Question 16.5: The preliminary design of an axial flow compressor is to be ...
The preliminary design of an axial flow compressor is to be based upon a simplified consideration of the mean diameter conditions. Suppose that the characteristics of a repeating stage of such a design are as follows:
Stagnation temperature rise \left(\Delta T_{s t}\right) 30 K
Degree of reaction ( ∧) 0.6
Flow coefficienty (V_{f} /U) 0.5
Blade speed (U) 300 m/s
Assuming constant axial velocity across the stage and equal absolute velocities at inlet and outlet, determine the blade angles of the rotor for a shock free flow.
(c_{p} for air = 1005 J/kg K).
Specific work input w=1005 \times 30 J/kg
From Eq. (16.17)
\Delta T_{s t}=\Delta T_{s}=\frac{U V_{f}}{c_{p}}\left(\tan \beta_{1}-\tan \beta_{2}\right) (16.17)
1005 \times 30=(300)^{2} \times(0.5)\left(\tan \beta_{1}-\tan \beta_{2}\right)
or, \tan \beta_{1}-\tan \beta_{2}=0.67 (16.53)
Again from Eq. (16.24),
\Lambda=\frac{V_{f}}{2 U}\left(\tan \beta_{1}+\tan \beta_{2}\right) (16.24)
0.6=\frac{0.5}{2}\left(\tan \beta_{1}+\tan \beta_{2}\right)
\tan \beta_{1}+\tan \beta_{2}=2.4 (16.54)
Eqs (16.53) and (16.54) give
\beta_{1}=56.92^{\circ}, \quad \beta_{2}=40.86^{\circ}