Aerodynamic Performance of Large Centrifugal Compressors

3812_3v001t01a009_82_gt_17.pdf

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Aerodynamic Performance of Large

Centrifugal Compressors

The aerodynamic performance of impellers and diffusers of the large cent rifugal compressor were studied. A performance design procedure based on the qua si- three-dimensional flow analysis which is combined with the boundary laye r theory was developed. The conditions of the boundary layer at the impeller exit and at the diffuser vane throat were calculated, and the three-dimensional measurem ents were carried out. This result shows that the low momentum flow is accumulated at the corner of the shroud and the blade suction side of the impeller. These r esults were applied to the development of a large four-stage isothermal compressor w hich handles the air for an air separation apparatus. This was tested in the field and showed an isothermal efficiency of 76 percent.Fumikata Kano

Senior Researcher

Noriyuki Tazawa

Researcher

Yoshiteru Fukao

Researcher

Mechanical Engineering Research Laboratory,

Kobe Steel, Ltd.,

Kobe, Japan

NOMENCLATURE

B = blockage due to boundary layer

b = meridional width

C = area averaged absolute velocity, JPCdA/fpdA

C = mass averaged absolute velocity, jpC

2dA/5pCdA

Cf = local skin friction factor

C p = static pressure recovery coefficient

D = diameter

DF = velocity distortion factor, C / C

0o = length of blade shroud line

n = index for power-law profile

PS = peripheral speed

Q = flow rate

U = velocity at boundary layer edge

u = streamwise velocity component in boundary layer v = crosswise velocity component in boundary layer

WD = diffuser width

Wl = relative velocity at inducer shroud

W2 = relative velocity at impeller exit

Wm = mean relative velocity on suction and pressure surface of blade along shroud line Ws = relative velocity along shroud line on suction surface of blade AW = relative velocity difference between pressure side and suction side of blade x,y,z = streamline co-ordinate system, Fig.3 = area averaged mean flow angle, tan -1 Cm/t a = mass averaged mean flow angle, tan -1 Cm/ tAa=a-a

2S = divergence angle, 2 tan-1 WD4 Dth, where A is

mean channel length

6 = boundary layer thickness, at u = 0.99U

61 = boundary layer displacement thickness

Contributed by the Gas Turbine Division of the ASME.0 = boundary layer momentum thickness v = kinematic viscosity p = density lox , -c = x and z components of wall shear stress

Subscripts

ch = channel region d = design condition i = semi-vaneless region m = radial component max = maximum min = minimum t = tangential component th = vaned diffuser throat

2 = impeller exit

3 = vaned diffuser entrance

4 = vaned diffuser exit

INTRODUCTION

The centrifugal compressor is one of the impor-

tant equipment in plants and recent trends indicate the need for a higher flow rates.

The efficiency of the compressor is also impor-

tant for concerving energy. The flow within the im- peller is three dimensional and is distorted due to boundary layer migration. The relation between im- peller performance and inviscid flow velocity distri- bution has been reported by some researchers (1)(2). The loss in the impeller is mainly caused by the total pressure decrease due to the friction and adverse pressure gradient. This depends on the velocity dis- tribution and the shape of the impeller blade. It is important to investigate the boundary layer distribu- tion as well as the inviscid flow in order to design good impellers and diffusers. The boundary layer analysis of backward curved impellers, in which the three dimensional flow is considered approximately, was performed and the actual impeller exit flow was measured.

The vaned diffuser increases the efficiency of

the centrifugal compressor. The channel type diffuserCopyright © 1982 by ASMEDownloaded from http://asmedigitalcollection.asme.org/GT/proceedings-pdf/GT1982/79566/V001T01A009/2394134/v001t01a009-82-gt-17.pdf by guest on 15 August 2023

is more effective in converting dynamic pressure in- to static pressure than other types of diffusers, since it provides large static pressure recovery and the shape is simple. The performance of the two- dimensional channel diffuser with uniform inlet flow has been studied by many researchers. They have published many performance maps as functions of the area ratio, the aspect ratio, the length of channel, the Mach number and the inlet blockage. However, it is not possible to apply this data to the diffuser in the centrifugal compressor, because the diffuser in the centrifugal compressor has a semi-vaneless region at the inlet, and the inlet flow is distorted three dimensionally. The vaned diffusers reported here have the shape of the NASA 65-series profile for the semi-vaneless region and a nearly straight two-dimen- sional channel downstream of the throat. A large static pressure recovery is obtained in the semi- vaneless region. This produces a boundary layer, and the throat boundary layer blockage affects the per- formance of the channel downstream of the throat. The diffusers were studied to determine their optimum incidence angle, performance and stall. The analysis was made by dividing them into two regions; one is the semi-vaneless region and the other is the channel region.

A world-wide large isothermal centrifugal com-

pressor was designed. The specifications are as follows: 3 flow rate 70 m/sec total pressure ratio 6.9 number of stage 4 (in one shaft) driver output 20,000 kW In addition, a similar compressor which handles 55 m3/sec of air was also designed. These compressors have been serving as air compressors in air separa- tion apparatus.

EXPERIMENTAL FACILITY AND MEASUREMENTS

Prior to designing the actual machine, experi-

ments on scaled downed components were performed. The sectional view of the test rig of a centrifugal compressor is shown in Fig.l. The centrifugal com- pressor is driven by an electric motor through a speed increasing gear. The air flows through a straightener at the inlet of the compressor. The in- let conditions were almost same as the ambient con- ditions. The external surface of the compressorcasing is covered with a 60 mm thick insulation ma- terial to eliminate the heat leakage effect on the total temperature. Three impellers, which have back- ward leaning blades, and fourteen diffusers of vari- ous shapes were tested. The tests were performed with a vaneless diffuser to measure the three-dimen- sional velocity distribution in the vaneless diffuser and to measure the impeller characteristics. Vaned diffuser tests were then performed.

The measurements are as follows:

o Static pressure and total pressure distri- bution at impeller exit. Static pressure is measured on diffuser wall at radius of r/r2 = 1.05. The total pressure distribu- tion is measured by three-hole cobra probe at positions of r/r2 = 1.05, 1.10 and 1.20. o Static pressure distribution at shroud side wall of vaned diffuser. o Total pressure distribution at diffuser throat, using a 1.0 mm diameter, one hole yawmeter. o Time dependent pressure variation in vaned diffuser at the start of surge.

Table 1 Parameters of tested impellers

Parameters

Impeller

ABC

Exit blade angle60 5060deg. from tangential line

No. of blade

181818

Specific speed,m

3/min,m,rpm340330310

W1/w21.711.541.68

Ws, max/W2

1.971.641.74

W1/Wm, min1.771.731.86

4W max/Wm

0.930.780.95

(W1/W2)/(2o/D2)

4.50 4.21 3.94

Peripheral speed, m/s

330287400

Inducer tip diameter, mm

155225147

Inducer hub diameter, mm

759061

Exit diameter, mm

250 380250

Blade tip clearance, mm0.40.70.4

Table 2 Specifications of tested vaned diffusers

Diffuser

No.

Snec.ala2a3a4a5a6blb2b3b4 b5b6b7 b8

Incidence angle i

in design condition-3.5-2.5-1.5 -0.5+0.5 +3.2-2.0-0.5+2.0+4.0-0.5+2.0-0.5+2.0(deg. )

28 deg.

18.218.618.518.218.218.813.0 13.2 13.613.813.113.415.815.9

A deg.2.02.02.02.02.06.0 9.09.09.09.09.09.0 9.0 9.0

Aspect ratio

bth/wD th0.5860.5630.5420.5220.4870.5220.7120.6620.6100.580 9.6620.6100.6620.610 l/WDth

3.493.293.133.002.693.185.234.904.534.374.724.404.85 4.49

WD4/WD

th2.122.062.021.961.862.05 2.202.142.08 2.06 2.082.042.352.26 D3/D2

1.171.161.16 1.151.141.141.101.101.091.081.101.091.101.09

D4/D2

1.661.67 1.671.69 1.661.681.721.731.761.77 1.701.731.711.73Downloaded from http://asmedigitalcollection.asme.org/GT/proceedings-pdf/GT1982/79566/V001T01A009/2394134/v001t01a009-82-gt-17.pdf by guest on 15 August 2023

X 2 U = u ( 1- S ) E (4) y,Normal to wall C Imr In caio Time dependent total pressure variation at the impeller exit. o Total pressure, static pressure and total temperature at the suction and discharge of compressor. o Discharge flow rate by orifice meter.

The specifications of tested impellers and dif-

fusers are shown in Table 1 and Table 2 respectively. The geometry of a typical vaned diffuser is shown in

Fig.2. The impellers are three-dimensional with

backward leaning blades, but without a shroud. The divergence angle 2P of vaned diffuser is approximate- ly 19 deg. for the a-series and 14 deg. for the b- series. The incidence angle i is the angle between the vane camber line and the flow angle a at the vane leading edge. All the diffusers have 15 vanes each. The Reynolds number, PSxb2/v, is 3.0x105 for impeller A, 4.2xl05 for impeller B and 3.lx105 for impeller C. Impeller A was used with the diffusers of a-series and impeller B was used with the diffusers of b- series. Impeller C was used with diffuser b5.

FLOW IN IMPELLER

The secondary flow arising within the boundary

layer which is induced by the pressure gradient causes the accumulation of low momentum fluid at the suction side of the blade. These phenomena have also been found by others (3)(4). From these results, it seems that a core flow may exist. The core flow was analysed by using a quasi-three-dimensional method which assumed that the core flow was an inviscid and compressible flow. The boundary layer analysis was combined with the core flow analysis interactively.

In the boundary layer flow, the centrifugal force

caused by rotation and flow path curvature, the Coriolis force and the pressure gradient do not bal- ance. This unbalance causes the cross flow. A typical three-dimensional boundary layer velocity Throat oR

Incidenceangle suction side ^.

/ Press uside Di

D2 D3D4

Fig.2 Vaned diffuser geometry and nomenclature

profile is illustrated in Fig.3. The streamwise ve- locity profile and shear stress in a three-dimensional turbulent boundary layer were assumed to be repre- sented by two-dimensional relations (5)(6). The streamwise momentum integral equation is shown as S 00 + (2+ e) o aX + lz az f (U-u)vdy = Cf (1) U 0 It is assumed that the streamwise velocity distribu- tion is represented by a power - law profile. 1/n U = (^—) (2) In this analysis, the effects of curvature and rota- tion on the streamwise boundary layer growth are not considered, except the momentum transport resulting from cross flow. The local skin friction factor was determined by the next equation of Ludwieg & Tillmann.

Cf = 0.246x10-0.678HxRe8-0.268

(3) The cross flow velocity profile is represented by the

Prandtl-Mager model.

Fig.l Sectional view of the test rig of centrifugal Fig.3 Three-dimensional boundary layer velocity compressor profile

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t.90 a) a)a E .85 aD_ .80The factor 6 is defined as the shear stress ratio on the wall. Toz (5) T ox This factor is variable and depends on the magnitude of the cross flow. The momentum equation of the cross flow is defined for each stream line as f

6pv2dy s

^X f 'SpuvdyO + au OJ = aL pdy - ToZ (6) 0 where p is the force per unit area which acts in the direction of Z-axis. In this analysis, p is deter- mined only from the pressure gradient normal to the stream line calculated by the core flow analysis, the centrifugal force due to flow line curvature, the Coriolis force in the streamwise boundary layer and the centrifugal force by rotation.

The equations described above were applied to

the internal flow in the impeller by assuming that the shape of flow path was simplified as the rotatingflow channel which is curved two-dimensionally.

The boundary layer migrates through the corner

regions. The boundary layer behavior in this region may be different from other areas. In the present analysis, this region was simply considered as the developed surface.

The boundary layer at the suction side of the

impeller blade tends to separate in the radial por- tion of the impeller. This is mainly due to thicken- ing by the migration of the boundary layer from pres- sure side of the blade, the hub and the shroud.

After the boundary layer separates, the wake is

assumed to grow in the same manner as before the separation in the present analysis. On the surface of the blade pressure side and the hub, the low mo- mentum fluid is taken away by the pressure gradient normal to the core flow, and the boundary layer on the surface does not grow so rapidly.

In the case of the open impeller, the fluid on

the shroud surface flows in the combined direction of rotation and relative velocity of the core flow in the impeller. The boundary layer calculation should be performed in accordance with this combined direction. In addition, the blade tip acts to cut the boundary layer, and some fluid enters into the next flow path through the tip clearance. However, in the present analysis, the shroud side boundary layer was calculated by the same method used for the covered impeller to avoid the very complicated flow at the blade tip.

The internal loss of impeller can be approxi-

mated by the momentum thickness of the boundary layer. The loss A is represented by the following relation. B e.w . w2c

An = g.(1_g(Sl) H0

(7) where B6: blockage by the momentum thickness at impeller exit, 1

72max IA (w -w) dAmax

A2 PBS1: blockage by the displacement thickness at im- peller exit, 1

A2• wmax JA2 (w max - w ) dA

w : mean relative velocity of the core flow along stream line from the root mean square radius at inlet to the exit,

H0 : theoretical head

w2 c: relative velocity of the core flow at impeller exit g : acceleration due to gravity

IMPELLER PERFORMANCE

The inviscid flow velocity distributions are

shown in Fig.4. The diffusion ratio along the suc- tion surface of impeller A is higher than the other impellers. The loading of the blade

AWmax/Wm, which

is related to the blade-to-blade pressure difference, is smallest in impeller B. The mean velocity gra- dient along the shroud line, (W1/W2)/(ko/D2), is re- lated to the boundary layer growth. This factor is maximum in impeller A and minimum in impeller C. The smaller mean relative velocity causes a lower fric- tion loss due to the shear force on the bounding sur- face. On the other hand, the loss associated with the effect of adverse velocity gradients on the 360
E 320

Ws. max

280 - \

0 240 > 200

C-- -dWmcx

Q1l60 .2 12 0 -17W

80---A

^^ .Wmmin

40-C20 - C0 0.5 1.0

Blade camber line

Distance l/Lo

Fig.4 Relative velocity distribution along shroud

line of impeller .95 I.- >5Ca)U ■ ■ A A gOC 0.7 0.8 0.9 I.0 1.1 1.2

Flow rate Q/Qd

where A is flow path area, w is relative velocity

Fig.5 Impeller efficiency

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V o. H 6 0. a,a•d0. E 0.U

Suction side

Pressure side J ce 0 Impeller CFig.6 Radial velocity distribution at r/r2 = 1.05 to be 12% at the measured radius. From the present analysis, a blockage of 13% was obtained at the im- peller exit. The variation due to mixing in the vaneless region to r/r2 = 1.05 should be taken into consideration. The relation between the impeller ef- ficiency and the loss Ark is shown in Fig.7 for the design flow rate. This means that the momentum thick- 1.0 ness calculated by the present analysis represents the ub internal loss and is related to the impeller efficien- cy. The loss An is the calculation result.

Impellers A, B and C have almost the same charac-

teristics in the head coefficient. The velocity dis- tribution at the impeller exit is nonuniform. There- fore, the peak of the time averaged meridional veloc- ity is not located at the middle of diffuser width, but it is shifted toward the hub side. The meridional velocity is very low at the shroud side, though the tangential velocity is almost uniform. The time aver- aged velocity distribution at the impeller exit is shown in Fig.8. The boundary layer blockage due to the displacement thickness at the exit of the impeller is 3.8% for impeller A, 6.6% for impeller B and 4.3% for impeller C in the design condition. The absolute velocity was used to calculate the blockage. boundary layer growth and the cross flow in the boundary layer is influenced by W1/W2 , (Wl/W2)/(9.o/

D2) and AWmax/wm-

The efficiency of each impeller is shown in

Fig.5. From these results, the maximum efficiency

at the design flow rate is obtained when the inviscid relative velocity ratio W1/W2 is about 1.62 - 1.67 and the mean velocity gradient (W1/W2)/(2o/D2) is be- low 4.0.

According to the present analysis, the boundary

layer migrates to the suction side of blade at the shroud. The radial velocity distribution at r/r2 =

1.05 for impeller A is shown in Fig.6. This was

calculated from the total pressure distribution meas- ured by a high frequency pressure transducer. In this calculation, the static pressure in the meridi- onal plane is assumed to be uniform between the shroud and the hub. The circumferential unsteady static pressure was the value measured on the shroud wall. This indicates that the low momentum fluid accumulates on the shroud suction side. This was measured for impeller A. The blockage by the momen- tum thickness of the radial flow component was foundSTATIC PRESSURE RECOVERY IN SEMI-VANELESS REGION in this paper, the semi-vaneless region means the space from the impeller exit to the diffuser throat. The static pressure recovery was calculated by the iteration between the inviscid core flow analy- sis and the boundary layer analysis, which is the same method used for the impeller. The core flow at the inlet condition of the diffuser was assumed to be uni- form and axisymmetric flow. The boundary layer dis- placement thickness and momentum thickness at the in- let of the diffuser were determined from experimental data measured by a cobra probe. For these calcula-. tions, the inlet conditions of the diffuser were varied in accordance with the operating flow rates. The comparison between the calculated and measured static pressure recovery C pi is shown in Fig.9. The measured static pressure recovery was calculated as C pi = 2 (Pth - P2)/PC, where C2 is the area averaged impeller exit velocity. P2 is the static pressure which is determined by averaging measured values at three points on same radius of r/r2 = 1.05. Pth is 0.86 r 0.90-u C . 2 0.95 ^ ^ D E ^^\ 1.00 2 3 4 5 6 7X102 Loss o►^V E ao' .*'. 200 20 v` 200 250y 0> li 150
10 150 10 100
150
' loo 50
X ^C= 0 0 b/b2 1.0 010 b/b2 1.0

Impeller A

Impeller B

0Absolute velocity, &Absolute flow angle, X Meridional velocity

Fig.7 Relation between impeller efficiency

Fig.8 Velocity distribution at impeller exit and loss Ar,

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0 0 00 0 00 C pi Measured0.6 0.4 v 0.2 0V a -0.2 -0.2 0 0.2 0.4 0.6the averaged static pressure at the throat. All measured and calculated values, in which off-design conditions are included, are shown in Fig.9. The small discrepancies between the calculated and the measured values are believed to be due to inlet dis- tortion and incidence.

The isobars of static pressure in the diffuser,

measured for diffuser b2, are shown in Fig.10. The static pressure distribution in the semi-vaneless region varies in accordance with operating condi- tions. The incidence angle at the leading edge is minus 0.5 deg. at design flow rate Q/Qd = 1.0, and the wedge angle is about 12 deg., so the angle be- tween velocity C3 and suction surface is minus 6.5 deg. The incidence angle to the camber line is +

6.0 deg. at Q/Qd = 0.75, so the angle between veloc-

ity C3 and the suction surface is almost zero and the isobars are therefore nearly normal to the suc- tion surface.

The boundary layer distributions in the throat

section are shown in Fig.11 for diffuser b2. In this figure, the calculated line was determined by the present analysis, and the measured value is displacement thickness determined from velocity dis- tribution measured by a traversing yawmeter.

The scale of the boundary layer thickness S1 in

this figure is shown as twice as that of the throat area. The boundary layer blockage Bth at the throat is shown in Fig.12. From these results, the bound- ary layer distribution is not uniform in the semi- vaneless space and the throat section. There is a large growth of the boundary layer on the pressure side, though it is a very small amount on the suc- tion side.

It seems that the three-dimensional boundary

layer growth at the leading edge is included in this thick boundary layer on the pressure side. The smaller the flow rate is, the larger the throat blockage becomes. This is mainly due to the large velocity deceleration. In the case of diffusers b5 and b7, blockages are approximately 12% at Q/Qd =

1.0 and 22% at Q/Qd = 0.73.

INCIDENCE ANGLE AND DIFFUSER PERFORMANCE

The velocity distribution in the semi-vaneless

region is affected by the incidence angle, as shownpreviously. The flow distribution at the impeller exit, even after the jet and the wake are mixed, is three-dimensional and the flow angles of each point across the diffuser width are different. The flow angle between the absolute velocity and a tangential line is small at the shroud side. The velocity dis- tortion factors for the meridional and the tangential

2666 Pa

(20mmH ) ,•^•9 1.74 x 105 Pa '• 1.47x10 Q/Qd=0.75 • 1.63 x105 1.41 X 10 Q/Qd=1.03 .\ ,^ 1.41x105 1.46x 1 ^' • 1.22x10 !.32x105 Q/Qd=1.15 Fig.10 Isobars of static pressure in the diffuser, diffuser b2 a, v N

0N om,co>U)

Shroud side

Q/Qd =0.78

mm Si L2U, - 0-o N N cy>a 0

Q/Qd =1.02

-------o--- -.o-o---

Q/Qd =1.15

Fig.9 Static pressure recovery in semi-vaneless

regionFig.11 Boundary layer distribution in throat, diffuser b2

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1.1 1.225

01 i 1 i

0.7 0.8 0.9 I.0

Q/Qd1.24

L02 1.20

DFm Q/Qd

1.15 LL

0 Impeller A A

BO

1.10 Cq

Q/Qd

1.05Impeller A A

BO C q I.I5 x.02 0.75 Q/Qd ^SiozT5b2 b5 b7

Calculated --- - ---

20 _\ Measured q p 0 15 m

10 _ \ O

5

Fig.12 Boundary layer blockage at throat

components, DF m and DFt, were determined for each radius by measuring the velocity distribution in the vaneless diffuser. These results are shown in Fig.13.

For example, in the case of impeller B, DF

m in con- dition of Q/Qd = 0.75 is 1.16 at a radius of r/r 2 =

1.05 and it increases to 1.23 at r/r2 = 1.20.

The smaller the flow rate is, the more the flow

is distorted. DFt is nearly unity and almost constant. The incidence angle at the vane leading edge seemed to be evaluated more accurately by using flow angle a = tan-1 C5,/Ct, determined from the mass averaged velocity, than by using flow angle a = tan -1 Cm/Ct, determined from the area averaged velocity. The dif- ference between a and a, Aa = a - a, is shown in Fig.

13b as a function of the radius. This value is fair-

ly large. For example, in impeller B, Aa is about 3 deg. at a radius of r/r2 = 1.10. This is important in order to find the optimum incidence angle.

The channel, downstream of the throat, is two-

dimensional. The flow distribution at the entrance of the channel, namely the throat, is nonuniform, so the performance of the channel is different from that which has a uniform inlet condition. The static pressure recovery of the channel was compared with straight two-dimensional diffuser data of Reneau (8) in order to evaluate the effects of the nonuniform inlet conditions on the diffuser performance. The tested diffuser channel is not straight but slightly curved. This effect of curvature was corrected by using the experimental data of Sagi (9).

The static pressure recovery coefficients of the

semi-vaneless region and the channel are shown in Fig.

14. The relation between the static pressure recovery

of the channel region in the vaned diffuser and that of the straight two-dimensional diffuser is defined as follows:

Cpch = C

ps + ACpl + 4Cp2

Cpch : static pressure recovery coefficient of

tested diffuser channel1.0 L

I.0 1.1 1.2 1.25 1.0 1.1 1.2 1.25r/r2 r/r2.41

a b

Fig.13 Velocity distortion in vaneless diffuser

Table 3 Optimum incidence angle, at the vane leading edge Vane

Q/Qdat peak of Cpchi

deg.4adeg.i=i-Aa deg. al

0.94-1.50.9-2.4

a20.98-2.00.9-2.9 a31.02-2.50.9-3.4 a41.00-0.50.9-1.4 a5

1.02-0.50.9-1.4

a6

1.05+1.30.9+0.4

bl

0.88+1.03.3-2.3

b2

0.92+2.03.4-1.4

b3

1.00+2.03.6-1.6

b4

1.06+2.03.7-1.7

b5

0.97+0.53.5-3.0

b6

0.99+2.03.6-1.6

b7

0.96+0.53.5-3.0

b8

1.02+1.03.6-2.6

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0.I 0 -0.1 -0.3 -0.4 -0 5wi deg. -8 -4 0 4 i deg.

Fig.15 Value of AC

pl14

8 100.5

0.4 0.2 U 0 -0.2 -0.3 0.8 0.6r -m a I

® a 3

m 04 0 a5 ® a6 1.0 1.2Q /Qd0.6 0.4 •a 0.2 U 0 - 0.1 -0.2 0.6

0.6 r0.8

Q/Qd 1.0 1.2 1 a

1.20A^

R9 Q/Qd W' WV Fig.14 Static pressure recovery coefficients of semi-vaneless region and channel0.4 La

0.20.4

U dU 03 M 0.1

Cps :static pressure recovery coefficient

of straight two-dimensional diffuser 0

ACpl :

effect of nonuniformity on pressure recovery-0.1ACp2difference of static pressure recovery between straight and curved diffuser, vane number al - a5 ACp2 = 0.00-0.2 a6 -0.02 bl - b8 -0.03Va -0.3

The values of ACpl are shown as a function of

the incidence angle in Fig.15. The incidence angle i, -0.4 where AC plis maximum, was approximately -2 deg. for diffuser a-series and +2 deg. for diffuser b-series.-0 5a 00- 8

10This difference of 4 deg. was caused by the inlet -8 -4 0 4

distortion at the throat. Namely, as shown in Table

3, when incidence angle i, determined by correcting

i with Aa shown in Fig.13, is used for evaluation, approximately -2 deg. is obtained as the optimum in- cidence angle for all diffusers. In the case of the uniform inlet condition, the maximum pressure re- covery is obtained at zero incidence. However, when the inlet flow is nonuniform such as the centrifugal diffuser channel, the maximum pressure recovery is obtained at about a -2 deg. incidence angle of the mass averaged flow.

These phenomena are due to the following reasons.

The boundary layer in semi-vaneless region migrates and affects the blockage and velocity distribution at the throat. The boundary layer growth on the suction surface of the semi-vaneless region is restrained by the dynamic pressure component normal to the surface. So the pressure recovery in the channel becomes maxi- mum at about a -2 deg. incidence angle, due to the balance of deterioration by the incidence and effect of restraint of the boundary layer growth.

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oI 0 w a U Ca,U d 0E a`, 0

NHThe surge of a centrifugal compressor is caused

by the stall in the impeller or the diffuser in many cases. In this performance test, the flow rate Q/Qd, when surge occurred, is clearly larger in the case of the vaned diffuser than in the case of the vane- less diffuser. The static pressure recovery coef- ficients of the channel, shown in_ ig.14, were de- termined as Cpch = 2 (P4 - Pth)/PCth based on dynamic pressure at the throat. P4 is the static pressure at the diffuser exit. The value of C pch in the off- design condition is smaller than in the design con- dition. The values of diffusion ratio C2/Cth are between 1.4 and 1.6 for all tested diffusers at the flow rate which is close to the surge initiation. The calculated maximum shape factor H12 of the bound- ary layer at the throat is between 1.5 and 1.6. How- ever, the maximum measured shape factor is 1.9. This measured value is the maximum value in all diffusers and is obtained at the pressure side of the throat.

It does not seem that there is a thick boundary

layer on the vane suction surface judging from the velocity distribution at the throat. The stream trace of coating film also indicates that there is no low momentum, namely a thick boundary layer, on the vane suction surface. These phenomena depend on the boundary layer migration from the suction side to the pressure side due to the static pressure un- balance as shown in Fig.10. There is a possibility that the boundary layer at the throat pressure side begins to separate before the surge. This may be the three-dimensional separation at the leading edge.

N 0.90

H >. . 0.80 O'^^^\ \ u \ 1 ^ 1 !I a 0.70 1 U' I u o 0.60

Pr}-Jtx enment 90 Speed -105D

a

0.70I 75According to Fig.14, the pressure recovery C

pch de- creases at a small flow rate before surge. This de- crease of the pressure recovery in the channel is caused by the throat blockage and the flow separation on the pressure surface in the channel. The small flow separation on the pressure surface of the chan- nel was observed in the operating condition between the surge and the design flow rate. This small sepa- ration becomes larger, and the pressure recovery of the channel becomes low and the diffuser stall even- tually occurs.

STAGE PERFORMANCE AND APPLICATION TO THE ACTUAL

MACHINE

The adiabatic stage efficiency and head coeffi-

cient for impeller C and diffuser b5 are shown in Fig.

16. In this figure, the comparison between predicted

values and measured values are shown. These show fairly good agreement, and high efficiency was ob- tained.

These results were applied to the one shaft,

four stage isothermal centrifugal compressors in which the speed is about 90% of the stage experiment. The desired high efficiency was obtained. The char- acteristic curve, which was obtained from a field test, is shown in Fig.17. This isothermal efficiency of 76%, which is the ratio of a theoretical isother- mal compression work and a shaft power, is the highest level in the world. The three compressors have al- ready been in operation. One of them handles the air of 70 m

3/sec, which is largest in the world for this

application of a centrifugal compressor. It was de- monstrated that because of its high efficiency and mechanical toughness the centrifugal compressor was suitable for a large isothermal compressor. Accord- ing to our new design method, it is possible to design up to the capacity of 112 m3/sec and a pres- sure ratio of 8.

CONCLUSIONS

1) The boundary layer analysis, which considers the

secondary flow and is combined with the core flow, predicts the condition of the internal flow. The results show fairly reasonable agreement with the experimental data. 0.60 0

00.50 1I

U 0.40 I= U

7590 100105

0.30 ' 1 1 1 1 1 I 1 1

0.4 0.5

0.6 0.7 0.8 0.9 1.0 1.1 1.2age - ^

60 deg.

90 de50 45 deg. Inletguide vane
opening

Flow rate Q/Qd

0.6 0.7 0.8 0.9 1.0 1.1

Flow rate Q/ Qd

Fig.16 Adiabatic stage efficiency and head coef-

Fig.17 Characteristic curve of isothermal centrifu- ficient, impeller C and diffuser b5 gal compressor

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2)

The impeller efficiency is influenced by the

boundary layer momentum thickness which is pre- dicted roughly by the present analysis. The pres- ent prediction is useful for designing high ef- ficient impellers. The maximum efficiency is ob- tained at W1/W2 = 1.62 ' 1.67 as in the inviscid flow analysis. 3) The velocity distribution at throat is nonuniform. The boundary layer is thicker on the pressure sur- face than on the suction surface. The result of the calculation shows a similar distribution. The calculated blockage factor is almost same as the measured one. 4)

The pressure recovery of the vaned diffuser chan-

nel, downstream of throat, is different from the two-dimensional straight diffuser. This differ- ence is minimum when the incidence angle, which is determined from the mass averaged velocity, is about -2 deg. The minimum difference of pressure recovery is between -0.1 and 0. 5)

It became possible to design the large isothermal

centrifugal compressor which had a high efficiency.

ACKNOWLEDGEMENTS

The authors wish to express their appreciations

to Mr. M. Ito, Mr. K. Kajiki, Mr. N. Ishiguro for their performance test of the actual machines. The authors also acknowledge the Rotating Machinery Works for permission to publish the paper.

References

1.

Dallenbach, F., "The Aerodynamic Design and Per-

formance of Centrifugal and Mixed-Flow Compres- sors." SAE Technical Progress Series, Vol. 3,

1961, pp. 2 - 30.

2.

Rodgers, C., "Impeller Stalling as Influenced by

Diffusion Limitations," Centrifugal Compressor and

Pump Stability, Stall and Surge, ASME, New York,

1976, pp. 37 - 67.

3.

Eckardt, D., "Flow Field Analysis of Radial and

Backswept Centrifugal Compressor Impellers, Part

1: Flow Measurements Using a Laser Velocimeter,"

Performance Prediction of Centrifugal Pumps and

Compressors, ASME, New York, 1980, pp. 77 - 86.

4.

Fowler, H.S., "Some Measurements of the Flow

Pattern in a Centrifugal Compressor Impeller,"

ASME Paper 65-WA/GTP-7, 1965.

5.

Mager, A., "Generalization of Boundary Layer Mo-

mentum Integral Equations to Three-Dimensional

Flow Including Those of Rotating Systems," NACA

Report 1067, 1952.

6.

Prahlad, T.S., "Mean Velocity Profiles in Three-

Dimensional Incompressible Turbulent Boundary Lay- ers," AIAA Journal, Vol. 11, No. 3, Mar. 1973, pp.

359 - 365.

7.Head, M.R., "Entrainment in the Turbulent Boundary

Layer," A.R.C.R. & M. 3152, 1958.

8.Reneau, L.F., Johnston, J.P., Kline, S.J., "Per-

formance and Design of Straight, Two-Dimensional

Diffusers," Trans. ASME, Series D, Vol. 89, No.1,

Mar. 1967, pp. 141 - 150.

9. Sagi, C.J., Johnston, J.P., "The Design and Per-

formance of Two-Dimensional, Curved Diffusers,"

Trans. ASME, Series D, Vol.89, No.4, Dec. 1967,

pp. 715 - 731.

10.Runstadler,P.W., JR., Dean, R.C., JR., "Straight

Channel Diffuser Performance at High Inlet Mach

Numbers," Trans. ASME, Series D. Vol. 91, No.3,

Sep. 1969, pp. 397 - 422.

ll.Wolf, S., Johnston, J.P., "Effects of NonuniformInlet Velocity Profiles on Flow Regimes and Per- formance in Two-Dimensional Diffusers," Trans.

ASME, Series D, Vol.91, No.3, Sep. 1969, pp. 462

- 474. 12.

Senoo,Y., Nakase,Y., "An Analysis of Flow Through

a Mixed Flow Impeller," Trans. ASME, Series A,

Vol. 94, No.1, 1972, pp. 43 - 50.

13.

Katsanis,T., "Computer Program for Calculating

Velocities and Streamlines on a blade-to-Blade

Stream Surface of a Turbomachine," NASA TN, D-

4252, 1968.

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