Computational modelling of turbulent swirling flows with second-moment closures.
This work focuses on the simulation of turbulent swirling flows within the framework
of second-moment closure. The main objectives are to assess the performance of
currently available turbulence models in predicting such flows, and to develop new
closure models which would further enhance current predictive ability, and hence, to
provide a reliable turbulence model for engineering applications that would help the
design process and reduce the development costs of industrial combustion systems.
Attention is confined to isothermal flows, and predictions have been carried out
for three major swirling cases: a weakly and a strongly swirling free jet and a confined
strongly swirling flow in which an annular swirling stream is discharged together with
a non-swirling central jet into a suddenly enlarging circular chamber. In the last case,
mass transfer has also been examined by predicting the behaviour of an inert scalar
tracer with which the central jet has been laced.
The existing turbulence models examined are the standard versions of the k — e
Boussinesq-viscosity model, the algebraic stress closure and the differential stress closure
(BVM, ASM and DSM, respectively), as well as modified ASM and DSM variants.
One outcome of this study is that neither the standard versions of the BVM,
ASM and DSM nor their previously modified forms examined here predict adequately
swirling-flow behaviour. An important conclusion emerging from preliminary efforts
has been that the algebraic approximation of stress transport in terms of the transport
of turbulence energy—which is a widely used practice—is fundamentally flawed
in the presence of swirl. Specifically, the method returns a physically unrealistic behaviour
of the normal stresses. It is this conclusion which eventually led to the ASM
methodology being discarded and to the exclusive use of the differential methodology.
Within the framework of differential closures, two new pressure-strain models
have been proposed, namely the Isotropization of Production and Convection Model
(IPCM) and the Cubic Quasi-Isotropic Model (CQIM). The former emerged as an
extension of the standard DSM approach with the inclusion of the convection tensor
into the turbulence isotropization mechanism, whereas the latter follows from a more
rational and fundamental approach in which non-linear anisotropy effects have been
incorporated, with the resulting model made to satisfy the limit of two-dimensional
turbulence. Comparisons between predicted solutions and measurements for swirling
flow show that the IPCM produces a marked improvement over all the other models
considered, while it does not significantly alter the behaviour of the standard stress
closure in non-swirling conditions. Only very limited improvement is achieved by the
CQIM, however, despite its success in predicting nearly homogeneous shear flows.
The merits and weaknesses of all the models examined are discussed in detail, and
the IPCM is recommended as the best approach for predictions of swirling flows.
Within the study of the confined case, considerations were extended to the modelling
of scalar transport by a second-moment flux closure, and comparisons are made
between eddy-diffusivity and flux-closure calculations and experimental data. Computational
results show that the distribution of the scalar field is primarily governed
by aero-dynamic features. There are indications, however, that the flux model is
superior to the eddy-diffusivity model.