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Numerical simulation of an inertial spheroidal particle in Stokes flow
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
2015 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesisAlternative title
Numerisk simulering av en trög sfäroidisk partikel i Stokesflöde (Swedish)
Abstract [en]

Particle suspensions occur in many situations in nature and industry. In this master’s thesis, the motion of a single rigid spheroidal particle immersed in Stokes flow is studied numerically using a boundary integral method and a new specialized quadrature method known as quadrature by expansion (QBX). This method allows the spheroid to be massless or inertial, and placed in any kind of underlying Stokesian flow.

 

A parameter study of the QBX method is presented, together with validation cases for spheroids in linear shear flow and quadratic flow. The QBX method is able to compute the force and torque on the spheroid as well as the resulting rigid body motion with small errors in a short time, typically less than one second per time step on a regular desktop computer. Novel results are presented for the motion of an inertial spheroid in quadratic flow, where in contrast to linear shear flow the shear rate is not constant. It is found that particle inertia induces a translational drift towards regions in the fluid with higher shear rate.

Abstract [sv]

Partikelsuspensioner förekommer i många sammanhang i naturen och industrin. I denna masteruppsats studeras rörelsen hos en enstaka stel sfäroidisk partikel i Stokesflöde numeriskt med hjälp av en randintegralmetod och en ny specialiserad kvadraturmetod som kallas quadrature by expansion (QBX). Metoden fungerar för masslösa eller tröga sfäroider, som kan placeras i ett godtyckligt underliggande Stokesflöde.

 

En parameterstudie av QBX-metoden presenteras, tillsammans med valideringsfall för sfäroider i linjärt skjuvflöde och kvadratiskt flöde. QBX-metoden kan beräkna kraften och momentet på sfäroiden samt den resulterande stelkroppsrörelsen med små fel på kort tid, typiskt mindre än en sekund per tidssteg på en vanlig persondator. Nya resultat presenteras för rörelsen hos en trög sfäroid i kvadratiskt flöde, där skjuvningen till skillnad från linjärt skjuvflöde inte är konstant. Det visar sig att partikeltröghet medför en drift i sidled mot områden i fluiden med högre skjuvning.

Place, publisher, year, edition, pages
2015.
Series
TRITA-MAT-E, 2015:88
Keyword [en]
Fluid mechanics, Stokes flow, rigid body dynamics, spheroidal particles, inertia, integral equations, boundary integrals, double layer potentials, quadrature by expansion, Jeffery orbits, linear shear flow, quadratic flow, paraboloidal flow
Keyword [sv]
Strömningsmekanik, Stokesflöde, stelkroppsdynamik, sfäroidiska partiklar, tröghet, integralekvationer, randintegraler, dubbellagerpotentialer, quadrature by expansion, Jeffery-banor, linjärt skjuvflöde, kvadratiskt flöde, paraboloidiskt flöde
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-180290OAI: oai:DiVA.org:kth-180290DiVA: diva2:892288
Subject / course
Scientific Computing
Educational program
Master of Science - Applied and Computational Mathematics
Supervisors
Examiners
Available from: 2016-01-09 Created: 2016-01-09 Last updated: 2016-01-09Bibliographically approved

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