Lagrangian Particle Tracking

Transcription

1 FD with OpenFOAM software Lagrangian article Tracking Jelena Andric December 2009, Gothenburg

2 About multiphase flows great importance can occur even more frequently than single phase flows correct formulation of the governing equations for multiphase flowsstill subject to debate Interaction between different phases- flows are complicated and very difficult to describe theoretically present in various forms in industrial practice (transient flows, separated flows, dispersed two-phase flows) dispersed two-phase flows - one phase is present in the form of particles, droplets, or bubbles in a continuous carrier phase (gas or liquid)

3 Different regimes of two-phase flows a)transient two-phase flow, b)separated two-phase flow, c)dispersed two-phase flow

4 Different regimes of dispersed two-phase flows One-Way coupling - influence of the particle on the fluid flow may be neglected

5 Forces acting on particles The motion of particles in fluids is described in a Lagrangian way Set of ordinary differential equations along the trajectory is solved in order to calculate the change of particle location and the linear and angular components of particle velocity. The relevant forces acting on the particle need to be taken into account. For spherical particles the differential equations for calculating the particle location and velocity are given by Newtonian second law: dx = u dt d u m dt d ω I dt = = T F i

6 Analytical solutions - available for small Reynolds numbers An extension to higher Reynolds-including a coefficient in front of the force( based on empirical correlations derived from experiments DNS) In most fluid-particle systems - the drag force is dominating the particle motion. Its extension to higher particle Reynolds number -introduction of a drag coefficient : drag coefficient drag force particle Re number D Re F D = ρ F 2 ρf d = 3 ρf m = 4 ρ d F D 2 ( uf u ) A u μ D F F u ( uf u ) uf u

7 drag coefficient= function (particle Re number) Different flow regimes: Stokes flow Re < 0.5 Transient region 0.5 Re < 1000 < D = 24 Re ( Re ) = D D = f Re Re Newtonian region D 0.44

8 Drag of non-spherical particles ylinders-regularly shaped particles Aspect ratio E = L D non-spheroidal particles no analytical solution for the drag even in the creeping flow limit introducing the shape factor the surface and the projected area ratios shape factor A surf A surf 2 π d For inders, A proj A proj π d L E, A d surf = f shape 2E 2 ( 18E ) D, shape D, sphere f, d = d shape 3E 2 D, shape D, sphere 1 2 = A A Re << 1 creeping flow f shape proj surf 1 3. Re << 1 & const. vol.

9 Newtonian regime: 4 10 < Re < 10 5 D, shape, crit shape = D, spherecrit, = D, sphere, crit cont. vol. shape A surf ( A 1), E > 1 surf Intermediate Reynolds number flow: combination of the Stokes drag correction and the Newton-drag correction dependence similar for all particle shapes, difference correction at two extremes dependency result of dimensional analysis ( Re ), D = f D =, D D = 24 Re [ ( ) ] Re shape ,500 ( Re ) 1.16 Re = shape f shape Re for circular S

10 Implementation in OpenFOAM lass solidarticle - simple solid spherical particle class with oneway coupling with the continuous phase lass solidarticleloud oding-advanced ++style plus complex inheritance Spherical particles-rigid bodies article properties diameter, coefficient of restitution, friction coefficient, density Box test case - two spherical particles are inserted at different initial velocities into the fluid at test Solver solidarticlefoam solves for the particel position and velocity Forces drag and gravity

11 Implementation of new classes solidylinder solidylinderloud reated in order to track the motion of indrical particles orrection in geometrical properties inder length needs to be specified orrection in drag force in order to take into account for the change in particle shape Solving for indrical particles

12 Reynolds numbers inders - higher Re-numbers sphere and inder with higher initial velocity firstly have rather high Re- numbers, but for a quite short time are approaching very low values sphere and inder with lower initial velocity - decreasing trend for Re-numbers ;except for the beginning of the simulation the values remain higher

13 Drag forces approaching steady-state Drag force higher for inders Achieving steady-state condition steady state after 0.8s

14 Drag coefficients sphere ad inder with lower initial velocity physical agreement different flow regions can be identified

15 sphere and inder with higher initial velocity (t=1s) sphere and inder with higher initial velocity (t=0.8s)

16 urpose and project idea Mechanical model of a fiber How to take into account for contact forces?!