doc: English version of trashrack head losses

Refs #401

docs/en/calculators/devalaison/grille.md

-# Calculation of the head loss on a water intake grid
+# Calculation of the head loss on a water intake trashrack
+
+Head loss \(\Delta H\) on a water intake trashrack is calculated as follows:
+
+$$ \Delta H = \xi \frac{V_1^2}{2g} $$
+
+Upstream flow velocity \(V_1\) is calculated from the discharge \(Q\), the water height \(H_1\)
+and the intake width \(B\) upstream the trashrack:
+
+$$ V_1 = \frac{Q}{H_1 \times B} $$
+
+The calculation of the head loss coefficient \(\xi\) is based on the characteristics of the trashrack. For a full description of the assumptions, formulas and limitations of the method, please refer to the Raynal et al. (2012) report[^1] available here (in French): https://continuite-ecologique.fr/wp-content/uploads/2019/11/2012_014.pdf
+
 
 <div style="position: relative"><a id="grille-conventionnelle" style="position: absolute; top: -60px;"></a></div>
-## Conventional grid
+## Conventional trashrack
 
-Conventional grid planes: perpendicular to the flow and slightly inclined to the horizontal
+Conventional trashracks: perpendicular to the flow and slightly inclined to the horizontal.
 
 ### Formula
 
-Use of the F1 formula of Raynal et al (2012) to calculate the head losses.
+Use of the F1 formula of Raynal et al (2012)[^1] to calculate the head losses.
+
+$$\xi = a * K_O * K_\beta$$
+
+With:
+
+- \(\xi\): total head loss coefficient (-)
+- \(a\): bar shape coefficient (-), see "Bar profile" below
+- \(K_O\): blockage head loss coefficient due to bars, spacers and clogging (-)
+- \(K_\beta\): head loss coefficient due to the angle of the trashrack (-)
 
-$$\xi = K_F * K_O * K_\beta = a * \left ( \frac{O}{1-O} \right )^{1.6} * \left ( 1 - \cos{\beta} \right )^{0.39}$$
+$$K_O = \left ( \frac{O_C}{1-O_C} \right )^{1.6}$$
 
+With \(O_C\) blockage ratio due to bars, spacers and clogging (-):
+
+$$ O_C = O + (1 - O) \times C $$
+
+With:
+
+- \(O\) blockage ratio due to bars and spacers
+- \(C\) clogging ratio
+
+$$K_\beta = \left ( 1 - \cos{\beta} \right )^{0.39}$$
+
+With \(\beta\) the angle of inclination of the trashrack in reference to the vertical (°).
 
 <div style="position: relative"><a id="grille-orientee" style="position: absolute; top: -60px;"></a></div>
-## Oriented grid
+## Angled trashrack
 
-Flow-oriented and near-vertical grid planes.
+Flow-oriented and near-vertical trashracks.
 
-![Oriented grid](grille-orientee.jpg)
+![Angled trashrack](grille-orientee.jpg)
 
 *Courret, D. et Larinier, M. Guide pour la conception de prise d’eau ichtyocompatibles pour les petites centrales hydroélectriques, 2008. <https://doi.org/10.13140/RG.2.1.2359.1449>.*
 
 ### Formula
 
-Use of the F2 formula of Raynal et al (2012) to calculate the head losses.
+Use of the F2 formula of Raynal et al (2012)[^1] to calculate the head losses (Also in Equation (7) of Raynal et al. (2013)[^2]).
+
+$$\xi = a * K_O * K_\alpha$$
+
+With \(K_\alpha\) head loss coefficient due to inclination in reference to the horizontal (-)
+
+$$K_\alpha = 1 + c * \left ( \frac{90 - \alpha}{90} \right )^{2.35} * \left ( \frac{1 - O}{O} \right )^{3} $$
 
-$$\xi = K_F * K_O * K_\alpha = a * \left ( \frac{O}{1-O} \right )^{1.6} * \left ( 1 + c * \left ( \frac{90 - \alpha}{90} \right )^{2.35} * \left ( \frac{1 - O}{O} \right )^{3} \right )$$
+With:
 
+- \(\alpha\): inclination angle  of the trashrack in reference to the horizontal (°)
+- \(c\): bar shape coefficient (-), see "Bar profile" below
 
 <div style="position: relative"><a id="grille-inclinee" style="position: absolute; top: -60px;"></a></div>
-## Inclined grid
+## Inclined trashrack
 
-Grid planes perpendicular to the flow, and inclined with respect to the horizontal
+trashracks perpendicular to the flow, and inclined with respect to the horizontal
 
-![Inclined grid](grille-inclinee.jpg)
+![Inclined trashrack](grille-inclinee.jpg)
 
-![Inclined grid](grille-inclinee-b.jpg)
+![Inclined trashrack](grille-inclinee-b.jpg)
 
 *Courret, D. et Larinier, M. Guide pour la conception de prise d’eau ichtyocompatibles pour les petites centrales hydroélectriques, 2008. <https://doi.org/10.13140/RG.2.1.2359.1449>.*
 
 ### Formula
 
-Use of the F3 formula of Raynal et al (2012) to calculate the head losses.
+Use of the F3 formula of Raynal et al (2012)[^1] to calculate the head losses (Also in Equation (11) of Raynal et al. (2013)[^3]).
 
-$$\xi = K_{F, b} * K_b * K_\beta + K_{Fent} * K_{entH} = a * \left ( \frac{O_b}{1-O_b} \right )^{1.65} * \left ( \sin \beta \right )^{2} + c * \left ( \frac{O_{entH}}{1-O_{entH}} \right )^{0.77}$$
+$$\xi = a * K_b * K_\beta + K_{Fent} * K_{entH}$$
 
+With:
 
+- \(K_b\): blockage head loss coefficient due to bars and clogging (-)
+- \(K_{Fent}\): spacer shape coefficient (-), see "Bar profile" below
+- \(K_{entH}\): blockage head loss coefficient due to spacers (-)
+
+$$K_b = \left ( \frac{O_{b,C}}{1-O_{b,C}} \right )^{1.65}$$
+
+With \(O_{b,C} = O_b + (1 - O_b) \times C\) et \(O_b\) blockage ratio due to bars.
+
+$$K_\beta = \left ( \sin \beta \right )^{2}$$
+
+$$K_{entH} = \left ( \frac{O_{entH}}{1-O_{entH}} \right )^{0.77}$$
+
+With \(O_{entH}\) blockage ratio due to spacers.
 
 ## Parameters
 
 <div style="position: relative"><a id="cote-du-sommet-immerge-du-plan-de-grille" style="position: absolute; top: -60px;"></a></div>
-### Elevation of the immersed vertex of the grid plane
+### Elevation of the immersed vertex of the trashrack
 
-May be different from the water level if the top of the grid plane is drowned.
+May be different from the water level if the top of the trashrack is drowned.
 
 <div style="position: relative"><a id="largeur-de-la-section" style="position: absolute; top: -60px;"></a></div>
-### Section width
-
-#### Conventional or inclined grid
+### Section width \(B\)
 
-Must also correspond to the width of the grid plane.
+For conventional or inclined trashrack, it mMust also correspond to the width of the trashrack.
 
 <div style="position: relative"><a id="vitesse-dapproche-moyenne-pour-le-debit-maximum-turbine-en-soustrayant-la-partie-superieure-eventuellement-obturee" style="position: absolute; top: -60px;"></a></div>
-### Average approach speed for the maximum turbinated flow, subtracting the upper part, if any, blocked
+### Average approach speed for the maximum turbinated flow, subtracting the upper blocked part, if any
 
 "Maximum" value of the approach speed taken into account in the calculation of the head loss in a safety approach.
 
 <div style="position: relative"><a id="inclinaison-par-rapport-a-lhorizontale" style="position: absolute; top: -60px;"></a></div>
 ### Inclination with respect to the horizontal
 
-#### Conventional grid
+#### Conventional trashrack
 
 Scope of the formula: 45 ≤ β ≤ 90°
 
-#### Oriented grid
+#### Angled trashrack
 
-Vertical grid planes (β = 90°).
+Vertical trashracks (β = 90°).
 
-The slight inclination of the grid planes (β≈ 75/80°), often set up for screening purposes, can be neglected.
+The slight inclination of the trashracks (β≈ 75/80°), often set up for screening purposes, can be neglected.
 
-#### inclined grid
+#### inclined trashrack
 
 Scope of the formula: 15° ≤ β ≤ 90°
+
 Recommended for fish guidance: β ≤ 26°
 
 <div style="position: relative"><a id="orientation-par-rapport-a-la-direction-de-lecoulement" style="position: absolute; top: -60px;"></a></div>
 ### Orientation with respect to the direction of flow
 
-#### Conventional grid
+#### Conventional trashrack
 
-Grid planes perpendicular to the flow (α = 90°)
+trashracks perpendicular to the flow (α = 90°)
 
-#### Oriented grid
+#### Angled trashrack
 
 Scope of the formula: 30° ≤ α ≤ 90°
 
 Recommended for fish guidance: α ≤ 45°
 
-#### inclined grid
+#### inclined trashrack
 
-Grid planes perpendicular to the flow (α = 90°)
+trashracks perpendicular to the flow (α = 90°)
 
 <div style="position: relative"><a id="vitesse-normale-moyenne-pour-le-debit-maximum-turbine" style="position: absolute; top: -60px;"></a></div>
-### Average normal speed for maximum turbinated flow rate
-
-#### Conventional grid
+### Average normal speed for maximum turbinated flow rate \(V_N\)
 
-Recommended to avoid plating fish on the grid plane (physical barrier) or their premature passage through (behavioural barrier): VN ≤ 0.5 m/s.
+Recommended to avoid plating fish on the trashrack (physical barrier) or their premature passage through (behavioural barrier): VN ≤ 0.5 m/s.
 
-#### Oriented or inclined grid
-
-Recommended to avoid plating fish on the grid plane (physical barrier) or their premature passage through (behavioural barrier): VN ≤ 0.5 m/s.
+#### Angled or inclined trashrack
 
 Above the average value calculated here, it is essential to refer to the recommendations derived from the experimental characterization of the actual velocity values.
 
 <div style="position: relative"><a id="rapport-de-forme-des-barreaux" style="position: absolute; top: -60px;"></a></div>
-### Bar shape ratio
+### Bar shape ratio \(b/p\)
 
-#### Oriented grid
+#### Angled trashrack
 
-Validity range of the formula: ratio b / p close to 0.125
+Validity range of the formula: ratio \(b/p\) close to 0.125
 
 <div style="position: relative"><a id="rapport-espacementepaisseur-des-barreaux" style="position: absolute; top: -60px;"></a></div>
 ### Ratio of spacing / bar thickness
 
-#### Oriented grid
-
-Scope of validity of the formula: 1 ≤ e / b ≤ 3
+#### Angled trashrack
 
-<div style="position: relative"><a id="obstruction-globale-du-plan-de-grille-barreaux-entretoises-elements-de-supports-longitudinaux-et-transversaux-retenue" style="position: absolute; top: -60px;"></a></div>
-### Overall obstruction of the grid plane (bars + spacers + longitudinal and transverse support elements) retained
+Scope of validity of the formula: \(1 \leq e / b \leq 3\) with \(e\) space between bars.
 
-To be determined from the grid plans.
+<div style="position: relative"><a id="obstruction-globale-du-plan-de-grille-pour-les-grilles-conventionnelles-et-orientees" style="position: absolute; top: -60px;"></a></div>
+### Overall obstruction for conventional and angled trashracks
 
-#### Conventional grid
+Calculated from bars + spacers + longitudinal and transverse support elements retained, it has to be determined from the trashrack plans.
 
-Scope of validity of the formula: 0.2 ≤ O ≤ 0.60
+Scope of validity of the formula for conventional trashracks: \(0.2 \leq O \leq 0.60\)
 
-#### Oriented grid
+Scope of validity of the formula for angled trashracks: \(0.35 \leq O \leq 0.60\)
 
-Scope of the formula: 0.35 ≤ O ≤ 0.60
+<div style="position: relative"><a id="obstruction-globale-du-plan-de-grille-pour-les-grilles-inclinees" style="position: absolute; top: -60px;"></a></div>
+### Overall obstruction for inclined trashracks
 
-#### inclined grid
+It consists of two parts.
 
-Obstruction due to the bars and longitudinal support elements retained \(O_b\). To be determined from the grid plans.
+Obstruction due to the bars and longitudinal support elements retained \(O_b\). To be determined from the trashrack plans.. It must be higher or equal to bar blockage ratio given by \(b / (b + e)\). Scope of validity of the formula: \(0.28 \leq O \leq 0.53\).
 
-Scope of validity of the formula: 0.28 ≤ Ob ≤ 0.53
+Blockage ratio due to spacers. Scope of validity of the formula: \(O_{entH} \leq 0.28\)
 
 <div style="position: relative"><a id="profil-des-barreaux" style="position: absolute; top: -60px;"></a></div>
 ### Bar profile
@@ -154,33 +203,31 @@ Scope of validity of the formula: 0.28 ≤ Ob ≤ 0.53
 
 *Raynal, Sylvain. « Étude expérimentale et numérique des grilles ichtyocompatibles ». Sciences et ingénierie en matériaux, mécanique, énergétique et aéronautique - SIMMEA, 2013.*
 
-#### Conventional grid
+#### Conventional trashrack
 
 The shape coefficient of the bars \(a\) is 2.89 for the rectangular profile (PR) and 1.70 for the hydrodynamic profile (PH).
 
-#### Oriented grid
+#### Angled trashrack
 
 The shape coefficient of the bars is 2.89 for the rectangular profile (PR) and 1.70 for the hydrodynamic profile (PH).
 
 The shape coefficient of the bars \(c\) is 1.69 for the rectangular profile (PR) and 2.78 for the hydrodynamic profile (PH).
 
-#### inclined grid
+#### inclined trashrack
 
 The shape coefficient of the bars \(a\) is 3.85 for the rectangular profile (PR) and 2.10 for the hydrodynamic profile (PH).
 
-<div style="position: relative"><a id="obstruction-effective-due-aux-entretoises-et-elements-de-support-transversaux-rapportee-a-la-section-decoulement" style="position: absolute; top: -60px;"></a></div>
-### Effective obstruction due to spacers and transverse support elements in relation to the flow cross-section
-
-#### inclined grid
-
-To be determined from the grid plans.
-Scope of the formula: OentH ≤ 0.28
-
 <div style="position: relative"><a id="coefficient-de-forme-moyen-des-entretoises-et-elements-transversaux-ponderes-selon-leurs-parts-respectives" style="position: absolute; top: -60px;"></a></div>
 ### Average shape coefficient of spacers and transverse elements, weighted according to their respective shares
 
-#### inclined grid
+#### inclined trashrack
 
-To be determined from the grid plans.
+To be determined from the trashrack plans.
 
 For example, 1.79 for cylindrical spacers, 2.42 for rectangular spacers, and around 4 for square beams and IPNs.
+
+[^1]: Raynal, S., Courret, D., Chatellier, L., Larinier, M., David, L., 2012. Définition de prises d’eau ichtyocompatibles -Pertes de charge au passage des plans de grille inclinés ou orientés dans des configurations ichtyocompatibles et champs de vitesse à leur approche (POLE RA11.02). https://continuite-ecologique.fr/wp-content/uploads/2019/11/2012_014.pdf
+
+[^2]: Raynal, S., Chatellier, L., Courret, D., Larinier, M., David, L., 2013. An experimental study on fish-friendly trashracks–Part 2. Angled trashracks. Journal of Hydraulic Research 51, 67–75.
+
+[^3]: Raynal, S., Courret, D., Chatellier, L., Larinier, M., David, L., 2013. An experimental study on fish-friendly trashracks–Part 1. Inclined trashracks. Journal of Hydraulic Research 51, 56–66.

docs/fr/calculators/devalaison/grille.md

@@ -62,7 +62,7 @@ Avec \(K_\alpha\) coefficient de perte de charge dû à l'inclinaison de la gril
 
 $$K_\alpha = 1 + c * \left ( \frac{90 - \alpha}{90} \right )^{2.35} * \left ( \frac{1 - O}{O} \right )^{3} $$
 
-Avec:
+Avec :
 
 - \(\alpha\) : angle d’inclinaison de la grille par rapport à l'horizontale (°)
 - \(c\) : coefficient de forme des barreaux, voir ci-dessous le paragraphe "Profil des barreaux"