Flow through a Venturi pipe at medium up to high Reynolds number 

Computational details


Short description and remarks


Aim of these simulations


Quantitative comparisons


Conclusion


Visualization



Short description and remarks
The objective of the following test calculations is to examine in a quantitative and qualitative
manner the resulting
accuracy of the employed flow solver if it is applied to
nonsteady flows
with complex behaviour. In contrast to the
`flow around a cylinder' Benchmarksimulations
which "only" showed periodical vortex shedding behind a
circle, we present now results for a flow
which exhibits much more complex flow patterns in space and
time.
The interesting flow quantity in this simulation is the flux
through the
upper small channel (see the following typical coarse mesh
for a sketch of the geometry).
In "real life", this Venturi pipe represents a small device used to drain sailing boats.
If the flow speed is sufficiently high, then
 due to the Bernoulli principle  the narrowing section
enforces a low pressure which
creates a flux through this small device, out of the boat.
Therefore, we are
mainly interested in controlling the flux through this
device, as a function of time.
In this simulation (until T=30), the inflow is steady
parabolic, and we start from the corresponding Stokes solution.
More explanations and remarks can be found in our
Paper Archive , particularly
in http://www.featflow.de/ture/paper/habil.ps.gz
and in
Stefan Turek's CFDbook, Springer.




Aim of these simulations
We aim to show how hard it is  for this medium Reynolds
number range  to calculate the
`grid independent' solution by simply refining the mesh only,
if we ask for a quantitatively exact representation of the
flux
(through the upper inlet) or the integral mean value of
the pressure (on the lower wall)!
We employed the following two types of meshes `a' and `b'
which are shown for level 3, i.e., after two regular refinements.
Grid a:
Grid b:




Quantitative comparisons
The following diagrams show the resulting flux and integral
pressure coefficients in time. As explained more carefully in
the
Computational details
, we prescribed a fixed velocity profile only at the left edge, and let the others
as free as possible ('zero mean pressure'!). The resulting
flux through the upper small device depends on the geometry and
Reynolds number; and in this case, the result is that `flow
is sucked from the boat'!!!
We applied an adaptive time step control with very small
error tolerances so that the shown results are (more or less)
`exact in time',
that means that only the spatial error should be visible!
For more information about different types of time stepping
techniques (what happens for time steps too large, which time
step size is
needed to guarantee sufficient accuracy, how does the time
step depend on the used `NavierStokes solver???) and the
comparison of various `NavierStokes solvers'
(projectionlike, fractional step, pressure correction, fully coupled,
linearization
techniques for the nonlinearity, ...) can be found in the
previously described
Paper Archive, and particularly
in
Stefan Turek's CFDbook, Springer.
The following plots show the results on different mesh levels
(up to level 9!), on meshes `a' and `b'. While the results on
levels 8 and 9 show at least some similar dynamic bahviour,
we cannot talk about the "grid independent" solution.




Conclusion
The following conclusions for flow simulations in this Reynolds number regime can be stated which should be compared with the analogous results for the lower Reynolds number simulations:
For the mathematical background concerning these observations
and suggestions for improvements, and with respect to general
CFD for incompressible flow problems, look at our Paper
Archive, and there especially at
http://www.featflow.de/ture/paper/habil.ps.gz
and in
Stefan Turek's CFDbook, Springer.




Visualization




Please send any comments and suggestions to: featflow@featflow.de 