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## Modelling of the particle suspension in turbulent pipe flow

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**Modelling of the particle suspension in turbulent pipe flow**Ui0 23/08/07 Roar Skartlien, IFE**The SIP – project (strategic institute project)**• Joint project between UiO and IFE, financed by The Research Council of Norway. 4-yrs, start 2005 • Main goal: Develop models for droplet transport in hydrocarbon pipelines, accounting for inhomogeneous turbulence • UiO: Experimental work with particle image velocimetry (David Drazen, Atle Jensen) • IFE: Modelling (Roar Skartlien, Sven Nuland)**Droplet distribution and entrainment**• Simulation by Jie Li et.al. from Stephane Zaleski’s web-site**Droplets in turbulence (two-phase):**Wall film with capillary waves Entrainment and deposition of droplets Turbulent gas • Mean shear • Inhomogeneous turbulence • Interfacial waves Turbulent fluid Turb. gas/fluid + waves**Droplet transport (three-phase):**Concentration profiles Mean velocity profile Droplet mass fluxes = Concentration profiles x Velocity profile Gas Oil Water • Additional liquid transport**Droplet concentration profiles depend on:**• Particle diffusivity (turbulence intensity, particle inertia and kinetic energy) • Entrainment rate (pressure fluctuation vs. surface tension) • Droplet size distribution (splitting/merging controlled by turbulence) h t**Modelling**• Treat droplets as inertial particles • Inhomogeneous turbulence • Splitting and coalescence neglected so far • Entrainment is a boundary condition • Use concepts from kinetic theory -- treat the particles as a ”gas”: use a ”Boltzmann equation” approach (Reeks 1992) • The velocity moments of the pdf yield coupled conservation equations for particle density, momentum, and kinetic stress**The ensemble averaged ”Boltzmann equation”**Conservation equation for the ensemble averaged PDF <W> (Reeks 1992, 1993, Hyland et. al. 1999): Strong property of Reeks theory: There is an exact closure for the diffusion current, if the fluctuating force obeys Gaussian statistics • Reduces to the Fokker-Planck equation for ”heavy” particles, • which experience Brownian motion. • In general, the motion may be considered as a • Generalized Brownian motion (the force is ”colored” noise)**Conservation equations for particle gas, in 1D stratified**turbulent stationary flow Friction Turbulent source Stress tensor component Kinetic wall-normal stress Particle diffusivity Dispersion tensor components, depend only on correlations functions of the particle force (set up by the fluid). Here: Explicit forms in homog. approx.**Rewrite momentum balance for stationary flow -> Vertical**mass flux balance Particle diffusivity Diffusion due to fluid Particle kinetic stress Particle relaxation time Gravity corrected for buoyancy and added mass Particle density Turbulent diffusion Turbophoresis Gravitational flux Note: Must solve for kinetic stress, before particle density is solved for**Test against particle – water data**• Experiments conducted by David Drazen and Atle Jensen. Water and polystyrene in horizontal pipe flow, 5 cm diameter • Use Reeks kinetic theory • Input: profiles for fluid wall-normal stress and fluid velocity correlation time • Output: particle concentration profile and particle wall-normal stress**Conclusions**• The study of turbulent transport of droplets in (inhomogeneous) turbulence is experimentally (and theoretically) difficult, so • The PIV-experiments are initiated for water laden with polystyrene particles, to test and develop theory and experimental method • Modelling: need to include added mass effect for current experiments. May need to consider particle collisions in dense regions (near pipe floor) • Droplets in gas: no added mass effect: kinetic model less complicated. Next step: use glass particles in water • Droplets in gas: gas turbulence model (Reynolds stress) accounting for gas-fluid interface is needed