Hydraulic Turbines: Lecture Notes, Suitability, Runaway Speed and Draft Tube| Fluid Mechanics

Hydraulic Turbines: Lecture Notes, Suitability, Runaway Speed and Draft Tube. [With equations and examples]

Note # 1. Introduction to Hydraulic Turbines:

A hydraulic turbine is a prime mover which converts a substantial part of the potential and kinetic energy of flowing water to mechanical energy. Water stored in high level reservoirs like dams has enormous potential energy. This water having high energy is brought down the penstock pipes and directed to run the turbines.

The mechanical energy of the turbines can be converted into electrical energy by a generators which is directly coupled to the turbine shaft. Hydroelectric power constitutes the major part of the total power developed from all sources. Power developed from oil, coal and such sources are insignificantly small compared to hydroelectric power.

Hydroelectric Plant:

A hydroelectric plant has the following units:

(a) A dam to store water at a high level creating a reservoir.

(b) Head race system providing the means to convey the water from the reservoir to the power house, using large diameter pipes or tunnels.

(c) A surge tank to protect the pipe line from bursting due to sudden changes in the discharge rate.

(d) Penstock pipes which are pressure pipes laid at steep slope.

(e) Power house where the turbine and generator are installed.

(f) Tail race to carry the water discharged by the turbine. This is usually in the form of channels.

Hydroelectric power production is of great advantage compared with other methods of power generation. Hydroelectric plants involve relatively simple construction needing lesser maintenance. These units automatically respond and adjust to changing loads. The water discharged finally by the turbines can be utilized for irrigation.

There are however shortcomings like scanty rain fall disturbing power supply, high initial cost of various civil engineering works and high cost of transmission lines.

Fig. 19.4 shows a layout of a hydroelectric power plant.

Turbines:

A hydraulic turbine consists of (i) a wheel called the runner provided with a number of curved vanes on its periphery, (ii) a guiding apparatus to direct the flow of water at inlet in the specified direction. A turbine needs a source of water supply say a reservoir from which the water is drawn by pipes.

Turbines may be classified in two ways, viz. (a) based on the nature of energy head of water at inlet, and (b) based on the direction of flow along the vanes.

(a) Classification of Turbines Based on the Nature of Energy Head Possessed by Water at Inlet:

Turbines may be classified into Reaction or pressure turbines and Impulse or velocity turbines.

(i) Reaction or Pressure Turbine:

A reaction turbine is a turbine in which the water entering the runner possesses pressure as well as kinetic energy. Obviously this type of turbine is always enclosed by a casing.

(ii) Impulse or Velocity Turbines:

An impulse turbine is a turbine in which the water entering the runner possesses kinetic energy only, i.e., in this case, the water is throughout at atmospheric pressure.

Examples:

(i) Reaction turbines – Francis turbine, Kaplan turbine, Thomson turbine, Scotch turbine or Barker’s mill.

(ii) Impulse turbines – Pelton wheel, Turgo wheel, Jonval turbine, Girard turbine.

(b) Classification of Turbines Based on the Direction of Flow of Water:

In a radial flow turbine the water moves along the vanes towards the axis of rotation of the runner or away from it. When the flow is towards the axis of rotation, the turbine is called an inward flow turbine. When the flow is away from the axis of rotation of the turbine is called an outward flow turbine.

When the water flows parallel to the axis of rotation, the turbine is called an axial or parallel flow turbine.

In a mixed flow turbine the water enters radially inwards at inlet and discharge at outlet in a direction parallel to the axis of rotation of the runner.

Examples:

Inward flow turbine – Francis (radial flow), Thomson, Girard (radial).

Outward flow turbine – Fourneyron turbine.

Axial or parallel flow turbines – Pelton wheel, Turgo wheel, Kaplan turbine, Jonval turbine, Girard (axial).

Mixed flow turbine- Francis (mixed flow).

The Francis, Kaplan and Pelton wheel turbines are the most commonly adopted turbines.

Note # 2. Suitability of Turbines:

A particular type of turbine is most suitable at a particular site. The suitability of a turbine at a site depends on the head of water available, the speed of three turbine and the power to be developed.

Based entirely on the head available the type of turbine to be recommended is given in the table below:

The above method of selecting the type of turbine is only approximate. The best method of selecting a type of turbine to suit the condition at the site is by finding the specific speed requirement. The specific speed of a turbine is the speed of a turbine under a head of 1 metre so as to develop a power of 1 kilo watt.

If a turbine works under a head H metres and runs at N rpm and develops P kilowatts of power then the specific speed of the turbine is given by –

The specific speed is a type characteristic. A type of turbine has a specific speed within a definite speed range.

The following table indicates the specific speeds of the commonly adopted turbines:

Note # 3. Runaway Speed:

Suppose a turbine is working under maximum head at full gate opening. If now the external load (i.e., the generator) is disconnected from the unit, the speed of the turbine will go on increasing and will reach a certain maximum value. This maximum speed reached by the turbine after the removal of the external load is called runaway speed. The various rotating components of the turbine should be designed to remain safe at the runaway speed.

The runaway speeds of the various turbines are given below:

Note # 4. The Draft Tube:

It may be realized that the pressure at water at the outlet of a reaction turbine is below the atmospheric pressure and obviously water at such low pressure cannot be discharged directly to the tail race. So, the water leaving the turbine is passed through a gradually diverging pipe leading to the tail race, letting the pressure to rise gradually to reach the atmospheric pressure. This pipe of gradually increasing area is called the draft tube. Generally the outlet of the draft tube is provided about 1 metre below the tail water level.

Function of a Draft Tube:

A draft tube has these functions:

(i) A part of the kinetic energy of the water leaving the runner is converted into useful pressure energy,

(ii) With the provision of the draft tube, it is possible to set the turbine above the tail race without any loss of head. Moreover by placing the turbine above the tail race, the turbine becomes accessible for routine inspection and maintenance.

Figs. 20.58 and 20.59 show the usual forms of draft tubes provided.

(a) Vertical divergent draft tube – This draft tube has the shape of the frustum of a cone. This is generally provided for low specific speed. The cone angle is not to exceed 8°. For greater values of the cone angle it is seen that the flowing body of water may not touch the sides of the draft tube. This will lead to eddy formation bringing down the efficiency of the draft tube.

(b) Moody’s draft tube or hydraucone – This is a bell-mouthed draft tube consisting of a conical tube with a solid conical central core. The whirl of the discharged water is very much reduced in this arrangement.

(c) Elbow draft tube – This draft tube affords to discharge the water horizontally to the tail race.

(d) Elbow draft tube with circular inlet and rectangular outlet – This is a further improvement of the simple elbow draft tube. In all the types mentioned above, the outlet of the draft tube should be situated below the tail water level.

Theory of the Draft Tube.

Consider a vertical divergent draft tube of length I. Let the bottom of draft tube be at a depth y below the tail race level. Consider levels 2-2 and 3-3 corresponding to inlet and outlet of draft tube. Applying Bernoulli’s equation to inlet and outlet of the draft tube –

Draft Tube Efficiency.

This is the ratio of the actual dynamic suction head to the theoretical dynamic suction head.

Note # 5. Cavitation:

When water flows through a passage having different areas at different sections the velocities will be different at different sections. These are accompanied by corresponding pressure changes in accordance with Bernoulli’s equation. The pressure of water should not fall below a critical value which is equal to the vapour pressure.

At this stage the water begins to vapourise forming bubbles of vapour. In a turbine also in regions of low pressure such vapour bubbles may be formed. These vapour bubbles are carried on by the moving stream to zones of higher pressure where these vapour bubbles condense into water again.

As this happens a cavity in place of the bubble is suddenly formed. The water surrounding the cavity will close in from all the directions to fill the cavity. This results in a high local pressure which may at times be as high as 7000 times the atmospheric pressure. Such sudden introduction of high pressure will produce pitting on the runner blades and on the draft tube, which get damaged gradually. This phenomenon is known as cavitation due to the formation of the cavities.

Effects of Cavitation:

(a) The metallic or concrete walls containing the water stream may be severely damaged.

(b) Considerable cracking or rattling may be produced leading to objectionable vibrations.

(c) The pressure velocity distribution in this affected region is greatly distorted.

(d) The efficiency of the hydraulic machinery will be reduced due to vibrations and pitting.

The following precautions may be taken to safeguard against cavitation:

The draft tube should be so designed that nowhere the pressure may fall below the vapour pressure of water.

The interior surface may be made of stainless steel to resist formation of pits or cavities.

The velocity should be controlled so as not to exceed a safe limit.

The height Z_t above the tail water level at which a turbine should be set should be such that cavitation at the exit of the runner is prevented.

Let,

p_e = Absolute pressure head at exit of runner

p_a = Pressure head at tail water level

v_e = Velocity of water at exit to runner

v_t = Velocity of tail water.

h_fd = Loss of head in the draft tube

Applying Bernoulli’s equation,