R. Maduta

On “Steady” RANS Modeling for improved Prediction of Wall-bounded Separation

It is well-known that the separation process is inherently a highly unsteady phenomenon. To capture it correctly LES-relevant models – conventional LES and hybrid LES/RANS models (DES schemes, PITM, PANS) have to be applied. Because of their high spatial and temporal requirements the application of these methods is not straightforwardly affordable for the flow configurations of industrial relevance. On the other hand, apart of the backward-facing step flow geometry characterized by the sharpe-edge separation of a flat plate boundary layer which can be reasonably well solved by an advanced steady RANS model, the flows involving separation are in general beyond the reach of the conventional RANS method independent of the modeling level. Typical outcome is a low level of turbulence activity in the separated shear layer and a correspondingly long recirculation zone. The latter issues motivated the present work demonstrating the possibility to appropriately improve the computational results pertinent to the flow configurations featured by wall-bounded separation in the “Steady RANS” framework. An appropriately designed term modeled in terms of the von Karman length scale (adopted from the SAS modeling strategy for ”unsteady” flow computations, Menter and Egorov, 2010) was introduced into the scale-supplying equation governing the homogeneous part of the inverse time scale ( = ⁄ ). This term (denoted by ) being active only in the narrow area of the separation region acts towards an appropriate enhancement of the (fully-modeled) turbulence in the separated shear layer resulting in a correct mean velocity development and proper size of the recirculation zone. Predictive performances of the proposed model equation solved in conjunction with the Jakirlic and Hanjalic’s Reynolds stress model equation (2002) were illustrated by computing several configurations featured by boundary layer separation including the flow over a periodical arrangement of smoothly contoured 2D hills in a range of Reynolds numbers, flow over a wall-mounted fence and in a 3D diffuser.

Sensitized-RANS Modelling of Turbulence: Resolving Turbulence Unsteadiness by a (Near-Wall) Reynolds Stress Model

A turbulence model designed and calibrated in the steady RANS (Reynolds-Averaged Navier-Stokes) framework has usually been straightforwardly applied to an unsteady calculation. It mostly ended up in a steady velocity field in the case of confined wall-bounded flows; a somewhat better outcome is to be expected in globally unstable flows, such as bluff body configurations. However, only a weakly unsteady mean flow can be returned with the level of unsteadiness being by far lower compared to a referent database. The latter outcome motivated the present work dealing with an appropriate extension of a near-wall Second-Moment Closure (SMC) RANS model towards an instability-sensitive formulation. Accordingly, a Sensitized-RANS (SRANS) model based on a differential, near-wall Reynolds stress model of turbulence, capable of resolving the turbulence fluctuations to an extent corresponding to the model’s self-balancing between resolved and modelled (unresolved) contributions to the turbulence kinetic energy, is formulated and applied to several attached and separated wall-bounded configurations—channel and duct flows, external and internal flows separating from sharp-edged and continuous curved surfaces. In most cases considered the fluctuating velocity field was obtained started from the steady RANS results. The model proposed does not comprise any parameter depending explicitly on the grid spacing. An additional term in the corresponding length scale-determining equation providing a selective assessment of its production, modelled in terms of the von Karman length scale (formulated in terms of the second derivative of the velocity field) in line with the SAS (Scale-Adaptive Simulation) proposal (Menter and Egorov, Flow Turbul Combust 85:113–138, (2010) [14]), represents here the key parameter.

An Eddy-Resolving Reynolds Stress Model for the Turbulent Bubbly Flow in a Square Cross-Sectioned Bubble Column

An instability-sensitive, eddy-resolving Reynolds Stress Model of turbulence, employed in the Eulerian-Eulerian two-fluid framework, is formulated and validated by computing the gas-liquid bubble column in a three-dimensional square cross-sectioned configuration in the homogeneous flow regime. Interphase momentum transfer is modelled by considering drag, lift and virtual mass forces. The turbulence in the continuous liquid phase is captured by using a Second-Moment Closure model employed in the Unsteady Reynolds-Averaged Navier Stokes framework implying the solving of the differential transport equations for the Reynolds stress tensor and the homogeneous part of the inverse turbulent time scale ωh. This uiuj – ωh model is appropriately extended in accordance with the Scale-Adaptive Simulation proposal, enabling so the development of the fluctuating turbulence. The results obtained are analysed along with a reference experiment with respect to the evolution of the mean flow and turbulent quantities in both gas and liquid phases. The model described is implemented in the numerical code OpenFOAM.Copyright

Sensitizing Second-Moment Closure Model to Turbulent Flow Unsteadiness

Different scale-supplying equations formulated in the term-by-term manner at the Second-Moment Closure modeling level were a priori tested (the velocity and Reynolds stress data were taken from the available DNS database) in the flow in a plane channel in the Reynolds number range between (Re_tau=395) and 2003 (DNS from Moser et al. (Phys. Fluids 11: 943–945, 1999) and Hoyas and Jimenez (Phys. Fluids 18: 011702, 2006)), the flow over a backward facing step (DNS: Le and Moin (J. Fluid Mech. 330: 349–374, 1997)) and the periodic flow over a 2-D hill utilizing the results of the highly resolved LES by Breuer (New Reference Data for the Hill Flow Test Case, http://www.hy.bv.tum.de/DFG-CNRS/, 2005). The starting basis of this activity are the model equations governing the total viscous dissipation rate e and its homogeneous part (varepsilon_h=varepsilon-0.5 nu partial^2 k/(partial x_j partial x_j)) proposed by Jakirlic and Hanjalic (J. Fluid Mech. 439: 139–166, 2003). The third equation governing the specific viscous dissipation rate (omega=varepsilon/k), i.e. (omega_h=varepsilon_h/k) has been directly derived from the corresponding e h -equation. Afterwards, the transport equation of the inverse turbulent time scale ω h is extended in line with the (k-omega) SST-SAS (Scale-Adaptive Simulation) model of Menter and Egorov (Notes on Numerical Fluid Mechanics, 2009) and applied to the afore-mentioned flow configurations in conjunction with the Jakirlic and Hanjalic Reynolds stress model equation (J. Fluid Mech. 439: 139–166, 2003).