The release notes for CFX-5.7.1 mention that there was an improvement
in the accuracy of the Redlich-Kwong equation of state near the critical point.
The 5.7.1 documentation on the Redlich-Kwong EOS only gives details on the
original formulation. What changes have been made to the RK EOS in
5.7.1? Does this improvement only affect the Redlich Kwong equation of state
or does it involve other property evaluations (entrophy, enthalpy table look up)
near a critical point.
CFX-5.7 contained the standard original implementation of the RK equation
that dates back to 1949.
In 5.71, slightly modified version from Aungier ("A Fast, Accurate Real Gas Equation
of State for Fluid Dynamic Analysis Applications", Journal of Fluids Engineering,
June 1995, V117, p277) was implemented.
The motivation for this was mainly to answer the needs of clients who defined
temperature and pressure ranges which spanned the region of the critical point.
In this case the flow solver could fail to build a table due to the poor behaviour
of standard Redlich Kwong in this region.
If you make a p = f(v) plot at values of temperature close to critical
(eg: T/Tcrit > 0.96) for the standard Redlich-Kwong EOS you will see
that the isotherm makes a signficant wiggle into the dome in that region.
The standard EOS is tuned such that the critical isotherm is perfect but the
problem is that isotherms just below critical wiggle everywhere.
Aungier's modification simply makes this wiggling much less
pronounced than it is with the standard equation.
It also greatly increases the accuracy of the critical isotherm.
Consider the following data for water:
T v p1 p2 p2-pcrit p1-pcrit
647.14 0.003101 24503764.7 22096134.9 32134.9 2439764.7
647.14 0.003102 24492094.8 22088179.1 24179.1 2428094.8
647.14 0.003104 24480474.9 22080264.8 16264.8 2416474.9
647.14 0.003105 24468904.7 22072391.7 8391.7 2404904.7
647.14 0.003107 24457384.2 22064559.6 559.6 2393384.2
647.14 0.003108 24445913.1 22056768.5 -7231.5 2381913.1
647.14 0.003110 24434491.2 22049018.0 -14982.0 2370491.2
647.14 0.003111 24423118.3 22041308.1 -22691.9 2359118.3
647.14 0.003113 24411794.2 22033638.6 -30361.4 2347794.2
In the table, p1 is for the standard RK, while p2 is the modified form used in 5.7.1.
So, at T=Tcrit=647.14, vcrit for water is 0.00310660748 m^3/kg, pcrit
for water is actually 22064000 Pa. Note that the p2 values are much
closer to pcrit for v=vcrit in the table. The standard RK implementation
is out by 2.3 MPa and the modified version almost goes right through
The main consequence of the modifications to the RK equation should be that it is less
likely in 5.7.1 for table generation errors to occur and you should hopefully get a result
that is more accurate anywhere that the solution approaches the critical point.
An image file that shows the implementation of the Aungier modification
of the RK equation in 5.7.1 is attached.