Thermodynamics

1
Thermodynamics CFD

• Harris et al (1996) numerical solution ... in
  a flow geometry of interest, together with
  subsidiary sets of equations transport,
  diffusion and reaction of chemical species.
• Kuipers and van Swaaij (199?) The SIMPLE
  algorithm (Patankar, 1980) forms the basis of
  PHOENICS, FLUENT, FLOW3D additional transport
  equations can be added with relative ease.

2
SIMPLE

• The solver controls V, p, E, m as functions of
  and t,x,u
• This gives four dependent variables, which is one
  too many compared to thermodynamic theory
• Thermodynamic relation p p(V,E,m)
• Is there a way to correct this flaw without
  rewriting the solver(?)

3
Incompressible flow

• The solver controls U,b (and V, p, Ek , Ep ) as
  functions of and t,x,u
• Two dependent variables in accordance with
  thermodynamic theory

4
Compressible flow

• The solver controls V, U,b (and Ek , Ep ) as
  functions of and t,x,u (barycenter)
• Three dependent variables in accordance with
  thermodynamic theory

5
Compressible flow (continued)

• The solver controls extensive variables xi
• Thermodynamic EOS supplies intensive properties
  ci needed in transport equations and alike
• Bilinear coupling
• Reformulation into from Lagrange to Euler
  cordinates?