Capturing Effects of Rotation in Sudden Expansion Channels Using Detached Eddy Simulation

Abstract

T HE effects of system rotation are of interest in flows in hydro/ turbo machinery especially in the design of centrifugal compressor impellers and runner blades. When the direction of rotation is in tandem with the fluid rotation vector, that is, the vorticity, the flow is stabilized, whereas the flow is destabilized if the directions are opposing. As with boundary layers, shear layers are also stabilized or destabilized by rotation. Rotation (or streamline curvature) generates extra strain rates that significantly affect turbulent stress production. Bradshaw [1] formulated an analogy between meteorological parameters and parameters describing rotation about the axis normal to the plane of rotation. He defined an effective Richardson number (Ri) for flows undergoing rotation that is used to define amodifiedmixing length [l l0 1 Ri ].Most of the later studies also propose a similar definition, where the effects of rotation are modeled by formulating corrections using a rotation Richardson number. Nilsen and Andersson [2] used an algebraic second moment closure model to predict the rotational effects on backward facing step flows. It was observed that rotation induced variation in the mean flow pattern was a result of significant changes in turbulent fluctuations in the free shear layer. However quantitative predictions of the reattachment length showed only partial agreement with the experimental data (Rothe and Johnston [3]). A similar study was carried out on rotating flows using a v–f model by Iaccarino et al. [4]. Both the original and a modified version of the model were used to predict the reattachment length downstream of a backward facing step. The modified model predicted the reattachment length better than the originalmodel. However itwas observed that the predictions of the modified model, like the algebraic second moment (ASM) model of Nilsen and Andersson [2] showed only partial agreement with the experiments. Therefore in spite of the continual development of Reynolds-averagedNavier–Stokes (RANS)models, predicting the effects of rotation in turbulent flows is a major challenge. The eddies formed in themassively separated regions downstream of the step are geometry specific. The “detached” eddies are not as universal as the eddies in typical thin shear layers where RANS models are calibrated. This is the reasonwhyRANSmodels are often observed to fail in flows undergoing massive separation. Large eddy simulation (LES) resolves the large energy carrying eddies while modeling the smaller isotropic eddies using a subgrid scale stress model. LES is a viable and a reliable method for simulating flows undergoing massive separation. However the near-wall resolution necessary for LESmakes it prohibitively expensive at high Reynolds numbers. A solution to the computational challenges associated with the reliable prediction ofmassively separated turbulent flows is detached eddy simulations (DES). DES sensitizes a RANS model to grid length scales, thereby allowing it to function as a subgrid scalemodel in critical regions of interest. This allows the natural instabilities of the flow in this region to develop, the energy cascade to grow, and improves the quality of the solution in this region. Though DES was initially proposed for the Spalart–Allmaras model, it can be easily extended to other models (Strelets [5]), by appropriately defining a turbulent length scale. The credibility of the approach has been validated by numerous applications in the literature for external and internal flows. The objective of the current study is to investigate the capabilities of DES in capturing the effects of rotation induced Coriolis forces on turbulent separation and reattachment in a backward facing step geometry. To evaluate the accuracy of the scheme in predicting the effects, the reattachment lengths predicted by DES are compared with experimental measurements by Rothe and Johnston [1] and also compared with other RANS models from the literature.