Clearance and windage losses
A clearance gap must exist between the rotor vanes and the shroud. Because of the pressure difference between the pressure and suction surfaces of a vane, a leakage flow occurs through the gap
introducing a loss in efficiency of the turbine. The minimum clearance is usually a compromise between manufacturing difficulty and aerodynamic requirements. Often, the minimum clearance is determined by the differential expansion and cooling of components under transient operating conditions that can compromise the steady state operating condition. According to Rohlik (1968), the loss in specific work as a result of gap leakage can be determined with the simple proportionality
where Δh0 is the turbine specific work uncorrected for clearance or windage losses and c/bm is the ratio of the gap to average vane height ½i:e:; bm 5 ð1=2Þðb2 1 b3Þ]. A constant axial and radial gap,
c = 0.25 mm, was used in the analytical study of Rohlik quoted earlier. According to Rodgers (1969), extensive development on small gas turbines has shown that it is difficult to maintain clear- ances less than about 0.4 mm. One consequence of this is that as small gas turbines are made progressively smaller the relative magnitude of the clearance loss must increase.
The nondimensional power loss due to windage on the back of the rotor has been given by Shepherd (1956) in the form
where Ω is the rotational speed of the rotor and Re is a Reynolds number. Rohlik (1968) used this expression to calculate the loss in specific work due to windage,
where m_ is the total rate of mass flow entering the turbine and the Reynolds number is defined by Re 5 U2D2/ν2, ν2 being the kinematic viscosity of the gas corresponding to the static temperature T2 at nozzle exit.
Cooled 90 IFR turbines
The incentive to use higher temperatures in the basic Brayton gas turbine cycle is well known and arises from a desire to increase cycle efficiency and specific work output. In all gas turbines designed for high efficiency, a compromise is necessary between the turbine inlet temperature desired and the temperature that can be tolerated by the turbine materials used. This problem can be minimized by using an auxiliary supply of cooling air to lower the temperature of the highly stressed parts of the turbine exposed to the high temperature gas. Following the successful application of blade cooling techniques to axial-flow turbines, methods of cooling small radial gas turbines have been developed.
According to Rodgers (1969), the most practical method of cooling small radial turbines is by film (or veil) cooling (Figure 8.16) where cooling air is impinged on the rotor and vane tips. The main problem with this method of cooling being its relatively low cooling effectiveness, defined by
Rodgers refers to tests that indicate the possibility of obtaining ε 5 0.30 at the rotor tip section with a cooling flow of approximately 10% of the main gas flow. Since the cool and hot streams rapidly mix, effectiveness decreases with distance from the point of impingement. A model study of the heat transfer aspects of film-cooled radial-flow gas turbines is given by Metzger and Mitchell (1966).