Mean-flow data assimilation based on minimal correction of turbulence models: Application to turbulent high Reynolds number backward-facing step

Linear and nonlinear sensor placement strategies for mean-flow reconstruction via data assimilation

“…Instead of relying on the laminar RANS equations, future work could include the consideration of an actual turbulence model in order to tackle higher flows, as performed by Franceschini et al. (2020). Incidentally, this study suggested that punctual measurements could still be relevant for the reconstruction of turbulent mean flows.…”

“…by invoking the turbulent-viscosity hypothesis, we here rely on punctual mean velocity measurements and the data assimilation procedure in § 2.5 to determine f . It should be emphasized that this forcing is here directly targeted following Foures et al (2014), Symon et al (2017) and Franceschini et al (2020), instead of the individual components of the Reynolds stress tensor. This may make the data assimilation problem better posed and exempt, among others, from the consideration of realizability conditions as investigated in Xiao et al (2016).…”

“…(2017) and Franceschini et al. (2020), instead of the individual components of the Reynolds stress tensor. This may make the data assimilation problem better posed and exempt, among others, from the consideration of realizability conditions as investigated in Xiao et al.…”

“…Data assimilation therefore appears as a prominent tool in all above mentioned data-driven approaches in the context of RANS modelling. The question of the appropriate choice of the model correction which forms the control vector in the data assimilation procedure remains open, and is discussed in Xiao & Cinnella (2019), Franceschini, Sipp & Marquet (2020).…”

Machine learning-augmented turbulence modeling for RANS simulations of massively separated flows

“…For the outputs, we start by noting that industrial applications have favoured up to now the use of a simple linear modeling of the Reynolds stresses, the Boussinesq approximation, due to its low induced-cost and increased robustness. Yet, Franceschini et al [24] recently showed, in the context of mean-flow data-assimilation, that the Boussinesq approximation could induce rigid models, that were able to only approximately reconstruct, through DA, simple mean-flows, such as the one obtained in backward-facing steps which exhibit separation and pressure gradients. In simple shear-dominated flows, the approximation is in fact known to be "effective" (turbulence essentially enhances mixing in an isotropic way, which is compatible with a linear constitutive relation), but actually not even strictly valid (Monier et al [25] showed that the Reynolds stresses were only roughly aligned with the local velocity gradient in turbulent boundary-layers).…”