本研究藉由實驗方法，探討小圓柱與平板之間的距離對小圓柱尾流衝擊平板所形成之流場特徵與氣動力性能的影響。藉由雷射光頁輔助煙霧可視化技術，觀察小圓柱尾流之流場特徵以及小圓柱尾流衝擊平板時之平板上游流場特徵；使用熱線風速儀量測小圓柱尾流區的速度場；以質點影像速度儀(PIV)量測受小圓柱尾流衝擊時的平板上游流場結構與速度特性，並與流場可視化之流場特徵作比對；使用壓力掃描器量測平板上游的表面壓力，探討小圓柱與平板之間的距離對平板上游表面壓力的影響。改變雷諾數、小圓柱直徑以及小圓柱至平板距離，流場可視化、背風面壓力、迎風面壓力、速度場及渦度場量測結果顯示：當小圓柱直徑固定時，在雷諾數以及小圓柱與平板距離的場域內，受到不同模態(例如：creeping flow, standing vortices,unstable standing vortices, and Kármán-Bénard eddies)之小圓柱尾流衝擊時，平板上游垂直面流場特徵模態可識別為parallel flow (平行流)、vorticity concentrated mode (兩個轉向相反且近似對稱的旋轉流)、vortex formation mode (蕈狀渦漩結構)、transitional mode Ⅰ (蕈狀渦漩結構側邊呈現多個小渦漩結構)、transitional mode Ⅱ (蕈狀渦漩結構上游呈現多個小渦漩結構)、unstable vortex mode (蕈狀渦漩結構呈現不規則的逸放行為)。小圓柱尾流速度缺陷的梯度導致小圓柱尾流在撞擊平板上游面之前，因減速而累積渦度，在渦度夠大時形成捲起的渦流。當尾流接近平板時，水平面的流體橫向流動而越過平板兩側，側向速度對渦流形成渦漩拉伸作用，增強渦流的渦度，形成蕈狀反向旋轉渦流，此渦流主控流場的特性。由於平板表面上游蕈狀渦漩結構的生成，橫風不會直接衝擊平板表面，使得平板上游表面壓力係數降低。
隨著平板與小圓柱之距離越遠，小圓柱尾流在衝擊平板前的寬度會增加，蕈狀渦漩結構與平板之間的距離會縮短、蕈狀渦漩結構中心渦度值變小，平板之平均阻力係數下降。蕈狀渦漩結構中心渦度值變小時，渦旋集中模態(vortex concentration mode)以及蕈狀渦漩模態(vortex formation mode)會延後發生，是造成阻力係數隨著小圓柱與平板距離增加而降低的主因。

The effects of the distance between flat plate and small cylinder on the flow characteristics around the upstream face of a flat plate with a finite width impinged by the cylinder wake were experimentally studied in a wind tunnel. The smoke flow patterns, velocity field, streamline patterns, vorticity distributions, pressure coefficients, and drag coefficients were measured and discussed. The visual flow patterns were obtained by the laser-light-sheet-assisted smoke flow visualization method. The velocity field was measured by particle image velocimetry. The streamline and vorticity distributions were calculated from the measured velocity data. The topological flow patterns were proposed according to the streamline patterns to assist with the understanding of the characteristic flow structures. The surface pressure distributions across the width of the flat plate were measured by installing pressure taps on the surfaces of the plate.The pressure and drag coefficients were calculated using the measured surface pressures to characterize the influence of wake impingement of the aerodynamic force. The physical mechanism of vortex formation was discussed on the basis of the measured flow patterns and vorticity distributions. Six characteristic flow modes (parallel flow,vorticity concentrated mode, vortex formation mode, transitional mode Ⅰ and Ⅱ, and unstable vortex modes) were observed around the upstream face of the wake-impinged flat plate. These characteristic flow modes appeared in different regimes in the domain of the small-diameter cylinder Reynolds number and the non-dimensional distance between cylinder and flat plate. The cylinder wake presented velocity defects across the wake and persisted to the far downstream region. The velocity gradients of the velocity defects led to the accumulation of vorticities in the vertical plane around the upstream face of the wake-impinged flat plate. When the wake flows approached the flat plate, the vorticities in the wake made the flows curved towards the centre plane and induced a reverse flow going towards upstream. The upstream-going flow met the IV freestream and diverted laterally to form mushroom-type counter-rotating vortices, which primarily dominated the flow field. The lateral vortex-stretching effect induced by the finite width of the flat plate increased the vorticities in the counter-rotating vortices because of the angular momentum conservation. Because the vortex formation mode on the upstream face of the flat plate was generated, it avoided the direct impingement of the freestream on the flat plate.Therefore, the pressure and drag coefficients of the wake-impinged flat plate were reduced.The width of the cylinder wake decreased with increasing the distance between the cylinder and flat plate. The distance between vortices and flat plate, vorticities, drag coefficient of flat plate wake all decreased with the increase of the distance between the cylinder and flat plate. The primary physical dominating parameter was the vorticity. The decrease in the distance between the cylinder and the flate plate would increase the vorticities approaching the flat plate, which would change the appearances of characteristic flow modes. The drag coefficient therefore was changed with the change of characteristic flow modes. This principle applied to flat plate width and Reynolds number as well. Increasing the flat plate width would increase the vortex stretching of the vortices, and hence would increase vorticity which leading to change of characteristic flow modes. Increasing Reynolds number would also increase the vorticities in the cylinder wake and would change the characteristic flow modes, which in term changed the drag coefficient.

[1]Böttcher J, Wedemeyer E (1989) The flow downstream of screens and its influence on the flow in stagnation region of cylindrical bodies. J Fluid Mech 204:501-522
[2]Dhanak M, Stuart J (1995) Distortion of the stagnation-point flow due to cross-stream vorticity in the external flow, Philos Trans R Soc Lond A Math Phys Eng Sci 352(1700):443-452
[3]Feltham G, Ekmekci A(2014) Vorticity amplification near the stagnation point of landing gear wheels. Phys Fluids 26(4):045,106
[4]Gifford AR, Diller TE, Vlachos PP (2011) The physical mechanism of heat transfer augmentation in stagnating flows subject to freestream turbulence. J Heat Tranf 133(2):021901
[5]HODSON, P. R. & NAGIB, H. M. 1977 Vortices induced in a stagnation region by wakes-their incipient formation and effect on heat transfer. AIAA-Paper 77-790
[6]Huang, R. F., Chen, J. M., and Hsu C. M., “Modulation of surface flow and vortex shedding of a circular cylinder in the subcritical regime by self-excited vibration rod,” Journal of Fluid Mechanics, Vol. 555, May 2006, pp. 321-352.
[7]Kestin J, Maeder P, Sogin H (1961) The influence of turbulence on the transfer of heat to cylinders near the stagnation point. J Appl Math phys 12(2):115-132
[8]KESTIN, J. & WOOD, R. T. 1970 On the instability of two-dimensional stagnation flow. J. Fluid Mech. 44, 461.
[9]Kerr OS, Dold J (1994) Periodic steady vortices in a stagnation-point flow. J Fluid Mech 276:307-325
[10]LIAN, Q. X. & SU, T. C. 1994 Large vortex in front of stagnation region of a square plate induced by a fine vortex generating wire. Sci China (Ser. A) 37, 469.
[11]LEWEKE, T. & WILLIAMSON, C. H. K. 1998 Cooperative elliptic instability of a vortex pair. J. Fluid Mech. 360, 85.
[12]Lu Y, Gopalan B, Celik E, Katz J, Van Wie DM (2010) Stretching of turbulence eddies generates cavitation near a stagnation point. Phys Fluids 22(4):041,702
[13]Le, M. D, Hsu, C. M., and Huang*, R. F., “Flow characteristics and velocity fields of swirling double-concentric jets at a high central jet Reynolds numbers, ” accepted for publication by Journal of Marine Science and Technology on August 6, 2018.
[14]Mosiria, D. B., Huang*, R. F., and Hsu, C. M., “Effectsof small backward inclination on characteristics of a stack-issued combusting transverse jet in crossflow, ” Heat and Mass Transfer, Vol. 55, No. 3,2019, pp. 733-751. DOI:
10.1007/s00231-018-24886-0
[15]Oo AN, Ching CY (2001) Effect of turbulence with different vertical structures on stagnation region heat transfer. J Heat Transf 123(4):665-674
[16]Sadeh WZ, Brauer HJ (1980) A visual investigation of turbulence in stagnation flow about a circular cylinder. J Fluid Mech 99(01):53-64
[17]Sadeh WZ, Sutera SP, Maeder PF (1970) Analysis of vorticity amplification in the flow approaching a two-dimensional stagnation point. J Appl Math Phys 21(5):699-716
[18]Schrader LU, Brandt L, Mavriplis C, Henningson DS (2010) Receptivity to free-stream vorticity of flow past a flat plate with elliptic leading edge. J Fluid Mech 653:245-271
[19]Sutera S (1965) Vorticity amplification in stagnation-point flow and its effect on heat transfer. J Fluid Mech 21(03):513-534
[20]Wang J, Pan C , Choi KS, Gao L, Lian QX (2013) Formation, growth and instability of vortex pairs in an axisymmetric stagnation flow. J Fluid Mech 725:681-708
[21]Wei CY, Miau JJ (1992) Stretching of freestream turbulence in the stagnation region. AIAA J 30(9):2196-2203
[22]Wei CY, Miau JJ (1993) Characteristics of stretched vortical structures in two-dimensional stagnation flow. AIAA J 31(11):2075-2082
[23]Xiong Z, Lele SK (2004) Distortion of upstream disurbances in a hiemenz boundary layer. J Fluid Mech 519:201-232
[24]張冠翔, 小圓柱尾流衝擊平板時的流場特徵與氣動力性能, 國立台灣科技大學機械工程研究所碩士論文, 2017.
[25]張庭瑋, 平板受小圓柱尾流衝擊時之流場特徵與氣動力性能, 國立台灣科技大學機械工程研究所碩士論文, 2018.
[26]張育興, 小圓柱尾流衝擊平板時的流場特徵, 國立台灣科技大學機械工程研究所碩士論文, 2019.