Flow through a perforated plate
Tuning CFD Porosity Parameters with modeFRONTIER In many engineering systems it is common to find geometric features which have a significant impact on the flow, but whose structure makes direct CFD analysis expensive, due to the high number of cells which would be needed to model them accurately. Examples of such are catalytic converters, heat
The problem, however, which often faces the CFD
exchangers, filters, packed bed reactors and
application engineer is that the values of α and β
perforated plates. The common way of including
are not known.
the effects of such features is to assign a distributed resistance to certain cells in STAR-CD
In the absence of this information, it is necessary
(a full description of the methodology can be found
to create an experimental set-up to measure the
in the STAR-CD User Manual), which lead to the
pressure drop across the feature of interest at a
same behaviour, without the necessity of locally
few flow points (these should be chosen within the
refining the mesh to capture the
entire range of velocities expected), and then try to
find suitable values of the coefficients, such that
In such cases, the pressure drop
the curve obtained using the porous cells matches
across the region in the xi direction
that produced by experiment.
is given by Δp/Δxi = αi|ui|ui + βiui, where αi and βi are the user-defined
Such a curve fitting exercise is tedious, and is
porosity coefficients for direction i.
seldom carried out, due to the large number of CFD analyses which need to be run, mostly by way
It is apparent that this equation is
of a trial-and-error approach.
non-linear, and that the pressure loss, which can be anisotropic, will
An alternative method, presented here, is to use an
be highly dependent on the local flow conditions. A
optimisation software, such as modeFRONTIER®,
typical velocity-pressure curve is shown in Fig. 1.
to perform the curve fitting automatically.
modeFRONTIER® is a registered product of ESTECO Srl | Copyright© ESTECO Srl 1999-2009
email@example.com | www.esteco.it
Tu n i n g C F D P o r o s i t y P a r a m e t e r s w i t h m o d e F R O N T I E R ®
2 of 2
Programmes like modeFRONTIER® are most commonly used to optimise the design of systems, seeking to achieve user-defined goals (e.g. maximising efficiency or minimising pressure loss) by varying input parameters. However, for parameter tuning, the variables of the optimisation become the values of α and β, and the goal becomes the minimisation of the error between the experimental curve, and that obtained using the porosity coefficients. Example: Tuning α and β for a Perforated Plate To show how this procedure can be applied, a perforated plate was chosen. Perforated plates are employed in many industries for a wide variety of purposes, such as acoustic control, flow stabilisation, pressure reduction, and heat transfer. Such plates can be treated as zero thickness baffles in STAR-CD, in which case the pressure equation becomes Δp = -ρ(α|u| + β)u, where Δp is the pressure drop across the baffle, ρ the fluid density, u the local velocity normal to the baffle surface, and, again, α and β the user-defined coefficients. Obtaining the Test Data As an experimental flow rig was not available, STAR-CD was used to create the “experimental” data; that is, for a certain hole pattern a number of CFD analyses were run, one for each of the flow rates required. The resulting pressure drops were used as the curve values to be matched. modeFRONTIER® was used to set up, control and run the experiments; the fluid properties, plate properties, and the velocity points to be calculated are entered by the user, allowing all cases to be run, and thereby the automatic creation of the velocity-pressure curve. Determining α and β by Curve Matching Fig. 2 shows the workflow in modeFRONTIER®, which passes each value of α and β to every flow analysis to be run, compares the resulting velocity-pressure curve with that obtained by experiment, and thereby calculates the RMS error. The direct integration with Excel in modeFRONTIER® was used to calculate the error between the 2 curves. The Simplex optimisation algorithm was used here, and the automatic reduction of the RMS error is shown in Fig. 3. In this case α and β were treated as discrete variables, and each allowed to vary between 0 1000. The start values of α and β were chosen at random; thereafter, the optimisation algorithm reduced the error by a process of triangulation. Fig. 4 shows the value for α and β for each analysis; these stabilised to α = 24.2 and β = 4.9, after fewer than 50 CFD analyses, which took less than an hour of total calculation time. The user could now use a course grid, with layers of porous cells instead of the plate, applying these values of α and β with confidence.
The methodology shown here is just as useful for any situation where a porous medium is to be used, but where the porosity parameters are unavailable and need to be determined. Please contact ESTECO for more information on this and many other applications of modeFRONTIER®.
modeFRONTIER® is a product of ESTECO Srl© 1999-2009 | www.esteco.com