A COMPARATIVE STUDY OF TWO TURBULENCE MODELS FOR MAGNUS EFFECT IN SPINNING PROJECTILE
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摘要: 弹箭设计、弹道计算和稳定性研究都需要准确预测旋转弹箭的马格努斯力和力矩，国内针对旋转弹箭气动特性的数值模拟工作集中在旋成体上，对带翼外形进行完全时间相关的非定常研究鲜有见到；国外虽然有对带翼外形开展研究，但以验证方法为主，对湍流模型在复杂外形弹箭旋转中的研究未曾见到.采用完全时间相关的非定常N-S方程，对带翼弹箭开展计算，对比了一方程SA（Spalart-Allmaras）湍流模型和两方程k-!SST（shear-stress-transport）湍流模型对马格努斯效应产生的影响，并分析了旋转导致的边界层和涡非对称畸变，以及周向压力分布和剪切应力分布非对称畸变.结果表明：旋转引起的物面流场参数变化主要体现在弹体中后部，SA和SST湍流模型预测的全弹马格努斯特性与阿诺德工程发展中心（Arnold Engineering Development Center，AEDC）实验及陆军研究实验室（Army Research Laboratory，ARL）的计算结果一致性很好，对动导数而言两湍流模型计算精度相当.两湍流模型计算的弹体左侧流场参数差异比右侧大，分析认为正向旋转使左侧壁面速度方向与来流速度相反，相互阻碍使气流脉动效应更强.壁面附近湍流黏性系数SA结果大于SST结果，y=0截面物面压力SA结果小于SST结果、最大相差6%，摩阻系数SA结果大于SST结果、最大相差35%.SA对旋转产生的分离抑制作用强于SST.Abstract: Magnus force and moment must be predicted precisely during calculating trajectories and designing rotating projectiles.Domestic studies have focused on adult spin projectile, and foreign studies have not compared turbulence model utility in spinning wind-body combination either.This paper simulated the flow field around a spinning wind-body combination by solving unsteady compressible three dimensional Navier-Stokes equations with dual time step method.At the same time the discrepancy between Splalrt-Allmaras (SA) and k-!shear stress transport (SST) turbulence models are studied.For both turbulence models, dynamic coefficients have a good agreement with the Arnold Engineering Development Center (AEDC) experimental data and Army Research Laboratory (ARL) computational data.Flow field parameters such as velocity gradient, pressure magnitude, show significant change in the latter half profile due to spin.Distortion of boundary layer in middle and rear part is conspicuous.Asymmetric distortion of circumferential surface pressure and shear stress is the fundamental reasons for the Magnus effect.Flow field parameters on the left side of body show larger variance between SA and SST turbulence models than the right side, indicating that speed pulse and pressure fluctuation are stronger on the left.The turbulent viscosity coefficient near the wall computed by SA is larger than SST.According to the slice of y=0 m, surface pressure shows SA is smaller than SST, reaching a maximum difference of 6%, and shear stress of SA is larger than SST, up to a maximum difference of 35%.The inhibition strength for flow separation indicates that SA is stronger than SST.
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Key words:
- turbulence model /
- wing-body combination /
- spinning projectile /
- Magnus effect /
- numerical simulation
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图 3 不同网格侧向力系数对比规律($T$表示周期，$t$为时间)
Figure 3. Side force coefficient for different grids
图 5 湍流黏性系数云图($\alpha =20^\circ$，$t=T/8 $)
Figure 5. Turbulent viscosity coefficient contour (SST on the left，SA on the right，$\alpha =20^\circ$，$t=T/8 $)
图 6 $x/D =8$,$y =0$截面的速度型分布($\alpha =20^\circ$，$t= T/8 $)
Figure 6. Velocity Profile at $x/D =8$，$y =0$ ($\alpha =20^\circ$，$t= T/8 $)
图 7 $x/D =8$,$y =0$截面的压力分布($\alpha =20^\circ$，$t=T/8 $)
Figure 7. Pressure distribution at $x/D=8$，$y=0$ ($\alpha =20^\circ$，$t=T/8 $)
图 8 $x/D=9.5$截面的空间马赫、压力云图及流线分布($\alpha =20^\circ$，$t=T/8 $)
Figure 8. Mach,pressure contour and streamline distribution near the cross section $x/D=9.5$ ($\alpha =20^\circ$，$t=T/8 $)
图 9 不同周向角对应弹身表面摩阻系数沿轴向分布 \($\alpha =20^\circ$，$t= T/8 $)
Figure 9. Axis surface friction coefficient distribution versus different circumferential angle ($\alpha =20^\circ$，$t= T/8 $)
图 10 不同周向角对应弹身表面压力沿轴向分布 ($\alpha =20^\circ$，$t=T/8 $)
Figure 10. Axis surface pressure distribution versus different circumferential angle ($\alpha =20^\circ$，$t=T/8 $)
表 1 计算条件
Table 1. Calculation condition
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