Example: Axial compressor stage calculation

Calculate:1) velocity triangle, temperature and pressure of compressor stage2) Rotor and stator cascde geometry 3) Stage work, efficiency

Plot1) Rotor and stator cascade geometry and velocity triangles2) Entalpy entropy diagram3) temperature and pressure diagram in the compressor stage

Examplegiven:axial velocity in section 1 cx1 [m/s] 180 cp=100 [J/kg/K]blade speed U [m/s] 280 k=1,4flow speed in section 1 c1 [m/s] 190 R=287 [J/kg/K]

cy2 [m/s] 180pressure in section 1 p1 [Pa] 100000temperature in section 1 T1 [K] 300rotor relative pressure losses R=p02rel/p01rel 0,98stator pressure losses S=p03/p02 0,985

AssumptionAssumptionaxial velocity is constant cx consstage is normal c3=c1rotor and stator incidence i=0

Velocity triangle calculation rotor inletc1y=(c1^2-c1x^2)^0,5 60,82762531=acos(Cx1/C1) 18,68118863Wy1=U-Cy1 219,1723747W1=(Wy1^2+Cx)^0,5 283,61334561=acos(Cx1/W1) 50,63038476

rortor outletc2=(Cy2^2+Cx2^2)^0,5 254,5584412Wy2=U-Cy2 100W2=(Cx2^2+Wy2^2)^0,5 205,91260282=acos(Cx2/C2) 45,022824652=acos(Cx2/W2) 29,06934102

stator outletc3=c1 1903=1 18,68118863

Presented diagram should be a scaled plot

Temperature and pressure Presented diagram should318,05 be a scaled plot

T01=T1+C1^2/(2*cp) 122690,0965p01=p1*(T01/T1)^(k/(k-1)) 340,2182649T01rel=T1+W1^2/(2*cp) 155319,9698p01rel=p1*(T01rel/T1)^(k/(k-1))

152213,5704p02rel=R*p01rel 340,2182649T02rel=T01rel 319,0182649T2=T02rel-W2^2/(2cp) 351,4182649T02=T2+C2^2/(2cp) 121522,3346p2=p02rel*(T2/T02rel)^(k/(k-1)) 170485,2613p02=p2*(T02/T2)^(k/(k-1))

167927,9824p03=S*p02 351,4182649T03=T02 333,3682649T3=T03-c3^2/(2cp) 139628,0928p3=p03*(T3/T03)^(k/(k-1))

stage pressure ratio 1,368716687=p03/p01

W=cp*(T03-T01) 33368,26492W=U*(Cy2-Cy3)

efficiency 0,89426734=(^((k-1)/k)-1)/(T03/T01-1)

Reaction degree 0,569950669R=cp(T2-T1)/(cp(T3-T1))Reaction degree /pressure 0,54310801Rp=(p2-p1)/(p3-p1)

Geometry designHowell corelationROTOR 0,894097734s/l=(1,55/(tg1-tg2)-1)/1,5 1,118445961l/s 21,56104375I iteration - assumption ==1-2i=0 50,630384761'=1+i 0,115638682m=0,23*(0,5)^2+2/500 2,357574422=m**(s/l)^0,5 31,426915442'=2+ 19,20346932=1'-2' 2,0997874052'=2+ 19,20346932=1'-2' 2,099787405=m**(s/l)^0,5 31,169128422'=2+ 19,46125634=1'-2' 2,127974912=m**(s/l)^0,5 31,197315932'=2+ 19,43306883 camber angle=1'-2' 40,91385034 stagger=1/2*(1'+2')

STATOR 0,894097734s/l=(1,55/(tg2-tg3)-1)/1,5 1,118445961l/s 26,34163602I iteration - assumption ==2-3i=0 45,022824652'=2+i 0,094862377m=0,23*(0,5)^2+3/500 2,362812423=m**(s/l)^0,5 21,044001053'=3+ 23,9788236=2'-3' 2,150871049=m**(s/l)^0,5 20,832059683'=3+ 24,19076497=2'-3' 2,16988193=m**(s/l)^0,5 20,851070563'=3+ 24,17175409=2'-3' 32,93694761=1/2*(2'+3')