Analysis and Improvement of a Two-Stage Centrifugal Compressor Used in an MW-Level Gas Turbine

applied sciences

Article Analysis and Improvement of a Two-Stage Centrifugal Compressor Used in an MW-Level Gas Turbine

Wei Zhu, Xiao-Dong Ren, Xue-Song Li * ID and Chun-Wei Gu

Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, China; [email protected] (W.Z.); [email protected] (X.-D.R.); [email protected] (C.-W.G.) * Correspondence: [email protected]

Received: 6 July 2018; Accepted: 7 August 2018; Published: 10 August 2018

Featured Application: A two-stage centrifugal compressor used in an MW-level gas turbine is optimized, especially for diffusers. The experiences can also be used for other similar equipment.

Abstract: The performance of a low/high-pressure-stage centrifugal compressor in a land-use MW-level gas turbine with a pressure ratio of approximately 11 is analyzed and optimized with a 1D aerodynamic design and modeling optimization system. 1D optimization results indicate that the diameter ratio of the low-pressure-stage centrifugal compressor with a vane-less diffuser, and the divergent angle of the high-pressure-stage centrifugal compressor with a vaned diffuser, are extremely large and result in low efficiency. Through modeling design and optimization system analysis, a tandem vaned diffuser is used in the low-pressure stage, and a tandem vaned diffuser with splitter vanes is adopted in the high-pressure stage. Computational fluid dynamics (CFD) results show that the pressure ratio and efficiency of the optimized low/high-pressure-stage centrifugal compressor are significantly improved. Coupling calculations of the low/high-pressure stage of the original and optimized designs are conducted based on the results of MW-level gas turbine cycles. CFD results show that the pressure ratio and efficiency of the optimized two-stage centrifugal compressor increase by approximately 8% and 4%, respectively, under three typical load conditions of 100%, 90%, and 60%.

Keywords: centrifugal compressor; low/high-pressure-stage; optimization design; diffuser

1. Introduction As pressure-generator devices, centrifugal compressors have been applied in the industry since the 19th century [1]. Centrifugal compressors are commonly used when the flow rate is low, typically 1~4 kg/s. Experimental research on the application of centrifugal compressors to gas turbines began in the early 20th century. In 1903, Elling [2] successfully built a gas turbine that could transmit power outward. The real motivation for research on centrifugal compressors was the application of these machines in flight propulsion. From 1928–1941, Frank Whittle, a British engineer, and Hans Joachim Pabst von Ohain, a German physicist, independently developed the world’s first jet engine. They adopted a centrifugal compressor for the selected air compressor device. Gas turbines with centrifugal compressors are frequently used in the engines of tanks or small aircraft due to their limited through-current capacity. The pursuit of a compact engine and a high thrust-to-weight ratio promoted the development of centrifugal compressors decades after the invention of jet engines. In the past

Appl. Sci. 2018, 8, 1347; doi:10.3390/app8081347 www.mdpi.com/journal/applsci Appl. Sci. 2018, 8, 1347 2 of 22

Appl.60 years, Sci. 2018 many, 8, 1347 scholars have investigated centrifugal compressors and obtained a deep understanding2 of 20 of the internal flow phenomenon. InIn 1976, 1976, Eckardt Eckardt [3] [3] measure measuredd the the jet jet-wake-wake phenomenon phenomenon in in the the outlet outlet of of a a centrifugal centrifugal compressor compressor with a a pressure pressure ratio ratio of of 2.1. 2.1. Karin Karin [4 []4 also] also measure measuredd a centrifugal a centrifugal compressor compressor with with a pressure a pressure ratio ratio of 4.of Hah 4. Hah [5] [performed5] performed a 3D a 3D numerical numerical simulation simulation of of a acentrifugal centrifugal compressor. compressor. Krain Krain [ [66,,77]] measured measured thethe shock shock wave wave in in the the inlet inlet of of a centrifugal a centrifugal compressor compressor that that had had an inlet an inlet tip Mach tip Mach number number of 1.3 of and 1.3 aand pressure a pressure ratio ratio of 6.1. of 6.1. Hah Hah [8] [ conducted8] conducted a numerical a numerical simulation simulation of of this this centrifugal centrifugal compressor. compressor. Meanwhile,Meanwhile, Senoo Senoo [ [99]] measured measured the the shock shock wave wave and and pressure pressure distribution distribution in in the the inlet inlet of of a a centrifugal centrifugal compressorcompressor with with a a pressure pressure ratio ratio of of 10. 10. Higashimo Higashimoriri [10,11 [10,11]] measured measured a a centrifugal centrifugal compressor compressor with with aa pressure pressure ratio ratio of of 11 11 and and analyzed analyzed its its flow flow characteristic. characteristic. Hosseini Hosseini [12] [ 12investigate] investigatedd the theeffects effects of the of radialthe radial gap gapratio ratio on a on high a high-pressure-pressure ratio ratio centrifugal centrifugal compressor compressor and andthe flow the flow phenomena phenomena inside inside the compressorthe compressor components components by using by using numerical numerical simulations. simulations. Ebrahimi Ebrahimi [13] analy [13]zed analyzed the matching the matching of the vanedof the vaneddiffuser diffuser with the with impeller the impeller for different for different working working conditions conditions.. Sun [14 Sun] investigate [14] investigatedd the flow the instabilityflow instability of centrifugal of centrifugal compressors compressors with with vaned vaned diffuser diffuserss experimentally experimentally and and presented presented diverse diverse instabilityinstability patterns patterns and and transient transient behavior behavior in detail. in detailZheng. [15 Zheng] investigated [15] investigate the instabilityd the mechanisms instability mechanismsof a high-speed of a turbochargerhigh-speed turbocharger centrifugal centrifugal compressor compressor with a vaneless with a diffuser vaneless using diffuser the using unsteady the unsteadysimulation simulation method. method. FigureFigure 1 shows the the development development trend trend of of centrifugal centrifugal compressors compressors for for commercial commercial use use during during the pastthe pastfew few decades. decades. The The pressure pressure ratios ratios of of single single-stage-stage centrifugal centrifugal compressors compressors have have improved improved continually,continually, and centrifugal compressors with single single-stage-stage pressure r ratiosatios over 10 have been been put put into into practicalpractical use.

(a) (b)

FigureFigure 1. 1. DevelopmentDevelopment trend trend of of centrifugal centrifugal compressors compressors:: ( (aa)) Development Development trend trend of of total total pressure pressure ratio ratio;; ((bb)) Relation Relation between between pressure pressure ratio and efficiency efﬁciency..

The required pressure ratio for a tank or helicopter engine is between 8 and 12, and the efficiency The required pressure ratio for a tank or helicopter engine is between 8 and 12, and the efficiency is approximately 80%. Centrifugal compressors with multi-stage low-load design are frequently is approximately 80%. Centrifugal compressors with multi-stage low-load design are frequently adopted to obtain high efficiency and low cost. Considering that the ratio of a single-stage compressor adopted to obtain high efficiency and low cost. Considering that the ratio of a single-stage compressor cannot meet this requirement, gas turbines mostly adopt a two-stage centrifugal or multi-stage axis cannot meet this requirement, gas turbines mostly adopt a two-stage centrifugal or multi-stage axis compressor with a single-stage centrifugal compressor, as shown in Figure 2. For example, the compressor with a single-stage centrifugal compressor, as shown in Figure2. For example, the TPE331 TPE331 turboprop engine developed by Garrett Al in 1959 uses a two-stage centrifugal compressor turboprop engine developed by Garrett Al in 1959 uses a two-stage centrifugal compressor with a flow with a flow mass of 3.49 kg/s and a pressure ratio of 10.8 [16]. The Light Helicopter Turbine Engine mass of 3.49 kg/s and a pressure ratio of 10.8 [16]. The Light Helicopter Turbine Engine Company [17] Company [17] developed a high-performance two-stage centrifugal compressor for the T800-LHT- developed a high-performance two-stage centrifugal compressor for the T800-LHT-800 helicopter 800 helicopter engine. Its design flow mass, compression ratio, adiabatic efficiency, and surge margin are 3.3 kg/s, 14:1, >80%, and >15%, respectively. An MW-level engine compressor is composed of a low/high-pressure two-stage centrifugal compressor. The pressure ratio of this two-stage centrifugal compressor is approximately 11, resulting in poor performance. Ref. [18] adopted a 1D aerodynamic optimization design system and Appl. Sci. 2018, 8, 1347 3 of 22 engine. Its design flow mass, compression ratio, adiabatic efficiency, and surge margin are 3.3 kg/s, 14:1, >80%, and >15%, respectively. An MW-level engine compressor is composed of a low/high-pressure two-stage centrifugal compressor.Appl. Sci. 2018, 8 The, 1347 pressure ratio of this two-stage centrifugal compressor is approximately3 of 11, 20 Appl.resulting Sci. 2018 in, 8,poor 1347 performance. Ref. [18] adopted a 1D aerodynamic optimization design system3 of 20 andused used the the computational computational fluid fluid dynamics dynamics (CFD) (CFD) commercial commercial software software Numec Numecaa (Numeca, (Numeca, Brussels, used the computational fluid dynamics (CFD) commercial software Numeca (Numeca, Brussels, Belgium)Belgium) toto perform perform numerical numerical calculations, calculations, performance performance analysis, and optimization of the poor poor Belgium) to perform numerical calculations, performance analysis, and optimization of the poor performanceperformance ofof thethe two-stagetwo-stage centrifugalcentrifugal compressor.compressor. performance of the two-stage centrifugal compressor.

Figure 2. Comparison of centrifugal compressor pressure ratios. FigureFigure 2. 2. ComparisonComparison of of centrifugal centrifugal compressor compressor pressure pressure ratios ratios.. 2. Analysis of the Performance of Low/High-Pressure Two-Stage Centrifugal Compressor 2.2. Analysis Analysis of of the the Performance Performance of of Low/High Low/High-Pressure-Pressure Two Two-Stage-Stage Centrifugal Centrifugal Compressor Compressor The structure of an MW-level gas turbine is shown in Figure 3. The low/high-pressure two-stage TheThe structure structure of of an an MW MW-level-level gas gas turbine turbine is is shown shown in in Figure Figure 33.. The low/high low/high-pressure-pressure two two-stage-stage centrifugal compressor is composed of an inlet guide vane, an impeller, and a diffuser. A vaned centrifugalcentrifugal compressor is is composed composed of of an an inlet inlet guide guide vane, vane, an impeller, an impeller, and a and diffuser. a diffuser. A vaned A diffuser vaned diffuser is used to connect the two stages. The geometric structure of the centrifugal compressor is diffuseris used is to used connect to connect the two the stages. two stages. The geometric The geometric structure structure of the centrifugalof the centrifuga compressorl compressor is shown is shown in Figure 4. shownin Figure in Figure4. 4.

Figure 3. Structure of an MW-level gas turbine. FigureFigure 3. 3. StructureStructure of of an an MW MW-level-level gas gas turbine. turbine.

(a) (b) (a) (b) Figure 4. Geometric structure of a low/high-pressure two-stage centrifugal compressor: (a) Low- Figure 4. Geometric structure of a low/high-pressure two-stage centrifugal compressor: (a) Low- pressure stage (b) High-pressure stage. pressure stage (b) High-pressure stage. Appl. Sci. 2018, 8, 1347 3 of 20 used the computational fluid dynamics (CFD) commercial software Numeca (Numeca, Brussels, Belgium) to perform numerical calculations, performance analysis, and optimization of the poor performance of the two-stage centrifugal compressor.

Figure 2. Comparison of centrifugal compressor pressure ratios.

2. Analysis of the Performance of Low/High-Pressure Two-Stage Centrifugal Compressor The structure of an MW-level gas turbine is shown in Figure 3. The low/high-pressure two-stage centrifugal compressor is composed of an inlet guide vane, an impeller, and a diffuser. A vaned diffuser is used to connect the two stages. The geometric structure of the centrifugal compressor is shown in Figure 4.

Appl. Sci. 2018, 8, 1347 4 of 22 Figure 3. Structure of an MW-level gas turbine.

(a) (b)

Figure 4. 4. GeometricGeometric structure structure of a low/highof a low/high-pressure-pressure two-stage two-stage centrifugal centrifugal compressor compressor:: (a) Low- (pressurea) Low-pressure stage (b) stage High (-bpressure) High-pressure stage. stage. Appl. Sci. 2018, 8, 1347 4 of 20

TheThe low low-pressure-stage-pressure-stage impeller’s impeller’s rotation rotation speed speed is is 28,000 28,000 rpm, rpm, and and the the rim rim speed speed is is 478 m/s. FigureFigure 5 5 shows shows the the CFD CFD calculation calculation resultsresults for for the the performance performance curve curve of of the the low-pressure-stage low-pressure-stage centrifugalcentrifugal compressor. compressor. The The pressure pressure ratio ratio of of the the low low-pressure-stage-pressure-stage centrifugal centrifugal compressor compressor is is 3.92, 3.92, andand its its efficiency efﬁciency is 79.9% in the design condition [1 [188].

FigureFigure 5. 5. PerformancePerformance curve curve of of the the low low-pressure-stage-pressure-stage centrifugal centrifugal compressor. compressor.

The high-pressure-stage impeller’s rotation speed is 38,000 rpm, and the rim speed is 501 m/s. The high-pressure-stage impeller’s rotation speed is 38,000 rpm, and the rim speed is 501 m/s. Figure 6 shows the CFD calculation results for the performance curve of the high-pressure-stage Figure6 shows the CFD calculation results for the performance curve of the high-pressure-stage centrifugal compressor. The pressure ratio of the high-pressure-stage centrifugal compressor is 2.85, centrifugal compressor. The pressure ratio of the high-pressure-stage centrifugal compressor is 2.85, and its efficiency is 80.5% in the design condition [18]. and its efﬁciency is 80.5% in the design condition [18].

Figure 6. Performance curve of the high-pressure-stage centrifugal compressor. Appl. Sci. 2018, 8, 1347 4 of 20

The low-pressure-stage impeller’s rotation speed is 28,000 rpm, and the rim speed is 478 m/s. Figure 5 shows the CFD calculation results for the performance curve of the low-pressure-stage centrifugal compressor. The pressure ratio of the low-pressure-stage centrifugal compressor is 3.92, and its efficiency is 79.9% in the design condition [18].

Figure 5. Performance curve of the low-pressure-stage centrifugal compressor.

The high-pressure-stage impeller’s rotation speed is 38,000 rpm, and the rim speed is 501 m/s. Figure 6 shows the CFD calculation results for the performance curve of the high-pressure-stage centrifugal compressor. The pressure ratio of the high-pressure-stage centrifugal compressor is 2.85, Appl. Sci. 2018, 8, 1347 5 of 22 and its efficiency is 80.5% in the design condition [18].

Figure 6. Performance curve of the high-pressure-stagehigh-pressure-stage centrifugal compressor.compressor.

The performance analysis shows that the efﬁciency of the low/high-pressure two-stage centrifugal compressor is lower than that of a unit with a similar pressure ratio, as shown in Figure1. This observation indicates that several limitations exist in the design of the low/high-pressure two-stage centrifugal compressor, and that the design needs to be optimized.

3. Optimization of the Low-Pressure-Stage Centrifugal Compressor An optimized design system [18] was adopted to optimize the aerodynamic layout of the low-pressure-stage centrifugal compressor. A comparison of the parameters of the original and optimized designs is shown in Table1. The geometric impeller parameters after optimization changed minimally and, mainly due to a slight increase in the outlet width, b2, the efficiency of the optimized design increased by approximately 0.3% compared with the original design. This result shows that the impeller parameters are set reasonably in the original design. After optimization, the outlet efficiency of the vaned diffuser was 2.29% higher than that of the original design. This finding indicates that the mismatch between the diffuser and impeller mainly leads to the low efficiency in the original design. For the vane-less diffuser, pressure can be increased by increasing diameter ratio D3/D2. However, if the increase in the diameter ratio is overly large, the efficiency of the entire stage would decrease. Thus, the ratio of D3/D2 = 1.05:1.2 is recommended. In the original design, the diameter ratio, D3/D2, is 1.34, which is much higher than the recommended value. In the optimized design, D3/D2 is 1.1, which is within the reasonable design range. Thus, the loss in the vane-less diffuser was significantly reduced, leading to an increase in the efficiency of the entire stage. Appl. Sci. 2018, 8, 1347 6 of 22

Table 1. Comparison of the parameters of the optimized and original designs.

Parameter Optimized Design Original Design

D1s (m) 0.075 0.082 D1t (m) 0.190 0.202 D2 (m) 0.326 0.326 Lz (m) 0.075 0.080 b2 (m) 0.0158 0.0151 D3 (m) 0.358 0.440 D4 (m) 0.601 0.601 D3/D2 1.10 1.34 η2 95.15% 94.87% η3 92.63% 86.29% η4 83.38% 81.09%

The 1D optimization results showed it was necessary to reduce D3/D2 to improve the efficiency of the entire stage of the low-pressure-stage centrifugal compressor. When D3/D2 was reduced, if the original shape of the vanes was still used in the vaned diffuser, the throat area of the vaned diffuser decreased, as shown in optimized design 1 in Figure7. Then, the chock mass flow of the vaned diffuser decreased to have an influence on the matching of the diffuser and impeller. In order to improve the performance of the entire stage after optimization, it is necessary to analyze the matching of the diffuser and impeller. To achieve the best matching performance of the diffuser and impeller, the design ratio, * * Ad /Ai , should be as close to the theoretical level as possible [19]. * * * * The ratio of design Ad /Ai to theoretical Ad /Ai is 1.161 in the original design as shown in Table2. It indicates that the chock mass flow of the vaned diffuser is larger than that of the impeller. When the * * * * vaned diffuser is moved toward the impeller, the ratio of design Ad /Ai to theoretical Ad /Ai would be decreased to 0.922. The choke area decreased significantly to make the chock mass flow in the vaned diffuser much lower than that of the impeller, which cannot meet the design requirements. Therefore, it is necessary to redesign the vaned diffuser to leave the chock mass flow of the unit unchanged when the diameter ratio D3/D2 is reduced. Considering all factors, the original vaned diffuser was replaced by a tandem vaned diffuser as shown in optimized design 2 in Figure7. By using the optimized * * * * method, the ratio of design Ad /Ai to theoretical Ad /Ai was 1.043, which is closer to 1 and indicates the better matching of the diffuser and impeller. The throat area of the vaned diffuser was slightly larger than that of the impeller, which made the choke mass flow of the optimized design consistent with that of the original design. Appl. Sci. 2018, 8, 1347 6 of 20 Appl. Sci. 2018, 8, 1347 6 of 20 to 1 and indicates the better matching of the diffuser and impeller. The throat area of the vaned to 1 and indicates the better matching of the diffuser and impeller. The throat area of the vaned diffuser was slightly larger than that of the impeller, which made the choke mass flow of the diffuser was slightly larger than that of the impeller, which made the choke mass flow of the Appl.optimized Sci. 2018 design, 8, 1347 consistent with that of the original design. 7 of 22 optimized design consistent with that of the original design.

(a) Original design (a) Original design

(b) Optimized design 1 (c) Optimized design 2 (b) Optimized design 1 (c) Optimized design 2 Figure 7. Geometric structure of the vaned diffuser. FigureFigure 7.7. Geometric structure ofof thethe vanedvaned diffuser.diffuser.

* * * * Table 2. Ratio of design A* d /A*i to theoretical Ad*/Ai .* TableTable 2. 2Ratio. Ratio of of design designAd A/d*A/Ai i* toto theoreticaltheoreticalA Add*/AAi*i. . Original Design Optimized Design 1 Optimized Design 2 ** OriginalOriginal Design Design Optimized Optimized Design Design 1 1 Optimized Optimized Design Design 2 2 AAdi**/ (A∗/(A∗) )design d ( AAi didesign/ ) ∗ ∗ design 1.1611.161 0.922 0.922 1.043 1.043 (A /A **) d AAi **theory/ 1.161 0.922 1.043 ( AAdi/ )theory ( di)theory

TheThe steady steady simulations simulations were were performed performed using the using commercial the commercial software Numeca. software The Numeca. Spalart- The steady simulations were performed using the commercial software Numeca. The Spalart- TheAllmaras Spalart-Allmaras (SA) turbulence (SA) turbulence model was model used. wasGrids used. were Grids generated were generated by grid generation by grid generation software Allmaras (SA) turbulence model was used. Grids were generated by grid generation software softwareAutoGrid AutoGrid (Numeca, (Numeca,Brussels, Belgium) Brussels,. The Belgium). grid number The grid of the number original of design the original was 1,100,000 design; after was AutoGrid (Numeca, Brussels, Belgium). The grid number of the original design was 1,100,000; after 1,100,000;optimization, after it optimization,was 1,400,000. it T wasotal pressure 1,400,000. of Total 101,300 pressure Pa was of set 101,300 at the Painlet was and set the at back the inlet-pressure and optimization, it was 1,400,000. Total pressure of 101,300 Pa was set at the inlet and the back-pressure thewas back-pressure set at the outlet was for set boundary at the outlet conditions. for boundary The wall conditions. was adiabatic The with wall a was sliding adiabatic surface. with The a was set at the outlet for boundary conditions. The wall was adiabatic with a sliding surface. The slidingcalculation surface. results The are calculation shown in results Figure are 8, and shown the in1D Figure calculations8, and theare 1Dalso calculations shown for arecomparison. also shown forcalculation comparison. results are shown in Figure 8, and the 1D calculations are also shown for comparison.

(a) (b) (a) (b) Figure 8. Performance map of the original and optimized designs for the low-pressure stage: (a) Figure 8. Performance map of the original and optimized designs for the low-pressure stage: (a) FigureReduced 8. massPerformance flow vs. total map pressure of the ratio original; (b) Reduced and optimized mass flow designs vs. isentropic for the low-pressureefficiency. stage: (Reduceda) Reduced mass mass flow flow vs. vs.total total pressure pressure ratio ratio;; (b) ( bReduced) Reduced mass mass flow flow vs. vs. isentropic isentropic efficiency efficiency.. Appl. Sci. 2018, 8, 1347 8 of 22 Appl. Sci. 2018, 8, 1347 7 of 20

The calculation results show that the pressure ratio of the original design was 4.152, and the efficiencyefficiency was 80.35%. The pressure ratio of the optimized design was 4.291, and the efficiency efficiency was 82.79%. Compared with the pressure ratio and efficiency efficiency of thethe original design, those of the optimized design represented a a significant significant improvement improvement.. The The trend trend of of the the 1D 1D calculation calculation results results was was similar similar to tothat that of the of the Numeca Numeca calculation calculation results. results. The Thepressure pressure ratio ratio and efficiency and efficiency of the of original the original design design were were4.218 4.218and 8 and1.09%, 81.09%, respectively, respectively, whereas whereas the thepressure pressure ratio ratio and and efficiency efficiency of of the the optimized optimized design were 4.339 and 83.20%, respectively. Compared with the pressure ratio of the original design, that of optimized design increased by 2.87%, and the efficiencyefficiency increasedincreased byby 2.11%.2.11%. Figure 99 shows shows thethe inletinlet attackattack angleangle distributiondistribution ofof thethe vanedvaned diffuser.diffuser. InIn thethe originaloriginal design,design, because of the separation area in the vaneless diffuser, the separation vortex worsened the flowflow condition atat thethe vanedvaned diffuser diffuser inlet inlet with with the the variable variable scope scope of of the the inlet inlet attack attack angle angle close close to 50 to◦ .50°. In the In optimizedthe optimized design, design, the separation the separation vortex disappearedvortex disappeared in the vane-less in the vanediffuser,-less and diffuser, the flow and condition the flow of thecondition vaned diffuserof the vaned inlet significantly diffuser inlet improved significantly with theimproved decrease with in diameter the decrease ratio, inD3 / diameterD2. The range ratio, ◦ ◦ ofD3/ angleD2. Th ofe attackrange of along angle the of span attack was along reduced the span from was 50 reducedto 15 . from 50° to 15°.

Figure 9. Inlet attack angle distribution of the vaned diffuser in the optimized design.

4. Optimized Design of the High-Pressure-StageHigh-Pressure-Stage Centrifugal Compressor The optimized optimized design design system system [1 [818] was] was adopted adopted to optimize to optimize the aerodynamic the aerodynamic layout layout of the of high the- high-pressure-stagepressure-stage centrifugal centrifugal compressor. compressor. Table 3 Table shows3 shows a comparison a comparison of the parameters of the parameters of the original of the originaland optimized and optimized designs. designs.The geometric The geometric parameters parameters after optimization after optimization changed changedonly sligh onlytly, slightly,and the andefficiency the efficiency of the ofoptimized the optimized design design increased increased by approximately by approximately 0.2% 0.2% compared compared with with the the original original design. This This finding finding shows shows that that the the impeller impeller parameters parameters are are set set reasonably reasonably in in the the original original design. design. After optimization, optimization, the the efficiency efficiency of theof the vaned vaned diffuser diffuser outlet outlet was 2.61%was 2.61% higher higher than that than of the that original of the design.original Thisdesign. result This indicates result indicates that the that mismatch the mismatch between between the diffuser the diffuser and impeller and impeller mainly ma leadinly to lead the lowto the efficiency low efficiency in the originalin the original design. design. Compared with the value of the divergent angleangle,, 2 θ,, inin thethe original design, the value in the optimized design decreased significantly.significantly. TheThe divergentdivergent angleangle isis defineddefined asas follows:follows:

DDD43−− D tan θ == 4 3 . 2L . ◦ For the diffuser design, 2 θ shouldshould be less than 1212° to avoid gas over over-expansion-expansion and separation. The experimental experimental results results showed showed that that the theloss losscoefficient coefficient of the of vaned the diffuservaned diffuser is related is to related the divergent to the ◦ angle.divergent In general,angle. In the general, loss was the minimal loss was when minimal 2θ = when 6 , and 2θ gradually = 6°, and increasedgradually withincreased the growth with the of 2growthθ. If the of value 2θ. If of the 2 θ valueis too of large, 2θ is it too could large, be it reduced could be by reduced increasing by the increasing diameter the and diameter number and of blades.number Byof blades. contrast, By the contrast, increase the in increase diameter in anddiameter blade and number blade increasednumber increased the loss inthe flow loss passage. in flow Therefore,passage. Therefore, the influence the influence of various of parameters various param on theeters performance on the performance of the diffuser of the should diffuser be considered should be comprehensivelyconsidered comprehensively in the design. in the In thedesign. original In the design, original the design, large divergent the large angledivergent increases angle the increases loss in the loss in the vaned diffuser, which, in turn, leads to the low efficiency of the entire stage. In the Appl. Sci. 2018, 8, 1347 9 of 22 Appl. Sci. 2018, 8, 1347 8 of 20 theoptimized vaned diffuser,design, the which, divergent in turn, angle leads was to theeffectively low efficiency reduced, of and the entirethe efficiency stage. In of the the optimized unit was design,improved the by divergent increasing angle the wasblade effectively number and reduced, length. and the efficiency of the unit was improved by increasing the blade number and length. Table 3. Comparison of the parameters of the optimized and original designs. Table 3. ComparisonParameter of theOptimized parameters Design of the optimized Original and Design original designs. D1s (m) 0.071 0.073 Parameter Optimized Design Original Design D1t (m) 0.192 0.134 D (m) 0.071 0.073 1s D2 (m) 0.252 0.252 D (m) 0.192 0.134 1t Lz (m) 0.057 0.058 D2 (m) 0.252 0.252 Lz (m)b2 (m) 0.0570.0956 0.00948 0.058 b2 (m)D3 (m) 0.09560.274 0.282 0.00948 D3 (m)D4 (m) 0.2740.392 0.388 0.282 D4 (m)DD/ 0.392 0.388 32 1.09 1.12 D3/D2 1.09 1.12 2θ 2θ 11.911.9 15.715.7 Z Z 2020 17 17 η2 η2 95.47%95.47% 95.24% 95.24% η 92.88% 92.37% 3 η3 92.88% 92.37% η4 84.12% 82.29% η4 84.12% 82.29%

TheThe divergentdivergent angleangle waswas reducedreduced inin thethe 1D1D optimizedoptimized designdesign systemsystem byby increasingincreasing thethe bladeblade numbernumber and length, length, as as shown shown in in Figure Figure 10b, 10 b,and and the theefficiency efﬁciency of the of design the design was improved. was improved. This Thisoptimization optimization method method reduced reduced the the throat throat area area of of the the vaned vaned diffuser diffuser and and changed changed the matching matching characteristicscharacteristics of thethe vanedvaned diffuserdiffuser andand impeller.impeller. Therefore,Therefore, itit isis necessarynecessary toto makemake anan optimizedoptimized designdesign onon thethe matchingmatching characteristicscharacteristics ofof thethe impellerimpeller andand vanedvaned diffuser.diffuser.

(a) Original design

(b) Optimized design 1 (c) Optimized design 2

Figure 10. Geometric structure of the vaned diffuser.

The ratio of design Ad*/Ai* to theoretical Ad*/Ai* is 1.09 in the original design as shown in Table 4. The ratio of design A */A * to theoretical A */A * is 1.09 in the original design as shown in Table4. It indicates that the chockd massi flow of the vanedd diffuseri is larger than that of impeller. When the It indicates that the chock mass flow of the vaned diffuser is larger than that of impeller. When the number of blades is increased and the blade diffuser is moved close to the impeller, the ratio of design number of blades is increased and the blade diffuser is moved close to the impeller, the ratio of design Ad*/Ai* to theoretical Ad*/Ai* would be decreased to 0.948. The choke area decreased significantly to A */A * to theoretical A */A * would be decreased to 0.948. The choke area decreased significantly to maked thei chock mass flowd ini the vaned diffuser much lower than that of impeller, which cannot meet make the chock mass flow in the vaned diffuser much lower than that of impeller, which cannot meet the design requirements. Therefore, it is necessary to redesign the vaned diffuser to leave the chock the design requirements. Therefore, it is necessary to redesign the vaned diffuser to leave the chock mass flow of the unit unchanged, when the diameter ratio D3/D2 is reduced. Considering all factors, Appl. Sci. 2018, 8, 1347 10 of 22 Appl. Sci. 2018, 8, 1347 9 of 20 massthe original flow of vaned the unit diffuser unchanged, was replaced when the by diameter a tandem ratio vanedD3 /diffuserD2 is reduced. as shown Considering in optimized all factors,design the2 in originalFigure 10 vanedc. diffuser was replaced by a tandem vaned diffuser as shown in optimized design 2 in FigureIn the 10 firstc. row, 15 small vanes were selected, which is less than the 17 of the original design. In this way,In the the first throat row, area 15 small of the vanes vaned were diffuser selected, slightly which decrease is lesss when than thethe 17diameter of the originalratio decreases. design. InThe this second way, row the throat combines area 15 of large the vaned vanes diffuser and 15 slightlysplitter vanes. decreases In this when way, the the diameter divergent ratio angle decreases. of the Thevaned second diffuser row can combines be reduced 15 large to prevent vanes andseparation. 15 splitter Meanwhile, vanes. In the this friction way, the loss divergent on the inner angle surface of the vanedof the vaned diffuser diffuser can be with reduced the toincrease prevent in separation.the vane number Meanwhile, would the not friction be significant loss on. the inner surface of the vaned diffuser with the increase in the vane number would not be significant. By using the optimized method, the ratio of design Ad*/Ai* to theoretical Ad*/Ai* is 1.037, which is * * * * closeByr to using 1 and the indicates optimized the method,better matching the ratio of of the design diffuserAd / andAi toimpeller. theoretical TheA throatd /Ai areais 1.037, of the which vaned is closerdiffuser to i 1s andslightly indicates larger thethan better that matchingof the impeller, of the which diffuser ma andkes impeller.the choke The mass throat flow area of the of optimized the vaned diffuserdesign consistent is slightly with larger that than of thatthe original of the impeller, design. which makes the choke mass flow of the optimized design consistent with that of the original design.

Table 4. Ratio of design Ad*/Ai* to theoretical Ad*/Ai*. * * * * Table 4. Ratio of design Ad /Ai to theoretical Ad /Ai . Original Design Optimized Design 1 Optimized Design 2 AA**/ Original Design Optimized Design 1 Optimized Design 2 ( di)design (A∗/A∗) d i**design 1.09 0.948 1.037 ∗ ∗ 1.09 0.948 1.037 (A /AAA ) / d( iditheory )theory

The steady simulations were performed using the commercial code Numeca. The S S-A-A turbulence model was used. Grids were generated by AutoGrid. The grid number of the original design was 1,180,000;1,180,000; afterafter optimization,optimization, itit waswas 1,740,000.1,740,000. TotalTotal pressurepressure ofof 101,300101,300 PaPa waswas setset atat the inlet and the back-pressureback-pressure was set at the outletoutlet forfor boundaryboundary conditions.conditions. The wall waswas adiabatic with a slidingsliding surface. The The calculation calculation results results are are shown shown in in Figure Figure 11 11, and, and the the 1D 1D calculations calculations are arealso also show shownn for forcomparison. comparison. The calculationcalculation results show that the pressure ratio of the original design was 2.838, and the efficiencyefficiency was 80.68%. The pressure ratio of the optimized design was 2.967, and the efficiencyefficiency was 85.03%. Compared with the pressure ratio and efficiencyefficiency of the original design, those of the optimized design 22 representedrepresented aa significantsignificant improvement. improvement The. The trend trend of of the the 1D 1D calculation calculation results results was was similar similar to thatto that of of the the Numeca Numeca calculation calculation results. results. In In the the design design condition, condition, the the pressurepressure ratioratio andand efficiencyefficiency of the original design were 2.894%2.894% and 82.29%, respectively, whereas the pressure ratio and efficiencyefficiency of the optimizedoptimized design were 2.952% 2.952% andand 84.52%, 84.52%, respectively.respectively. Compared with the values in the original design, the pressure ratio and efficiencyefficiency of thethe optimizedoptimized design increasedincreased by 2.01% and 2.23%, respectively.

(a) (b)

Figure 11. PerformancePerformance map map of of the the original original and and optimized optimized designs designs for forthethe high high-pressure-pressure stage stage:: (a) (Reduceda) Reduced mass mass flow flow vs. vs.total total pressure pressure ratio ratio;; (b) (Reducedb) Reduced mass mass flow flow vs. vs.isentropic isentropic efficiency efficiency..

Figure 12 shows the inlet attack angle distribution of the vaned diffuser. Compared with the attack angle in the original design, the angle in the optimized design was reduced to a certain extent. Specifically, the attack angle decreased by approximately 5° near the blade root, which changed the Appl. Sci. 2018, 8, 1347 11 of 22

Figure 12 shows the inlet attack angle distribution of the vaned diffuser. Compared with the attackAppl. Sci. angle 2018, in8, 1347 the original design, the angle in the optimized design was reduced to a certain10 extent. of 20 Appl. Sci. 2018, 8, 1347 10 of 20 Speciﬁcally, the attack angle decreased by approximately 5◦ near the blade root, which changed the rangerange ofof thethe attackattack angleangle fromfrom thethe bladeblade rootroot toto bladeblade tiptip lessless thanthan 88°.◦. InIn the original design,design, thethe rangerange range of the attack angle from the blade root to blade tip less than 8°. In the original design, the range ofof thethe attackattack angleangle waswas closeclose toto 1515°.◦. of the attack angle was close to 15°.

FigureFigure 12.12. InletInlet attackattack angleangle distributiondistribution ofof thethe vanedvaned diffuser.diffuser. Figure 12. Inlet attack angle distribution of the vaned diffuser. 5. Coupling Calculations of the Original and Optimized Designs 5. Coupling Coupling Calculations Calculations of the Original and Optimized Designs After the low/high-pressure-stage centrifugal compressor was optimized and designed, circular After the the low/high low/high-pressure-stage-pressure-stage centrifugal centrifugal compressor compressor was optimized was optimized and designed, and designed, circular calculations of the MW-level gas turbine were performed under three typical load conditions of 100%, calculationscircular calculations of the MW of the-level MW-level gas turbine gas turbinewere performed were performed under three under typical three typicalload conditions load conditions of 100%, of 90%, and 60%. The operating parameters of circular calculation are shown in Table 5. To analyze the 90%,100%, and 90%, 60%. and The 60%. operating The operating parameters parameters of circular of circular calculation calculation are shown are shown in Table in Table 5. To5. analyze To analyze the actual performance of the low/high-pressure-stage centrifugal compressor, we conducted coupling actualthe actual performance performance of the of the low/high low/high-pressure-stage-pressure-stage centrifugal centrifugal compressor, compressor, we we conducted conducted coupling coupling calculations and analysis of the original and optimized designs under different working conditions calculationcalculationss and analysisanalysis ofof thethe original original and and optimized optimized designs designs under under different different working working conditions conditions for for an entire week. The calculated geometric model is shown in Figure 13. Numeca software was used foran entirean entire week. week. The The calculated calculated geometric geometric model model is shown is shown in Figurein Figure 13. 13. Numeca Numeca software software was was used used for for calculations, and an S-A turbulence model was employed. forcalculations, calculation ands, and an S-Aan S turbulence-A turbulence model model was was employed. employed.

(a) The original design (b) The optimized design (a) The original design (b) The optimized design Figure 13. Geometric structure. Figure 13. Geometric structure. Figure 13. Geometric structure. Table 5. Parameters of circular calculation. Table 5. Parameters of circular calculation. 100% Load 90% Load 60% Load 100% Load 90% Load 60% Load Mass flow (kg/s) 4.17 3.52 2.33 Mass flow (kg/s) 4.17 3.52 2.33 Rotation speed of low-pressure stage (rpm) 28,300 26,500 22,100 Rotation speed of low-pressure stage (rpm) 28,300 26,500 22,100 Rotation speed of high-pressure stage (rpm) 37,200 36,800 34,100 Rotation speed of high-pressure stage (rpm) 37,200 36,800 34,100 Table 6 shows a comparison of the pressure ratio and efficiency of the original and optimized Table 6 shows a comparison of the pressure ratio and efficiency of the original and optimized designs of the low/high-pressure-stage compressor under three typical load conditions. The designs of the low/high-pressure-stage compressor under three typical load conditions. The Appl. Sci. 2018, 8, 1347 12 of 22

Table 5. Parameters of circular calculation.

100% Load 90% Load 60% Load Mass ﬂow (kg/s) 4.17 3.52 2.33 Rotation speed of low-pressure stage (rpm) 28,300 26,500 22,100 Rotation speed of high-pressure stage (rpm) 37,200 36,800 34,100

Table6 shows a comparison of the pressure ratio and efficiency of the original and optimized designs of the low/high-pressure-stage compressor under three typical load conditions. The optimized design performed better than the original design. At 100% load, the low-pressure-stage pressure ratio increased by 4.01%, and the efficiency increased by 2.90%. The high-pressure-stage pressure ratio increased by 4.12%, and the efficiency increased by 3.00%. The pressure ratio of the unit increased by 8.4%, and its efficiency increased by 3.70%. At 90% load, the low-pressure-stage pressure ratio increased by 5.22%, and the efficiency increased by 3.30%. The high-pressure-stage pressure ratio increased by 3.41%, and the efficiency increased by 3.10%. The pressure ratio of the unit increased by 9.37%, and its efficiency increased by3.80%. At 60% load, the low-pressure-stage pressure ratio increased by 2.33%, and the efficiency increased by 4.80%. The high-pressure-stage pressure ratio increased by 4.72%, and the efficiency increased by 4.70%. The pressure ratio of the unit increased by 7.70%, and its efficiency increased by 5.40%. The specific performance of the low/high-pressure-stage centrifugal compressor under different working conditions was analyzed as follows.

Table 6. Computational ﬂuid dynamics (CFD) calculation results of the MW-level gas turbine.

100% Load 90% Load 60% Load Optimized Relative Optimized Relative Optimized Relative Original Original Original Design Error Design Error Design Error Design Design Design Low-pressure stage 4.24 4.41 4.01% 3.64 3.83 5.22% 2.58 2.64 2.33% pressure ratio Low-pressure 0.793 0.822 2.90% 0.797 0.830 3.30% 0.783 0.831 4.80% stage efficiency High-pressure stage 2.574 2.68 4.12% 2.64 2.73 3.41% 2.54 2.66 4.72% pressure ratio High-pressure 0.826 0.856 3.00% 0.819 0.850 3.10% 0.807 0.854 4.70% stage efficiency Pressure ratio of 10.83 11.74 8.4% 9.50 10.39 9.37% 6.49 6.99 7.70% the unit Efficiency of the unit 0.770 0.807 3.70% 0.772 0.810 3.80% 0.764 0.818 5.40%

5.1. 100% Load Figure 14 shows the meridional streamline chart at 100% load and illustrates a large separation vortex in the vane-less diffuser in the original design. In the optimized design, the separation vortex disappeared in the vane-less diffuser with the decrease in diameter ratio, D3/D2. The flow condition at the vaned diffuser inlet improved. Therefore, a separation area was not observed in the vaned diffuser. Figure 15 shows the Mach number distribution in different spans of the original and optimized designs of the low-pressure-stage centrifugal compressor at 100% load. An obvious backflow was observed at the vaned diffuser inlet in the original design at 10% span because the diameter ratio was large, and the separation vortex in the vane-less diffuser worsened the flow condition at the vaned diffuser inlet. The overall flow in the vaned diffuser was good with no obvious vortex. Appl. Sci. 2018, 8, 1347 13 of 22 Appl. Sci. 2018, 8, 1347 12 of 20 Appl. Sci. 2018, 8, 1347 12 of 20

(a) Original design (b) Optimized design (a) Original design (b) Optimized design Figure 14. Meridional streamline at 100% load. Figure 14. Meridional streamline at 100% load.

(a) 10% span (a) 10% span

(b) 50% span (b) 50% span

(c) 90% span (c) 90% span Figure 15. Mach number distribution at different spans of the original and optimized designs of the Figure 15. Mach number distribution at different spans of the original and optimized designs of the Figurelow-pressure 15. Mach-stage number centrifugal distribution compressor at different at 100% spans load. of the original and optimized designs of the low-pressure-stagelow-pressure-stage centrifugalcentrifugal compressorcompressor atat 100%100% load.load. In the optimized design, the diameter ratio of the vane-less diffuser decreased, and the flow was In the optimized design, the diameter ratio of the vane-less diffuser decreased, and the flow was uniform without separation due to the use of the tandem diffuser. Therefore, the vaned diffuser inlet uniform without separation due to the use of the tandem diffuser. Therefore, the vaned diffuser inlet Appl. Sci. 2018, 8, 1347 14 of 22

In the optimized design, the diameter ratio of the vane-less diffuser decreased, and the flow was uniform without separation due to the use of the tandem diffuser. Therefore, the vaned diffuser inlet was in a good condition without backflow. An obvious low-speed area was observed at the end of the second-row diffuser, and no obvious separation was observed in the passage. The inlet flow was not affected and had no backflow at 50% span because the vaned diffuser inlet flow was far from the vane-less diffuser separation area. The gas flow in the vaned diffuser was stable, and a large separation area appeared at the vaned diffuser outlet. In the optimized design, a high Mach number area existed in the diffuser inlet on the first row because the vaned diffuser inlet was close to the impeller. A large low-speed area was observed in the diffuser end on the second row, similar to the 10% span. At 90% span, the separation area inside the vaned diffuser had no influence on the vaned diffuser inlet flow in the original design, and the inlet condition was improved. The flow showed significant deceleration in the vaned diffuser, and the Mach number in the middle of the vaned diffuser dropped to approximately 0.2. The low-speed area at the vaned diffuser outlet expanded further and occupied approximately 80% of the flow passage. In the optimized design, the flow deceleration process was obvious in the vaned diffuser, and the Mach number at the outlet dropped to below 0.2. However, the flow in the passage was stable with no obvious separation phenomenon. In general, in the original design, the flow condition was affected by the separation area in the vaneless diffuser, and the Mach number distribution was completely different at different spans. The flow condition near the blade root was poor with obvious backflow at the vaned diffuser inlet. The closer to the tip, the better the flow. However, the condition at the vaned diffuser outlet was the opposite. The flow near the blade root was smooth with no obvious low-speed area. The farther away from the blade root, the smaller the Mach number. Serious blockage existed near the tip. In the optimized design, the flow at the vaned diffuser inlet was similar in different spans because no separation occurred in the vane-less diffuser. The flow in the vaned diffuser was nearly the same, and an obvious low-speed area existed at the end. Figure 16 shows the Mach number distribution in different spans of the original and optimized designs of the high-pressure-stage centrifugal compressor at 100% load. An obvious low-speed area was observed at the end of the vaned diffuser in the original design at 10% span, and this area occupied more than 50% of the flow passage. An obvious separation phenomenon was observed in the low-speed area. In the optimized design, the flow in the flow passage was stable due to the addition of splitter vanes on the second row. However, a small separation area was observed on the pressure side of the second large vane row. At 50% span, the position of the low-speed area in the vaned diffuser moved slightly backward compared with the original design. However, the low-speed area still occupied approximately 50% of the passage. An obvious separation phenomenon was still observed in the low-speed area, but the range was reduced. The optimized design was similar to the original design. The low-speed region in the vaned diffuser was also backward and occupied approximately 50% of the passage. However, the flow was steady in the low-speed area with no separation. At 90% span, the low-speed area in the passage and the separation area were significantly reduced in the original design. In the optimized design, the low-speed area obviously decreased in the vaned diffuser. Appl. Sci. 2018, 8, 1347 13 of 20

was in a good condition without backflow. An obvious low-speed area was observed at the end of the second-row diffuser, and no obvious separation was observed in the passage. The inlet flow was not affected and had no backflow at 50% span because the vaned diffuser inlet flow was far from the vane-less diffuser separation area. The gas flow in the vaned diffuser was stable, and a large separation area appeared at the vaned diffuser outlet. In the optimized design, a high Mach number area existed in the diffuser inlet on the first row because the vaned diffuser inlet was close to the impeller. A large low-speed area was observed in the diffuser end on the second row, similar to the 10% span. At 90% span, the separation area inside the vaned diffuser had no influence on the vaned diffuser inlet flow in the original design, and the inlet condition was improved. The flow showed significant deceleration in the vaned diffuser, and the Mach number in the middle of the vaned diffuser dropped to approximately 0.2. The low-speed area at the vaned diffuser outlet expanded further and occupied approximately 80% of the flow passage. In the optimized design, the flow deceleration process was obvious in the vaned diffuser, and the Mach number at the outlet dropped to below 0.2. However, the flow in the passage was stable with no obvious separation phenomenon. In general, in the original design, the flow condition was affected by the separation area in the vaneless diffuser, and the Mach number distribution was completely different at different spans. The flow condition near the blade root was poor with obvious backflow at the vaned diffuser inlet. The closer to the tip, the better the flow. However, the condition at the vaned diffuser outlet was the opposite. The flow near the blade root was smooth with no obvious low-speed area. The farther away from the blade root, the smaller the Mach number. Serious blockage existed near the tip. In the optimized design, the flow at the vaned diffuser inlet was similar in different spans because no separation occurred in the vane-less diffuser. The flow in the vaned diffuser was nearly the same, and an obvious low-speed area existed at the end. Figure 16 shows the Mach number distribution in different spans of the original and optimized designs of the high-pressure-stage centrifugal compressor at 100% load. An obvious low-speed area was observed at the end of the vaned diffuser in the original design at 10% span, and this area occupied more than 50% of the flow passage. An obvious separation phenomenon was observed in the low-speed area. In the optimized design, the flow in the flow passage was stable due to the addition of splitter vanes on the second row. However, a small separation area was observed on the pressure side of the second large vane row. At 50% span, the position of the low-speed area in the vaned diffuser moved slightly backward compared with the original design. However, the low-speed area still occupied approximately 50% of the passage. An obvious separation phenomenon was still observed in the low-speed area, but the range was reduced. The optimized design was similar to the original design. The low-speed region in the vaned diffuser was also backward and occupied approximately 50% of the passage. However, the flow was steady in the low-speed area with no separation. At 90% span, the low-speed area in the passage and the separation area were significantly Appl.reduced Sci. 2018 in, 8 ,the 1347 original design. In the optimized design, the low-speed area obviously decreased15 in of 22 the vaned diffuser.

Appl. Sci. 2018, 8, 1347 14 of 20 (a) 10% span

(b) 50% span

Figure 16. Mach number distribution at different spans of the original and optimized designs of the Figure 16. Mach number distribution at different spans of the original and optimized designs of the high-pressure-stage centrifugal compressor at 100% load. high-pressure-stage centrifugal compressor at 100% load. In general, the divergent angle of the vaned diffuser was overly large in the original design, leadingIn general, to obvious the divergent separation angle in different of the spans. vaned The diffuser closer was to the overly tip, large the better in the the original flow. In design, the leadingoptimized to obvious design, separationthe addition inof differentsplitter vanes spans. effectively The closer reduced to the the tip, divergent the better angle the of flow.the vaned In the optimizeddiffuser. design, Therefore, the no addition separation of splitter existed, vanes although effectively a low reduced-speed area the divergent was observed angle in of the the flow vaned diffuser.passage. Therefore, Similar to no the separation original design, existed, the although closer to a low-speedthe tip, the area better was the observed flow. The in overall the flow flow passage. in Similarthe vaned to the diff originaluser was design, significantly the closer improved. to the tip, the better the flow. The overall flow in the vaned diffuser was significantly improved. 5.2. 90% Load 5.2. 90%Figure Load 17 shows the meridional flow diagram at 90% load. Similar to the situation with 100% load,Figure a large 17 sepashowsration the area meridional was observed flow diagram in the vaned at 90% diffuser load. in Similar the original to the design, situation and with a small 100% load,separation a large area separation was found area near was the observed tip of the in vaned the vaned diffuser diffuser outlet. inIn thethe originaloptimized design, design, and the aflow small separationwas still steady area was in the found flow near passage the tipwithout of the obvious vaned diffuserseparation. outlet. In the optimized design, the flow was still steady in the flow passage without obvious separation.

(a) Original design (b) Optimized design

Figure 17. Meridional streamline at 90% load. Appl. Sci. 2018, 8, 1347 14 of 20

(b) 50% span

Figure 16. Mach number distribution at different spans of the original and optimized designs of the high-pressure-stage centrifugal compressor at 100% load.

In general, the divergent angle of the vaned diffuser was overly large in the original design, leading to obvious separation in different spans. The closer to the tip, the better the flow. In the optimized design, the addition of splitter vanes effectively reduced the divergent angle of the vaned diffuser. Therefore, no separation existed, although a low-speed area was observed in the flow passage. Similar to the original design, the closer to the tip, the better the flow. The overall flow in the vaned diffuser was significantly improved.

5.2. 90% Load Figure 17 shows the meridional flow diagram at 90% load. Similar to the situation with 100% load, a large separation area was observed in the vaned diffuser in the original design, and a small Appl. Sci. separation2018, 8, 1347 area was found near the tip of the vaned diffuser outlet. In the optimized design, the flow 16 of 22 was still steady in the flow passage without obvious separation.

(a) Original design (b) Optimized design

Figure 17. Meridional streamline at 90% load. Figure 17. Meridional streamline at 90% load.

Appl. Sci. 2018, 8, 1347 15 of 20 Figure 18 shows the Mach number distribution in different spans of the original and optimized designs of theFigure low-pressure-stage 18 shows the Mach centrifugal number distribution compressor in different at 90% spans load. of Forthe original the original and optimized and optimized designs,designs the Mach of the number low-pressure distribution-stage centrifugal in different compressor spans andat 90% the load. flow For in the the original flow passageand optimized were similar designs, the Mach number distribution in different spans and the flow in the flow passage were to those at 100% load. However, the blockage increased in the vaned diffuser outlet in the original similar to those at 100% load. However, the blockage increased in the vaned diffuser outlet in the design atoriginal 90% span,design makingat 90% span, the making blade tip theshow blade tip an show obvious an obvious backflow backflow area. area.

(a) 10% span

(b) 50% span

Figure 18. Mach number distribution at different spans of the original and optimized designs of the Figure 18. Mach number distribution at different spans of the original and optimized designs of the low-pressure-stage centrifugal compressor at 90% load. low-pressure-stage centrifugal compressor at 90% load. Figure 19 shows the Mach number distribution in different spans of the original and optimized designs of the high-pressure stage centrifugal compressor at 90% load. In the high-pressure stage, the high Mach number distribution and flow condition at different spans were similar to those at 100% load in the original and optimized designs, and the overall flow features had no obvious change. In general, compared with the situation in the 100% load, the flow characteristics did not change considerably in the original and optimized designs of the low/high-pressure-stage centrifugal compressor at 90% load. In the original design, the low/high-pressure centrifugal compressor was affected by its design limitation, and several poor flows were observed in the flow passage. In the Appl. Sci. 2018, 8, 1347 17 of 22

Figure 19 shows the Mach number distribution in different spans of the original and optimized designs of the high-pressure stage centrifugal compressor at 90% load. In the high-pressure stage, the high Mach number distribution and flow condition at different spans were similar to those at 100% load in the original and optimized designs, and the overall flow features had no obvious change. In general, compared with the situation in the 100% load, the flow characteristics did not change considerably in the original and optimized designs of the low/high-pressure-stage centrifugal compressorAppl. Sci. 2018 at 90%, 8, 1347 load. In the original design, the low/high-pressure centrifugal compressor16 of 20 was affectedoptimized by its design design, limitation, the flow in and the several low/high poor-pressure flows-stage were observed centrifugal in compressor the flow passage. obviously In the optimizedimpro design,ved. the flow in the low/high-pressure-stage centrifugal compressor obviously improved.

(a) 10% span

(b) 50% span

Figure 19. Mach number distribution at different spans of the original and optimized designs of the Figure 19. Mach number distribution at different spans of the original and optimized designs of the high-pressure-stage centrifugal compressor at 90% load. high-pressure-stage centrifugal compressor at 90% load. 5.3. 60% Load 5.3. 60% Load Figure 20 shows the meridional streamline chart at 60% load. In the original design, a separation Figurearea was 20 observed shows the near meridional the edge of streamline the impeller chart inlet at rim 60%, in load. addition In the to the original separation design, area a separationin the area wasvane- observedless diffuser near and thevaned edge diffuser of the outlet. impeller This inletcondition rim, indicates in addition that t tohe theoperating separation condition area of in the vane-lessthe low diffuser-pressure and-stage vaned compressor diffuser was outlet. close This to the condition surge line. indicates In the optimized that the operatingdesign, the conditionoverall of the low-pressure-stageflow in the passage was compressor stable, but was separation close toareas the were surge observed line. In near the the optimized impeller design,inlet rim theof the overall low-pressure-stage compressor. ﬂow in the passage was stable, but separation areas were observed near the impeller inlet rim of the Figure 21 shows the Mach number distribution in different spans of the original and optimized low-pressure-stagedesigns of the low compressor.-pressure-stage centrifugal compressor at 60% load. For the original and optimized designs, the Mach distribution in different spans and the flow in the passage were nearly similar to those at 90% load. Appl. Sci. 2018, 8, 1347 18 of 22

Figure 21 shows the Mach number distribution in different spans of the original and optimized designs of the low-pressure-stage centrifugal compressor at 60% load. For the original and optimized designs, the Mach distribution in different spans and the ﬂow in the passage were nearly similar to those atAppl. 90% Sci. load. 2018, 8, 1347 17 of 20 Appl. Sci. 2018, 8, 1347 17 of 20

(a) Original design (b) Optimized design (a) Original design (b) Optimized design Figure 20. Meridional streamline at 60% load. FigureFigure 20. 20.Meridional Meridional streamline at at60% 60% load. load.

(a) 10% span (a) 10% span

(b) 50% span (b) 50% span

(c) 90% span (c) 90% span Figure 21. Mach number distribution at different spans of the original and optimized designs of the Figurelow-pressure 21. Mach-stage number centrifugal distribution compressor at different at 60% spans load. of the original and optimized designs of the Figure 21. Mach number distribution at different spans of the original and optimized designs of the low-pressure-stage centrifugal compressor at 60% load. low-pressure-stage centrifugal compressor at 60% load. Appl. Sci. 2018, 8, 1347 19 of 22 Appl. Sci. 2018, 8, 1347 18 of 20

Figure 22 shows the Mach number distribution in different spans of the original and optimized designs of the high-pressure-stagehigh-pressure-stage centrifugal compressor at 60% load. In In the high high-pressure-pressure stage, the high Mach number distribution and the flow flow in the passage were similar to those at 90% load in the original and optimized designs, and the overall flowflow featuresfeatures hadhad nono obviousobvious change.change. In general, the largest difference between 100%,100%, 90%, and 60% loads was the emergence of separation areas areas near near the the low low-pressure-pressure stage stage impeller impeller inlet inlet rim. rim. This This condition condition shows shows that the that low thelow-pressure-stagepressure-stage compressor compressor operation operation points points were were near near the surge the surge line, line, which which is an is unstable an unstable factor factor for forthe theoperation operation of the of theunit unit and and requires requires appropriate appropriate attention attention to avoid to avoid accidents. accidents. UnderUnder three three typical typical load loadconditions conditions of 100%, of 90% 100%, and 60%, 90% the and flow 60%,in the thelow/high flow-pressure in thelow/high-pressure-stagestage centrifugal compressor centrifugal had several compressor undesirable hadconditions several in the undesirable original design. conditions However, in the originalflow was design. improved However, effectively the flow in the was optimized improved design effectively. in the optimized design.

(a) 10% span

(b) 50% span

Figure 22. Mach number distribution at different spans of the original and optimized designs of the high-pressure-stagehigh-pressure-stage centrifugal compressor atat 60%60% load.load.

Appl. Sci. 2018, 8, 1347 20 of 22

6. Results This study presented an optimized design method for centrifugal compressors based on 1D calculations and analyses. A low/high-pressure-stage centrifugal compressor in an MW-level gas turbine was optimized by the proposed method. According to the calculation results of the MW-level gas turbine cycle, three typical load conditions of 100%, 90%, and 60% were calculated for the original and optimized designs. The main conclusions are summarized as follows. For the low-pressure-stage centrifugal compressor, the analysis showed that the diameter ratio of the vaned diffuser was overly large, which led to an increase in loss and low efficiency. The diameter ratio was reduced in the optimized design. To optimize the ratio of the throat area between the impeller and diffuser, a tandem diffuser was used to replace the original single-stage diffuser. After optimization, the pressure ratio increased by more than 3%, and efficiency improved by more than 2%. For the high-pressure-stage centrifugal compressor, the calculation results of the 1D optimal design system showed that the divergent angle of the vaned diffuser was overly large and led to unit performance degradation. In the optimized design, the divergent angle was reduced by using a vaned diffuser with splitter vanes. After optimization, the pressure ratio and efficiency increased by more than 4%. Through the coupling calculations at 100%, 90%, and 60% loads, the performances of optimized design were significantly improved compared to those of the original design in the low/high-pressure-stage centrifugal compressor. Under the three load conditions, the pressure ratio of the unit increased by approximately 8%, and efficiency improved by approximately 4%.

Author Contributions: Conceptualization, X.S.L. and C.W.G.; Methodology, W.Z. and X.D.R.; Investigation, W.Z. and X.D.R.; Validation, W.Z. and X.D.R.; Writing-Original Draft Preparation, W.Z. and X.S.L.; Writing-Review & Editing, W.Z. and X.S.L.; Visualization, X.S.L.; Supervision, C.W.G. Funding: This research was funded by [National Natural Science Foundation of China] grant number [51736008]. Conﬂicts of Interest: The authors declare no conﬂicts of interest.

Nomenclature

the theoretical ratio of the impeller and the diffuser throat areas when A */A * d i the impeller and the vaned diffuser choke at the same time B hub to shroud passage width b* ratio of vaneless diffuser inlet width to impeller exit width B aerodynamic blockage cf skin friction coefficient C absolute velocity Cp specific heat at constant pressure Cm absolute meridional velocity Cθ absolute tangential velocity D diameter dHB hydraulic diameter Df diffusion factor ∆hth euler work LB impeller flow length LZ axial length of impeller m mass flow rate U Impeller periphery velocity W relative velocity Z number of blade Appl. Sci. 2018, 8, 1347 21 of 22

α absolute flow angle β relative angle Φ flow coefficient γ meridional inclination angle η Efficiency ε wake fraction of blade-to-blade space µ slip factor µ = Cθ2/Cθ2∞ ρ density σ slip factor σ = 1 − Cslip/U2 Subscripts 1 impeller inlet condition 2 impeller outlet condition 3 vaneless diffuser outlet condition 4 vaned diffuser outlet condition M meridional direction θ tangential direction h hub s shroud

References

1. Krain, H. Review of centrifugal compressor’s application and development. ASME J. Turbomach. 2005, 127, 25–34. [CrossRef] 2. Johnson, D.G. The Norwegian Gas Turbine Pioneer: Aegidius Elling. Energy World 1985, 1, 10–13. 3. Eckardt, D. Detailed flow investigations within a high-speed centrifugal compressor impeller. J. Fluids Eng. 1976, 98, 390–399. [CrossRef] 4. Krain, H. Swirling impeller flow. J. Turbomach. 1988, 110, 122–128. [CrossRef] 5. Hah, C.; Krain, H. Secondary flows and vortex motion in a high-efficiency backswept impeller at design and off-design conditions. J. Turbomach. 1990, 112, 7–13. [CrossRef] 6. Krain, H.; Hoffmann, B. Aerodynamics of a Centrifugal Compressor Impeller with Transonic Inlet Conditions; ASME Paper 95-GT-079; ASME: New York, NY, USA, 1995. 7. Eisenlohr, G.; Krain, H.; Richter, F.A.; Tiede, V. Investigations of the Flow through a High Pressure Ratio Centrifugal Impeller; ASME Paper; ASME: New York, NY, USA, 2002; pp. 649–657. 8. Hah, C.; Krain, H. Analysis of Transonic Flow Fields Inside a High Pressure Ratio Centrifugal Compressor at Design and off Design Conditions; ASME Paper; ASME: New York, NY, USA, 1999; p. 446. 9. Senoo, Y.; Hayami, H.; Kinoshita, Y.; Yamasaki, H. Experimental study on flow in a supersonic centrifugal impeller. J. Eng. Gas Turbines Power 1979, 101, 32–39. [CrossRef] 10. Higashimori, H.; Hasagawa, K.; Sumida, K.; Suita, T. Detailed flow study of Mach number 1.6 high transonic flow with a shock wave in a pressure ratio 11 centrifugal compressor impeller. ASME J. Turbomach. 2004, 126, 473–481. [CrossRef] 11. Higashimori, H.; Morishita, S.; Suita, T. Detailed Flow Study of Mach Number 1.6 High Transonic Flow in a Pressure Ratio 11 Centrifugal Compressor Impeller; ASME Paper; ASME: New York, NY, USA, 2007; pp. 1071–1080. 12. Hosseini, M.; Sun, Z.; He, X.; Zheng, X. Effects of Radial Gap Ratio between Impeller and Vaned Diffuser on Performance of Centrifugal Compressors. Appl. Sci. 2017, 7, 728. [CrossRef] 13. Ebrahimi, M.; Huang, Q.; He, X.; Zheng, X. Effects of Variable Diffuser Vanes on Performance of a Centrifugal Compressor with Pressure Ratio of 8.0. Energies 2017, 10, 1–15. 14. Sun, Z.; Zheng, X.; Kawakubo, T. Experimental investigation of instability inducement and mechanism of centrifugal compressors with vaned diffuser. Appl. Therm. Eng. 2018, 13, 464–471. [CrossRef] 15. Zheng, X.; Liu, A.; Sun, Z. Investigation of the instability mechanisms in a turbocharger centrifugal compressor with a vaneless diffuser by means of unsteady simulations. Inst. Mech. Eng. 2017, 231, 1558–1567. [CrossRef] 16. Frignac, J.P. The Growth and Evolution of the TPE311; ASME Paper 79-GT-164; ASME: New York, NY, USA, 1979. Appl. Sci. 2018, 8, 1347 22 of 22

17. Palmer, D.L.; Waterman, W.F. Design and development of an advanced two-stage centrifugal compressor. J. Turbomach. 1995, 117, 205–212. [CrossRef] 18. Li, P.Y.; Gu, C.W.; Song, Y. A new optimization method for centrifugal compressors based on 1D calculations and analyses. Energies 2015, 8, 4317–4334. [CrossRef] 19. Casey, M.; Rusch, D. The Matching of a Vaned Diffuser with a Radial Compressor Impeller and Its Effect on the Stage Performance. J. Turbomach. 2014, 136, 121004. [CrossRef]

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).