激波诱导边界层分离的研究
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摘要
激波与边界层相互作用在高速飞行中无所不在，通常发生在飞机、导弹和火箭的内、外流场，激波诱导的边界层分离常带来如流道雍塞等诸多棘手问题，是当今热点研究课题之一。
本文针对二维平板／楔结构，数值模拟了由尖楔产生的激波冲击平板诱导平板边界层产生分离的现象。通过分别改变来流马赫数M_∞及楔角θ以改变入射激波强度，计算并比较了不同强度入射激波与平板边界层相互干扰的情况。
通过数值模拟，分别得到了层流边界层和湍流边界层分离条件、壁面参数分布规律、干扰点后激波系结构及湍流边界层厚度变化趋势。结果表明，除入射激波强度外，边界层厚度也是影响湍流边界层分离的主导因素；当湍流边界层发生分离时，干扰点后的边界层可能增厚，可能不变也可能变薄；分离区近壁温度可能降低；在同一楔角的情况下，随着来流马赫数的增加，第一道和第二道反射激波的相对位置发生改变，由平行变为相交。
在简单的二维平板／楔结构研究的基础上，本文还进行了超燃冲压发动机进气道内边界层分离的数值分析，为解决航空航天领域的一些工程实际问题提供了理论参考。
Shock-Wave/Boundary-Layer Interaction is ubiquitous in high-speed flight, occurring in an almost limitless number of external and internal flow problems relevant to aircraft, missiles, and rockets. That the separation of boundary layer induced by shock wave causes a series of problems such as flowing block in air passage is worth studying.
The separation of boundary layer induced by different intensity of impinging shock wave generated by 2D wedge/plate configuration is numerically studied in the present paper. Mach number of coming flow and wedge angle determine the intensity of shock wave. The interaction between shock waves, which are varied with Mach number of coming flow and wedge angle, and flat boundary layer is compared and analyzed.
The separation conditions of laminar and turbulent boundary layer, the distribution of the parameters along wall, the configuration of shock waves and the change of thickness for turbulent boundary layer behind the interaction plot are illustrated in details. The results show, the thickness of turbulent boundary layer is the crucial factor of the state of separation, besides the intensity of impinging shock wave; the separation makes the thickness of turbulent boundary layer at the downstream zone of impinging point may increase, may equal, or may decrease; the temperature along wall surface at the impinging point may decrease; with the increase of mach number for the coming flow under the condition of the same wedge angle, the relative position of the first and the second reflection shock waves become intersecting instead of paralleling.
Based on hereinbefore research, the interaction of shock wave/boundary in inlet for scramjet is simulated here. The study can be used as theoretical reference on relative issues in the field of aviation and aerospace.
本文针对二维平板／楔结构，数值模拟了由尖楔产生的激波冲击平板诱导平板边界层产生分离的现象。通过分别改变来流马赫数M_∞及楔角θ以改变入射激波强度，计算并比较了不同强度入射激波与平板边界层相互干扰的情况。
通过数值模拟，分别得到了层流边界层和湍流边界层分离条件、壁面参数分布规律、干扰点后激波系结构及湍流边界层厚度变化趋势。结果表明，除入射激波强度外，边界层厚度也是影响湍流边界层分离的主导因素；当湍流边界层发生分离时，干扰点后的边界层可能增厚，可能不变也可能变薄；分离区近壁温度可能降低；在同一楔角的情况下，随着来流马赫数的增加，第一道和第二道反射激波的相对位置发生改变，由平行变为相交。
在简单的二维平板／楔结构研究的基础上，本文还进行了超燃冲压发动机进气道内边界层分离的数值分析，为解决航空航天领域的一些工程实际问题提供了理论参考。
Shock-Wave/Boundary-Layer Interaction is ubiquitous in high-speed flight, occurring in an almost limitless number of external and internal flow problems relevant to aircraft, missiles, and rockets. That the separation of boundary layer induced by shock wave causes a series of problems such as flowing block in air passage is worth studying.
The separation of boundary layer induced by different intensity of impinging shock wave generated by 2D wedge/plate configuration is numerically studied in the present paper. Mach number of coming flow and wedge angle determine the intensity of shock wave. The interaction between shock waves, which are varied with Mach number of coming flow and wedge angle, and flat boundary layer is compared and analyzed.
The separation conditions of laminar and turbulent boundary layer, the distribution of the parameters along wall, the configuration of shock waves and the change of thickness for turbulent boundary layer behind the interaction plot are illustrated in details. The results show, the thickness of turbulent boundary layer is the crucial factor of the state of separation, besides the intensity of impinging shock wave; the separation makes the thickness of turbulent boundary layer at the downstream zone of impinging point may increase, may equal, or may decrease; the temperature along wall surface at the impinging point may decrease; with the increase of mach number for the coming flow under the condition of the same wedge angle, the relative position of the first and the second reflection shock waves become intersecting instead of paralleling.
Based on hereinbefore research, the interaction of shock wave/boundary in inlet for scramjet is simulated here. The study can be used as theoretical reference on relative issues in the field of aviation and aerospace.
引文
[1] David S Dolling. Fifty Years of Shock-Wave/Boundary-layer Interaction Research: What Next?. AIAA Journal. 2001, 39(8): 1517-1531 P
[2] Gefroh D, Loth E, Dutton C, Hafenrichter E. Aero-elastically deflecting flaps for shock/boundary-layer interaction control. Journal of Fluids and Structures. 2003,17: 1001-1016 P
[3] Doyle Knight, Hong Yan, Argyris G, Panaras, Alexander Zheltovodov. Advances in CFD prediction of Shockwave turbulent boundary layer interactions. Progress in Aerospace Sciences 39, 2003:121-184 P
[4] Ferri A, Atti di Guidonia. Experimental results with airfoils tested in the high speed tunnel at Guidonia. NACATM 946, 1939
[5] Fage A, Sargent R F, Shock Wave and Boundary Layer Phenomena Near a Flat Surface. Proceedings of the Royal Society of London, Series A: Mathematical and Physical Sciences, 1947(190): 1-20 P
[6] Ackeret J, Feldmann F, Rott N. Investigations of compression shocksand boundary layer in gases moving at high speed. NACA TM 1113, 1947
[7] Liepmann H W. The interaction between boundary layer and shock waves in transonic flow. JAS 13, 1946: 623-637 P
[8] Donaldson, Dup C. Effects of Interaction between Boundary Layer and Shock Waves in Transonic Flow. NACACB 4A27, 1944
[9] Liepmann H W, Roshko A, Dhawan S. On reflection of shock waves from boundary layer. Coll. Aero. Cranfiled, Note No. 93, 1959
[10] Bogdonoff S M, Kepler C E. Separation of a supersonic turbulent boundary layer. JAS 22, 1955: 414-424 P
[11] Barry F W, Shapiro A H, Neumann E P. The Interaction of Shock Waves with Boundary Layer. Philosophical Magazine, Series 7, 1951, 18(4): 229-238 P
[12] Bardsley O, Mair W A. The Interaction between an Oblique Shock Wave and a Turbulent Boundary Layer. Philosophical Magazine, Series 7, 1951, 42(324): 29-36P
[13] Johannesen N H. Experiments on Two-Dimensional Supersonic Flow in Corners and over Concave Surfaces. British Aeronautical Research Council, 1952, 14(607): 10-15 P
[14] Donaldson, Dup C, Lange R H. Study of the Pressure Rise Across Shock Waves Required to Separate Laminar and Turbulent Boundary Layers. NACA TN 2770, 1952
[15] Argyris G Panaras. Review of the physics of swept-shock/boundary layer interactions. Prog. Aerospace Sci. 1996, 32:173-244 P
[16] Frederic Thivet, Dlyle D Knight, Alexander A Zheltovodov, Alexander I Maksimov. Analysis of observed and computed crossing-shock-wave/turbulent-boundary-layer interactions. Aerospace Science and Technology. 2002, 6: 3-17 P
[17] 魏庆鼎．湍流边界层分离的实验研究．空气动力学学报．1986，3：30-38 P
[18] 中国力学学会．中国科学院力学研究所编．郭永怀文集．北京：科学出版社，1982
[19] Knight D D, Degrez G. Shock Wave Boundary-Layer Interactions in High Mach Number Flows. A Critical Survey of Current Numerical Prediction Capabilities. Advisory Rept. 319. AGARD, 1998(12), 2: 11-13 P
[20] Marat A Goldfeld, Roman V Nestoulia, Alexei V Starov. The boundary layer interaction with shock wave and expansion fan. Journal of Thermal Science. 2000, 9: 109-114 P
[21] Gefroh D, Loth E, Dutton C, E Hafenrichter. Aeroelastically deflecting flaps for shock/boundary-layer interaction control. Journal of Fluids and Structures. 2003, 17:1001-1016 P
[22] Yegna K, Narayan, Seshadri S N. Types of flow on the lee side of delta wings. Prog. Aerospace Sci. 1997, 33:167-257 P
[23]史里希廷．边界层理论．科学出版社．1988：37 P,146．149 P,292 P,256-358 P,293 P,329 P,363 P,67 P,142-144 P,804 P
[24] Emmons H W, Brainerd J G. Temperature effects in a laminar compressible fluid boundary layer along a flat plat. J. Appl. Mech. 8, A 105(1941) and J. Appl. Mech. 9, I, 1942
[25] Boussinesq J. Eessi sur la theorie des eaux conrantes. Mem, Pres. Acad. SCl. XXIII, 46, Paris, 1877
[26] Prandtl L. Bemerkungen zur Theorie der freien Turbulenz. ZAMM 22, 1942, 241-243 P
[27] von Karman Th. Mechanische Ahnlichkeit und Turbulenz, Nachr. Ges. Wiss. Gottingen, Math. Phys, Klasse, 58(1930) and Proc. 3~(rd). Intern. Congress Appl. Mech., Stookholm, Part I, 85(1930):NACA TM 611(1931); also Coll. Works II, 337-356 P
[28] Bjorgum O. On the steady turbulent flow along an infinitely long smooth and plane wall. Universitaet I. Bergen, Arbok,Naturvitenskapeling Rekke. No. 7,1951
[29] Angela D, McConnell. Roughness Effects on Impinging Shock Wave /Turbulent Boundary Layer Interactions. The paper of Master of Cambridge University Engineering Department. 1999, 8: 33P
[30] Kistler A L. Fluctuation measurements in a supersonic turbulent boundary layer. Phys. Fluids 2,1959: 290-296 P
[31] Chapman D R, Xeater R H. Measurements of turbulent skin friction on cylinders in axial flow at subsonic and supersonic velocities. JAS 20. 1953: 441-448 P
[32] Eckert E R G. Engineering relations for friction and heat transfer tosurfaces in high velocity flow. JAS 22, 1955: 585-587 P
[33] O'Donnell RM. Experimental investigation at Mach number of 2.41 of average skin friction coefficients and velocity profiles for laminar and turbulent boundary layers and assessment of probe effects. NACA TN 2132, 1954
[34] Dedssler R G.. Analysis of turbulent heat transfer, mass transfer, and friction in smooth tube at high Prandtl and Schmidt numbers. NACA TR. 1210, 1955
[35] Rotta J C. Ueber den Einfluss tier Machischen Zahl und des Warmeuebergange auf das Wandgesetz turbulentes Stroemungen. ZFW 7, 1959: 264-274P
[36] 童秉纲，孔祥言，邓国华．气体动力学．高等教育出版社．123-125页
[37] Rott N. Unsteady viscous flow in the vicinity of a stagnation point. Quart. Appl. Math. 13, 1956: 444-451P
[38] 陶文铨．数值传热学．西安交通大学出版社．333页
[39] 蒋旭旭，唐强，王革．超燃冲压发动机进气道的边界层分离．中国宇航学会2006年固体火箭发动机第23届年会论文集(发动机分册)．2006：530-536页
[40] Stull F. Scramjet Propulsion. AIAA 89-5012
[41] Billig F S. Research on Supersonic Combustion. AIAA 92-0001
[42] 牟让科，杨永年，叶正寅．超临界翼型的跨音速抖振特性．计算物理．2001(05)：477-480页
[43] 章赛进，夏南．二维激波边界层干扰的数值分析．上海大学学报(自然科学版)．2004(03)：255-263页
[44] 陈雄，郑亚，周长省，鞠玉涛．冲压增程弹丸进气道复杂湍流流场数值仿真．兵工学报．2005(03)：303-307页
[45] MacComack R W. Numerical solution of the interaction of a shock wave with a laminar boundary layer. Lecture Notes in Physics, 1971: 151-163P
[46] Beam R M, Warming R F. An implicit factored scheme for the compressible Navier-Stokes equation. AIAA. 1978. 16: 393-402P
[47] Tsien, Hsue-shen, Finston M. Interaction between parallel streams of subsonic and supersonic velocities, J. Aero. Sci., 1949, 16(9): 515-528P
[48] Howarth L. The propagation of steady disturbances in a supersonic stream bounded on one side by a parallel subsonic stream. Proc Cambridge Phil. Soc. 1947. 380-390P
[49] 张瑜．叶轮机械中激波与边界层的干扰问题．中国科学技术大学学报，1982(S1)：12-15页
[50] 董志勇，韩肇元，刘延宁．运动激波与非定常边界层干扰的实验研究．中国科学技术大学学报，1996，(力学与工程应用专刊)：155-159页
[51] 王汝权，焦履琼，刘学宗．简化Navier-Stokes方程的数值解法．空气动力学学报，1984(01)：10-14页
[52] 郭应钧．超声速进气道流场和边界层计算．空气动力学学报，1990(01)：15-18页
[53] 徐立功，冉政．一种计算超声速流中由湍流剪切层脉动引起的激波振荡频率的方法．应用数学和力学，1991(08)：7-10页
[54] 邓学蓥，廖锦华．尖楔和半锥引起的激波／边界层干扰中相关特性研究．北京航空航天大学学报，1993(01)：1-5页
[55] 王力，傅德薰．用CSCM格式模拟二维收缩管道内的流动．航空学报，1993(05)：1-5页
[56] 张树道，韩肇元，徐胜利，司徒明．双燃式(超燃)冲压发动机中激波与边界层之间相互作用对内部流动的影响．流体力学实验与测量，1999(02)：2-6页
[57] 黄国平，梁德旺．块结构的MUSCL算法求解三维进气道流场．空气动力学学报，2000(02)：9-13页
[58] 张树道，司徒明，韩肇元．SFD方法模拟高超声速进气道中激波与边界层干扰．推进技术，2000(01)：5-9页
[59] 张红杰，马晖扬，童秉纲．高超声速复杂流动中湍流模式应用的评估．空气动力学学报，2001(02)：11-15页
[60] Bodonyi R J, Smith F T. Shock-wave laminar boundary-layer interaction in supercritical transonic flow. Computers & Fluids. 1986, 2: 97-108P
[61] Jean Paul Dussauge, Pierre Dupont, Jean-Francois Debieve. Unsteadiness in shock wave boundary layer interactions with separation. Aerospace Science and Technology. 2006(3), 10, 2: 85-89P
[2] Gefroh D, Loth E, Dutton C, Hafenrichter E. Aero-elastically deflecting flaps for shock/boundary-layer interaction control. Journal of Fluids and Structures. 2003,17: 1001-1016 P
[3] Doyle Knight, Hong Yan, Argyris G, Panaras, Alexander Zheltovodov. Advances in CFD prediction of Shockwave turbulent boundary layer interactions. Progress in Aerospace Sciences 39, 2003:121-184 P
[4] Ferri A, Atti di Guidonia. Experimental results with airfoils tested in the high speed tunnel at Guidonia. NACATM 946, 1939
[5] Fage A, Sargent R F, Shock Wave and Boundary Layer Phenomena Near a Flat Surface. Proceedings of the Royal Society of London, Series A: Mathematical and Physical Sciences, 1947(190): 1-20 P
[6] Ackeret J, Feldmann F, Rott N. Investigations of compression shocksand boundary layer in gases moving at high speed. NACA TM 1113, 1947
[7] Liepmann H W. The interaction between boundary layer and shock waves in transonic flow. JAS 13, 1946: 623-637 P
[8] Donaldson, Dup C. Effects of Interaction between Boundary Layer and Shock Waves in Transonic Flow. NACACB 4A27, 1944
[9] Liepmann H W, Roshko A, Dhawan S. On reflection of shock waves from boundary layer. Coll. Aero. Cranfiled, Note No. 93, 1959
[10] Bogdonoff S M, Kepler C E. Separation of a supersonic turbulent boundary layer. JAS 22, 1955: 414-424 P
[11] Barry F W, Shapiro A H, Neumann E P. The Interaction of Shock Waves with Boundary Layer. Philosophical Magazine, Series 7, 1951, 18(4): 229-238 P
[12] Bardsley O, Mair W A. The Interaction between an Oblique Shock Wave and a Turbulent Boundary Layer. Philosophical Magazine, Series 7, 1951, 42(324): 29-36P
[13] Johannesen N H. Experiments on Two-Dimensional Supersonic Flow in Corners and over Concave Surfaces. British Aeronautical Research Council, 1952, 14(607): 10-15 P
[14] Donaldson, Dup C, Lange R H. Study of the Pressure Rise Across Shock Waves Required to Separate Laminar and Turbulent Boundary Layers. NACA TN 2770, 1952
[15] Argyris G Panaras. Review of the physics of swept-shock/boundary layer interactions. Prog. Aerospace Sci. 1996, 32:173-244 P
[16] Frederic Thivet, Dlyle D Knight, Alexander A Zheltovodov, Alexander I Maksimov. Analysis of observed and computed crossing-shock-wave/turbulent-boundary-layer interactions. Aerospace Science and Technology. 2002, 6: 3-17 P
[17] 魏庆鼎．湍流边界层分离的实验研究．空气动力学学报．1986，3：30-38 P
[18] 中国力学学会．中国科学院力学研究所编．郭永怀文集．北京：科学出版社，1982
[19] Knight D D, Degrez G. Shock Wave Boundary-Layer Interactions in High Mach Number Flows. A Critical Survey of Current Numerical Prediction Capabilities. Advisory Rept. 319. AGARD, 1998(12), 2: 11-13 P
[20] Marat A Goldfeld, Roman V Nestoulia, Alexei V Starov. The boundary layer interaction with shock wave and expansion fan. Journal of Thermal Science. 2000, 9: 109-114 P
[21] Gefroh D, Loth E, Dutton C, E Hafenrichter. Aeroelastically deflecting flaps for shock/boundary-layer interaction control. Journal of Fluids and Structures. 2003, 17:1001-1016 P
[22] Yegna K, Narayan, Seshadri S N. Types of flow on the lee side of delta wings. Prog. Aerospace Sci. 1997, 33:167-257 P
[23]史里希廷．边界层理论．科学出版社．1988：37 P,146．149 P,292 P,256-358 P,293 P,329 P,363 P,67 P,142-144 P,804 P
[24] Emmons H W, Brainerd J G. Temperature effects in a laminar compressible fluid boundary layer along a flat plat. J. Appl. Mech. 8, A 105(1941) and J. Appl. Mech. 9, I, 1942
[25] Boussinesq J. Eessi sur la theorie des eaux conrantes. Mem, Pres. Acad. SCl. XXIII, 46, Paris, 1877
[26] Prandtl L. Bemerkungen zur Theorie der freien Turbulenz. ZAMM 22, 1942, 241-243 P
[27] von Karman Th. Mechanische Ahnlichkeit und Turbulenz, Nachr. Ges. Wiss. Gottingen, Math. Phys, Klasse, 58(1930) and Proc. 3~(rd). Intern. Congress Appl. Mech., Stookholm, Part I, 85(1930):NACA TM 611(1931); also Coll. Works II, 337-356 P
[28] Bjorgum O. On the steady turbulent flow along an infinitely long smooth and plane wall. Universitaet I. Bergen, Arbok,Naturvitenskapeling Rekke. No. 7,1951
[29] Angela D, McConnell. Roughness Effects on Impinging Shock Wave /Turbulent Boundary Layer Interactions. The paper of Master of Cambridge University Engineering Department. 1999, 8: 33P
[30] Kistler A L. Fluctuation measurements in a supersonic turbulent boundary layer. Phys. Fluids 2,1959: 290-296 P
[31] Chapman D R, Xeater R H. Measurements of turbulent skin friction on cylinders in axial flow at subsonic and supersonic velocities. JAS 20. 1953: 441-448 P
[32] Eckert E R G. Engineering relations for friction and heat transfer tosurfaces in high velocity flow. JAS 22, 1955: 585-587 P
[33] O'Donnell RM. Experimental investigation at Mach number of 2.41 of average skin friction coefficients and velocity profiles for laminar and turbulent boundary layers and assessment of probe effects. NACA TN 2132, 1954
[34] Dedssler R G.. Analysis of turbulent heat transfer, mass transfer, and friction in smooth tube at high Prandtl and Schmidt numbers. NACA TR. 1210, 1955
[35] Rotta J C. Ueber den Einfluss tier Machischen Zahl und des Warmeuebergange auf das Wandgesetz turbulentes Stroemungen. ZFW 7, 1959: 264-274P
[36] 童秉纲，孔祥言，邓国华．气体动力学．高等教育出版社．123-125页
[37] Rott N. Unsteady viscous flow in the vicinity of a stagnation point. Quart. Appl. Math. 13, 1956: 444-451P
[38] 陶文铨．数值传热学．西安交通大学出版社．333页
[39] 蒋旭旭，唐强，王革．超燃冲压发动机进气道的边界层分离．中国宇航学会2006年固体火箭发动机第23届年会论文集(发动机分册)．2006：530-536页
[40] Stull F. Scramjet Propulsion. AIAA 89-5012
[41] Billig F S. Research on Supersonic Combustion. AIAA 92-0001
[42] 牟让科，杨永年，叶正寅．超临界翼型的跨音速抖振特性．计算物理．2001(05)：477-480页
[43] 章赛进，夏南．二维激波边界层干扰的数值分析．上海大学学报(自然科学版)．2004(03)：255-263页
[44] 陈雄，郑亚，周长省，鞠玉涛．冲压增程弹丸进气道复杂湍流流场数值仿真．兵工学报．2005(03)：303-307页
[45] MacComack R W. Numerical solution of the interaction of a shock wave with a laminar boundary layer. Lecture Notes in Physics, 1971: 151-163P
[46] Beam R M, Warming R F. An implicit factored scheme for the compressible Navier-Stokes equation. AIAA. 1978. 16: 393-402P
[47] Tsien, Hsue-shen, Finston M. Interaction between parallel streams of subsonic and supersonic velocities, J. Aero. Sci., 1949, 16(9): 515-528P
[48] Howarth L. The propagation of steady disturbances in a supersonic stream bounded on one side by a parallel subsonic stream. Proc Cambridge Phil. Soc. 1947. 380-390P
[49] 张瑜．叶轮机械中激波与边界层的干扰问题．中国科学技术大学学报，1982(S1)：12-15页
[50] 董志勇，韩肇元，刘延宁．运动激波与非定常边界层干扰的实验研究．中国科学技术大学学报，1996，(力学与工程应用专刊)：155-159页
[51] 王汝权，焦履琼，刘学宗．简化Navier-Stokes方程的数值解法．空气动力学学报，1984(01)：10-14页
[52] 郭应钧．超声速进气道流场和边界层计算．空气动力学学报，1990(01)：15-18页
[53] 徐立功，冉政．一种计算超声速流中由湍流剪切层脉动引起的激波振荡频率的方法．应用数学和力学，1991(08)：7-10页
[54] 邓学蓥，廖锦华．尖楔和半锥引起的激波／边界层干扰中相关特性研究．北京航空航天大学学报，1993(01)：1-5页
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