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A stable fluid-structure-interaction solver for low-density rigid particles using the immersed boundary projection method
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.ORCID iD: 0000-0003-3094-0848
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.ORCID iD: 0000-0002-8209-1449
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Dispersion of particles with complex geometries and very low or close to unity density ratios are ubiquitous in both natural and industrial environments. We show that while explicit methods for coupling the incompressible Navier-Stokes equations and Newton's equations of motion are often sufficient to solve for motion of cylindrical and spherical particles with low density ratios, for more complex particles they become unstable. For example, the critical density ratio, for which numerical method becomes unstable, is significantly increased for an explicit coupling, compared to implicit coupling, in simulations of the flow around cylinder with a splitter plate. We present an implicit formulation of the coupling between rigid body dynamics and fluid dynamics within the framework of the immersed boundary projection method. In addition to the Navier-Stokes equations, we solve Newton's equations of motion for a rigid body. In a similar manner to previous work on the immersed boundary projection method, the resulting matrix equation in the present approach is solved using a block-LU decomposition. Each step of the block-LU decomposition is modified to incorporate the rigid body dynamics. We ensure that our method preserve the efficiency and second-order accuracy in space and third-order accuracy in time of the original method, only with small additional computational cost. We find that implicit coupling yields stable solution for density ratios as low as .

Keyword [en]
Immersed boundary method, Newton's equations of motion, Implicit coupling, Numerical stability, Low density ratios, Complex particles
National Category
Computer Science
URN: urn:nbn:se:kth:diva-158316OAI: diva2:776156
Swedish Research Council, VR-2010-3910

QS 2015

Available from: 2015-01-07 Created: 2015-01-07 Last updated: 2015-01-19Bibliographically approved
In thesis
1. Nature-inspired passive flow control using various coatings and appendages
Open this publication in new window or tab >>Nature-inspired passive flow control using various coatings and appendages
2015 (English)Licentiate thesis, comprehensive summary (Other academic)
Alternative title[sv]
Passiv styrning av strömmning inspirerad av naturen
Abstract [en]

There is a wide variety of tails, fins, scales, riblets and surface coatings, which are used by motile animals in nature. Since organisms currently living on earth have gone through millions of years of evolution, one can expect that their design is optimal for their tasks, including locomotion. However, the exterior of living animals has range of different functions, from camouflage to heat insulation; therefore it is a very challenging task to isolate mechanisms, which are beneficial to reduce the motion resistance of the body.

There are two general categories of mechanisms existing in locomotion and flow control. The first is active flow control, when an organism is actively moving some parts or the whole body (exerts energy) in order to modify the surrounding flow field (for example, flapping bird wings). The second is passive flow control, in which an organism has an appendage or a coating, which is not actively controlled (no energy is spent), but is interacting with surrounding flow in a beneficial way. Our aim is to find novel mechanisms for passive flow control.

We start by looking at a simple model of an appendage (splitter plate) behind a bluff body (circular cylinder). If a recirculation region forms behind the body, already in this simple system there is a symmetry breaking effect for sufficiently short plates, which passively generates turn and drift of the body. We have found that this effect is caused by the pressure forces in the recirculation region, which pushes the plate away from the vertical in a manner similar to how a straight inverted pendulum falls under the influence of gravity. In order to investigate this symmetry breaking, we developed an extension of the immersed boundary projection method, in which the rigid body dynamics and fluid dynamics are coupled implicitly. The method is capable of solving for particle motion in a fluid for very small density ratios. We also explain our findings by a simple yet quantitative reduced-order model and soap-film experiments.

To extend our work, we investigate flow around bodies, which are coated by a porous and elastic material. We have analysed various theoretical approaches to modeling a coating in a continuous manner. We aim to solve the governing equations numerically. We have selected multi-scale expansion approach, of which we present some initial results. 

Abstract [sv]

Många djur använder sig av fjäll, päls, hår eller fjädrar för att öka sin förmåga att förflytta sig i luft eller vatten. Evolutionen har främjat ojämna, sträva eller gropiga ytor, vilka har en tendens att minska det totala motståndet som uppstår när en kropp rör sig i vatten eller luft, jämfört med en helt slät och jämn yta.Det finns två kategorier av metoder för manipulering av strömning (så kallad flödeskontroll). Den första är en aktiv metod, där organismer aktivt rör hela eller delar av kroppen (förbrukar energi) för att manipulera omgivande strömningsfält. Den andra metoden är passiv, där organismer har utväxter eller ytbeläggningar som de inte är aktivt har kontroll över (ingen energi förbrukas), men som samverkar med omgivande strömningsfält på ett fördelaktigt sätt. Vårt mål är att hitta nya mekanismer för passiv flödeskontroll.Vi börjar med att studera en enkel modell för hur en utväxt samverkar med en strömmande fluid genom att fästa en platta på en cirkulär cylinder. Om en vak (så-kallad återcirkulationsregion) bildas bakom kroppen, bryts symmetrin i strömningsfältet då plattan är tillräckligt kort. Som en konsekvens av detta roterar kroppen och driver i sidled. Vi visar att detta fenomen orsakas av tryckkrafter i återcirkulationsregionen, som förskjuter plattan från dess vertikala läge. Vi argumenterar att denna mekanism är samma mekanism som får en inverterad pendel att falla under inverkan av gravitation. För att analysera symmetribrytningen, utvecklade vi en numerisk metod (immersed boundary projection method), som implicit kopplar stelkropps- och strömningsdynamik. Med hjälp av denna metod kan vi simulera partiklar i fluider med väldigt låga densitetsskillnader. Våra resultat förklaras även med hjälp av en enkel modell av låg ordning och med hjälp av såphinneexperiment.Som nästa steg i vårt arbete, ämnar vi att studera strömningen kring kroppar som är belagda av tät, porös och elastisk beläggning. Vi har analyserat möjliga tillvägagångssätt för att modellera beläggningar med kontinuumteori. Vi har valt en metod baserad på en flerskalig expansionsmetod, från vilken vi presenterar våra preliminära resultat.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2015. x, 17 p.
TRITA-MEK, ISSN 0348-467X ; 2014:28
flow control, passive appendage, surface coating, pressure drag, friction drag, Flödeskontroll, passiva bihang, ytbeläggning, tryckmotstånd, friktionsmotstånd
National Category
Fluid Mechanics and Acoustics
urn:nbn:se:kth:diva-158319 (URN)978-91-7595-427-1 (ISBN)
2015-01-29, D3, Lindstedtsvägen 5, Stockholm, 10:15 (English)
Swedish Research Council, VR-2010-3910

QC 20150119

Available from: 2015-01-19 Created: 2015-01-07 Last updated: 2015-01-19Bibliographically approved

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