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Constitutive equations for granular flow with uniform mean shear and spin fields
Numerical simulations of two-dimensional granular flows under uniform shear and external body torque were performed in order to extract the constitutive equations for the system. The outcome of the numerical simulations is analyzed on the basis of the micropolar fluid model. Uniform mean shear field...
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Інститут фізики конденсованих систем НАН України
2011
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irk-123456789-1199382017-06-11T03:04:38Z Constitutive equations for granular flow with uniform mean shear and spin fields Takechi, K. Yoshida, K. Arimitsu, T. Numerical simulations of two-dimensional granular flows under uniform shear and external body torque were performed in order to extract the constitutive equations for the system. The outcome of the numerical simulations is analyzed on the basis of the micropolar fluid model. Uniform mean shear field and mean spin field, which is not subordinate to the vorticity field, are realized in the simulations. The estimates of stresses based on kinetic theory by Lun [Lun, J. Fluid Mech., 1991, 233, 539] are in good agreement with the simulation results for a low area fraction ν = 0.1 but the agreement becomes weaker as the area fraction gets higher. However, the estimates in the kinetic theory can be fitted to the simulation results up to ν = 0.7 by renormalizing the coefficient of roughness. For a relatively dense granular flow (ν= 0.8), the simulation results are also compared with Kanatani’s theory [Kanatani, Int. J. Eng. Sci., 1979,17, 419]. It is found that the dissipation function and its decomposition into the constitutive equations in Kanatani’s theory are not consistent with the simulation results. Для того, щоб виокремити матерiальнi рiвняння для системи були здiйсненi числовi симуляцiї двовимiрних гранульованих потокiв пiд дiєю однорiдного зсуву i зовнiшнього крутильного моменту. Результат чисельних симуляцiй проаналiзовано на основi моделi мiкрополярного плину. В симуляцiях реалiзується поле однорiдного середнього зсуву, яке не є пiдпорядковане полю вихоровостi. Оцiнки напружень, зробленi на основi кiнетичної теорiї Люна [Lun, J. Fluid Mech.233 (1991) 539], добре узгоджуються з результатами симуляцiй в областi низьких часток ν = 0.1, але узгодження погiршується, якщо ця величина зростає. Проте, оцiнки, зробленiв кiнетичнiй теорiї можуть бути пiдiгнанiдо результатiв симуляцiй аж до ν = 0.7 шляхом ренормалiзацiї коефiцiнта шорсткостi. Для вiдносно густого гранульованого потоку(ν= 0.8), результати симуляцiй також порiвнюються з теорiєю Канатанi [Kanatani, Int. J. Eng. Sci17(1979) 419]. Знайдено, що дисипативна функцiя i її декомпозицiя в матерiальнi рiвняння в теорiї Канатанiне узгоджується з результатами симуляцiй. 2011 Article Constitutive equations for granular flow with uniform mean shear and spin fields / K. Takechi, K. Yoshida, T. Arimitsu // Condensed Matter Physics. — 2011. — Т. 14, № 1. — С.13401: 1-22. — Бібліогр.: 31 назв. — англ. 1607-324X PACS: 45.70.Mg, 47.57.Gc, 47.50.-d DOI:10.5488/CMP.14.13401 arXiv:1106.5306 http://dspace.nbuv.gov.ua/handle/123456789/119938 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| language |
English |
| description |
Numerical simulations of two-dimensional granular flows under uniform shear and external body torque were performed in order to extract the constitutive equations for the system. The outcome of the numerical simulations is analyzed on the basis of the micropolar fluid model. Uniform mean shear field and mean spin field, which is not subordinate to the vorticity field, are realized in the simulations. The estimates of stresses based
on kinetic theory by Lun [Lun, J. Fluid Mech., 1991, 233, 539] are in good agreement with the simulation results for a low area fraction ν = 0.1 but the agreement becomes weaker as the area fraction gets higher. However, the estimates in the kinetic theory can be fitted to the simulation results up to ν = 0.7 by renormalizing the coefficient of roughness. For a relatively dense granular flow (ν= 0.8), the simulation results are also compared with Kanatani’s theory [Kanatani, Int. J. Eng. Sci., 1979,17, 419]. It is found that the dissipation
function and its decomposition into the constitutive equations in Kanatani’s theory are not consistent with the simulation results. |
| format |
Article |
| author |
Takechi, K. Yoshida, K. Arimitsu, T. |
| spellingShingle |
Takechi, K. Yoshida, K. Arimitsu, T. Constitutive equations for granular flow with uniform mean shear and spin fields Condensed Matter Physics |
| author_facet |
Takechi, K. Yoshida, K. Arimitsu, T. |
| author_sort |
Takechi, K. |
| title |
Constitutive equations for granular flow with uniform mean shear and spin fields |
| title_short |
Constitutive equations for granular flow with uniform mean shear and spin fields |
| title_full |
Constitutive equations for granular flow with uniform mean shear and spin fields |
| title_fullStr |
Constitutive equations for granular flow with uniform mean shear and spin fields |
| title_full_unstemmed |
Constitutive equations for granular flow with uniform mean shear and spin fields |
| title_sort |
constitutive equations for granular flow with uniform mean shear and spin fields |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/119938 |
| citation_txt |
Constitutive equations for granular flow with uniform mean shear and spin fields / K. Takechi, K. Yoshida, T. Arimitsu // Condensed Matter Physics. — 2011. — Т. 14, № 1. — С.13401: 1-22. — Бібліогр.: 31 назв. — англ. |
| series |
Condensed Matter Physics |
| work_keys_str_mv |
AT takechik constitutiveequationsforgranularflowwithuniformmeanshearandspinfields AT yoshidak constitutiveequationsforgranularflowwithuniformmeanshearandspinfields AT arimitsut constitutiveequationsforgranularflowwithuniformmeanshearandspinfields |
| first_indexed |
2023-10-18T20:35:41Z |
| last_indexed |
2023-10-18T20:35:41Z |
| _version_ |
1796150603777310720 |