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docs/examples/gas_network.jl

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@@ -33,7 +33,7 @@ perform dimensionality checks.
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There are 2 node models used in the paper. The first node type has a constant
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pressure.
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Additionally, we ad some "internal" state `q̃_inj` which we want to plot later.
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Additionally, we ad some "internal" state `q̃_inj` which we want to plot later (see also [Observables](@ref)).
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=#
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@mtkmodel ConstantPressureNode begin
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@parameters begin
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nothing #hide
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#=
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The second node model is a variable pressure node. It has one output state, the pressure and one input state,
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The second node model is a variable pressure node. It has one output state (the pressure) and one input state,
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the aggregated flows from the connected pipes.
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As an internal state we have the injected flow from our source/load.
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The source/load behaviour itself is provided via a time dependent function.
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The equivalent "pressure capacity" at the nodes is calculated as a sum of the connected
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pipe parameters according ot (28).
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pipe parameters according to (28).
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Here use defintions based on the speed and "standard" conditions. But is this correct?
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Here use defintions based on the speed and "standard" conditions.
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=#
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C₂ = L₁₂*A/(2*ρ̃*^2) + L₂₃*A/(2*ρ̃*^2) # (28)
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C₃ = L₁₃*A/(2*ρ̃*^2) + L₂₃*A/(2*ρ̃*^2) # (28)
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nothing #hide
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Alternatively, could calculate Z2 and Z3 based on the actuel pressure and simulation temperature.
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Alternatively, we could calculate `Z2` and `Z3` based on the actuel pressure and simulation temperature.
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Then we could calculated the speed of sound for the "correct" conditions at the node.
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It seems to have very little effect on the actual results so I kept it simple.
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## Load Profile
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The paper specifies the load profile at two nodes. We use the package `LinearInterpolations`
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The paper specifies the load profile at two nodes. We use the package [`LinearInterpolations.jl`](https://github.com/jw3126/LinearInterpolations.jl)
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to get a callable object which represents this picewise linear interpolation.
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However, this function is not Symbolics.jl compatible, so we need to stop Symbolics.jl/ModelingToolkit.jl

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