# Turbulence-resolving Simulations of Swirling Flows

[Doktorsavhandling]

A series of numerical investigations is undertaken using a wide range of turbulence mod- els including conventional and non-conventional URANS models, hybrid URANS-LES methods and LES to capture a large variety of physical mechanisms that produce pres- sure pulsations in the swirling flows. The available knowledge about these pulsations, which are usual in hydropower, are still far from complete. When the swirl is moder- ately low, a stable on-axis structure generates in the pipe. If the swirl exceeds a certain level, the flow patterns associated with the swirl dominated vortex motions vacillate. A key feature of strongly swirling flows is vortex breakdown. The vortex breakdown is an abrupt change in the core of a slender vortex and typically develops downstream into a recirculatory “bubble” or a helical pattern. The swirl effects are usually seen as either the desired result of design or unavoidable, possibly unforeseen, side effects which comprise a forced vortex core centered around its axis of rotation. The vortex breakdown is an invis- cid process and the pulsations caused by the vortex breakdown and their impact on the efficiency and hydraulic structures of water turbines depend on the flow rate, the velocity distribution after the runner, the shape of the draft tube, and the dynamic response of the whole hydraulic structure. The high level of unsteadiness in the flow field necessitates the utilization of appropriate turbulence treatments to predict the complexity of the flow structures. Time-accurate Reynolds-averaged Navier-Stokes (URANS) models are primarily use- ful for capturing large-scale flow structures, while the details of the small-scale turbu- lence eddies are filtered out in the averaging process. In many cases also the large-scale structures are damped by the URANS modeling which is formulated to model all the turbulence. The swirling flows in a pipe are dominated by large-scale detached eddies, therefore the URANS models should be capable of predicting the flow fields. The qual- ity of the URANS results is very dependent on the underlying turbulence model. The knowledge about URANS is limited to the simplest (most robust) linear eddy-viscosity models which are available in the proprietary codes. The inability of the conventional linear eddy-viscosity models available in a CFD code should thus not be generalized to the URANS method alone. The conventional linear eddy-viscosity model provides a direct link between the turbulent stress tensor and the mean strain rate, forcing them to be directly in phase, which is wrong. In the highly swirling flows, the curvature of the streamlines should be taken into account for a better predicting of the flow fields. Reynolds Stress Models (RSM) have the potential to significantly improve the flow pre- dictions by resolving anisotropy and incorporating more sensitivity and receptivity of the 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 because of instability in the rapid part of the pressure-strain term in the transport equa- tion. The Explicit Algebraic Reynolds Stress Models (EARSMs) are simplified RSMs that are much more numerically and computationally robust and have been found to be comparable to standard two-equation models in computational effort. The EARSMs assume that the Reynolds stress tensor can be expressed in the strain and vorticity rate tensors. A more advanced approach, also called the second generation URANS method, is the hybrid URANS-LES method which is capable of capturing the high level of unsteadiness and handling the anisotropic and highly dynamic character of turbulent swirling flows. An extended series of turbulence models is scrutinized in this work while the main focus is on the Detached-eddy simulation (DES) method. The DES method is a promising hy- brid URANS-LES strategy capable of simulating internal flows dominated by large-scale detached eddies at practical Reynolds numbers. Another hybrid URANS-LES method is scale-adaptive simulation (SAS). This method is based on detecting the unsteadiness according to the velocity gradients in the flow field. This method gives better results than LES in a highly swirling flow in a pipe using a relatively coarse resolution.

**Nyckelord: **Hydropower, Swirling Flow, Vortex Breakdown, Flow Control, Turbulence Modeling, URANS, Hybrid URANS-LES, DDES, SAS, LES

Denna post skapades 2016-05-13. Senast ändrad 2016-05-16.

CPL Pubid: 236470