T9: Heat transport:
equilibrating and historic cooling of amphitheaters

Before the tutorials:

Think about:

• What does heat transport mean?
• What happens when two fluids with different temperatures are in contact?
• How can you demonstrate that conduction is an irreversible process?
• What does a cooling cycle (in your fridge or in your air conditioner) generally look like?
• How can heat transport combined with T08 be used to mimic an ancient air conditioning system where the entrances to theaters had conical shapes?

During the tutorials:

To run the first experiment, we first need to

• Use the 200x10x10 setup of T06 to check the equilibration by heat transport of a slab with two different temperatures at its ends.
  • Mark all particles as boundary particles (i.e., set their ID to zero).
  • Give one side a 5 times higher temperature.
  • When compiling the code, do not forget to switch on CONDUCTION and CONDUCTION_CONSTANT (and SPH_BND_PARTICLES) in the Config.sh file.
  • Add ConductionEfficiency 0.2 and MaxSizeConductionStep 0.05 to the parameter file.
• Look at the evolution of the internal energy and explain what happens.
• Try to plot the entropy and see what happens.
• As a second experiment, you can try to build an air cooler.
  • Use the 400x20x20 setup of T08,
  • but make the tube much shorter, to have some of the original volume on the left.
  • Split the moving wall in two pieces, leaving the right part at rest with an hole to allow a flow through it.
  • Also, reduce the overall velocity
  • Hint: Here a sketch of the geometry:
    
• You can run the simulation with and without conduction switched on.
• Is there a difference in temperature in the left chamber?
• Have a closer look at the differences. What happens in the run without conduction?

Programming goals for T8:

Improve your ability to set up special geometries in the initial conditions.

Solutions

• Again, extending the setup script from T06 for the first test problem.
  • setup_slab.pro in IDL (see setup_test1)
• To look at the evolution of the internal energy.
  • show_slab.pro in IDL
  you should get something like shown below
  
• Example using Fortran and gnuplot:
  • ifort -g -traceback -check all -fpe0 -o slabsetup slabsetup.f90
    (this uses glass.txt from T04)
  • ./slabsetup
  • gnuplot grid.plt (to check that the particle positions are set up correctly)
  • compile Gadget with PERIODIC and NOGRAVITY and with LONG_X=10, LONG_Y=1, and LONG_Z=1.
  • run Gadget using slab.ic as the initial conditions file and output as the snapshot file base in the parameter file, and BoxSize = 1
    (and TimeMax = 100, TimeBetSnapshot = 0.1, and ConductionEfficiency = 10)
  • ifort -g -traceback -check all -fpe0 -o readsnap readsnap.f90
  • for file in output_???; do ./readsnap $file >$file.txt; done
  • gnuplot slab.plt
    (this requires ffmpeg, which is installed on our ltsp machines)
  • xine -l slab.mp4
    
• Again, extending the setup script from T08 for the first test problem.
  • setup_nozzle.pro in IDL (see setup_test2)
  you should get something like shown below
  
• Again, you can basically use the script from T08 for looking at the results.
  • show_nozzle.pro in IDL
  you should get something like shown below
  
• Example using Fortran and gnuplot:
  • ifort -g -traceback -check all -fpe0 -o nozzlesetup nozzlesetup.f90
    (this uses glass.txt from T04)
  • ./nozzlesetup
  • gnuplot grid2.plt (to check that the particle positions are set up correctly)
  • compile Gadget with PERIODIC and NOGRAVITY and with LONG_X=30, LONG_Y=1, and LONG_Z=1.
  • run Gadget using nozzle.ic as the initial conditions file and output as the snapshot file base in the parameter file, and BoxSize = 1
    (and TimeMax = 100, TimeBetSnapshot = 0.1, and ConductionEfficiency = 100)
  • ifort -g -traceback -check all -fpe0 -o readsnap readsnap.f90
  • for file in output_???; do ./readsnap $file >$file.txt; done
  • gnuplot nozzle.plt
    (this requires ffmpeg, which is installed on our ltsp machines)
  • xine -l nozzle.mp4
    • with ConductionEfficiency = 100:
      
    • with ConductionEfficiency = 0: