Design and Optimization of a Single Stage Centrifugal ... - Springer Link

Journal of Thermal Science Vol.22, No.5 (2013) 404412

DOI: 10.1007/s11630-013-0642-x

Article ID: 1003-2169(2013)05-0404-09

Design and Optimization of a Single Stage Centrifugal Compressor for a Solar Dish-Brayton System Yongsheng Wang1,2, Kai Wang1, Zhiting Tong1, Feng Lin1, Chaoqun Nie1, Abraham Engeda3 1. Key Laboratory of Advanced Energy and Power Chinese Academy of Sciences, Institute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing 100190, China 2. Graduate University of Chinese Academy of Science, Beijing 100049, China 3．Department of Mechanical Engineering, Michigan State University, East Lansing 48823, USA © Science Press and Institute of Engineering Thermophysics, CAS and Springer-Verlag Berlin Heidelberg 2013

According to the requirements of a solar dish-Brayton system, a centrifugal compressor stage with a minimum total pressure ratio of 5, an adiabatic efficiency above 75% and a surge margin more than 12% needs to be designed. A single stage, which consists of impeller, radial vaned diffuser, 90° crossover and two rows of axial stators, was chosen to satisfy this system. To achieve the stage performance, an impeller with a 6:1 total pressure ratio and an adiabatic efficiency of 90% was designed and its preliminary geometry came from an in-house one-dimensional program. Radial vaned diffuser was applied downstream of the impeller. Two rows of axial stators after 90° crossover were added to guide the flow into axial direction. Since jet-wake flow, shockwave and boundary layer separation coexisted in the impeller-diffuser region, optimization on the radius ratio of radial diffuser vane inlet to impeller exit, diffuser vane inlet blade angle and number of diffuser vanes was carried out at design point. Finally, an optimized centrifugal compressor stage fulfilled the high expectations and presented proper performance. Numerical simulation showed that at design point the stage adiabatic efficiency was 79.93% and the total pressure ratio was 5.6. The surge margin was 15%. The performance map including 80%, 90% and 100% design speed was also presented.

Keywords: Single Stage, Centrifugal Compressor, Design, Optimization

Introduction Ever since the demand for fossil fuels has begun to rise, solar energy technologies have become a major source for providing the clean and renewable energy. A dish-solar-hybrid power system directly heating a gas turbine’s pressurized air when the combustor is turned off, in combination with a highly efficient recuperated Brayton cycle system, can result in significant cost reductions

for electric power. The whole system consists of a centrifugal compressor, recuperator (heat exchanger), solar receiver, fuel combustor, turbine and generator, shown in Fig.1. In the daytime, solar energy is used to heat the compressed air and during nighttime, supplemental fuels such as natural gas, biogas and others can be used in the conventional combustor. Since long distance power transmission causes too much power loss and needs auxiliary equipments, remote villages can benefit a lot from

Received: April 2013 Kai Wang: Assistant Professor This work is supported by the National Natural Science Foundation of China (Grant No.51010007) and China Scholarship Council (CSC). www.springerlink.com

Yongsheng Wang et al.

Design and Optimization of a Single Stage Centrifugal Compressor for a Solar Dish-Brayton System

Nomenclature b blade height (mm) D diameter (mm) Lz impeller axial length (mm) m mass flow rate (kg/s) mdesign mass flow rate at design point (kg/s) N rotational speed (r/min) Ndesign rotational speed at design point (r/min) Ns specific speed Z number of blades Greek letters inlet flow coefficient  β blade angle relative to the tangential direction

Fig. 1

A solar dish-Brayton generation system

this solar dish-Brayton system. Enough power can be provided by connecting a couple of the solar Braytonsystems. Due to the high flow loss in the solar receiver, recu-perator and other flow components, a high pressure ratio centrifugal compressor is critical for such a solarized gas turbine system. Such a compressor needs to be operated with a minimum total pressure ratio of 5, an adiabatic efficiency above 75% and a surge margin more than 12% to meet the needs of a 50 kW solar dishBrayton system. The exit flow direction of the centrifugal compressor should be in the axial direction to reduce flow loss. Centrifugal compressors used in this system feature low flow rate, but high pressure ratio and belong to the medium flow coefficient (=0.02‒0.2) compressors. Based on the current compressor design development, three main design plans may be suitable in this study: (1) Impeller, radial vaned diffuser, 90° crossover and two rows of axial diffusers, (2) Impeller, radial cascade diffuser, 90° crossover and one row of axial diffuser, (3) Impeller, radial vaned diffuser (trailing edge extends into 90° crossover), 90° crossover and one row of axial diffuser. The predominant difference of design thought in these three plans is whether main flow turning occurs in the

δ π Subscripts 1 2 3 b h s imp dif

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tip clearance total pressure ratio impeller inlet impeller outlet radial diffuser vane inlet blade hub shroud impeller diffuser

radial diffuser or not. In the first plan, the flow turning angle in the diffuser is approximately between 12° and 18°, which means the main flow turning occurs downstream of the radial diffuser. That’s the reason why two rows of axial diffusers are arranged just after 90° crossover. In the second and third plans, bigger flow turning angle is expected in the radial diffuser. Either cascade diffuser or long vaned diffuser extending into crossover can fulfill the expectations. The aim of this study is to design and develop a centrifugal compressor stage for a solar dish-Brayton system, which will be applied in the real environment. Therefore, considering the simplicity of the structure and manufacturing cost, the first plan is the proper one. In the open literatures, limited quantity information about the detailed centrifugal compressor stage design similar to the first plan can be found [1]. Generally, most of the researches concentrate on the design and optimization of every single flow component [2-5]. In this study, not only every component design is included, but also the match between each component is involved. Since jet-wake flow, shockwave and boundary layer separation coexist in the impeller-diffuser region, research should be focused on this area and searches for appropriate geometry data of the radial vaned diffuser within empirical range. So optimization on the radius ratio of radial diffuser vane inlet to impeller exit, diffuser vane inlet blade angle and number of diffuser vanes at design point will be implemented and the final optimized geometrical data will be presented and applied in the rest of this study.

Design and Optimization Impeller In order to satisfy the requirements of the whole system, a centrifugal compressor with a total pressure ratio of 6 and an adiabatic efficiency of 90% needs to be de-

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signed. The geometry of the impeller came from an inhouse one-dimensional program, which was calibrated by one of the Krain’s well studied impellers [6, 7]. According to the design requirement, the rotational speed was fixed at 51000 r/min. The material limits the tip speed at impeller exit less than 525 m/s. In consideration of the shaft design, hub diameter at inlet was chosen at 45 mm. Splitter vanes were employed to reduce slip and widen the choke margin. So the blade set was divided into 10 full blades and 10 splitter blades. The leading of splitter was located in the 30% chord of full blades. The blade angle at impeller outlet was 60° [8] and the blade distribution throughout the impeller followed the method proposed by Aungier [9]. This method uses a cubic equation for both hub and shroud curves, which both have a zero gradient at trailing edge. Additionally, it forces the leading edge of the shroud curve to have a zero gradient [10]. Three-dimensional model of the impeller is shown in Fig.2. Main impeller parameters are listed in Table 1.

Fig. 2 Table 1

Impeller 3-D geometry

Impeller design parameters N

51000

π

6

Ns

0.085



0.05

Zimp

20( 10+10 )

Dh1/Ds1

0.42

Ds1/D2

0.54

b2/D2

0.06

δ/b2

0.077

Lz/D2

0.305

Radial Vaned Diffuser Once the geometrical data of the impeller was fixed, designing radial diffuser to match the impeller can be started afterwards. The interaction between impeller and radial diffuser is considered to have strong influence on the performance of the centrifugal compressor due to jet-wake flow, shockwave and boundary layer separation

coexisting in this region and presenting highly complex unsteady phenomenon [11-13]. Therefore, how to choose the parameters such as the radius ratio of diffuser vane inlet to impeller exit, diffuser inlet blade angle and number of the blades and others is worth of being paid more attention. According to researchers’ experience and the information in the open literatures, the radius ratio of diffuser vane inlet to impeller exit (r3/r2) should be limited between 1.05 and 1.15 [14]. However, when this ratio reaches lower limit, the unsteady interaction in the impeller-diffuser region is much stronger. Finally, this ratio was set within 1.089-1.15 in this study. As for diffuser vane inlet blade angle (β3b), it mainly depends on the flow field downstream of the impeller, especially on the absolute flow angle. 1-D code shows this angle is 13.1° at the impeller exit and CFD gives an averaged value of 11.6°. 11°, 13° and 15° were chosen as diffuser vane blade angle respectively to see which one was appropriate. Number of diffuser vanes (Zdif) was set from 15 to 19. A fixed value was from a comparison of optimization procedure. Therefore, CFD optimizations with impeller and radial vaned diffuser only on the r3/r2 with a radial distance increment of 2mm, β3b with an increment of 2° and Zdif with an increment of 1 were carried out and present the optimum combination providing highest adiabatic efficiency and total pressure ratio. In this optimization numerical simulation, the parts of hub and shroud curves covering the following 90° crossover and axial diffusers, shown in Fig.3, were also involved. In addition, considering the installation of casing or housing, the maximum thickness of diffuser vane must be above 6 mm as required. Fig.4 shows the blade thickness distribution throughout the radial diffuser. Fig.5 shows the performance comparisons at design point. The maximum value in each figure is marked by its corresponding one. The height of every cylinder can clearly show the obvious difference. The maximum efficiency difference is around 4%, seen in Fig. 5(b), and this

Note: The locations of three dash lines are a, b and c, which will be referred to in the rest of this paper.

Fig.3

Meridional view with impeller only

Yongsheng Wang et al.

Fig.4

Design and Optimization of a Single Stage Centrifugal Compressor for a Solar Dish-Brayton System

Thickness distribution

407

proves that it’s really worth doing the optimization comparison, which includes 60 samples in total. Every 20 samples have the same values for the vane inlet blade angle. In Fig. 5(a), (b), it’s found that the samples with r3/r2 of 1.089 and 1.15 show worse performances. It’s not clear to tell the effect of number of the vanes on the performance distribution trend. The highest total pressure ratio and efficiency come from the same sample with r3/r2 of 1.129 and Zdif of 17 while β3b is fixed at 11°. When β3b changes to 13°, shown in Fig. 5(c), (d), the performances of the centrifugal compressor are improved as Zdif is increased. This is obviously seen with r3/r2 at 1.089 and

Fig. 5 Total pressure ratio and adiabatic efficiency comparisons at design point. (a) Total pressure ratio versus r3/r2 and Zdif at β3b=11°, (b) Adiabatic efficiency versus r3/r2 and Zdif at β3b=11°, (c) Total pressure ratio versus r3/r2 and Zdif at β3b=13°, (d) Adiabatic efficiency versus r3/r2 and Zdif at β3b=13°, (e) Total pressure ratio versus r3/r2 and Zdif at β3b=15°, (f) Adiabatic efficiency versus r3/r2 and Zdif at β3b=15°.

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1.129. Even though the effect of r3/r2 on the performance trend is still hard to tell, the samples with r3/r2 of 1.129 present better ones. The highest total pressure ratio and efficiency come from the sample with r3/r2 of 1.129 and Zdif of 19 while β3b is fixed at 13°. The rest of the samples with β3b of 15° provide relatively worst results, especially for the adiabatic efficiency, seen in Fig. 5(f). However, the overall distribution trend is much clearer either versus the r3/r2 or Zdif. Fig. 5(e) and (f) present similar performance trend versus r3/r2 and Zdif. The effciency and total pressure ratio keep going up as Zdif is increased. The effect of r3/r2 is similar to that of Zdif from 1.089 to 1.129. The performances begin to drop when r3/r2 is reduced from 1.129 to 1.15. Therefore, the highest values for total pressure ratio and efficiency are located at the sample with r3/r2 of 1.129 and Zdif of 19 when β3b equals 15°. Based on the above optimization analysis, it turns out that r3/r2 at 1.129 is the most appropriate one to be used no matter which value is set to radial diffuser vane inlet blade angle. Lower r3/r2 may cause strong interaction between impeller and radial diffuser while higher one makes more flow loss, which drops both total pressure and efficiency. In general, it is thought that more vanes will increase friction loss in the diffuser passages and drop the efficiency. However, that is based on the premise that all the other geometry parameters such as throat area, blade angle, solidity and others don’t change at all, which will be scarcely possible in the practical design. So it’s reasonable as CFD shows 19 vanes will improve the centrifugal compressor performances. Because the blade angle, solidity, throat area, the radius and area ratios of radial diffuser outlet to inlet are related and work jointly [15-16]. Since the objective of this optimization procedure is to get higher values for total pressure ratio and efficiency, the sample with r3/r2 of 1.129, Zdif of 19 and β3b of 13° is selected to provide the final fixed parameters for radial diffuser. Through the optimization, CFD simulation with impeller and radial vaned diffuser can only obtain a maximum total pressure ratio of 5.571 and an adiabatic efficiency of 79.4%. Fig. 6 shows the model of radial vaned diffuser. The First Row Axial Diffuser (FRAD) According to design requirements, the exit flow direction of the centrifugal compressor should be as axial as possible. The flow angle distribution at the axial location of “a”, shown in Fig.3, should be known before axial diffusers design. It can be provided by the simulation together with impeller and radial diffuser only at the optimum sample and the detailed distribution trend is shown by red points in Fig.7. An averaged value of 62° was chosen as the blade angle at the leading edge of the

J. Therm. Sci., Vol.22, No.5, 2013

first row axial diffuser. The flow turning angle was set to 30° to avoid separation in the passages. So the blade angle at the trailing edge was 32°. The axial length was 30 mm. The black points in Fig.8 indicate that the absolute flow angle distribution at the same location is improved and becomes more uniform after applying the FRAD.

Fig.6

Fig.7

Radial vaned diffuser

Flow angle distribution comparison at the axial location of “a”

The Second Row Axial Diffuser (SRAD) To design the SRAD, numerical simulation together with impeller, radial diffuser and the FRAD should be performed in advance to provide the information of the flow field. As shown in Fig.8, the flow angles at trailing edge of the FRAD are mostly around 42°, which means only 20° flow turning angle is achieved in the FRAD. In order to turn the flow as axial as possible in the SRAD, the axial gap between two rows of axial diffusers should be small enough or even overlapping. In consideration of modeling and grid meshing issues, 2 mm axial gap was chosen finally. In Fig.8, “a” refers to the location of the trailing edge of the FRAD and “c” is the location where the leading edge of the SRAD will be set. The simulation without the SRAD shows that the flow angle distribution at the axial location of “c” doesn’t change too much except the region near hub and shroud when compared to that at the trailing edge of the FRAD,

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Design and Optimization of a Single Stage Centrifugal Compressor for a Solar Dish-Brayton System

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seen in Fig. 8. Finally, the SRAD vane inlet blade angle was set 35°. The axial length of the SRAD was fixed at 33 mm. The circumferential interval of these two rows of axial diffusers was 1/4 blade space [17-18], clearly shown in Fig.9.

Fig. 10

Fig. 8 Flow angle distribution comparison under the simulation with impeller, radial diffuser and the FRAD

Meridional view of the whole stage

Fig. 11

Fig. 12

3-D model of the whole stage

Impeller relative Mach number contour at 50% span

Fig. 9 Blade-to-Blade view of axial diffusers

Results and Analysis Each component in the centrifugal compressor was designed one after another. Based on the design and optimization procedure, the geometry data of the whole stage was fixed. Its meridional view is shown in Fig.10. Visual three-dimensional model can be found in Fig.11. At design point, no large separation is found in the passage of the impeller even though a small low flow region present off the suction side near the trailing edge, shown in Fig.12. The flow exit flow direction of the stage is not absolutely in the axial direction. Fig.13 shows the detailed flow angle distribution at the stage exit. The maximum deviation angle from the axial is located at the 70% span. Since a high pressure vessel will be applied after the centrifugal compressor in the solar dish-brayton system, the stage exit flow with the angle distribution shown in Fig. 13 will not cause too much flow loss.

Fig. 13

Flow angle distribution at the stage exit

Figs. 14 and 15 present contour plots of static pressure and entropy on the meridional plan of the whole centrifugal compressor stage. Static pressure distributes smoothly throughout the stage as expected. Larger en-

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tropy is found in the tip clearance region extending to the hub direction a litter bit near the leading edge of the splitter. The area near the shroud between impeller and radial diffuser also presents higher entropy as well, which is associated with the flow separation there, clearly shown in Fig.16. Generally, this kind of flow situation between impeller and radial diffuser is usually found in the centrifugal compressors for industrial applications. Another small zone with flow separation is found near the hub side in the 90° crossover, which may be avoided by modifying the hub curve reasonably. Overall, these two regions of low velocity fluid mentioned are acceptable and the current design doesn’t have to be changed. Except for those two regions, the flow situation is really good in the rest of the stage. Figs. 17, 18 and 19 show the streamlines in the radial diffuser, the FRAD and the SRAD, respectively. From these three plots, we can see

that the stationary components are well designed in this paper. A close-up at the leading edge is especially presented in Fig.18.

Fig. 14 Static pressure contour

Fig. 18 Streamlines in the FRAD passage

Fig. 17

Streamlines in the radial diffuser passage

Fig. 19 Streamlines in the SRAD passage Fig. 15

Entropy contour

Fig. 16 Streamline distribution

The performance map is provided by numerical simulation and shown in Fig.20. At design point, the total pressure ratio of the stage is 5.6 and the adiabatic efficiency is 79.93%, which completely meet the needs of the design goals. The power consumption is 228.46 kW. Plus the 50 kW for generator, the solar dish-Brayton system needs to produce a minimum power output of 278.46 kW including the portions consumed by the centrifugal compressor and others. Through calculation, the axial thrust generated by this system is 2138.9 N. The surge margin is 15% at design speed, which satisfies the design requirement. Another two speed-line simulations were also performed, at 80% and 90% design

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be manufactured and tested in the future. Performance comparisons between computational and experimental data will be provided to evaluate and validate this design. The third design plan mentioned in this paper will be attempted if possible.

Acknowledgement This work was supported by the National Natural Science Foundation of China under Grant No.51010007 and China Scholarship Council (CSC).

References

Fig. 20

Performance map of the centrifugal compressor including three speed lines

speed. On the whole, the surge line on the left is smooth, seen in Fig.20 (a). The performance of the centrifugal compressor designed in this paper presents a good performance and can fulfill the expectations. Field test will be carried out in the future to evaluate and validate this design.

Conclusions To satisfy the requirements of a solar dish-Brayton system, a single stage centrifugal compressor was designed. The stage consisted of impeller, radial vaned diffuser, 90° crossover and two rows of axial diffusers. Each component was designed one after another. Optimizations on the radius ratio of radial diffuser vane inlet to impeller exit, diffuser vane inlet blade angle and number of vanes were carried out. Finally, the performance of this single stage centrifugal compressor was evaluated by CFD. At design point, the adiabatic efficiency was 79.93% and total pressure ratio was 5.6. The surge margin was 15%. The maximum flow angle at the stage exit was 12°. No serious flow separation was found. Three different speed-line performance curves showed that the surge line was very smooth. Basically, this design fulfilled the high expectations and satisfied the aerodynamic design requirements. The centrifugal compressor designed in this paper will

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