A partially-averaged Navier–Stokes model for the simulation of turbulent swirling flow with vortex breakdown

Abstract

a b s t r a c tThis paper presents the development and validation of a new partially-averaged Navier-Stokes (PANS) model which can successfully predict turbulent swirling flow with vortex breakdown. The proposed PANS model uses an extended low Reynolds number k-e model as the baseline model. Furthermore, a new formulation for the unresolved-to-total turbulent kinetic energy ratio f k is developed using partial integration of the complete turbulence energy spectrum. Therefore, the present formulation of f k is believed to be superior to the previously used constant or computed values. The newly developed PANS model is used in unsteady numerical simulations of two turbulent swirling flows containing vortex breakdown, namely swirling flow through an abrupt expansion and flow in a draft tube of a hydraulic turbine operating under partial load. The present PANS model accurately predicts time-averaged and root-mean-square (rms) velocities in the case of the abrupt expansion, while it is shown to be superior to the Delayed Detached Eddy Simulation (DDES) and Shear Stress Transport (SST) k-x models. Predictions of the reattachment length using the present model shows at least 14% and 23% improvements compared to the DDES and the SST k-x models respectively. Also, transient features of the flow, e.g. vortex rope formation and precession, is well captured in the case of the complex draft tube flow. The frequency of the vortex rope precession, which causes severe fluctuations and vibrations, is well predicted by only 7% deviations from the experimental data.

The State of the Art of Hybrid RANS/LES Modeling for the Simulation of Turbulent Flows

“…139 throughout the whole computation was applied to simulate the test case of an axisymmetric jet at different grid resolutions [38]. A new formulation of the function f k has been used afterwards [45] based on partial integration of the complete Von Kármán energy spectrum E ( κ ) as introduced earlier in PITM [26, 30] leading to a new extended PANS formalism hereafter denoted EXPANS to avoid confusion with PANS . In the PANS model, the diffusion terms can be embedded in the equations for simulating non-homogeneous flows [39, 40].…”

“…Although the PITM method has been developed in the spectral space on the basis of the physical processes of transfer of energy into the spectral zone of the spectrum whereas the PANS method has been empirically developed in the physical space involving a self similarity evolution hypothesis, the PANS method has made an important step towards PITM when Foroutan and Yavuzkurt [45] introduced the technique of partial integration of a Von Karman spectrum as previously developed in PITM, in the new extended PANS denoted EXPANS. In both approaches, relatively to the RANS equations (13) and (14), the corresponding subfilter-scale equations (122) and (124) look like identical to the RANS equations but the coefficient appearing in the destruction term of the dissipation-rate is no longer constant whereas the coefficient is the same as the RANS coefficient .…”

Partially-averaged Navier–Stokes simulations of two bluff body flows

“…There are attempts to predict f k using other formulations. Foroutan and Yavuzkurt [33] recently proposed a formulation for f k that ensures that the predicted value is between 0 and 1. Some researchers are also revisiting early work of Speziale [34], who provided another form of f k in the framework of a Very Large Eddy Simulation.…”

Fluid flow and conjugate heat transfer in a matrix of surface-mounted cubes: A PANS study

“…For example, Foroutan and Yavuzkurt (2013) recently proposed the formulation for f k which ensures that the predicted value is between 0 and 1. It is also worth of revisiting the work of Speziale (1998), see also Hussaini et al (2006), who provided a possible path in deriving the f k value in the framework of the Very Large Eddy Simulation.…”