Water hammer in penstock and surge tank

Water hammer is the sudden rise (or fall) of pressure in a penstock when the velocity of water is changed quickly, for example when the turbine gates close quickly after a load rejection. The moving column of water is suddenly stopped; its kinetic energy is converted into pressure energy, and a pressure wave travels up and down the pipe with a hammering effect.

Magnitude (Joukowsky relation): for instantaneous or rapid closure ($t_c \le 2L/a$),

$$\Delta p = \rho\, a\, \Delta v \quad\text{or}\quad \Delta H = \frac{a\,\Delta v}{g}$$

where $a$ = speed of the pressure wave in the pipe (about 1000–1400 m/s), $\Delta v$ = change in velocity, $L$ = pipe length. For slow (gradual) closure ($t_c > 2L/a$) the rise is smaller. Rigid-column theory gives $\Delta p \approx \rho L \Delta v / t_c$; Michaud's formula, which allows for the reflected pressure wave, gives about $2\rho L \Delta v / t_c$.

 Reservoir
 ~~~~~~~ |
         |\  penstock (length L)
         | \
         |  \  pressure wave
         |   \  <---->
         |    \______[gate]--turbine
                      closes

Effects: very high pressure can burst the penstock and damage valves and the turbine casing; negative pressure on opening can collapse the pipe or cause cavitation; it causes vibration and noise; and it makes speed governing more difficult.

Surge tank

A surge tank is an open-top vertical tank (or shaft) connected to the conduit just before the penstock, close to the power house. Its water level rises and falls with the load.

 Reservoir     low-pressure tunnel     surge tank
 ~~~~~~~ |____________________________ | ~~~~ |
                                       |      |
                                       |__  __|
                                          \ penstock
                                           \
                                            [turbine]

Advantages of a surge tank

1. Reduces water hammer: the free surface reflects the pressure wave, so only the short penstock between the tank and the turbine is exposed to high pressure. The long tunnel is protected and can be thinner and cheaper.
2. On load rejection: when the gates close, the water coming down the tunnel enters the tank and its level rises, storing water instead of creating high pressure.
3. On load increase: the tank supplies the extra water immediately until the tunnel flow accelerates. So the turbine is not starved of water and the governor responds faster.
4. Reduces the effective water starting time ($T_w$), giving better speed regulation and stability.
5. Reduces pressure fluctuation in the tunnel and prevents negative pressure and collapse.
6. Allows faster gate operation and therefore better frequency control.

Types: simple tank, restricted orifice (throttled) tank, differential tank, closed (air-cushion) tank and inclined tank.