Lect-33. In this lecture... Tutorial on centrifugal compressors. Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay

Transcription

1 Let- 33

2 In this leture... Let-33 utorial on entrifugal ompressors

3 Problem # At the inlet of a entrifugal ompressor eye, the relative Mah number is to be limited to he hub-tip radius ratio of the induer is 0.4. he eye tip diameter is 0 m. If the inlet veloity is axial, determine, (a) the maximum mass flow rate for a rotational speed of 960 rpm, (b) the blade angle at the induer tip for this mass flow. he inlet onditions an be taken as 0.3 kpa and 88 K. 3

4 Problem # U r t rm r h β V 4

5 M M Let-33 Solution: Problem # he rotational speed at the induer tip is U πdn / 60 π / m / s From the veloity traingle, we an see that rel rel 0 V γr γr( Simplifying, / γr U P / 00) 0. U m / s / 00 5

6 Solution: Problem # A 0 P γ /( γ ) P0 0 P Substituting, ρ /R m / kPa. 57kg / m Annulus area at the inlet, P P 3 A / K π d 4 ( r h /r t ) 6

7 Solution: Problem # Sine the flow is axial, a m ρ he blade inlet angle at the tip is tanβ β A /U o kg / s 7

8 Problem # A entrifugal ompressor has a pressure ratio of 4: with an isentropi effiieny of 80% when running at 5000 rpm and induing air at 93 K. urved vanes at the inlet give the air a pre-whirl of 5 o to the axial diretion at all radii. he tip diameter of the eye of the impeller is 50 mm. he absolute veloity at inlet is 50 m/s and the impeller diameter is 600 mm. alulate the slip fator. 8

9 Problem # 5 V w U 9

10 Δ Δ w. 005 Let-33 Solution: Problem # Exit stagnation temperature is 0 ( )( γ ) / γ π 93( 4) herefore the isentropi temperature rise, 0s K he atual temperature rise, K Work done per unit mass is, w kJ/kg (. 4 ) /. 4 Δ K P Δ Δ 0s 0 / η 0

11 Solution: Problem # Peripheral veloity at the tip of the eye, U w πdn / 60 π 0. 5 sin m / s 5000 / m / s Peripheral veloity at the tip of the impeller, U πdn / 60 π / m / s

12 Solution: Problem # We know that power input is, w U w U w 79 or, 0 w m / s w herefore, the slip fator is, σ s w /U 0. 86

13 Problem # 3 Air at a stagnation temperature of enters the impeller of a entrifugal ompressor in the axial diretion. he rotor, whih has 7 radial vanes, rotates at 5,000 rpm. he stagnation pressure ratio between diffuser outlet and impeller inlet is 4. and total-to-total effiieny is 83%. Determine the impeller tip radius. Assume the air density at impeller outlet is kg/m 3 and the axial width at entrane to the diffuser is mm, determine the absolute Mah number at that point. Assume that the slip fator σ - /N, where N is the number of vanes. 3

14 Problem # 3 he speifi work required is w Sine Expres sing U σ /N / Substituting all other values, herefore, the impeller radius is r t U U p w w 0, w ( π U U ( γ ) / γ tt w ) Sine, Ω 5000 π 0 ση / Ω 0. 88m U w σu in terms of effiieny and pressure U / rad / s 45 m / s ratio, 4

15 Problem # 3 Mah number, M / a / γr where, m /( ρ πr b r w We σu know herefore, 400 that or, or, M t w 400 h m / s 0 h ) r /( h h / w K π σu. 4 m / s ( σu h 87 0 σu ) / ) p m / s 5

16 Problem # 4 A entrifugal ompressor with bakward leaning blades develops a pressure ratio of 5: with an isentropi effiieny of 83 perent. he ompressor runs at 5000 rpm. Induers are provided at the inlet of the ompressor so that air enters at an absolute veloity of 0 m/s. he inlet stagnation temperature is 50 K and the inlet air is given a pre-whirl o to the axial diretion at all radii. he mean diameter of the eye of the impeller is 50 mm and the impeller tip diameter is 600 mm. Determine the slip fator and the relative Mah number at the impeller tip. 6

17 Problem # 4 U β V a Induer Ω U α V Fixed inlet guide vane Exit veloity triangle Inlet veloity triangle 7

18 0 0s Δ 0s K Let-33 Solution: Problem # 4 ( π ) K Atual temperature rise, he speifi work required, Given that ( γ ) / γ 50( 5) Δ 50 m / s, 0. 4 /. 4 0atual w w K 5. 6K p kj /kg Δ Δ 0s / 0atual sin α η 56. m / s / sin 8

19 Solution: Problem # 4 U and Sine, U w πd m w N / 60 π / m / s πd N / 60 π / U w m / s he slip fator, σ t U w w w /U / m / s

20 Problem # 4 U β V a Induer Ω U α V Fixed inlet guide vane Exit veloity triangle Inlet veloity triangle 0

21 From the V M M 0 and rel Solution: Problem # 4. 9 m / s V 0 0 a impeller (U / γr / 0s w w 0 a ) exit K veloity / K. 9 / ( ) m / s he relative Mah number at the impeller tip is rel η p ( os α triangle, ) (U w )