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Question 13.7: A seven-stage axial compressor has the following data: Overa......

A seven-stage axial compressor has the following data:
Overall pressure ratio 4.15
Mean rotational speed 266 m/s
Axial velocity 150 m/s
Stage efficiency 0.9
Inlet temperature and pressure are 288 K, 101 kPa.
Calculate the following variables for each stage:

\pi_{\text{s}}, \Delta T_{0\text{s}}, \alpha_1 , \beta_1, \alpha_2, \beta_2 , \alpha_3 , \Lambda, \text{DH}_s,\text{DH}_r

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The total temperature rise for the compressor is calculated following the procedure described in Example 6 and its value is 164.5 K.
The above procedure is followed and the results are arranged in Table 13.7.
The summation of total temperature rise for seven stages is 165.3, which is in good comparison to the value calculated above (164.5).

TABLE 13.7 Variations of the Aerodynamic and Thermodynamic Properties of the Seven-Stage Compressor
Stage 1 2 3 4 5 6 7
T_{01} \text{( K)} 288 315.4 340.4 364.1 386.6 409.2 431.8
\Delta T_{0\text{s}} \text{ (K)} 27.4 25 23.7 22.5 22.6 22.6 21.5
\pi_{\text{s}} 1.333 1.273 1.238 1.208 1.196 1.185 1.165
\alpha_1 0 11.86 11.73 9.48 9.05 9.05 9.05
\beta_1 60.6 57.4 57.5 58.05 58.05 58.05 58.05
\alpha_2 35.16 41.59 41.51 40.5 40.5 40.5 39.56
\beta_2 47 41.65 42.69 42.7 42.7 42.7 43.57
\alpha_3 11.86 11.73 9.84 9.05 9.05 9.05 0
Λ 0.804 0.69 0.692 0.71 0.71 0.71 0.72
\text{DH}_{\text{r}} 0.72 0.72 0.72 0.72 0.72 0.72 0.73
\text{DH}_{\text{s}} 0.72 0.764 0.76 0.77 0.77 0.77 0.77

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