Flow through a Venturi pipe at low up to medium 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 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' benchmark simulations
which "only" showed periodical vortex shedding behind a
circle, we present now results for a flow
which does not seem to exhibit such an easy flow pattern 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=20), the inflow is steady
parabolic, and we start from the corresponding Stokes solution.
The aim of the following calculations is to demonstrate
`graphically' the described results and problems via performing
such types of CFD simulations. 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  even for this low up to
medium Reynolds number range  to calculate the
`grid independent' solution by simply refining the mesh in
space and time 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', and a zoomed version
with the
results on the finest meshes to demonstrate that the result
is (almost) mesh size and grid typeindependent!
While mesh levels 5  7 are too coarse, we can see that, on
grid `a', the results on level 8 and 9 are almost identical,
concerning flux as well as pressure values (note: the
pressure values to be controlled are positioned directly on the
boundary!!!).
Additionally, the solutions on mesh type `b', and here
particularly on level 8, strongly converge to the same solution
(level 9) as
on mesh `a' which seems to be the `grid independent'
reference solution!




Conclusion
Some conclusions for flow simulations in this Reynolds number regime can be stated:
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 