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Under the assumption of the low magnetic Reynolds number, the coupled model is established for the turbulent flow field and the externally applied magnetic field. The AUSMPW+ scheme and LUSGS method are used to solve turbulent magnetohydrodynamics (MHD) flow equations, in which the Spalart-Allmaras one-equation turbulence model is used. A series of numerical simulations over various geometry configurations, namely, a flat plate and a compression corner, is conducted by using an external electromagnetic field. Results show that the performance of MHD boundary layer flow control is determined mainly by the Lorentz force in the streamwise direction. With an external magnetic field used, the low velocity fluid in the boundary layer can decelerate and increase the static temperature locally. Moreover, the counter-flow Lorentz force always brings a negative effect on the turbulent skin friction coefficient, and the location for the MHD zone has a great influence on the control efficiency of the ramp-induced separation. A reasonable magnetic field layout scheme should be configured in practical engineering application.
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Keywords:
- magnetohydrodynamics /
- turbulent boundary layer /
- multi-field coupling /
- flow control
[1] 谭慧俊, 李程鸿, 张悦, 李光胜 2016 推进技术 37 11
Google Scholar
Tan H J, Li C H, Zhang Y, Li G S 2016 J. Propuls. Technol. 37 11
Google Scholar
[2] Babinsky H, Harvery J K 2011 Shock Wave Boundary Layer Interactions (New York: Cambridge University Press) pp5, 6
[3] Van D M, Nedungadi A 2004 40th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Fort Lauderdale, Florida, July 11–14 2004, AIAA 2004–4129
[4] Bisek N J, Gosse R, Poggie J 2013 J. Spacecraft Rockets 50 927
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[5] 丁明松, 江涛, 董维中, 高铁锁, 刘庆宗, 傅杨奥骁 2019 68 174702
Google Scholar
Ding M S, Jiang T, Dong W Z, Gao T S, Liu Q Z, Fu Y A X 2019 Acta Phys. Sin. 68 174702
Google Scholar
[6] 李开, 柳军, 刘伟强 2017 66 054701
Google Scholar
Li K, Liu J, Liu W Q 2017 Acta Phys. Sin. 66 054701
Google Scholar
[7] 李逸翔, 汪球, 罗凯, 李进平, 赵伟 2021 力学学报 53 2493
Google Scholar
Li Y X, Wang Q, Luo K, Li J P, Zhao W 2021 Chin. J. Theor. Appl. Mech. 53 2493
Google Scholar
[8] Fujino T, Matsumoto Y, Ishikawa M 2016 J. Spacecraft Rockets 53 528
Google Scholar
[9] Bobashev S V, Mende N P, Sakharov V A 2003 41st Aerospace Sciences Meeting and Exhibit Reno, Nevada, January 6–9 2003, AIAA 2003-169
[10] Meyer R, Chintala N, Bystrivky B 2004 42nd AIAA Aerospace Sciences Meeting and Exhibit Reno, Nevada, January 5–8 2004, AIAA 2004-510
[11] Zaidi S H, Smith T, Macheret S 2006 44th AIAA Aerospace Sciences Meeting and Exhibit Reno, Nevada, January 9–12 2006, AIAA 2006-1006
[12] Saito S, Udagawa K, Kawaguchi K 2008 46th AIAA Aerospace Sciences Meeting and Exhibit Reno, Nevada, January 7–10 2008, AIAA 2008-1091
[13] Nagata Y, Yamada K, Abe T 2013 J. Spacecraft Rockets 50 981
Google Scholar
[14] 李益文, 樊昊, 张百灵 2017 航空学报 38 120368
Google Scholar
Li Y W, Fan H, Zhang B L 2017 Acta Aeronaut. Astronaut. Sin. 38 120368
Google Scholar
[15] Wang D, Wang J F, Li L F 2022 Aerosp. Sci. Technol. 126 107598
Google Scholar
[16] 田正雨 2008 博士学位论文 (长沙: 国防科学技术大学)
Tian Z Y 2008 Ph. D. Dissertation (Changsha: National University of Defense Technology) (in Chinese)
[17] 丁明松, 江涛, 董维中, 高铁锁, 刘庆宗 2017 航空学报 38 121030
Google Scholar
Ding M S, Jiang T, Dong W Z, Gao T S, Liu Q Z 2017 Acta Aeronaut. Astronaut. Sin. 38 121030
Google Scholar
[18] Li K 2017 Ph. D. Dissertation (Changsha: National University of Defense Technology) (in Chinese)
[19] 李开, 刘伟强 2016 65 064701
Google Scholar
Li K, Liu W Q 2016 Acta Phys. Sin. 65 064701
Google Scholar
[20] Sinha K, Candler G 1998 29th AIAA, Fluid Dynamics Conference Albuquerque, NM, June 15–18 1998, AIAA 98-2649
[21] 贺旭照 2007 博士学位论文 (绵阳: 中国空气动力研究与发展中心)
He X Z 2007 Ph. D. Dissertation (Mianyang: China Aerodynamics Research and Development Center) (in Chinese)
[22] 姚宵, 刘伟强, 谭建国 2018 67 174702
Google Scholar
Yao X, Liu W Q, Tan J G 2018 Acta Phys. Sin. 67 174702
Google Scholar
[23] Dietiker J K 2002 Ph. D. Dissertation (Wichita: Wichita State University)
[24] Settles G S, Dodson L J 1991 AIAA 22nd Fluid Dynamics, Plasma Dynamics & Lasers Conference, Honolulu, HI, June 24–26 1991, AIAA 91–1763
[25] Aithal S, Munipalli R, Shankar V 2004 Performance Enhancement of High Speed Inlets Using MHD (USA: Defense Technical Information Center) pp13–23
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图 1 完全气体磁流体湍流流场计算示意图 (
${\mu _{\text{t}}}$ 为湍流黏性系数,${k_{\text{t}}}$ 为湍流热传导系数,${F_{{\text{step}}}}$ 为耦合计算过程流场迭代步数)Figure 1. Schematic of coupling computations of the magnetohydrodynamic turbulent flows based on the perfect gas model (
$ {\mu _{\text{t}}} $ is the turbulent viscosity coefficient,${k_{\text{t}}}$ is the turbulent heat transfer coefficient,${F_{{\text{step}}}}$ is the number of iteration steps of the flow field in the coupling calculation process).
图 3 绝热壁条件下, 壁面热流分布对比
Figure 3. Comparison of wall heat flow distribution under the adiabatic wall.
图 5
${B_y} = 6.472{\text{ T}}$ , 压力沿驻点线线压力分布对比Figure 5. Comparison of the pressure distribution along axial line with
${B_y} = $ $ 6.472{\text{ T}}$ .
图 6 OREX外形
Figure 6. Geometry for the OREX.
图 7 不同网格下壁面热流计算结果对比
Figure 7. Heat flux distributions under different normal grid spacing at the wall.
图 8
$x = 0.06{\text{ m}}$ 时, 不同磁感应强度下的层流边界层速度分布的对比Figure 8. Comparison of laminar velocity profiles under the different magnetic field strength with x = 0.06 m.
图 9
$x = 0.06\; {\rm{m}}$ 时, 不同磁感应强度下的湍流边界层速度型面对比Figure 9. Comparison of turbulent velocity profiles under the different magnetic field strength with x = 0.06 m.
图 10 x = 0.06 m时, 不同磁感应强度下的湍流边界层温度剖面对比
Figure 10. Comparison of the turbulent temperature profiles under the different magnetic field strength with x = 0.06 m.
图 11 x = 0.06 m时, 不同磁感应强度下湍流摩阻系数对比
Figure 11. Comparison of turbulent skin friction coefficients under the different magnetic field strength with x = 0.06 m.
图 12 34°压缩拐角MHD流动控制系统局部受力机理分析
Figure 12. Analysis of local force mechanism of 34° the ramp compression corner MHD flow control system.
图 13 MHD作用位置对壁面压力系数及摩阻系数分布影响 (a) 壁面压力系数分布; (b) 摩阻系数分布
Figure 13. Effect of MHD position on wall pressure coefficient and skin friction coefficient distribution: (a) Wall pressure distribution; (b) skin friction coefficient distribution.
图 14 MHD作用位置对x = 0.4 m站位截面速度及温度分布影响 (a) 速度剖面; (b) 温度剖面
Figure 14. Effect of MHD position on velocity and temperature distribution at x = 0.4 m station section: (a) Profiles of velocities; (b) profiles of temperatures.
表 1 超声速平板湍流流动计算自由流条件
Table 1. Freestream conditions for the supersonic flat plate flow.
参数 符号 数值 马赫数 $M{a_\infty }$ 2.244 来流温度 T∞/K 278 单位雷诺数 Re∞ 4.31×107 来流密度 ρ∞/(kg·m–3) 1.0 
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表 2 圆球绕流算例计算自由流条件
Table 2. Freestream conditions for the hemisphere flow.
参数 符号/单位 数值 马赫数 $M{a_\infty }$ 5.0 来流温度 ${T_\infty }/{{\rm{K}}}$ 100 来流压力 ${P_\infty }/{ {\rm{Pa} } }$ 1587 球头半径 r/m 0.01 壁面温度 ${T_{\text{w} } }/{{\rm{K}}}$ 130 电导率 ${\sigma _{\text{e} } }/({\rm{S}} \cdot { {\text{m} }^{ - 1} })$ 794
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表 3 超声速平板磁流体湍流流动计算自由流条件
Table 3. Freestream conditions for the flat plate magnetohydrodynamic turbulent flows.
参数 符号/单位 数值 马赫数 $M{a_\infty }$ 2.0 来流温度 T∞/K 300 雷诺数 Re∞,L 3.75 × 106 来流压力 P∞/(N·m–2) 1.706 × 105 平板长度 L/m 0.08 电导率 σe/(S·m–1) 800
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表 4 34°压缩拐角磁流体湍流流动自由流条件
Table 4. Freestream conditions for the 34° ramp magnetohydrodynamic turbulent flows.
参数 符号/单位 数值 马赫数 $M{a_\infty }$ 9.22 来流温度 T∞/K 64.5 单位雷诺数 Re∞ 4.31×107 来流密度 ρ∞/(kg·m–3) 0.1368 前平板长度 L/m 0.56 壁面温度 Tw/K 295
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表 5 电磁流动控制参数
Table 5. Electromagnetic flow control parameters.
计算工况 ${x_1}/{{\rm{m}}}$ ${x_2}/{{\rm{m}}}$ ${B_{\max } }/{{\rm{T}}}$ ${\sigma _{\text{e} } }/\left( { {\rm{S} } {\cdot} { {\rm{m} }^{ - 1} } } \right)$ Case 1 0.30 0.40 4.0 4.0 Case 2 0.35 0.45 4.0 4.0 Case 3 0.40 0.50 4.0 4.0 Case 4 0.45 0.55 4.0 4.0
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[1] 谭慧俊, 李程鸿, 张悦, 李光胜 2016 推进技术 37 11
Google Scholar
Tan H J, Li C H, Zhang Y, Li G S 2016 J. Propuls. Technol. 37 11
Google Scholar
[2] Babinsky H, Harvery J K 2011 Shock Wave Boundary Layer Interactions (New York: Cambridge University Press) pp5, 6
[3] Van D M, Nedungadi A 2004 40th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Fort Lauderdale, Florida, July 11–14 2004, AIAA 2004–4129
[4] Bisek N J, Gosse R, Poggie J 2013 J. Spacecraft Rockets 50 927
Google Scholar
[5] 丁明松, 江涛, 董维中, 高铁锁, 刘庆宗, 傅杨奥骁 2019 68 174702
Google Scholar
Ding M S, Jiang T, Dong W Z, Gao T S, Liu Q Z, Fu Y A X 2019 Acta Phys. Sin. 68 174702
Google Scholar
[6] 李开, 柳军, 刘伟强 2017 66 054701
Google Scholar
Li K, Liu J, Liu W Q 2017 Acta Phys. Sin. 66 054701
Google Scholar
[7] 李逸翔, 汪球, 罗凯, 李进平, 赵伟 2021 力学学报 53 2493
Google Scholar
Li Y X, Wang Q, Luo K, Li J P, Zhao W 2021 Chin. J. Theor. Appl. Mech. 53 2493
Google Scholar
[8] Fujino T, Matsumoto Y, Ishikawa M 2016 J. Spacecraft Rockets 53 528
Google Scholar
[9] Bobashev S V, Mende N P, Sakharov V A 2003 41st Aerospace Sciences Meeting and Exhibit Reno, Nevada, January 6–9 2003, AIAA 2003-169
[10] Meyer R, Chintala N, Bystrivky B 2004 42nd AIAA Aerospace Sciences Meeting and Exhibit Reno, Nevada, January 5–8 2004, AIAA 2004-510
[11] Zaidi S H, Smith T, Macheret S 2006 44th AIAA Aerospace Sciences Meeting and Exhibit Reno, Nevada, January 9–12 2006, AIAA 2006-1006
[12] Saito S, Udagawa K, Kawaguchi K 2008 46th AIAA Aerospace Sciences Meeting and Exhibit Reno, Nevada, January 7–10 2008, AIAA 2008-1091
[13] Nagata Y, Yamada K, Abe T 2013 J. Spacecraft Rockets 50 981
Google Scholar
[14] 李益文, 樊昊, 张百灵 2017 航空学报 38 120368
Google Scholar
Li Y W, Fan H, Zhang B L 2017 Acta Aeronaut. Astronaut. Sin. 38 120368
Google Scholar
[15] Wang D, Wang J F, Li L F 2022 Aerosp. Sci. Technol. 126 107598
Google Scholar
[16] 田正雨 2008 博士学位论文 (长沙: 国防科学技术大学)
Tian Z Y 2008 Ph. D. Dissertation (Changsha: National University of Defense Technology) (in Chinese)
[17] 丁明松, 江涛, 董维中, 高铁锁, 刘庆宗 2017 航空学报 38 121030
Google Scholar
Ding M S, Jiang T, Dong W Z, Gao T S, Liu Q Z 2017 Acta Aeronaut. Astronaut. Sin. 38 121030
Google Scholar
[18] Li K 2017 Ph. D. Dissertation (Changsha: National University of Defense Technology) (in Chinese)
[19] 李开, 刘伟强 2016 65 064701
Google Scholar
Li K, Liu W Q 2016 Acta Phys. Sin. 65 064701
Google Scholar
[20] Sinha K, Candler G 1998 29th AIAA, Fluid Dynamics Conference Albuquerque, NM, June 15–18 1998, AIAA 98-2649
[21] 贺旭照 2007 博士学位论文 (绵阳: 中国空气动力研究与发展中心)
He X Z 2007 Ph. D. Dissertation (Mianyang: China Aerodynamics Research and Development Center) (in Chinese)
[22] 姚宵, 刘伟强, 谭建国 2018 67 174702
Google Scholar
Yao X, Liu W Q, Tan J G 2018 Acta Phys. Sin. 67 174702
Google Scholar
[23] Dietiker J K 2002 Ph. D. Dissertation (Wichita: Wichita State University)
[24] Settles G S, Dodson L J 1991 AIAA 22nd Fluid Dynamics, Plasma Dynamics & Lasers Conference, Honolulu, HI, June 24–26 1991, AIAA 91–1763
[25] Aithal S, Munipalli R, Shankar V 2004 Performance Enhancement of High Speed Inlets Using MHD (USA: Defense Technical Information Center) pp13–23
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