NUMERICAL MODELLING OF TURBULENT FLOW IN PACKED BEDS

                    Jan Tobis
 Institute of Physical Chemistry  PAS , Warsaw, Poland


A detailed knowledge of flow phenomena in packed beds is essential in many fields
of  the chemical engineering science. Packed beds have important applications mainly
as catalytic reactors, nuclear reactors but also as mass or heat transfer equipment
(absorption columns, heat exchangers etc.). The broad field of applications extends in
shaft furnaces. Among these there are various shaft shelters, blast furnaces or lime
kilns as fixed bed gasification reactors. Moreover, it has been estimated that 25% of all
refinery vacuum towers world-wide are equipped with structured packing. Their huge
investment cost stimulates investigation of  the bed geometry just adequate for the
process in question.

The flow modelling remains a domain of the fluid mechanics science. However,
exercise on its achievements is not easy  because the bed geometry forms the complex
system of boundary conditions which have never been analysed explicitly. On the
other hand, a lot of simple phenomenological models of pressure drop in packed beds
are presented in literature. The most popular is the Ergun model.  It has been
developed from the analogy between the packed bed structure and the bundle of fine
tubes characterised by the same specific surface. An extension of the utility of  such
intuitively derived models lies in development of  theory and in creation of new
experimental data that might be compared with theoretical predictions. The packed bed
composed of the spheres in cubic arrangement was chosen as suitable for the
anemometric investigation.  The remarkable  changes of the turbulence intensity and
the bed  flow resistance were modelled with aid of various obstacles inserted within
the voids between the spheres. The  significant anizotropic effects were observed in the
case of obstacles in a shape of bands when the two-dimensional flow field was
generated  within the packed bed volume. Hence, the experimental data were compared
with the model taking into acount the second order tensor of the hydrodynamic
resistance. The tensor elements were determined in this approach by the separate
experimental method .

However, to complete the numerical modelling of turbulent flow in packed bed of
arbitrary chosen geometry the feature of the hydrodynamic resistance tensor has to be
predicted. This can be done by the solution of the closure model within the
representative volume of the system. The method of direct numerical solution of  the
Navier-Stokes equation seems to be unfeasible at turbulent flow conditions. Instead,
the various models of turbulence are recommended in literature. The k-e model, the
Reynolds Stress Model (RSM) and  the ReNormalisation Group methods (RNG) are
being tested with use of  the Fluent software facilities. An outcome from these
numerical estimations will be presented.