Draft tube: purpose, setting and efficiency

Purpose of a draft tube

A draft tube is a gradually expanding pipe connecting the runner outlet to the tailrace. It is provided to:

• allow the turbine to be set above tailwater level (for easy access) without losing the head between the runner and the tailwater;
• regain kinetic energy at the runner outlet by reducing the velocity from $V_1$ to $V_2$ and converting it into pressure, thus creating a suction (low pressure) at the runner exit and increasing the effective head;
• discharge the water safely into the tailrace.

   runner outlet (1)
      |  |            ^
      |  |            | H_s
 -----+  +----------  | 
       \  /  TWL ~~~~~|~~~~
        \/   (2)  exit under water

Maximum permissible setting

Let section 1 be the draft tube inlet (runner outlet), at height $H_s$ above tailwater, with velocity $V_1$ and pressure $p_1$. Section 2 is the draft tube outlet submerged in the tailwater, with velocity $V_2$ and pressure $\approx p_{atm}$. Bernoulli's equation between 1 and 2 (datum at tailwater), with loss $h_f$ in the tube:

$$\frac{p_1}{\gamma} + \frac{V_1^2}{2g} + H_s = \frac{p_{atm}}{\gamma} + \frac{V_2^2}{2g} + h_f$$ $$\frac{p_1}{\gamma} = H_{atm} - H_s - \left[\frac{V_1^2 - V_2^2}{2g} - h_f\right]$$

Draft tube efficiency

It is the ratio of the kinetic energy actually regained to the kinetic energy at the inlet:

$$\eta_d = \frac{\dfrac{V_1^2 - V_2^2}{2g} - h_f}{\dfrac{V_1^2}{2g}}$$

Substituting in the pressure equation,

$$\frac{p_1}{\gamma} = H_{atm} - H_s - \eta_d\frac{V_1^2}{2g}$$

To avoid cavitation, $p_1 \ge p_v$ (vapour pressure), so

$$H_{s,max} = H_{atm} - H_v - \eta_d\frac{V_1^2}{2g}$$

In terms of the Thoma coefficient $\sigma = \dfrac{H_{atm} - H_v - H_s}{H}$:

$$H_{s,max} = H_{atm} - H_v - \sigma_c H$$

A smaller $\sigma_c$ allows a higher setting. Because the exit velocity head $V_2^2/2g$ and the friction loss $h_f$ are not recovered, $\eta_d$ is less than 1, typically 0.75 to 0.90.