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

u

∞x=U 1

2 w×xE⋅x ux=1 2 [5r

2−3E⋅x−2 x x⋅E⋅x]1

2 w×x

E= 1/1a a/1a −1

a= E22 E11

Simplifications

x y , yx ,a 1 a x−x ,w y−w y ,wz−wz z−z , wx −wx , wy−wy

0≤a≤1

w=wx ,wy ,wz−wy ,−wx ,−wz

w y≥0 wz≥0

Parameters of interest

• a = 1 - Axisymmetric
• ω = (ωx,0,ωz)

– ω = 0 – ω - inline with z-axis – ω - oriented off z-axis

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 = 0

ω - inline with z-axis

• ψ exists

t=t0

ω – oriented off z-axis

• Chaotic Streamlines

–Fixed orientation (36º) –Fixed ω magnitude

• ω = 0.1
• ω = 2.0
• a = 1.0
• ω = ( wx,0,wz)

Theta = 36º

ω = 0.1

ω = 2.0