Swirling flow in a conical diffuser generated with rotor-stator interaction

Application Challenge AC6-14 © copyright ERCOFTAC 2024

Overview of CFD Simulations

A series of numerical simulations was undertaken to study a highly swirling turbulent flow generated by rotor-stator interaction in a swirl generator \cite{Javadi2015c}. The purpose was to assess the applicability of different turbulence models in a swirling flow with a high level of unsteadiness and a significant production and dissipation of turbulence in the flow away from the wall. Nine turbulence models are compared: four high-Reynolds number models URANS, two low-Reynolds number models URANS and three hybrid URANS-LES models. These are the standard $k-\epsilon$, SST $k-\omega$, realizable $k-\epsilon$, RNG $k-\epsilon$, Launder-Sharma $k-\epsilon$, Lien-Cubic $k-\epsilon$, delayed DES Spalart-Allmaras \cite{Spalart2006}, DDES SST $k-\omega$ \cite{Gritskevich2012} and improved DDES-SA \cite{Shur2008} models. The URANS models are capable of capturing the main unsteady feature of this flow, the so-called helical vortex rope, which is formed by the strong centrifugal force and an on-axis recirculation region. However, the size of the on-axis recirculation region is overestimated by the URANS models. Although the low-Reynolds number URANS formulations resolve the boundary layers in the runner and the draft tube more accurately, they still encounter difficulties in predicting the main flow features in the adverse pressure gradient region in the draft tube. It is shown that a more detailed resolution, which is provided by the hybrid URANS-LES methods, is necessary to capture the turbulence and the coherent structures.

SIMULATION CASE CFD

Solution Strategy

The calculations reported herein are made using the finite-volume method in the OpenFOAM-1.6-ext CFD code. The second-order central differencing scheme is used to discretize the diffusion terms. The linear-upwind differencing is used in URANS simulations to approximate the convection term. The blended numerical scheme is used in the hybrid method. The scheme is a combination of linear-upwind differencing in the URANS region and a limited linear total variation diminishing (TVD) scheme with a conformance coefficient in the LES region. The convection term in the LES region is interpolated by 15\% linear-upwind differencing and 85\% central differencing. The larger the part of the central differencing in the LES region is, the smaller the time-step required. Furthermore, the second-order van Leer TVD scheme is used to approximate the convection term in the hybrid method. The numerical schemes have only small effects on the time-averaged values. Time marching is performed with an implicit second-order accurate backward differentiating scheme.

Computational Domain

Figure \ref{Comp_domain} shows the complete computational domain. The domain is meshed in four regions in ICEM CFD using a structured multi-block approach with \textit{O}-grids around the blades and in the draft tube. The strut region is included in the high-Reynolds number model simulations, but omitted in the low-Reynolds number model and hybrid URANS-LES simulations. Those simulations employ the interpolated data from the URANS simulation as inlet condition before the guide vanes. Three mesh resolutions are created, one for high-Reynolds number URANS, one for low-Reynolds number URANS, and one for hybrid URANS-LES model. Figure \ref{fig3} shows the mesh for the hybrid URANS-LES simulations.

The General Grid Interface (GGI)is used at the interfaces between the rotating and stationary regions, and to simplify the mesh generation of the strut region. The General Grid Interface (GGI) connections refer to the class of grid connections where the grid on either side of the two connected surfaces does not match. In general, GGI connections permit non-matching of node location, element type, surface extent, surface shape and even non-matching of the flow physics across the connection.