Question 2 The following data refer to a single stage axial flow gas turbine: In

Question

Question 2 The following data refer to a single stage axial flow gas turbine: Inlet stag. Temp., Toi Stage Efficiency, ??? Flow coefficient, ? Gas enters the stage, Axial velocity, Cx-const. 240 m/s The stage reaction, R Assuming y 1.33 (specific heats ratio) & Gas Constant R -0.287 kJ/kgK 1200 K 0.91 0.80 0 50% Determine: (a) The stator blade angles (011 & ?2) (b) The rotor blade angles (B2 & ?3) (c) The stage total/stagnation temperature drop (d) Show that -+ cos-?3 nis 7 (e) Determine n,

Explanation / Answer

(a) , (b)Here flow coefficient is given and by using that from data book the stage loading coefficient ? is assumed to be 2.7

?=(Ca/U)(Tan?2+tan??3)

Rx=(Ca/U)(-Tan?2+tan??3) /2

simplifying the equations we get tan??3=[(?/2)+R]/(Ca/u) and

tan??2=[(?/2)-R]/(Ca/u)

(Ca/u)=0.80

by substituting all the values in the above equations we get

??3 =68.2°?

??2=46.98 °?

since the stage reaction is 50% ?2=?3=68.2 °?

?3=?2=46.98 °

(c) C2=Ca/cos?2?=(?U)/cos68.2=(0.80*240)/0.371=517.007m/s

T2=T01-[(C22)/2Cp]=1200-(5172)/(2*1330)=1099.515K

therefore the total temperature drop = 1200-1099.515=100.484K

(e) ??ts= wt    = 0.892

CpT01[1-(pressure ratio)(?-1?)/??]

since pressures are not given the temperatures are taken into consideration and thus wt values are taken according to them and also considering MACH number from the chart and thus finally we obtain as 89.2% efficiency

(d) Efficiency of nozzle ?n = [1-(T2/T01)]/[1-(pressure ratio)((?-1?)/?)]

thus by solving we get nozzele efficiency as 0.96

by substituting all the values in equation we can prove left hand side =right hand side

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