﻿ 俯仰阻尼导数分量的CFD数值模拟
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1. 北京航空航天大学 航空科学与工程学院, 北京 100191;
2. 中国科学院 计算机网络信息中心, 北京 100190

Numerical simulation of individual components of pitch-damping coefficient sum
XI Ke1, YAN Chao1 , HUANG Yu1, WANG Wen1, YUAN Wu2
1. School of Aeronautic Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China;
2. Computer Network Information Center, Chinese Academy of Sciences, Beijing 100190, China
Abstract:An approach for predicting the direct damping derivatives that formed the pitch-damping sum was presented. Application of the technique was made to the axisymmetric projectile configuration as well as the non-axisymmetric winged vehicle. The plunging derivatives and pitch-damping sum were obtained using forced heave and angular motions that excited the different angular rates under the basis of Etkin's unsteady aerodynamic model. The numerical calculation method of pitch damping derivatives was studied. The investigations of HBS and Basic Finner standard model and Hyflex show that the predicted pitch-damping coefficient sum obtained by adding the individually determined coefficients is in excellent agreement with the pitch-damping coefficient sum predicted by forced angular motions and with experimental data, and the variation of the damping derivative components with the location of gravity center is also consistent with the theoretical prediction. As for winged vehicle, the plunging derivative plays a leading role in the pitch-damping coefficient sum in the supersonic region.
Key words: computational fluid dynamics     numerical simulation     direct damping derivative     plunging derivative     pitch-damping coefficient sum

1 计算方法 1.1 流动控制方程

1.2 直接阻尼导数计算方法

Cm0通过定常计算获得;Cm的计算需要考虑俯仰角速度引起的牵连速度的影响以反映局部迎角的变化,本文在空间格式及壁面边界条件中加入牵连速度的贡献,同时网格保持不动,采用准定常方法进行时间推进,经过一段暂态效应,最终力和力矩收敛到定常结果.

1.3 洗流时差导数计算方法

2 数值模拟结果及分析

2.1 HBS外形研究

HBS为一个半球柱、带有两段扩张裙部的高超声速弹道外形标模,如图 1所示.其动态特性有较为精确的试验结果[11],常被用来验证计算结果的准确程度.

 图 1 弹道外形示意图Fig. 1 Schematic of hyperballistic shape (HBS)

 图 2 弹道外形计算结果Fig. 2 Calculation results of hyperballistic shape (HBS)

 图 3 弹道俯仰阻尼导数计算结果与试验结果对比Fig. 3 Calculation and experiment results of pitch-damping derivatives for hyperballistic shape (HBS)

 α/(°) Cmq Cmq+ 0 -20.19 1.92 -18.27 -18.14 5 -20.89 3.46 -17.43 -17.58 10 -22.71 5.82 -16.89 -16.72 15 -29.33 4.17 -25.16 -25.52 20 -43.97 -10.99 -54.96 -56.05
2.2 基本带翼导弹外形研究

 图 4 基本带翼导弹外形Fig. 4 Schematic of Basic Finner

 图 5 各阻尼导数随攻角变化曲线Fig. 5 Variations of pitch-damping derivatives with angles of attack

 图 6 各阻尼导数随质心位置变化曲线Fig. 6 Variations of pitch-damping derivatives with center of gravity (CG) location

2.3 Hyflex外形研究

Hyflex(Hypersonic Flight Experiment)是日本HOPE-X计划中有关大气层再入项目的带翼升力体外形高超声速飞行器,用于验证制导和控制以及热防护材料和结构等技术.它于1996年2月进行飞行试验,本文选取其飞行末端弹道点(马赫2.0,高度30km)进行研究[15],该弹道点处于飞行器减速伞开伞前,其动态特性对于减速伞的开启有着至关重要的影响.飞行器外形三视图及网格图见图 7.

 图 7 Hyflex外形及网格图Fig. 7 Schematic and mesh of Hyflex

 α/(°) Cmq Cmq+ 0 -0.241 -0.243 -0.484 -0.468 5 -0.249 -0.308 -0.557 -0.538 10 -0.252 -0.783 -1.035 -0.968 15 -0.270 -0.989 -1.259 -1.253 20 -0.286 -0.146 -0.432 -0.412

3 结 论

1) 采用的方法能够准确预测飞行器外形的俯仰阻尼导数的各个分量,即使对于大攻角状态也具有较好的预测精度,具备一定的工程实用价值;

2) 对于弹丸类弹道物体,其在超声速及高超声速状态下,洗流时差导数在俯仰阻尼导数中所占比例较小,但其符号可能大于零,起动不稳定作用,并且数值随质心后移而增大;对于带翼飞行器,超声速状态下,洗流时差导数在俯仰阻尼导数中所占比例较大.

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#### 文章信息

XI Ke, YAN Chao, HUANG Yu, WANG Wen, YUAN Wu

Numerical simulation of individual components of pitch-damping coefficient sum

Journal of Beijing University of Aeronautics and Astronsutics, 2015, 41(2): 222-227.
http://dx.doi.org/10.13700/j.bh.1001-5965.2014.0094