10th International Symposium on Turbulence and Shear Flow Phenomena (TSFP10), Chicago, USA, July, 2017
A-priori and a-posteriori assessment of LES subgrid models for liquid jet
atomization
S. Ketterl∗ , M. Klein
Department of Aerospace Engineering, Universität der Bundeswehr München
Werner-Heisenberg Weg 39, 85577 Neubiberg, Germany
∗ Corresponding author: [email protected]
This contribution is targeted towards large eddy simulation (LES) of turbulent two-phase flow. Due the excessive computational costs stemming from a wide range of length and time scales, direct numerical simulation (DNS) of liquid jet atomization
for industrial applications will remain out of scope in the near future. In order to predict the primary breakup, it is strived for
an LES framework and the required development of appropriate subgrid scale (SGS) models is one of the urgest challenges
(Tryggvason et al., 2013). In contrast to single phase flow, not only turbulent structures but also interfacial deformations remain
smaller than the mesh size. Turbulent two-phase LES depends on the interaction of turbulence with the interface at the unresolved
scale. These effects are captured by additional terms in the governing LES equations which arise due to the filtering of variables
across the discontinuous phase interface. The most important of these terms which have been considered in this work are:
τρuu,i j = ρ ui u j − ρ ui u j
τnn,i = σ ni κ δS − σ ni κ δS
ταu,i = α ui − α ui
The tensor τρuu,i j is the subgrid stress which is known from single-phase flow, τnn,i contains subgrid capillary forces and ταu,i
denotes the subgrid interfacial term. A variety of LES models are tested. Two structural models and four eddy viscosity models
for the subgrid stress are investigated, among them the well known Smagorinsky model and eddy viscosity models which include
a special treatment of the phase interface and the shear layer. The unresolved surface tension force and the subgrid interfacial term
are modeled by the scale similarity hypothesis. The accuracy of the proposed SGS closures is first a-priori assessed with respect
to explicitly filtered DNS data of liquid jet atomization. Afterwards, a-posteriori LES of liquid jet breakup are conducted, as
shown for one setup in Fig. 1 (left). Results are compared to DNS data by means of flow statistics and droplet size distributions.
Exemplarily shown are the lateral velocity fluctuations in Fig. 1 (right). Eddy viscosity models tend to suppress interface
instabilities but this effect is less pronounced for those models that are able to dampen the turbulent viscosity towards the phase
interface. The overall influence of eddy viscosity models remains small. It is shown that the primary breakup strongly depends
on the numerical discretization of the nonlinear momentum advection term. A-priori and a-posteriori studies demonstrate that the
numerical error has the same order of magnitude and partially dominates the effect of the subgrid stress model. Incorporating the
unresolved surface tension force and the subgrid interfacial term ameliorates a-posteriori LES results to some extend. Subgrid
capillary forces enhance the disintegration of the liquid jet while the subgrid interfacial term leads to later ligament breakup and
reduces the formation of small drops.
REFERENCES
Tryggvason, G., Dabiri, S., Aboulhasanzadeh, B. & Lu, J. 2013 Multiscale considerations in direct numerical simulations of
multiphase flows. Physics of Fluids (1994-present) 25 (3), 031302.
0.2
ταu
τnn
U-DNS
0.1
p
hv0v0i/hUcl i
0.15
0.05
0
0
0.5
1
1.5
2
2.5
3
r1/2 /D
Figure 1. Liquid isosurface of a spatially developing round Diesel jet of an a-posteriori LES computation (left). Normalized lateral velocity
fluctuations plotted against the lateral direction obtained by including the subgrid scale interfacial or surface tension term.
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