1. Universität Stuttgart ICBGM ´01 Modeling Multi-Phase Systems Using Bond Graphs University of Arizona 9. Jan 2001 Jürgen Greifeneder, François Cellier 1 Modeling Multi-Phase Systems Using Bond Graphs

2. Universität Stuttgart ICBGM ´01 Modeling Multi-Phase Systems Using Bond Graphs University of Arizona 9. Jan 2001 Jürgen Greifeneder, François Cellier 2 Contents 1.Introduction 2.Basic Model 3.Determination of Variables 4.Condensation on Cold Surfaces 5.Model of a Pressure Cooker 6.Conclusions

3. Universität Stuttgart ICBGM ´01 Modeling Multi-Phase Systems Using Bond Graphs University of Arizona 9. Jan 2001 Jürgen Greifeneder, François Cellier 3 Basic Model CF gas 3 Ø CD, DVA, Evaporation (and Condensation) 3 CF liq 3 Ø 3

4. Universität Stuttgart ICBGM ´01 Modeling Multi-Phase Systems Using Bond Graphs University of Arizona 9. Jan 2001 Jürgen Greifeneder, François Cellier 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. Universität Stuttgart ICBGM ´01 Modeling Multi-Phase Systems Using Bond Graphs University of Arizona 9. Jan 2001 Jürgen Greifeneder, François Cellier 5 Condensation on Cold Surfaces CF liq CF Gas CF Surface 3 3 Ø Ø Rand- schicht 3 3 Conduction (CD) Volume work (DVA) Condensation- and Evaporation 33 CD DVA RF 3 3 CD DVA RF CF liq CF Gas 3 3 Ø Ø 3 3 T S. Conduction (CD) Volume work (DVA) Condensation- and Evaporation CD gas s T S CD liq s. Boundary layer Ø 3

6. Universität Stuttgart ICBGM ´01 Modeling Multi-Phase Systems Using Bond Graphs University of Arizona 9. Jan 2001 Jürgen Greifeneder, François Cellier 6 Model of a Pressure Cooker SE : 293 K SE : 393 K water Air steam Air in Boundary layer Steam in Boundary layer CD (t) Cond DVA CD Cond CDDVA CD RF:  p RF:  p CD DVA CD CD (t)

7. Universität Stuttgart ICBGM ´01 Modeling Multi-Phase Systems Using Bond Graphs University of Arizona 9. Jan 2001 Jürgen Greifeneder, François Cellier 7 Pressure Cooker: Temperature Graph

8. Universität Stuttgart ICBGM ´01 Modeling Multi-Phase Systems Using Bond Graphs University of Arizona 9. Jan 2001 Jürgen Greifeneder, François Cellier 8 Pressure Cooker: Pressure Graph

9. Universität Stuttgart ICBGM ´01 Modeling Multi-Phase Systems Using Bond Graphs University of Arizona 9. Jan 2001 Jürgen Greifeneder, François Cellier 9 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. Universität Stuttgart ICBGM ´01 Modeling Multi-Phase Systems Using Bond Graphs University of Arizona 9. Jan 2001 Jürgen Greifeneder, François Cellier 10 Thank you.

11. Universität Stuttgart ICBGM ´01 Modeling Multi-Phase Systems Using Bond Graphs University of Arizona 9. Jan 2001 Jürgen Greifeneder, François Cellier 11 Modeling Air Bubbles CF gas CF Gas 3 3 Ø Ø 3 3 CD, DVA, Evaporation (and Condensation) 3 3 CF liq CF 3 3 Ø Ø 3 3 3 3 CD, DVA, Condensation (and Evaporation) Transition element Transition element Gas Phase Fluid Phase boundary CD, DVA 3 3 Phase-