Question

TQi The rotor and stator rows arrangement of an axial compressor stage and their general velocity diagrams are shown in Figure 1.1 (a) and (b), respectively. The compressor rotor blade speed is set at 100 m's and the inlet absolute flow velocity for rotor (C1) and stator (C:) are given in APPENDIX A (Each student will have different data) Consider normal stage condition and constant axial flow throughout the stage at 50 m's 01 C 0 SS 93 ROTOR t=100 m/s W2 -50 m/s W 6 STATOR Figure 1.1(a) A compressor stage Figure 1.166) Velocity diagrams U (a) By using a graphical method, draw the velocity diagrams at the inlet and outlet of the rotor. State all the vectors including its vector components. (Take 1 cm: 10 m/s). (12 marks) (b) Howell (1942) graph in APPENDIX B can be manipulated to calculate the total-to-total efficiency of a compressor stage through Equation 1.1. By using Howell (1942) graph and data from the velocity diagrams, determine the total- to-total efficiency. Assume both inlet rotor blade angle (as) and inlet stator blade angle (22) are at 44.5°. Take air density as 1.225 kg/m Aporotor + Apo stator Mt1 pU(Cy2-cyl) (1.1) (9 marks) () If three dimensional analysis is considered for the actual stage work, calculate the total-to-total efficiency for 4 stages compressor by taking into account the value of mean work done factor in APPENDIX C. (4 marks)

Answer 1

We are going to represent the velocity diagram as follows: Subindex 1 represents inlet, and 2 the outlet CA and C2 are the absolute velocities. Cwn and Cur are the swirl velocities. Cry and Crz are the blade relative velocities. Cf1 and Cf2 are the axial flow velocities. U is the linear reloaty of the blade. vane angle. a is the guide ß is the blade angle.

U inlet velocity triangle C=55m/= 5.5cm C2 = 93m/s = 9.3cm U= 100M)10 cm Cui Crn CHA Rotor blades Br Cr2 Cz dr Cf2 outlet Velocity triangle Cw2 U Engineering model: Constant axial flow throughout the stage, Cf1 = Cf2 50 mls we consider normal stage condition. so 5.0 cm

Thus, the swirl velocities are : 2 c=c+c w1 m Cw = 16-01 = V552 - 50² = 22.91 . = 2.3cm S m Cw2 =V6-02 = 1932 - 502 = 78.41 - : 7.8cm S The guide vane angles are Cw = Citan a w1 Ai = tan = tan 22.91 50 = 24.6 Cw2 = Cf2tan az A2 = tan (= tan 75:1) = 575

Now, the blade relative velocities are Cr1 = (U-C.)* + c)n = V(100 - 22.91)” + 50º = 91.88. m = 9.2cm C= V(U - c..)? + c} n = V(100 - 78.41) + 50° = 54.46. m = 5.5cm S Then, the blade angle: C f1 cos ß, = Cri C f1 Biz = COS = COS 50 91.9 = 57° C, rl f2 B2=cos = COS 50 54.46 = = 23.30 r2