Investigations of the Performance on Vaned Diffusers for Low Specific Speed Centrifugal Compressor

Tsukinami KAWANISHI1 , Yasumasa TOHBE2 , Naoki KANAZAWA2

1Kawasaki Heavy Industries, Ltd. 1-1 Kawasaki-Cho, Akasi City, 673-8666, JAPAN Phone: +81-78-921-1798, FAX: +81-78-921-5309

2Kawasaki Heavy Industries, Ltd.

International Journal of Gas Turbine, Propulsion and Power Systems

ABSTRACT In this paper, the performance of vaned diffusers on low

specific speed centrifugal compressors, was investigated experimentally and analytically. There is a problem of non-uniform distribution of the flow at impeller exit, as a factor to deteriorate the performance of the diffuser. This problem appears remarkably on the low specific speed type, because the blade height is relatively small and the flow inclines toward circumferential direction. The experiment was carried out with 2nd stage compressor of two-stage centrifugal type, focusing on the effect of number of diffuser vanes, vaneless ratio and throat area. Furthermore, unsteady fluid analysis was carried out by using Non Linear Harmonic method in order to understand about the phenomenon associated with the problem of non-uniform distribution of the flow.

NOMENCLATURE Ath throat area of diffuser AR area ratio of diffuser from throat to exit b blade heightBL blockage factor (= 1- effective area / geometrical area)Cp static pressure recovery coefficient, Cp = ( p - p2 ) /(P2 - p2 )cv Specific heat at constant volumeD diameter G mass flow

’ non-dimensional flow, = G ( R T1 ) 0.5/ ( D2 2 P1 )

ad Non-dimensional adiabatic head = adiabatic head / (RT1) ad = { /( 1)}( /( 1) 1)

M absolute Mach number ’ Non-dimensional revolution speed

’ = D2 /(R T1) 0.5

S specific speed (non-dimensional value) S = ’ ’0.5/ ad

3/4 P total pressure p static pressure Q volume flow R gas constant S entropy (meridional mass-average value per unit mass)

S = cv ln{( p / pin ) /( / in ) }T total temperature u blade speed

ZB number of impeller blades Zv number of diffuser vanes

3V Inlet angle of diffuser (from tangential direction) 2B backswept angle of impeller (from radial direction)

adiabatic efficiency (total to static) specific heat ratio pressure ratio (total to static) , = p4 /P1

density flow coefficient, = Q1 /( u2 D2

2/4) work coefficient, = R T1 { /( 1)}(T2 /T1 1)/( u2

2 /2 ) angular velocity of revolution

Subscripts 1 compressor stage inlet in impeller inlet 2 impeller exit 3 diffuser inlet (leading edge) th diffuser throat 4 diffuser exit (stage outlet)

INTRODUCTION The performance of vaned diffuser was investigated to improve

the performance of centrifugal compressor for gas turbines. Because degree of reaction of impeller for the compressor are usually from 0.4 to 0.5, about half of total pressure at impeller exit is dynamic pressure. Therefore, it is important that the dynamic pressure is converted into static pressure efficiently in the diffuser to improve the performance of centrifugal compressor.

By the way, there is a problem of non-uniform distribution of the flow at impeller exit as a factor to deteriorate the static pressure recovery. In case of supersonic flow at impeller exit, shock loss generated by a shock wave deteriorates further the static pressure recovery of the diffuser. The flow conditions at impeller exit are determined by the design specifications of the compressor. Here, relations between the design specifications and the flow conditions at impeller exit were examined, and the diffusers were classified in the low specific speed type, the high subsonic type and the supersonic type.

In this paper, the diffuser of low specific speed type was taken up as the subject of the study, and the experiment was carried out, paying attention to the diffuser inlet specifications, such as number of vanes, vaneless ratio and throat area. Furthermore, unsteady fluid analysis was carried out . Then, the phenomenon of the flow in the diffuser was analysed and discussed.

International Journal of Gas Turbine, Propulsion and Power SystemsFebruary 2014, Volume 6, Number 1

Copyright © 2014 Gas Turbine Society of Japan

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Manuscript Received on July 13, 2013 Review Completed on January 10, 2014

DIFFUSER CHOSEN AS THE SUBJECT OF THE STUDY The flow discharged from impeller is highly viscous,

non-uniform and unsteady. This non-uniform flow is carried into the diffuser, and also potential effect from the diffuser causes an unsteady pressure change for the flow at the impeller exit. In case of low specific speed type diffuser, the effect of nonuniformity on performance of the diffuser becomes remarkable, because the blade height is relatively small and the flow inclines to the tangential direction. Furthermore, shock loss is generated by a shock wave, when the flow at impeller exit becomes supersonic condition by increase of pressure ratio.

The parameters at impeller exit, such as absolute Mach numberM2 and absolute flow angle 2 are determined by design specifications of , and 2B which are related closely to and . Relation between and is shown in Fig.1. Relation ,

and , M2 is shown in Fig.2 . These figures were made under the condition of 2B of 40 deg . Also, the examples for single-stage compressor and 1st, 2nd stage of two-stage compressor with 2Bfrom 30 to 50deg are plotted in these figures. The diffusers of centrifugal compressor are classified in ( ) low specific speed type, ( ) high subsonic type and ( ) supersonic type, shown in Fig.2. In this report, the low specific speed type diffusers of the compressor with from 0.5 to 0.55 were chosen as the subject of the study.

EXPERIMENTAL PROCEDURE Experiment was carried out with 2nd stage compressor of

two-stage centrifugal type modified for the experiment, shown in Fig.3. Air flow was measured with a flow nozzle installed in the upper side of 1st stage compressor. Temperature and pressure at

inlet and exit of the compressor were measured at the position shown in Fig. 3. And static pressure was measured in 4 points at radius ratio R/R2 of 1.01 to separate the performance of the impeller and the diffuser. Also, static pressure was measured at 5 locations along center line of flow path of the diffuser.

The main particulars of impeller and diffuser used for the experiment are shown respectively in table 1 and table 2. Two impellers of backswept type with blade number of 22 were used for the experiment. Tip diameter and width for these impeller are slightly different, with same design of the blade. All difusers are channel types. Three kinds of diffusers (A-1,A-2,A-3) were prepared for type A impeller to confirm the effect of number of vanes. Vaneless ratio D3/D2 and throat area Ath of these diffusers are the same. Four kinds of diffusers (B-1,B-2,B-3,B-4) were prepared for type B impeller to confirm the effect of D3/D2 and Ath.

METHOD OF UNSTEADY FLUID ANALYSIS Unsteady fluid analysis was carried out, using commercial code

of a three dimensional, viscous,unsteady RANS solver especially employed for turbomachinery design and simulation. Non Linear Harmonic (NLH) method was used for unsteady fluid analysis. By NLH method, the flow values are divided into the time-mean value and the time-dependent value which is transformed into the frequency domain by a Fourier-transformation. In case of turbomachine, there are periodic perturvations caused by the frequency of the rotating parts to the stationary parts. By NLH method, unsteady analysis with one period of the blade is enabled

Fig.1 Relation between N’ and had

0 0.05 0.1 0.15 0.22

3

4

5 0.4 0.5 0.6 0.7 0.8 0.9

1.0(1.1)

(1.0)(0.95)

(0.9)

(0.8)

Fig.2 Relation between G’, N’ and Ns, M2 Value in ( ) is M2

Fig.3 Experimental apparatus (two-stage compressor)

Single-stage compressor 1st stage of two-stage compressor 2nd stage of two-stage compressor

2 3 4 50

1

2

3

4

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by the complex decomposition of the period ingredient (He and Ning, 1998). The spalart-Allmaras turbulence model with excellent calculation precision and stability, was used (Spalart and Allmaras, 1992).

Computational grid is shown in Fig.4. The number of grid is 0.94 million for the impeller, 0.54 million for the diffuser and 0.26 million for the exit parts. So, total number of grid for the stage is 1.74 million. The number of grid in the span between hub to shroud is 73 for the impeller and 57 for the diffuser. The hub wall of the impeller is moving with the impeller blade, while the diffuser hub remains stationary with the diffuser vane. The whole shroud is kept stationary. Non-slip and adiabatic conditions were adopted for all solid walls. Periodic conditions were imposed along the pichwise boundaries. Total pressure, total temperature and flow angle (no prewhirl) were specified for the inlet boundary, whereas static pressure was imposed for the outlet boundary at each operating conditions.

RESULTS AND DISCUSSION In case of handling of experimental data, total pressure P2 at

impeller exit was calculated by the equation of continuity, using static pressure p2 measured at impeller exit side. Here, blockage factor BL at impeller exit was set in a value of 0.1 which was calculated, considering the radial velocity distribution of unsteady fluid analysis. The performance obtained from the unsteady fluid analysis is evaluated by the time-averaged values, and the results shown below are the time-averaged values except the time-depending figures.

Effect of number of vanes ZvFig.5 shows the experimental results of A-1, A-2 and A-3

whose number of vane Zv are 17, 15 and 13 respectively. Here, flow coefficient and work coefficient are the ratio to the value at design point respectively. Stage efficiency are the ratio to the value of A-1 at design flow point ( 1). For A-1 and A-3, the calculated results are plotted at the point of 1 and 1.1, and the calculated results are confirmed to agree well with the experimental results. Comparing the static pressure recovery coefficient Cp of A-1 with that of A-3, Cp of A-1 is a little higher than that of A-3 at the point of 1, but the difference becomes larger at the point of 1.1. The tendency of stage efficiency corresponds to that of Cp.

Fig.6 shows the experimental and calculated results about the change of Cp along the center line of the diffuser flow path for A-1 and A-3 at the point of 1 and =1.1. The calculated results agree with the experimental results, and it is considered that the actual phenomena can be analysed sufficiently. The difference of Cp between A-1 and A-3 increases to diffuser throat, and the difference at the throat remains to the diffuser exit. Fig.7 shows the calculated results of static pressure in the flow path of diffuser A-1 and A-3 at the point of =1 and =1.1.

Fig.8 shows the change of meridional mass-averaged entropy Sfrom impeller inlet to diffuser exit at the point of 1 and 1.1. Comparing S of A-1 and A-3, it is found that both the value of S is the same at impeller exit, and S of A-3 is larger than that of A-1 in the diffuser. The tendency of S corresponds to that of Cp. Although the loss from impeller exit to diffuser throat depends on mixing, friction and deceleration of the flow, the difference of both diffusers is considered to be generated by mixing and friction because of same throat area of both diffusers. The loss of A-3 is larger than that of A-1 particularly at the point 1.1. The reason is considered that the nonuniformity of the flow distribution of A-3 at the point of

=1.1 is remarkable as compared with that of A-1, as is seen in diffuser inlet flow angle in Fig.9.1 and diffuser inlet Mach number M3 in Fig.9.2. This tendency is also observed from the instantaneous contours of absolute Mach number between impeller exit to diffuser throat, shown in Fig.10.

Blade-to-blade Meridian plane

Fig.4 Three-dimensional computational grid

Fig.5 Effect of number of vanes

Fig.6 Static pressure recovery coefficient from mpeller exit to diffuser exit

A-1 A-2 A-3Experimental value Calculated value

0.95 1 1.05 1.1 1.150.9

1

1.10.940.960.98

11.020.58

0.60.620.640.660.68

0.70.72

P

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Fig.8 Meridional averaged entropy from impeller inlet to diffuser exit (Calculated results of A-1 and A-3)

Fig.9.1 (a)Absolute flow angle at impeller exit 2 and (b)flow angle at diffuser inlet 3

(Calculated results of A-1 and A-3)

Fig.9.2 (a)Absolute Mach number at impeller exit M2 and (b)Mach number at diffuser inlet M3

(Calculated results of A-1 and A-3)

Fig.7 Distribution of static pressure in diffuser (Calculated results at mid-span of A-1 and A-3)

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Effect of vaneless ratio D3/D2Fig.11 shows the results which were obtained from the

experiments carried out on B-1 with D3/D2 of 1.072 and on B-4 with D3/D2 of 1.053, using impeller B. In both case of =1 and =1.1, the static pressure recovery coefficient Cp of B-4 is higher than that of B-1, so that the stage efficiency of B-4 is higher relatively in ab. 1% than that of B-1.

Fig.12 shows the calculated results of the change of Cp along center line of the diffuser flow path of B-1 and B-4. The difference of Cp between both diffusers at the throat remains to the diffuser exit.

Fig.10 Instantaneous contours of absolute Mach number between impeller exit and diffuser throat

(Calculated results of A-1 and A-3 at mid-span)

Fig.11 Effect of vaneless ratio D3/D2

Fig.12 Static pressure recovery coefficient from impeller exit to diffuser exit (Calculated value of B-1 and B-4)

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Figure 13 shows the calculated results of the change of meridional mass-averaged entropy S in the flow path from the impeller inlet to the diffuser exit. S of B-4 is lower at the diffuser inlet (leading edge) than that of B-1. Distribution of diffuser inlet flow angle and Mach number M3 are shown respectively in Fig.14.1 and Fig.14.2. Because distribution of and M3 of B-4 are approximately similar to those of B-1 as shown in these figures, it is understood that distributin of the flow of D3/D2 of 1.053 and D3/D2 of 1.072 are almost the same. Therefore, it is considered that high Cp of B-4 is caused by the reduction of friction loss due to the decrease of vaneless area.

Effect of throat area AthFig.15 shows the results which were obtained from the

experiments carried out on B-1, B-2 and B-3, using impeller B. Throat area ratio of B-2 to B-1 is 0.944, and that of B-3 to B-1 is 1.086. Concerning the static pressure recovery coefficient Cp at the point of =1, Cp of B-3 is similar to that of B-1, and that of B-2 is lower. Concerning Cp at the point of =1.1, those values are very different, that is, CP of B-3 is highest and that of B-2 is lowest.

Fig.13 Meridional averaged entropy from impeller inlet to diffuser exitt (Calculated results of B-1 and B-4)

Fig.14.1 (a)Absolute flow angle at impeller exit 2 and (b)flow angle at diffuser inlet 3 (Calculated results of B-1 and B-4)

Fig.14.2 (a)Absolute Mach number at impeller exit M2 and (b)Mach number at diffuser inlet M3 (Calculated results of B-1 and B-4)

Fig.15 Effect of throat area

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Here, Cp is divided into Cp1 and Cp2. Cp1 is static pressure recovery from impeller exit to diffuser throat and CP2 is that from throat to diffuser exit.

Cp1 = (pth - p2) /(P2 - p2) Cp2 = (p4 - pth) /(P2 - p2)

Reduction ratio of flow velocity DF ( absolute velocity at impeller exit / velocity at diffuser throat) is important. When DF becomes larger by increasing Ath, Cp1 increases but Cp2 decreases because of increase in the throat blockage . To the contrary, when DF becomes smaller by decreasing Ath, Cp1 decreases but Cp2 increases because of decrease in the throat blockage. Thus, there is a value of Athwhere overall Cp becomes most suitable for each point of . Fig.16 shows the calculated results of the change of Cp along center line of the diffuser flow path of B-1, B-2 and B-3. The tendency mentioned above is also indicated in Fig.16. That is, CP of B-3 is high particularly in the point of = 1.1.

Fig.17 shows the calculated results of the change of meridional mass-averaged entropy S in the flow path from the impeller inlet to the diffuser exit for B-1, B-2 and B-3 in the point of =1 and =1.1. It is understood from this figure that the tendency of loss corresponds well to that of Cp. From diffuser inlet flow angle 3 and Mach number M3 shown respectively in Fig.18.1 and Fig.18.2, it is recognized that there is little difference in distribution of the flow between B-1, B-2 and B-3 in the point of =1. But it is seen that the distribution of the flow of B-2 becomes ununiform more in the point of =1.1.

Fig.16 Static pressure recovery coefficient from impeller exit to diffuser exit (Calculated value of B1,B-2,B-3)

Fig.17 Meridional averaged entropy from impeller inlet to diffuser exit (Calculated results of B-1,B-2 and B-3)

Fig.18.1 Flow angle at diffuser inlet 3 (Calculate value of B-1,B-2 and B-3)

Fig.18.2 Mach number at diffuser inlet M3(Calculated value of B-1,B-2 and B-3)

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CONCLUSION The experiment was carried out with low specific speed

compressor of from 0.5 to 0.55, focusing on the effect of number of diffuser vanes , vaneless ratio and throat area, and the effects of these specifications on static pressure recovery coefficient were confirmed. Also, unsteady fluid analysis was carried out by using Non Linear Harmonic method and it was confirmed that the calculated results by the analysis corresponded well to the experimental results. Then, the phenomenon of the flow in the diffuser could be analysed and discussed .

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