac{\delta \left(x\right)}{x}}\cong {\displaystyle \frac{0.37}{R_e(x{)}^{1/5}}}$$

(3)

where δ(x) is the boundary layer thickness (m), x is the distance in the flow direction (m) and R_e(x) is the Reynolds number (-).

In contrast to URANS simulations, the anisotropy of the near-wall mesh must be minimized in LES. To resolve the inner-layer vortices, the streamwise and spanwise grid sizes in wall unit Δx⁺ ≅ 100 and Δz⁺ ≅ 20, respectively, were used [40].

In URANS, a starting water level is imposed at the output of the simulation domain (Figure 5). This results in a residual water level in the VSF. This initial state corresponds to a configuration in which the fishway entrance is closed and the exit remains open. In LES, the initial conditions are derived from the URANS calculations. These include pressure, velocity, and fluid volume fraction.

To meet precision requirements, the computational time step was set to Δt = 10 ms, based on the cell size of the computational domain and the flow kinematics. In the case of the URANS simulation, equilibrium of the water levels in each pool is reached after 20 s. The calculation of statistical turbulent quantities is performed only from this equilibrium state. The overall simulation time was set to 300 s corresponding to the acquisition time of the experimental measurements. As the flow is already fully developed at the beginning of the LES simulations, the total simulation time is based on the convergence of the mean and fluctuating component of velocity in the center of each pool.

2.3. Validation

Experiments were carried out to provide a basis of comparison to the numerical study. They were undertaken in a laboratory VSF, located at the Prime Institute of the University of Poitiers, France. The physical and numerical models of the VSF share identical characteristics (5 pools, B/b = 9, Q = 0.023 m³/s and s = 7.5%). A detailed description of the experimental apparatus is provided in [33]. In the configuration with macro-roughnesses, flow velocity measurements were performed using an Acoustic Doppler Velocimeter (ADV). The sampling rate of the ADV was 50 Hz over a 300 s acquisition time. A phase/space filter was applied [41]. A transverse profile (T) was defined in a plane parallel to the floor at a distance of Z/b = 2 and X/b = 4.67. For this profile, the first and last measurement points were located 50 mm from the walls. A vertical profile (V) was also measured along the Z-axis at Y/b = 2.95 from X/b = 4.5 at the first point, located 10 mm above the macro-roughnesses, to X/b = 4.8 at the free surface. The longitudinal profile L (Y/b = 2.95) was defined along the X-axis at Y/b = 2.95. The sampling interval for all profiles is 15 mm. The location of the profiles is shown in Figure 6.

A comparative analysis of the flow characteristics was conducted to determine which simulation method—URANS or LES—is more appropriate to model the flow. The velocity magnitude and the turbulent kinetic energy were normalized using the maximum velocity defined by

$$V_d=\sqrt{2·g·s·L}$$

(4)

where V_d is the maximum velocity (m/s), g is the acceleration due to gravity (m/s²), s is the slope of the VSF and L is the length of the pools (m).

The 3D non-dimensional magnitude of the flow velocity and turbulent kinetic energy profiles obtained from experimental measurements and from both URANS and LES simulations are plotted in Figure 6. As mentioned above, the estimated errors due to spatial discretization in the URANS simulations were assessed using the Grid Convergence Index (GCI) method [37]. For the experimental measurements, uncertainties were estimated on the specifications provided by the ADV manufacturer. The method used to assess these uncertainties follows the Guide to the Expression of Uncertainty in Measurement [42]. The total relative uncertainty associated with each mean velocity component was calculated using the general uncertainty propagation equation, with a coverage factor of k = 2 (corresponding to a 95% confidence interval). Based on the uncertainties in both the mean and instantaneous velocity, the uncertainties in the mean velocity magnitudes (4%) and in the turbulent kinetic energy (12%) were determined [43]. These uncertainties are represented as error bars in Figure 6.

To compare the experimental and numerical results, the correlation coefficient r² and the relative standard deviation ${\sigma }_m$ between the curves were calculated. The correlation coefficient was used to quantify the degree of agreement between the experimental and numerical data. The values of ${\sigma }_m$ and r² are reported in

Table 1. σ_m and r² values calculated between the velocity and turbulent kinetic energy profiles obtained from numerical simulations and those derived from the experimental measurements.

		Profile T		Profile V		Profile L
		${\mathit{\sigma }}_{\mathit{m}}$ (%)	$\mathit{r}²$ (-)	${\mathit{\sigma }}_{\mathit{m}}$ (%)	$\mathit{r}²$ (-)	${\mathit{\sigma }}_{\mathit{m}}$ (%)	$\mathit{r}²$ (-)
${\displaystyle \frac{{‖V‖}_{3D}}{V_d}}$	URANS	28.8	0.87	15.7	0.56	22.6	0.92
	LES	28.5	0.89	14.2	0.91	11.3	0.95
${\displaystyle \frac{k_{3D}}{V_d^2}}$	URANS	66.0	0.95	55.4	0.55	65.0	0.26
	LES	28.8	0.98	27.0	0.74	38.0	0.64

.

The mean velocity curves ${\displaystyle \frac{{‖V‖}_{3D}}{V_d}}$ of the transverse profiles T obtained from both URANS and LES simulations are similar to those obtained experimentally. The jet flow induces a sharp increase in both velocity and turbulent kinetic energy at Y/b = 3. On either side of the jet, two lower-intensity zones with local velocity minima reveal the presence of two recirculation zones indicating the existence of the first flow pattern [1]. Both URANS and LES simulations clearly capture this flow topology.

This visual observation is confirmed by high correlation coefficients, for both the URANS and LES simulations (Table 1). The errors on the mean velocity are nearly equivalent in URANS and LES and remain relatively low for all profiles T, V and L (${\sigma }_m$ = 18.7% for the LES and ${\sigma }_m$ = 19.3% for the URANS). The turbulent kinetic energy ${\displaystyle \frac{k_{3D}}{V_d^2}}$ is underestimated by both methods. However, LES models turbulent kinetic energy more accurately than URANS for all profiles with ${\sigma }_m$ = 27% compared to ${\sigma }_m$ = 58.5% for URANS. It is worth noting that the correlation coefficients between the LES simulation and the experimental profiles are higher for profiles T, V and L than those obtained using the URANS method. This indicates that LES provides a more accurate distribution of turbulent kinetic energy in the flow within the VSF.

Regarding computation time, it is intrinsically dependent on the methods and the respective mesh resolution. For the VSF configuration studied, 320 s of unsteady flow was simulated. For the URANS method, the computational time per iteration is 1.9 s on a machine with 128 cores. For LES, this time increases to 5.2 s per iteration. This corresponds to a total computation time of 17 h for the URANS method, compared with 46 h for LES. Turbulent kinetic energy plays a key role in fish behavior within the basins and in their ability to pass through them. The LES simulation provides more accurate results for TKE than URANS, justifying its use despite the higher computational cost, which remains reasonable (under two days).

3. Results

During the validation of the numerical simulations, the velocity profiles discussed in the previous section highlighted the three-dimensional nature of the flow. This is also clearly illustrated in Figure 7 and Figure 8, which show the influence of macro-roughnesses on the three-dimensionality of the flow. These figures display the mean flow streamlines in a micro-pool basin with and without macro-roughnesses, simulated using LES. In the smooth configuration, the two-dimensional nature of the flow is confirmed, with vortex structures whose centers remain aligned along a vertical axis. In configuration with dr = 15%, the lower vortex also retains a vertical axis. However, the axis of the upper vortex becomes steeply inclined, turning horizontal near the macro-roughnesses. This development highlights a significant modification of the mean flow, which becomes three-dimensional well beyond the immediate influence of the canopy. The jet remains, on average, two-dimensional. It feeds the upper recirculation zone by plunging towards the central deflector, primarily due to the strong velocity gradient induced by the presence of macro-roughness.

The LES model was used to study the flow generated both through and over the macro-roughnesses. The flow is primarily described using two normalized heights (Z/hr) and (Z/b) relative to the roughness height (hr) and the slot width (b) in order to facilitate comparisons with results from the literature.

Regarding the macro-roughness configuration, the flow topology on the plane furthest from the floor (Z/hr = 4.5) is consistent from one basin to the next. The jet follows a curved trajectory, generating two counter-rotating recirculation zones on either side. Compared to the smooth floor configuration, the upper vortex is deformed and its center is shifted downstream. At Z/hr = 1.2, the flow remains nearly identical in each basin, although it appears more disturbed, particularly in the upper vortex, which exhibits a less well-defined structure. This flow pattern, referred to as type 1, was clearly identified by Wang [5].

The Z/hr = 0.75 plane provides a useful view of the average flow within the canopy’s macro-roughness elements. When encountering the first macro-roughness, the jet splits into two asymmetrical parts. At the bottom of the various basins, most of the flow is directed to the right of the first macro-roughness, flowing directly to the second element located along the same alignment. It then divides into two fairly symmetrical streams and continues toward the downstream slot, following the path formed by the aligned macro-roughnesses. The second part of the flow is deflected to the left of the first macro-roughness towards the opposite wall of the slot. This portion then encounters other macro-roughnesses aligned along a diagonal centered on the first cylinder and oriented at an angle of 60° to the longitudinal axis. As a result, the jet is distributed over a large portion of the available canopy surface, generating numerous wake zones and promoting the dissipation of turbulent kinetic energy. In Figure 9, the iso-contours of the mean velocity field in the vertical planes passing through the center of the slots show that the jet experiences greater velocity variations across the water column in this configuration than in the configuration without macro-roughnesses.

Figure 10 shows the spatial distributions of the mean velocity magnitude and the turbulent kinetic energy on a plane close to the bottom with and without macro-roughnesses. It is clearly observed that the presence of roughness reduces the regions of high intensity, both in terms of velocity and turbulent kinetic energy. The roughness element near the bottom diffuses the jet, causing it to widen and fragment across the entire basin surface. The vertical extent of the flow influenced by the roughness is also significant, as illustrated in Figure 11. These figures demonstrate that the peaks in velocity or TKE magnitude are dampened by the presence of roughness over a substantial layer near the bottom of the basins. As a result, in this near-bottom region, the local flow characteristics become more favorable for the movement and development of fish with more limited swimming capabilities, particularly benthic species.

This three-dimensionality of the flow also influences the flow dynamics as described in [7]. Unsteady phenomena, such as jet oscillation (or “jet beating”), do not necessarily exhibit the same frequency and amplitude throughout the entire water column. To verify this (Figure 12), instantaneous velocity fields of the three phases of the flow were plotted on a plane at Z/hr = 3 and simultaneously on a plane close to the roughness element at Z/hr = 1.2. Between these two planes (Z/hr = 1.2 and Z/hr = 3), the unsteady flow structures differ significantly. In particular, during phase (b), the velocity burst feeding the upper recirculation zone is not observed in the plane closest to the bottom. This observation aligns with the previous analysis of the mean flow field, which showed that the upper vortex was strongly inclined, suggesting it is primarily fed “from above”.

In the configuration with dr = 15%, the flow is generally less intense in the upper recirculation zone, regardless of the phase observed. This reduction in kinetic energy in the main flow is a consequence of the increased dissipation near the bottom within the rough underlayer. The high rate of turbulent kinetic energy dissipation within the canopy and in the rough underlayer is illustrated in Figure 13.

Beyond the zones of high turbulent kinetic energy (TKE) dissipation located near the walls, it is essential to evaluate the capacity of the numerical simulation to capture the full range of turbulent scales. To this end, the temporal evolution of the velocity magnitude was compared at a representative point (X/b = 2.4 and Y/b = 3.2, Z/hr = 3) where TKE levels are high (Figure 14). A significant difference is observed between the results depending on the simulation methods. The amplitude of velocity fluctuations is considerably reduced in the URANS model compared to the LES model. A Fourier analysis of the velocity data highlights the intrinsic characteristics of each method. The URANS approach explicitly resolves only the largest scales of motion and models the smaller-scale fluctuations representative of turbulent agitation. It thus behaves as a spatial or temporal filter. The cut-off frequency of this filter is defined by the integral scale (length or time) of the turbulence model, which, for the chosen mesh and time step, corresponds to 1 Hz. In contrast to the RANS method—which models all scales of turbulence—the LES (Large Eddy Simulation) method resolves the large-scale structures, which are strongly influenced by the geometry, and only models the smaller more universal scales. A spatial filter is implicitly defined by the mesh size, determining which scales are resolved and which are modeled. In our LES simulation, the FFT spectrum of the velocity magnitude shows significant amplitudes at high frequencies, indicating that the mesh accurately resolves the energy cascade down to small-scale eddies, as discussed by Quaresma et al. (2025) [36].

4. Conclusions

The objective of this study was to validate unsteady 3D flow simulations inside a vertical slot fishway with and without roughness elements placed on the bottom of the pools. LES and URANS simulations were performed in the presence of a free surface and compared to ADV measurements conducted in the same geometry. Overall, the LES results showed better agreement with the experimental data than those obtained with URANS. Therefore, the analysis of flow behavior—with or without macro-roughnesses—should primarily rely on LES results. Moreover, LES provides a more accurate description of the unsteady nature of the flow. While the average velocity tends to be slightly overestimated and TKE is underestimated by approximately 30%, the overall flow topology and the spatial distribution of the kinematic quantities closely match experimental observations.

The hydraulic analysis revealed that adding macro-roughnesses inside the VSF alters the flow structure. To quantify this influence, velocity and turbulent kinetic energy profiles were compared between the smooth configuration and the roughened configuration with dr = 15% using LES simulations. For the studied basin width (B/b = 9), the presence of macro-roughnesses enhances the three-dimensionality of the mean flow by tilting the axis vortex of the upper recirculation zone. The analysis of unsteady flow demonstrated that the three characteristic flow phases observed in a conventional VSF are still present when macro-roughnesses are introduced. However, in the roughened sub-layer, the dynamics and intensity of these unsteady phases are reduced due to increased energy dissipation. Since the overall dynamics in the water column are not negatively affected, macro-roughnesses do not impair the hydraulic efficiency of the VSF.

On the contrary, the flow dynamics near the bottom are significantly modified by the roughness elements, suggesting an increase in passage efficiency for benthic species. The size and spacing of the macro-roughnesses will need to be optimized based on the target fish species present in the river system. To confirm the conclusions of this study, field trials on existing vertical slot fishways will be conducted by the Office Français de la Biodiversité (OFB) over the next two years.