Modeling Convective Flows Using Bond Graphs

1
Modeling Convective Flows Using Bond Graphs
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Contents

1. Introduction
2. Choice of Variables
3. The C-field
4. The R-field

3
Choice of Variables

• Describing a thermodynamical problem
  necessitates 3 variables
• Typically we prefer mass M, temperature T, and
  pressure p

4
Balance of Energy
5
The C-field
0
.
T
S
C
CF
C
C
g
q
.
p
M
0
0
6
Ø
CF
3
7
Conventions for Elements in Bond Graphs

• 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

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Conduction
CF
CF
2
1
3
3
T
T
2
1
1
Ø
Ø
.
.
S
S
1
1
.
.
.
DT
S
T
T
S
S
1
D
.
D
1
2
1x
2x
S
DT
1
0
2
mGS
mGS
.
DT
S
1
2
3
3
CD
Icon
CF
CF
2
1
9
Volume Work
CF
CF
1
2
3
3
p
p
1
Ø
1
Ø
2
q
q
.
.
T
S
p
q
T
D
1
D
S
1x
D
2
2x
q
p
D
2
0
mGS
mGS
p
q
D
2
3
3
DVA
Icon
CF
CF
2
1
10
The R-field
r
r
, S
, S
1
1
2
2
CF
CF
2
1
3
3
Ø
Ø
3
3
RF
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R-field Schematic
T
T
1
2
.
1
.
S
S
p
p
1
2
1
q
q
g
g
1
.
2
.
1
M
M
.
.
T
g
p
q
S
M
D
D
D
mGS
mGS
mGS
T
T
T
2
2
2
T
0
2
.
S
D
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R-field, General Case
g
g
1
.
1
.
2
M
M
mGS
T
T
1
1
0
.
1
2
.
S
S
1
2
0
0
Sw
Sw
mGS
mGS
mGS
p
p
1
1
2
q
q
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Conclusions

• The elements introduced suffice to model simple
  thermodynamical problems
• Models are limited to mono-phase and
  mono-element systems

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Thank you.
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Balance of Impulse
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Balance of Impulse II