Seite - 1381 - in Book of Full Papers - Symposium Hydro Engineering

Analytic modelling At the point of convergence at the end of draft tube the momentum relationships can be written with the equation of momentum, reduced by the pressure component. IE=∑(m∙ dv⃗⃗⃗⃗ ⃗ dt )=∑ρ∙Q∙v⃗ =ρ∙Q∙vE [5] ∑ρ∙Q∙v⃗ =∑𝑃 ∆𝑡 ∑𝑃 ∆𝑡 =0 [6] ρ∙QT ∙vT+ρ∙QE ∙vE,H=ρ∙(QT+QE) ∙vcomb [7] On the basis of the research project, we determined a factor for the effect of the ejector in our calculation approach, which takes into account the difference between the optically visible water level at the decisive confluence point and the actually effective pressure level in the draft tube. This factor is linked to the momentum component of the ejector flow, as the determining parameter for the gain in head. The equation of momentum linked to the energy equation can now be written as: ρ∙QE ∙vE,H ∙ 𝐟 𝐕 𝐄 +ρ∙Q∙vT =ρ∙(QE+QT) ∙veff [8] The significant result is the useable speed of the mixed flows (veff) of turbine and ejector: veff = QE∙vE,H∙𝐟 𝐕 𝐄 +QT∙vT QE+QT [9] The result for the velocity of the mixed flows (veff) out of the equation of momentum can be also directly linked to the equation of energy at the confluence point (Fig. 24). ℎ𝑈 𝑊 ,𝐵 + vT,B 2 2 g =ℎ𝑈 𝑊 ,𝑒 𝑓 𝑓 + veff 2 2g [10] zH=ℎ𝑈 𝑊 ,𝐵 −ℎ𝑈 𝑊 ,𝑒 𝑓 𝑓 zH ... gain in net head [11] zH= veff 2 2g − vT,B 2 2 g [12] The energy related conditions of the convergence point are projected into the confluence point. 1381