From 5ee76728c880701ff83ef62a21282e705683e8c1 Mon Sep 17 00:00:00 2001 From: David Dorchies <david.dorchies@irstea.fr> Date: Mon, 15 Feb 2021 18:45:28 +0100 Subject: [PATCH] doc(macrorugo): update for new values of Cd0, r and fF(F) Refs cassiopee/jalhyd#283 --- .vscode/settings.json | 9 ++++ .../cassan2016_flow_chart_design_method.png | Bin 0 -> 104955 bytes docs/en/calculators/pam/macrorugo_theorie.md | 44 +++++++++++++++--- docs/fr/calculators/pam/macrorugo_theorie.md | 14 +++--- scripts/check-translations.js | 4 +- 5 files changed, 54 insertions(+), 17 deletions(-) create mode 100755 docs/en/calculators/pam/cassan2016_flow_chart_design_method.png diff --git a/.vscode/settings.json b/.vscode/settings.json index 0b2301e3f..bfe798cdd 100644 --- a/.vscode/settings.json +++ b/.vscode/settings.json @@ -6,5 +6,14 @@ "latex", "plaintext", "markdown" + ], + "cSpell.words": [ + "Cassan", + "DICHO", + "MACRORUGO", + "fdescribe", + "jalhyd", + "nghyd", + "prms" ] } \ No newline at end of file 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rock-ramp pass corresponds to the implemen ## General calculation principle + + +*After Cassan et al., 2016[^1]* + There are three possibilities: - the submerged case when \(h \ge 1.1 \times k\) @@ -106,19 +110,23 @@ $$\alpha = 1 - (a_y / a_x \times C)$$ ## Formulas used -### Throughput speed *V* +### Bulk velocity *V* $$V = \frac{Q}{B \times h}$$ ### Average speed between blocks *V<sub>g</sub>* +From Eq. 1 Cassan et al (2016)[^1] and Eq. 1 Cassan et al (2014)[^2]: + $$V_g = \frac{V}{1 - \sqrt{(a_x/a_y)C}}$$ <div style="position: relative"><a id="coefficient-de-trainee-dun-bloc-cd0" style="position: absolute; top: -60px;"></a></div> ### Drag coefficient of a single block *C<sub>d0</sub>* \(C_{d0}\) is the drag coefficient of a block considering a single block -infinitely high with \(F << 1\) (Cassan et al, 2016[^1]). +infinitely high with \(F << 1\) (Cassan et al, 2014[^2]). The coefficient has been readjusted in Cassiopée version 4.14.0 from the coefficients originally proposed in Cassan et al, 2014[^2], Table 2. + +It is now 1.1 for a circular block and 2.6 for a flat-faced block. ### Block shape coefficient *σ* @@ -126,11 +134,15 @@ Cassan et al. (2014)[^2], et Cassan et al. (2016)[^1] define \(\sigma\) as the r block area in the \(x,y\) plane and \(D^2\). For the cylindrical form of the blocks, \(\sigma\) is equal to \(\pi / 4\) and for a square block, \(\sigma = 1\). -The formula used in Cassiopée has been revised to better correspond to the experimental measurements and to take into account the intermediate block shapes between circular and square.: +### Ratio between the average speed downstream of a block and the maximum speed *r* -$$ \sigma = 0.4 C_{d0} + 0.7 $$ +Cassan et al. (2014) [^2], Table 2 gives experimental measurements of this ratio for cylindrical blocks (\(r=1.2\)), rounded faces (\(r=1.2)\) and flat faces (\(r=1.5\)). -We now have \(\sigma = 1.1\) for a circular block and \(\sigma = 1.5\) for a square block. +The formula used in Cassiopeia allows to take into account shapes of intermediate blocks between circular and square shapes from the values of \(C_{d0} = 1.1\) for cylindrical blocks and \(C_{d0} = 2.6\) for blocks with flat faces: + +$$ r = (C_{d0} *0.4 + 1.121) / 1.5 $$ + +We now have \(r = 1.1\) for circular blocks and \(r = 1.35\) for flat-faced blocks. ### Froude *F* @@ -142,11 +154,29 @@ If \(F < 1.3\) (Eq. 5, Cassan et al., 2016) $$f_F(F) = \mathrm{min} \left( \frac{\sigma}{1- (F^2 / 4)}, \frac{1}{F^{\frac{2}{3}}} \right)^2$$ -else +else (The distinction is only numerical because \(1- (F^2 / 4)\) is not defined for \(F > 2\)) $$f_F(F) = F^{\frac{-4}{3}}$$ -(The distinction is only numerical because \(1- (F^2 / 4)\) is not defined for \(F > 2\)) +### Maximum speed *u<sub>max</sub>* + +According to equation 19 of Cassan et al, 2014[^2] : + +$$ f_F(F) = \left( \dfrac{U_d}{V_g} \right)^2 $$ + +And equation 4: + +$$ \frac{u_{max}}{V_g} = r \dfrac{u_d}{V_g} $$ + +It is deduced that : + +$$ u_{max} = V_g r \sqrt{f_F(F)} $$ + +### Drag coefficient correction function linked to relative depth *f<sub>h\*</sub>(h<sub>\*</sub>)* + +The equation used in Cassiopeia differs slightly from Equation 20 of Cassan et al. 2014 [^2] and Equation 6 of Cassan et al. 2016 [^1]. Indeed, recent experiments have shown a better correlation with the following formula : + +$$ f_{h_*}(h_*) = \min \left((1 + 1 / h_*^2), 3 \right) $$ ### Coefficient of friction of the bed *C<inf>f</inf>* diff --git a/docs/fr/calculators/pam/macrorugo_theorie.md b/docs/fr/calculators/pam/macrorugo_theorie.md index 6f47f4e90..a2a99f4aa 100644 --- a/docs/fr/calculators/pam/macrorugo_theorie.md +++ b/docs/fr/calculators/pam/macrorugo_theorie.md @@ -122,9 +122,9 @@ $$V_g = \frac{V}{1 - \sqrt{(a_x/a_y)C}}$$ ### Coefficient de trainée d'un bloc *C<sub>d0</sub>* -\(C_{d0}\) est le coefficient de trainée d'un bloc de hauteur infinie pour un Froude \(F << 1\) (Cassan et al, 2016[^1]). +\(C_{d0}\) est le coefficient de trainée d'un bloc de hauteur infinie pour un Froude \(F << 1\) (Cassan et al, 2014[^2]). Le coefficient a été réajusté dans la version 4.14.0 de Cassiopée par rapport aux coefficients initialement proposés dans Cassan et al, 2014[^2], Table 2. -Il vaut 1 pour un plot circulaire et 2 pour un plot carré. +Il vaut désormais 1.1 pour un bloc circulaire et 2.6 pour un plot à face plane. ### Coefficient de forme de bloc *σ* @@ -135,11 +135,9 @@ On a donc \(\sigma = \pi / 4\) pour un bloc circulaire et \(\sigma = 1\) pour un Cassan et al. (2014)[^2], Table 2 donne des mesures expérimentales de ce ratio pour les blocs cylindriques (\(r=1.2\)), aux faces arrondies (\(r=1.2)\) et aux faces planes (\(r=1.5\)). -La formule utilisée dans Cassiopée a été remaniée pour mieux correspondre aux mesures expérimentales et permettre une prise en compte de formes de plots intermédiaires entre les formes circulaire et carré : +La formule utilisée dans Cassiopée permet une prise en compte de formes de plots intermédiaires entre les formes circulaire et carré à partir des valeurs de \(C_{d0} = 1.1\) pour les blocs cylindriques et \(C_{d0} = 2.6\) pour les blocs à faces planes : -$$ r = 0.4 C_{d0} + 0.7 $$ - -On a désormais \(r = 1.1\) pour un plot circulaire et \(r = 1.5\) pour un plot carré. +$$ r = (C_{d0} *0.4 + 1.121) / 1.5 $$ ### Froude *F* @@ -149,7 +147,7 @@ $$F = \frac{V_g}{\sqrt{gh}}$$ Si \(F < 1.3\) (Eq. 19, Cassan et al., 2014[^2]) -$$f_F(F) = \min \left( \frac{r}{1- F^2 / 4}, \frac{1}{F^{\frac{2}{3}}} \right)^2$$ +$$f_F(F) = \min \left( \frac{1}{1- F^2 / 4}, \frac{1}{F^{\frac{2}{3}}} \right)^2$$ sinon (distinction numérique car \(\frac{r}{1- (F^2 / 4)}\) est non défini pour \(F > 2\)) @@ -173,7 +171,7 @@ $$ u_{max} = V_g r \sqrt{f_F(F)} $$ L'équation utilisée dans Cassiopée diffère légèrement de l'équation 20 de Cassan et al. 2014[^2] et l'équation 6 de Cassan et al. 2016[^1]. En effet, les récentes expériences ont montré une meilleure corrélation avec la formule suivante : -$$ f_{h_*}(h_*) = (1 + 1 / h_*^2) $$ +$$ f_{h_*}(h_*) = \min \left((1 + 1 / h_*^2), 3 \right) $$ ### Coefficient de friction du lit *C<inf>f</inf>* diff --git a/scripts/check-translations.js b/scripts/check-translations.js index 4143d689e..d15fc3de6 100644 --- a/scripts/check-translations.js +++ b/scripts/check-translations.js @@ -4,7 +4,7 @@ * 1) Reads Message enum in jalhyd, and for every message code in it, checks * that there is a translation in each nghyd's locale/*.json file (ie. for * every language) - * + * * 2) For every nghyd calculator, checks that the translated keys are the same * in all language files */ @@ -35,7 +35,7 @@ jm = jm.replace(/[ \t]+/g, ""); // remove line breaks jm = jm.replace(/\n/g, ""); -// split on ";" +// split on "," const messages = jm.split(","); // remove import on 1st line (wtf) @clodo -- GitLab