UFR 2-11 Evaluation
High Reynolds Number Flow around Airfoil in Deep Stall
Flows Around Bodies
Underlying Flow Regime 2-11
Evaluation
Comparison of CFD Calculations with Experiments
A dramatic improvement in solution fidelity for DES compared to URANS, first reported by Shur et al. [22], was observed in the extensive cross-validation exercise carried out in the EU FLOMANIA project [4]. Figure 4 depicts the relative deviation from experimental drag achieved by DES and URANS within this work.
Figure 4: Comparison of URANS and DES for the prediction of mean drag coefficient for the NACA0012 airfoil at α = 60°. Results of 11 different simulations conducted by different partners with different codes and turbulence models within the EU FLOMANIA project [4]. Experimental data cited by Hoerner [6] are used as reference. |
The effect of spatial and temporal numerical schemes on DES was
investigated for the NACA0012 case at α = 45° by
Shur et al. (2004)
[23]. Using a localised "hybrid" convection
scheme [29] (in which 4th
order central differences are applied within the vortical wake region)
and a 2nd order temporal integration was seen to resolve fine turbulent
structures to a scale near to that of the local grid spacing. Switching
the convection scheme to 3rd order upwind or, to a lesser extent, the
temporal scheme to 1st order was seen to strongly damp the fine
vortices in the wake (Figure 5). Correspondingly, a strong under-
prediction of the Power Spectral Density (PSD) of the drag and lift
forces at higher frequencies was observed. The effect on the mean
forces and pressure distributions was however comparatively mild for
this case.
Figure 5: Effect of different spatial and temporal numerical schemes on the resolved wake structures of the NACA0012 at α = 45° [23]. "Hybrid" refers to the localized blending between 4th order central and 3rd or 5th order upwind convection schemes proposed by Travin et al. [29] |
Having clearly demonstrated the benefits of DES compared to URANS [4, 22]
(Figure 4),
no further URANS computations were carried out in the
successor EU project DESider [5], and the
focus shifted to cross-comparison of different turbulence-resolving approaches.
Figure 6
compares flow visualizations from 3 simulations carried out with the
use of different approaches (k – ω
SST SAS and DES based on SA and CEASM
RANS models) in the form of instantaneous fields of the vorticity
magnitude. They reveal quite similar flow and turbulent structures thus
supporting a marginal sensitivity of the simulations to the turbulence
modelling approach and numerics used.
Figure 6: Comparison of snapshots of vorticity magnitude from three simulations |
The same is to a major extent correct regarding the PSD of the lift
coefficient and mean pressure distributions over the airfoil shown in
Figure 7.
Figure 7(a) also suggests that all
the simulations are
capable of predicting the experimental spectra, particularly the main
shedding frequency and its harmonic, fairly well, whereas
Figure 7(b)
reveals a systematic difference between the predicted and measured
pressure on the suction side. Note also that SAS results somewhat
deviate from those of SA DES and are closer to the experiment. The same
trend is observed for the integral lift and drag forces
(Table 5).
A concrete reason for the difference between the SAS and DES predictions
is not clear but, in any case, it is not significant when compared to
e.g. the differences between DES and URANS or between different URANS
approaches (see Figure 4).
This justifies the above conclusion on the
weak sensitivity of the predictions to the turbulence modelling
approach and numerics used in different turbulence-resolving
simulations.
(a) | (b) |
Figure 7: Comparison of PSD of the lift coefficient (left) and mean pressure distributions over the airfoil (right) from three simulations with experimental data [27, 28] |
Partner and approach | μ [Cl] | Statistical 95% CI* | μ [Cd] | Statistical 95% CI* |
ANSYS (k – ω SST SAS, Lz=4) | 0.915 | ±0.017 | 1.484 | ±0.030 |
EADS-M (SA DES, in wind-tunnel) | 0.889 | ±0.016 | 1.425 | ±0.029 |
NTS (SA DES, Lz=4) | 0.879 | ±0.007 | 1.381 | ±0.012 |
TUB (SA DES, Lz=4) | 0.875 | ±0.007 | 1.33 | ±0.012 |
Experiment [24, 25] | 0.931 | ±0.004 | 1.517 | ±0.008 |
The parameters to which the results of the simulations turned out to be
very sensitive include the span-size of the computational domain and
time sample the turbulence statistics is calculated for. These
parameters are therefore the most important in the sense of formulation
the BPG for the considered UFR, and for this reason below we focus
exactly on those studies which analyse their effect. These studies
along with some original results related to this issue were summarized
in [2], so the further presentation of
the material closely follows this work.
Effect of time sample
Obtaining accurate estimates of statistical quantities naturally requires a sufficient statistical sample. This raises fundamental questions concerning the engineering application of computationally expensive turbulence-resolving methods: how many time steps must be computed to estimate the statistical quantities of interest to the desired accuracy? The inverse perspective is just as important: what is the error bar on the statistical quantities when only a given number of time steps are affordable? The implications of this issue for the cost planning of industrial computational studies and the avoidance of false conclusions are clear.
An arbitrary section of the time series for the lift and drag coefficients from the experiment is shown in Figure 8. The quasi-periodic von Kármán vortex shedding cycles are seen (with a time period of roughly 5 convective time unites, (c / |U∞ |) together with a strong low- frequency intermittency. This represents an apparently multi-modal behaviour of the flow, in which alternating weak and strong vortex shedding modes occur. The duration of each such mode as well as its initiation are random. As a result, it can intuitively be recognised that very long time samples will be required for accurate mean values of this flow.
Figure 8: Sample lift and drag coefficients time traces from the experimental data of Swalwell [27, 28], showing occurrence of weak and strong shedding behaviour. |
A common method to obtain an impression of the time sample effect on
the mean values is the computation of running averages. Indeed, this
approach was applied in the DESider project study of this
test case [5].
Figure 9 demonstrates such a running average for the experimental
Cd trace, from which an indication is given that the
mean Cd is still
not reliable to the second decimal place after 4000 non-dimensional
time units. Although useful in this respect, the running average
technique does not provide any quantitative estimate of the statistical
error. A potential peril therefore arises: were the data acquisition to
have been ceased at = 800, the strong and sudden drift that occurs
shortly thereafter would not be anticipated[1].
In order to get a
quantitative estimate of the statistical error, a novel signal
processing algorithm has been developed. The details of this technique
have been summarised in [2]
and published in more detail in [15]. For a
given input signal, the magnitude of the statistical error as a
function of sample length is estimated. The 95% confidence intervals
for the experimental drag coefficient have been obtained in this way
and plotted over the running average in Figure 9.
Contributed by: Charles Mockett; Misha Strelets — CFD Software GmbH and Technische Universitaet Berlin; New Technologies and Services LLC (NTS) and Saint-Petersburg State University
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