Lect-23. In this lecture... Tutorial on axial flow turbines. Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay
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1 Lect-
2 In this lecture... Lect- utoril on xil flow turbines Prof. Bhskr Roy, Prof. A M Prdeep, Deprtment of Aerospce, II Bomby
3 Problem # Lect- A single stge gs turbine opertes t its design condition with n xil bsolute flow t entry nd exit from the stge. he bsolute flow ngle t the nozzle exit is 70 deg. At stge entry, the totl pressure nd temperture re kp nd 850 o respectively. he exhust sttic pressure is 00 kp, the totl to sttic efficiency is 0.87 nd men blde speed is 500 m/s. Assuming constnt xil velocity through the stge, determine () the specific work done (b) the Mch number leving the nozzle (c) the xil velocity (d) totl to totl efficiency (e) stge rection. Prof. Bhskr Roy, Prof. A M Prdeep, Deprtment of Aerospce, II Bomby
4 Problem # Lect- α Sttor/Nozzle β α V Rotor U V β α Prof. Bhskr Roy, Prof. A M Prdeep, Deprtment of Aerospce, II Bomby 4
5 c Lect- Solution: Problem # We know tht totl to sttic efficiency, η ts p w [ (P /P ) ] ( γ ) / γ Specific work is, t w t η ts c p kJ /kg [ ] ( γ ) / γ (P /P) [ ( /. ) ] (b) M From the At w the / w nozzle γr velocity t /U exit, tringle, 76 0 themch number / 500 w 0, w t 55 m / s is U w Prof. Bhskr Roy, Prof. A M Prdeep, Deprtment of Aerospce, II Bomby 5
6 We Lect- Solution: Problem # w know Hence, M / sin α tht 588 / 588m / s. 87 / c p 97 97K (c) he xil velocity, cos α 00 m / s (d) he totl - to - totl efficiency is relted to the totl - to - sttic efficiency s : η tt η tt η ts 0. 9 w t Prof. Bhskr Roy, Prof. A M Prdeep, Deprtment of Aerospce, II Bomby 6
7 Lect- Solution: Problem # P P P P 0 s 0s 0 P c p s Expnsion process in turbine stge s Prof. Bhskr Roy, Prof. A M Prdeep, Deprtment of Aerospce, II Bomby 7
8 Lect- Solution: Problem # (e) tnβ R Degree From the x U / of velocity ( rection, nd tringle, tnβ /U)tn α R x / 000 tnα ( /U)(tnβ U / tnβ ) Prof. Bhskr Roy, Prof. A M Prdeep, Deprtment of Aerospce, II Bomby 8
9 Problem # Lect- ombustion gses enter the first stge of gs turbine t stgntion temperture nd pressure of 00 K nd 4.0 br. he rotor blde tip dimeter is 0.75m, the blde height is 0. m nd the shft speed is 0,500 rpm. At the men rdius the stge opertes with rection of 50%, flow coefficient of 0.7 nd stge loding coefficient of.5. Determine () the reltive nd bsolute flow ngles for the stge; (b) the velocity t nozzle exit; (c) the sttic temperture nd pressure t nozzle exit ssuming nozzle efficiency of 0.96 nd the mss flow. Prof. Bhskr Roy, Prof. A M Prdeep, Deprtment of Aerospce, II Bomby 9
10 Lect- Solution: Problem # V U α β β V V U V Sttor/Nozzle Rotor Prof. Bhskr Roy, Prof. A M Prdeep, Deprtment of Aerospce, II Bomby 0
11 Lect- Solution: Problem # () he stge loding is given by ψ Also, tnβ Δh 0 R x ( ψ 68. /U o ( / + nd (V w R) /( w /U)(tnβ Simplifying the bove equtions, V Substituting vlues of ψ, β ) /U For 50% rection stge, β + o tnβ ( ( /U) nd α /U)(tnβ ) / tnβ /U) φ nd β 68. o ( ψ R x + nd tnβ / α ) R) /( β /U) o Prof. Bhskr Roy, Prof. A M Prdeep, Deprtment of Aerospce, II Bomby
12 Lect- Solution: Problem # (b) At the blde the men rdius, r speed,u he xil velocity, ( 0500 ( φu 0. ) / 0. 5m / 0) π m / s nd herefore, velocity t the nozzle exit, / cos α / cos m / s m m m m / s (c) he 0 sttic temperture t the nozzle exit, / c p /( 60) 6. K Prof. Bhskr Roy, Prof. A M Prdeep, Deprtment of Aerospce, II Bomby
13 Lect- Solution: Problem # he nozzle efficiency, (P P /P ) 4 ( γ ) / γ η n η n h h /. 986br h h s (P /P / ) ( γ ) / γ he mss flow rte is m m ( / 87 ρ A (P 6. ) /R )A kg / s Prof. Bhskr Roy, Prof. A M Prdeep, Deprtment of Aerospce, II Bomby
14 Problem # Lect- A single stge xil flow turbine opertes with n inlet temperture of 00 K nd totl pressure of.4 br. he totl temperture drop cross the stge is 44 K nd the isentropic efficiency of the turbine is 0.9. he men blde speed is 98 m/s nd the mss flow rte is 8.75 kg/s. he turbine opertes with rottionl speed of 000 rpm. If the convergent nozzle is operting under choked condition determine () blde-loding coefficient (b) pressure rtio of the stge nd (c) flow ngles. Prof. Bhskr Roy, Prof. A M Prdeep, Deprtment of Aerospce, II Bomby 4
15 Problem # Lect- α Sttor/Nozzle β α V Rotor U V β α U Prof. Bhskr Roy, Prof. A M Prdeep, Deprtment of Aerospce, II Bomby 5
16 () ψ Problem # he blde loding is defined s cpδ U 98 Lect- (b) he isentropic efficiency of turbine, η P0 Δ0 or 0. 5 P ηt he pressure rtio of the turbine is P P K Δ K nd P 0 γ /( γ ). 8 br 0 ( γ ) / γ [ (P /P ) ] Prof. Bhskr Roy, Prof. A M Prdeep, Deprtment of Aerospce, II Bomby t 0 0s Δ 0 6
17 Problem # Lect- (c)since the nozzle is choked, the exit Mch number is unity. herefore, nd therefore, he xil cos α γ + he sttic temperture t the nozzle exit is he bsolute velocity of the gses leving the choked nozzle is velocity From the velocity tringles, 0 / γr m / s. Uφ m / s. 8 / nd α K. o Prof. Bhskr Roy, Prof. A M Prdeep, Deprtment of Aerospce, II Bomby 7
18 Problem # Lect- U tnβ he or or U nd tnα turbine tnα α tnβ tnα c o p U therefore, tnβ specific Δ φ o tnα β φ tnα work, w or tnβ o or t c p φ 9. 6 Δ β + o o tnα U (tn α tnα ) Prof. Bhskr Roy, Prof. A M Prdeep, Deprtment of Aerospce, II Bomby 8
19 Problem # 4 Lect- A multi-stge xil turbine is to be designed with impulse stges nd is to operte with n inlet pressure nd temperture of 6 br nd 900 K nd outlet pressure of br. he isentropic efficiency of the turbine is 85 %. All the stges re to hve nozzle outlet ngle of 75 o nd equl inlet nd outlet rotor blde ngles. Men blde speed is 50 m/s nd the xil velocity is 50 m/s nd is constnt cross the turbine. Estimte the number for stges required for this turbine. Prof. Bhskr Roy, Prof. A M Prdeep, Deprtment of Aerospce, II Bomby 9
20 Problem # 4 Lect- w w α β U α V w V V β V w V β V α β Sttor/Nozzle U Rotor Prof. Bhskr Roy, Prof. A M Prdeep, Deprtment of Aerospce, II Bomby 0
21 Hence, P P 0e Δ Lect- Solution: Problem # 4 Since the overll pressure rtio is known, 0es 0es ( γ ) / γ 0overll K From the velocity tringles, 0 / c Since, there is no chnge in stgntion temperture in the nozzle, + / c p p η t 6 0. /. ( 900 0es ) 0. 85( 900 / c / cos α p ) 74. 6K / K 50 / cos m / s Since this is n impulse turbine, the degree of R x h h h h 0 or h h K rection, R x 0 Prof. Bhskr Roy, Prof. A M Prdeep, Deprtment of Aerospce, II Bomby
22 tnβ V We cn see tht herefore, Δ ( /( Lect- Solution: Problem # 4 From the velocity tringles t rotor entry, β sin α / cos β 44. 5m / s he temperture drop per stge is K he number of stges required for the turbine is 0overll o 0 0 V ) U) / + V / c ( sin 75 50) / p for cons tn t xil velocity K / stges. / 48 Prof. Bhskr Roy, Prof. A M Prdeep, Deprtment of Aerospce, II Bomby
23 Exercise Problem # Lect- An xil flow turbine operting with n overll stgntion pressure of 8 to hs polytropic efficiency of Determine the totl-to-totl efficiency of the turbine. If the exhust Mch number of the turbine is 0., determine the totl-to-sttic efficiency. If, in ddition, the exhust velocity of the turbine is 60 m/s, determine the inlet totl temperture. Ans: 88%, 86.7%, 70.6 K Prof. Bhskr Roy, Prof. A M Prdeep, Deprtment of Aerospce, II Bomby
24 Exercise Problem # Lect- he men blde rdii of the rotor of mixed flow turbine re 0. m t inlet nd 0. m t outlet. he rotor rottes t 0,000 rev/min nd the turbine is required to produce 40kW. he flow velocity t nozzle exit is 700 m/s nd the flow direction is t 70 to the meridionl plne. Determine the bsolute nd reltive flow ngles nd the bsolute exit velocity if the gs flow is kg/s nd the velocity of the through-flow is constnt through the rotor. Ans: α 70 deg, β7.0 deg, α 8.4 deg, β 50.7 deg Prof. Bhskr Roy, Prof. A M Prdeep, Deprtment of Aerospce, II Bomby 4
25 Exercise Problem # Lect- An xil flow gs turbine stge develops.6mw t mss flow rte of 7. kg/s. At the stge entry the stgntion pressure nd temperture re 77 kp nd 77, respectively. he sttic pressure t exit from the nozzle is 48 kp nd the corresponding bsolute flow direction is 7 to the xil direction. Assuming the xil velocity is constnt cross the stge nd the gs enters nd leves the stge without ny bsolute swirl velocity, determine () the nozzle exit velocity; (b) the blde speed; (c) the totl-to-sttic efficiency; (d) the stge rection. Ans: 488m/s, 66. m/s, 0.8, 0.8 Prof. Bhskr Roy, Prof. A M Prdeep, Deprtment of Aerospce, II Bomby 5
26 Exercise Problem # 4 Lect- A single stge xil turbine hs men rdius of 0 cm nd blde height t the sttor inlet of 6 cm. he gses enter the turbine stge t 900 kp nd 00 K nd the bsolute velocity leving the sttor is 600 m/s nd inclined t n ngle of 65 deg to the xil direction. he reltive ngles t the inlet nd outlet of the rotor re 5 deg nd 60 deg respectively. If the stge efficiency is 0.88, clculte () the rotor rottionl speed, (b) stge pressure rtio (c) flow coefficient (d) degree of rection nd (e) the power delivered by the turbine. Ans: 550 rpm,.46, 0.6, 0.4, 4.6 MW Prof. Bhskr Roy, Prof. A M Prdeep, Deprtment of Aerospce, II Bomby 6
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