Axial Turbine Stages

An axial flow turbine operates in the exactly reverse of an axial flow compressor. A set of static guide vanes or nozzle vanes accelerates and adds swirl to the fluid and directs it to the next row of turbine blades mounted on a turbine rotor.

Stage velocity triangle

The angles in the absolute system are noted by alpha (α) and the angles in the relative system are noted by beta (β). Axial and tangential components of both absolute and relative velocities are shown in the figure. Static and stagnation values of pressure and enthalpy in the absolute and relative systems are also shown.

Velocity triangle for a turbine stage

It is often assumed that the axial velocity component remains constant through the stage. From this condition we get,
c_x = c₁ cos α₁ = c₂ cos α₂:= w₂ cos β₂ = c₃ cos α₃ = w₃ cos α₃ Also, for constant axial velocity yields a useful relation:

tan α₂ + tan α₃ = tan β₂ + tan β₃

Single impulse stage

A single-stage impulse turbine is shown in Figure

Single-stage impulse turbine

There is no change in the static pressure through the rotor of an impulse machine. The variation of pressure and velocity of the fluid through the stage is also shown in Figure.

The absolute velocity of the fluid increases corresponding to the pressure drop through the nozzle blade row in which only transformation of energy occurs. The transfer of energy occurs only across the rotor blade row. Therefore, the absolute fluid velocity decreases through this as shown in the figure. In the absence of any pressure drop through the rotor blades the relative velocities at their entry and exit are the same for fricitionless flow. To obtain this condition the rotor blade angles must be equal. Therefore, the utilization factor is given by

$E = U \frac{(c_{y2} + c_{y3})}{\frac{1}{2} c_{2}}$

Multi stage velocity compounded impulse

When the pressure drop available is large, it cannot all be used in one turbine stage. A single stage utilizing a large pressure drop will have an impractically high peripheral speed of its rotor. This would lead to either a larger diameter or a very high rotational speed. Therefore, machines with large pressure drops employ more than one stage.
One of the methods to employ multi-stage expansion in impulse turbines is to generate high velocity of the fluid by causing it to expand through a large pressure drop in the nozzle blade row. This high velocity fluid then transfers its energy in a number of stages by employing many rotor blade rows separated by rows of fixed guide blades. A two-stage velocity compounded impulse turbine is shown in Figure

Two-stage velocity-compounded impulse turbine

The decrease in the absolute velocity of the fluid across the two rotor blade rows (R₁ and R₂) is due to the energy transfer; the slight decrease in the fluid velocity through the fixed guide blades (F) is due to losses. Since the turbine is of the impulse type, the pressure of the fluid remains constant after its expansion in the nozzle blade row. Such stages are referred to as velocity or Curtis stages.

Multi stage pressure compounded impulse

There are two major problems in velocity-compounded stages:
*The nozzles have to be of the convergent-divergent type for generating high (supersonic) steam velocity. This results in a more expensive and difficult design of the nozzle blade rows.

• High velocity at the nozzle exit leads to higher cascade losses. Shock waves are generated if the flow is supersonic which further increase the losses.

To avoid these problems, another method of utilizing a high pressure ratio is employed in which the total pressure drop is divided into a number of impulse stages. These are known as pressure-compounded or Rateau stages. On account of the comparatively lower pressure drop, the nozzle blade rows are subsonic (M < 1). Therefore, such a stage does not suffer from the disabilities of the velocity stages.

Two-stage pressure-compounded impulse turbine

Figure shows the variation of pressure and velocity of steam through the two pressure stages of an impulse turbine. The nozzle blades in each stage receive flow in the axial direction.

Some designers employ pressure stages up to the last stage. This gives a turbine of shorter length as compared to the reaction type, with a penalty on efficiency.

Reaction stages

Figure shows two reaction stages and the variation of pressure and velocity of the gas in them. The gas pressure decreases continuously over both fixed and moving rows of blades. Since the pressure drop in each stage is smaller as compared to the impulse stages, the gas velocities are relatively low. Besides this the flow is accelerating throughout. These factors make the reaction stages aerodynamically more efficient though the tip leakage loss is increased on account of the relatively higher pressure difference across the rotor blades.

Two-stage reaction turbine

Multi-stage reaction turbines employ a large pressure drop by dividing it to smaller values in individual stages. Thus the reaction stages are like the pressure-compounded stages with a new element of “reaction” introduced in them, i.e. of accelerating the flow through rotor blade rows also.

Blade-to-gas speed ratio

The blade-to-gas speed ratio parameter (velocity ratio) σ = u/c₂. Efficiencies of the turbine stages can also be plotted against this ratio. Such plots for some impulse and reaction stages are shown in Figure.

Variation of utilization factor and stage
efficiency with blade-to-gas speed ratio

The performance of steam turbines is often presented in this form. The curves in Figure also show the optimum values of the velocity ratio and the range of off-design for various types of stages. The fifty per cent reaction stage shows a wider range. Another important aspect that is depicted here is that in applications where high gas velocities (due to high pressure ratio) are unavoidable, it is advisable to employ impulse stages to achieve practical and convenient values of the size and speed of the machine. Sometimes it is more convenient to use an isentropic velocity ratio. This is the ratio of the blade velocity and the isentropic gas velocity that would be obtained in its isentropic expansion through the stage pressure ratio.

Losses and efficiencies

The losses occur in an actual turbine due to disc and bearing friction. Figure shows the energy flow diagram for the impulse stage of an axial turbine. Numbers in brackets indicate the order of energy or loss corresponding to 100 units of isentropic work (h₀₁ – h_03ss).

Energy flow diagram for the impulse stage of an axial turbine

It is seen that the energy reaching the shaft after accounting for stage cascade losses (nozzle and rotor blade aerodynamic losses) and leaving loss is about 85% of the ideal value; shaft losses are a negligible proportion of this value.

See also

Axial Compressor
Centrifugal Compressor

References

• Yahya, S M (2010). Turbines, Compressors and Fans 4th Edition. TATA McGraw-Hill Education. ISBN 9780070707023.
• Venkanna, B. K. Fundamentals of Turbomachinery. Prentice-Hall Of India. ISBN 9788120337756.
• Onkar, Singh. Applied Thermodynamics. New Age International(P) Ltd., New Delhi - 2009.