Aerodynamics of Compressors and Turbines (AE 651) Autumn Semester - - PowerPoint PPT Presentation

Aerodynamics

• f

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

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AE 651- Prof Bhaskar Roy, IITB

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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

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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

AE 651- Prof Bhaskar Roy, IITB

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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

AE 651- Prof Bhaskar Roy, IITB

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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 : a) High impeller outlet flow velocity b) High outlet static pressure c) High specific energy input d) High noise

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AE 651- Prof Bhaskar Roy, IITB

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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

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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

AE 651- Prof Bhaskar Roy, IITB

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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

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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

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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

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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

AE 651- Prof Bhaskar Roy, IITB

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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

AE 651- Prof Bhaskar Roy, IITB

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Solved Example on Centrifugal Compressor

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AE 651- Prof Bhaskar Roy, IITB

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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 P01 = 100 kPa, and T01 = 300 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.

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AE 651- Prof Bhaskar Roy, IITB

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iii) For an absolute velocity of 150 m/s, diffuser efficiency

• f 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

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AE 651- Prof Bhaskar Roy, IITB

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Solution: i) For the given radial vaned impeller of the centrifugal compressor, β2 = 0. The slip factor may be computed from Stanitz slip factor relation = 0.9057. The power to drive the compressor is: = 2.3 x 0.9057 x 5002 = 521 kW Hence, the shaft power required , Pshaft is = 542.5 kW

s

0.63.π σ = 1- N

Total

2 c s 2

W = m.H = m.σ .U

.

• mech

c mech

W / η = m.H / η

• AE 651- Prof Bhaskar Roy, IITB

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AE 651- Prof Bhaskar Roy, IITB

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ii) The total-to-total efficiency of the compressor is:

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// // 03 01 03 01 03 01 03 01

h

• h

T

• T

= = h

• h

T - T

0c

η

= 0.82 Now from, π0C, we can extract P03 = 536.5 kPa And using the isentropic law,

2 s 2 0c p 01

(Ψ.σ .(U ) 1+ η C T

γ γ-1

= ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦

03 3

P = = , P

// // 03 03 2 p 3 03 3 03 03 01 01

T T T T -C / 2.c where, H = (H

• H ) + H

= 528 kJ / kg

γ γ γ-1 γ-1

⎛ ⎞ ⎛ ⎞ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠

AE 651- Prof Bhaskar Roy, IITB

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hence, P3 = 519 kPa iii) At the impeller exit (at tip) Mach number M2 = C2 / a2 , where a2 is the local speed of sound. Now C2 = and a2 where for a degree of reaction 0.5, H2- H1 = ½ (H3 - H1) Now, H3 - H1 = (H03 – H01) + = 232.5 kJ/kg; & hence, H2- H1 =116.25 kJ/kg So, H2 = (H01 – ½ . Cw2) + (H2 – H1) = 406.7 kJ/kg ; And, hence, C2 = 492 m/s, and a2 = 472 m/s; whereby M2 = 1.221

( ) ( )

02 2 03 01 01 2 03 02

2 H

• H

= 2 H

• H )+(H
• H

, since H = H

2

(γ -1).H

2

γ.R.T = =

( )

1 2 2 C - C 1 3 2

AE 651- Prof Bhaskar Roy, IITB

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Now the diffuser efficiency may be written as :

γ γ-1 3 2 / 2 3 2 diff -vane 3 2 3 2

P H

• 1

P H - H η = = H - H H - H ⎡ ⎤ ⎛ ⎞ ⎢ ⎥ ⎜ ⎟ ⎢ ⎥ ⎝ ⎠ ⎢ ⎥ ⎣ ⎦

From which the static pressure ratio across the diffuser may be computed as , P3/P2 = 2.126 And, hence P2 = 244 kPa, and

γ γ 3.5 // // γ-1 γ-1 02 02 02 2 2 2

P T H 528 = = = = 2.4925 P T H 406.5 ⎛ ⎞ ⎛ ⎞ ⎡ ⎤ ⎜ ⎟ ⎜ ⎟ ⎢ ⎥ ⎣ ⎦ ⎝ ⎠ ⎝ ⎠

so that P02 = 608.2 kPa

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AE 651- Prof Bhaskar Roy, IITB

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From the impeller exit velocity triangle, Cr22 = C22 – Cw22 = C22 – (σs.U2)2 , whence it may be computed Cr2 = 193 m/s

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AE 651- Prof Bhaskar Roy, IITB

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iv) For the impeller the total-to-total efficiency,

( )

γ-1 γ 01 02 01 // 02 01 02 01 03 01

H . P / P

• 1

h

• h

= = h

• h

H

• H

0c

η ⎡ ⎤ ⎢ ⎥ ⎣ ⎦

= 0.9 (or 90%) Assuming that the angular momentum is conserved : i.e r.Cw = constant , r3 / r2 = Cw3 / Cw2 = C3/ σs.U2 = 0.22 (assuming the diffuser exit is fully tangential).

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AE 651- Prof Bhaskar Roy, IITB

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vi) The angular velocity of the impeller is, ω = U2/(2π.r2) Now, using the continuity condition in radial plane, ω = U2.ρ2.b2.Cr2/ Which yields, the rotational speed , n = 530 rps ≈ 31800 rpm

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m

• AE 651- Prof Bhaskar Roy, IITB

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Take Home assignment on Centrifugal Compressor

AE 651- Prof Bhaskar Roy, IITB

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Centrifugal compressor tutorial problem set

• 1. A centrifugal compressor operates with air entering

the impeller with axial velocity of 100 m/s. The impeller is radial vaned. At rotor exit the relative air angle measured with respect to radial direction is 26.60, radial velocity is 120 m/s and the tip sped is 500 m/s. For an air flow rate of 2.5 kg/s and ηmechanical = 95% compute the power required to drive the compressor. At the impeller eye if the radius ratio is 0.3 compute a suitable inlet

• uter diameter, assuming the entry flow to be
• incompressible. If the compressor efficiency is given as

η0C = 80% compute the overall stagnation pressure ratio

• achieved. Assume exit diffuser velocity to be negligible.

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AE 651- Prof Bhaskar Roy, IITB

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2) a) The design point data of a centrifugal compressor is given as : 7 kg/s, P01 = 100 kPa, T01 =300 K respectively and the geometry is given as straight radial vanes and no inlet guide vanes, and at inlet eye tip a blade angle

• f β1t= 500 and the design point Mach number of 0.9.

The inlet eye hub/tip radius ratio is 0.5. The tip speed is 450 m/s. Compute : i) the air density at the inlet plane; ii) Eye tip diameter; iii) the rotor rpm, iv) the impeller tip diameter. b) If the same centrifugal compressor operates in a situation where the relative axial entry velocity is same as the relative exit radial velocity of the impeller. The impeller has 30 vanes. Compute at the impeller exit : i) the stagnation temperature ratio of the impeller; ii) Stagnation pressure ratio of the impeller, iii) the axial width of the impeller at the tip.

AE 651- Prof Bhaskar Roy, IITB

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3) The impeller tip speed of a centrifugal compressor is 366 m/s. Compute the impeller exit mach number for a slip factor of 0.90 and exit radial velocity of 30 m/s. If the impeller tip flow area is 0.1 m2 and that the impeller works with efficiency, η0-impeller of 90% compute the mass flow rate. 4) At the entry to a centrifugal compressor the eye hub / tip ratio is 0.4, maximum tip relative Mach number is 0.9 , with the flow coming in axially in absolute

• sense. If the mass flow is specified as 4.536 kg/s

compute the, i) rotating speed, ii) eye tip diameter, and iii) flow coefficient, Ca/U at the impeller inlet eye tip.

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AE 651- Prof Bhaskar Roy, IITB

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5) Guide vanes designed with free-vortex principles is added in front of a centrifugal compressor, to turn the flow away so as to reduces the relative velocity at inlet to the impeller. At eye tip air leaves the guide vane at 91.5 m/s and at 200 to the axial

• direction. Compute, i) the maximum inlet relative

Mach number, and ii) impeller total-to-total efficiency, assuming a no-loss flow in the guide

• vanes. Given: Reye_tip = 0.457 m, Rimpeller_tip = 0.762m,

Slip Factor = 0.9, Vr2 = 53.4 m/s , n = 11,000 rpm, P2 = 223 kPa

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AE 651- Prof Bhaskar Roy, IITB

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