Modelling of the particle suspension in turbulent pipe flow Ui0 23/08/07 Roar Skartlien, IFE.
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Transcript of Modelling of the particle suspension in turbulent pipe flow Ui0 23/08/07 Roar Skartlien, IFE.
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):
Turbulent fluid
Turbulent gasEntrainment and deposition of droplets
Wall film with capillary waves
•Mean shear •Inhomogeneous turbulence•Interfacial waves
Turb. gas/fluid + waves
Droplet transport (three-phase):
Droplet mass fluxes = Concentration profiles x Velocity profile
Water
Oil
Gas
Mean velocity profileConcentration profiles
•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)
t
h
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
Dispersion tensor components, depend only on correlations functions of the particle force (set up by the fluid).Here: Explicit forms in homog. approx.
Stress tensor component
Friction Turbulent source
Particle diffusivity
Kinetic wall-normal stress
Rewrite momentum balance for stationary flow -> Vertical mass flux balance
Turbulent diffusionTurbophoresis
Gravitational flux
Particle density
Particle diffusivity
Particle relaxation time Gravity corrected for buoyancy and added mass
Particle kinetic stress
Diffusion due to fluid
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
Vertical profiles, Re=43000,no added mass effect
Vertical profiles, Re=43000, added mass in diffusivity
Vertical profiles, Re=43000also calculated normal stress
Vertical profiles, Re=43000added mass not accounted for
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