1. Universität Stuttgart Modeling Convective Flows Using Bond Graphs University of Arizona 9. Jan 2001 Jürgen Greifeneder, François Cellier 1 Modeling Convective Flows Using Bond Graphs

2. Universität Stuttgart Modeling Convective Flows Using Bond Graphs University of Arizona 9. Jan 2001 Jürgen Greifeneder, François Cellier 2 1.Introduction 2.Choice of Variables 3.The C-field 4.The R-field Contents

3. Universität Stuttgart Modeling Convective Flows Using Bond Graphs University of Arizona 9. Jan 2001 Jürgen Greifeneder, François Cellier 3 Describing a thermodynamical problem necessitates 3 variables Typically we prefer mass M, temperature T, and pressure p Choice of Variables

4. Universität Stuttgart Modeling Convective Flows Using Bond Graphs University of Arizona 9. Jan 2001 Jürgen Greifeneder, François Cellier 4 Balance of Energy

5. Universität Stuttgart Modeling Convective Flows Using Bond Graphs University of Arizona 9. Jan 2001 Jürgen Greifeneder, François Cellier 5 The C-field p q T S g M.. 0 0 0 CF CC C

6. Universität Stuttgart Modeling Convective Flows Using Bond Graphs University of Arizona 9. Jan 2001 Jürgen Greifeneder, François Cellier 6 CF 3 Ø

7. Universität Stuttgart Modeling Convective Flows Using Bond Graphs University of Arizona 9. Jan 2001 Jürgen Greifeneder, François Cellier 7 C-fields do not know about each other C-fields can only be attached at Ø-junctions 3-dimensional bus-1-junctions do not exist All flows are calculated by dissipative elements Conventions for Elements in Bond Graphs

8. Universität Stuttgart Modeling Convective Flows Using Bond Graphs University of Arizona 9. Jan 2001 Jürgen Greifeneder, François Cellier 8 Conduction CF CF 1 TT  2 T S. T 1 1 1 S. 1 S. 1 2 0 mGS 2 T ØØ TT TT S. 1 2 S. 1 2 S. 1x S. 2x T 1  33 CF 1 CF 2 33 Icon: CD

9. Universität Stuttgart Modeling Convective Flows Using Bond Graphs University of Arizona 9. Jan 2001 Jürgen Greifeneder, François Cellier 9 Volume Work p q q 1 1 p 2 0 mGS 2 T 1 T Ø Ø 3 3 CF 1 CF 2  pq  p  p 2 q 2 q  S 1x.  S 2x. CF 1 CF 2 33 DVA Icon:

10. Universität Stuttgart Modeling Convective Flows Using Bond Graphs University of Arizona 9. Jan 2001 Jürgen Greifeneder, François Cellier 10 The R-field ØØ 3 RF 3 33 CF 1 CF 2 , S 11  22

11. Universität Stuttgart Modeling Convective Flows Using Bond Graphs University of Arizona 9. Jan 2001 Jürgen Greifeneder, François Cellier 11 R-field Schematic T S. p q g M. 1  1  g 1  p q mGS 0 S.  1 1 1 T S. p q g M. 2 2 2 T 2 T S. M. T 2 T 2 T 2

12. Universität Stuttgart Modeling Convective Flows Using Bond Graphs University of Arizona 9. Jan 2001 Jürgen Greifeneder, François Cellier 12 R-field, General Case p q 1 mGS 0 1 p q 2 1 11 0 0 T S. 1 T S. 2 12 g M. 1 g M. 2 Sw

13. Universität Stuttgart Modeling Convective Flows Using Bond Graphs University of Arizona 9. Jan 2001 Jürgen Greifeneder, François Cellier 13 Conclusions The elements introduced suffice to model simple thermodynamical problems Models are limited to mono-phase and mono-element systems

14. Universität Stuttgart Modeling Convective Flows Using Bond Graphs University of Arizona 9. Jan 2001 Jürgen Greifeneder, François Cellier 14 Thank you.

15. Universität Stuttgart Modeling Convective Flows Using Bond Graphs University of Arizona 9. Jan 2001 Jürgen Greifeneder, François Cellier 15

16. Universität Stuttgart Modeling Convective Flows Using Bond Graphs University of Arizona 9. Jan 2001 Jürgen Greifeneder, François Cellier 16 Balance of Impulse

17. Universität Stuttgart Modeling Convective Flows Using Bond Graphs University of Arizona 9. Jan 2001 Jürgen Greifeneder, François Cellier 17 Balance of Impulse II