## Single Stage Turbines

Work is defined as force exerted multiplied by the distance this force causes an object to move. So, the maximum force steam can exert on a turbine wheel occurs if the wheel is held stationary. As the wheel speed increases, the force falls until finally it reaches zero when the turbine blades are moving at the same speed as the stea0m. Distance moved is zero if the wheel is stationary reaching a maximum when the force falls to zero. Multiplying force x distance thus produces theoretical maximum work when the velocity of the turbine blades is approximately half the velocity of steam from the turbine- s nozzle(s). This is illustrated in Figure 8.11-In practice, the number (known as velocity ratio) turns out to be about 0.47 rather than 0.5.

For typical applications, this means that the turbine should rotate at around 9-10 000 rpm. However, most single stage turbines are driving pumps etc. and for existing installations there is rarely a gearbox to step down turbine speed due to concerns about reliability and initial cost. Therefore, where power is 50 Hz the turbine is set to 3000 rpm and at 60 Hz (e.g., USA) the turbine runs at 3600 rpm. Isentropic efficiency is severely reduced at 3000rpm to around 35%, compared with a possible 75% or more at the ideal correct velocity ratio. In other words,

Turbine speed

Figure 8.11 Turbine work vs. speed.

Turbine speed

### Figure 8.11 Turbine work vs. speed.

without a gearbox, steam consumption is doubled. Some argue that since the exhaust steam is used in the process, efficiency is not important. This is not correct since energy produced from the turbine is made up by energy from a boiler - usually at over 85% cycle efficiency. This is far better than the efficiency of marginal electrical energy, and so shaft work extracted from steam should be maximized.

For new installations, it is possible to purchase small single stage (or compound stage) machines with an integral gearbox. Isentropic efficiency then rises to 75% or higher.

A new generation of electronic governors is beginning to supersede the older style 'flywheel'-hydraulic governor. Electronic governors have a major energy-saving advantage in that they can be coupled to adjust turbine speed to match the required process variable. For instance, turbine driven boiler fans can run with wide open dampers and the speed controlled to match the set point for flue gas oxygen content. Boiler feed pumps can be run at a speed required to maintain steam drum level. (See also Section 8.2.2.1).

The majority of single stage turbines have simple drilled nozzle plates. If the pressure ratio from inlet to exhaust is supercritical (and it usually is), then maximum steam velocity equals sonic velocity and increasing upstream pressure only increases mass flow through steam becoming denser at the choke. It is possible to retrofit convergent-divergent nozzles which accelerate the steam to supersonic velocity, thus increasing output power without increasing steam flow.

Many single stage turbines are fitted manual overload valves (also called auxiliary valves or hand valves). These are intended for use only if the power required is higher than produced with the governor valve wide open. Unfortunately, many operators do not realize that this can waste steam. The effect of leaving a manual valve open is illustrated in Figure 8.12 .