Turbulence-resolving Simulations of Swirling Flows

A series of numerical investigations is undertaken using a wide range of turbulence mod-\nels including conventional and non-conventional URANS models, hybrid URANS-LES\nmethods and LES to capture a large variety of physical mechanisms that produce pres-\nsure pulsations in the swirling flows. The available knowledge about these pulsations,\nwhich are usual in hydropower, are still far from complete. When the swirl is moder-\nately low, a stable on-axis structure generates in the pipe. If the swirl exceeds a certain\nlevel, the flow patterns associated with the swirl dominated vortex motions vacillate. A\nkey feature of strongly swirling flows is vortex breakdown. The vortex breakdown is an\nabrupt change in the core of a slender vortex and typically develops downstream into a\nrecirculatory “bubble” or a helical pattern. The swirl effects are usually seen as either the\ndesired result of design or unavoidable, possibly unforeseen, side effects which comprise a\nforced vortex core centered around its axis of rotation. The vortex breakdown is an invis-\ncid process and the pulsations caused by the vortex breakdown and their impact on the\nefficiency and hydraulic structures of water turbines depend on the flow rate, the velocity\ndistribution after the runner, the shape of the draft tube, and the dynamic response of\nthe whole hydraulic structure. The high level of unsteadiness in the flow field necessitates\nthe utilization of appropriate turbulence treatments to predict the complexity of the flow\nstructures.\nTime-accurate Reynolds-averaged Navier-Stokes (URANS) models are primarily use-\nful for capturing large-scale flow structures, while the details of the small-scale turbu-\nlence eddies are filtered out in the averaging process. In many cases also the large-scale\nstructures are damped by the URANS modeling which is formulated to model all the\nturbulence. The swirling flows in a pipe are dominated by large-scale detached eddies,\ntherefore the URANS models should be capable of predicting the flow fields. The qual-\nity of the URANS results is very dependent on the underlying turbulence model. The\nknowledge about URANS is limited to the simplest (most robust) linear eddy-viscosity\nmodels which are available in the proprietary codes. The inability of the conventional\nlinear eddy-viscosity models available in a CFD code should thus not be generalized\nto the URANS method alone. The conventional linear eddy-viscosity model provides a\ndirect link between the turbulent stress tensor and the mean strain rate, forcing them\nto be directly in phase, which is wrong. In the highly swirling flows, the curvature of\nthe streamlines should be taken into account for a better predicting of the flow fields.\nReynolds Stress Models (RSM) have the potential to significantly improve the flow pre-\ndictions by resolving anisotropy and incorporating more sensitivity and receptivity of\nthe underlying instabilities and unsteadiness. Since they are difficult to use they arenot widely used in industry. Most of the RSMs are not robust for highly swirling flows\nbecause of instability in the rapid part of the pressure-strain term in the transport equa-\ntion. The Explicit Algebraic Reynolds Stress Models (EARSMs) are simplified RSMs\nthat are much more numerically and computationally robust and have been found to\nbe comparable to standard two-equation models in computational effort. The EARSMs\nassume that the Reynolds stress tensor can be expressed in the strain and vorticity rate\ntensors.\nA more advanced approach, also called the second generation URANS method, is the\nhybrid URANS-LES method which is capable of capturing the high level of unsteadiness\nand handling the anisotropic and highly dynamic character of turbulent swirling flows.\nAn extended series of turbulence models is scrutinized in this work while the main focus\nis on the Detached-eddy simulation (DES) method. The DES method is a promising hy-\nbrid URANS-LES strategy capable of simulating internal flows dominated by large-scale\ndetached eddies at practical Reynolds numbers. Another hybrid URANS-LES method\nis scale-adaptive simulation (SAS). This method is based on detecting the unsteadiness\naccording to the velocity gradients in the flow field. This method gives better results\nthan LES in a highly swirling flow in a pipe using a relatively coarse resolution.