Modeling MultiPhase Systems Using Bond Graphs

1
Modeling Multi-Phase Systems Using Bond Graphs
2
Contents

• Introduction
• Basic Model
• Determination of Variables
• Condensation on Cold Surfaces
• Model of a Pressure Cooker
• Conclusions

3
Basic Model
Ø
CD, DVA, Evaporation (and Condensation)
Ø
3
3
3
3
CF
CF
gas
liq
4
Determination of Variables

• State transition elements are modeled as special
  R-fields, however
• Mass flows are determined as a function of
  pressure and the corresponding saturation
  pressure
• Volume flows are determined as the product of
  mass flow and the saturation volume at the
  corresponding temperature
• Entropy flows will be superposed with enthalpy
  of evaporation

5
Condensation on Cold Surfaces
Boundary layer
CF
CF
Gas
Gas
Rand- schicht
3
3
CD DVA RF
3
3
Ø
.
Ø
CD
s
T
S
3
gas
3
Conduction (CD) Volume work (DVA) Condensation-
and Evaporation
Conduction (CD) Volume work (DVA) Condensation-
and Evaporation
CF
3
Ø
Surface
.
s
3
T
3
S
liq
CD DVA RF
3
3
Ø
Ø
CD
3
3
CF
CF
liq
liq
6
Model of a Pressure Cooker
Air in Boundary layer
SE 393 K
CD (t)
CD
DVA
CD (t)
Air
RF Dp
CD (t)
CD
CD
SE 293 K
CD
DVA
CD
DVA
Cond
water
CD
CD
steam
RF Dp
CD (t)
DVA
Cond
CD
Steam in Boundary layer
CD (t)
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Pressure Cooker Temperature Graph
8
Pressure Cooker Pressure Graph
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Conclusions

• Phase transitions cannot be described in general
  without making assumptions
• Simple phase transitions can now be modeled
• This model accounts also for liquid within the
  gaseous phase and air bubbles within the fluid
  phase.
• Condensation on cold surfaces can be modeled
  easily.

10
Thank you.
11
Modeling Air Bubbles