Turbulent separated inert and reactive flows over a triangular bluff body

Application Challenge AC2-12 © copyright ERCOFTAC 2019

Best Practice Advice

Key Fluid Physics

The Reynolds numbers based on the side of the bluff-body and bulk velocity are estimated as Re=28,000 – 47,000, and the flow can be considered to be in the sub-critical regime for the inert simulations. The combustion is characterized by the lean, premixed propane-air mixture of equivalence ratio ?=0.58-0.65 (“thin reaction zone” regime). The key features of the flow mechanics are the laminar boundary layer, separated shear layer, wake and the flow instabilities that provide complex, nonlinear interactions between them. The wake is dominated by two types of instabilities: the convective instabilities or asymmetric vortex shedding the (Bénard/von Kármán instability) and Kelvin–Helmholtz instability (sometimes called absolute) of the separated shear layer. For the reactive cases, the flame introduces additional phenomena trough effects of exothermicity and flow dilatation on the flow field, which leads to the large differences between the non-reacting and the reacting wakes.

Application Uncertainties

A word of caution should be given here concerning the estimation of the adiabatic flame temperature since two sets of experiments were performed: the CARS measurements [3] and the gas analysis [1]. Sjunnesson et al. [3] provided the adiabatic temperatures for the CARS measurements (? = 0.58?0.61) as Tad = 1713 K and Tad = 1876 K for the cases C1 and C2, respectively. However, all present numerical results were calculated for the conditions with ? = 0.65 relevant to the gas measurements [1]. The estimated adiabatic temperatures for the cases C1, C2 and ? = 0.65 were Tad = 1800 K and Tad = 2035 K, respectively, which were used in the previous sections for all figures to normalize temperature. The calculated adiabatic temperatures were consistent with the temperatures calculated on the basis of the chemical equilibrium assumption (Teq ) as well. Table 6 summaries all these findings.

Table 6: Adiabatic and chemical equilibrium flame temperatures for C1 and C2 flow conditions

Discretisation and Grid Resolution

Concerning discretization errors both spatial and temporal discretization errors should be considered. Usually the spatial discretization error effects are larger than the errors arising from the time integration [23]. It can be shown that in the case of fully developed turbulent flows, existing small time and space scales are simply advected by the most energetic eddies [23]. This argument yields an accuracy time-scale similar to the Courant-Friedrichs-Lewy (CFL) criterion. Thus, in all present calculations, the stability condition CFL < 0.75 was employed, which guaranteed that the actual time step was close to the accuracy time step. Several calculations were performed to investigate the spatial discretization error of the present SAS and LES results. It was interesting to see that the non-reactive SAS results obtained on the refined mesh provided some improvement in the accuracy of the mean flow field, both for the first and second order statistics, while at the same time keeping the similarity in the flow dynamics (energy spectra and vortex shedding).On the other hand, the reactive SAS calculations did not show any significant improvement in the predictions for the mean flow field as well as the wake dynamics. The results obtained by the combustion LES on the two grids showed some improvement in the accuracy for the second order statistics, while the first order statistics and wake dynamics were captured approximately with the same level of precision. Finally, satisfactory agreement was obtained between the measured and resolved turbulence kinetic energy by the present SAS and LES, which indicates, at least qualitatively, that the spatial resolution of the used grids was adequate.

Recommendations for Future Work

The focus of future work should be on the following aspects:

Several approaches have been discussed, including the conventional RANS/URANS, the large-eddy simulation and the scale-adaptive simulation. However, it will be interesting to assess the detached-eddy simulation (both inert and reactive) for the present benchmark as well;
The shear layer instabilities were qualitatively captured (based on the flow visualization) for both inert and combustion cases. However, quantitative information (frequencies) was not examined. Thus, it will be useful to estimate the frequencies of the shear layer instabilities and compare them to those for other bluff-bodies (etc., circular cylinder);
Finally, one of the important aspects of unsteady combustion physics is the lean blowoff (LBO). The simplicity of the test setup makes it a very attractive platform for further investigation of the different LBO modeling approaches.