151
References
3.8.12 Axial Turbine
Consider an axial turbine according to Fig. 1.9 (Chap. 1). The outer diameter
of the turbine and the supply duct diameter are 1 m. The hub diameter is 0.5 m.
n = 300 rpm, ρ = 1000 kg/m
3
. On the arithmetically average radius ( r = 0.375 m), the
stator deviates the flow by + 30° with respect to the axial direction, while the rotor
outflow is at − 60°. The absolute flow leaves the rotor axially on the entire rotor
radius. Stator vanes and rotor blades are designed for constant work and constant
axial velocity along the radius.
1. Sketch the velocity triangles on the average radius (upstream and downstream
of the rotor). Determine the axial velocity and the flow rate. Determine the rotor
inlet angle with respect to the axial direction on the average radius.
2. Determine rotor torque and rotor power.
3. Determine the pressure on the inlet manometer (gauge pressure: relative to
atmospheric pressure), assuming that the inlet manometer is on the supply duct
(at a somewhat larger distance upstream of the turbine inlet than suggested by
the figure) with centre of the manometer 3 m above the downward water level
(tail water). Assume for the loss coefficients: stator: ξ = 0.05 related to the outlet
kinetic energy v 1
2
2
/ ; rotor: ξ = 0.05 related to the kinetic energy of the outlet
relative velocity w 2
2
2
/ ; diffuser ξ = 0.50 related to the inlet kinetic energy v 2
2
2
/
(all velocities on the mean radius).
4. Determine stator outlet angle and rotor outlet angle at the rotor periphery, measured to the axial direction.
A: Q = 4.01 m
3
/s; β 1 = −49.1º; P rot = 185.4 kW; p-p a = 21.56 kPa; α 1 = 23.4º;
β 2 = − 66.6º.
References
1. Adachi T, Sugita N, Yamada Y (2004) Study on the performance of a Sirocco fan. Int J of
Rotating Mach 10:415–424
2. Aungier RH (2000) Centrifugal compressors: a strategy for aerodynamic design and analysis.
ASME Press. ISBN 0-7918-0093-8
3. Bleier FP (1998) Fan handbook. McGraw-Hill. ISBN 0-07-005933-0
4. Eck B (1972) Ventilatoren, 5th edn. Springer. ISBN 3-540-05600-9
5. Gülich JF (2010) Kreiselpumpen, 3th edn. Springer. ISBN 978-3-642-05478-5
6. Japikse D, Marscher WD, Furst RB (1997) Centrifugal pump design and performance,
Concepts ETI. ISBN 0-933283-09-1
7. Kim K-Y, Seo S-J (2004) Shape optimization of the forward-curved-blade centrifugal fan
with Navier-Stokes analysis. J Fluids Eng 126:735–742
8. Kim S, Park J, Choi B, Baek J (2012) Flow analysis and assessment of loss models in the
symmetric volute of a turbo-blower. J Fluids Eng 134:011101
9. Pfleiderer C (1961) Die Kreiselpumpen für Flüssigkeiten und Gase, 5th edn. Springer. no ISBN
10. Qiu X, Japikse D, Zhao J, Anderson MR (2011) Analysis and validation of a unified slip factor model for impellers at design and off-design conditions. J Turbomach 133:041018
11. Von Backström TW (2006) A unified correlation for slip factor in centrifugal impellers. J
Turbomach 128:1–10
References
3.8.12 Axial Turbine
Consider an axial turbine according to Fig. 1.9 (Chap. 1). The outer diameter
of the turbine and the supply duct diameter are 1 m. The hub diameter is 0.5 m.
n = 300 rpm, ρ = 1000 kg/m
3
. On the arithmetically average radius ( r = 0.375 m), the
stator deviates the flow by + 30° with respect to the axial direction, while the rotor
outflow is at − 60°. The absolute flow leaves the rotor axially on the entire rotor
radius. Stator vanes and rotor blades are designed for constant work and constant
axial velocity along the radius.
1. Sketch the velocity triangles on the average radius (upstream and downstream
of the rotor). Determine the axial velocity and the flow rate. Determine the rotor
inlet angle with respect to the axial direction on the average radius.
2. Determine rotor torque and rotor power.
3. Determine the pressure on the inlet manometer (gauge pressure: relative to
atmospheric pressure), assuming that the inlet manometer is on the supply duct
(at a somewhat larger distance upstream of the turbine inlet than suggested by
the figure) with centre of the manometer 3 m above the downward water level
(tail water). Assume for the loss coefficients: stator: ξ = 0.05 related to the outlet
kinetic energy v 1
2
2
/ ; rotor: ξ = 0.05 related to the kinetic energy of the outlet
relative velocity w 2
2
2
/ ; diffuser ξ = 0.50 related to the inlet kinetic energy v 2
2
2
/
(all velocities on the mean radius).
4. Determine stator outlet angle and rotor outlet angle at the rotor periphery, measured to the axial direction.
A: Q = 4.01 m
3
/s; β 1 = −49.1º; P rot = 185.4 kW; p-p a = 21.56 kPa; α 1 = 23.4º;
β 2 = − 66.6º.
References
1. Adachi T, Sugita N, Yamada Y (2004) Study on the performance of a Sirocco fan. Int J of
Rotating Mach 10:415–424
2. Aungier RH (2000) Centrifugal compressors: a strategy for aerodynamic design and analysis.
ASME Press. ISBN 0-7918-0093-8
3. Bleier FP (1998) Fan handbook. McGraw-Hill. ISBN 0-07-005933-0
4. Eck B (1972) Ventilatoren, 5th edn. Springer. ISBN 3-540-05600-9
5. Gülich JF (2010) Kreiselpumpen, 3th edn. Springer. ISBN 978-3-642-05478-5
6. Japikse D, Marscher WD, Furst RB (1997) Centrifugal pump design and performance,
Concepts ETI. ISBN 0-933283-09-1
7. Kim K-Y, Seo S-J (2004) Shape optimization of the forward-curved-blade centrifugal fan
with Navier-Stokes analysis. J Fluids Eng 126:735–742
8. Kim S, Park J, Choi B, Baek J (2012) Flow analysis and assessment of loss models in the
symmetric volute of a turbo-blower. J Fluids Eng 134:011101
9. Pfleiderer C (1961) Die Kreiselpumpen für Flüssigkeiten und Gase, 5th edn. Springer. no ISBN
10. Qiu X, Japikse D, Zhao J, Anderson MR (2011) Analysis and validation of a unified slip factor model for impellers at design and off-design conditions. J Turbomach 133:041018
11. Von Backström TW (2006) A unified correlation for slip factor in centrifugal impellers. J
Turbomach 128:1–10