Extension of the OpenFOAM CFD tool
set for modelling multiphase flow
Ridhwaan Suliman
Johan Heyns
Oliver Oxtoby
Advanced Computational Methods Research Group, CSIR
South Africa
Introduction Sloshing Heat transfer Weakly compressible Conclusion
Overview
1
Introduction
2
Sloshing
3
Heat transfer
4
Weakly compressible
5
Conclusion
Introduction Sloshing Heat transfer Weakly compressible Conclusion
Applications
Microfluidics
Naval
Hydro
Sloshing
analysis
Energy
Pro
ces
s
Casting
Introduction Sloshing Heat transfer Weakly compressible Conclusion
OpenFOAM
Open source CFD tool set
•
Modular (OOP C++ with templates)
•
Extensive set of libraries
•
Large community
Solution
Extended
software
Problem
Modified
solution
Existing
software
Modified
problem
Introduction Sloshing Heat transfer Weakly compressible Conclusion
Free surface modelling
Incompressible two-fluid flow governing equations
∂
u
i
∂
x
i
=
0
∂ α
∂
t
+
∂
∂
x
i
(
α
u
i)
=
0
∂ ρ
u
i
∂
t
+
∂
∂
x
j
ρ
u
i
u
j
−
∂
p
∂
x
i
=
∂
∂
x
j
µ
∂
u
i
∂
x
j
+
ρ
g
i
Improvements/Extensions:
•
Surface capturing
•
Non-isothermal
•
Heat and mass transfer
•
Chemical reactions
•
Weakly compressible
Introduction Sloshing Heat transfer Weakly compressible Conclusion
Volume-of-fluid
Navier-Stokes with volume fraction
α
(
x
i
,t
) =
1
for the point (
x
i
,t
) in the liquid
0
for the point (
x
i
,t
) in the gas
Mixture properties
•
ρ
=
α ρ
l
+ (1
−
α
)
ρ
g
•
µ
=
α µ
l
+ (1
−
α
)
µ
g
Advantages
•
Conservative
•
Merging and breakup of free-surface
•
Arbitrary unstructured 3D (parallel)
δx2 δx1 liquid gas αu|x1∆x2 αu|x1+∆x∆x2 αu|x2∆x1 αu|x2+∆x∆x1
Introduction Sloshing Heat transfer Weakly compressible Conclusion
Higher-resolution artificial compressive scheme (HiRAC)
α
n
+1
−
α
n
∆
t
=
−
1
2
∂
(
u
i
α
)
∂
x
i
n
+1
+
∂
(
u
i
α
)
∂
x
i
n
−
∂
∂
x
i
[
u
c
|
i
α
(1
−
α
)]
|
n
+1
Temporal discretisation:
•
2
nd
order Crank-Nicolson
Spacial discretisation:
•
Blended higher-resolution
•
TVD slope limiting
Artifical compressive term:
•
Normal to interface
ψ
r
2 1 1 2 κ-scheme Central differencing First order upwinding Second order upwinding First order downwinding TVD CBCIntroduction Sloshing Heat transfer Weakly compressible Conclusion
Violent sloshing
0 2 4 6 8 10 12 Pressure t (s) Experimental MULES CICSAM HiRACvlc.png
Introduction Sloshing Heat transfer Weakly compressible Conclusion
Liquid rocket fuel sloshing
High fidelity numerical sloshing code
•
Low cost alternative
•
Various geometrical and loading conditions
•
Automated pre- and post-processing
•
Compare with linear wave sloshing experiments
•
Case study: Space vehicle entering jet stream
•
Sharp lateral loading
Introduction Sloshing Heat transfer Weakly compressible Conclusion
Linear wave sloshing
Introduction Sloshing Heat transfer Weakly compressible Conclusion
Linear wave sloshing
Introduction Sloshing Heat transfer Weakly compressible Conclusion
Non-linear violent sloshing
S/R = 0.1, W/R = 0.2
vlc.png
S/R = 0.1, W/R = 0.1vlc.png
No bafflesvlc.png
Introduction Sloshing Heat transfer Weakly compressible Conclusion
Non-linear violent sloshing
Vertical direction
-120000 -115000 -110000 -105000 -100000 -95000 -90000 0 1 2 3 4 5 6 7 8 9 Forces in Y direction, Fy (N) Time,t(s) No bafflesS1W1 S1W2Lateral direction
-20000 -15000 -10000 -5000 0 5000 10000 15000 20000 0 1 2 3 4 5 6 7 8 9 Forces in x direction, Fx (N) Time,t(s) No bafflesS1W1 S1W2Introduction Sloshing Heat transfer Weakly compressible Conclusion
Heat transfer
Assumptions
•
Incompressible fluid - density variations negligible except in
buoyancy term
•
Immiscible fluids
Averaged VOF energy equation
ρ
k
c
p
∂
T
∂
t
+
ρ
k
c
p
u
j
∂
T
∂
x
j
−
∂
∂
x
j
k
m
∂
T
∂
x
j
=
0
Boussinesq approximation
ρ
k
= 1
−
β
(
T
−
T
ref
)
Introduction Sloshing Heat transfer Weakly compressible Conclusion
1D heat transfer
Introduction Sloshing Heat transfer Weakly compressible Conclusion
Non-isothermal multiphase flow
ρb≈ρt
ρb>ρt
Introduction Sloshing Heat transfer Weakly compressible Conclusion
Weakly compressible
Model
•
High density ratios
•
Low Mach number flows
•
Large pressure variations
Existing FSM solvers
•
Incompressible
•
Compressible
•
Full set of equations
Introduction Sloshing Heat transfer Weakly compressible Conclusion
Weakly compressible
Assumptions
•
Homogeneous flow (
u
g
=
u
l
,
p
g
=
p
l
)
•
Low mach number flow
•
Isothermal
Non-dimensional analysis
∂ α
∂
t
+
∂
(
α
u
j)
∂
x
j
=
0
(1
−
α
)
ρ
g
∂ ρ
g
∂
t
=
−
∂
u
j
∂
x
j
∂
(
ρ
u
i)
∂
t
+
∂
(
ρ
u
i
u
j)
∂
x
j
+
∂
p
∂
x
i
=
∂
∂
x
j
µ
∂
u
i
∂
x
j
+
α ρ
l
g
i
Ideal gas law
ρ
g
−
ρ
g o
=
1
c
2
g
Introduction Sloshing Heat transfer Weakly compressible Conclusion
Validation: Weakly compressible
Introduction Sloshing Heat transfer Weakly compressible Conclusion
Validation: Weakly compressible
Absolute
Introduction Sloshing Heat transfer Weakly compressible Conclusion
Non-isothermal and weakly compressible flows
Assumptions
•
Low mach number flow
•
Large density ratios (liquid-gas)
Non-dimensional analysis
∂ α
∂
t
+
∂
(
α
u
j
)
∂
x
j
=
0
(1
−
α
)
ρ
g
1
RT
∂
P
∂
t
−
(1
−
α
)
1
T
∂
T
∂
t
=
−
∂
u
j
∂
x
j
∂
(
ρ
u
i
)
∂
t
+
∂
(
ρ
u
i
u
j
)
∂
x
j
+
∂
p
∂
x
i
=
∂
∂
x
j
µ
∂
u
i
∂
x
j
+
ρ
k
g
i
∂
T
∂
t
+
u
j
∂
T
∂
x
j
−
∂
∂
x
j
k
m
∂
T
∂
x
j
=
1
ρ
k
c
p
D
(1
−
α
)
P
Dt
Equations of state
ρ
g
=
P
RT
;
ρ
l
= 1
−
β
(
T
−
T
ref
)
Introduction Sloshing Heat transfer Weakly compressible Conclusion
Non-isothermal compression
vlc
Introduction Sloshing Heat transfer Weakly compressible Conclusion
Conclusion
•
OpenFOAM tool set
•
Modular, easily extensible
•
Large community
•
Multiphase modelling applications
•
Violent sloshing of fuel in aircraft and rockets
•
Non-isothermal flows
•
Weakly compressible formulation
