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Mobility and Coalescence of Water Droplet Formed in Fuel Cells

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Two-step time discretization of momentum equation: Step (i): evaluate convective, viscous and surface tension effects explicitly ... – PowerPoint PPT presentation

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Title: Mobility and Coalescence of Water Droplet Formed in Fuel Cells


1
Mobility and Coalescence of Water Droplet Formed
in Fuel Cells
2
Overview
  • Introduction
  • Objectives
  • Mathematical Modeling
  • Sample Simulations

3
Introduction
  • A unit cell of PEMFC is composed of a membrane
    electrode assembly, two diffusion media, and
    bipolar plates.
  • The diffusion medium needs to be optimized to
    enhance the cell performance.
  • In cathode diffusion medium, the product water
    flows towards the channel through gas-phase
    diffusion or liquid-phase motion.

Porous Cathode
H2O
H2
O2
H
Porous Anode
4
  • At high current densities, the liquid flow
    rate increases due to the increased condensation,
    and when the channel is at the local vapor
    saturation condition, liquid water flows out of
    diffusion medium and surface droplet are formed.

5
Fiber Screens
  • Stacked fiber screens, and the same exposed to
    water-vapor saturated atmosphere.

6
Objective
  • Characterization of the mobility of micro-drops
    in the diffusion medium.
  • Growth of the micro drops through coalescence.
  • Consider effect of
  • Initial droplet number density
  • Initial droplet size
  • Vapor diffusion rates
  • Rate of droplet onset
  • Growth rate of drops
  • Surface contact angles
  • Thickness of the membrane.

7
Proposed Porous Model
8
Mathematical Model
  • Basic assumptions
  • Laminar flow incompressible and Newtonian fluid
  • Governing equations
  • Continuity
  • Momentum
  • Free-surface tracking
  • Modified flow equations in presence of solid
    walls
  • Finite volume method structured mesh
    Youngs algorithm volume fraction for walls

9
Energy Equation- Enthalpy Method
  • Original Energy Equation
  • Final Energy Equation

10
Free Surface Tracking
  • Step 1. Specify liquid domain using VOF method
  • Define a function
  • Represent actual liquid domain by corresponding
    values

Volume of Fluid representation
Actual liquid region
11
Modeling Solid Walls
  • Step 1 Define a Volume Fraction
  • Step 2 Use ? instead of a
    stair-step model
  • Step 3 Modify fluid flow
    equations

12
Modified Fluid Equations
  • Continuity, Momentum and VOF Equations

13
Sample Simulations
  • Impaction of a water Drop on a fiber
  • Droplet diameter 2 mm

two perpendicular tubes (0.5 mm)
no offset
3.18 mm tube 1 m/s offset 1.55 mm
14
Code Validation
Droplet 2 mm, 1 m/s Tube 3.18 mm (0.125
in) Offset 1.55 mm
15
Code validation (continued)
Droplet 2 mm, 1 m/s Tube 3.18 mm (0.125
in) Offset 1.55 mm
16
Droplet impact with heat transfer
17
Droplet flow through a modeled Porous Medium
  • Radial Capillary
  • A staggered array of perforated
    plates

18
Draw back and coalescenceDrop Spacing 42 ?m
Droplets coalesce
Contact Angle 45o
Contact Angle 120o
19
Drop Spacing 44 ?m Contact Angle 120o
Droplets do not coalesce
20
Droplet Collisions
  • Head- On Collisions
  • Permanent Coalescence
  • Reflexive Separation
  • Off-axis Collisions
  • Permanent Coalescence
  • Stretching Separation then Permanent
    Coalescence
  • Stretching Separation
  • Tearing

or
or
21
Droplet Coalescence
Drop Collisions Experiments vs. Simulations
Experimental
Numerical
22
Coalescence collision of two drops.
23
Off-Axis CollisionsTearing (Water, We56,
Re2392, X0.73 and ?0.5)
24
Thank you
25
Summary
  • Our 3D free surface code can simulate the
    detailes of the droplet dynamics in porous
    systems.

26
Continuity and Momentum
  • Two-step time discretization of momentum
    equation
  • Step (i) evaluate convective, viscous and
    surface tension effects explicitly
  • Step (ii) combine with continuity equation to
    obtain the Poisson pressure equation

27
Free Surface Tracking
  • Step 2. Use function to advect the free
    surface to a new location at each time step
  • Step 3. Reconstruct the free surface shape at
    the new location using Youngs algorithm

Obtain normal and use values of get
free surface cutting planes
28
Youngs 3D-VOF
  • Interfaces - piecewise planes
  • Interface plane is fitted within a single cell
  • Interface slope and fluid position are determined
    from inspection of neighboring cells

Pentagonal Section
29
Youngs 3D - Cases
Quadrilateral - A
Triangle
Quadrilateral - B
Hexagon
Pentagon
30
Youngs VOF Implementation
Surface Reconstruction Using f-field determined
cell normal (i.e. ) Determine case
using normal Position plane with known slope
based upon volume fraction Compute plane area
and vertices Fluid Advection, Compute flux
across cell side (case dependent) Operator Split
(i.e. do for x, y and z sweeps)
31
General Solution Procedure
  • Specify initial surface geometry and velocities
  • Begin Cycle, increment time and repeat 2-6 until
    done
  • Explicitly update
  • convective terms
  • viscous terms
  • surface tension terms
  • Implicitly calculate using ICCG Method
  • Update with and apply BCs
  • Advect f-field using Youngs VOF and re-apply BCs

32
Nondimensional Parameters
Impact Parameter
V
Weber Number
s
b
Relative Velocity
Size Ratio
d
V
l
X
(X0)
(Xgt0)
33
Head-on CollisionsSeparation (Water, We58,
Re1127)
34
Off-axis CollisionsCoalescence (Water, We25,
Re740, X0.7)
35
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