**CENTRIFUGAL PUMPS:**

The three important parts of centrifugal pumps are (1) the impeller, (2) the volute casing, and (3) the diffuser.

The centrifugal pump is used to raise liquids from a lower to a higher level by creating the required pressure with the help of centrifugal action. Whirling motion is imparted to the liquid by means of backward curved blades mounted on a wheel known as the impeller.

As the impeller rotates, the fluid that is drawn into the blade passages at the impeller inlet or eye is accelerated as it is forced radially outwards. In this way, the static pressure at the outer radius is much higher than at the eye inlet radius. The water coming out of the impeller is then lead through the pump casing under high pressure. The fluid has a very high velocity at the outer radius of the impeller, and, to recover this kinetic energy by changing it into pressure energy, diffuser blades mounted on a diffuser ring may be used. The stationary blade passages have an increasing cross-sectional area. As the fluid moves through them, diffusion action takes place and hence the kinetic energy is converted into pressure energy. Vaneless diffuser passages may also be used. The fluid moves from the diffuser blades into the volute casing. The functions of a volute casing can be summarized as follows: It collects water and conveys it to the pump outlet. The shape of the casing is such that its area of cross-section gradually increases towards the outlet of the pump. As the flowing water progresses towards the delivery pipe, more and more water is added from the outlet periphery of the impeller. Figure 2.1 shows a centrifugal pump impeller with the velocity triangles at inlet and outlet. For the best efficiency of the pump, it is assumed that water enters the impeller radially, i.e., a1 ¼ 908 and Cw1 ¼ 0. Using Euler’s pump equation, the work done per second on the water per unit mass of fluid flowing

Where Cw is the component of absolute velocity in the tangential direction. E is referred to as the Euler head and represents the ideal or theoretical head developed by the impeller only. The flow rate is

Where Cr is the radial component of absolute velocity and is perpendicular to the tangent at the inlet and outlet and b is the width of the blade. For shockless entry and exit to the vanes, water enters and leaves the vane tips in a direction parallel to their relative velocities at the two tips.

As discussed, the work done on the water by the pump consists of the following three parts:

1. The part (C2 2 – C1 2 )/2 represents the change in kinetic energy of the liquid.

2. The part (U2 2 – U1 2 )/2 represents the effect of the centrifugal head or energy produced by the impeller.

3. The part (V2 2 2 V1 2 )/2 represents the change in static pressure of the liquid, if the losses in the impeller are neglected.

**Turbines:**

In a hydraulic turbine, water is used as the source of energy. Water or hydraulic turbines convert kinetic and potential energies of the water into mechanical power. The main types of turbines are (1) impulse and (2) reaction turbines.

The predominant type of impulse machine is the Pelton wheel, which is suitable for a range of heads of about 150–2,000 m.

The reaction turbine is further subdivided into the Francis type, which is characterized by a radial flow impeller, and the Kaplan or propeller type, which is an axial-flow machine. In the sections that follow, each type of hydraulic turbine will be studied separately in terms of the velocity triangles, efficiencies, reaction, and method of operation.

__Hydraulic efficiency.__

It is defined as the ratio of power developed by the runner to the power supplied by the water jet.

__Radial Flow:__

A radial turbine is a turbine in which the flow of the working fluid is radial to the shaft. The difference between axial and radial turbines consists in the way the air flows through the components (compressor and turbine). Whereas for an axial turbine the rotor is ‘impacted’ by the air flow, for a radial turbine, the flow is smoothly orientated at 90 degrees by the compressor towards the combustion chamber and driving the turbine in the same way water drives a watermill. The result is less mechanical and thermal stress which enables a radial turbine to be simpler, more robust and more efficient (in a similar power range as axial turbines). When it comes to high power ranges (above 5 MW) the radial turbine is no longer competitive (heavy and expensive rotor) and the efficiency becomes similar to that of the axial turbines.

__Velocity triangle for Radial FLow:__

Figure 7.11 shows the velocity triangles for radial flow turbine. Figure 7.12 shows the Mollier diagram for a 90⁰ ﬂow radial turbine and diffuser.

As no work is done in the nozzle, we have h_{01} = h_{02}. The stagnation pressure drops from P_{01} to P_{02} due to irreversibilities. The work done per unit mass ﬂow is given by Euler’s turbine equation

If the whirl velocity is zero at exit then

__Velocity triangle for Axial Flow:__

The velocity diagram at inlet and outlet from the rotor is shown in Fig. 7.2. Gas with an absolute velocity C_{1} making an angle α_{1}, (angle measured from the axial direction) enters the nozzle (in impulse turbine) or stator blades (in reaction turbine). Gas leaves the nozzles or stator blades with an absolute velocity C_{2}, which makes and an α_{2} with axial direction. The rotor-blade inlet angle will be chosen to suit the direction β_{2} of the gas velocity V_{2} relative to the blade at inlet. Β_{2} and V_{2} are found by subtracting the blade velocity vector U from the absolute velocity C_{2}.

It is seen that the nozzles accelerate the ﬂow, imparting an increased tangential velocity component. After expansion in the rotor-blade passages, the gas leaves with relative velocity V_{3} at angle β_{3}. The magnitude and direction of the absolute velocity at exit from the rotor C_{3} at an angle α_{3} are found by vectorial addition of U to the relative velocity V_{3}. α_{3} is known as the swirl angle.

__Centrifugal pumps: __

Centrifugal pumps are a sub-class of dynamic axisymmetric work-absorbing turbomachinery. Centrifugal pumps are used to transport fluids by the conversion of rotational kinetic energy to the hydrodynamic energy of the fluid flow. The rotational energy typically comes from an engine or electric motor. The fluid enters the pump impeller along or near to the rotating axis and is accelerated by the impeller, flowing radially outward into a diffuser or volute chamber (casing), from where it exits.

Common uses include water, sewage, petroleum and petrochemical pumping. The reverse function of the centrifugal pump is a water turbine converting potential energy of water pressure into mechanical rotational energy.

__Working of centrifugal Pumps:__

Like most pumps, a centrifugal pump converts mechanical energy from a motor to energy of a moving fluid. A portion of the energy goes into kinetic energy of the fluid motion, and some into potential energy, represented by fluid pressure (Hydraulic head) or by lifting the fluid, against gravity, to a higher altitude.

The transfer of energy from the mechanical rotation of the impeller to the motion and pressure of the fluid is usually described in terms of centrifugal force, especially in older sources written before the modern concept of centrifugal force as a fictitious force in a rotating reference frame was well articulated. The concept of centrifugal force is not actually required to describe the action of the centrifugal pump.

The outlet pressure is a reflection of the pressure that applies the centripetal force that curves the path of the water to move circularly inside the pump. On the other hand, the statement that the “outward force generated within the wheel is to be understood as being produced entirely by the medium of centrifugal force” is best understood in terms of centrifugal force as a fictional force in the frame of reference of the rotating impeller; the actual forces on the water are inward, or centripetal, since that is the direction of force need to make the water move in circles. This force is supplied by a pressure gradient that is set up by the rotation, where the pressure at the outside, at the wall of the volute, can be taken as a reactive centrifugal force. This was typical of nineteenth and early twentieth century writings, mixing the concepts of centrifugal force in informal descriptions of effects, such as those in the centrifugal pump.

__Turbine__

A turbine is a rotary mechanical device that extracts energy from a fluid flow and converts it into useful work. A turbine is a turbo machine with at least one moving part called a rotor assembly, which is a shaft or drum with blades attached. Moving fluid acts on the blades so that they move and impart rotational energy to the rotor. Early turbine examples are windmills and waterwheels.

__Theory of operation:__

**Fig: Schematic of impulse and reaction turbines, where the rotor is the rotating part, and the ****stator**** is the stationary part of the machine.**

A working fluid contains potential energy (pressure head) and kinetic energy (velocity head). The fluid may be compressible or incompressible. Several physical principles are employed by turbines to collect this energy:

Impulse turbines change the direction of flow of a high velocity fluid or gas jet. The resulting impulse spins the turbine and leaves the fluid flow with diminished kinetic energy. There is no pressure change

of the fluid or gas in the turbine blades (the moving blades), as in the case of a steam or gas turbine; all the pressure drop takes place in the stationary blades (the nozzles). Before reaching the turbine, the fluid’s pressure head is changed to velocity head by accelerating the fluid with a nozzle. Pelton wheels and de Laval turbines use this process exclusively. Impulse turbines do not require a pressure casement around the rotor since the fluid jet is created by the nozzle prior to reaching the blading on the rotor. Newton’s second law describes the transfer of energy for impulse turbines.

Reaction turbines develop torque by reacting to the gas or fluid’s pressure or mass. The pressure of the gas or fluid changes as it passes through the turbine rotor blades. A pressure casement is needed to contain the working fluid as it acts on the turbine stage(s) or the turbine must be fully immersed in the fluid flow (such as with wind turbines). The casing contains and directs the working fluid and, for water turbines, maintains the suction imparted by the draft tube. Francis turbines and most steam turbines use this concept. For compressible working fluids, multiple turbine stages are usually used to harness the expanding gas efficiently. Newton’s third law describes the transfer of energy for reaction turbines.

In the case of steam turbines, such as would be used for marine applications or for land-based electricity generation, a Parsons type reaction turbine would require approximately double the number of blade rows as a de Laval type impulse turbine, for the same degree of thermal energy conversion. Whilst this makes the Parsons turbine much longer and heavier, the overall efficiency of a reaction turbine is slightly higher than the equivalent impulse turbine for the same thermal energy conversion.

In practice, modern turbine designs use both reaction and impulse concepts to varying degrees whenever possible. Wind turbines use an airfoil to generate a reaction lift from the moving fluid and impart it to the rotor. Wind turbines also gain some energy from the impulse of the wind, by deflecting it at an angle. Cross flow turbines are designed as an impulse machine, with a nozzle, but in low head applications maintain some efficiency through reaction, like a traditional water wheel. Turbines with multiple stages may utilize either reaction or impulse blading at high pressure. Steam turbines were traditionally more impulse but continue to move towards reaction designs similar to those used in gas turbines. At low pressure the operating fluid medium expands in volume for small reductions in pressure. Under these conditions, blading becomes strictly a reaction type design with the base of the blade solely impulse. The reason is due to the effect of the rotation speed for each blade. As the volume increases, the blade height increases, and the base of the blade spins at a slower speed relative to the tip. This change in speed forces a designer to change from impulse at the base, to a high reaction style tip.

Classical turbine design methods were developed in the mid 19th century. Vector analysis related the fluid flow with turbine shape and rotation. Graphical calculation methods were used at first. Formulae for the basic dimensions of turbine parts are well documented and a highly efficient machine can be reliably designed for any fluid flow condition. Some of the calculations are empirical or ‘rule of thumb’ formulae, and others are based on classical mechanics. As with most engineering calculations, simplifying assumptions were made.

Velocity triangles can be used to calculate the basic performance of a turbine stage. Gas exits the stationary turbine nozzle guide vanes at absolute velocity V_{a1}. The rotor rotates at velocity U. Relative to the rotor, the velocity of the gas as it impinges on the rotor entrance is V_{r1}. The gas is turned by the rotor and exits, relative to the rotor, at velocity Vr2. However, in absolute terms the rotor exit velocity is V_{a2}. The velocity triangles are constructed using these various velocity vectors. Velocity triangles can be constructed at any section through the blading (for example: hub, tip, midsection and so on) but are usually shown at the mean stage radius. Mean performance for the stage can be calculated from the velocity triangles, at this radius, using the Euler equation:

Hence:

where:

specific enthalpy drop across stage

turbine entry total (or stagnation) temperature

turbine rotor peripheral velocity

The turbine pressure ratio is a function of and the turbine efficiency.

Modern turbine design carries the calculations further. Computational fluid dynamics dispenses with many of the simplifying assumptions used to derive classical formulas and computer software facilitates optimization. These tools have led to steady improvements in turbine design over the last forty years.

The primary numerical classification of a turbine is its specific speed. This number describes the speed of the turbine at its maximum efficiency with respect to the power and flow rate. The specific speed is derived to be independent of turbine size. Given the fluid flow conditions and the desired shaft output speed, the specific speed can be calculated and an appropriate turbine design selected.

The specific speed, along with some fundamental formulas can be used to reliably scale an existing design of known performance to a new size with corresponding performance.

Off-design performance is normally displayed as a turbine map or characteristic.

__Performance Curve for pump:__

The pump performance curve shows the correlation between media flow (Q) and the pressure differential or head (H) that the pump creates.

Fig: Pump curve

The pump performance curve shows the correlation between media flow (Q) and the pressure differential or head (H) that the pump creates. Flow is normally given in m^{3}/h or l/s. Pressure differential or head is given in kPa or mws (meter water column).

For variable-speed pumps, the performance curve is given at minimum and maximum RPM.

When several pumps are connected, the final performance curve is achieved by combining the characteristics of the individual pumps.

Parallel-connected pumps are added horizontally to increase Q. For two identical pumps, the maximum Q will double, yet maximum H will be the same. This principle is commonly used in pump systems.

Series-connected pumps are added vertically to increase H. For two identical pumps, the maximum H will double. Maximum Q will remain the same. This principle is commonly used in multi-stage pumps.

The performance curve is used together with the system characteristics when dimensioning and selecting pumps.

**Characteristic curves of a Turbine:**

These are curves which are characteristic of a particular turbine which helps in studying the performance of the turbine under various conditions. These curves pertaining to any turbine are supplied by its manufacturers based on actual tests.

The data that must be obtained in testing a turbine are the following:

1. The speed of the turbine N

2. The discharge Q

3. The net head H

4. The power developed P

5. The overall efficiency h_{o}

6. Gate opening (this refers to the percentage of the inlet passages provided for water to enter the turbine)

The characteristic curves obtained are the following:

a) Constant head curves or main characteristic curves

b) Constant speed curves or operating characteristic curves

c) Constant efficiency curves or Muschel curves

**Constant head curves:** Maintaining a constant head, the speed of the turbine is varied by admitting different rates of flow by adjusting the percentage of gate opening. The power P developed is measured mechanically. From each test the unit power P_{u}, the unit speed Nu, the unit discharge Q_{u} and the overall efficiency o are determined. The characteristic curves drawn are

a) Unit discharge v/s unit speed

b) Unit power v/s unit speed

c) Overall efficiency v/s unit speed

**Constant speed curves:** In this case tests are conducted at a constant speed varying the head H and suitably adjusting the discharge Q. The power developed P is measured mechanically. The overall efficiency is aimed at its maximum value.

The curves drawn are

Constant efficiency curves: These curves are plotted from data which can be obtained from the constant head and constant speed curves. The object of obtaining this curve is to determine the zone of constant efficiency so that we can always run the turbine with maximum efficiency.

This curve also gives a good idea about the performance of the turbine at various efficiencies.