Design Of An Axial Flow Turbine

CHAPTER 3

DESIGN OF AN AXIAL FLOW TURBINE

3.1 AXIAL TURBINE DESIGN

Before designing of any component of gas turbine it is necessary to discuss various parameters that can affect the performance of the component. The important design points that affect the performance of an axial flow turbine are discussed below:

The starting point will be given turbine specification. These should include at least the fluid to be used, fluid stagnation temperature and pressure at inlet, the fluid stagnation or static pressure at outlet, either the fluid mass flow or the turbine power output required and perhaps the shaft speed.

The velocity diagrams at mean diameter.

The number of blades for each blade row.

Centrifugal and fluid bending stresses are calculated for the turbine blades so produced.

The turbine inlet faces have very high stagnation temperature so for this temperature to design the turbine and choose the proper material.

In axial flow turbine the gas high velocity and temperature are coupled. For this high velocity stresses produced in turbine blades so need for safe design and to control vibrations.

In axial flow turbine design the outlet pressure is an important parameter. If it is less than the atmospheric pressure than the chance of cavitations and it is very danger for turbine structural components.

To design the turbine on basis of degree of reaction. Degree of reaction may change from hub to tip.

Turbine design with some non-dimensional parameters like specific speed, flow coefficient etc.

3.2 TURBINE BLADE CASCADES

To design an axial flow turbine blade in 2D followed by mainly free vortex design and constant nozzle angle design but in axial flow turbine free vortex design not much used. Blade design effect all turbine characteristic parameters and performance parameters.

The temperature at turbine inlet is very high almost more than 1000 K. more temperature we achieve more efficiency but the turbine blade material should be withstand for that temperature. The difference between stator blade and rotor blade temperature is almost 200 K so designed for perfect blade stress distribution is important from root to the tip. In axial flow turbine the temperature and velocity distribution are coupled. To consider cooling of turbine blade and with high temperature inlet to increase efficiency the blade design should be effective. In axial turbine blade with high chamber angle and negative stagger angle. Twist in rotor blade in land gas based power plants the nozzle does not choked because if it is choked then we should decrease the pressure ratio in aircraft the stator blade design like that the flow is choked.

A cascade is a stationary array of blades.

Cascade is constructed for measurement of performance similar to that used in axial turbines.

Cascades usually have porous end walls to remove boundary layer for 2D flow.

Radial variations in the velocity field can therefore be excluded.

Cascade analysis relates the fluid turning angles to blade geometry and measure losses in the stagnation pressure.

Turbine cascade are tested in wind tunnels.

However, turbines operate in an accelerating flow and therefore, the wind tunnel flow driver needs to develop sufficient pressure to cause this acceleration.

Cascade analysis provides the blade loading from the surface static pressure distribution and the total pressure loss across the cascade.

Elementary analysis of the flow through a cascade, determine the lift and drag forces acting on the blades.

3.2.1 Blade Theory

The blade section normally aerofoil section that may be defined as a streamlined from bounded principally by two flattened curves whose length and width are very large, relative to its thickness. The symmetrical aerofoil whose axis of symmetry is parallel to the direction of undisturbed velocity of approach is called symmetrical aerofoil. The flow divides around the aerofoil at the leading edge and then re-joins at the trailing edge. The force exerted in this case is only due to friction and the local disturbance.

If the aerofoil is inclined at an angle called as non-symmetrical aerofoil. The components of resultant force are lift and drag. Lift is normal to the direction of the approach velocity and drag parallel to it. The lift is due to unbalanced pressure distribution over the aerofoil surface. The drag force is due to the shearing stress at consequent boundary layer surface. The drag force is made up of a friction drag due to the pure skin friction effect.

The boundary layer is usually laminar for a short distance downstream of the leading edge and then is becomes turbulent. The drag due to a laminar boundary is less than a turbulent layer. If the pressure gradient is server that is if the rate of change of aerofoil profile is too rapid then the fluid in the boundary layer is brought to rest and leaves the surface in confused eddies. This phenomenon is called separation, break-way or flow reversal.

3.2.2 Blade Terminology

Blade profile are usually of aerofoil shape for optimum performance but simple geometrical shapes composed of circular arcs and straight lines are used when cost is more important than the efficiency. The flows around blades in turbines are different from flow around isolated aerofoil because of the effect of adjacent blades. Various geometrical parameters are shown in Fig. 3.1.

Fig. 3.1 Blade terminology

The gas flow around a blade is affected by the flow around an adjacent blade. This effect increases as the solidity ration increases. The gas turbine blades have high solidity. For testing of blade and the groups of blades of constant profile are mounted in parallel fashion at the end of wind tunnel.

The number of blades comprising the cascade has to be sufficient to eliminate any wind tunnel boundary effects and suction slots or porous metal inserts are often provided in the tunnel walls to control the boundary layer. The pressure, velocity and air flow angles are measured at the inlet and outlet of the cascade.

The results obtained from cascades testing require corrections because of the differences between the flow in the actual machine and flow through the cascade.

These differences are:

Annulus wall boundary layers exist at the blade hub and tip.

Adjacent blade rows interfere with the flow pattern around the blade row.

The solidity decreases from hub to tip.

Blade velocity varies from hub to tip and this affects around the blade row.

3.3 LOSSES IN AXIAL FLOW TURBINE

An ideal turbine would develop work equivalent to the isentropic heat drop of the gas but in practice, the actual work obtained from a turbine is much less than the theoretical work or isentropic work. This difference is due to the various losses.

Viscous losses

Profile losses: on account of the profile or nature of the aerofoil cross-sections

Annulus losses: growth of boundary layer along axis.

3-D effects

Secondary flow: flow through curved blade passages

Tip leakage flow: flow from pressure surface to suction surface at the blade tip.

Shock losses

Mixing losses

In axial turbine the secondary losses dominate like tip leakage loss but in turbine the primary loss is less because it work the favourable pressure gradient. Profile and boundary layer losses are less as compare to axial turbine.

3.4 AXIAL TURBINE PERFORMANCE CHARACTERISTIC

The characteristics of axial turbine depends on parameters like diffusion factor, mass flow rate, flow coefficient, work coefficient etc.

For an axial turbine

(3.1)

In terms of non-dimensional parameters

(3.2)

By these the axial turbine performance curve for pressure ratio and efficiency is as per Fig. 3.3.

Fig 3.2 Pressure ratio v/s Efficiency [1]

The efficiency plot shows that it is constant over a wide range of rotational speeds and pressure ratios. This is because the accelerating nature of the flow permits turbine blades to operate with a wide range of incidence.

Fig 3.4 Chocking mass flow [1]

Maximum mass flow is limited by chocking of the turbine. The mass flow characteristics tend to merge into a single curve independent of speed for larger number of stages. When the turbine operates close to its design point (low incidence), the performance curves can be reduced to a single curve. As the number of stages is increased, there is a noticeable tendency for the characteristic to become ellipsoidal. With increase in the number of stages, the chocking mass flow also reduces.

Fig 3.5 Mass flow with multistage

The performance of turbine is limited by some factors:

Compressibility limits the mass flow that can pass through a turbine.

Stress limits the rotational speed.

Inlet high temperature turn affects the stress.

For a given pressure ratio and adiabatic efficiency, the turbine work per unit mass is proportional to the inlet stagnation temperature. Therefore typically a 1% increase in the turbine inlet temperature can produce 2-3% increase in the engine output. Therefore there are elaborate methods used for cooling the turbine nozzle and rotor blades. Turbine blades with cooling can withstand temperature higher than that permissible by the blade materials.

3.4.1 Exit Flow Matching

The operation of a turbine is affected by components upstream (compressor) and downstream (nozzle). The compressor and turbine performance characteristics form an important part of this performance matching. Turbines do not exhibit any significant variation in non-dimensional mass flow with speed. However the turbine operating region is severely affected by nozzle. The nozzle exit area has a significant influence on the off-design operation of a turbine and the engine in general. The operation of the nozzle under choked or unchoked condition also influences the matching. The similarity between the flow characteristic of a nozzle and a turbine is the fact that thermodynamically, both are flow expanders. The matching between the turbine and the nozzle is identical to that between a free-turbine / power-turbine and the main turbine.

Fig 3.6 Matching characteristics of turbine and nozzle

Once the nozzle is choked, the nozzle non-dimensional flow will reach its maximum value and will become independent of the nozzle pressure ratio and therefore the flight speed. This result in the turbine operating point fixed because of matching requirement between turbine and nozzle. Therefore, when the nozzle is choking, the equilibrium running line will be uniquely determined by the fixed turbine operating point and will independent of flight mode.

3.4.2 Turbine Blade Design Methods

In axial flow turbine the design of these blades depend upon the passage Mach number, stress levels and various other parameters. The thickness distributions, suction surface curvature and trailing edge shape are varied for particular application. Turbines blade could be designed specifically for subsonic, transonic or supersonic Mach numbers. The blade profiles with circular arc and parabolic arc camber. Profiles derived graphically or empirically from a specified pressure or Mach number distribution.

Fig 3.7 Conventional blade profiles: steam turbine sections and T6 aerofoil section

Spacing between blades is a critical parameter in turbomachine performance. Closer spacing means lower loading per blade but more number of blades, increased weight and frictional losses. Larger spacing means higher blade loading and lower weight, losses etc. optimum numbers of blades are usually empirical. Pressure distribution over turbine blade is to be analysed with both suction and pressure side. The stagnation pressure property is also to be studied. This analysis is to be done in to 2D blade optimization design methods in AxSTREAM turbomachinery suite.

Fig 3.8 Pressure and velocity distributions on a conventional turbine blade [1]

3.4.3 Three Dimensional Flow Theories

3D flow models in axial turbine are often used for design and analysis

Free vortex design

For constant stagnation enthalpy across the annulus and constant axial velocity, the whirl component of velocity is inversely proportional to the radius.

.r = Constant (3.3)

Constant nozzle exit angle

In this case the nozzle exit angle is constant for turbine stator and rotor blade designs.

= constant (3.4)

Arbitrary vortex case

= (3.5)