Note: CFD-calculations have been deactivated in version 2.7 due to unsatisfactory results. A new approach is being pursued.
A further example is the laminar viscous compressible flow about a naca012
airfoil. Results for this problem were reported by [51]. The entrance
Mach number is 0.85, the Reynolds number is 2000. Of interest is the steady
state solution. In CalculiX this is obtained by performing a transient
CFD-calculation up to steady state. The input deck for this example is called
naca012_visc_mach0.85.inp and can be found amoung the CFD test
examples. Basing the Reynolds number on the unity chord length of the airfoil,
an entrance unity velocity
and a entrance unity density leads to a dynamic viscosity of
. Taking
and
leads to a specific gas constant
(all in consistent units). Use of gthe entrance Mach number
determines the entrance static temperature to be
. Finally, the
ideal gas law leads to a entrance static pressure of
. Taking the
Prandl number to be one determines the heat conductivity
. The surface of the airfoil is assumed to be adiabatic.
The results for the pressure and the friction coefficient at the surface of
the airfoil are shown in Figures
40 and 41, respecively, as a function of the shock
smoothing coefficient. The pressure coefficient is defined by
, where p is the local static
pressure,
,
and
are the static pressure,
density and velocity at the entrance, respectively. From Figure 40
it is clear that a reduction of the shock smoothing coefficient improves the
results. For a zero shock smoothing coefficient, however, the results
oscillate and do not make sense any more. Taking into account that the
reference results do not totally agree either, a shock smoothing coefficient
of 0.025, which is the smallest smoothing coefficient yielding non-oscillating
values,
leads to the best results. The friction coefficient is defined by
, where
is the local shear
stress. Here too, a too large shock smoothing coefficient clearly leads to
wrong results. A value of 0.05 best agrees with the results by Mittal,
however, in the light of the
-results from the literature a value of
0.025 might be good as well. The
-peak at the front of the airfoil is not
very well hit: the literature result is 0.17, the CalculiX peak reaches only
up to 0.15. While decreasing the shock smoothing coefficient increases the
peak, a too coarse mesh density at that location may also play a role. The
general advice is to use as little shock smoothing as possible.