Pressure curves for compressible flow with slip through constricted cylinders

The goal of this research is to determine more accurate pressure curves for compressible flow with slipthrough cylinders that have a local constriction.  Existing analyses for compressible flow with slip througha  local  constriction  linearize  the  pressure  gradient  equation,  and  higher-order  derivatives  are  dropped  as well.  The equation to be developed as part of this research retains quadratic pressure gradient terms.  The corresponding  solution  for  the  pressure  gradient  is  found  following  existing  analysis  in  the  literature  for incompressible,  no-slip  flow,  and  subsequently  the  pressure  is  found  using  numerical  integration.   Results are compared to those from the linearized pressure gradient equation to see the extent of the improvement. Results are also assessed and compared to pressure and density curves available in the literature for some specific constrictions.  Improvements may be obtained when the second-order derivatives are kept as well inthe pressure gradient equations, which can be assessed and analyzed in the same context. Pressure curves are assessed in different idealized flow geometries including the Gaussian model, a cosinu-soidal model, and a smooth piece-wise polynomial model.  In each case the pressure is found, and hence alsothe density.  A range of Reynolds numbers, degrees of constriction, length of the constriction, compressibilityand slip are considered. Density  curves  are  separately  compared  to  existing  particle-based  results  obtained  from  a  stochastic particle dynamics using multiparticle collision dynamics.