# Design optimization of a trash-rack bar for hydro power plant fish friendly water intakes

Guillaume Bon, Ludovic Chatellier, Yves Le Guer, Cécile Bellot, Xavier Casiot, Nassim Razaaly, Laurent David

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Guillaume Bon, Ludovic Chatellier, Yves Le Guer, Cécile Bellot, Xavier Casiot, et al. Design optimization of a trash-rack bar for hydro power plant fish friendly water intakes. 10th International Symposium on Hydraulic Structures (ISHS 2024), ETH Zürich, Jun 2024, Zürich, Switzerland. pp.681 - 690, 10.3929/ethz-b-000676014. hal-04864150

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# Design optimization of a trash-bar for hydro power plant fish friendly water intakes

## Conference Paper

## Author(s):

Bon, Guillaume; Chatellier, Ludovic; Le Guer, Yves; Bellot, Cécile; Casiot, Xavier; Razaaly, Nassim; David, Laurent

## Publication date:

2024

## Permanent link:

https://doi.org/10.3929/ethz-b-000676014

## Rights / license:

Creative Commons Attribution 4.0 International
# Design optimization of a trash-rack bar for hydro power plant fish friendly water intakes

G. Bon<fnref n="1" />, L. Chatellier<fnref n="1" />, Y. Le Guer<fnref n="2" />, C. Bellot<fnref n="3" />, X. Casiot<fnref n="3" />, N. Razaaly<fnref n="1" /> & L. David<fnref n="1" />

E-mail: guillaume.bon@univ-poitiers.fr

**Abstract:** Ecological continuity in rivers has become a major concern for low-head hydroelectric power plants. The implementation of new fish protection systems and particularly the updated recommendations regarding inclined trash-racks with small bar spacing, present new challenges. The bar profile of the trash-rack is crucial for reducing head losses and preventing clogging issues. This paper presents the findings of the optimization of an inclined trash-rack bar design for hydroelectric power plant water intakes. It consists in minimizing the head loss coefficient and drag force coefficient of bars while considering dimensioning and feasibility constraints. A parameterized profile is defined to ensure feasible bar shapes in large volumes. The head loss and drag coefficient are calculated using 2D CFD simulations and a genetic algorithm is used to perform a global optimization. In previous bar shape studies, researcher primarily focused on some profiles with low head losses and with specific circular spacers. However, bar shapes must be adapted for different types of spacers, especially with circular and comb spacers. The inclination angle of the trash-rack is also an important parameter to consider when looking for a suitable bar profile. This work aims to address to the adaptation of profiles based on new recommendations for trash-rack inclination and new techniques for maintaining bar spacings. New profiles with minimal head losses have been found for specific trash-rack configurations.

**Keywords:** Trash-rack, Head loss, CFD simulations, Optimization, Fish guidance intake structure, Fluid mechanics.

## 1. Introduction

The increased concern for biodiversity and ecological continuity in rivers has prompted new recommendations from European and National organizations (Courret and Larinier 2008). To ensure downstream fish migration, inclined trash-racks with small bars spacing and bypasses have been installed in power plants intake. Inclined trash-racks have been used for a long time but the narrow bar spacings and trash-rack inclination angle recommendations lead to new problems and operational difficulties, such as intense clogging, particularly during the autumn season. The angle of inclination of the trash-rack has been lowered and now set around 26 degrees to ensure effective attraction of bypasses for downstream migration, including trout, salmon and eels (Courret et al. 2015). Reducing the bar spacing to 20 mm has led to increased clogging problems (caused by leaves, pebbles, etc.) during fall season. Even small leaves can now be trapped by the trash-rack. The bar profile has also an impact on the clogging issue that must be considered when designing the shapes of these bars. These new problems have prompted the search for new bar shapes that minimize head losses for trash-racks inclined at 26 degrees and avoid the sediments retention.

Simple rectangular bars have been gradually replaced by more streamlined bar shapes, often comprising circular, ellipsoidal, and foil-shaped tips (Meister et al. 2020, Lemkecher et al. 2020). These new designs have significantly reduced the head losses through inclined trash-racks, making them essential for trash-racks with small bar spacing. Most of the selected bar profiles are adapted to trash-rack assemblies using circular spacers (Figure 1) that comply with the existing recommendations. A flat section is therefore needed on the profile to allow the use of such compressed cylindrical spacers. Although circular spacers are commonly used, new types of comb spacers are increasingly used (Figure 1). Those consists in a laser-cut bar holders designed according to the bar shape on which they are welded. This new solution opens the door to new shapes of hydrodynamic bar that have rarely been used due to their higher complexity of assembly.

The objective of this study is to develop a new profile suitable for new configurations, spacers technology, and clogging issues. Design optimization is an appropriate approach to create the new profile with minimal head losses. Free-Form optimization (Sederberg and Parry 1986) can be performed to find new shapes based on a trivariate Bernstein polynomial. This consists in a manipulation of control points that allows a free deformation of the initial profile. The method is mainly used for aerodynamic profiles optimization (Hu et al. 2022, Anitha et al. 2011). The process does not really seem adapted for the studied case. To implement the bar in large volumes, using too complicated shapes could be very difficult to construct and with a high cost. A second approach is to parametrize the

<footnote n="1">¹Institut PPRIME, UPR3346, CNRS, Université de Poitiers, ENSMA, 86073 Poitiers, France.</footnote>

<footnote n="2">²Laboratoire SIAME, Université de Pau et Pays de l'Adour E2S UPPA-IPRA, 64000 Pau, France</footnote>

<footnote n="3">³France Hydro Electricité, 75008 Paris, France.</footnote>
bar profile by associating shape elements according to a set of adjustable coordinates and dimensions (Park et al. 2009). Research works on bar shape optimization are rather rare. Lučin et al. (2020) designed some optimized forms for hydroelectric power plant intake systems. A simplified geometry was used in order to perform optimization of the head loss coefficient of a trash-rack with horizontal bars. The lack of studies on this subject and the recent modifications of trash-rack bar fixations have prompted the need to perform such optimization processes. In the present study, a multi-objective genetic algorithm (MOGA) (Murata and Ishibuchi 1995) is used to optimize the head loss and drag force coefficient for a specifically designed family of bar profiles. Constraints are applied to the optimization process in order to comply with mechanical requirements, clogging aspects and spacer technology.

<figure><img src="image_2.png" /><figcaption>**Figure 1.** Section of a trash-rack with circular spacers (on the left) and comb spacers (on the right).</figcaption></figure>

## 2. Model and methods

### 2.1. Parameterized bar shape

The bar shape is defined by a series of simple forms, including circular arcs and straight lines. Figure 2 illustrates the parameterized bar shape. The space between two bars is fixed at 20 mm as actual recommendations (Courret and Larinier 2008, Ebel G. 2013, among others). Each parameter (shown in blue) can vary and change the overall shape. Table 1 indicates the limits of each parameter. The leading-edge consists of a circular arc whose radius is fixed to 4 mm to ensure a constant trash-rack obstruction ratio. Point p1 represents the end point of the circular leading edge and is parametrized by the distance between this point and the origin point (0,0) in the x-direction ($x_1$). The profile is terminated by a semi-circular trailing edge of radius $R_2$. The trailing edge and leading edge are connected to a central section using three additional segments. Along the profile, parameters $d_i$ and $y_i$ control the distribution of the intermediate point $i$ defining the connecting segments. The width parameters are limited to 4 mm maximum to avoid any increase of the obstruction ratio, and the position parameters allow profiles of 192 mm maximum depth $p$ ([m]). A constraint limits the maximum total depth $p$ to 120 mm. The succession of these simple forms allows a wide range of possible shapes, from a circle to a flattened airfoil profile, with the possibility of obtaining rounded rectangles or a teardrop-shaped bars.

<figure><img src="image_3.png" /><figcaption>**Figure 2.** Parametrization of the bar shape for optimization.</figcaption></figure>
<table><caption>**Table 1.** Dimensional limits for each parameter defining the shape of the bars.</caption><thead><tr><th></th><th>x1 [mm]</th><th>D2 [mm]</th><th>Y2 [mm]</th><th>D3 [mm]</th><th>Y3 [mm]</th><th>D4 [mm]</th><th>R2 [mm]</th></tr></thead><tbody><tr><th>Lower bound</th><td>4</td><td>0</td><td>0.5</td><td>0</td><td>0.5</td><td>0</td><td>0.5</td></tr><tr><th>Upper bound</th><td>8</td><td>60</td><td>4</td><td>60</td><td>4</td><td>60</td><td>4</td></tr></tbody></table>

As shown in Figure 3, the flow can be considered 2D and parallel to the channel floor, even between the bars. This assumption has been numerically verified by 3D simulations and PIV measurements on existing trash-racks. Therefore, the section of the bar traversed by the flow is not the nominal section, but rather a section projected in the flow plane, as long as it is distant from the spacers and the free surface. Once defined, the inclined bar shape section is then transformed according to this projection.

<figure><img src="image_4.png" /><figcaption>**Figure 3.** Projection of the bar profile to be adapted to a 26 degrees inclined trash-rack.</figcaption></figure>

## 2.2. Flow simulation

Computational fluid dynamics (CFD) is employed to determine the drag and head loss coefficient of a bar subset. The OpenFOAM computational library is used for these simulations. The Reynolds number of the bar $Re_b$ [-] indicates a moderately turbulent flow regime (see Table 2). Meusburger H. (2002), Raynal et al. (2013) and Albayrak et al. (2018, 2020) investigated the impact of the Reynolds number on the head loss coefficient and confirmed its independence for Reynolds numbers greater than approximately 1500. The Reynolds-averaged Navier-Stokes equations (RANS) is solved using the simpleFoam solver, in which the pressure-velocity coupling is accomplished with the Semi Implicit Linked Equations algorithm. The $k-\omega$ SST turbulent model has been chosen as it has already provided accurate results for such simulations (Raynal et al. 2013). Wall functions are applied to $\omega$ and $\nu$. The turbulence intensity (TI) is set on to 5 % as Raynal et al. (2013) demonstrated the independence of head loss results for turbulence intensity ranging from 1% to 10 %. As illustrated in Figure 4, a central bar is inserted in the domain with two half-bars on each side to model the influence of neighbouring bars. Symmetry conditions are set on the sides of the fluid domain to represent an infinitely large trash-rack. The inlet velocity $v$ [m.s$^{-1}$] is set to a standard velocity present in such channel (0.7 m.s$^{-1}$). The mesh is structured (see dimensions at Table 2) and then refined close to the bars to ensure a dimensionless wall distance $y^+$ values lower than 5. Mesh convergence tests have been carried out to validate the chosen meshing parameters.

<table><caption>**Table 2.** Characteristics of the simulation domain.</caption><thead><tr><th rowspan="2">U<sub>0</sub> [m.s<sup>-1</sup>]</th><th rowspan="2">Re<sub>b</sub> [-]</th><th colspan="2">Domain</th><th colspan="2">number of cells (structured)</th><th colspan="2">Cell size (structured)</th><th colspan="2">y<sup>+</sup> [-]</th></tr><tr><th>x [m]</th><th>y [m]</th><th>N<sub>x</sub> [-]</th><th>N<sub>y</sub> [-]</th><th>x [m]</th><th>y [m]</th><th>Mean</th><th>Max</th></tr></thead><tbody><tr><td>0.7</td><td>5600</td><td>0.5</td><td>0.056</td><td>900</td><td>300</td><td>5.56 x 10<sup>-4</sup></td><td>1.87 x 10<sup>-4</sup></td><td>1</td><td>5</td></tr></tbody></table>
<figure><img src="image_5.png" /><figcaption>Figure 4. Numerical domain for the optimization process (a) and an example of the refinement at the leading edge of a profile.</figcaption></figure>

## 2.3. Functions to optimize and constraints

The optimization function is set to the head losses coefficient (Lučin et al. 2020) and the drag force coefficient (Park et al. 2009). The head loss coefficient is calculated from the pressure difference between two sections, far from upstream and downstream of the bars (see Eq. (1)). The independence of pressure average depending on the position of each section have been tested.

The nondimensional head loss coefficient $\xi$ [-] is:

$$ \xi = \Delta p \frac{2}{\rho \nu^2} \qquad (1) $$

Where $\Delta p$ the pressure drop [Pa], $\rho$ the water density [kg.m⁻³] and $\nu$ the velocity [m.s⁻¹].

The head loss coefficient corresponds to a rack inclined at 26 degrees as the profile is deformed by projection to this angle (see Figure 3). The drag force coefficient is directly calculated by the OpenFOAM solver. The force applied on the profile is obtained by integrating the pressure and the stress tensor along the profile. The drag coefficient is then calculated directly from the drag force (see Eq. (2)). The reference area is set to the projected area see by the flow and so calculated using the width of the bar $b$ ($b = 2R = 8 mm$).

The nondimensional drag force coefficient $c_d$ [-] is:

$$ c_d = \frac{2F_d}{\rho\nu^2 A} \qquad (2) $$

Where $F_d$ is the drag force [N] and $A$ the reference area [m²]

Some mechanical constraints may be added depending on the optimization goal. For example, the total depth of the bar is constrained to a minimum value. A bar with a small depth can be challenging to assemble with spacers and can be more prone to bending during clogging seasons and cleaning operations. A small bar depth requires additional spacers and supports to compensate the lack of rigidity. However, these additional supports inevitably increase the head loss. A flat part of minimum length can be constrained to ensure the good positioning of the circular spacers. On the other hand, for comb spacers, it is possible to impose a slope for each profile section to facilitate drainage of pebbles through the bars. The limits of each design parameters represent additional dimensioning constraints. The location of the maximum width is fixed by the leading circular arc at the upstream section of the bar to guarantee an efficient trash-rack cleaning performance. The coefficients for head loss and drag force are determined by conducting a 2D CFD simulation for each bar shape during the optimization process.

## 2.4. Genetic algorithm

The optimization is performed using Sandia laboratory's DAKOTA optimization software (Adams et al. 2021). A genetic algorithm is used to perform multi-objective multi-parametric constraint optimization. A multi-objective genetic algorithm (MOGA) method is performed. The genetic algorithm is inspired by biology and utilizes techniques such as crossover, mutation and selection, which makes it well suited to such simulations. Its ability to find the global minimum and not just a local minimum is really useful for optimizations with many parameters and multiple local minima. The algorithm consists of several steps. A population of 50 bar shapes is primarily initialized, then, the algorithm enters in a loop to optimize the profile. An evaluation of the population thanks to the 2D simulation is performed. A part of the population is then selected by a fitness calculation method and the selected "parents" pass through a crossover step to produce "children". A mutation is applied to certain members of the population to ensure that the algorithm do not get caught by a local minimum. The new population then replaces the initial population and
the loop continues until the convergence criteria is satisfied. For the crossover method, the choice is to use a random shuffle method. It consists in a creation of children from a combination of parameters of its two parents randomly. These children will get some parameters from one parent, and others from the second parent. The crossover rate is fixed to 0.8. The mutation process involves modifying certain parameters of some members of the population to avoid getting trapped in local minima. The mutation method used consists in a parameter replacement by randomly selecting and modifying a design parameter to another valid value. The mutation rate has been set to 0.08. The global parameters of the optimization method are summarized in Table 3.

<table><caption>**Table 3.** Optimization parameters.</caption><thead><tr><th>Method</th><th>Convergence tolerance</th><th>Maximum function evaluations</th><th>Mutation rate</th><th>Crossover rate</th><th>Initial population</th></tr></thead><tbody><tr><td>MOGA</td><td>1e<sup>-6</sup></td><td>1000</td><td>0.08</td><td>0.8</td><td>50</td></tr></tbody></table>

### 3. Sensitivity analysis

The dependence of objective functions on all parameters simultaneously creates complexity in examining the relationship between individual parameters and optimization functions. In order to determine this correlation despite the parameter dependency, a sensitivity analysis is performed. A LHS sampling procedure (Mckay et al. 1979) is implemented to create a quasi-random bar-shaped population of 2000 members in the global space. From the simulations of this population, the relationship between each parameter and the head loss coefficient is determined. The sensitivity coefficient is defined as a partial rank correlation coefficient (PRCC).

The partial rank correlation coefficient is:

$$PRCC_{x_j, y} = \frac{cov((x_j - \hat{x}_j), (y - \hat{y}))}{\sqrt{var(x_j - \hat{x}_j)var(y - \hat{y})}} \quad (3)$$

where $x_j$ is a parameter of the bar design [m], $y$ the objective function (the head loss coefficient for example) [-], $\hat{x}_j$ and $\hat{y}$ are linear regressions. $\hat{x}_j = c_0 + \sum_{p=1, p \neq j}^{N} c_p x_p$ and $\hat{y} = c_0 + \sum_{p=1, p \neq j}^{N} c_p y_p$. $c_p$ are constants values [-] and N is the number of parameters [-].

This coefficient is highly resilient for sensitivity analysis since it measures non-linear but monotonic relationships between an entry parameter and the objective function (Marino et al. 2008). The LHS matrix is ranked and then the partial rank correlation coefficient (PRCC), expressed in Eq (3), is calculated. The coefficient varies between -1 and +1 where 0 represents independence from the analyzed parameter.

The sensitivity of the head loss coefficient to each parameter is illustrated in Figure 5. The linear interpolation of each graph illustrates the overall trend of the head loss coefficient in relation to the governing parameter. The head loss coefficient generally increases with each parameter particularly for the trailing edge (R2), as shown in Figure 5 (a) and the different distances (d2, d3 and d4), presented in Figures 5 (b), (d), and (f). This graph provides some information on the impact of each parameter, but it is more qualitative than quantitative. To quantify this global dependence, the partial rank correlation coefficient is plotted for all parameters in Figure 6. The trailing edge of the profile (R2) appears to have the greatest impact on the head loss coefficient as its correlation coefficient (PRCC) almost reaches 0.8 (see Figure 6). The total length of the profile (x1 + d2 + d3 + d4 + R2) is also of significant influence. The impact of the width of the bars at positions 2 and 3 (y2 and y3) appears to be less important even if their impacts are not negligible regarding to their PRCC values. This phenomenon can be explained by the fact that the leading-edge radius is fixed to a greater value than the width limits for points 2 and 3. The correlation between the head loss coefficient and the drag coefficient is significant and the same observations holds true for the drag coefficient.
<figure><img src="image_6.png" /><figcaption>**Figure 5.** Evolution of the head loss coefficient depending on each inlet parameter.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>**Figure 6.** Partial rank correlation coefficient (PRCC) between each dimensional parameter and the head loss coefficient.</figcaption></figure>

## 4. Results and discussion

Two different optimizations are produced. The first one is computed without any constraints to allow the identification of a global optimum (see Eq. 4). Such an unconstrained profile maybe be better suited to laser cut comb spacers. A MOGA optimization is used to determine a global minima and the algorithm has converged in less than 500 members.
Figure 7 displays the head loss coefficient based on member generation. The algorithm converged to the final minimum head loss coefficient, represented by a blue line. For the latest generations, practically all individuals have a head loss coefficient near to the minimum. Only some mutated members appear with higher head loss coefficient. The drag force coefficient and the head loss coefficient have a strong correlation, as evidenced by the correlation factor of more than 0.96 measured during the sensibility analysis. Similar outcomes were observed for the head loss coefficient and the drag force coefficient. The Pareto front provides a pair of two closely located global solutions.

The optimization goal is:

$$ \begin{cases} \min \xi(\theta) \\ \min c_d(\theta) \end{cases} \qquad (4) $$

Where $\theta$ represents the design vector, whose limits are explained in Table 1.

<figure><img src="image_8.png" /><figcaption>Figure 7. Head loss coefficient $\xi$ as a function at the number of the bar profile (the blue line represents the optimum $\xi$).</figcaption></figure>

Figure 8 illustrates the final profile shape found with this optimization process. The profile has a small depth of 26 mm and takes on the shape of an elongated water droplet. According to Table 4, the head loss coefficient of the shape, optimized for a rack inclined at 26 degrees, is lower than for other classical or modified profiles. This is also true for the drag force coefficient. The results presented for the various classical profiles have been calculated using the same 2D simulation with a 26 degrees projection as the optimized profiles, allowing for direct comparison. The head loss coefficient for the classical profiles calculated using the 2D simulation are higher than calculated using the analytical formula of Meister et al. (2020). The determination of the head loss is here calculated using pressure difference thanks to simple 2D simulations rather than head difference. Assuming a 2D simulation and using the pressure difference may explain the observed difference without compromising the optimization process as all profiles are compared with the same method. The optimized profile is slightly better than other streamlined profiles but it cannot be directly compared to them due to its shallower bar depth. The second optimization is performed to find a profile adapted to circular spacers hence reserving a flat part to position circular spacers. A minimum of 20 mm flat part is added as a constraint, as feedback from circular spacers used in existing HPPs seem to have diameters no lesser than 20 mm. Figure 9 shows the optimized resulting profile for this optimization. Its depth is approximately 41 mm with a flat part of 20 mm. The optimized profile is very similar when a 30 mm minimum flat part is imposed in case of larger spacers. This profile also presents a very small head loss coefficient (see Table 4) and is similar to the S4 foil shaped profile designed by Meister et al. (2020). It differs from an ellipsoidal or circular tip profile by the angle of the slopes between the points p1 and p2, and the points p3 and p4. Here, the resulting mild slope avoids a recirculation zone, which can cause clogging issues on the trash-rack and result in increased head losses. These two profiles are optimized for a 26 degrees inclination of the trash-rack, at which they minimize the head losses and should prevent clogging issues (particularly with bars with comb spacers).
<figure><img src="image_9.png" /><figcaption>**Figure 8.** Optimized profile without a constraint for circular spacers.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>**Figure 9.** Optimized profile with a constraint to place circular spacers.</figcaption></figure>

<table><caption>**Table 4.** Comparison of head loss coefficient and drag coefficient for different profiles, $C_p$ is the pressure coefficient (form drag) [-] and $C_f$ the friction coefficient (friction drag) [-].</caption><thead><tr><th>Bar shape</th><th>depth [mm]</th><th>ξ [-]</th><th>C<sub>d</sub> [-]</th><th>C<sub>p</sub> [-]</th><th>C<sub>f</sub> [-]</th><th>C<sub>p</sub>/C<sub>f</sub> [-]</th></tr></thead><tbody><tr><td>Rectangular</td><td>60</td><td>0.798</td><td>2.714</td><td>2.155</td><td>0.559</td><td>3.937</td></tr><tr><td>Circular tip (Meister et al. 2020)</td><td>60</td><td>0.316</td><td>1.034</td><td>0.587</td><td>0.447</td><td>1.313</td></tr><tr><td>Foil-shaped (Meister et al. 2020)</td><td>60</td><td>0.182</td><td>0.590</td><td>0.334</td><td>0.256</td><td>1.301</td></tr><tr><td>Optimized 1 (Figure 8)</td><td>26</td><td>0.093</td><td>0.310</td><td>0.168</td><td>0.142</td><td>1.178</td></tr><tr><td>Optimized 2 (Figure 9)</td><td>41</td><td>0.126</td><td>0.437</td><td>0.195</td><td>0.242</td><td>0.804</td></tr></tbody></table>

The pressure drop through the bar profiles reflects the head loss coefficient in a forced flow and is closely connected to the drag force coefficient. The drag force depends on the pressure exerted on the profile, which corresponds to the form drag, and the friction on the profile, also known as friction drag. The effect of each drag component varies depending on the profile shape. As demonstrated in Table 4, the ratio between the pressure and friction coefficient is significantly higher for a rectangular profile than for hydrodynamic profiles. This ratio is approximately 1 for an optimized profile, with a significant decrease of the pressure coefficient. Logically, incorporating a flat part in the optimization process results in a sensible increase of the friction drag, and, to a lesser extent, of the pressure drag. Consequently, the ratio between these two coefficients is significantly lowered. The difference of depth has an impact on these results. Understanding the hydraulic performance of a profile requires an examination of the flow around the profile. Figure 10 displays the streamlines around a rectangular profile and the two optimized bar shapes. For the rectangular profile, recirculation zones due to flow detachment are located at the leading and trailing edges, resulting in increased head loss and drag force. For the two optimized profiles, the moderately diffusing slopes downstream of the leading edge and immediately upstream of the trailing edge prevent the establishment of any recirculation zones. The absence of flow detachment around and in between side-by-side bars also prevents the artificial increase of the obstruction ratio due to the recirculation zones generated upstream of the rectangular bars. Downstream of the trailing edges, the combination of mild slopes and small curvature radii act in favour of an efficient pressure recovery that limit the drag forces and pressure losses.
<figure><img src="image_11.png" /><figcaption>**Figure 10.** Current lines of the two optimized profiles and the rectangular profile with a 26-degree projection. The velocity in the y-direction is represented by $u(y)$ [m.s$^{-1}$], while the inlet velocity (defined in Table 2) is represented by $U_0$ [m.s$^{-1}$].</figcaption></figure>

**5. Conclusion**

In an effort to improve the efficiency of bar-racks used at low head hydroelectric power plant water intakes, the study examines the correlation between head losses, drag force and bar shape through a genetic optimization algorithm applied to CFD results. The optimization procedure is applied to a bar rack inclined at 26 degrees with 20 mm bars spacing, which is a standard inclination and bar spacing according to the existing recommendations. These two values can be adapted without difficulty to other simulations. Simple parametric shapes are optimized to define new bar profiles that are easily reproducible in large dimensions and adapted for various assembly processes. The comparison of the optimized profile designed for circular spacers with other profiles in use confirms good performance of the chosen shape. Removing the shape constraint induced by the use of spacers results in a shortened teardrop profile approaching a simplified airfoil shape of 28% thickness ratio. Such a profile has the additional advantage of avoiding a flat zone, thus preventing debris from getting stuck between the bars. It is adapted to comb spacers fixation, that are increasingly used in power plants and additional calculations are required to determine if can withstand mechanical stress on the trash-rack.

In future work, another multi-objective optimization will be implemented to consider the stiffness of the bars. The final goal will be to find a new bar shape with low head losses but also with a good respond in regard of clogging problems and overall stiffness. During autumn season, the head loss due to clogging is highly important, and the impact of the shape of the bars becomes negligible. It is therefore essential to take into account shapes that are better suited to clogging. This works will also focus on the bar depth and width to compare with actual bar shapes in same conditions.

**6. ACKNOWLEDGMENTS**

This work was funded by France Hydro Electricité (Paris, France) and the National Association for Technological Research (ANRT) - CIFRE N° 2021/1425. This work was carried out in collaboration with the Institute PPRIME (Poitiers, France) and the Laboratory SIAME (Pau, France). Their support and help are greatly appreciated.
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