離心式壓縮機廣泛應用於微型渦輪引擎、渦輪增壓系統與高轉速旋轉機械中，其性能表現與葉輪、擴散器及渦殼之流場匹配密切相關。渦殼主要負責收集擴散器出口之氣流並將其導向出口管路，若其截面積分布、入口位置或出口導流設計不佳，將造成局部加速、二次流、壁面剪應力增加與總壓損失上升，進而影響整體壓縮機效率與壓力回收能力，最終量測之準確性降低。因此針對高轉速壓縮機測試平台進行擴散器與渦殼流場分析及外型優化，對於提升測試段性能與建立後續設計方法具有重要意義。
本研究以成功大學高轉速壓縮機測試平台為研究對象，建立包含入口管段、葉輪、擴散器與渦殼之完整數值模型，採用計算流體力學（Computational Fluid Dynamics, CFD）分析不同幾何參數對測試段性能之影響。研究首先針對改良基準設計進行比較，包含有導葉擴散器與無導葉擴散器、渦殼入口偏心率以及渦殼截面積成長率等幾何參數。最終選定無導葉擴散器設計、渦殼入口偏心率（e=0.85）與渦殼截面積成長指數（n=1.0）作為後續伴隨算子（Adjoint Operator）優化前之改良基準設計，並將其定義為Adjoint 0th。
渦殼外型優化方面，本研究以60,000 rpm設計點為操作條件，採用ANSYS Fluent Adjoint Solver，以降低渦殼總壓損失為主要目標函數，對渦殼壁面進行局部外型修正。隨著外型逐步優化，渦殼中後段與出口附近之流道面積分布獲得改善，使氣流收集與轉向更加平順，其中Adjoint 4th為最佳外型，整體表現相較初始設計明顯提升，包含總壓損失降低45.7%、壓力回收（total pressure recovery）能力提升及壁面剪應力減少，流場中高剪應力區域與二次流結構亦獲得抑制，出口前速度與總壓恢復分布更為均勻。最後並將該最佳外型應用於不同轉速與質量流率之設計點外性能測試，模擬測試結果顯示在低與中轉速條件下可穩定降低損失並提升壓力回收，具良好適用性；而在高轉速設計點流量條件下雖仍具改善效果，設計點流量外的操作點但整體性能仍受葉輪出口流場、擴散器流動與渦殼入口匹配之耦合影響。
研究建立由改良基準設計、設計點經計算流體力學伴隨算子（CFD-Adjoint Method）外型優化至優化外型對於非設計點之性能驗證之完整數值分析流程。使渦殼外型不僅在單一設計點具有最低損失，壓縮機測試平台也能在較寬廣操作範圍內維持穩定性並提高量測之準確性。

Centrifugal compressors are widely used in microturbine engines, turbocharging systems, and high-speed rotating machinery. Their performance is closely related to the aerodynamic matching among the impeller, diffuser, and volute. The volute is primarily responsible for collecting the flow discharged from the diffuser outlet and guiding it toward the outlet duct. If its cross-sectional area distribution, inlet location, or outlet flow-guiding design is improper, local flow acceleration, secondary flow, increased wall shear stress, and higher total pressure loss may occur, thereby affecting the overall compressor efficiency and pressure recovery capability and ultimately reducing the accuracy of experimental measurements. Therefore, flow-field analysis and shape optimization of the diffuser and volute in a high-speed compressor test rig are important for improving the performance of the test section and establishing a practical design methodology for future applications.
In this study, the high-speed compressor test rig developed at National Cheng Kung University is adopted as the research subject. A complete numerical model consisting of the inlet duct, impeller, diffuser, and volute is established, and computational fluid dynamics (CFD) is employed to investigate the effects of different geometric parameters on the performance of the test section. First, comparisons are conducted to establish an improved baseline design, including diffuser type, volute inlet eccentricity, and volute cross-sectional area growth rate. Finally, the vaneless diffuser design, a volute inlet eccentricity of e = 0.85, and a volute cross-sectional area growth exponent of n = 1.0 are selected as the improved baseline design before the subsequent adjoint-based optimization, and this configuration is defined as Adjoint 0th.
For the volute shape optimization, the operating condition at 60,000 rpm is selected as the design point. The ANSYS Fluent Adjoint Solver is employed to perform local shape modifications on the volute wall, with the reduction of total pressure loss in the volute selected as the primary objective function. As the geometry is progressively optimized, the flow-passage area distribution in the middle and downstream sections of the volute and near the outlet region is improved, resulting in smoother flow collection and turning. Among the optimized configurations, Adjoint 4th is identified as the best-performing geometry. Compared with the original NCKU test rig, the overall performance is significantly improved, including a 45.7% reduction in total pressure loss, enhanced total pressure recovery capability, and reduced wall shear stress. In addition, regions with high wall shear stress are reduced, secondary-flow structures are suppressed, and the velocity and total pressure recovery distributions upstream of the outlet become more uniform. Finally, the best-performing geometry is applied to off-design simulations under different rotational speeds and mass flow rates. The simulation results show that, under low- and medium-speed conditions, the optimized geometry can consistently reduce losses and improve pressure recovery, demonstrating good applicability. Under high-speed conditions near the design mass flow rate, although improvement is still observed, the overall performance at off-design mass flow rates remains affected by the coupled interactions among the impeller exit flow, diffuser flow behavior, and volute inlet matching.
This study establishes a complete numerical analysis procedure, including the development of an improved baseline design, CFD-adjoint-based shape optimization at the design point, and off-design performance validation of the optimized geometry. The optimized volute geometry not only achieves the lowest loss at a single design point but also enables the compressor test rig to maintain stable performance over a wider operating range, thereby improving the accuracy of experimental measurements.

[1]F. Oppong, S. J. Van Der Spuy, and A. L. Diaby, "An overview on the performance investigation and improvement of micro gas turbine engine," R&D Journal of the South African Institution of Mechanical Engineering, vol. 31, pp. 35–41, 2015.
[2]K. R. Miller, "Design of a centrifugal compressor research facility for low specific speed applications," M.S. thesis, School of Mechanical Engineering, Purdue University, 2012.
[3]J. Reinhart, "Design of a Small-Turbojet Compressor Test Facility," M.S. thesis, Department of Mechanical and Aerospace Engineering, University of Dayton, 2021.
[4]D. J. Struwig, "The development and verification of a centrifugal compressor test bench," M.S. thesis, Department of Mechanical and Mechatronic Engineering, Stellenbosch University, 2014.
[5]陳佳駿，"利用微型渦輪軸引擎驅動之高轉速壓縮機測試平台設計與測試"，碩士論文，國立成功大學航空太空工程學系，2023.
[6]廖子誼，"利用微型渦輪軸引擎驅動之高轉速壓縮機測試平台性能驗證"，碩士論文，國立成功大學航空太空工程學系，2025.
[7]C.-H. Wu and Y.-T. Kung, "A parametric study on oil/air lubrication of a high-speed spindle," Precision Engineering, vol. 29, no. 2, pp. 162–167, 2005.
[8]ASME, Measurement of Fluid Flow in Closed Conduits Using Multiport Averaging Pitot Primary Elements. The American Society of Mechanical Engineers, 2006.
[9]ASME, Performance Test Code on Compressors and Exhausters. The American Society of Mechanical Engineers, 1997.
[10]K. Schreckling, Home built model turbines. Traplet Publications Limited, 2005.
[11]M. Casey and C. Robinson, Radial flow turbocompressors. Cambridge University Press, 2021.
[12]H. Mohtar, P. Chesse, D. Chalet, J.-F. Hetet, and A. Yammine, "Effect of diffuser and volute on turbocharger centrifugal compressor stability and performance: Experimental study," Oil & Gas Science and Technology–Revue d’IFP Energies nouvelles, vol. 66, no. 5, pp. 779–790, 2011.
[13]Q. Zhang, Q. Huo, L. Zhang, L. Song, and J. Yang, "Effect of vaneless diffuser shape on performance of centrifugal compressor," Applied Sciences, vol. 10, no. 6, Art. no. 1936, 2020.
[14]J. Issac, N. Sitaram, and M. Govardhan, "Effect of diffuser vane height and position on the performance of a centrifugal compressor," Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy, vol. 218, no. 8, pp. 647–654, 2004.
[15]T. C. S. Reddy, G. R. Murty, P. Mukkavilli, and D. Reddy, "Effect of the setting angle of a low-solidity vaned diffuser on the performance of a centrifugal compressor stage," Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy, vol. 218, no. 8, pp. 637–646, 2004.
[16]L. McLaughlin, S. Spence, D. Rusch, L. Galloway, M. Geron, K. K. So, and M. Fischer, "Numerical and experimental investigation of a radially reduced diffuser design concept for a centrifugal compressor performance at design point," Aerospace Science and Technology, vol. 126, Art. no. 107590, 2022.
[17]M. M. Cui, "Comparative study of unsteady flows in a transonic centrifugal compressor with vaneless and vaned diffusers," International Journal of Rotating Machinery, vol. 2005, no. 1, pp. 90–103, 2005.
[18]P. Demircioglu, I. Bogrekci, B. Sert, M. Abbakar, and A. Gogebakan, "Effect of vaned and vaneless diffuser on the performance of turbo blowers," Engineering Review, vol. 44, no. 3, pp. 138–146, 2024.
[19]S. M. Gunadal and M. Govardhan, "Performance improvement of a centrifugal compressor using partial vaned diffusers," International Journal of Fluid Machinery and Systems, vol. 13, no. 1, pp. 177–189, 2020.
[20]D. Japikse, Centrifugal compressor design and performance, Concepts ETI, 1996.
[21]N. A. Cumpsty,Compressor aerodynamics, Harlow, U.K.: Longman Scientific & Technical, 1989.
[22]J. Kurokawa, "Theoretical determinations of the flow characteristics in volutes," Proceedings of the 10th IAHR Symposium on Hydraulic Machinery and Cavitation, Tokyo, Japan, 1980, vol. 1, pp. 623–634.
[23]S.-R. Chen, S. S. Lee, and Y. M. Huang, "A mathematical model for the analysis of fluid flow in a scroll," Journal of Fluids Engineering, vol. 108, no. 1, pp. 6–11, 1986.
[24]R. A. Van den Braembussche and B. M. Haende, "Experimental and theoretical study of the swirling flow in centrifugal compressor volutes," Journal of Turbomachinery, vol. 112, no. 1, pp. 38–43, 1990.
[25]E. Ayder, R. Van den Braembussche, and J. Brasz, "Experimental and theoretical analysis of the flow in a centrifugal compressor volute," Journal of Turbomachinery, vol. 115, no. 3, pp. 582–589, 1993.
[26]R. Van den Braembussche, E. Ayder, D. Hagelstein, M. Rautenberg, and R. Keiper, "Improved model for the design and analysis of centrifugal compressor volutes," Journal of Turbomachinery, vol. 121, no. 3, pp. 619–625, 1999.
[27]H. Chen, D. Tong, and X. Wang, "Vortices and performance of internal and external volutes," in Proc. ASME Turbo Expo 2015: Turbine Technical Conference and Exposition, Montreal, QC, Canada, 2015, paper GT2015-42624.
[28]A. J. Stepanoff, Centrifugal and axial flow pumps : Theory, Design, and Application, 2nd ed. New York, NY, USA: Wiley, 1957.
[29]R. Hottois, A. Châtel, and T. Verstraete, "Adjoint-based design optimization of a volute for a radial compressor," International Journal of Turbomachinery, Propulsion and Power, vol. 8, no. 4, p. 41, 2023.
[30]M. Heinrich and R. Schwarze, "Genetic algorithm optimization of the volute shape of a centrifugal compressor," International Journal of Rotating Machinery, vol. 2016, no. 1, Art. no. 4849025, 2016.
[31]D. Altafi, M. Mojaddam, and M. Bastankhah, "Entropy generation rate analysis of turbocharger radial flow compressor in range from surge to choke," Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy, vol. 238, no. 3, pp. 401–426, 2024.
[32]M. Anbarsooz and C. Xu, "Design and fluid dynamics of volutes in centrifugal compressors: A comprehensive review," Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, vol. 239, no. 13, pp. 1547–1576, 2025.
[33]C. Robinson, M. Casey, B. Hutchinson, and R. Steed, "Impeller-diffuser interaction in centrifugal compressors," Proceedings of the ASME Turbo Expo 2012: Turbine Technical Conference and Exposition, Copenhagen, Denmark, 2012, Paper GT2012-69151.
[34]C. Cornelius, T. Biesinger, P. Galpin, and A. Braune, "Experimental and computational analysis of a multistage axial compressor including stall prediction by steady and transient CFD methods," Journal of Turbomachinery, vol. 136, no. 6, Art. no. 061013, 2014.
[35]F. R. Menter, "Two-equation eddy-viscosity turbulence models for engineering applications," AIAA Journal, vol. 32, no. 8, pp. 1598–1605, 1994.
[36]P. E. Smirnov and F. R. Menter, "Sensitization of the SST turbulence model to rotation and curvature by applying the Spalart–Shur correction term," Journal of Turbomachinery, vol. 131, no. 4, Art. no. 041010, 2009.
[37]H. Mendis, "Better meshing using ANSYS Fluent Meshing," LinkedIn, 2018. [Online]. Available: https://www.linkedin.com/pulse/better-meshing-using-ansys-fluent-hashan-mendis/. [Accessed: Jul. 2, 2026].
[38]T. Skamagkis, E. M. Papoutsis‐Kiachagias, and K. C. Giannakoglou, "On the stabilization of steady continuous adjoint solvers in the presence of unsteadiness, in shape optimization," International Journal for Numerical Methods in Fluids, vol. 93, no. 8, pp. 2677 –2693, 2021.
[39]E. M. Papoutsis-Kiachagias and K. C. Giannakoglou, "Continuous adjoint methods for turbulent flows, applied to shape and topology optimization: industrial applications," Archives of Computational Methods in Engineering, vol. 23, no. 2, pp. 255–299, 2016.
[40]G. M. Streuber and D. W. Zingg, "Evaluating the risk of local optima in aerodynamic shape optimization," AIAA Journal, vol. 59, no. 1, pp. 75–87, 2021.