UFR 3-31 Evaluation: Difference between revisions
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!Model||<math>{x_{sep}/H}</math> || <math>{x_{att}/H}</math> || <math>{L_{sep}}</math> || <math>\Delta</math> (%) || Inflow condition | !Model||<math>{x_{sep}/H}</math> || <math>{x_{att}/H}</math> || <math>{L_{sep}}</math> || <math>\Delta</math> (%) || Inflow condition | ||
|- | |- | ||
-- | |LES || 0.83 || 4.36 || 3.53 || n.a. || n.a. | ||
|- | |||
|Standard <math>{k-\varepsilon}</math> || 1.25 || 4.36 || 3.11 || 12 || <amth>{\varepsilon_{\mathrm{inflow}}=0.001></math> | |||
|} | |} | ||
<!-- | |||
LES & 0.83 & 4.36 & 3.53 & n.a. & n.a. \\ | |||
Standard $k-\varepsilon$ & 1.25 & 4.36 & 3.11 & 12 & $\varepsilon_{\mathrm{inflow}}=0.001$ \\ | |||
Realizable $k-\varepsilon$ & 1.19 & 4.905 & 3.71 & 5 & $\varepsilon_{\mathrm{inflow}}=0.001$ \\ | |||
Standard $k-\omega$ & 0.98 & 5.12 & 4.14 & 17 & $\omega_{\mathrm{inflow}}=0.1 U_{in}/H$ \\ | |||
SST $k-\omega$ & 0.87 & 5.62 & 4.75 & 34.5& $\omega_{\mathrm{inflow}}=0.1 U_{in}/H$ \\ | |||
--> | |||
Revision as of 08:58, 7 June 2012
Flow over curved backward-facing step
Semi-confined flows
Underlying Flow Regime 3-31
Evaluation
Comparison of LES results with experiments
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Figure 4: Skin-friction and pressure coefficients at the wall. Symbols: experiment \cite{zhang2010experimental}, solid line: simulation. |
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Comparisons of the simulation results with the experimental measurements of
Zhang and Zhong \cite{zhang2010experimental} are shown in Figs. 4 – 6. Only results obtained
with the fine mesh (ie. corresponding to the data provided), are shown here.
Comparisons with the coarse mesh results are given in Lardeau and Leschziner
\cite{lardeau2011interaction}. General agreement of the profiles is very good,
both for mean flow velocity Fig. 5 and
for the three components of the Reynolds stress tensor (Fig. 6). The major discrepancies are found
on the wall-measurements: the skin-friction coefficient is slightly overestimated
close to the separation, with a large peak of not present in the experimental results.
The experimental skin friction data should be taken with care, as they were computed
from the measured velocity field (bound to greater error in the near-wall region)
rather than from direct measurements at the wall.
Comparison of RANS results with LES results and experiments
Results obtained with the four RANS models are shown in Figs. 7 – 11}. Only four quantities (wall shear stress, pressure coefficient, streamwise velocity and turbulent kinetic energy) are shown, but other parameters can of course be compared, such as dissipation or Reynolds-stress if using second-moment closure.
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Figure 7: Comparison of RANS results with simulation data for (left column) wall shear stress and (right column) pressure coefficient . |
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Model | (%) | Inflow condition | |||
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LES | 0.83 | 4.36 | 3.53 | n.a. | n.a. |
Standard | 1.25 | 4.36 | 3.11 | 12 | <amth>{\varepsilon_{\mathrm{inflow}}=0.001></math> |
The streamwise evolution of the wall shear stress and the pressure coefficient
are shown in Fig. 7. As mentioned in the section (\S \ref{sec:RANS}),
the inflow condition was designed to match the behaviour of the wall shear stress up
to (including the peak near ), and this is indeed the case for all the
models. The difference between the models occurs just downstream of the peak:
both models return a slightly too late separation, while the two
models are in much better agreement with the LES data, up to . Inside
the separated region, all four models predict more or less the same wall shear stress. The only
model to return a correct reattachment point is the standard model, but
the recovery region downstream (from ) is much better predicted by both
models. Corresponding values for the separation and the reattachment points are
given in table \ref{tab:RansResults}. These observations are also valid for the
pressure coefficient : before separation, the flow is fairly well predicted by
all four models, compared to the LES data, with the same difference (too little
flow acceleration) compare to the experimental data, included in the plot.
Differences between the models only arise close to the separation point, with a
slightly larger flow acceleration predicted by the models. Overall, any of the
two models return a much better qualitative picture than the
formulations. However, table \ref{tab:RansResults} shows that the separation bubble
is much larger (up to 35%) than in the LES. Other, more advanced,
models were found to give better results for this test case, but once again, the
objective of this document is to provide guidelines, not an assessment of model capabilities.
The differences between the different models in predicting wall data
can be better understood by comparing profiles of the streamwise velocity component (Figs. 8 and 10) and the turbulent kinetic
energy (Figs. 9 and 11) at different
locations upstream of the bump, in the separated region and in the recovery region.
The two sets of models ( and ) have clear differences,
especially close to the inlet (from to ).
For ,
velocity and turbulence profiles are close to the simulated one up to , despite
the use of a constant value for across the inlet, which further reinforces
our choice for the inflow. Once separation sets in (too late with ),
the turbulent kinetic energy increases, but too slowly as expected, and the
separation bubble remains very thin, less than half the height of the simulated
one. The combination of a thinner separation bubble, late separation and low level
of turbulent kinetic energy (hence mixing) leads to a correct reattachement, despite
a delayed separation. The incorrect turbulent content is also found (transported)
downstream, in the recovery region.
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(a) | (b) |
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(c) | (d) |
Figure 9: Comparison of turbulent kinetic energy profiles with simulation data for the two models. |
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(a) | (b) |
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(c) | (d) |
Figure 10: Comparison of velocity profiles with simulation data for the two models. |
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For the models, there is a mismatch between
the simulated and computed velocity profile immediately downstream of the inlet.
The flow is accelerating in the viscous sub-layer (), while
the turbulence profile remains correct. The standard formulation
notoriously underpredict in that region, and this overshoot of velocity
is due to the imposition of an incompatible turbulence energy. A consistent
flow field is only fully established from . Once separation sets in
(), the model returns the same under-prediction of as the
variants, both in the separated region and further downstream.
Note however that the flow velocity from the Std model in the recirculation
provides the best agreement with the LES data, with a correct bubble size.
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(a) | (b) |
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(c) | (d) |
Figure 11: Comparison of turbulent kinetic energy profiles with simulation data for the two models.. |
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For the most common turbulence models, the results are found to be consistent with
previous studies: tends to predict a too late separation,
which in turns affects the prediction of the reattachment.
The opposite trend is observed for both models. For all cases, the
inflow condition is found to be a very influential parameter, and its definition must be
done with great care. An alternative approach, not used in the RANS calculations but in the LES,
is to perform a precursor simulation using the same turbulence model that will be tested
and save all the relevant quantities at the location where the momentum thickness
reaches the desired value.
Contributed by: Sylvain Lardeau — CD-adapco
© copyright ERCOFTAC 2024