Dear colleagues,
When investigating the behaviour of a fuel injector, usually optical measurements are carried out. The vapor phase of the spray is usually captured by Schlieren-Imaging. The experiment is often carried out more than once, because of shot-to-shot variations. If one then superpositions the pictures, an ensemble-averaged image is created.
I want to compare an ensemble averaged measurement image with a RANS-CFD simulation. I plan to use the density as the plotted variable in the CFD simulation - This procedure is sometimes seen in publications.
I do now have the following question - The RANS-CFD simulation is usually Favre-averaged, whereas the measurement image (in my case) is an ensemble averaged image. Would this difference in the averaging technique have to be considered in any way or is this not necessary because I am looking at the density in the CFD-simulation?
The Favre averaging concept is independent of the method for defining the statistical mean, i.e. time or ensemble averaging. It is a mathematical procedure applicable to flows with 'density variation' to avoid the necessity to mathematically model the correlations of (density fluctuations* velocity fluctuations) that contribute to the Reynolds stresses. The implication is that if you decide not to use the Favre average, then you need the explicit modelling of these correlations in the Reynolds stress model (or equivalently any commonly used 2-equation turbulence model, e.g. k-epsilon model). In the case of a vaporizing spray, the question becomes how important is the contribution of this term to the momentum exchange between the spray and the air, compared with the ' primary' processes driven by the 'mean' flow variables (i.e the aerodynamic drag and bulk expansion due to liquid vaporization). Also, the question is what the measurement technique is measuring (e.g. it is argued that LDA provides a non density-weighted velocity data while hot-wire provides a value close to the Faver-average velocity). It is impossible to state with certainty, but in the circumstances of your test, the velocity data extracted from the ensemble imaging is likely close to a Favre-average (on the grounds that the data is not a point-wise measurement and globally it incorporates all turbulent exchange processes, including those due to density fluctuations).
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