Assessment of turbulence model performance: Large streamline curvature and integral length scales

Abstract

For the flow over curved surfaces, an extra wall-normal pressure gradient is imposed to the flow through excessive surface pressure, such that the flow turns in alignment with the surface. In turn, turbulent fluctuations are suppressed over the convex surface; whereas, they are enhanced over the concave. Recently, the direct numerical simulation (DNS) of turbulent channel flow experiencing a 60 degree circular bend shows highly complex flow phenomena. Particularly, the mean flow properties are directly related to the channel geometry; in the impulse response of the mean flow to the step change of streamline curvature, sudden changes in mean strain rate and extra rates of strain emerge. This mean flow process is prior to the response of the turbulence structures. Due to the large streamline curvature, the underlying turbulence lagging mechanism and the stress strain misalignment are difficult to model. For this, the new DNS data for the wall bounded flow with high streamline curvature and large integral length scales is used to explore RANS performance. For eddy-viscosity models, this leads to the Boussinesq approximation being questionable. Also, for a Reynolds-stress model (RSM) with closure approximations applicable to homogeneous turbulent flows that are nearly in equilibrium, the current case can result in substantial predictive error. This is because of, for example, the linear approximation for the rapid pressure–strain correlation. To help move towards better turbulence modelling, Reynolds-averaged Navier–Stokes (RANS) predictions are compared for the same flow configuration as the DNS, using some popular turbulent models. These models include the second-order closure with the stress-ω formulation, the standard k−ω and the Menter’s shear-stress transport (SST) models, the standard Spalart–Allmaras (S-A) model with and without the corresponding strain–vorticity correction. As expected, overall, the RSM provides closer predictions to the DNS data than the selected eddy-viscosity models, even though the predictive accuracy needs to be further improved. Potentially, a non-linear constitutive relation or second-order closure, incorporating a relaxation approximation for the lagging mechanism, may lead to a remedy for the current non-equilibrium flow. Moreover, all models would also benefit from sensitisation to the impact of the large integral length scales.