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Size scaling relation of velocity field in granular flows and the Beverloo law

机译：颗粒流中速度场的大小比例关系和Beverloo定律

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摘要

In a hopper with cylindrical symmetry and an aperture of radius R, the vertical velocity of granular flow v z depends on the distance from the hopper's center r and the height above the aperture z and v z = v z (r, z; R). We propose that the scaled vertical velocity v z (r, z; R)/v z (0, 0; R) is a function of scaled variables r/R r and z/R z, where R r = R - 0.5d and R z = R - k 2 d with the granule diameter d and a parameter k 2 to be determined. After scaled by v 2 z (0, 0; R)/R z, the effective acceleration a eff (r, z; R) derived from v z is a function of r/R r and z/R z also. The boundary condition a eff (0, 0; R) = - g of granular flows under earth gravity g gives rise to v z (0, 0; R). v g R - k 2 d 1/2. Our simulations using the discrete element method and GPU program in the three- dimensional and the two- dimensional hoppers confirm the size scaling relations of v z (r, z; R) and v z (0, 0; R). From the size scaling relations, we obtain the mass flow rate of D- dimensional hopper W. v g(R - 0.5d) D- 1 (R - k 2 d) 1/2, which agrees with the Beverloo law at R d. It is the size scaling of vertical velocity field that results in the dimensional R- dependence of W in the Beverloo law.
机译：在具有圆柱对称性且孔径为R的漏斗中，颗粒流的垂直速度v z取决于距漏斗中心r的距离和孔径z上方的高度，并且v z = v z（r，z; R）。我们提出标度垂直速度vz（r，z; R）/ vz（0，0; R）是标度变量r / R r和z / R z的函数，其中R r = R-0.5d和R z ＝ R-k 2 d，其中颗粒直径为d，参数为k 2待确定。在按v 2 z（0，0; R）/ R z缩放后，从v z导出的有效加速度a eff（r，z; R）也是r / R r和z / R z的函数。边界条件a eff（0，0; R）=-在地球重力g下的颗粒流g产生v z（0，0; R）。 v g R-k 2 d 1/2。我们在三维和二维料斗中使用离散元素方法和GPU程序进行的仿真确定了v z（r，z; R）和v z（0，0; R）的尺寸比例关系。从尺寸比例关系中，我们获得D维料斗W的质量流率。vg（R-0.5d）D-1（R-k 2 d）1/2，这与B d。在Beverloo定律中，垂直速度场的尺寸缩放导致W的尺寸与R的关系。

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  • 来源
    《Granular matter》 |2019年第2期|21.1-21.6|共6页
  • 作者

    Hu Gaoke; Lin Ping; Zhang Yongwen; Li Liangsheng; Yang Lei; Chen Xiaosong;

  • 作者单位

    Chinese Acad Sci, Inst Theoret Phys, Key Lab Theoret Phys, POB 2735, Beijing 100190, Peoples R China|Univ Chinese Acad Sci, Sch Phys Sci, 19A Yuquan Rd, Beijing 100049, Peoples R China;

    Chinese Acad Sci, Inst Modern Phys, 509 Nanchang Rd, Lanzhou 730000, Gansu, Peoples R China;

    Chinese Acad Sci, Inst Theoret Phys, Key Lab Theoret Phys, POB 2735, Beijing 100190, Peoples R China|Univ Chinese Acad Sci, Sch Phys Sci, 19A Yuquan Rd, Beijing 100049, Peoples R China;

    Sci & Technol Electromagnet Scattering Lab, Beijing 100854, Peoples R China;

    Chinese Acad Sci, Inst Modern Phys, 509 Nanchang Rd, Lanzhou 730000, Gansu, Peoples R China;

    Chinese Acad Sci, Inst Theoret Phys, Key Lab Theoret Phys, POB 2735, Beijing 100190, Peoples R China|Univ Chinese Acad Sci, Sch Phys Sci, 19A Yuquan Rd, Beijing 100049, Peoples R China;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Granular flow; Beverloo law; Size scaling relation;

    机译：颗粒流;贝弗卢定律;尺寸比例关系;

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