Aerodynamics of Compressors and Turbines (AE 651) Autumn Semester 2009 Instructor : Bhaskar Roy Professor, Aerospace Engineering Departm ent I .I .T., Bom bay e-m ail : aeroyia@aero.iitb.ac.in 1
Quiz - 3 1. Gas Turbines Rotors are normally : (a) Pure Impulse Blading (b) Pure Reaction Blading, (c) A combination of impulse and Reaction bladings, (d) None of these 2. Gas Turbine Stators are : (a) Pure Impulse Blading (b) Pure Reaction Blading, (c) A combination of impulse and Reaction bladings, (d) None of these 2 2 AE 651 - Prof Bhaskar Roy, IITB Tutorial-3
3. Impulse blading is associated with : (a) Constant Pressure flow through the blades (b) Constant Temperature flow through the blades (c) Constant Velocity flow through the blades (d) Constant Enthalpy flow through the blades 4. Reaction blading is normally associated with (a) Reduction in Temperature across the blading (b) Reduction in pressure across the blading (c) Reduction in both Temp & Pressure across the blading (d) Reduction in velocity across the blading 3 3 AE 651 - Prof Bhaskar Roy, IITB Tutorial-3
5. Axial flow turbine rotor work is facilitated by (a) High entry Temperature, (b) High entry density (c) High entry velocity (d) High entry Pressure 6. Mechanical work of the turbine rotor is produced by (a) Large change in axial momentum of the fluid, (b) Large change in radial momentum of the fluid (c) Large change in tangential momentum of the fluid, (d) All three 4 4 AE 651 - Prof Bhaskar Roy, IITB Tutorial-3
7. In most gas turbines the flow is chocked at : (a) Stator nozzle entry (b) Stator-nozzle exit (c) Rotor entry (d) Rotor exit 8 . Degree of Reaction in an axial flow turbine is normally (a) Nearly 1.0 (b) Nearly 0 (c) Between 0 and 0.5 (d) Between 0.5 and 1.0 5 5 AE 651 - Prof Bhaskar Roy, IITB Tutorial-3
9. In axial turbine rotor bladed passages main source of losses are (a) Surface friction loss (b) Cooling heat loss (c) Passage vortex loss (d) Rotor-stator interaction loss 10. In axial turbine design the most utilized design law is : (a) Constant Reaction Design law (b) Free Vortex design law ( c) Constant stator exit angle , α 2 ( r) = constant (d) Constant Rotor exit angle , β 3 (r) = constant 6 6 AE 651 - Prof Bhaskar Roy, IITB Tutorial-3
11. In transonic axial turbines the flow is expected to go critical first (a) At the Stator entry (b) At the stator exit (c) At the rotor entry (d) At the rotor exit 12. Turbine Rotors going supersonic may encounter this problem (a) Shock related blade vibration (b) The leading and trailing edges would be difficult to cool (c) Shocks would reduce the work extraction capability ( d) No tangible benefit may accrue 7 7 AE 651 - Prof Bhaskar Roy, IITB Tutorial-3
13 The critical zone for turbine blade cooling is (a) Stator exit station (near T.E) b) Rotor exit station (near T.E.) ( c) Stator entry station (near L.E.) (d) Rotor entry station (near LE) 14. Film Cooling effects cooling by : (a) By blowing a jet of air on the LE by an external blower-injector (b) By passing air through the blades and letting them out at blade tip (c ) By allowing some of the internal passing air to come out through holes (d) By applying a film of coating on the blade surfaces 8 8 AE 651 - Prof Bhaskar Roy, IITB Tutorial-3
15. A typical modern gas turbine cooling technique promotes effective blade cooling of the order of : (a) 50 deg C (b) 200 deg C (c) 500 deg C (d) 1000 deg C 16. If the boundary layer is Turbulent on the blade surface then we get (a) Lower heat transfer from hot gas to blade (b) Higher heat transfer from hot gas to blade ( c) Complete isolation of blade from the hot gas (d) None of the above would hold good 9 9 AE 651 - Prof Bhaskar Roy, IITB Tutorial-3
17. A Radial Turbine rotor typically produces pressure drop of : (a) 2 (b) 4 ( c) 8 (d) 10 18. Maximum temperature in a radial turbine is limited because of (a) High speed of rotation (b) High jet velocity from the stator-nozzle around the rotor tip ( c) Lack of cooling Technology for rotors (d) Limitation on the rotor vane thermal stress 10 10 AE 651 - Prof Bhaskar Roy, IITB Tutorial-3
19. Rothalpy across a radial turbine rotor is assumed as: (a) Relative Total Enthalpy across the is conserved (b) Relative Kinetic energy is conserved (c) Only Rotational Kinetic energy is conserved (d) Relative Total enthalpy minus rotational kinetic energy is conserved 20. Flow in a exit duct of a radial turbine may be diffused (a) to allow higher static pressure at the rotor exit plane (b) to allow lower static pressure at the rotor exit plane (c) to allow higher mass flow through the rotor (d) to allow higher rotor entry tmperature 11 11 AE 651 - Prof Bhaskar Roy, IITB Tutorial-3
Solved examples– Axial Turbines Problem Gas entering a cooled axial flow turbine has following properties. T 01 = 1780 K , P 01 = 1.4 MPa and carries a mass flow of 40 kg/s. The mean radius data are follows : M 1 = 0.3, M 2 = 1.15, U=400 m/s; T 03 = 1550 K, α 1 = α 3 = 0, r m = 0.4 m, C a2 /C a3 = 1 ; =0.04, = w w noz rotor 0.08, γ = 1.3, R = 287 J/kg.K. Compute : i) the flow properties all along the mean line of the stage ii) the degree of reaction iii) Total temperature ∆ T 0 based stage loading Ψ iv) the isentropic efficiency v) the flow areas at various axial stations vi) the hub and tip radii at stations : a) inlet to nozzle, b) exit to nozzle, c) rotor exit 12 12 AE 651 - Prof Bhaskar Roy, IITB Tutorial-3
Solution 13 13 AE 651 - Prof Bhaskar Roy, IITB Tutorial-3
T 1 = T 01 / [1+ ( γ -1).M 1 2 /2] = 1756.3 K; and P 1 = P 01 .(T 1 /T 01 ) γ /( γ -1) = 1321 kPa Therefore, C 1 = M 1 √ ( γ RT 1 ) = 0.3 √ (1.3 x 287 x 1756.3) = 242.8 m/s = C a1 , and C w1 = 0 � m Hence, Area at station 1, A 1 = / ρ 1 .C a1 = 0.0628 m 2 gas Applying same method as before, T 2 = T 02 / [1+ ( γ -1).M 2 2 /2] = 1485.4 K, and C 2 = 856.1 m/s if 4% of the kinetic head is lost in the nozzle blades, ideal T 2 / = 1503.55 K, and C 2 / = 877 m/s and hence, from isentropic laws , one can compute P 02 = 1370.2 kPa and P 2 = 625.5 kPa Given that α 3 = 0 , α 2 = Sin –1 [ Ψ .U/C 2 ], as, from the definitions Ψ = ∆ H 0 /U 2 = (Ca/U). tan α 2 14 14 AE 651 - Prof Bhaskar Roy, IITB Tutorial-3
Using, c p = γ R/( γ -1) > Ψ = ∆ H 0 /U 2 = c p . ∆ T 0 / U 2 = 1.7878; Therefore, α 2 = 56.6 0 , C a2 = C 2 .Cos α 2 = 470 m/s ; & C w2 = C 2 .sin α 2 = 715 m/s, & V w2 = 715 – 400 = 315 m/s Therefore, β 2 = tan –1 {V w2 ./C a2 } = 33.80 0 ; Now also it can be computed that M 2-rel = 0.76 � m At station 2, A 2 = / ρ 2 .C a2 = = 0.58 m 2 gas Axial velocity at stage exit, C a3 = C 3 .cos α 3 = {(C a2 /C a3 ).(cos α 2 /cos α 3 ).C 2 }cos α 3 = 470 m/s Tangential velocity, C w3 = 0; and therefore V w3 = 400 m/s and V3 = √ ( V t3 2 + C a3 2 ) =617 m/s Therefore : exit flow angle β 3 = tan –1 [V w3 /C a3 ] = 40.30 Static temp. at station 3, T 3 = T 03 – C 3 2 /2c p = 1461 K; whence, a 3 = 738.3 m/s 15 15 AE 651 - Prof Bhaskar Roy, IITB Tutorial-3
Using the simplified definition of Degree of reaction, C + C Ψ DR = 1 - w1 w2 = 1 - = 0.106 2.U 2 Mach number at exit, M 3 = 0.6375, and relative exit mach number, M 3-relative = V 3 / a 3 = 0.836 Relative total temperature and pressure at exit, T 03-rel = T 3 + V 3 2 /2c p = 1614 K; and from P 02-rel = 897.3 kPa we can obtain by applying rotor loss coefficient, P 03-rel = 872.7 kPa Using isentropic relation, P3 = 566 kPa and P03 = 731 kPa � m The exit area at station 3, A 3 = / ρ 3 .C a3 = 0.063 m 2 gas 16 16 AE 651 - Prof Bhaskar Roy, IITB Tutorial-3
The final performance parameters are : Temperature ratio, τ T = T 01 /T 03 = 1780/1550 = 1.148 Pressure ratio, π 0T = P 01 /P 03 = 1400 / 731 = 1.915 Efficiency, η 0T = (1- τ T )/ [1- π 0T γ /( γ -1) ] = 92.9% At each station, bade height hi = Ai/(2 π .r m ) Station 1 2 3 Area (m 2 ) 0.06285 0.05792 0.0629 Height (m) 0.025 0.023 0.025 Tip radius (m) 0.4125 0.4115 0.4125 Hub radius (m) 0.3875 0.3885 0.3875 17 17 AE 651 - Prof Bhaskar Roy, IITB Tutorial-3
Problem : Radial Turbines A radial inward-flow turbine with an outer nozzle ring operates with following parameters : Mass flow=2 kg/s, P 01 = 400 kPa, T 01 = 1100 K, P 02 =0.99 P 01 ; Nozzle exit angle, α 2 = 70 0 , Poly eff, η poly = 0.85, Rotor maximum diameter = 0.4 m , V 2r = C a3 , hub/tip radius ratio at rotor exit = 0.4, T 03 = 935 K; [use γ =1.33; R =287 kJ/kg.K ; c p =1.158 kJ/kg-K.] Compute the following : i) Rotor tip speed, rotational speed and rpm of the rotor ii) Mach number, velocities, rotor width at tip, and T 02 -rel iii) Stagnation pressure, Mach number and hub and tip radii at rotor exit iv) At the rotor exit plane V 3 , T 03-rel , β 3 , M 3-rel at r mean v) Values of β 3 , M 3-rel at different radii at rotor exit 18 18 AE 651 - Prof Bhaskar Roy, IITB Tutorial-3
H -H = c .(T - T ) i) Rotor tip speed, U 2 = 01 03 p 01 03 = 1158.(1100- 935) = 437 m / s rotational speed, ω = U 2 / r 2 = 2185 rad/s, hence, RPM, n = 20,870 rpm ii) At rotor tip, C 2 = U 2 / sin α 2 = 437 / sin 70 0 = 465 m/s, And V 2r = C 2 .cos α 2 = 159 m/s 19 19 AE 651 - Prof Bhaskar Roy, IITB Tutorial-3
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