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刘耀峰 , 徐文灿 , 吴甲生 . 翼身组合体超声速来流与横向喷流干扰流场的数值模拟 [J ] . 兵工学报 , 2007 , 28 ( 8 ): 965 - 969 . 利用对称TVD格式和重叠网格技术数值求解层流N-S方程，模拟了翼身组合体构形的横向喷流干扰流场，研究了该流场的涡系结构、波系结构及流动分离等流场特性，讨论了干扰效应对气动性能的影响，计算了干扰力放大因子和干扰力矩系数，其结果与实验结果基本相符。

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王玉芳 , 杨树兴 . 旋转状态下姿态控制发动机喷流流场的数值模拟 [J ] . 兵工学报 , 2006 , 27 ( 5 ): 948 - 952 . 为了对姿态控制发动机在旋转状态时的喷流流场进行数值模拟，并避开复杂的滑移网格技术，将惯性坐标系下的控制方程和数值计算边界条件用弹体旋转坐标系来表达，选用雷诺平均的旋转坐标系下的Navier-Stokes方程，算例计算结果与采用滑移网格技术得到的流场结构相比更接近实测且计算容易收敛，表明这种方法正确且简单可行。数值计算结果表明：在弹体直径以及喷口大小及入口条件一定的前提下，由于旋转引起的喷流流动的非对称性将直接影响到姿态喷流控制力的大小和方向，进而影响到姿态控制发动机的工作效率；随着旋转角速率的增大，推力矢量明显变化，控制推力偏转，使有效揎制推力减小，从而影响远程火箭弹的稳定性和姿态控制精度，并在一定程度上增加了燃气消耗量。

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王树军 , 胡俊 , 吴甲生 , 等 . 旋转导弹横向喷流/超声速来流干扰数值模拟 [J ] . 兵工学报 , 2008 , 29 ( 10 ): 1220 - 1226 . 以旋转坐标系下Navier- Stokes方程为控制方程，用有限体积法、对称TVD格式和重叠网格技术对带有单股和两股横向喷流旋转导弹的喷流干扰流场进行了数值模拟，计算了喷流与来流、喷流与喷流之间的干扰情况。结果表明：两股喷流增强了与来流之间的干扰，喷流与喷流间也存在干扰；两种干扰影响使力放大因子较单股喷流高；旋转使喷口前的分离区形状改变；在背风面喷流时，旋转使喷流羽流发生周向偏转，影响喷流干扰力放大因子。

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ZHANG J W , LEI J M , NIU J P . Numerical investigation of aerodynamic characteristics of free-spinning tail projectile with canards roll control [J ] . Proceedings of the Institution of Mechanical Engineers Part G Journal of Aerospace Engineering , 2020 , 235 ( 6 ): 687 - 702 . DOI: 10.1177/0954410020953316 http://doi.org/10.1177/0954410020953316 http://journals.sagepub.com/doi/10.1177/0954410020953316 http://journals.sagepub.com/doi/10.1177/0954410020953316 To reduce aerodynamic coupling between the canards and the tail fins of a canard-controlled projectile, the afterbody of the projectile is decoupled from the forebody by a bearing structure, namely, a free-spinning tail. A series of numerical simulations was conducted for different angles of attack using NASA’s canard-controlled projectile with a free-spinning tail. The results were then compared with the wind tunnel test data. The spin rate of the free-spinning tail shows that, with the canard roll control, the tail section will rotate at lower angles of attack and “lock-in” at higher ones, demonstrating nonlinearization between the rotating rate and the angle of attack. According to a flow structure analysis, the circular flow velocity induced by canards is responsible for the non-linear characteristics of the tail. Moreover, the change in position of the circular flow velocity results in a reverse of the rolling moment of the “+” fixed tail projectile at different angles of attack. Furthermore, a comparison of the aerodynamic characteristics of the fixed (“+” and “x”) and free-spinning tail configurations proves that when the tail is spinning, all the aerodynamic coefficients of the free-spinning tail projectile are between those of the “+” and “x” fixed tail projectiles. The longitudinal difference in aerodynamic characteristics is related to the rolling angle, whereas the lateral difference is related to both the rolling angle and rotation rate. When the tail section “locks-in,” different rolling angles lead to different characteristics in both the longitudinal and lateral directions.

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GAO Y , LEI J M , YIN J T . Magnus effect over aerodynamic components of spinning missile [J ] . International Journal of Aeronautical and Space Sciences , 2022 , 23 ( 3 ): 447 - 460 . DOI: 10.1007/s42405-022-00452-9 http://doi.org/10.1007/s42405-022-00452-9 To reveal the flow mechanism of the Magnus effect of the spinning missile, the flow field under supersonic conditions was numerically simulated based on the unsteady Reynolds-time-averaged Navier–Stokes equation, and the implicit dual-time stepping method and sliding mesh method were used. Validation was performed to ensure the reliability of the numerical methods. The results of the numerical simulation and the wind-tunnel experimental data coincided quite well. The aerodynamic characteristics of various configurations while spinning were calculated. The effect of aerodynamic components and aerodynamic interference between components on the Magnus effect were analyzed. The results indicate that for the projectile body, the interference of the canard enlarges the time-averaged side force; when the slenderness ratio becomes large, from the view of the base, the left leeward separation vortex is close to the surface, resulting in a low-pressure region, and the direction of the side force and yawing moment are changed. The fin installation angle can weaken the body Magnus effect to some extent. For the projectile fin, the influence of leeward separation vortices on the fin depends on their relative positions. The fin installation angle can weaken and even cause the reversal of the side force direction.

VITI V , NEEL R , SCHETZ J A . Detailed flow physics of the supersonic jet interaction flow field [J ] . Physics of Fluids , 2009 , 21 ( 4 ): 046101 . DOI: 10.1063/1.3112736 http://doi.org/10.1063/1.3112736 https://pubs.aip.org/pof/article/21/4/046101/314289/Detailed-flow-physics-of-the-supersonic-jet https://pubs.aip.org/pof/article/21/4/046101/314289/Detailed-flow-physics-of-the-supersonic-jet The supersonic jet interaction flow field generated by a sonic circular jet with a pressure ratio of 532 exhausting into a turbulent MACH 4.0 cross flow over a flat plate was investigated using numerical simulations. The simulations made use of the three-dimensional Reynolds-averaged Navier–Stokes (RANS) equations coupled with Wilcox’s 1998 k-ω turbulence model. The numerical solution was validated with experimental data that include the pressure distribution on the flat plate, with an empirical formula for the height of the barrel shock, and with the Schlieren pictures showing the location and shape of the main shock formations. The simulations correctly captured the location and shape of the main flow features and compared favorably with the experimental pressure distribution on the flat plate. The validated numerical simulation was used to investigate in detail the flow physics. The flow field was found to be dominated by the shock formations and their coupling with the strong vortical structures. Three primary shock formations were observed: a barrel shock, a bow shock, and a separation-induced shock wave. While the general structure of the barrel shock was found to be similar to that of the underexpanded jet exhausting into a quiescent medium, two unique features distinguished the flow field: the concave indentation in the leeside of the recompression (barrel) shock and the folding of the windward side of the barrel shock due to an inner reflection line. The presence of the steep pressure gradients associated with the shocks creates strong vortical motions in the fluid. Six primary vortices were identified: (i) the well-known horseshoe vortex, (ii) an upper trailing vortex, (iii) two trailing vortices formed in the separation region and, aft of the bow shock wave, (iv) two more trailing vortices that eventually merge together into one single rotational motion. The low-pressure region aft of the injector was found to be generated by the combined effect of the concave indentation in the leeside of the barrel shock and the lower trailing vortices. The trailing vortices were found to be the main mechanism responsible for the mixing of the injectant with the freestream fluid.

CORTELEZZI L , KARAGOZIAN A R . On the formation of the counter-rotating vortex pair in transverse jets [J ] . Journal of Fluid Mechanics , 2001 , 446 : 347 - 373 . DOI: 10.1017/S0022112001005894 http://doi.org/10.1017/S0022112001005894 https://www.cambridge.org/core/product/identifier/S0022112001005894/type/journal_article https://www.cambridge.org/core/product/identifier/S0022112001005894/type/journal_article Among the important physical phenomena associated with the jet in crossflow is \nthe formation and evolution of vortical structures in the flow field, in particular \nthe counter-rotating vortex pair (CVP) associated with the jet cross-section. The \npresent computational study focuses on the mechanisms for the dynamical generation \nand evolution of these vortical structures. Transient numerical simulations of the \nflow field are performed using three-dimensional vortex elements. Vortex ring rollup, \ninteractions, tilting, and folding are observed in the near field, consistent with the \nideas described in the experimental work of Kelso, Lim & Perry (1996), for example. \nThe time-averaged effect of these jet shear layer vortices, even over a single period \nof their evolution, is seen to result in initiation of the CVP. Further insight into \nthe topology of the flow field, the formation of wake vortices, the entrainment of \ncrossflow, and the effect of upstream boundary layer thickness is also provided in this \nstudy.