Example 4: Distribution of compressed air (2)

• Extended Model (Zimmer 2020):
  • introduce inertial pressure difference Δr
    • 
    • inertance L is given by geometry of a component
    • can be derived from Euler equation
  • split pressure into quasi-static part and inertial part
    • 
  • at junctions use instead of p
    • approximation of transient behaviour
    • leads to decoupling of component equations
  • consequences
    • independent small non-linear parts instead of a huge coupled system
    • total coupling by relaxation using simple linear ODE
    • new parameter L (usually having default value)
  • free DLR ThermoFluidStream Library
    • provides components for vessels, pipes and machines based on these ideas
    • use it to model pneumatic system → runs
  • result
    • 
    • approximate relaxation for t < 1
    • quasistatic behaviour for t > 1