Tesi di Laurea Break-up of inertial aggregates in turbulent channel flow Frammentazione di aggregati inerziali in flusso turbolento Relatore: Dott. Ing. Cristian Marchioli Correlatore: Prof. Alfredo Soldati Candidato: Marco Svettini U NIVERSITÀ DEGLI S TUDI DI U DINE Facoltà di Scienze Matematiche Fisiche e Naturali CdLS in F ISICA C OMPUTAZIONALE Anno Accademico 2011/2012

Premise What is turbulence? Turbulent flux characteristics: Unstable and unstationary (Reynolds) Tridimensional Diffusive Dissipative ( Kolmogorov l.s.) Rotational: =rot(u)≠0 Coherent Jet flow DNS solver req.: Length scale: CFL condition: Random nature of turbulent flow: u = U+u’ (Reynolds decomp.)

Premise Aggregate Break-up in Turbulence What kind of application? Processing of industrial colloids Polymer, paint, and paper industry

Premise Aggregate Break-up in Turbulence What kind of application? Processing of industrial colloids Polymer, paint, and paper industry Environmental systems Marine snow as part of the oceanic carbon sink

Premise Aggregate Break-up in Turbulence What kind of application? Processing of industrial colloids Polymer, paint, and paper industry Environmental systems Marine snow as part of the oceanic carbon sink Aerosols and dust particles Flame synthesis of powders, soot, and nano-particles Dust dispersion in explosions and equipment breakdown

Premise Aggregate Break-up in Turbulence What kind of aggregate? Aggregates consisting of colloidal primary particles Schematic of an aggregate

What kind of aggregate? Aggregates consisting of colloidal primary particles Break-up due to Hydrodynamics stress (D p << ) Schematic of break-up Premise Aggregate Break-up in Turbulence

Problem Definition Description of the Break-up Process Focus of this work! SIMPLIFIED SMOLUCHOWSKI EQUATION (NO AGGREGATION TERM IN IT!)

Turbulent flow laden with few aggregates (one-way coupling) Aggregate size < O() with  the Kolmogorov length scale Heavy aggregates: Aggregates break due to hydrodynamic stress Tracer-like aggregates: Brittle and deformable aggregates Problem Definition Further Assumptions

Problem Definition Strategy for Numerical Experiments Consider a fully-developed statistically-steady flow Seed the flow randomly with aggregates of mass  at a given location Neglect aggregates released at locations where  cr Follow the trajectory of remaining aggregates until break-up occurs Compute the exit time,   cr (time from release to break-up)

Problem Definition Strategy for Numerical Experiments Consider a fully-developed statistically-steady flow Seed the flow randomly with aggregates of mass  at a given location Neglect aggregates released at locations where  cr Follow the trajectory of remaining aggregates until break-up occurs Compute the exit time,   cr (time from release to break-up)

Problem Definition Strategy for Numerical Experiments Consider a fully-developed statistically-steady flow Seed the flow randomly with aggregates of mass  at a given location Neglect aggregates released at locations where  cr Follow the trajectory of remaining aggregates until break-up occurs Compute the exit time,   cr (time from release to break-up)

Problem Definition Strategy for Numerical Experiments Consider a fully-developed statistically-steady flow Seed the flow randomly with aggregates of mass  at a given location Neglect aggregates released at locations where  cr Follow the trajectory of remaining aggregates until break-up occurs Compute the exit time,   cr (time from release to break-up)

Problem Definition Strategy for Numerical Experiments  For j th aggregate breaking after N j time steps: x 0 =x(0) x   x  cr  tt nn+1  j  cr,j  N j · t Consider a fully-developed statistically-steady flow Seed the flow randomly with aggregates of mass  at a given location Neglect aggregates released at locations where  cr Follow the trajectory of remaining aggregates until break-up occurs Compute the exit time,   cr (time from release to break-up)

Problem Definition Strategy for Numerical Experiments Break up of brittle aggregates occours instantly if  cr (power per unit mass) The break-up rate is the inverse of the ensemble-averaged exit time:  For j th aggregate breaking after N j time steps: x 0 =x(0) x   x  cr  tt nn+1  j  cr,j  N j · t

Problem Definition Strategy for Numerical Experiments The break-up rate is the inverse of the ensemble-averaged exit time: Break-up of deformable aggregates occour if: Aggregate start to deform ( cr ): deformation activation Deformation exceed the maximum allowed deformation (E > E cr ) Aggregate returns to a relaxed state when  cr Deformation is proportional to the dissipated energy per unit mass:

Flow Instances and Numerical Methodology Channel Flow Pseudospectral DNS of 3D time-dependent turbulent gas flow 256x256x257 grid resolution Shear Reynolds number: Re  = u  h/ = 150 Near wall particles transfer model Navier-Stokes equations:

Particle Tracer and Numerical Methodology Stokes number Equation of motion for a small spherical particle in a nonuniform flow (Maxey & Riley, 1983) – wall units: Time-integration: 4th order Runge-Kutta scheme Fluid velocity interpolation: 6th order Lagrange polynomials Inertial particles behaviour: Stokes number dependence

Channel Flow Choice of Critical Energy Dissipation Characterization of the local energy dissipation in bounded flow: Wall-normal behavior of mean energy dissipation Tracers dissipation plot Inertial aggregates dissipation plot

Break-up analysis Tracer aggregates Spanwise channel view Streamwise channel view

Break-up analysis Tracer aggregates Brittle aggregate

Break-up analysis Tracer aggregates Deformable aggregate

Break-up analysis Inertial aggregates Spanwise channel view Streamwise channel view

Break-up analysis Inertial aggregates Brittle aggregate

Break-up analysis Inertial aggregates Deformable aggregate

Break-up analysis (brittle aggr.) Choice of Critical Dissipation Distribution is strongly affected by flow anisotropy (skewed shape) Whole channel dissipation Wall-normal behavior of mean dissipation 0 < z + < 150

Break-up analysis (brittle aggr.) Choice of Critical Dissipation Bulk dissipation Wall-normal behavior of mean dissipation Bulk  cr Distribution is strongly affected by flow anisotropy (skewed shape) 40 < z + < 150

Break-up analysis (brittle aggr.) Choice of Critical Dissipation Intermediate dissipation Wall-normal behavior of mean dissipation Intermediate  cr Distribution is strongly affected by flow anisotropy (skewed shape) 10 < z + < 40

Break-up analysis (brittle aggr.) Choice of Critical Dissipation Wall dissipation Wall-normal behavior of mean dissipation Wall  cr Distribution is strongly affected by flow anisotropy (skewed shape) 0 < z + < 10

Break-up analysis (brittle aggr.) Choice of Critical Dissipation Distribution of local dissipation Inertia affect very much the dissipation distribution Inertial aggregates sample higher dissipation channel region and empty the bulk Increasing Stokes cause higher dissipation events (near wall region)  + =0.2 is Stokes invariant

Break-up analysis (brittle aggr.) Where does aggregates break-up? Tracers released in the middle of the channel Inertial aggregates released in the middle of the channel

Break-up analysis (brittle aggr.) Where does aggregates break-up? Bulk dissipationIntermediate dissipation Wall dissipation Generally speaking, inertial aggregates have lower probability to reach regions far from the middle of the channel  due to segregation process, inertial aggregates sample regions with higher dissipation values

Break-up analysis (brittle aggr.) Break-up frequency Break-up frequency of brittle aggregates as function of inertia and critical dissipation threshold Break-up frequency increase with Stokes number as consequence of the segregation process Break-up estimation is over estimated for  cr > 0.02 due to simulation finite length For low threshold values break- up decreasing function can be fitted with a power law

Break-up analysis (brittle aggr.) Break-up frequency Break-up frequency increase with Stokes number as consequence of the segregation process Break-up estimation is over estimated for  cr > 0.02 due to simulation finite length For low threshold values break- up decreasing function can be fitted with a power law First exit time break-up events distribution Bulk dissipation Intermediate dissipation

Break-up analysis (brittle aggr.) Break-up frequency Break-up frequency of brittle aggregates as function of inertia and critical dissipation threshold Break-up frequency increase with Stokes number as consequence of the segregation process Break-up estimation is over estimated for  cr > 0.02 due to simulation finite length For low threshold values break- up decreasing function can be fitted with a power law

Break-up analysis (deformable aggr.) Choice of Critical Deformation Distribution of deformation values as a function of dissipation and deformation threshold Dissipated energy per unit mass goes from 0.01 to 100 For increasing dissipation threshold we observe:  Higher energy events  Shorter event duration Events number depend on the Stokes number

Break-up analysis (deformable aggr.) Break-up frequency Break-up frequency tends to the brittle case if E cr reduce to zero Bulk dissipation region is particularly affected by deformation (red curve on the right plot) Brittle and deformable cases overlap if:  E cr = 0.04 and  cr >  E cr = 0.4 and  cr > 0.12  E cr = 2.8 and  cr > 0.7

Break-up analysis (deformable aggr.) Break-up frequency Inertia affect break-up deformation plot only quantitatively but not qualitatively