Application of the PITM Method Using Inlet Synthetic Turbulence Generation for the Simulation of the Turbulent Flow in a Small Axisymmetric Contraction

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

“…120, it is a simple matter to compute the ratio k s f s / k , leading to the more accurate computation of the coefficient than Eq. 119 as In practice [30–36], the coefficients used in Eq. 120 are α = 3 and γ = 2/9 .…”

“…Moreover, the part of the modeled energy can be appreciable in comparison with the resolved part of energy. For instance, the modeled energy represents roughly 50% of energy even in the center of the channel far away from the walls for the simulation of the flow in a small axisymmetric contraction while providing fair results [36]. These PITM simulations allowed a drastic reduction of the required computational resources in comparison with those necessary for performing highly resolved LES.…”

“…138 which recovers the original PITM formulation considering that f 𝜖 reduces to unity. In practice, the PITM method was used to derive both two-equation subfilter scale models [26, 29] as well as seven equation subfilter scale stress models [27, 30–36] and is amenable to the derivation of companion subfilter models for almost any usual RANS model. Up to now, the PANS method was mainly applied to devise two-equation subfilter models [39, 40] as well as four equation subfilter models [43].…”

“…122 , 124 , 123 was used to simulate turbulent pulsed flows [ 26 ] and a mixing of two turbulent flows of differing scales [ 29 ], but also with an additional equation for the temperature variance, thermal convection at high Rayleigh numbers [ 132 ], whereas the subfilter scale stress models accounting for Eqs. 126 and 124 was applied to perform rotating flows encountered in turbomachinery at the bulk Reynolds number R b = U b δ / ν = 14000 and at different rotation numbers R o = Ω δ / U b varying from moderate, medium and very high rotation rates R o = 0.17, 0.50 and 1.50 [ 31 ], flows in a plane channel with appreciable fluid injection through a permeable wall which corresponds to the propellant burning in solid rocket motors [ 27 ], flows over periodic hills with separation and reattachment of the boundary layer both at the Reynolds number R e = 10595 [ 34 , 133 , 134 ] and R e = 37000 [ 35 ], airfoil flows at the Reynolds number R e = 1.64 × 10 6 for an angle of attack 12 ∘ [ 135 ], a turbulent flow in a small axisymmetric contraction at the bulk Reynolds number R b = 4.47 × 10 5 [ 36 ]. Overall, it is found that the subfilter scale model behaves like a RANS model in the wall region and like LES in the core flow.…”

“…They are essentially based on hybrid zonal methods but non-zonal methods have also emerged recently [ 14 ]. In this framework, different hybrid RANS/LES methods such as the very large eddy simulation (VLES) [ 15 , 16 ], the detached eddy simulation (DES) [ 17 – 25 ], the partially integrated transport modeling (PITM) method [ 26 – 36 ], the partially averaged Navier-Stokes (PANS) method, [ 37 – 45 ], and the scale adaptive simulation (SAS) [ 46 – 48 ], have been developed for tackling these identified challenges. According to the literature [ 49 – 51 ], these hybrid methods can be classified into two categories, zonal and non-zonal methods.…”