turbocharge design - calculation sample

8/14/2019 Turbocharge Design - Calculation sample

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Fluid properties - Assume constant properties:

1.333:=... Ratio of specific heat

Cp 1147

J

kg K:= ... Specific heat of air standard at constant

pressure

kJ 1000J:=

kmol 1000 mol:=

... Gas constantR 287

J

kg K:=

P1 1.6bar 0.16 MPa=:=

r 18.5:=

ASSUMPTIONS

rc 2:= ... V3 per V2, cut off ratio

T1 300K 26.85 C=:= ... Temperature inlet of cylinder

11

r 1

rc

1

rc 1( )

0.569=:=


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STAGE 1:

P1 0.16 MPa=

T1 300 K =

u1 214.07kJ

kg:=

r1 621.2:=

1R T1

P1

0.538m

3

kg

=:=

11

11.858

kg

m3

=:=

STAGE 2:

r2r1

r33.578=:=

From table T-9

T2 900K r2 34.31

32.18 34.31920 900( ) K+ 906.87K=:=

h2 932.93kJ

kg

r2 34.31

32.18 34.31955.38 932.93( )

kJ

kg+ 940.641

kJ

kg=:=

P2 P1T2

T1 r 8.948MPa=:=

2R T2

P20.029

m3

kg=:=

21

234.379

kg

m3

=:=

STAGE 3:

T3 rc T2 1813.739373 K=:=


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CENTRIFUGAL COMPRESSOR - TURBOCHARGER

D 92mm:=

Stroke 93.8mm:=

N 4:=... Number of cylinders

V1_2 D

2

4 Stroke N 2494.183293 cm

3=:=

V2V1_2

r 1142.525 cm

3=:=

V1 V2 r 2636.708052 cm3

=:= 2494cm3

2.494L=

V1 V2 2494.183293 cm3

=

RPM 3000rpm:=

m_exhaust 4 V1 V2( )RPM

2 0.728

kg

s=:=

Given (request) data:

mf m_exhaust 0.728kg

s=:= ... The mass flow rate

PR13P1

1atm1.579=:= ... Pressure ratio of compresor

Svaneless 5mm:= ... Vaneless space (between impeller anddiffuser)

rdt 55mm:=... The diffuser throat radius

rdo 65mm:= ... The diffuser outlet radius

Ndif 15:= ... Number of channels of diffuser

Guess & suggestion data:

rperR 0.5:= ... (r/R) The ratio of hub to shroud diameter at theeye

t 0.82:= ... Overall efficiency

0.525:= ... Head coefficient, from Aungier Fig. 1-9


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1.04:= ... Power input factor

0.835:= ... The slip factor

m 0.95:= ... Mechanical efficiency of compressor

limitedness:

W3max 90m

s:= ... Maximum outlet velocities

a3max 11:= ... The maximum included angle of the vaneddiffuser passage

Umax 460m

s:= ... Maksimum tip speed

M1Wmax 0.8:= ... Suggested maximum Mach number at inletimpeller - W1 direction

Tmax 400K := ... Maximum static temperature


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T1To1

1 1( ) M1

2

2+

:= T1 280.673 K=

C1 M1 R T1:= C1 131.074m

s=

Ca1 C1:=

From the isentropic relationship at a point

1Po1

R To1

T1

To1

1

1

:= 1 1.132kg

m3

=

P1 Po1T1

To1

1

:= P1 91.203 kPa=

Therefore the eye tip diameter at inlet is:

R1tmf

1 k Ca1:= R1t 45.630499 mm=

D1t 2 R1t:= D1t 91.261 mm=

And the hub diameter at inlet is:

D1r D1t rperR:= D1r 45.63 mm=

Peripheral speed at the impeller eye tip (shroud) & 1t:

U1t D1tRPM

rev:= U1t 226.974699

m

s=

1t atan Ca1U1t :=

1t 30.006 =

Peripheral speed at the impeller eye root (hub) & 1r:

U1r D1rRPM

rev:= U1r 113.48735

m

s=

1r atanCa1

U1r

:= 1r 49.113096 =

1.b. The impeller outlet diameter


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From Eq (4-11) the stagnation temperature difference is

To3 To1To1

tPR13

1

1

+:= To3 330.632 K=

To3 To1 42.482 K=

From Eq (4-9)

U2To3 To1( ) Cp

:= U2 236.877

m

s=

And Tip flow coefficient (2) at exit of impeller

D2U2 rev

RPM:= D2 95.242 mm=

The new value of To3 & t,

U2 D2 RPM

rev:= U2 236.877

m

s=

To3U2

2

Cp

To1+:= To3 330.632 K=

tTo1 PR13

1

1

To3 To1

:= t 0.82=

Therefore the tip flow coefficient is:

r2D2

2:= r2 47.621175 mm=

2mf

o1 r22 U2

:= 2 0.352109=

The Number of Blades:

Z0.63

1 .83:= Z 11.642=

Z 12:=

10.63

Z:= 0.835= ... Will be used re-calculate


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1.c. Velocity at exit and the the losses in the impeller and diffuser are the same, The

axial depth of the impeller is:

First guess M2 = 0.8 and iteration. The overall loss is proportional to (1 - c) = (1 - 0.82). Half of

the overall loss is therefore 0.5(1 - 0.82) = 0.09 and therefore the effective efficiency of theimpeller in compressing from Po1 to Po2 is (1 - 0.09) ...

M2 1:=

c 1 0.5 1 t( ):= c 0.91=

From Eq (4-11) afer rearranging the subscripts, and To3 = To2:

To2 To3:= To2 330.632 K=

T2To2

1M2

2 R

2 Cp+

:= T2 283.373 K=

PR12 1 cTo2 To1( )

To1+

1

:= PR12 1.655=

P2 Po1T2

To2

1PR12

:= P2 90.456 kPa=

2P2

R T2:=

2 1.112kg

m3

=

Po2P2

T2

To2

1

:= Po2 94.009 kPa=

And TOTAL enthalphy rise (Hrev) at exit of impeller

To2s c To2 To1( ) To1+:= To2s 326.808 K=

H_adiabatic Cp To2s To1( ):= H_adiabatic 44341.039968m

2

s2

=

The head coefficient become ....


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1r 49.113096 =

At outlet section (2):

D2 95.242 mm=

b2 8.311479 mm=

2 atanU2 Cax2

Cr2

:= 2 8.443 =

W2Cr2

cos 2( ):= W2 266.099

m

s=

C2 329.257 ms

=

Cax2 197.808m

s=

Cr2 263.216m

s=

2 acosCr2

C2

:= 2 36.925 =

Z 12=

RPM 47500 rpm=

2 0.352=

0.835=

2. DIFFUSER

In the vaneless space between the impeller outlet and diffuser vanes the flow is that of a free

vortex which at any radius requires that Cx.r = constant.

At the diffuser vane leading edge the radius is (r2 + 10)mm = (47.62 + 10) mm = 57.62 mm

r2D2

2:= r2 47.621 mm=

r2v r2 Svaneless+:= r2v 52.621175 mm=


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Ar3i 2 r2v b2:= Ar3i 0.002748m2

=

Cr3imf

3i Ar3i:= Cr3i 302.407

m

s=

by ITERATION ...

Cr3i 302.407m

s:= ... change this value for iteration

C3i Cr3i2

Cx3i2

+:= C3i 424.543m

s=

T3i To2C3i

2

2 Cp:= T3i 252.063 K=

P3i Po1T3i

To2

1

PR12:= P3i 56.608 kPa=

3iP3i

R T3i:= 3i 0.783

kg

m3

=

Ar3i 2 r2v b2:= Ar3i 0.002748m2

=

Cr3imf

3i Ar3i:= Cr3i 338.5755428

m

s=

No further iterations are necessary. Thus at the inlet to the vanesCr,3,i = 246.2013186 m/s.

3i atanCx3i

Cr3i

:= 3i 41.350188 =

Moving to the radius at the diffuser throat, at the throat radius, 343 mm

Cx3tC2 r2

rdt:= Cx3t 285.084

m

s=

by ITERATION again to find propertes at diffuser throat section ...

Start with assuming Cr,3 = Cr,3,i

Cr3t Cr3i:= Cr3t( ) 338.576m

s=

Cr3t 1308.0100793m


C3t Cx3t2

Cr3t2

+:= C3t 1.339 103

m

s=


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T3t To2C3t

2

2 Cp:= T3t 450.608 K=

P3t Po1T3t

To2

1 PR12:= P3t 579.136 5.464i+( ) kPa=

3tP3t

R T3t:= 3t 4.478 0.042i( )

kg

m3

=

Ar3t 2 rdt b2:= Ar3t 0.002872m2

=

Cr3tmf

3t Ar3t:= Cr3t 56.5986266 0.5339793i+( )

m

s=

It may be seen that there is no change in the new values sothe radial velocity at the diffuser

throat = 184.0268017 m/s

3t atanCx3t

Cr3t

:= 3t 78.770868 0.103249i( ) =

A3tAr3t Cr3t

C3t:= A3t 0.000121 0.000001i+( ) m

2=

As we have 15 diffuser vanes, the width of each throat is:

Throat_widthA3t

Ndif b2

:= Throat_width 0.974021 0.009189i+( ) mm=

2 r2v 105.242 mm=

rdt 2 110 mm=

Svaneless 5 mm=

Moving to the radius at the diffuser outler, at the outlet radius, 550 mm

Cx3C2 r2

rdo:= Cx3 241.225

m

s=

by ITERATION again to find propertes at diffuser outlet section . ..

Start with assuming Cr,3 = Cr,3,i

Cr3o Cr3t:= Cr3o 56.599 0.534i+( )m

s=

Cr3o 87.84762m



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C3o Cx32

Cr3o2

+:= C3o 256.723m

s=

T3o To2 C3o2

2 Cp:= T3o 301.902 K=

P3o Po1T3o

To2

1

PR12:= P3o 116.559 kPa=

3oP3o

R T3o:= 3o 1.345

kg

m3

=

Ar3o 2

rdo

b2:=

Ar3o 0.003394m

2=

Cr3omf

3o Ar3o:= Cr3o 159.4398561

m

s=

It may be seen that there is no change in the new values sothe radial velocity at the diffuser

throat = 87.84762 m/s

3o atanCx3

Cr3o

:= 3o 56.536926 =

A3oAr3o Cr3o

C3o:= A3o 0.002108m

2=

As we have 15 diffuser vanes, the width of each throat is:

Throat_width_outletA3o

Ndif b2:= Throat_width_outlet 16.909629 mm=

Overall dimension of DIFFUSER:

At inlet:

r2v 52.621 mm=

3i 41.350188 =

At throat:

rdt 55 mm=


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3t 78.770868 0.103249i( ) =

Throat_width 0.974021 0.009189i+( ) mm=

At outlet:

rdo 65 mm=

3o 56.536926 =

Throat_width_outlet 16.909629 mm=

Ndif 15=

TURBINE - TURBOCHARGER

P4 0.474MPa=

T4 888.694 K=

From previous data - calculation:

Po1 P4 0.474 MPa=:= ... Stagnation pressure at inlet to nozzles

To1 T4 888.694 K =:= ... Stagnation temperature at inlet to nozzles

m_flow m_exhaust 0.728kg

s=:= ... The mass flow of exhaust gas available to the turbine

Assumptions :

P2 .725 Po1 0.344MPa=:= ... Static pressure at exit from nozzles

T2 0.9275 To1 824.264 K=:= ... Static temperature at exit from nozzles

P3 0.5 Po1 0.237MPa=:= ... Static pressure at exit from rotor

T3 0.86325 To1 767.165 K=:= ... Static temperature at exit from rotor

To3 1.002 T3 768.7K=:= ... Stagnation temperature at exit from rotor

r3av_r2 0.5:= ... Ratio r,ave / r1


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RPM 47500rpm= ... Rotational speed

Analysis:

a). The total-to-static efficiency is given by


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t_ts

1To3

To1

1 P3Po1

1

0.849=:=

b). The outer diameter of rotor, inlet diameter

Cx3 0:= Cx2 U2=

U2 Cp To1 To3( ) 370.99m

s=:=

D2U2 rev

RPM 149.166 mm=:=

c). The enthalphy loss coefficient for the nozzles and rotor rows

Nozzle loss coefficient:

T2s To1P2

Po1

1

820.093 K=:=

NT2 T2s

To1 T20.064736=:=

Rotor loss coefficient:

U3 U2 r3av_r2 185.495m

s

=:=

C3 2 Cp To3 T3( ) 59.328m

s=:= C3

23519.754213

m2

s2

=

W3 C32

U32

+ 194.752m

s=:= W3

237928.205778

m2

s2

=

h3_h3s Cp T3P3

P2

1( )

T2

18314.248869m

2

s2

=:=


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Rh3_h3s

r3av_r2 W32

0.966=:=

d). The blade outlet angle at the mean diameter 3,av, and

3av acotC3

U3

72.264 =:=

e). The total-to-total efficiency of the turbine

t_t1

1

t_ts

1

2r3av_r2 cot 3av( )( )

2

0.858558=:=

f). The volume flow rate at rotor exit

Po3P3

T3

To3

1

238.888 kPa=:=

ho1_ho3ss Cp To1 1Po3

Po1

1

160.353

kJ

kg=:=

3

P3

R T3 1.076

kg

m3=:=

Q3m_flow

30.676

m3

s=:=

g). The hub and tip diameters of the rotor at exit

Q3 r3t2

r3h2

( ) C3=

Q3 2 r3av h C3=


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- END of CALCULATION -


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turbocharge design - calculation sample

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