توسعه روش پیش‌شرط توانی برای شبیه‌سازی جریان‌های ناپایای سیالات ویسکوالاستیک

نوع مقاله : مقاله پژوهشی

نویسندگان

مهندسی مکانیک، دانشگاه صنعتی شاهرود، شاهرود، ایران

چکیده

یکی از ویژگی منحصربه‌فرد سیالات ویسکوالاستیک در جریان‌های برشی ناپایای، رفتار نوسانی میراشونده در میدان سرعت بدون اعمال نوسان و نیروی خارجی است؛ عامل به وجود آورنده این ویژگی خاصیت الاستیک آن است. در مقاله حاضر، برای اولین بار از روش پیش‌شرط‌توانی حسگر محلی تنش برای پایداری حل عددی جریان‌های ناپایای سیال ویسکوالاستیک در حال عبور از بین دو صفحه موازی ثابت استفاده می‌شود. برای شبیه‌سازی حاضر، از مدل ماکسول ساده استفاده شده است. در این روش با افزودن جمله مشتق زمانی کاذب به معادلات حاکم، شکل معادلات هذلولوی می‌شود. با به دست آوردن ماتریس پیش‌شرط این معادلات که از رابطه‌توانی میدان تنش به صورت محلی تصحیح می‌شود، با استفاده از یک الگوریتم دوزمانه که شامل حلقه داخلی و خارجی است، حل معادلات جریان ناپایای تراکم‌ناپذیر به‌صورت تراکم‌پذیری مصنوعی امکان‌پذیر می‌شود. جهت همگرایی حلقه داخلی ، از روش عددی وثوقی‌فر چهارمرحله‌ای استفاده می‌شود. جهت گسسته‌سازی معادلات از روش تفاضل محدود و شبکه جابجا شده استفاده شده است. محاسبات جریان‌های ناپایای سیال ویسکوالاستیک برای اعداد رینولدز، اعداد وایزنبرگ و مقادیر نسبت لزجت مختلف ارائه شده است. نتایج به دست آماده دارای انطباق مناسبی با نتایج عددی دارد. نتایج نرخ همگرایی نشان می‌دهد که روش پیش‌شرط توانی حسگر محلی تنش برای نسبت لزجت کمتر از 0/5 دارای پایداری زیاد، افزایش سرعت همگرایی و کاهش هزینه زمانی محاسبات می‌شود.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

The development of power-law preconditioning approach for simulation of unsteady viscoelastic flows

نویسندگان [English]

  • Hamidreza Ghiyasi Shahraky
  • Mahmood Norouzi
  • Ali Abbas Nejad
  • Pooria Akbarzadeh
Energy Conversion, Faculty of Mechanics, Shahroud University of Technology, Shahroud
چکیده [English]

One of the particular features of viscoelastic liquids in unstable shear flows is the damping oscillatory behavior in the velocity field without imposing external force and oscillation. This behavior is seen because of the elastic property of the liquid. In the present paper, for the first time, the preconditioning method of local stress censor has been employed for numerically simulating unstable viscoelastic liquids passing through fixed parallel plates. In this regard, the Maxwell model has been used. In this method, by adding fake time derivation to governing equation, hyperbolic equations will be generated. By obtaining the preconditioning matrix of these equations corrected locally through the power relation of stress field and employing binary algorithm for time including inner and outer loop, solving incompressible unsteady flows can be possible in the form of artificial compressible flows. In order to converge the inner loop, the four-step Vossooghifar's method has been implemented. Equations were discretized through the finite difference and shifted network. Calculation of unsteady viscoelastic flows has been performed for various Reynolds numbers, Weissenberg numbers and viscosity ratios have been presented. The results are in good agreement with the numerical results. Results of the convergence rate indicate that the locally preconditioning power censor method is the appropriate one for a viscosity ratio lower than 0.5 demonstrating a higher convergence rate and reduced time cost of calculations.

کلیدواژه‌ها [English]

  • preconditioning power method
  • stress censor
  • binary implicit algorithm
  • unsteady viscoelastic flow
  • and convergence rate
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