Suspensions of finite-size rigid spheres in different flow cases by Walter Fornari November 2015 Technical Reports Royal Institute of Technology Department of Mechanics SE-100 44 Stockholm, Sweden Akademisk avhandling som med tillst˚and av Kungliga Tekniska H¨ogskolan i Stockholm framl¨agges till offentlig granskning f¨or avl¨aggande av teknologie licentiatsexamen torsdag den 17 december 2015 kl 14.00 i sal D3, Kungliga Tekniska H¨ogskolan, Lindstedtsv¨agen 5, Stockholm. (cid:13)cWalter Fornari 2015 Universitetsservice US–AB, Stockholm 2015 “Considerate la vostra semenza: fatti non foste a viver come bruti, ma per seguir virtute e canoscenza” Dante Alighieri, Divina Commedia, Inferno, Canto XXVI Suspensions of finite-size rigid spheres in different flow cases Walter Fornari Linn´e FLOW Centre, KTH Mechanics, Royal Institute of Technology SE-100 44 Stockholm, Sweden Abstract Dispersed multiphase flows occur in many biological, engineering and geo- physical applications such as fluidized beds, soot particle dispersion and pyro- clasticflows. Understandingthebehaviorofsuspensionsisaverydifficulttask. Indeedparticlesmaydifferinsize,shape,densityandstiffness,theirconcentra- tion varies from one case to another, and the carrier fluid may be quiescent or turbulent. When turbulent flows are considered, the problem is further com- plicated due to the interactions between particles and eddies of different size, ranging from the smallest dissipative scales up to the largest integral scales. Most of the investigations on the topic have dealt with heavy small particles (typically smaller than the dissipative scale) and in the dilute regime. Less is known regarding the behavior of suspensions of finite-size particles (particles that are larger than the smallest lengthscales of the fluid phase). Inthepresentwork,wenumericallystudythebehaviorofsuspensionsoffinite- sizerigidspheresindifferentflows. Inparticular,weperformDirectNumerical Simulations using an Immersed Boundary Method to account for the solid phase. Firstlyisinvestigatedthesedimentationofparticlesslightlylargerthan the Taylor microscale in sustained homogeneous isotropic turbulence and qui- escent fluid. The results show that the mean settling velocity is lower in an already turbulent flow than in a quiescent fluid. By estimating the mean drag actingontheparticles,wefindthatnonstationaryeffectsexplaintheincreased reduction in mean settling velocity in turbulent environments. We also consider a turbulent channel flow seeded with finite-size spheres. We change the solid volume fraction and solid to fluid density ratio in an idealized scenario where gravity is neglected. The aim is to independently understand the effects of these parameters on both fluid and solid phases statistics. It is found that the statistics are substantially altered by changes in volume frac- tion, while the main effect of increasing the density ratio is a shear-induced migration toward the centerline. However, at very high density ratios (∼100) the two phases decouple and the particles behave as a dense gas. Finallywestudytherheologyofconfineddensesuspensionsofspheresinsimple shear flow. We focus on the weakly inertial regime and show that the suspen- sion effective viscosity varies non-monotonically with increasing confinement. The minima of the effective viscosity occur when the channel width is approx- imately an integer number of particle diameters. At these confinements, the particles self-organize into two-dimensional frozen layers that slide onto each other. v Descriptors: particlesuspensions, sedimentation, homogeneousisotropictur- bulence, turbulent channel flow, rheology. vi Suspensioner av stora stela sf¨arer i olika fl¨odesfall Walter Fornari Linn´e FLOW Centre, KTH Mekanik, Kungliga Tekniska H¨ogskolan SE-100 44 Stockholm, Sverige Sammanfattning I m˚anga biologiska, tekniska och geofysiska till¨ampningar f¨orekommer fler- fasstr¨omning.Fluidiseradeb¨addar,f¨ordelningavsotpartiklarochpyroklastiska fl¨oden¨arn˚agraexempelp˚as˚adanatill¨ampningar.Attf¨orst˚apartikelsuspensio- ner och dess egenskaper ¨ar en sv˚ar uppgift. Partiklarna kan variera i storlek, form,densitetochstyvhet,partikelkoncentrationenkanvarierafr˚anfalltillfall, och den transporterande v¨atskan kan vara stilla, men ¨aven turbulent. Komplexiteten ¨okar d˚a flerfasstr¨omningen ¨ar turbulent. Detta beror p˚a att partiklar interagerar med virvlar vars storlek och d¨ar storleksordning p˚a virv- larna kan vara liten som de minsta dissipativa l¨angdskalorna och stora som de st¨orstal¨angdskalorna.Deflestastudierg¨allandeovanst˚aendefl¨odenharfokuse- rat p˚a sm˚a tunga partiklar (vanligtvis mindre ¨an de dissipativa l¨angdskalorna) i flerfasfl¨oden med l˚aga partikelkoncentrationer. D¨aremot, hur partikelsuspen- sioner inneh˚allande st¨orre partiklar beter sig ¨ar mindre k¨ant. Med st¨orre par- tiklar menas partiklar som ¨ar st¨orre ¨an de minsta l¨angdskalorna som˚aterfinns i v¨atskefasen. I detta arbete studeras beteendet hos suspensioner best˚aende av stela sf¨arer (st¨orre¨andeminstaturbulentavirvlarna)f¨orolikastr¨omningsfallmedhj¨alpav Direktnumerisksimulering(DNS).Isimuleringarnahanteraspartikelfasen(so- liden) med hj¨alp av en s˚akallad Immersed Boundary metod. F¨orst unders¨oker vi sedimentationen hos partiklar som ¨ar n˚agot st¨orre ¨an Taylors mikroskala i uppr¨atth˚allen homogen isotropisk turbulens samt i en stilla fluid. Resulta- ten visar att den genomsnittliga sedimenteringshastigheten ¨ar l¨agre i en redan turbulent str¨omning j¨amf¨ort den i en stilla fluid. Genom att uppskatta det ge- nomsnittliga motst˚andet p˚a partiklarna, finner vi att icke-station¨ara effekter f¨orklarar den ¨okade minskningen i genomsnittliga sedimenteringshastigheten som˚aterfinns i turbulenta milj¨oer. Turbulent kanalstr¨omning inneh˚allande sf¨ariska partiklar studeras ocks˚a in- om ramen f¨or detta arbete. Partikelns volymfraktion varieras samt densitet f¨orh˚allandetpartikelochv¨atskad˚astr¨omningen¨ars˚adanattgravitationenkan f¨orsummas. M˚alet ¨ar att f¨orst˚a hur de oberoende effekterna av ovanst˚aende parametrarp˚averkardestatistiskaegenskapernahosb˚adev¨atske-ochpartikel- fasen. Resultaten visar att de statistiska egenskaperna f¨or¨andras avsev¨art d˚a volymfraktionen ¨andras medan den huvudsakliga effekten av f¨or¨andring i den- sitetsf¨orh˚allandet ¨ar en skjuvinducerad f¨orflyttning av partiklarna mot cent- rumlinjen.Vidv¨aldigth¨ogadensitetsf¨orh˚allanden(∼100)separerasemellertid de tv˚a faserna˚at och partiklarna beter sig som en t¨at gas. Slutligen studerar vi reologin hos avgr¨ansade suspensioner med h¨og partikel- koncentrationen av sf¨arer i en enkel skjuvstr¨omning. Vi fokuserar p˚a den svagt vii tr¨oga regimen och visar att suspensionens effektiva viskositet varierar icke- monotont med ¨okad avgr¨ansninggrad. Den effektiva viskositeten uppvisar ett minsta v¨arde d˚a kanalens bredd ¨ar approximativt en multipel av partikeldia- metern.Viddessaavgr¨ansningard¨aravst˚andetmellantv˚av¨aggarminskasmer och mer s˚a ordnar sig partiklarna i tv˚adimensionella lager som glider ovanp˚a varandra. Deskriptorer: partikelsuspensioner, sedimentering, homogen isotropisk tur- bulens, turbulent kanalstr¨omning, reologi. viii Preface This thesis deals with the study of the behavior of suspensions of finite-size particles in different flow cases. An introduction on the main ideas and ob- jectives, as well as on the tools employed and the current knowledge on the topic is presented in the first part. The second part contains three articles. The first paper has been submitted to Journal of Fluid Mechanics, the second paper to Physics of Fluids, and the third paper to Physical Review Letters. The manuscripts are fitted to the present thesis format without changing any of the content. Paper 1. W. Fornari, F. Picano & L. Brandt. Sedimentation of finite- size spheres in quiescent and turbulent environments. Accepted in J. Fluid Mech. (2015) Paper 2. W. Fornari, A. Formenti, F. Picano & L. Brandt. The effect of particle density in turbulent channel flow laden with finite size parti- cles in semi-dilute conditions. Submitted to Physics of Fluids (2015) Paper 3. W. Fornari, L. Brandt, P. Chaudhuri, C. Umbert Lo´pez, D. Mitra & F. Picano. Rheology of extremely confined non-Brownian sus- pensions. Submitted to Physical Review Letters (2015) November 2015, Stockholm Walter Fornari ix Division of work between authors The main advisor for the project is Prof. Luca Brandt (LB). Prof. Minh Do- Quang (MD) acts as co-advisor. Paper 1 The simulation code for interface resolved simulations developed by Wim-Paul Breugem (WB) was made tri-periodic by Walter Fornari (WF), who also in- troduced a forcing to create a sustained homogeneous isotropic turbulent field. Simulations and data analysis were performed by WF. The paper has been written by WF with feedback from LB and Prof. Francesco Picano (FP). Paper 2 The computations were performed by Alberto Formenti (AF) with support from WF. Data analysis has been performed by WF and AF. The paper has been written by WF with feedback from LB and FP. Paper 3 ThecomputationshavebeenperformedbyWFandCyanUmbertL´opez(CL). DataanalysishasbeenperformedinpartbyCLandmostlybyWF.Thepaper hasbeenwrittenbyProf. DhrubadityaMitra(DB),WFandFPwithfeedback from LB and Pinaki Chaudhuri (PC). x