本研究目的為探討超音速微型風洞內之流場現象，以及在微觀尺度中超音速流經過不同形狀結構物下的震波現象，並以壓力螢光感測塗料(Pressure sensitive paint)之實驗技術與數值模擬相互驗證及比對。針對微型超音速風洞之設計，根據理論分析建立噴嘴出口馬赫數為2，出口面積與喉部面積比Ae/A*為1.687，喉部寬度為500 m，且噴嘴長度為1450 m的超音速噴嘴，並在噴嘴出口後方加入長為1800 m的風洞測試段，流道深度為150 m之微型超音速風洞。接著利用ANSYS Fluent模擬軟體進行不同入出口壓力條件的設定，發現與前人實驗相同之流場現象，由於黏性邊界層的增長，風洞測試段內壓力上升、馬赫數下降，故藉由漸擴角向外開3.8度重新設計風洞測試段，能於測試段內部形成穩定馬赫數1.6之流場。後續在測試段中加入直徑與底邊為50 m之圓柱與三角柱模型，並進行微型超音速風洞實驗測試。
本實驗在入口總壓100 kPa，出口靜壓20 kPa，且實際馬赫數為1.55的情況下，成功觀察到圓柱微結構物前方弓形震波造成壓力驟升的現象，壓力由30 kPa上升至48 kPa，並由於黏滯邊界層在圓柱前方厚度增加，使黏性流在與震波交會後，於分離區中產生馬蹄形渦旋的現象，以及量測到結構物後方之對稱的膨脹波低壓區，沿y = 50 m之軸向壓力由31.6 kPa降低至20.8 kPa。另外在頂角為20度之三角形實驗中，壓力會為沿著斜邊上升，最高壓力為35.6 kPa，相較於30度三角形則會在結構前有較高之壓力分佈，壓力為36.9 kPa，不同於斜震波壓力驟升的情況，考慮到PSP塗料由於旋佈在流道底部進行量測，在邊界層內之表面壓力分佈會受黏滯效應影響，使壓力為漸進式上升而非跨越震波的壓力躍升。
綜觀以上結果，本研究應用壓力螢光感測技術，成功量測不同形狀結構於為尺度超音速風洞內之壓力分佈，並探討震波形成現象，發現在低雷諾數下黏滯效應影響劇烈，而實驗提供的二維表面壓力分布，與模擬結果趨勢一致，有助於微尺度下超音速流場之研究。

The purpose of this study was to investigate the shock wave phenomena by applying pressure sensitive paint (PSP) measurements at micro scale. The supersonic micro wind tunnel was composed of a convergent-divergent nozzle and a test section with 3.8 degrees divergent angle. The design Mach number of the nozzle was 2.0 and the width of the throat and the channel depth were 500 m and 150 m, respectively. The pressure distribution along the nozzle centerline was measured by PSP sensors under different inlet/outlet pressure conditions, and the experiment results were in good agreement with the numerical results obtained from commercial CFD software ANSYS Fluent. It was observed that the velocity in the nozzle decreased and the pressure increased under high back pressure due to the growth of the boundary layer. A steady supersonic flow field with Mach number 1.55 can be obtained in the test section of the wind tunnel at the back pressure of 20 kPa and the total pressure of 100 kPa. The shock wave pattern with three test models: a circular cylinder and two wedge models with 10 degrees and 15 degrees half angles were examined with experiments and simulation.
The pressure raised sharply from 30 kPa to 48 kPa at the bow shock in front of the circular cylinder because of the increased thickness in the viscous boundary layer in front of the cylinder and the shock wave/boundary layer interaction (SWBLI) was identified. The lambda shock structure caused a complicated flow field as a horseshoe vortex generated in the separation zone. A low pressure area of 20.8 kPa caused by expansion waves was observed behind the circular cylinder model. For the pressure measurements with wedge models, the pressure raised of 35.6 kPa along the edge was found in the experiment of the wedge with half angle of 10 degrees. Compared the experimental results of the wedge with half angle of 15 degrees, a higher pressure distribution of 36.9 kPa was identified in front of the structure. This was different situation between wedge model with half angle of 10 and 15 degree where the oblique shock wave turned into a detached shock wave. It was noted that the surface pressure distribution in the boundary layer was affected by the viscous effect and the PSP sensor was coated on the channel side wall, the pressure rise obtained from PSP measurement was more gradually other than a pressure jump across the shock wave.

[1] D. J. Barnhart, T. Vladimirova, and M. N. Sweeting, "Very-small-satellite design for distributed space missions," Journal of Spacecraft and Rockets, vol. 44, no. 6, pp. 1294-1306, 2007.
[2] A. R. Tummala and A. Dutta, "An overview of cube-satellite propulsion technologies and trends," Aerospace, vol. 4, no. 4, p. 58, 2017.
[3] K. I. Parker, "State-of-the-art for small satellite propulsion systems," 2016.
[4] R. Bayt, A. Ayon, K. Breuer, R. Bayt, A. Ayon, and K. Breuer, "A performance evaluation of MEMS-based micronozzles," in 33rd Joint Propulsion Conference and Exhibit, 1997, p. 3169.
[5] G. N. Markelov and M. S. Ivanov, "Numerical study of 2D/3D micronozzle flows," in AIP Conference Proceedings, 2001, vol. 585, no. 1: American Institute of Physics, pp. 539-546.
[6] A. A. Alexeenko, D. A. Levin, S. F. Gimelshein, R. J. Collins, and B. D. Reed, "Numerical modeling of axisymmetric and three-dimensional flows in microelectromechanical systems nozzles," AIAA journal, vol. 40, no. 5, pp. 897-904, 2002.
[7] W. Louisos and D. Hitt, "Heat transfer & viscous effects in 2D & 3D supersonic micro-nozzle flows," in 37th AIAA Fluid Dynamics Conference and Exhibit, 2007, p. 3987.
[8] M. Liu, X. Zhang, G. Zhang, and Y. Chen, "Study on micronozzle flow and propulsion performance using DSMC and continuum methods," Acta Mechanica Sinica, vol. 22, no. 5, pp. 409-416, 2006.
[9] C. Xie, "Characteristics of micronozzle gas flows," Physics of Fluids, vol. 19, no. 3, p. 037102, 2007.
[10] J. Xu and C. Zhao, "Two-dimensional numerical simulations of shock waves in micro convergent–divergent nozzles," International Journal of Heat and Mass Transfer, vol. 50, no. 11-12, pp. 2434-2438, 2007.
[11] M. Darbandi and E. Roohi, "Study of subsonic–supersonic gas flow through micro/nanoscale nozzles using unstructured DSMC solver," Microfluidics and nanofluidics, vol. 10, no. 2, pp. 321-335, 2011.
[12] T. Liu, Pressure‐and Temperature‐Sensitive Paints. Wiley Online Library, 2005.
[13] K. Nakakita, M. Kurita, and K. Mitsuo, "Development of the Pressure-Sensitive Paint Measurement for Large Wind Tunnels at Japan Aerospace Exploration Agency," in ICAS, 2004, vol. 3, no. 2, p. 2004.
[14] S. Fujii, D. Numata, H. Nagai, and K. Asai, "Development of ultrafast-response anodized-aluminum pressure-sensitive paints," in 51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, 2013, p. 485.
[15] C.-Y. Huang, C.-M. Lai, and J.-S. Li, "Applications of pixel-by-pixel calibration method in microscale measurements with pressure-sensitive paint," Journal of Microelectromechanical Systems, vol. 21, no. 5, pp. 1090-1097, 2012.
[16] 陳瑩璇, "壓力螢光感測分子於突縮擴微流道流場的探討及應用," 清華大學動力機械工程學系碩士論文, 2013.
[17] 李佳烜, "壓力螢光感測技術於微流道內稀薄與可壓縮流場之探討及應用," 清華大學動力機械工程學系碩士論文, 2014.
[18] 姜可鈞, "應用壓力螢光感測塗料技術於 90 度微彎管內流場量測與分析," 清華大學動力機械工程學系碩士論文, 2014.
[19] T. Osafune, T. Kurotaki, and K. Asai, "Application of molecular sensors to micro objects in supersonic flow," in 42nd AIAA Aerospace Sciences Meeting and Exhibit, 2004, p. 1048.
[20] J. Crafton, A. Forlines, S. Palluconi, K.-Y. Hsu, C. Carter, and M. Gruber, "Investigation of transverse jet injections in a supersonic crossflow using fast-responding pressure-sensitive paint," Experiments in Fluids, vol. 56, no. 2, p. 27, 2015.
[21] J. Gregory, J. Sullivan, H. Sakaue, and C.-Y. Huang, "Molecular sensors for MEMS," in 40th AIAA Aerospace Sciences Meeting & Exhibit, 2002, p. 256.
[22] C. Huang, J. W. Gregory, and J. P. Sullivan, "Flow visualization and pressure measurement in micronozzles," Journal of visualization, vol. 10, no. 3, pp. 281-288, 2007.
[23] H. Nagai, R. Naraoka, K. Sawada, and K. Asai, "Pressure-Sensitive Paint Measurement of Pressure Distribution in a Supersonic Micronozzle," AIAA Journal, vol. 46, no. 1, pp. 215-222, 2008, doi: 10.2514/1.28371.
[24] 蕭辰宇, "微型超音速風洞之設計與研究," 清華大學動力機械工程學系碩士論文, 2018
[25] Y. Matsuda, T. Uchida, S. Suzuki, R. Misaki, H. Yamaguchi, and T. Niimi, "Pressure-sensitive molecular film for investigation of micro gas flows," Microfluidics and Nanofluidics, vol. 10, no. 1, pp. 165-171, 2011.
[26] Y. Matsuda, H. Yamaguchi, and T. Niimi, "Development of Pressure-Sensitive Channel Chip for Micro Gas Flows," in Journal of Physics: Conference Series, 2012, vol. 362, no. 1: IOP Publishing, p. 012036.
[27] T. Handa, Y. Matsuda, and Y. Egami, "Phenomena peculiar to underexpanded flows in supersonic micronozzles," Microfluidics and Nanofluidics, vol. 20, no. 12, p. 166, 2016.
[28] N. Murai, R. Yamamoto, K. Rikuno, and T. Toriyama, "Study on correlation between geometrical correction and aerodynamic performance of microscale supersonic wind tunnel," Electrical Engineering in Japan, vol. 205, no. 1, pp. 64-72, 2018.
[29] J. D. Anderson, Modern compressible flow, with historical perspective (no. BOOK). McGraw-Hill, 1990.
[30] J. Heine and K. Müller-Buschbaum, "Engineering metal-based luminescence in coordination polymers and metal–organic frameworks," Chemical Society Reviews, vol. 42, no. 24, pp. 9232-9242, 2013.
[31] F. Menter, "Zonal two equation kw turbulence models for aerodynamic flows," in 23rd fluid dynamics, plasmadynamics, and lasers conference, 1993, p. 2906.
[32] K. Matsuo, Y. Miyazato, and H.-D. Kim, "Shock train and pseudo-shock phenomena in internal gas flows," Progress in aerospace sciences, vol. 35, no. 1, pp. 33-100, 1999.
[33] T. Handa, K. Kitahara, Y. Matsuda, and Y. Egami, "Peculiarities of low-Reynolds-number supersonic flows in long microchannel," Microfluidics and Nanofluidics, vol. 23, no. 7, p. 88, 2019.
[34] K.-M. Chung and Y.-J. Chen, "Effect of High Blockage Ratios on Surface Pressures of an Inclined Flat Plate," Journal of Engineering, vol. 4, no. 2, pp. 82-92, 2016.
[35] M. K. Quinn, L. Yang, and K. Kontis, "Pressure-sensitive paint: effect of substrate," Sensors, vol. 11, no. 12, pp. 11649-11663, 2011.
[36] W. W. Y. Chow, K. F. Lei, G. Shi, W. J. Li, and Q. Huang, "Microfluidic channel fabrication by PDMS-interface bonding," Smart materials and structures, vol. 15, no. 1, p. S112, 2005.
[37] S. Lindörfer, C. Combs, P. Kreth, R. Bond, and J. Schmisseur, "Scaling of cylinder-generated shock-wave/turbulent boundary-layer interactions," Shock Waves, pp. 1-13, 2020.
[38] H. Ozawa and S. Laurence, "Experimental investigation of the shock-induced flow over a wall-mounted cylinder," Journal of Fluid Mechanics, vol. 849, pp. 1009-1042, 2018.
[39] J. J. Bertin, Hypersonic aerothermodynamics. AIAA, 1994.
[40] J. P. Hubner, B. F. Carroll, K. S. Schanze, and H. F. Ji, "Techniques for using pressure-sensitive paint in shock tunnel facilities," in ICIASF'97 Record. International Congress on Instrumentation in Aerospace Simulation Facilities, 1997: IEEE, pp. 30-39.