Journal of Thermal Science Vol.15, No.4 306―313

Received: June 20, 2006 T. Turunen-Saaresti: Ph. D. Research scientist

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diffuser.

DOI: 10.1007/s11630-006-0306-1

Computational and Experimental Study of Pinch on the Performance of a Vaneless Diffuser in a Centrifugal Compressor

T. Turunen-Saaresti A. Reunanen J. Larjola

Lappeenranta University of Technology, Department of Energy and Environmental Technology, Lappeenranta, Finland teemu.turunen-saaresti@lut.fi

This study focuses on the vaneless diffuser of a centrifugal compressor. The examined stage consists of an un-shrouded impeller, a parallel wall vaneless diffuser and a volute. The walls of the diffuser were movable allowing different pinch configurations to be investigated. The baseline geometry had no pinch i.e. the height of the dif-fuser was equal to the height of the impeller flow channel plus the axial running clearance. The work consists of both numerical and experimental parts. Quasi-steady, turbulent, fully 3D numerical simulations were conducted. The inlet cone, rotor and diffuser were modelled. Six different configurations were studied. The height of the pinch was altered and the pinch made to different walls was tested. Two of the numerically studied cases were also experimentally investigated. The overall performance of the compressor, the circumferential static and total pressure and the spanwise total pressure distribution before and after the diffuser were measured. The numerical and experimental studies showed that the pinch improved the efficiency of the compressor.

Keywords: Centrifugal compressor, vaneless diffuser, pinch CLC number: TK474.8+2 Document code: A Article ID: 1003-2169(2006)04-0306-08

Introduction

Vaneless diffusers are widely used in industrial centrifugal compressors where a wide operating range and inexpensive design are primary goals. The geometry of the vaneless diffuser is very simple. It consists of parallel or almost parallel walls, which form a radial passage from the impeller outlet radius to some outlet radius of the

The height of the diffuser and the radius ratio r3/r2 are the main geometrical parameters affecting the diffuser performance. Senoo and Kinoshita [1] and Van den Braembussche et al. [2] have shown that the critical flow angle α2c is higher (from radial direction) for the nar-rower diffuser and lower for the increased radius ratio. Ludtke [3] has tested four types of vaneless diffusers, one with the parallel walls, one highly tapered, one with con-

stant area, and one with the parallel walls but reduced width (pinched). The pinch was made to the shroud wall and it was 47.3% from the original width. The parallel wall diffuser showed best efficiency and narrowed dif-fuser decreased efficiency. The constant area diffuser appeared best since it improved the surge margin with minimum efficiency penalty. The highly tapered diffuser also improved the surge margin, although there was effi-ciency drop. The pinched diffuser showed minimum effi-ciency of the tested diffuser. Zhu and Sjolander [4] have tested vaneless diffusers with various taper angles. They found that small amount of wall convergence was bene-ficial and yielded better static pressure recovery at the intermediate flow rate than a parallel wall diffuser. Liberti et al. [5] have tested two different vaneless dif- fusers with different widths. They found out that the nar-rower (pinched) diffuser showed better efficiency and

T. Turunen-Saaresti et al. Study of Pinch on the Performance of a Vaneless Diffuser in a Centrifugal Compressor 307

Nomenclature b height of the diffuser, m α flow angle (from radial direction), °Cpr static pressure recovery coefficient ηis relative isentropic efficiency d diameter, m pressure ratio Kp total pressure loss coefficient Ω angular velocity, rad/s Ns dimensionless specific speed Subscripts P pressure, Pa 2 diffuser inlet qv volume flow, m3/h 3 diffuser outlet r radius, m c critical Δhs isentropic enthalpy rise, J/kg K t total

total-total pressure ratio than a wider diffuser. Unfor- tunately Liberti et al. [5] did not report whether the dif-fuser narrowed by moving the hub or the shroud wall.

The present paper reports the numerical results of six different vaneless diffuser constructions where the dif-fuser height is narrowed 5% and 10% from its original height. In Ludtke [3] larger pinch was found to be inef-fective and therefore larger pinches were not treated in this study. Pinches are made to the hub or to the shroud or both walls. Two of the numerically analyzed diffusers were also analyzed experimentally.

Numerical procedure

The quasi-steady approach was utilized to study the effect of different geometries. In the quasi-steady sim- ulation the impeller is calculated in a rotating co-ordinate system, but the grid is stationary. The inlet cone, the im- peller and the diffuser were modelled. The periodicity of the geometry was used and only one passage between full blades was modelled. The volute and the tip clear- ance were not modelled. In most cases simulation were only at the design point and the upstream effect of the volute is minimal. The flow solver Finflo was used to solve the flow field. The Finflo is a Navier-Stokes solver developed at Helsinki University of Technology (HUT). Detailed information about the flow solver can be found in Siikonen [6] and Siikonen et al. [7].

The Chien’s k-ε turbulence model [8] is used in the numerical calculation made in this paper. The Chien's k-ε turbulence model is a low Reynolds number turbulence model which means that no wall functions are used and the boundary layer is calculated if the grid size is suffi-cient. Therefore, emphasis has to be put on the grid den-sity and quality near the walls. Grids are constructed in a way that the y+ < 1 and the boundary layer is calculated properly.

Computed cases First, the original geometry with unpinched diffuser

was modelled. Second, the different kinds of pinches were tested. The calculations were conducted at the low, design and high flow rate at the design rotation speed

(see Figure 1). The amount of pinch was 5% and 10% of the height of the unpinched diffuser and the pinch was made by moving the hub or the shroud, or both. A sum-mary of the computed cases are shown in Table 1. The design operation point of the compressor was modelled for all geometries and the geometry with 10% pinch from the hub and the shroud was also modelled at the low and high flow rates. These correspond to 0.56, 1.00 and 1.34 times design volume flow of the compressor. The ge-ometry with 10% pinch from the hub and the shroud was also measured. The surface grid of the unpinched geome-try is shown in Figure 1 and details on the pinched dif-fusers in Figure 2.

Fig. 1 Compressor map and mass flows used in the detailed flow analysis (top) and surface grid of unpinched diffuser (bot-tom).

308 Journal of Thermal Science, Vol.15, No.4, 2006

Table 1 Detailed data of computed cases.

Cases b2/r2 r3/r2 pinch mass flows

A 0.1155 1.681 low, design, high

B 0.1095 1.681 hub 5% design

C 0.1095 1.681 shroud 5% design

D 0.1095 1.681 hub & shroud 5% design

E 0.1036 1.681 hub 10% design

F 0.1036 1.681 shroud 10% design

G 0.1036 1.681 hub & shroud 10% low, design, high

Fig. 2 Details of pinched diffusers.

Experimental facility

The different pinches were studied with a centrifugal compressor designed to be used in water-treatment plants. The examined stage consists of an unshrouded impeller (Ns = 0,8), a parallel wall vaneless diffuser and a volute. The specific speed of the compressor is defined as

0.751 /s v sN q h= Ω Δ The impeller has seven full and

seven splitter blades with 40° back lean from the radial direction. The ratio of inlet height to inlet radius b2/r2 = 0.1214 and the ratio of the outlet radius to inlet radius r3/r2 = 1.681 for the original unpinched diffuser. The pressure ratio π t−t of the compressor is 1.94 at the design point. The compressor was driven directly by a high-speed electric motor. An inverter accurately con-trolled the electric motor. A photo of the used compressor is shown in Figure 3.

Fig. 3 Test compressor used in this study.

Test stand and experimental procedure

The layout of the compressor test stand is shown in Figure 4 on the left hand side. The air entered to the test compressor through the mass flow nozzle, throttling valve A and flow straightener. The mass flow nozzle is ISA 1932 nozzle and it is placed at the beginning of the inlet pipe. The inlet pressure and temperature were measured. Also ambient pressure, temperature and hu-midity were measured. The pressure and the temperature were measured after the compressor and the flow passes through throttling valve B and muffler. The outlet pipe of

T. Turunen-Saaresti et al. Study of Pinch on the Performance of a Vaneless Diffuser in a Centrifugal Compressor 309

the test stand and the compressor were insulated to en-sure correct temperature measurement.

The test stand was used to measure the overall per-formance of the compressor. The analogue signals from the thermoelements, pressure transducers, humidity meter, tachometer and power analyzer were collected into a Fluke Hydra data logger. Data logger was connected to a PC. Measured data were analyzed on-line with an in-house developed data acquisition program and neces-sary data was recorded.

A three-hole cobra-probe and Kiel-probes with ther-moelement were used to measure the flow field inside of the compressor. Staff of Laboratory of Fluid Dynamics made all the probes. The cobra-probe was calibrated over a broad Mach number range in a free jet nozzle. Before the measurement the cobra-probe was nulled i.e. turned towards the flow. The Kiel-probes were calibrated over a broad Mach number range and yaw-angle range in the free jet nozzle. Also the recovery factor of the tempera-ture measurement was measured.

Static pressures were measured at the four different circumferential angles (90°, 180°, 270° and 0°/360°) at the diffuser inlet (din /d2 = 1.036) and outlet (dout / d2 = 1.67). Total pressure and temperature were measured at four different circumferential (14°, 104°, 194° and 284°) angles at the diffuser inlet and outlet. Measurements were made with Kiel-probes. Flow angles were also measured with Cobra-probe at the circumferential angle 194° at the diffuser inlet and outlet. Location of the static pressure taps and probe traverses are shown in Figure 4. These measurements are performed at the design rotation speed and for three different mass flow conditions.

The axial location of the impeller was measured. The measurements were made with Micro-Epsilon’s non-

contact displacement-sensor ES2. It is capable to meas- ure distances from 0 mm to 2 mm. The displacement- sensor was assembled at the circumferential angle 90° and under impeller at the diameter ratio dsensor/d2 = 0.969. Axial location was measured in order to define the loca-tion of the impeller versus location of the diffuser walls.

Experimental cases

The original geometry with the unpinched diffuser was first measured. This corresponds to case A in the numerical calculations. However, the ratio b2/r2 is slightly different in the numerical calculations with the measurements because the tip clearance was not mod-elled in the numerical calculations. The best pinched dif-fuser according to the numerical simulation was meas-ured. The pinch was made to the hub and the shroud wall and the amount of the pinch was 10%. This corresponds to the case G in the numerical calculations.

Fig. 4 Test stand (top) and locations of the static pressure taps and probe traverses (bottom).

Table 2 Detailed data of measured cases

cases b2/r2 r3/r2 pinch mass flows A 0.1214 1.681 − low, design, highG 0.1095 1.681 hub & shroud 10% low,design, high

Results

The numerical analysis was first made with all seven different geometries. Then the original geometry and the best geometry based on numerical analysis were analyzed experimentally.

Overall performance of the compressor

The calculated and measured relative isentropic effi-ciency and the total-total pressure ratio of the different configurations are shown in Table 3. The values are cal-culated to the diffuser outlet and the isentropic efficiency has been made relative by dividing it with the isentropic efficiency of the whole stage at the design point. The accuracy of the efficiency measurement is ±0.015 units and the pressure ratio measurements ±0.34 %. The work of the impeller is not shown here because it was found that there was no significant difference in the measured work at different configurations.

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Table 3 Calculated and measured total-total pressure ratio and relative isentropic efficiency at various configurations

π t−t ηis t-tcases mass flow CFD Meas. CFD Meas.

A low 1.93 1.89 1.024 0.959 A design 1.84 1.76 1.099 1.026 A high 1.60 1.56 1.034 0.879 B design 1.88 − 1.107 − C design 1.84 − 1.103 − D design 1.86 − 1.097 − E design 1.93 − 1.102 − F design 1.87 − 1.102 − G low 1.95 1.93 1.034 0.955 G design 1.89 1.82 1.131 1.048 G high 1.63 1.58 1.038 0.933

Different kinds of pinches are analyzed numerically.

Only the design operation point is modelled. The 5% pinch made to the hub wall (geometry B) shows only small increase in the isentropic efficiency and in the to-tal-total pressure ratio. The 5% pinch made to the shroud (geometry C) also shows the small increase in the isen-tropic efficiency but no increase in the total-total pressure ratio. The 5% pinch made to the hub and to the shroud walls (geometry D) shows small decrease in the isen-tropic efficiency and small increase in the total-total pressure ratio. The pinch is further increased to 10% of diffuser height and one can see that the isentropic effi-ciency is increased slightly in the geometries E and F compared to the diffuser without the pinch. On the other hand, the increase in the isentropic efficiency is slightly smaller than in the geometries B and C. The total-total pressure ratio shows larger increment in the 10% pinches than 5% pinches made to the hub or to the shroud wall.

The 10% pinch made to the hub and shroud wall (ge-ometry G) shows a significant increase in the isentropic efficiency at the design flow. The increase of the isen-tropic efficiency is also seen in the measurements but it is not as large as in the calculated case. The total-total pressure ratio is also slightly increased which is seen in the calculated and measured results. The small increment in the isentropic efficiency is also seen at the low flow rate in the calculated result. This increment is not seen in the measured result. On the contrary, isentropic effi-ciency is slightly decreased at the low flow rate in the measured results. The total-total pressure ratio is in-creased in the calculated and measured results at the low flow rate. The calculated results show that there is a small increment in the isentropic efficiency at the high flow rate. This increment of the isentropic efficiency is larger in the measured results than in the calculated re-sults. Also the total-total pressure ratio is increased in the calculated and the measured results.

The total-total pressure ratio is fairly well predicted compared to measured values at all constructions. This

can be seen especially at the low and high flow rate. The calculated values are slightly higher which can be ex-plained by the absence of the tip clearance. Also the vo-lute is not modelled which affects the calculated results at the off-design points. The isentropic efficiency is clearly over-predicted at all cases. The magnitude of the differ-ence is the same at all operation points. The nearly cor-rect pressure ratio and the clearly over-predicted isen-tropic efficiency indicate that the temperature rise is un-der-predicted.

Overall performance of the diffusers

The overall performance of the diffusers was evalu-ated using the static pressure recovery coefficient and the total pressure loss coefficient. The static pressure recov-ery coefficient is defined as

out inpr

tin in

p pC

p p−

=−

(1)

and the total pressure loss coefficient as

tin toutp

tin in

p pK

p p−

=−

(2)

where ptin and pin are the total and the static pressures at the inlet of the component under evaluation and ptout and pout are the total and the static pressures at the outlet of the component under evaluation.

The total pressure loss and the static pressure rise co-efficients calculated from the CFD and the measured results are shown in Table 4. The numerical results shows that the pinch made to the hub and the shroud wall give the best performance of the diffuser. The larger pinch gives the better performance. The pinch made to the hub wall shows lower total pressure loss of the diffuser than the pinch made to the shroud wall. However, the static pressure rise is slightly higher with the pinch made to the shroud wall.

The geometry A without the pinch and the geometry G were also studied at the off-design condition. The

Table 4 Calculated and measured total pressure loss and static pressure rise coefficient of the diffusers

Kp Cprcases mass flow CFD Meas. CFD Meas.

A low 0.392 0.224 0.306 0.480A design 0.346 0.171 0.340 0.517A high 0.148 0.201 0.538 0.436B design 0.244 − 0.342 − C design 0.315 − 0.350 − D design 0.239 − 0.392 − E design 0.171 − 0.362 − F design 0.217 − 0.387 − G low 0.330 0.227 0.358 0.462G design 0.163 0.145 0.526 0.504G high 0.161 0.146 0.511 0.425

T. Turunen-Saaresti et al. Study of Pinch on the Performance of a Vaneless Diffuser in a Centrifugal Compressor 311

The performance of the diffuser is under-predicted in the numerical simulations. The difference is the largest at the design and high flows and unpinched diffuser.

numerical study showed that the better the performance of the diffuser the higher the mass flow. This is obvious due the flow is more radial with the higher flow and therefore flow path is shorter and losses lower. On the other hand, this is not true in real compressor where the volute is affecting the flow field and losses at the off-design conditions. The difference between design and high flow rate is larger with the geometry A than with the geometry G.

Detailed flow field

Measured flow fields presented in Figures 5―8 are local. The CFD results are mass flow averaged in the circumferential direction because in the quasi-steady simulation the influence of the blades is otherwise seen. The circumferential variations do not significantly affect the results at the design operation point. However, the effect of the circumferential variation is larger at the low and high flow rates.

The experimental results also showed improved per-formance of the diffuser with the pinched diffuser (ge-ometry G) at the design and high mass flow. No im-provement was seen at the low mass flow rate. The per-formance of the diffuser is the best at the design condi-tion. The geometry G decreased the losses at the diffuser at the high flow rate almost the same level as at design flow rate. However, the static pressure rise is larger at the design flow than at the high flow rate.

Spanwise total pressure at the diffuser inlet with ge- ometries A and G is shown in Figure 5. The total pressure at the diffuser inlet is increased with the geometry G at all mass flow rates. This is seen in the numerical and

Fig. 5 Spanwise total pressure at the diffuser inlet. Fig. 6 Spanwise total pressure at the diffuser outlet.

312 Journal of Thermal Science, Vol.15, No.4, 2006

Fig. 7 Flow angle at the diffuser inlet. Fig. 8 Flow angle at the diffuser outlet.

experimental results. The experimental results show that the pinch (geometry G) moved the highest total pressure near the hub wall and increased the spanwise variation at the high flow rate. The spanwise total pressure is more uniform at the design flow rate with pinched geometry. On the other hand, there is larger variation in spanwise total pressure at the low flow rate with the geometry G than geometry A. This might be the reason why the per-formance of the diffuser is also lower at the low flow rate. No reason for better performance of the diffuser at the high flow rate is seen at the spanwise total pressure dis-tribution. Numerical distribution is more non-uniform than the measured one. The largest difference is seen at the low flow rate.

The spanwise total pressure at the diffuser outlet is shown in Figure 6. The distribution is more uniform at the diffuser outlet than at the diffuser inlet. No difference is seen in the measured total pressure distribution be-

tween geometry A and G. However, the calculated total pressure is slightly different between the geometries.

The flow angle at the diffuser inlet with geometries A and G is shown in Figure 7. The flow angle distribution at the diffuser inlet is more radial near the hub and more tangential near the shroud. This is due to secondary flow of the impeller blade passage. This phenomenon is stronger at the high flow rate. There is a reversed flow at the shroud with unpinched diffuser (geometry A) at the design flow rate. The flow angle turns to the radial direc-tion near the shroud with the pinched diffuser (geometry G). The flow angle does not change near the hub. A re-versed flow is not seen with the geometry G. The nu-merical results agree quite well with the measured results. However, there is reversed flow near the hub at the low flow rate in the numerical results. This is not seen in the measurements

The flow angle at the diffuser outlet with different

T. Turunen-Saaresti et al. Study of Pinch on the Performance of a Vaneless Diffuser in a Centrifugal Compressor 313

geometries is shown in Figure 8. The flow angle across the span is more homogenous at the diffuser outlet than at the inlet, and the difference between the hub and the shroud has decreased. The pinched diffuser turns the flow angle more radial near the shroud at the diffuser inlet, which is also seen at the diffuser outlet. The numerical simulations do not follow measured results well. The flow angle distribution is more non-uniform in the nu-merical simulations. This is seen especially with the pinched diffuser (geometry G).

Conclusions

Measurements and numerical simulation showed that the pinched diffuser improved the efficiency of the cen-trifugal compressor. Also the pressure ratio was slightly increased. The numerical results showed that the pinch made to the hub wall and shroud wall gave best per-formance of the compressor and the diffuser. Also the pinch made to the hub wall was better than pinch made to the shroud wall. However, our results are too limited to define optimum amount of pinch.

Numerical results predicted fairly well the pressure ra-tio of the compressor but the isentropic efficiency was over-predicted. The calculated spanwise distributions of total pressure and flow angle had quite good agreement with the measured values at the diffuser inlet. However, the agreement was not so good at the diffuser outlet. Es-pecially the flow angle with the pinched diffuser (geome-try G) was badly predicted in the numerical results.

Acknowledgements Financial support for this study provided by National

Technology Agency (TEKES) and High Speed Tech Oy Ltd is gratefully acknowledged. CSC- Scientific Com-

puting Ltd provided the computational resources for the numerical work.

References

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