LES Investigation of Boussinesq Constitutive Relation Validity in a Corner Separation Flow

Abstract

The present study aims at analysing the Boussinesq constitutive relation validity in a corner separation flow of a compressor cascade. The Boussinesq constitutive relation is commonly used in Reynolds-averaged Navier-Stokes (RANS) simulations for turbomachinery design. It assumes an alignment between the Reynolds stress tensor and the zero-trace mean strain-rate tensor. An indicator that measures the alignment between these tensors is used to test the validity of this assumption in a high fidelity large-eddy simulation. Eddy-viscosities are also computed using the LES database and compared. A large-eddy simulation (LES) of a LMFA-NACA65 compressor cascade, in which a corner separation is present, is considered as reference. With LES, both the Reynolds stress tensor and the mean strain-rate tensor are known, which allows the construction of the indicator and the eddy-viscosities. Two constitutive relations are evaluated. The first one is the Boussinesq constitutive relation, while the second one is the quadratic constitutive relation (QCR), expected to render more anisotropy, thus to present a better alignment between the tensors. The Boussinesq constitutive relation is rarely valid, but the QCR tends to improve the alignment. The improvement is mainly present at the inlet, upstream of the corner separation. At the outlet, the correction is milder. The eddy-viscosity built with the LES results are of the same order of magnitude as those built as the ratio of the turbulent kinetic energy k and the turbulence specific dissipation rate ω. They also show that the main impact of the QCR is to rotate the mean strain-rate tensor in order to realign it with the Reynolds stress tensor, without dilating it.

Importance of Nonequilibrium Modeling for Compressors

“…Weatheritt et al [7] found the validity of the Boussinesq approximation to be poor in the wake behind a low pressure turbine cascade and proposed a more complex relationship between τ i j and S i j to replace the Boussinesq approximation with, improving alignment of the two tensors. Monier et al [8] applied a similar methodology to a compressor corner separation using LES data.…”

Validation and analyses of QCR correction turbulence model in sub-/super-sonic inner flows

“…Dandois et al 11 applied QCR to their in-house solver elsA and calculated the separation at the wing-body junction and in the rectangular duct with shock-induced separation, respectively, showing that QCR can significantly improve the fidelity of the flow simulation at the geometric junction without deteriorating the accuracy of the simulation elsewhere. Monier et al 17 assessed the applicability of the Boussinesq constitutive relation for corner separation flow in a compressor cascade using LES-calculated data as a reference. The investigation demonstrated that the incorporation of the QCR correction improved the relationship between the mean strain rate tensor and the Reynolds stress tensor for corner separation at the inlet and upstream.…”

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

“…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). In view of drastically improving the fidelity of RANS computations, it therefore seems reasonable to lift this constraint in the modeling of the Reynolds stresses.…”