کمی‌سازی وقوع ناپایداری ویسکوز فینگرینگ جریان سیال در محیط متخلخل

نوع مقاله : مقاله پژوهشی

نویسندگان

1 خواجه نصیر

2 دانشگاه صنعتی خواجه نصیر الدین طوسی

چکیده

در این مقاله ناپایداری انگشتی لزج در فرایند جابجایی دو سیال قابل امتزاج با وجود ذرات نانو در یک محیط متخلخل همگن به صورت غیرخطی شبیه‌سازی و تحلیل فرکتالی شده‌است. با توجه به فرکتالی بودن مرز مشترک ناپایداری بین دو سیال، با معرفی بعد فرکتالی به عنوان مشخصه ناپایداری، برای پارامترهای موثر بر ناپایداری همچون ضریب رسوب، نسبت تحرک بین مولفه‌ها و ضرایب پخش، بعد فرکتالی در زمان‌های مختلف با استفاده از روش جعبه شمارنده محاسبه و در مورد آن بحث شده‌است. نتایج نشان می‌دهد که  افزایش ضریب رسوب باعث کاهش پیچیدگی الگوی‌های انگشتی و بعد فرکتالی‌ می‌شود و افزایش ضریب پخش ذرات نانو تاثیر چندانی بر بعد ندارد، این در حالی است که افزایش ضریب پخش سیال جابجاشونده به شدت بعد فرکتالی را افزایش و الگو‌ها را پیچیده‌تر می‌کند. همچنین بررسی فرکتالی نشان می‌دهد در صورت وجود ضریب رسوب، افزایش مقدار نسبت تحرک سیال تاثیری بر پیچیدگی الگوها نداشته و مقدار زمان موثر ثابت و برابر 275 باقی می‌ماند، اما هر دو واحد افزایش مقدار نسبت تحرک، 25 واحد شروع ناپایداری را به تاخیر می‌اندازد. نتایج نشان می‌دهد که آنالیز فرکتالی می‌تواند در کنار سایر مشخصه‌ها، یکی از مواردی باشد که به تحلیل ناپایداری انگشتی کمک می‌کند. 

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Quantifying of viscous fingering instability in porous media

نویسندگان [English]

  • mohammad reza shah nazari 1
  • Ali Saberi 2
1 associate prof./ Mechanical faculty/K.N.Toosi university of technology
2 mechanical faculty/ K.N.Toosi university of Technology
چکیده [English]

In this paper, nonlinear simulation of viscous fingering instability of miscible displacement involving nanofluid is investigated. Using vorticity and stream functions and the spectral method governing equations are obtained. Due to the fractality of fluid-fluid interface in instability phenomena, by using box counting method, its fractal dimension is calculated in different parameters such as deposition rate, mobility ratio and diffusion rates. The results show that increasing the deposition rate reduces the complexity of finger patterns and the diffusion rate of nanofluid has no effect on complexity of finger patterns while increasing the diffusion rate of displaced fluid has significant effect on patterns and makes it more complicated. The fractal analysis also shows that the effect of mobility ratio depends on the deposition rate.  By considering deposition rate, although the mobility ratio has no effect on fractal dimension and effective time is constant and equal to 275, start time of instability is delayed by 25 units. It can be concluded that fractal analysis of viscous fingering phenomena can be considered as one of the instability characteristics.

کلیدواژه‌ها [English]

  • Instability
  • Viscous fingering
  • Nanoparticle
  • Fractal Analysis
  • Nonlinear Simulation
 
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