Question 16.7: 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 ( \Delta T_{s t} ) | 30 K |
| Degree of reaction ( \Lambda ) | 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 \mathrm{~J} / \mathrm{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
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
The above two equations give
\beta_{1}=56.92^{\circ}, \quad \beta_{2}=40.86^{\circ}