SCIENCE CHINA Technological Sciences Special Topic: Engineering Thermophysics

January 2015 Vol.58 No.1: 29–36

• Article •

doi: 10.1007/s11431-014-5697-8

Aerodynamic effects of impeller-diffuser axial misalignment in low-flow-coefficient centrifugal compressor WANG ZhiHeng1, XI Guang1* & LIU QingFang2 1

School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China; 2 School of Mathmatics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China

Received August 14, 2014; accepted October 17, 2014; published online November 6, 2014

A numerical investigation on the aerodynamic effects of impeller-diffuser axial misalignment in the low-flow-coefficient centrifugal compressor is conducted through three-dimensional CFD analysis. The results show that the flow, especially near the diffuser inlet, is influenced by the axial misalignment obviously. When the impeller offsets to one side, the pressure at diffuser inlet close to this side will descend, and the vortex in the cavity on the other side will partially enter the diffuser and then result in the back flow. The performances of the stage and its components also change with the impeller-diffuser axial misalignment. There exists an optimum offset making the efficiency maximum at a given operating point. Furthermore, the effect of impeller-diffuser axial misalignment on the axial thrust is pronounced. The axial thrust is nearly increased linearly with the increase of axial misalignment. The aerodynamic effects of impeller-diffuser axial misalignment in the low-flow-coefficient centrifugal compressor behaves more remarkably at the large flow rate. To alleviate the aerodynamic effects of impeller-diffuser misalignment, a rounding in the meridional plane at the diffuser inlet can be applied. misalignment, compressor, low flow coefficient, impeller Citation:

Wang Z H, Xi G, Liu Q F. Aerodynamic effects of impeller-diffuser axial misalignment in low-flow-coefficient centrifugal compressor. Sci China Tech Sci, 2015, 58: 2936, doi: 10.1007/s11431-014-5697-8

1 Introduction The low-flow-coefficient centrifugal compressor stage used in the last stages of in-line multi-stage compressors for high-pressure applications typically features a small relative blade outlet width of impeller (b2/D2<0.02). The relatively narrow flow channels in the impeller, the diffuser and also the cavities between the impeller and the casing lead to high aerodynamic and parasitic losses. Moreover, the small flow channel makes the accurate alignment between the impeller and the diffuser hard to achieve due to the manufacturing and installation tolerances and the thermal expansion. Therefore, a special treatment is required for the analysis *Corresponding author (email: [email protected]) © Science China Press and Springer-Verlag Berlin Heidelberg 2014

and design of low-flow-coefficient centrifugal compressor [1]. Early researches by Paroubek et al. [2], Reddy et al. [3] and Engeda [4] have contributed to our knowledge of the performance and the flow of low-flow-coefficient centrifugal compressor. Their results showed that, there exist different flow patterns in the low-flow-coefficient centrifugal compressor and some commonly used criteria or correlation models may no longer be valid for the low-flow-coefficient centrifugal compressor. With the development of computer power and CFD techniques, many analysis and attempts to improve the performance of low-flow-coefficient centrifugal compressor have been done, such as Martelli et al. [5], Xu and Amano [6], Yagi et al. [7], Wang et al. [8] and Zhang et al. [9]. However, their studies are all based on the assumption that the impeller and diffuser are completely tech.scichina.com link.springer.com

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aligned. To the authors’ knowledge, there are quite few studies covering the aerodynamic influence of the impeller-diffuser misalignment. Especially in the low-flow-coefficient centrifugal compressor, the impeller-diffuser axial misalignment is most likely to happen, but its influences on the aerodynamic performance and the other related quantities are unclear. In the work conducted by Qian [10], the influence of a number of inlet configuration geometric parameters on the diffuser performance for a small flow rate radial compressor was numerically investigated. The parameters included the impeller-diffuser alignment, diffuser inlet edge radius, impeller tip gap width, flow angle and tip leakage/injection. Whereas, the 2-D axisymmetric numerical model was used in the study and the impeller flow channel was simplified to an inlet tube with a uniform flow specified, which make the numerical simulations lose some fidelity. The present work takes a practical centrifugal compressor with a low flow coefficient as the research object, and aims at the study of the influences of the impeller-diffuser axial misalignment on the aerodynamic performance and the impeller axial thrust. To achieve this, three-dimensional CFD analyses are carried out at the low, medium and large flow rates, respectively. The aerodynamic performances of the impeller and diffuser, and the axial thrust acting on the impeller are compared at different impeller-diffuser misalignment positions. The impeller-diffuser axial misalignment chosen for the study varies in the range of 20%20% of blade outlet width.

2 Description of research object The low-flow-coefficient centrifugal compressor considered in the paper consists of an impeller with splitter blades and a vaneless diffuser with the channel width equal to the impeller blade width (b3=b2). This stage is designed for the last stage of an industrial CO2 centrifugal compressor in the low-pressure cylinder. The blade width at the impeller outlet (r2=156.25 mm) is 3.75 mm. The design rotational speed of impeller is 16220 r/min. Both the other technical data of the compressor and the shape of flow path are detailed in [11]. In this low-flow-coefficient centrifugal compressor, the channel widths of the impeller and diffuser are so small that the large impeller-diffuser axial misalignment relative to the blade width of impeller is likely to occur due to the installation tolerance and/or the thermal expansion. To isolate the effect of impeller-diffuser axial misalignment in our study, the sizes of the impeller and the casing are set to be unchangeable, and only the axial position of the impeller relative to the diffuser is changed. As depicted in Figure 1, the impeller-diffuser axial offset () is nondimensionalized by the blade outlet width of impeller with eq. (1), and it is considered to be positive if the impeller offsets to the hub casing.

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=  /b2 .

(1)

In order to reveal the aerodynamic effects of impellerdiffuser axial misalignment, the performance of the impeller and diffuser and the axial thrust are analyzed with respect to changes in nondimensional impeller-diffuser axial misalignment in 0.05 intervals from 0.20 to 0.20.

3 CFD analysis method The commercial available CFD code EURANUS/TURBO from NUMECA International [12] is used to simulate the flow field in the stage by solving the steady, 3-D Reynolds-averaged Navier-Stokes equations. Implemented in the code is the Spalart-Allmaras model for turbulence closure. The numerical procedure is based on a four-stage RungeKutta scheme. With the assumption of the passage circumferential periodicity, one impeller passage with a main blade and a splitter, and the cavities on the hub and shroud sides having the same circumferential pitch with one impeller passage are considered as the computational domain. The cavities on the impeller’s hub and shroud sides are included with the aim to model the parasitic losses in connection with the disk friction and the seal leakage [11]. For simpleness, the leakage through the cavity on the hub side to the atmosphere is thought to be negligible and the leakage flow rate is set to be zero. To ensure a sufficient grid resolution near the solid walls, the value of y+ associated with the fist grid node off the blade or the endwall is controlled to be less than 10 for the grid generation. After the grid independency study, the multi-block structured mesh consisting of 1.99 million grid nodes is employed. Figure 2 shows the mesh in the numerical investigations. In the computation, the absolute flow angle, the uniform total pressure and total temperature at the

Figure 1

Impeller-diffuser axial misalignment (positive in the figure).

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4.1

Figure 2

Computational domain and grid.

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Comparison of flow simulation results

The flow in the region close to the impeller outlet and the diffuser inlet is directly affected by the impeller-diffuser axial misalignment. Accordingly, the flow in this region is mainly analyzed and compared. Figure 4 depicts the spanwise distributions of circumferentially averaged static pressure and flow angle (atan(Vr/Vθ)) at the diffuser inlet (r/r2=1.0128) . To represent the difference clearly, the results at =±0.05 and ±0.15 are not shown in the figure. When at the large flow coefficient, the static pressure at the diffuser inlet is low due to the low pressure rise, but the flow angle is high due to the high radial velocity. As Figure 4(a) shows, at all the three flow coefficients, the averaged static pressure at the diffuser inlet will be debased when an

inlet boundaries are imposed. The mass flow rate is specified for the outlet boundary condition. The adiabatic and non-slip conditions are prescribed at the solid walls. The isentropic and total work coefficient of the stage with no impeller-diffuser misalignment are predicted and shown in Figure 3. The outlet of stage locates at the section of r/r2=1.15. The maximum efficiency of the stage is less than 72.0%, which is distinctly lower than the efficiency of the common used stage with the medium or large flow coefficient. To compare the influences of impeller-diffuser misalignment at different operating conditions, three operating points, which are the low flow rate (  =0.0123), the nearly optimum efficiency point (  =0.0175) and the large flow rate (  =0.0203), are chosen to investigate.

4 Results and discussion Using the CFD model addressed above, the flow in the stages with nine different impeller-diffuser axial misalignment offsets are analyzed and compared at three operating flow coefficients (  =0.0123, 0.0175, and 0.0203). The misalignment offsets used in the numerical simulations are 0, ±0.05, ±0.10, ±0.15 and ±0.20. The effects of the misalignment on the axial thrust and the performance of impeller, diffuser and stage are investigated.

Figure 3

Stage performance at =0.

Figure 4 Spanwise distributions of circumferentially averaged static pressure and flow angle at diffuser inlet. (a) Static pressure; (b) flow angle.

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impeller-impeller axial offset exists. The bigger the offset to the hub or shroud casing is, the more the static pressure at the diffuser inlet is debased. Additionally, when the offset is to the shroud casing, the pressure descends more rapidly, which can be seen clearly at the large flow coefficient (  = 0.0203). The impeller-diffuser misalignment has an important influence on the spanwise distribution of static pressure at the diffuser inlet. At a positive offset, i.e. when the impeller has an offset to the hub casing, the static pressure near the hub is reduced obviously and much less than that near the shroud. At a negative offset, the result is contrary. This can be explained by virtue of Figure 1. The two dashed lines shown in Figure 1 shape a suppositional flow channel connecting the impeller outlet with the diffuser inlet. At a positive offset, as depicted in Figure 1, the outflow of the impeller is confined by a pinched “wall” near the hub and divergent near the shroud. As a result, the flow near the shroud has a better diffusion action than that near the hub. When at a negative offset, the static pressure rise of the impeller outflow near the shroud gets restricted. Besides, the leakage flow through the shroud cavity from the impeller outlet to the inlet has an aspiration effect. The addition of two factors makes the pressure reduction near the shroud more visible at the negative offset. The spanwise distributions of circumferentially averaged flow angle at the diffuser inlet are compared at different impeller-diffuser misalignments. The circumferentially averaged flow angles at the diffuser inlet are almost uniform in the 25%75% span at all the operating flow coefficients. The flow angle is reduced obviously close to the shroud at a positive offset while reduced close to the hub at a negative offset. The more the impeller offsets to the hub (or shroud) casing, the more the flow angle close to the hub (or shroud) is reduced. Especially, the back flow can be found near the hub at =+0.20 and near the shroud at =0.20. To further illustrate the flow patterns in the region close to the impeller outlet and the diffuser inlet, the distributions of circumferentially averaged static pressure and velocity streamlines at the flow coefficient  =0.0175 are shown in Figure 5. It can be found that, there exist complex vortex structures in both cavities on the hub and shroud sides. The impeller-diffuser misalignment has much influence on the static pressure in the cavities, which leads to the change of axial thrust of impeller. This will be discussed in detail in the following section. The position and size of the vortex cell also vary slightly when the impeller-diffuser misalignment happens. At =0.20, a small part of the vortex cell close to the diffuser inlet in the hub side cavity moves into the diffuser, which causes the back flow shown in Figure 4(b). Additionally, a closed separation bubble can be seen on the shroud side near the diffuser inlet. When at =+0.20, a small part

Figure 5 Distributions of circumferentially averaged static pressure and velocity streamlines near impeller outlet at  =0.0175.

of the vortex cell close to the diffuser inlet in the shroud side cavity enters the diffuser, and the flow recirculation occurs close to the shroud. Likewise, there generates a separation bubble close to the hub. Hence, it can be concluded that, when the impeller offsets to one side, the vortex in the other side cavity will partially enter the diffuser and then result in the back flow, and on the same side in the diffuser a separation bubble will appear. 4.2

Influence on aerodynamic performance

The variations of the total-to-total isentropic efficiency and total work coefficient of the impeller with the impeller-diffuser misalignment are analyzed and shown in Figure 6. It should be pointed out that, here the thermodynamic parameters at the impeller outlet using for the impeller performance calculation are taken from the diffuser inlet. In this case, the cavities on the both sides of impeller are involved, and the disk friction and leakage losses are considered to evaluate the overall performance of impeller. The influence of impeller-diffuser misalignment on the

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impeller performance at the large coefficient is more pronounced than that at other flow coefficients. The changes of the isentropic efficiency of impeller at  =0.0123 and 0.0175 are less than 0.6% in the investigated range of impeller-diffuser misalignment. However, the change of the efficiency at  =0.0203 reaches 4.0%. Generally, the impeller behaves a high efficiency when there is a positive impeller-diffuser offset. For the total work coefficient of impeller, there exists an optimum value of the offset close to =0.05 to make the total work coefficient minimum. When there is a positive offset, the total work coefficient increases with the increase of offset. Thus, to make the impeller offset to the hub side is favorable for achieving the high efficiency and high pressure ratio of low-flow-coefficient impeller. Figure 7 compares the diffuser performance at different impeller-diffuser misalignments. The total pressure loss coefficient and static pressure recovery coefficient are used to evaluate the diffuser performance, and defined respectively as follows:

Cp,t  ( pt ,3  pt ,4 ) ( pt ,3  p3 ) ,

(2)

Cp,s  ( p4  p3 ) ( pt ,3  p3 ).

(3)

The diffuser has a lower total presser loss coefficient at the large flow coefficient, because the larger flow angle at the diffuser inlet is propitious to reducing the friction loss, which is the main part in the diffuser with a narrow span width. Furthermore, at the large flow coefficient the diffuser has a higher static pressure recovery coefficient.

Figure 7 Comparison of diffuser performance. (a) Total pressure loss coefficient; (b) static pressure recovery coefficient.

When the impeller-diffuser misalignment occurs, the total pressure loss coefficient firstly keeps a nearly constant level, and then increases sharply when the offset to the hub or shroud side increases to a high value. For the static pressure recovery coefficient, it increases with the departure of the impeller-diffuser alignment position. It is surprising that, at the large flow rate point  =0.0203, the static pressure recovery coefficient begins to reduce instead when the impeller offset to the hub or shroud side more than 0.15b2. This indicates the complexity of the influence of the impeller-diffuser misalignment on the diffuser’s flow and performance. In general, the relationship curve between Cp,t or Cp,s and  is nearly symmetrical about =0. At the large flow coefficient, the influence of impeller-diffuser misalignment on the diffuser performance is more pronounced. Comparing the influences of impeller-diffuser misalignment on the impeller and diffuser performances, one can find that the trends of their changes according to the offset are not consistent. Hence, the influence of impeller-diffuser misalignment on the stage performance needs to be further analyzed. Figure 8 shows the change of the stage’s total-to-total isentropic efficiency according to the impeller offset. The total work coefficient of the stage is the same with that of the impeller, so it is not repeated to show. At the flow coefficients  =0.0123 and 0.0175, the stage has the maximum

Figure 6 Comparison of impeller performance. (a) Isentropic efficiency; (b) total work coefficient.

efficiency at =0. When the impeller deviates from the alignment position with the diffuser, the isentropic efficiency has a slight reduction. However, at the large flow coefficient

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Figure 8

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Comparison of stage isentropic efficiency.

 =0.0203, the maximum efficiency is obtained at =+0.1, and the impeller-diffuser misalignment affects the efficiency remarkably. It is clear from the results presented that the impellerdiffuser axial misalignment has a more pronounced influence on the aerodynamic performance at the large flow coefficient than that at the small flow coefficient. There is no united rule or trend to describe the influences of impeller-diffuser axial misalignment on the aerodynamic performances of impeller, diffuser and stage. For the impeller, a positive offset is favorable to achieving a design with a better efficiency and a higher load. The diffuser keeps a low level of total pressure loss coefficient when the offset is small, whereas a large offset benefits the static pressure recovery. For the stage, there exists an optimum offset making the efficiency maximum at a given operating point. The stage efficiency will decrease when the impeller has a departure from that optimum offset. 4.3

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when the impeller offsets to the shroud side more than 0.25b2 at the operating point  =0.0203. Figure 10 shows the distribution of circumferentially averaged static pressure on the outer surfaces of the hub and shroud to clarify the effect of impeller-diffuser axial misalignment. Due to the seal leakage from the impeller outlet back to the impeller inlet, the pressure on the outer surface of the shroud is reduced more rapidly with the reduction of radius than that on the outer surface of the hub. On the outer surface of the shroud, the pressure decreases abruptly when the leakage flows through the seal fins (r/r2<0.63), as shown in Figure 10(b). The pressure distribution on the outer surface of the hub shifts to the direction of pressure increase with the increase

Figure 9

Comparison of axial thrust acting on impeller.

Influence on axial thrust

The axial thrust in a centrifugal compressor has strong influences on the mechanical reliability and the operating safety. In the low-flow-coefficient centrifugal compressor, the main source of the axial thrust is the difference of radial pressure distributions on the outer surfaces of hub and shroud. As shown in Figure 5, the pressure in the cavities is influenced remarkably by the impeller-diffuser misalignment. Therefore, the impeller-diffuser misalignment is inevitable to affect the axial thrust. The axial thrusts at different impeller-diffuser misalignment are plotted in Figure 9. The axial misalignment has a strong effect on the axial thrust of centrifugal compressor. Take the axial thrust at the flow coefficient  =0.0175 for example, the axial thrust will increase by 7% when the impeller’s offset to the hub side increases 10% of the blade width. The predicted axial thrusts at three operating points are almost increased linearly with the increase of axial misalignment. At the large flow rate, the influence of axial misalignment on the axial thrust is more remarkable. It can be predicted that, the axial thrust direction will be reversed

Figure 10 Distribution of circumferentially averaged static pressure on outer surfaces of hub and shroud at =0.0175. (a) On outer surface of hub; (b) on outer surface of shroud.

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of nondimensional impeller-diffuser offset. Additionally, on the outer surface of the shroud, the pressure in the region except the seal fins’ location decreases with the increase of offset. This leads to the change of axial thrust with the impeller-diffuser misalignment shown in Figure 9. 4.4 Diffuser inlet rounding to alleviate the effect of misalignment

From the analysis and discussion addressed above, it can be concluded that the impeller-diffuser axial misalignment has an important influence on the aerodynamic performance and the axial thrust of impeller in a low-flow-coefficient compressor, especially operating at the large flow rate. How to alleviate the effects of the impeller-diffuser misalignment is of great concern to the practical designers and maintenance engineers. One of the methods is to make a rounding in the meridional plane at the diffuser inlet to control the flow. To validate the effect of diffuser inlet rounding, the diffuser is modified with a round radius Ra=0.3b2 at the diffuser entrance edge and investigated. Figure 11 shows the distribution of circumferentially averaged static pressure and velocity streamlines at the flow coefficient  =0.0175 when the diffuser inlet rounding exists. Compared with the velocity streamlines shown in Figure 5, the separation bubble disappears, which is presented at the diffuser inlet without a rounding when there is an impeller-diffuser misalignment. This is favorable to the improvement of the flow in the diffuser. Compared with the static pressure distribution in Figure 5, the variation of static pressure distribution with the axial misalignment gets smaller when the diffuser inlet rounding is adopted. This leads to the alleviation of axial misalignment’s effect on the axial thrust, as Figure 12 shows. In Figure 12, when the diffuser inlet rounding exists, the axial thrusts at different operating conditions are also almost increased linearly with the increase of axial misalignment, but the sensitivity of the axial thrust to the impeller-diffuser axial misalignment is effectively reduced. The comparison of the stage isentropic efficiency with the diffuser inlet rounding or not is shown in Figure 13. At the small or medium flow rates, the influence of the impeller-diffuser misalignment on the stage isentropic efficiency is neglectable when Ra/b2=0.3. At the large flow rate, the variation of stage isentropic efficiency with the impeller-diffuser misalignment gets smaller when there is a diffuser inlet rounding. One interesting observation from Figure 13 is that at the large flow rate, the maximum stage isentropic efficiency with a diffuser inlet rounding is lower than that without a diffuser inlet rounding. By the comparison, one can conclude that the diffuser inlet rounding can effectively alleviate the effect of impeller-diffuser misalignment on the aerodynamic performance and the axial thrust. In this paper, only one round radius of diffuser inlet is investigated. Factually, there is an optimal

Figure 11 Distributions of circumferentially averaged static pressure and velocity streamlines near impeller outlet at =0.0175 with diffuser inlet rounding.

Figure 12 0.0175).

Comparison of axial thrust with diffuser rounding or not ( =

rounding shape to alleviate the effect of impeller offset while keeping the stage performance at a high level. This will be investigated in the further study.

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Nomenclature

Figure 13 Comparison of stage isentropic efficiency with diffuser inlet rounding or not.

5 Conclusion A numerical investigation on the aerodynamic effects of impeller-diffuser axial misalignment in the low-flow-coefficient centrifugal compressor is conducted using threedimensional CFD analysis. The flow, the performance of impeller, diffuser and stage, and the axial thrust are analyzed with different impeller-diffuser axial misalignment. The following results are a summary of results. (1) The impeller-diffuser axial misalignment has an obvious effect on the flow near the diffuser inlet. When the impeller offsets to one side, the pressure at diffuser inlet close to this side will descend. Additionally, the vortex in the cavity on the other side will partially enter the diffuser and then result in the back flow, and on the same side a separation bubble can be seen in the diffuser. (2) There is no united rule or trend to describe the influences of impeller-diffuser axial misalignment on the aerodynamic performances of impeller, diffuser and stage. For the impeller, a positive offset is favorable to achieving a design with a better efficiency and a higher load. The diffuser keeps a low level of total pressure loss coefficient when the offset is small, whereas a large offset benefits the static pressure recovery. For the stage, there exists an optimum offset making the efficiency maximum at a given operating point. (3) The impeller-diffuser axial misalignment has a pronounced influence on the axial thrust. The axial thrust is nearly increased linearly with the increase of axial misalignment. (4) The impeller-diffuser axial misalignment in the lowflow-coefficient centrifugal compressor affects the flow, the performances of stage and its components, and the axial thrust more remarkably at the large flow rate. (5) To reduce the sensitivity of the aerodynamic performance and axial thrust to the impeller-diffuser axial misalignment, the diffuser inlet rounding is an effective method. This work was supported by the National Natural Science Foundation of China (Grant No. 51236006), and China Postdoctoral Science Foundation (Grant No. 2012M521771).

Notation b Cp,s Cp,t Faxial p pt Qm Ra r Tt V

span width; static pressure recovery coefficient; total pressure loss coefficient; axial thrust; static pressure; total pressure; mass flow rate; diffuser inlet round radius; radial cylindrical coordinate; total temperature; velocity;

     

total-to-total isentropic efficiency; offset; nondimensional offset; flow coefficient (=4Qm/(ρinU2r22)); density; work coefficient.

Subscript in imp stage r tot θ 2 3 4

station at inlet of computational domain; impeller; stage; component in radial direction; total; component in circumferential direction; station at impeller exit; station at diffuser inlet; station at diffuser outlet.

1 2 3

4 5 6 7

8

9 10 11 12

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