The Scale-Adaptive Simulation Method for Unsteady Turbulent Flow Predictions. Part 1: Theory and Model Description

Abstract

The article gives an overview of the Scale-Adaptive Simulation (SAS) method developed by the authors during the last years. The motivation for the formulation of the SAS method is given and a detailed explanation of the underlying ideas is presented. The derivation of the high-Reynolds number form of the equations as well as the calibration of the constants is provided. The concept of SAS is explained using several generic examples and test cases. In a companion article, the model is applied to more complex industrial-type applications.

Toward an equivalence criterion for Hybrid RANS/LES methods

“…The hybridization method can be based on various ways of modifying the scales involved in the equations: in the eddy-viscosity algebraic relation [15,16] or its transport equation [17], in the turbulent kinetic energy equation [18,19], or in the scale providing equation [20,21,22], or any combination of these methods [23,11]. In order to illustrate the procedure that can be followed and the conclusions that can be drawn from the application of the criterion, two particular hybrid methods are selected, the partially integrated transport model [20,5] (PITM) and the two-equation detached eddy simulation [18] (DES) model.…”

Desenvolvimento da modelagem de turbulência e interação fluido-estrutura para as vibrações induzidas por vórtices de cilindro rígido.

“…However, despite the somewhat superior theoretical content of this model, it did not really succeed in its original form, since it could not comply with the logarithmic law on the wall without further adjustments. It was not until about 30 years later that this model was revisited by Menter & Egorov (2004), Menter, Langtry & Volker (2006), Menter & Egorov (2010), in which the authors argument that in Rotta's model, a second derivative term from the Taylor expansion of kL did not vanish for inhomogeneous turbulence. Therefore, Menter and co-workers kept that term in the derivation of the equations and the boundary layer solution then followed the logarithmic law without any adjustments.…”

“…In fact, Menter & Egorov (2010) analyze the traditional two-equations models and conclude that the integral length scale produced is L ∼ √ k/ω. This means that the maximum length of eddies formed in a turbulent flow calculated with standard two-equations models is proportional to the thickness of the shear layer itself.…”

“…This was introduced by Egorov & Menter (2008), Menter & Egorov (2010) into the k − ω SST 2003 model. The equations for k and ω are derived as: 20) in which one notices that: i) the first equation is unchanged from the SST 2003 model and ii) in order to recover the performance of SST model in boundary layers, the SAS model was reformulated as an additional term to the ω equation, Q SAS , not disturbing the boundary layer performance of the SST, but allowing the SAS performance in unsteady situation.…”

“…As stated by Menter & Egorov (2010), there are mainly two schools of thought regarding the URANS approach: for the first, there is a separation of scales and URANS averages out all turbulent fluctuations and resolves only frequencies far lower than those of the turbulent fluctuations, which typically result from the variations in geometry or boundary conditions. For the other, URANS means application of turbulence models, derived based on the forming arguments of RANS, to the unsteady simulations, independent of the resolution content.…”