Chaotic Streamlines Inside Droplet Radoslav Bozinoski System - PowerPoint PPT Presentation

Chaotic Streamlines Inside Droplet Radoslav Bozinoski

System • Neutrally Buoyant – External Flow • Vorticity • Rate of Strain Tensor • Linear – Internal Flow • Nonlinear • Chaotic Streamlines

Flow field • Coordinate system moving with center-of- mass. • Inter-boundary tension is sufficiently large to maintain a spherical drop shape. • Far from the drop the fluid is assumed to undergo a steady linear motion

Governing Equations ∞  x = U  1 2 w × x  E ⋅ x u u  x = 1 2 − 3  E ⋅ x − 2 x x ⋅ E ⋅ x ] 1 2 [ 5r 2 w × x E =  − 1  1 / 1  a  0 0 E 22 a = 0 a / 1  a  0 E 11 0 0

Simplifications x  y , y  x ,a  1 a 0 ≤ a ≤ 1 w = w x ,w y ,w z − w y , − w x , − w z  x − x ,w y − w y ,w z − w z w z ≥ 0 z − z , w x − w x , w y − w y w y ≥ 0

Parameters of interest • a = 1 - Axisymmetric • ω = (ωx,0,ωz) – ω = 0 – ω - inline with z-axis – ω - oriented off z-axis

ω = 0 a = 1.0 w = (0,0,0 ) LCE = (0,0,-) Dot - Saddle fixed points Asterisks – Elliptic fixed points ψ = 0 -Nested family of tori

ω - inline with z-axis • ψ exists  t = t  0

ω – oriented off z-axis • Chaotic Streamlines –Fixed orientation (36º) –Fixed ω magnitude • a = 1.0 • ω = 0.1 • ω = ( wx,0,wz) • ω = 2.0

Theta = 36º

ω = 0.1

ω = 2.0