Turbine selection method and governing factors

Scientific method of turbine selection

Turbine selection by the scientific method is based on specific speed and the site's head–discharge data, checked against standard application charts.

1. Find net head $H$ and design discharge per unit $Q$ (e.g. $Q_{45}$ from the FDC less riparian release).
2. Find unit output $P = \eta_t \rho g Q H$.
3. Choose a synchronous speed $N = 120f/p$.
4. Calculate

$$N_s = \frac{N\sqrt{P}}{H^{5/4}}$$

(N in rpm, P in kW, H in m). 5. Select the type from the $N_s$ range: Pelton 10–35 (single jet), Francis 60–300, Kaplan 300–1000. 6. Cross-check with the head range (Pelton 50–1300 m, Francis 10–350 m, Kaplan 2–40 m) and the manufacturer's $H$–$Q$ chart; check cavitation (Thoma's $\sigma$) and part-load efficiency.

Major factors governing turbine selection

1. Net head: primary factor; fixes the broad type.
2. Discharge and its variation: low head–high flow suits Kaplan; high head–low flow suits Pelton.
3. Specific speed and rotational speed: higher speed gives smaller generator but more cavitation risk.
4. Part-load efficiency: Pelton and Kaplan have flat efficiency curves; Francis drops at low load.
5. Cavitation and setting: reaction turbines need submergence, adding excavation cost.
6. Sediment content: high silt erodes Francis runners; Pelton runners are easier to repair.
7. Number of units and unit size, transport limits.
8. Cost, maintenance and runaway speed.

Example

Net head 300 m, design flow 4 m³/s for one unit: $P \approx 9.81\times 4\times 300\times 0.9 \approx 10.6$ MW. At 600 rpm, $N_s = 600\sqrt{10595}/300^{5/4} \approx 49$, which is in the multi-jet Pelton range; a 2-jet or 4-jet Pelton (or a slow Francis) would be compared on cost and part-load efficiency.