506
13 Axial Compressors
number approximately 0.6). Determine the velocity triangles on the mean radius
taking into account that the deceleration ratios in the rotor ( w 2 /w 1 ) and the postconnected stator ( v 2 /v 3 ) cannot be lower than 0.7. Consider constant axial velocity
across the stage. Determine the work coefficient and the total pressure ratio, assuming a polytropic efficiency of 0.9 (A: ψ ≈ 0.49, p 03 /p 01 ≈ 1.56). Observe that is not
possible to realise the same work at the hub with the same limits on the deceleration
ratios. Determine the velocity triangles at the hub for constant axial velocity in the
stage and the strongest deceleration ratio at 0.7. Observe that this leads to a degree
of reaction approximately zero and a symmetric rotor blade profile (verify the realism on Fig. 12.9). Observe that at the casing, the free vortex flow condition leads
to a rather low work coefficient (A: ψ ≈ 0.25). So, larger work is possible (see next
exercise). Remark the somewhat larger values of work coefficient and flow coefficient on the mean radius of a fan, compared to a typical compressor (Sect. 13.3)
and the very large work coefficient at the hub (A: ψ ≈ 2).
13.6.6 Obtainable Pressure Ratio at the Tip of a Transonic Fan Stage Calculate the total pressure ratio over the fan rotor at the tip with the data of the previous exercise, assuming that the flow in the relative system is straight and that all
compression comes from a normal shock. Derive the flow parameters downstream
of the shock from balances of mass, momentum and energy. Observe that a quadratic equation in velocity is formed from the energy equation by substitution of
density as a function of velocity from the mass balance and substitution of pressure
as a function of velocity from the momentum balance (so, specific shock formulae
from fluid mechanics are not needed). Determine the Mach number at rotor inlet,
the work coefficient and the isentropic re-expansion efficiency of the rotor (A: M w1
≈ 1.42, p 02 /p 01 ≈ 2.11; ψ ≈ 0.42, η sre ≈ 0.95). Remark the large work coefficient, the
large pressure ratio and the high efficiency, but boundary layer losses in the rotor
are not taken into account and neither are the losses in the post-connected stator.
References
1. Boyer KM, O’Brien WF (2003) An improved streamline curvature approach for off-design
analysis of transonic axial compression systems. J Turbomach 125:475–481
2. Calvert WJ, Ginder RB (1999) Transonic fan and compressor design. IMechE J Mech Eng Sci
213:419–436
3. Cumpsty NF (1989) Compressor aerodynamics. Longman Scientific & Technical, New York,
ISBN 0-582-01364-X
4. Day IJ, Freeman C (1994) The unstable behavior of low and high-speed compressors. J Turbomach 116:194–201
5. Fischer A, Riess W, Seume JR (2004) Performance of strongly bowed stators in a four-stage
high-speed compressor. J Turbomach 126:333–338
6. Fottner L (1989) Review of turbomachinery blading design problems. Chapter 1 in AGARD
LS 167. Blading design of axial turbomachines. AGARD, ISBN 92-835-0512-3
7. Gümmer V, Wenger U, Kau H-P (2001) Using sweep and dihedral to control three-dimensional
flow in transonic stators of axial compressors. J Turbomach 123:40–48
13 Axial Compressors
number approximately 0.6). Determine the velocity triangles on the mean radius
taking into account that the deceleration ratios in the rotor ( w 2 /w 1 ) and the postconnected stator ( v 2 /v 3 ) cannot be lower than 0.7. Consider constant axial velocity
across the stage. Determine the work coefficient and the total pressure ratio, assuming a polytropic efficiency of 0.9 (A: ψ ≈ 0.49, p 03 /p 01 ≈ 1.56). Observe that is not
possible to realise the same work at the hub with the same limits on the deceleration
ratios. Determine the velocity triangles at the hub for constant axial velocity in the
stage and the strongest deceleration ratio at 0.7. Observe that this leads to a degree
of reaction approximately zero and a symmetric rotor blade profile (verify the realism on Fig. 12.9). Observe that at the casing, the free vortex flow condition leads
to a rather low work coefficient (A: ψ ≈ 0.25). So, larger work is possible (see next
exercise). Remark the somewhat larger values of work coefficient and flow coefficient on the mean radius of a fan, compared to a typical compressor (Sect. 13.3)
and the very large work coefficient at the hub (A: ψ ≈ 2).
13.6.6 Obtainable Pressure Ratio at the Tip of a Transonic Fan Stage Calculate the total pressure ratio over the fan rotor at the tip with the data of the previous exercise, assuming that the flow in the relative system is straight and that all
compression comes from a normal shock. Derive the flow parameters downstream
of the shock from balances of mass, momentum and energy. Observe that a quadratic equation in velocity is formed from the energy equation by substitution of
density as a function of velocity from the mass balance and substitution of pressure
as a function of velocity from the momentum balance (so, specific shock formulae
from fluid mechanics are not needed). Determine the Mach number at rotor inlet,
the work coefficient and the isentropic re-expansion efficiency of the rotor (A: M w1
≈ 1.42, p 02 /p 01 ≈ 2.11; ψ ≈ 0.42, η sre ≈ 0.95). Remark the large work coefficient, the
large pressure ratio and the high efficiency, but boundary layer losses in the rotor
are not taken into account and neither are the losses in the post-connected stator.
References
1. Boyer KM, O’Brien WF (2003) An improved streamline curvature approach for off-design
analysis of transonic axial compression systems. J Turbomach 125:475–481
2. Calvert WJ, Ginder RB (1999) Transonic fan and compressor design. IMechE J Mech Eng Sci
213:419–436
3. Cumpsty NF (1989) Compressor aerodynamics. Longman Scientific & Technical, New York,
ISBN 0-582-01364-X
4. Day IJ, Freeman C (1994) The unstable behavior of low and high-speed compressors. J Turbomach 116:194–201
5. Fischer A, Riess W, Seume JR (2004) Performance of strongly bowed stators in a four-stage
high-speed compressor. J Turbomach 126:333–338
6. Fottner L (1989) Review of turbomachinery blading design problems. Chapter 1 in AGARD
LS 167. Blading design of axial turbomachines. AGARD, ISBN 92-835-0512-3
7. Gümmer V, Wenger U, Kau H-P (2001) Using sweep and dihedral to control three-dimensional
flow in transonic stators of axial compressors. J Turbomach 123:40–48