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Applied Sciences
, Volume 8 (8) – Aug 10, 2018

/lp/multidisciplinary-digital-publishing-institute/analysis-and-improvement-of-a-two-stage-centrifugal-compressor-used-in-3uRkFoVDhR

- Publisher
- Multidisciplinary Digital Publishing Institute
- Copyright
- © 1996-2019 MDPI (Basel, Switzerland) unless otherwise stated
- ISSN
- 2076-3417
- DOI
- 10.3390/app8081347
- Publisher site
- See Article on Publisher Site

applied sciences Article Analysis and Improvement of a Two-Stage Centrifugal Compressor Used in an MW-Level Gas Turbine ID Wei Zhu, Xiao-Dong Ren, Xue-Song Li * 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; zw18@mails.tsinghua.edu.cn (W.Z.); rxd@mail.tsinghua.edu.cn (X.-D.R.); gcw@mail.tsinghua.edu.cn (C.-W.G.) * Correspondence: xs-li@mail.tsinghua.edu.cn 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 60 years, many scholars have investigated centrifugal compressors and obtained a deep understanding Appl. Sci. 2018, 8, 1347 2 of 20 of the internal ﬂow phenomenon. In 1976, Eckardt [3] measured the jet-wake phenomenon in the outlet of a centrifugal compressor In 1976, Eckardt [3] measured the jet-wake phenomenon in the outlet of a centrifugal compressor with a pressure ratio of 2.1. Karin [4] also measured a centrifugal compressor with a pressure ratio of with a pressure ratio of 2.1. Karin [4] also measured a centrifugal compressor with a pressure ratio 4. Hah [5] performed a 3D numerical simulation of a centrifugal compressor. Krain [6,7] measured of 4. Hah [5] performed a 3D numerical simulation of a centrifugal compressor. Krain [6,7] measured the shock wave in the inlet of a centrifugal compressor that had an inlet tip Mach number of 1.3 and the shock wave in the inlet of a centrifugal compressor that had an inlet tip Mach number of 1.3 a pressure ratio of 6.1. Hah [8] conducted a numerical simulation of this centrifugal compressor. and a pressure ratio of 6.1. Hah [8] conducted a numerical simulation of this centrifugal compressor. Meanwhile, Senoo [9] measured the shock wave and pressure distribution in the inlet of a centrifugal Meanwhile, Senoo [9] measured the shock wave and pressure distribution in the inlet of a centrifugal compressor with a pressure ratio of 10. Higashimori [10,11] measured a centrifugal compressor with compressor with a pressure ratio of 10. Higashimori [10,11] measured a centrifugal compressor with a pressure ratio of 11 and analyzed its flow characteristic. Hosseini [12] investigated the effects of the a pressure ratio of 11 and analyzed its ﬂow characteristic. Hosseini [12] investigated the effects of radial gap ratio on a high-pressure ratio centrifugal compressor and the flow phenomena inside the the radial gap ratio on a high-pressure ratio centrifugal compressor and the ﬂow phenomena inside compressor components by using numerical simulations. Ebrahimi [13] analyzed the matching of the the compressor components by using numerical simulations. Ebrahimi [13] analyzed the matching vaned diffuser with the impeller for different working conditions. Sun [14] investigated the flow of the vaned diffuser with the impeller for different working conditions. Sun [14] investigated the instability of centrifugal compressors with vaned diffusers experimentally and presented diverse ﬂow instability of centrifugal compressors with vaned diffusers experimentally and presented diverse instability patterns and transient behavior in detail. Zheng [15] investigated the instability instability patterns and transient behavior in detail. Zheng [15] investigated the instability mechanisms mechanisms of a high-speed turbocharger centrifugal compressor with a vaneless diffuser using the of a high-speed turbocharger centrifugal compressor with a vaneless diffuser using the unsteady unsteady simulation method. simulation method. Figure 1 shows the development trend of centrifugal compressors for commercial use during the Figure 1 shows the development trend of centrifugal compressors for commercial use during past few decades. The pressure ratios of single-stage centrifugal compressors have improved the past few decades. The pressure ratios of single-stage centrifugal compressors have improved continually, and centrifugal compressors with single-stage pressure ratios over 10 have been put into continually, and centrifugal compressors with single-stage pressure ratios over 10 have been put into practical use. practical use. (a) (b) Figure 1. Development trend of centrifugal compressors: (a) Development trend of total pressure ratio; Figure 1. Development trend of centrifugal compressors: (a) Development trend of total pressure ratio; (b) Relation between pressure ratio and efficiency. (b) Relation between pressure ratio and 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 Figure 2. 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. The pressure ratio of this two-stage centrifugal compressor is approximately 11, Appl. Sci. 2018, 8, 1347 3 of 20 Appl. Sci. 2018, 8, 1347 3 of 20 resulting in poor performance. Ref. [18] adopted a 1D aerodynamic optimization design system and used the computational ﬂuid dynamics (CFD) commercial software Numeca (Numeca, Brussels, used the computational fluid dynamics (CFD) commercial software Numeca (Numeca, Brussels, used the computational fluid dynamics (CFD) commercial software Numeca (Numeca, Brussels, Belgium) Belgium) to to perform perform numerical numerical calculations, calculations, performance performance analysis, analysis, and and optimization optimization of of the the poor poor Belgium) to perform numerical calculations, performance analysis, and optimization of the poor performance of the two-stage centrifugal compressor. performance of the two-stage centrifugal compressor. performance of the two-stage centrifugal compressor. Figure 2. Comparison of centrifugal compressor pressure ratios. Figure 2. Comparison of centrifugal compressor pressure ratios. Figure 2. Comparison of centrifugal compressor pressure ratios. 2. Analysis of the Performance of Low/High-Pressure Two-Stage Centrifugal Compressor 2. Analysis of the Performance of Low/High-Pressure Two-Stage Centrifugal Compressor 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 The structure of an MW-level gas turbine is shown in Figure 3. The low/high-pressure two-stage 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 centrifugal compressor is composed of an inlet guide vane, an impeller, and a diffuser. A vaned diffuser 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 is used to connect the two stages. The geometric structure of the centrifugal compressor is shown diffuser is used to connect the two stages. The geometric structure of the centrifugal compressor is shown in Figure 4. in Figure 4. shown in Figure 4. Figure 3. Structure of an MW-level gas turbine. Figure 3. Structure of an MW-level gas turbine. Figure 3. Structure of an MW-level gas 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. 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: pressure stage (b) High-pressure stage. (a) Low-pressure stage (b) High-pressure stage. Appl. Sci. 2018, 8, 1347 4 of 20 The The llow-pr ow-pressure essure-stage -stage iimpeller mpeller’s ’s ro rotation tation spee speed d iis s 2 28,000 8,000 rp rpm, m, a and nd th the e ri rim m spe speed ed iis s 4 478 78 m m/s. /s. Fi Figur gure e 5 5 sh shows ows th the e CFD CFD ca calculation lculation re results sults f for or th the e p performance erformance cur curve ve o of f th the e lo low-pr w-pressure essure-stage -stage centrifugal compressor. The pressure ratio of the low-pressure-stage centrifugal compressor is 3.92, centrifugal compressor. The pressure ratio of the low-pressure-stage centrifugal compressor is 3.92, a and nd iits ts ef effﬁciency iciency iis s 7 79.9% 9.9% in in th the e d design esign co condition ndition [1 [18 8]. ]. Figure 5. Performance curve of the low-pressure-stage centrifugal compressor. 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. 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 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, 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-stage centrifugal compressor. Figure 6. Performance curve of the high-pressure-stage centrifugal 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 Figure 1. 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 Table 1. The geometric impeller parameters after optimization changed minimally and, mainly due to a slight increase in the outlet width, b , 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 D /D . However, 3 2 if the increase in the diameter ratio is overly large, the efﬁciency of the entire stage would decrease. Thus, the ratio of D /D = 1.05:1.2 is recommended. In the original design, the diameter ratio, D /D , 3 2 3 2 is 1.34, which is much higher than the recommended value. In the optimized design, D /D is 1.1, 3 2 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 D (m) 0.075 0.082 1s D (m) 0.190 0.202 1t D (m) 0.326 0.326 Lz (m) 0.075 0.080 b (m) 0.0158 0.0151 D (m) 0.358 0.440 D (m) 0.601 0.601 D /D 1.10 1.34 3 2 h 95.15% 94.87% h 92.63% 86.29% h 83.38% 81.09% The 1D optimization results showed it was necessary to reduce D /D to improve the efﬁciency 3 2 of the entire stage of the low-pressure-stage centrifugal compressor. When D /D was reduced, if the 3 2 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 Figure 7. 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, * * A /A , should be as close to the theoretical level as possible [19]. d i * * * * The ratio of design A /A to theoretical A /A is 1.161 in the original design as shown in Table 2. d i d i 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 A /A to theoretical A /A would d i d i 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 D /D is reduced. Considering all factors, the original vaned diffuser was replaced 3 2 by a tandem vaned diffuser as shown in optimized design 2 in Figure 7. By using the optimized * * * * method, the ratio of design A /A to theoretical A /A was 1.043, which is closer to 1 and indicates d i d i 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. Sci. 2018, 8, 1347 7 of 22 optimized design consistent with that of the original design. 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. Figure 7. Geometric structure of the vaned diffuser. Figure 7. Geometric structure of the vaned diffuser. * * * * Table 2. Ratio of design Ad /Ai to theoretical Ad /Ai . * * * * Table 2. Ratio of design A /*A *to theoretical A */A* . d i d i Table 2. Ratio of design Ad /Ai to theoretical Ad /Ai . Original Design Optimized Design 1 Optimized Design 2 Original Design Optimized Design 1 Optimized Design 2 Original Design Optimized Design 1 Optimized Design 2 ** AA / ( ) di ** design (A /A ) AA / d( i design ) di 1.161 0.922 1.043 design 1.161 0.922 1.043 ** A /A ( ) i 1.161 0.922 1.043 d theory AA / ( ) ** di theory AA / ( ) di theory The steady simulations were performed using the commercial software Numeca. The steady simulations were performed using the commercial software Numeca. The Spalart- The steady simulations were performed using the commercial software Numeca. The Spalart- The Spalart-Allmaras (SA) turbulence model was used. Grids were generated by grid generation Allmaras (SA) turbulence model was used. Grids were generated by grid generation software Allmaras (SA) turbulence model was used. Grids were generated by grid generation software software AutoGrid (Numeca, Brussels, Belgium). The grid number of the original design was AutoGrid (Numeca, Brussels, Belgium). The grid number of the original design was 1,100,000; after AutoGrid (Numeca, Brussels, Belgium). The grid number of the original design was 1,100,000; after 1,100,000; after optimization, it was 1,400,000. Total pressure of 101,300 Pa was set at the inlet and optimization, it was 1,400,000. Total pressure of 101,300 Pa was set at the inlet and the back-pressure optimization, it was 1,400,000. Total pressure of 101,300 Pa was set at the inlet and the back-pressure the back-pressure was set at the outlet for boundary conditions. The wall was adiabatic with a was set at the outlet for boundary conditions. The wall was adiabatic with a sliding surface. The was set at the outlet for boundary conditions. The wall was adiabatic with a sliding surface. The sliding surface. The calculation results are shown in Figure 8, and the 1D calculations are also shown calculation results are shown in Figure 8, and the 1D calculations are also shown for comparison. calculation results are shown in Figure 8, and the 1D calculations are also shown for comparison. 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) Figure 8. Performance map of the original and optimized designs for the low-pressure stage: Reduced mass flow vs. total pressure ratio; (b) Reduced mass flow vs. isentropic efficiency. Reduced mass flow vs. total pressure ratio; (b) Reduced mass flow vs. isentropic efficiency. (a) Reduced mass ﬂow vs. total pressure ratio; (b) Reduced mass ﬂow vs. isentropic efﬁciency. Appl. Sci. 2018, 8, 1347 8 of 22 Appl. Sci. 2018, 8, 1347 7 of 20 The The calculation calculation re results sults sh show ow th that at t the he pr pressur essure e ratio ratio of of the the original original design design was was 4.152, 4.152, and and the the ef efﬁciency ficiency was was 80.35%. 80.35%. The The pr pressure essure ra ratio tio o of f the the optimized optimized d design esign w was as 4 4.291, .291, a and nd th the e ef eff ﬁ iciency ciency wa was s 82.79%. 82.79%. Co Compar mpare ed d with with th the e pr pressur essure e ratio ratio and and ef efﬁciency ficiency of of the the o original riginal design, design, those those o of f th the e o optimized ptimized design design re repr prese esented nted a a si signiﬁcant gnificant iimpr mproovement. vement. TThe he tre trn end d ofof ththe e 1D c 1Dacalculation lculation resul results ts wa was s sim similar ilar to to thathat t of th ofe the NuNumec meca ca alcul calculation ation resul results. ts. The The pressure pressur rati eorat anio d ef and ficief ency ﬁciency of the of origi then original al design design were wer 4.21e 8 4.218 and 8 and 1.0981.09%, %, respec respectively tively, wh , er wher eas eas the the pressure pressur ra e ti ratio o anand d efef fic ﬁiciency ency oof f th the e o optimized ptimized d design esign were 4.339 and 83.20%, respectively. Compared with the pressure ratio of the original design, that of were 4.339 and 83.20%, respectively. Compared with the pressure ratio of the original design, that of optimized optimized design design incr increased eased by by 2 2.87%, .87%, and and the the ef efﬁciency ficiency i incr ncreased eased by by 2 2.11%. .11%. Figure 9 shows the inlet attack angle distribution of the vaned diffuser. In the original design, Figure 9 shows the inlet attack angle distribution of the vaned diffuser. In the original design, because because o of f the the separation separation a ar re ea a i in n the the vaneless vaneless dif diff fuser user, , the the separation separation vortex vortex worsened worsened th the e ﬂow flow condition at the vaned diffuser inlet with the variable scope of the inlet attack angle close to 50°. In condition at the vaned diffuser inlet with the variable scope of the inlet attack angle close to 50 . In the optimized the optimidesign, zed desi the gnseparation , the separ vortex ation disappear vortex disa edppe in the ared vane-less in the va difn fuser e-less , and difthe fuser, ﬂow an condition d the floof w condition of the vaned diffuser inlet significantly improved with the decrease in diameter ratio, the vaned diffuser inlet signiﬁcantly improved with the decrease in diameter ratio, D /D . The range 3 2 of D3/ angle D2. Th of e attack range o along f anglthe e ofspan attacwas k alo rn educed g the sp fra om n w 50 as re tod15 uce.d from 50° to 15°. Fig Figure ure 9 9. . I Inlet nlet a attack ttack a angle ngle d distribution istribution o of f t the he v vaned aned di dif ffuser fuser in in the the optimized optimized design. design. 4. Optimized Design of the High-Pressure-Stage Centrifugal Compressor 4. Optimized Design of the High-Pressure-Stage Centrifugal Compressor The optimized design system [18] was adopted to optimize the aerodynamic layout of the high- The optimized design system [18] was adopted to optimize the aerodynamic layout of the pressure-stage centrifugal compressor. Table 3 shows a comparison of the parameters of the original high-pressure-stage centrifugal compressor. Table 3 shows a comparison of the parameters of the and optimized designs. The geometric parameters after optimization changed only slightly, and the original and optimized designs. The geometric parameters after optimization changed only slightly, efficiency of the optimized design increased by approximately 0.2% compared with the original and the efﬁciency of the optimized design increased by approximately 0.2% compared with the original design. This finding shows that the impeller parameters are set reasonably in the original design. design. This ﬁnding shows that the impeller parameters are set reasonably in the original design. After optimization, the efficiency of the vaned diffuser outlet was 2.61% higher than that of the After optimization, the efﬁciency of the vaned diffuser outlet was 2.61% higher than that of the original original design. This result indicates that the mismatch between the diffuser and impeller mainly lead design. This result indicates that the mismatch between the diffuser and impeller mainly lead to the to the low efficiency in the original design. low efﬁciency in the original design. Compared with the value of the divergent angle, 2θ, in the original design, the value in the Compared with the value of the divergent angle, 2q, in the original design, the value in the optimized design decreased significantly. The divergent angle is defined as follows: optimized design decreased signiﬁcantly. The divergent angle is deﬁned as follows: DD − D D 4 3 tan = tan q = . 2L 2L For the diffuser design, 2q should be less than 12 to avoid gas over-expansion and separation. For the diffuser design, 2θ should be less than 12° to avoid gas over-expansion and separation. The experimental results showed that the loss coefﬁcient of the vaned diffuser is related to the divergent The experimental results showed that the loss coefficient of the vaned diffuser is related to the angle. In general, the loss was minimal when 2q = 6 , and gradually increased with the growth of divergent angle. In general, the loss was minimal when 2θ = 6°, and gradually increased with the 2q. If the value of 2q is too large, it could be reduced by increasing the diameter and number of growth of 2θ. If the value of 2θ is too large, it could be reduced by increasing the diameter and blades. By contrast, the increase in diameter and blade number increased the loss in ﬂow passage. number of blades. By contrast, the increase in diameter and blade number increased the loss in flow Therefore, the inﬂuence of various parameters on the performance of the diffuser should be considered passage. Therefore, the influence of various parameters on the performance of the diffuser should be comprehensively in the design. In the original design, the large divergent angle increases the loss in considered comprehensively in the design. In the original design, the large divergent angle increases 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 optimized design, the divergent angle was effectively reduced, and the efficiency of the unit was the vaned diffuser, which, in turn, leads to the low efﬁciency of the entire stage. In the optimized improved by increasing the blade number and length. design, the divergent angle was effectively reduced, 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. Comparison of the parameters of the optimized and original designs. Parameter Optimized Design Original Design 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 D (m) 0.252 0.252 b2 (m) 0.0956 0.00948 Lz (m) 0.057 0.058 b (m) D3 (m) 0.0956 0.274 0.20.00948 82 D (m) 0.274 0.282 3 D4 (m) 0.392 0.388 D (m) 0.392 0.388 DD / 1.09 1.12 D /D 1.09 1.12 3 2 2θ 11.9 15.7 2q 11.9 15.7 Z 20 17 Z 20 17 h 95.47% 95.24% η2 95.47% 95.24% h 92.88% 92.37% η3 92.88% 92.37% h 84.12% 82.29% η4 84.12% 82.29% The divergent angle was reduced in the 1D optimized design system by increasing the blade The divergent angle was reduced in the 1D optimized design system by increasing the blade number and length, as shown in Figure 10b, and the efﬁciency of the design was improved. number and length, as shown in Figure 10b, and the efficiency of the design was improved. This This optimization method reduced the throat area of the vaned diffuser and changed the matching optimization method reduced the throat area of the vaned diffuser and changed the matching characteristics of the vaned diffuser and impeller. Therefore, it is necessary to make an optimized characteristics of the vaned diffuser and impeller. Therefore, it is necessary to make an optimized design on the matching characteristics of the impeller and vaned diffuser. design on the matching characteristics of the impeller and vaned diffuser. (a) Original design (b) Optimized design 1 (c) Optimized design 2 Figure 10. Geometric structure of the vaned diffuser. 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 Table 4. d i d i It indicates that the chock mass flow of the vaned diffuser 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 d i d i make the chock mass flow in 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 mass ﬂow of the unit unchanged, when the diameter ratio D /D is reduced. Considering all factors, 3 2 the original vaned diffuser was replaced by a tandem vaned diffuser as shown in optimized design the original vaned diffuser was replaced by a tandem vaned diffuser as shown in optimized design 2 2 in Figure 10c. in Figure 10c. In the first row, 15 small vanes were selected, which is less than the 17 of the original design. In In the ﬁrst row, 15 small vanes were selected, which is less than the 17 of the original design. this way, the throat area of the vaned diffuser slightly decreases when the diameter ratio decreases. In this way, the throat area of the vaned diffuser slightly decreases when the diameter ratio decreases. The second row combines 15 large vanes and 15 splitter vanes. In this way, the divergent angle of the The second row combines 15 large vanes and 15 splitter vanes. In this way, the divergent angle of the vaned diffuser can be reduced to prevent separation. Meanwhile, the friction loss on the inner surface vaned diffuser can be reduced to prevent separation. Meanwhile, the friction loss on the inner surface of the vaned diffuser with the increase in the vane number would not be significant. 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 * * * * By using the optimized method, the ratio of design A /A to theoretical A /A is 1.037, which is d i d i closer to 1 and indicates the better matching of the diffuser and impeller. The throat area of the vaned closer to 1 and indicates the better matching of the diffuser and impeller. The throat area of the vaned diffuser is slightly larger than that of the impeller, which makes the choke mass flow of the optimized diffuser is slightly larger than that of the impeller, which makes the choke mass ﬂow of the optimized design consistent with that of the original design. design consistent with that of the original design. * * * * Table 4. Ratio of design Ad /Ai to theoretical Ad /Ai . * * * * Table 4. Ratio of design A /A to theoretical A /A . d i d i Original Design Optimized Design 1 Optimized Design 2 ** Original Design Optimized Design 1 Optimized Design 2 AA / ( ) di design (A /A ) 1.09 0.948 1.037 d i design ** 1.09 0.948 1.037 AA / (A /A ) ( ) d i di theory theory The The steady steady simulations simulations wer were e performed performed using using the the commer commercial cial code code Numeca. Numeca. The The S S-A -A turb turbul ulence ence model model was was used. used. G Grids rids we wer re e generated generated by by AutoGrid. AutoGrid. The The gri grid d n number umber o of f t the he original original design design was was 1,180,000; 1,180,000; after after optimization, optimization, it it was was 1,740,000. 1,740,000. T Total otal pr pressur essure e of of 101,300 101,300 Pa Pa was was set set at at the the inlet inlet and and the the back-pr back-pressur essure e was was set set at at the the outlet outlet for for boundary boundary conditions. conditions. The The wall wall was was adiabatic adiabatic with with a a sliding sliding surface. surface. TThe he ca calculation lculation re rs esults ults are ar e sh shown own inin FiFigur gure 11 e 11 , a,nand d the the 1D 1D calcalculations culations arear aleso also shoshown wn for for com comparison. parison. The The calculation calculation r re esults sults show show that that the the pr pressur essure e ratio ratio of of the the original original design design was was 2.838, 2.838, and and the the ef efﬁciency ficiency was was 80.68%. 80.68%. The The pr pressure essure ra ratio tio of of the the optimized optimized d design esign w was as 2 2.967, .967, a and nd th the e ef efﬁ ficiency ciency was was 85.03%. 85.03%. Compar Compare ed d with with the the pr pressur essure e ratio ratio and and ef efﬁciency ficiency of of the the o original riginal design, design, those those of of th the e o optimized ptimized design design 2 2 rre epr presented esenteda asigniﬁcant significant impr impr ovement. ovementThe . The trtre end nd of othe f th1D e 1D calculation calculatior n esults resulwas ts wa similar s similto ar that to thof at o the f th Numeca e Numeccalculation a calculation results. resultsIn . In th th e e design designcondition, condition,the the pr pr essur essure e ratio ratio and and ef efﬁciency ficiency of of the the original original design design wer were e 2.894% 2.894% and and 82.29%, 82.29%, re respectiv spectivel ely y, , wher whereas eas the the pr pressur essure e ratio ratio and and ef efﬁ ficiency ciency of of the the optimized optimized design design wer were e 2.952% 2.952% and and 84.52%, 84.52%, r re espectively spectively. . Co Compar mpare ed d wi with th th the e values values in in the the original original design, design, th the e pr pressur essure e ratio ratio and and ef efﬁ ficiency ciency of of the the optimized optimized d de esi sign gn incr increased eased by by 2.01% 2.01% and and 2.23%, 2.23%, r re espectively spectively. . (a) (b) Figure 11. Performance map of the original and optimized designs for the high-pressure stage: (a) Figure 11. Performance map of the original and optimized designs for the high-pressure stage: Reduced mass flow vs. total pressure ratio; (b) Reduced mass flow vs. isentropic efficiency. (a) Reduced mass ﬂow vs. total pressure ratio; (b) Reduced mass ﬂow vs. isentropic 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 attack Appl. Scangle i. 2018, in 8, 1the 347 original design, the angle in the optimized design was reduced to a certain 10 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 range of the attack angle from the blade root to blade tip less than 8°. In the original design, the range range of the attack angle from the blade root to blade tip less than 8 . In the original design, the range range of the attack angle from the blade root to blade tip less than 8°. In the original design, the range of the attack angle was close to 15°. of the attack angle was close to 15 . of the attack angle was close to 15°. Figure 12. Inlet attack angle distribution of the vaned diffuser. Figure 12. Inlet attack angle distribution of the vaned diffuser. Figure 12. Inlet attack angle distribution of the vaned diffuser. 5. Coupling Calculations of the Original and Optimized Designs 5. Coupling Calculations of the Original and Optimized Designs 5. Coupling Calculations of the Original and Optimized Designs After the low/high-pressure-stage centrifugal compressor was optimized and designed, circular After the low/high-pressure-stage centrifugal compressor was optimized and designed, After the low/high-pressure-stage centrifugal compressor was optimized and designed, circular calculations of the MW-level gas turbine were performed under three typical load conditions of 100%, circular calculations of the MW-level gas turbine were performed under three typical load conditions of calculations of the MW-level gas turbine were performed under three typical load conditions of 100%, 90%, and 60%. The operating parameters of circular calculation are shown in Table 5. To analyze the 100%, 90%, and 60%. The operating parameters of circular calculation are shown in Table 5. To analyze 90%, and 60%. The operating parameters of circular calculation are shown in Table 5. To analyze the actual performance of the low/high-pressure-stage centrifugal compressor, we conducted coupling the actual performance of the low/high-pressure-stage centrifugal compressor, we conducted coupling actual performance of the low/high-pressure-stage centrifugal compressor, we conducted coupling calculations and analysis of the original and optimized designs under different working conditions calculations and analysis of the original and optimized designs under different working conditions for calculations and analysis of the original and optimized designs under different working conditions for an entire week. The calculated geometric model is shown in Figure 13. Numeca software was used an entire week. The calculated geometric model is shown in Figure 13. Numeca software was used for for an entire week. The calculated geometric model is shown in Figure 13. Numeca software was used for calculations, and an S-A turbulence model was employed. calculations, and an S-A turbulence model was employed. for calculations, and an S-A turbulence model was 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 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 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, D /D . The ﬂow condition at 3 2 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. 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 Figure 15. Mach number distribution at different spans of the original and optimized designs of the low-pressure-stage centrifugal compressor at 100% load. low-pressure-stage centrifugal compressor at 100% load. low-pressure-stage centrifugal compressor at 100% 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 reduced in the original design. In the optimized design, the low-speed area obviously decreased in Appl. Sci. 2018, 8, 1347 15 of 22 the vaned diffuser. Appl. Sci. 2018, 8, 1347 14 of 20 (a) 10% span (b) 50% span (c) 90% 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, 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 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 optimized diffuser. design, Therefothe re, n addition o separaof tiosplitter n existed vanes , althef ough fectively a low r- educed speed athe rea diver was gent obserangle ved in of th the e flvaned ow difpa fuser ssa.ge. Ther Sim efor ilar e,to no th separation e original d existed, esign, th although e closer to a low-speed the tip, the ar bea ette was r thobse e flow. rved Thin e o the verﬂow all flo passage. w in the vaned diffuser was significantly improved. 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 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 Figure 17 shows the meridional ﬂow diagram at 90% load. Similar to the situation with 100% separation area was found near the tip of the vaned diffuser outlet. In the optimized design, the flow load, a large separation area was observed in the vaned diffuser in the original design, and a small was still steady in the flow passage without obvious separation. separation area was found near the tip of the vaned diffuser 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 (c) 90% 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. 2018, 8, 1347 16 of 22 separation area was found near the tip of the vaned diffuser 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. 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 Figure 18 shows the Mach number distribution in different spans of the original and optimized designs of the low-pressure-stage centrifugal compressor at 90% load. For the original and optimized designs of the low-pressure-stage centrifugal compressor at 90% load. For the original and optimized designs, the Mach number distribution in different spans and the ﬂow in the ﬂow passage 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 at 90% span, making the blade tip show an obvious backﬂow area. original design at 90% span, making the blade tip show an obvious backflow area. (a) 10% span (b) 50% span (c) 90% 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 Appl. Sci. 2018, 8, 1347 16 of 20 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 optimized design, the flow in the low/high-pressure-stage centrifugal compressor obviously optimized design, the ﬂow in the low/high-pressure-stage centrifugal compressor obviously improved. improved. (a) 10% span (b) 50% span (c) 90% 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 area was observed near the edge of the impeller inlet rim, in addition to the separation area in the Figure 20 shows the meridional streamline chart at 60% load. In the original design, a separation vane-less diffuser and vaned diffuser outlet. This condition indicates that the operating condition of area was observed near the edge of the impeller inlet rim, in addition to the separation area in the the low-pressure-stage compressor was close to the surge line. In the optimized design, the overall vane-less diffuser and vaned diffuser outlet. This condition indicates that the operating condition of flow in the passage was stable, but separation areas were observed near the impeller inlet rim of the the low-pressure-stage compressor was close to the surge line. In the optimized design, 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-stage compressor. 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 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 at 90% load. Appl. Sci. 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. Figure 20. Meridional streamline at 60% load. Figure 20. Meridional streamline at 60% 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 Fig low ure -pr es 21 sur . Ma e-st ch a g ne um cen ber trifug dista rli b cut om io pr n es atso di rffe at r6 en 0% t spa loan d. s 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 Figure 22 shows the Mach number distribution in different spans of the original and optimized designs of the high-pressure-stage centrifugal compressor at 60% load. In the high-pressure stage, designs of the high-pressure-stage centrifugal compressor at 60% load. In the high-pressure stage, the high Mach number distribution and the ﬂow in the passage were similar to those at 90% load in the high Mach number distribution and the flow in the passage were similar to those at 90% load in the original and optimized designs, and the overall ﬂow features had no obvious change. the original and optimized designs, and the overall flow features had no obvious change. In general, the largest difference between 100%, 90%, and 60% loads was the emergence of In general, the largest difference between 100%, 90%, and 60% loads was the emergence of separation areas near the low-pressure stage impeller inlet rim. This condition shows that the separation areas near the low-pressure stage impeller inlet rim. This condition shows that the low- low-pressure-stage compressor operation points were near the surge line, which is an unstable factor pressure-stage compressor operation points were near the surge line, which is an unstable factor for for the operation of the unit and requires appropriate attention to avoid accidents. the operation of the unit and requires appropriate attention to avoid accidents. Under three typical load conditions of 100%, 90% and 60%, the ﬂow in the Under three typical load conditions of 100%, 90% and 60%, the flow in the low/high-pressure- low/high-pressure-stage centrifugal compressor had several undesirable conditions in the stage centrifugal compressor had several undesirable conditions in the original design. However, the original design. However, the ﬂow was improved effectively in the optimized design. flow was improved effectively in the optimized design. (a) 10% span (b) 50% span (c) 90% span Figure 22. Mach number distribution at different spans of the original and optimized designs of the Figure 22. Mach number distribution at different spans of the original and optimized designs of the high-pressure-stage centrifugal compressor at 60% load. high-pressure-stage centrifugal compressor at 60% 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 c skin friction coefﬁcient C absolute velocity C speciﬁc heat at constant pressure C absolute meridional velocity C absolute tangential velocity D diameter d hydraulic diameter HB D diffusion factor Dh euler work th L impeller ﬂow length L 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 a absolute ﬂow angle b relative angle F ﬂow coefﬁcient g meridional inclination angle h Efﬁciency " wake fraction of blade-to-blade space m slip factor m = C /C q 2 q 2 r density s slip factor s = 1 C /U slip 2 Subscripts 1 impeller inlet condition 2 impeller outlet condition 3 vaneless diffuser outlet condition 4 vaned diffuser outlet condition M meridional direction q 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. 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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/).

Applied Sciences – Multidisciplinary Digital Publishing Institute

**Published: ** Aug 10, 2018

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