Turbulence modelling in compressor passages continues to be a challenging problem. In order to better understand the shortcomings of turbulence modelling, a LES and a RANS computation were performed of a repeating compressor stage. The computation was carried out near the aerodynamic design point of the compressor stage, in order to minimise the challenge posed to the turbulence model. The use of a repeating stage configuration removes the need to specify the statistics of the incoming turbulent field; the statistics become an output of the simulation and not an input. This is a critical fact that greatly increases the credibility of the current LES compressor simulation over many previous simulations. As the computations are performed at mid-span, radial gradients can safely be assumed to be small, thus removing issues associated with capturing flow features attributed to 3D geometry. The flow field is assumed to be incompressible, which is required in order to achieve a true repeating stage environment. The RANS computation is based on a state-of-the-art turbulence model. At the same flow coefficient, the RANS simulation yielded a total pressure rise very near that of the LES simulation. However, there are nontrivial differences in the flow details. The mean flow and Reynolds shear stress boundary layer profiles are in good agreement in regions of favourable pressure gradient, but significant differences exist in the presence of adverse pressure-gradients. The turbulent kinetic energy profiles however are in poor agreement throughout the flow. The mean flow production rates predicted by the RANS computation are largely similar to those of the LES simulation forward of mid-chord where the pressure gradient is favourable. A notable exception is the leading-edge region where the LES predicts negative production i.e. a net transfer of energy to the time-mean flow, and the region aft of mid-chord where the pressure gradient is adverse. Outside of the viscous sub-layer, the dissipation rates are also predicted correctly by the RANS simulation forward of midchord where the pressure gradient is favourable. Aft of mid-chord however, there are significant differences in the dissipation rates.
The flow in devices, such as heat exchangers, can be idealized as turbulent flow past an array of regularly spaced obstacles. Engineering calculations in such devices are easily handled if the flow can be represented by its volume-average quantities. This paper reports an investigation into the volume-averaged flowfield in a regular array of cylinders of finite height in crossflow at two Reynolds numbers (ReD). The investigation is based on scale-resolving computations and is thus the first to analyze the true form of the macroscopic turbulent kinetic energy (TKE) conservation law in the presence of macroscopic shear. Volume-averaging is performed parallel to the end walls in order to obtain profiles of macroscopic flow quantities. In inner coordinates, the macroscopic velocity profiles are similar to the canonical turbulent channel flow profiles, but with different values of the von Kármán constant and log-law y-intercept. The volume-averaged TKE is defined so as to include contributions from both the macroscopic and microscopic components of the flow. While the macroscopic TKE profile is very different to that of channel flow, the macroscopic TKE budget terms are remarkably similar. One notable exception is that the production rate stays large throughout the domain rather than attenuating rapidly after a near-wall peak. An extension to a widely used macroscopic turbulence model is proposed, which enables it to match the volume-averaged TKE production rate predicted by the large eddy simulations.
This article studies how the proper orthogonal decomposition eigenvectors and eigenvalues of the two-point velocity correlation tensor scale with Reτ in turbulent channel flows. To this effect, the two-point correlation tensor is computed from velocity fields extracted from the Direct Numerical Simulations (DNS) of plane channel flows at Reτ = 547 and Reτ = 934. The analysis reveals that the eigenvalues exhibit a high degree of scaling with Reτ, across a very wide range of streamwise and spanwise wavenumbers. The eigenvectors also show near complete independence from Reτ, as long as the wall-normal lengthscales larger than the channel height are removed. The poor Reτ scaling of turbulent structures larger than the channel height is well documented in the literature, and thus one would not expect eigenvectors corresponding to these scales to exhibit favorable Reτ scaling. Two-point velocity correlations and their eigenvectors are also computed using Large Eddy Simulations (LES) at Reτ = 1000 and compared to the results of the DNS at Reτ = 934. Both the correlations and eigenvectors matched very well between LES and DNS.
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