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 fluid flows through the components (compressor and turbine). Whereas for an axial turbine the rotor is 'impacted' by the fluid flow, for a radial turbine, the flow is smoothly orientated perpendicular to the rotation axis, and it drives the turbine in the same way water drives a watermill. The result is less mechanical stress (and less thermal stress, in case of hot working fluids) which enables a radial turbine to be simpler, more robust, and more efficient (in a similar power range) when compared to axial turbines. When it comes to high power ranges (above 5 MW) the radial turbine is no longer competitive (due to heavy and expensive rotor) and the efficiency becomes similar to that of the axial turbines.

Compared to an axial flow turbine, a radial turbine can employ a relatively higher pressure ratio (≈4) per stage with lower flow rates. Thus these machines fall in the lower specific speed and power ranges. For high temperature applications rotor blade cooling in radial stages is not as easy as in axial turbine stages. Variable angle nozzle blades can give higher stage efficiencies in a radial turbine stage even at off-design point operation. In the family of hydro-turbines, Francis turbine is a very well-known IFR turbine which generates much larger power with a relatively large impeller.

Components of radial turbines

The radial and tangential components of the absolute velocity c2 are cr2 and cq2, respectively. The relative velocity of the flow and the peripheral speed of the rotor are w2 and u2 respectively. The air angle at the rotor blade entry is given by

$\,\tan {\beta _{2}}={\frac {c_{r2}}{(c_{\theta 2}-u_{2})}}$ Enthalpy and Entropy diagram

The stagnation state of the gas at the nozzle entry is represented by point 01. The gas expands adiabatically in the nozzles from a pressure p1 to p2 with an increase in its velocity from c1 to c2. Since this is an energy transformation process, the stagnation enthalpy remains constant but the stagnation pressure decreases (p01 > p02) due to losses. The energy transfer accompanied by an energy transformation process occurs in the rotor.

Spouting Velocity

A reference velocity (c0) known as the isentropic velocity, spouting velocity or stage terminal velocity is defined as that velocity which will be obtained during an isentropic expansion of the gas between the entry and exit pressures of the stage.

$\,C_{0}={\sqrt {2C_{p}\,T_{01}\,(1-({\frac {p_{3}}{p_{01}}})^{\frac {\gamma -1}{\gamma }})}}$ Stage Efficiency

The total-to-static efficiency is based on this value of work.

$\,\eta _{t}s\,=\,{\frac {(h_{01}-h_{03})}{(h_{01}-h_{3ss})}}$ $\,\eta _{t}s\,=\,{\frac {\psi \,u_{2}^{2}}{[C_{p}\,T_{01}(1-({\frac {p_{3}}{p_{01}}})^{\frac {(\gamma -1)}{\gamma }}]}}$ Degree of Reaction

The relative pressure or enthalpy drop in the nozzle and rotor blades are determined by the degree of reaction of the stage. This is defined by

R=${\frac {{\textrm {'}}'{static\,\,enthaply\,\,drop\,\,in\,\,rotor}''}{{\textrm {'}}'{stagnation\,\,enthalpy\,\,drop\,\,in\,\,stage}''}}$ The two quantities within the parentheses in the numerator may have the same or opposite signs. This, besides other factors, would also govern the value of reaction. The stage reaction decreases as Cθ2 increases because this results in a large proportion of the stage enthalpy drop to occur in the nozzle ring.

Stage losses

The stage work is less than the isentropic stage enthalpy drop on account of aerodynamic losses in the stage. The actual output at the turbine shaft is equal to the stage work minus the losses due to rotor disc and bearing friction.

• (a) skin friction and separation losses in the scroll and nozzle ring
They depend on the geometry and the coefficient of skin friction of these components.
• (b) Skin friction and separation losses in the rotor blade channels
These losses are also governed by the channel geometry, coefficient of skin friction and the ratio of the relative velocities w3/w2. In the ninety degree IFR turbine stage, the losses occurring in the radial and axial sections of the rotor are sometimes separately considered.
• (c) Skin friction and separation losses in the diffuser
These are mainly governed by the geometry of the diffuser and the rate of diffusion.
• (d) Secondary losses
These are due to circulatory flows developing into the various flow passages and are principally governed by the aerodynamic loading of the blades. The main parameters governing these losses are b2/d2, d3/d2 and hub-tip ratio at the rotor exit.
• (e) Shock or incidence losses
At off-design operation, there are additional losses in the nozzle and rotor blade rings on account of incidence at the leading edges of the blades. This loss is conventionally referred to as shock loss though it has nothing to do with the shock waves.
• (f) Tip clearance loss
This is due to the flow over the rotor blade tips which does not contribute to the energy transfer.

Blade to Gas Speed Ratio

The blade-to-gas speed ratio can be expressed in terms of the isentropic stage terminal velocity c0.

$\,\sigma _{s}={\frac {u_{2}}{c_{0}}}=[2(1+\phi _{2}\cot {\beta _{2}}]^{-1 \over {2}}$ for β2=90o σs=0.707