SLIDE 48 ( ) ( ) ( ) ( )
ρ ρ η η ρ ρ η η ρ ρ η η ρ ρ = + + = − = − = − = = & & & & & & ε ε ε ε ⋅ − + ⋅ − = − + − & & & & ρ η
Fluid junction
48
Require inStream operator to be continuously differentiable
( ) ( ) ( ) ( )
1 2 3 1 1 1 1 1 1 1 2 2 2 2 2 2 2 3 3 3 3 3 2 2 1 1 _ 1 1 _ 1 1
, , , , , , , , , , , , ( , , ( )) , ( ), ( )
mix ab ba ab ba mix ab ba ab ba mix ab ba ab ba ab mix a inflow a a inflow mix a a
m m m m f p p m f p p m f p p p T Xi T T p h Xi ρ ρ η η ρ ρ η η ρ ρ η η ρ ρ = + + = − = − = − = = inStream inStream inStream inStr & & & & & &
2 2 3 3 1 2 3
( , ) ( , ) ( ) ( , ) ( , ) ...
a a a
h max m h max m h max m max m ε ε ε ε ⋅ − + ⋅ − = − + − eam & & & & ρ η
σ
∑
≠ =
− = & σ
cus-
σ
defined value. h m σ σ
= ≠ = ≠
= ⋅ − −
∑ ∑
& & 3)
ℜ ∈ ε
ly
α
( ) ( ) ( ) ε
α α σ ⋅ − + ⋅ =
α
σ
( )
⎪ ⎪ ⎩ ⎪ ⎪ ⎨ ⎧ ≤ ≤ < ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − > = σ ε σ ε σ ε σ ε σ σ α
ε ε ε ε ε
= ≠ = ≠ = ≠ = ≠
⋅ = ⋅ = ⋅ − = −
∑ ∑ ∑ ∑
( ) ( )
ε σ =
Suggested regularization of inStream(h3)
- R. Franke, F. Casella, M. Otter, M. Sielemann, H. Elmqvist, S. E. Mattsson, and H. Olsson.
Stream connectors – an extension of modelica for device-oriented modeling of convective transport phenomena.
- Proc. of the 7-th International Modelica Conference, Como, Italy, Sept. 2009.
Iterate on pmix and two mass flow rates. The number of iteration variables for the above mixing problem was reduced from 22 to 3, and residual functions changed from discontinuous to continuous.
