Compilation of lecture notes on ‘Steam Turbines’ for engineering students.
Lecture Note # 1. Optimum Operating Conditions:
Lecture Note # 2. Blade Height of Turbine:
For impulse turbine the blade height at a particular section of a turbine will be function of mass flow rate (m), specific volume (v), area (A), and velocity of steam
P = pitch = distance between two blades.
N = number of blades covered by nozzle.
H = blade height (in metres)
We know the equation,
It means that in two row turbine, the work obtained in second row is one-fourth of total work and if there are three rows of moving blades, work obtained in the row is one eighth of total work. Thus we see that the increase in number of rows the work obtained in the last decreases. So the numbers of rows are limited.
In steam turbines when steam flows over the blades, the friction takes place. It results into reduction in the useful enthalpy drop. So the useful or effective enthalpy-drop is less than isentropic enthalpy drop. The energy lost in friction reheats the steam and the quality of steam at exit from the stage gets improved.
The reheat factor is always greater than one. It depends on stage efficiency, initial temperature and pressure and exit pressure. The value normally lies from 1.02 to 1.06
Lecture Note # 5. Study of Steam Turbine Systems:
The steam piping to or from the turbine consists of:
1. Main steam supply to turbine. Valves in this steam piping are isolating valve, the stop valve, and the governor or throttle valve.
2. Drain piping which is provided to drain out the water condensed during the start-up of the turbine.
This is normally provided at the lowest point at:
(a) Before the isolating valve,
(b) Between the stop valve and the throttle valve, and
(c) The turbine casing inlet. Valves are provided in the drain piping which will be opened during warming-up and closed after the turbine has been loaded to certain output.
3. Gland steam supply piping. Steam from the main steam piping is tapped off and supplied to the glands at the turbine shaft ends coming out of the cylinder to prevent the leakage of steam to the atmosphere and leakage of air into the turbine. The exhaust from the glands may be led to low pressure stages of turbine or condenser. The supply of steam to the glands is regulated by separate regulator.
Steam may also be tapped off to steam ejector which maintains vacuum in the condenser.
4. Extraction steam Piping. Steam may be extracted from the turbine at intermediate stage for use as heating medium or for driving auxiliaries.
Oil circuit is provided to supply oil at a pressure for lubrication of the bearings and also to operate the servo-motors through relays. A typical forced lubrication system as used on and turbines. The pump which is normally of the positive action gear type usually delivers the whole of the oil required for lubrication and governing at the pressure required for the governor gear oil relays.
As the oil for operating the relays is only required intermittently the surplus is allowed to passes through relief valve set to lift at the relay pressure. The oil used in the governor relays may or may not be cooled. Oil for lubrication is passed through a reducing valve which is so adjusted that the oil supply pressure at the bearings is about 0.5 to 1 bar.
It is passed through all the bearings. Similarly a large bus pipe collects the oil from all the bearings and leads it to the oil drain tank. This pipe must be large enough to carry the oil with the pipe only partly filled so that air bubbles have a chance to escape. Oil strainers are placed on the oil inlet side of the tank.
The auxiliary oil pump comes into operation at starting. Stopping when the oil pressure falls below a certain valve to supply oil to the bearings when the shaft is being rotated by turning gear, and also as emergency stand-by. It is capable of supplying same quantity as the main pump. The type-most commonly used is electric/turbo driven centrifugal pump.
Water is used to cool the lubricating oil. Oil tanks should be large, enough to allow considerable time to elapse between the oil draining back into the tank and re-entering the pump.
Lecture Note # 6. Velocity Diagram for Velocity Compounded Steam Turbine:
In this type of turbine, steam is first expanded in nozzles and is passed through set of moving blades fixed blades and then through second set of moving blades. The function of fixed blades is to change the direction of motion of steam received from earlier set of moving blades and to re-direct it to the next set of moving blades. The complete expansion of steam takes place in nozzle.
α1 = Nozzle angle
θ = Inlet angle for first set of moving blades
φ1 = Outlet angle for first set of moving blades
β1 = Inlet angle for first set of fixed blades
α2 = Exit angle for fixed blades
θ2 = Inlet angle for second set of moving blades
φ2 = Outlet angle for second set of moving blades
β2 = Inlet angle for second set of fixed blades
k = Friction coefficient
The velocity diagram for the first set of moving blades can be drawn easily if the required data is known. It will be similar to velocity diagram of simple impulse turbine.
Following points should be noted for drawing a velocity diagram for second set of moving blades:
(1) Angle α2 is exit angle of fixed-blades. The steam leaving fixed blades will enter smoothly in second set of moving blades. So α2 is similar to nozzle angle, if compared with velocity diagram of simple impulse turbine.
(2) If the friction is considered in blades, the relative velocity will decrease. If friction coefficient is k, we know that,
Vre1 = k.Vri1
The steam leaving the first set of moving blades will enter into fixed blades. Due to friction relative velocity will decreased.
and Vre2 = k.Vri2
(3) Angle β1 is exit angle of steam leaving first moving blade. It is same as blade angle at inlet for the first set of fixed blades.