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
Tutorial -2 1 AE 651- Prof Bhaskar Roy, IITB Tutorial-2
Quiz -2 1) Slip occurs in a centrifugal compressor because a) There is always a rotating slip between the impeller rotor & the shaft b) Flow separation near the impeller tip on the lagging surface. c) Flow doesn’t stay attached at the impeller entry (eye). d) Flow goes supersonic in the impeller vane passage 2) Slip in a centrifugal compressor can be reduced by : ( a) Decreasing the number of impeller vanes; (b) Increasing the number of impeller vanes; (c) Increasing the length of the impeller vanes; (d) Decreasing vane impeller thickness 2 AE 651- Prof Bhaskar Roy, IITB Tutorial-2
3) Slip in a centrifugal compressor is due to : a) Incomplete diffusion in the inlet guide vanes b) Incomplete diffusion in the impeller vanes c) Incomplete diffusion in the casing vanes d) Mis-match between the compressor and turbine 4) Operating speed of a Centrifugal Compressor compared to an Axial compressor is normally higher because : a) Tip speed limitation of axial compressors is more stringent b) Centrifugal compressors are more robust machines structurally c) Higher operating speeds allow Centrifugal compressors higher stall margins 3 AE 651- Prof Bhaskar Roy, IITB Tutorial-2
5) Backward curved centrifugal vanes, compared to forward curved vanes, provide : a) High impeller outlet flow velocity b) High outlet static pressure c) High specific energy input d) High noise 6) Forward curved centrifugal vanes, compared to Backward curved vanes, provide : The Question is a) High impeller outlet flow velocity wrongly posed. It b) High outlet static pressure stands cancelled c) High specific energy input d) High noise 3 AE 651- Prof Bhaskar Roy, IITB Tutorial-2
7) Discharge velocity from the centrifugal fan impeller is highest for : (a) Radial vaned (b) Forward curved (c) Backward curved vanes (d) Same for all the vane shapes 8) Loss in a centrifugal compressor is significantly dependant on a) Impeller surface area b) Inlet turbulence c) High exit kinetic energy d) Inlet incidence mis-match 4 AE 651- Prof Bhaskar Roy, IITB Tutorial-2
9) As per fluid mechanic hypothesis an ideal frictionless fluid when used in a centrifugal compr a) Shall effect maximum work transfer as there are no losses b) Shall be able to effect no work transfer at all. c) Shall bring the machine to a halt d) Shall need infinite number of blades to do any work 10) Simple Radial equilibrium theory considers that inside the flow domain radially: (a) Temperature is constant; (b) Pressure is constant, (c) density is constant, (d) All are constant 5 AE 651- Prof Bhaskar Roy, IITB Tutorial-2
11) A vaneless static diffuser in a centrifugal compressor gives: a) Higher efficiency b) Higher Flow Coefficient c) Higher Stall margin d) Higher flow operating range 12) Word Done factor is used as a design safety measure and allows for a) Higher work input for a centrifugal compressor than is required to allow higher turbine power rating b) Higher efficiency at design point c) Compensation for unknown aerodynamic losses d) Higher efficiency at various off-design operating points 6 AE 651- Prof Bhaskar Roy, IITB Tutorial-2
13) Inlet Guide vanes are used in Centrifugal compressor inlet eye primarily to: a) Avoid shocks and non-uniform flows at inlet b) Increase design point compressor efficiency c) Extend compressor operation to higher mass flows d) Guard the impeller inlet part from foreign objects 14) Backward curved vanes are used to promote a) Higher work input per unit mass flow b) Higher efficiency of the compressor unit c) Higher Impeller vane tip speeds d) Higher slip factor 7 AE 651- Prof Bhaskar Roy, IITB Tutorial-2
15) Backward curved vanes experience a) High stresses in the vanes to due to curved vanes b) High temperature rise in the impeller vanes c) Higher vibration d) Higher noise 16) Axial Compressors have gone transonic to a) Increase engine fuel efficiency b) Decrease engine weight c) Conform to new noise regulations d) To cater to transonic/supersonic speed aircraft 8 AE 651- Prof Bhaskar Roy, IITB Tutorial-2
17) Transonic axial compressors compared to the subsonic ones typically has : a) Higher mass flow operating range b) Lower mass flow operating range c) Same mass flow operating range d) Same mass flow range at a higher mass flows 18) Multiple Circular airfoils are used in transonic axial compressors to a) Control diffusion on the blade surfaces b) Promote higher blades stress tolerance d) Blade surface boundary layer control d) Allow controlled vortex blade design 9 AE 651- Prof Bhaskar Roy, IITB Tutorial-2
19) Variable stagger blades and vanes are used in compressors to promote : a) Higher pressure ratio b) Operation at High speeds c) Tolerance to non-uniform inlet flows d) Tolerance to blade vibration and stagger 20) Hysteresis in compressors occurs when a) The compressor is operating at very high speeds b) The compressor is operating at very low speeds c) The compressor is operating under stalled flow conditions d) Inter-cooling is used in compressors End of Quiz -2 10 AE 651- Prof Bhaskar Roy, IITB Tutorial-2
Solved Example on Centrifugal Compressor 11 AE 651- Prof Bhaskar Roy, IITB Tutorial-2
Solved Example of Centrifugal Compressor Problem Statement: A centrifugal compressor has an impeller with 21 vanes (radial) , a vaneless diffuser and no inlet guide vanes. At the entry P 01 = 100 kPa, and T 01 = 30 0 K. i) For an operating mass flow of 2.3 kg/s , the impeller tip speed of 500 m/s, and mechanical efficiency of 96% compute the power required to drive the compressor ii) For an diffuser exit velocity of 100 m/s and total-to-total efficiency of 82% compute the stagnation and static pressures at diffuser exit . 12 AE 651- Prof Bhaskar Roy, IITB Tutorial-2
iii) For an absolute velocity of 150 m/s, diffuser efficiency of 0.84 and a degree of reaction of 0.5, Compute the stagnation and static pressures, absolute Mach number and radial velocity at the impeller exit. iv) Compute the total-to-total efficiency of the impeller assuming conservation of angular momentum. Compute the radius ratio across the diffuser vanes. For an impeller tip width of 0.06 m compute the impeller rotational speed 13 AE 651- Prof Bhaskar Roy, IITB Tutorial-2
Solution: i) For the given radial vaned impeller of the centrifugal compressor, β 2 = 0. The slip factor may be computed from Stanitz slip factor relation 0.63. π σ = 1- = 0.9057. s N . The power to drive the compressor is: � � 2 = 2.3 x 0.9057 x 5002 = 521 kW W = m.H = m. σ .U c s 2 Total Hence, the shaft power required , P shaft is � � W / η = m.H / η = 542.5 kW mech c mech 14 AE 651- Prof Bhaskar Roy, IITB Tutorial-2
15 AE 651- Prof Bhaskar Roy, IITB Tutorial-2
ii) The total-to-total efficiency of the compressor is: // // h - h T - T 03 01 03 01 η = = 0c = 0.82 h - h T - T 03 01 03 01 γ ⎡ ⎤ 2 γ -1 ( Ψ . σ .(U ) = 1+ η s 2 Now from, π 0C , ⎢ ⎥ 0c C T ⎢ ⎥ ⎣ ⎦ p 01 we can extract P 03 = 536.5 kPa And using the isentropic law , γ γ ⎛ ⎞ ⎛ ⎞ // // T T γ -1 γ -1 P = 03 03 ⎜ ⎟ ⎜ ⎟ 03 = , 2 T T -C / 2.c ⎝ ⎠ ⎝ ⎠ P p 3 03 3 3 where, H = (H - H ) + H = 528 kJ / kg 03 03 01 01 16 AE 651- Prof Bhaskar Roy, IITB Tutorial-2
hence, P 3 = 519 kPa iii) At the impeller exit (at tip) Mach number M 2 = C 2 / a 2 , where a 2 is the local speed of sound . ( ) ( ) Now C 2 = 2 H - H = 2 H - H )+(H - H , since H = H 02 2 03 01 01 2 03 02 = = and a 2 γ .R.T ( γ -1).H 2 2 where for a degree of reaction 0.5, H 2 - H 1 = ½ (H 3 - H 1 ) ( ) 1 2 2 Now, H 3 - H 1 = (H 03 – H 01 ) + C - C 1 3 2 = 232.5 kJ/kg; & hence, H 2 - H 1 =116.25 kJ/kg So, H 2 = (H 01 – ½ . C w2 ) + (H 2 – H 1 ) = 406.7 kJ/kg ; And, hence, C 2 = 492 m/s, and a 2 = 472 m/s; whereby M 2 = 1.221 17 AE 651- Prof Bhaskar Roy, IITB Tutorial-2
Now the diffuser efficiency may be written as : ⎡ ⎤ γ ⎛ ⎞ P γ -1 ⎢ ⎥ H -1 3 ⎜ ⎟ ⎢ ⎥ 2 P ⎝ ⎠ ⎢ ⎥ / 2 H - H ⎣ ⎦ η = 3 2 = diff -vane H - H H - H 3 2 3 2 From which the static pressure ratio across the diffuser may be computed as , P 3 /P 2 = 2.126 And, hence P 2 = 244 kPa, and γ γ 3.5 ⎛ ⎞ ⎛ ⎞ // // ⎡ ⎤ P T H 528 γ -1 γ -1 02 = 02 = 02 = = 2.4925 ⎜ ⎟ ⎜ ⎟ ⎢ ⎥ P T H ⎣ 406.5 ⎦ ⎝ ⎠ ⎝ ⎠ 2 2 2 so that P 02 = 608.2 kPa 18 AE 651- Prof Bhaskar Roy, IITB Tutorial-2
From the impeller exit velocity triangle, Cr 22 = C 22 – C w22 = C 22 – ( σ s .U 2 ) 2 , whence it may be computed Cr 2 = 193 m/s 19 AE 651- Prof Bhaskar Roy, IITB Tutorial-2
iv) For the impeller the total-to-total efficiency , ⎡ ⎤ γ -1 ( ) H . P / P - 1 γ ⎢ ⎥ 01 02 01 // h - h ⎣ ⎦ 02 01 η = = 0c h - h H - H 02 01 03 01 = 0.9 (or 90%) Assuming that the angular momentum is conserved : i.e r.C w = constant , r 3 / r 2 = C w3 / C w2 = C 3 / σ s .U 2 = 0.22 (assuming the diffuser exit is fully tangential ). 20 AE 651- Prof Bhaskar Roy, IITB Tutorial-2
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