高速气体与椭圆柱云相互作用的数值研究

王雅 蒋灵杰 邓小龙

王雅, 蒋灵杰, 邓小龙. 高速气体与椭圆柱云相互作用的数值研究[J]. 高压物理学报, 2020, 34(1): 012301. doi: 10.11858/gywlxb.20190748
引用本文: 王雅, 蒋灵杰, 邓小龙. 高速气体与椭圆柱云相互作用的数值研究[J]. 高压物理学报, 2020, 34(1): 012301. doi: 10.11858/gywlxb.20190748
WANG Ya, JIANG Lingjie, DENG Xiaolong. Numerical Study of the Interaction between High-Speed Gas and Elliptical Column Cloud[J]. Chinese Journal of High Pressure Physics, 2020, 34(1): 012301. doi: 10.11858/gywlxb.20190748
Citation: WANG Ya, JIANG Lingjie, DENG Xiaolong. Numerical Study of the Interaction between High-Speed Gas and Elliptical Column Cloud[J]. Chinese Journal of High Pressure Physics, 2020, 34(1): 012301. doi: 10.11858/gywlxb.20190748

高速气体与椭圆柱云相互作用的数值研究

doi: 10.11858/gywlxb.20190748
基金项目: 中国工程物理研究院院长基金(201501043);国家自然科学基金(U1530401)
详细信息
    作者简介:

    王 雅(1994-),女,学士,主要从事流体力学研究. E-mail: wangya@csrc.ac.cn

    通讯作者:

    邓小龙(1981-),男,博士,特聘研究员,主要从事流体力学研究.E-mail: xiaolong.deng@csrc.ac.cn

  • 中图分类号: O359; O354.5

Numerical Study of the Interaction between High-Speed Gas and Elliptical Column Cloud

  • 摘要: 高速颗粒流在天文、自然灾害、工业安全、医疗工业和国防等领域有着重要应用。采用基于分层流模型的直接数值模拟方法,对平面激波与椭圆柱云的相互作用进行数值研究,重点关注椭圆柱横截面的不同长短轴之比和椭圆柱横截面长轴与来流方向所成角度对流场的影响,从气体来流方向上的速度、x轴和y轴方向上的均方根速度、动能、内能和湍动能的分布上进行分析,对能量在计算域的上游区域、椭圆柱云区域和下游区域进行定量分析。同时针对椭圆柱改进了一维体积平均模型,利用该模型拟合了由直接数值模拟得到的反射激波和透射激波位置,获得了最适配的一维体积平均模型中的人工有效阻力系数,并探讨此系数的分布规律。

     

  • 图  椭圆柱横截面几何示意图

    Figure  1.  Illustration of the geometry for the cross-section of the elliptical cylinder

    图  分层流模型示意图[25]i–1、ii + 1表示网格索引号,界面$\overline {ab} $$\overline {ef} $为气-气界面,$\overline {bc} $$\overline {fg} $为气-固界面,$\overline {cd} $$\overline {gh} $为固-固界面)

    Figure  2.  Illustration of the stratified flow model[25] (Where i –1, i and i + 1 are the indexes of the cell. $\overline {ab} $ and $\overline {ef} $ are the interfaces between the gas phases, $\overline {bc} $ and $\overline {fg} $ are the interfaces between the gas phase and solid phase, $\overline {cd} $ and $\overline {gh} $ are the interfaces between the solid phases.)

    图  网格收敛性分析实验示意图

    Figure  3.  Illustration of the convergence analysis experiment

    图  x-y平面计算区域设置示意图(右图为初始椭圆柱云分布图,蓝色表示低压区域,红色表示高压区域)

    Figure  4.  Illustration of the computational domain setting in the x-y plane (The right plot shows the initial distribution of the elliptical cylinder cloud. The red and blue regions represent the high-pressure and low-pressure regions, respectively.)

    图 λ = 2、θ = 0°时,不同无量纲时间下流场的无量纲压强分布

    Figure  5.  Distributions of the dimensionless pressure at different dimensionless time when λ = 2 and θ = 0°

    图  t = 3.5时不同λθ分别为0°、45°、90°、135°时的流场速度、流场内能和流场动能分布(灰色矩形区域表示椭圆柱云,RS、TS、UFC、DFC分别表示反射激波、透射激波、椭圆柱云上游边界、椭圆柱云下游边界)

    Figure  6.  Distributions of the fluid velocity, fluid internal energy and fluid kinetic energy with different λ when θ equals to 0°, 45°, 90°, 135° at dimensionless time t = 3.5 (The gray rectangular regions stand for the elliptical cylinder cloud. Hereafter, RS, TS,UFC and DFC mean reflected shock, transmitted shock, the upstream front of elliptical column cloud, and the downstream front of elliptical column cloud, respectively.)

    图  t = 3.5时不同θλ分别为2、3、4时,流场速度、流场内能和流场动能的分布(灰色矩形区域表示椭圆柱云)

    Figure  7.  Distributions of the fluid velocity, fluid internal energy and fluid kinetic energy with different θ, when λ equals to 2, 3, 4, at dimensionless time t = 3.5, where the gray rectangular regions stand for the elliptical cylinder cloud

    图  t = 3.5,θ = 0°, 45°, 90°, 135°时流场RMS速度${u''}$${v''}$以及湍动能k在不同λ下沿x方向的分布

    Figure  8.  Distributions of the fluid RMS velocity ${u''}$, ${v''}$ and turbulent kinetic energy k in the x-direction at different λ, when θ is equal to 0°, 45°, 90°, 135° at dimensionless time t = 3.5

    图  t = 3.5时不同θλ下流场内能、流场动能和流场湍动能在计算域上游区域($x \in \left[ { - 3.0, - 0.5} \right]$)、椭圆柱云区域($x \in \left[ { - 0.5,0.5} \right]$)和计算域下游区域($x \in \left[ {0.5, 4.0} \right]$)分布

    Figure  9.  Distributions of the fluid internal energy, fluid kinetic energy and fluid turbulent kinetic energy at different θ and λ in three different regions, that is the upstream area of the domain $x \in \left[ { - 3.0, - 0.5} \right]$, elliptical column cloud area $x \in \left[ { - 0.5,0.5} \right]$, the downstream area of the domain $x \in \left[ {0.5, 4.0} \right]$ at dimensionless time t = 3.5

    图  10  不同角度θ和不同λ下流场内能、流场动能和流场湍动能随无量纲时间t的变化

    Figure  10.  Variations of the fluid internal energy, fluid kinetic energy and fluid turbulent kinetic energy with dimensionless time t at different θ and λ

    图  11  t = 3.5时不同的λθ下一维体积平均模型与DNS拟合结果

    Figure  11.  Fitting results of the 1-D volume-averaged model and DNS at different λ and θ when the dimensionless time is equal to 3.5

    图  12  人工有效阻力系数Cd的最优取值分布

    Figure  12.  Distribution for the optimal value of artificial effective drag coefficient Cd

    表  1  网格收敛性分析实验中使用的4种网格

    Table  1.   Four meshes used in the convergence analysis experiment

    MeshnbNxNy
    1 811264
    216224128
    332448256
    464896512
    下载: 导出CSV

    表  2  平面激波与椭圆柱云相互作用数值模拟使用的网格设置

    Table  2.   Mesh settings in numerical simulation of the interaction between plane shock and elliptical column cloud

    λNpabΔx/10–4NxNyN/106
    24400.029 440.014 724.593 8942 176 8.5
    34400.036 040.012 023.754 7632 66612.7
    44400.041 640.010 413.255 5003 07816.9
    下载: 导出CSV

    表  3  人工有效阻力系数Cd的最优取值

    Table  3.   Optimal values of artificial effective drag coefficient Cd

    λCd
    θ = 0°θ = 15°θ = 30°θ = 45°θ = 60°θ = 90°θ = 135°
    21.191.061.061.422.22 6.001.68
    30.860.670.691.482.8014.001.29
    40.570.580.471.303.0036.001.15
    下载: 导出CSV
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  • 收稿日期:  2019-03-25
  • 修回日期:  2019-05-07

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