تأثیر گام زمانی بر دقت نتایج در شبیه‌سازی حرکت ذرات به روش اجزای گسسته (راگ)

نوع مقاله: مقاله پژوهشی

نویسندگان

چکیده

روش اجزای گسسته (راگ) جهت شبیه‌سازی حرکت ذرات در سیستم‌های فرآوری کاربرد وسیعی دارد. اساس این روش محاسبه نیروهای متقابل میان ذرات در هر برخورد و مدل کردن موقعیت جدید ذرات است. تعداد زیاد اجزا و روابط متعدد، باعث طولانی شدن زمان انجام محاسبات در راگ می‌شود. زمان لازم برای محاسبات بستگی زیادی به گام زمانی انتخاب‌شده برای شبیه‌سازی دارد. اگر گام زمانی کوچک در نظر گرفته شود، حجم محاسبات و به دنبال آن زمان لازم جهت شبیه‌سازی افزایش می‌یابد. از طرف دیگر، در صورتی که گام زمانی بزرگ در نظر گرفته شود، شبیه‌سازی به دلیل عدم توجه لازم به فرآیند برخورد، با خطا همراه خواهد بود. در راگ گام زمانی به صورت ضریبی از زمان تماس دو ذره در یک برخورد، در نظر گرفته می‌شود. هدف این پژوهش ارائه‌ی رابطه‌ای برای تعیین گام زمانی شبیه‌سازی با توجه به شرایط عملیاتی و میزان خطای شبیه‌سازی بود. برای این کار ابتدا رابطه‌ی بین ضریب زمان تماس و خطای شبیه‌سازی ارائه شد و روابط معمول زمان تماس اصلاح گردید. نتایج نشان دادند که گام زمانی لازم جهت شبیه‌سازی با خطای 5% برای ذراتی به شعاع 3 سانتیمتر، مدول الاستیسیته‌ی 210 گیگا پاسکال با سرعت نسبی برخورد 5/0 متر بر ثانیه، با استفاده از مدل نیروی برخورد هرتز- میندلین 3/2 میکروثانیه است که تقریباً 12 برابر بیشتر از مدل خطی است. به منظور سرعت بخشیدن به محاسبات که با بزرگ مقیاس کردن اندازه‌ی ذرات حاصل می‌شود، مشخص گردید که با افزایش شعاع ذرات به 1 متر، گام زمانی لازم برای شبیه‌سازی، 33 برابر افزایش می‌یابد. کاهش مدول الاستیسیته به مقدار 1/2 مگاپاسکال باعث افزایش 316 برابری گام زمانی در مدل خطی و 100 برابری در مدل هرتز- میندلین گردید.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Effect of Time Step in Accuracy of Particle Movement Prediction using Discrete Element Method (DEM)

نویسندگان [English]

  • A Ghasemi
  • S.O Mousavi
  • S Banisi
چکیده [English]

Discrete Element Method (DEM) is extensively used to simulate the behavior of particles in various processing units. This method is based on modeling the forces acting between particles in any contact and consequently calculating the new position of particles. The high number of elements and numerous equations is very time-consuming even when using computers with very fast processors. The required computation time mainly depends on the time step. If the time step is chosen very short, the computation time will significantly increase. On the other hand, if the time step is chosen very long, the simulation will be Inaccurate due to not fully observing the contacts. In DEM calculations, the time step is chosen as a fraction of the collision time. In this research, a relationship was proposed between the contact time fraction and the error of simulation. In other words, to select the time step in addition to physical parameters, the accuracy of the simulation was also accommodated in the frequently-used relationships. The required time steps to achieve the simulation error of 5% were calculated for two common contact-force models namely, Hertz-Mindlin and linear spring-dashpot. The simulation was performed for two particles with radius of 3 cm, Elasticity modulus of 210 GPa, Poisson's ratio of 0.3 and relative velocity of 0.5 m/s. The required time steps were found to be 2.3 and 0.19 µs for the Hertz-Mindlin and linear spring-dashpot contact-force models, respectively. Results showed that with a scale-downing the modulus from 210 GPa to 2.1 MPa, the required time steps for the Hertz-Mindlin and linear spring-dashpot contact force models, with equal simulation error, increased by 100 and 316 times, respectively.

کلیدواژه‌ها [English]

  • Time step
  • DEM
  • Simulation Error
  • Contact models
  • Computation time
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