### Joule-Brayton Process with Ideal Gas

- First Version:
- start with ThermoSimT model
- replace thermodynamic components
- define initial pressure and temperature

- mass flow not defined explicitly
- dynamical variable in ThermoDLR
- mainly depending on compressor parameters

- run → "Failed ... during initialization"

- Finding parameters for compressor and turbine:
- create simple test model Source - Compressor - Sink
- use input state, output pressure and torque from
above → doesn't run
- reason: completely different turbine
characteristic
- use formula to compute ω from mass flow and
pressures
- use energy balance to compute τ
- use ω as initial value, and 0 for initial mass
flow ("powering up")

- run → mass flow rises almost to correct value
- difference due to regularization in equations

- similar procedure for turbine
- quadratic equation has no real root!
- simple workaround: adapt parameter m_flow_ref

- Finishing steps:
- use computed parameters in initial version
- → runs and almost reproduces desired values

- finetuning
- change τ to get exact final pressure
- use scaling of all extensive parameters to get
correct mass flow

- close the circle
- add cooler after turbine
- delete Source and Sink and add intermediate
Volume
- initial state now defined in Volume