شبيه سازي عددي قطره در جريان پواسل تحت اثر نيروي شناوري

چكيده انگليسي :

Numerical Simulation of Drops in a Poisseuile Flow under Gravity Force Hamed Khalili Dermani h khalilidermani@me iut ac ir Date of Submission 2012 26 02 Department of Mechanical Engineering Isfahan University of Technology Isfahan 84156 83111 Iran Degree M Sc Language FarsiSupervisor Saeed Mortazavi s mortazavi@cc iut ac irAbstract The motion of drops suspended in another fluid has a wide variety of practical applications Theseinclude the flow of oil and water through pipelines the recovery of oil through porous rock the flow ofslurries and polymer processing The lateral migration of deformable particles in Poisseuile flow has beenthe subject of many investigations The lateral migrations of immersed objects in carrier fluids are veryimportant in transport processes where mass momentum and energy are exchanged The lateral migration of a buoyant drop in poisseuile flow is studied numerically in two dimensions Themechanism of lateral migration for one drop was explained by Feng et al The wall repulsion force which isknown as a lubrication effect drives the drop to the channel centerline A magnus type lift force acts on thedrop which depends on drop rotation and drop slip velocity The direction of this lift depends on whetherthe drop leads or laggs the flow For density ratios less than unity the drop leads the flow and this forcepoints towards the channel wall When the density ratio is larger than one the drop laggs the flow and theforce is towards the channel centerline The curvature of velocity profile also imposes a lateral force thatalways drives the drop to the channel wall Besides the inertia of flow develops a lateral force which isknown as inertia lift Saffman lift that depends on the direction of the slip velocity The equilibriumposition of the drop is a result of balance between the aforementioned forces It is found that the drop migrates to an equilibrium position which is close to the walls for a slightlybuoyant drop at density ratios less than one If the drop is relatively more buoyant the equilibrium positionmoves to the centerline At density ratios greater than one the equilibrium position also moves to thecenterline The equilibrium position of drop depends on Froude number The equilibrium position alsodepends on deformation and inertia of flow When the Capillary number is raised the equilibrium positionmoves away from the wall The effect of Reynolds number on the equilibrium position has been alsostudied by a few simulations It is found that at relatively large Froude number the drop oscillate with finiteamplitude inside the channel At a relatively large Reynolds number 120 and moderate Froude number 43 drop shows oscillations across the channel and does not obtain a stable equilibrium position Theequilibrium position of drop agrees qualitatively with perturbation theories and numerical results availablefor solid particles Suspensions of buoyant drops at low and moderate areal fractions are studied at non zero Reynolds numberin Poisseuile flow The flow is studied as a function of the Capillary number the Reynolds number theFroude number and density ratio It is found that the effective viscosity decreases with Capillary number The effective viscosity increases with Froude number at density ratios smaller than 1 and the effectiveviscosity decreases with Froude number at density ratios greater than 1 The distribution and the fluctuationenergy of drops across the channel are non uniform for buoyant drops that depends on the Froude number The density ratio also affects the distribution and fluctuation energy of drops across the channel Effect ofReynolds number is same as Froude number The difference between two area fractions is the degree offreedom of motion of drops in the low areal fraction Keywords Equilibrium position Poisseuile flow Density ratio Froude number Capillary number suspension of buoyant drops

خليلي درمني، حامد

شبيه سازي عددي قطره در جريان پواسل تحت اثر نيروي شناوري

مكان تعادل , نسبيت چگالي , عدد فرود , عدد رينولدز , عدد كپيلاري , سوسپانسيون , قطرات شناور