Algebraic Nonlocal Transition Modeling of Laminar Separation Bubbles Using k−ω Turbulence Models

Abstract

Algebraic transitional extensions for the accurate computation of laminar separation bubbles are developed for use with k-ω models. The transitional model, based on integral boundary-layer parameters and transition criteria, introduces streamwise-variable weighting of the production terms in the k-ω equations and delay of the shear-stresslimiter activation. Calibration to fit available DNS data yields satisfactory results for a flat-plate reference case, both for skin-friction and velocity-profiles. It is shown that the model can be adapted to different k-ω variants by appropriate calibration of coefficients. The model is then validated for 2 airfoil test-cases, both for very low and higher Reynolds numbers, a NACA 0012 airfoil at chord-based Reynolds number Re c = 10 5 and angle-of-attack α = 10.55 deg and a S809 airfoil at Re c = 2 × 10 6 and α = 1 deg. For both application cases comparison with available data is satisfactory. Nomenclature c = airfoil chord length (m) C lim = shear-stress limiter delay function Cp = pressure coefficient

RANS modeling of Laminar Separation Bubbles around Airfoils at Low Reynolds conditions

“…Several transitional RANS approaches applied to a collection of low Reynolds number aerodynamic flows were assessed. The recently proposed non-local Laminar Separation Transition Triggering (LSTT) [41] approach, originally designed for use with k − ω [35,52,71,72] turbulence models and transition criteria [44,53], was extended to the one-equation Spalart-Allmaras [51] turbulence model. The LSTT approach was compared to typical Step off-on [34,39] activation of RANS turbulence models and transport equation-based γ −Re θt [17,18,69,70,73] transitional model.…”

“…The Step approach is presented with the shear stress limiter enabled. The closure constants of the LSTT model ( s a , s b , s c and a) were calibrated [41] to reproduce the c f distribution of the bubble of a flat-plate DNS reference [47] using k-ω models. In Table 1 we also present the calibration adapted to the Spalart-Allmaras turbulence model, as shown in Fig.…”

“…A too pronounced minimum c f peak is observed for the Spalart-Allmaras model, which is also present in the other flows considered in the present study (Figs. 2, 3 and 4 [8] (b) k − ω [52] LSTT [41] (c) k − ω [52] Step (d) Spalart-Allmaras [51] LSTT [41] (e) Spalart-Allmaras [51] Step The authors believe that the reason why the LSTT approach is in better agreement with LES data than γ −Re θt and Step activations, is because LSTT is designed to account for the relatively fast rate of production of Reynolds shear stress in the transitional region, whereas the other approaches underestimate this rate of growth. In order to verify this point, a closer look on the Reynolds shear stress is done in Fig.…”

“…Numerous existing methods focus on correctly predicting the transition onset, but the transition region prediction still relies on the turbulence model's unapprehended ability to correctly produce turbulence at and downstream of the transition onset. In this paper we present and evaluate a recently developed [41] transition modeling formulation that intends to account for the turbulence growth within a LSB and in the downstream relaxation flow region. To this purpose, laminar separation transition triggering (hereafter LSTT) in the RANS model is progressive in the streamwise direction (s), from the criteria-determined [42][43][44] transition onset to full turbulence.…”

Validation of Modified Algebraic Model during Transitional Flow in HVAC Duct

“…The comparisons shows that for transitional flow the best result are obtained with k − ωSST and V-SA model. Recently, for the transitional flow was proposed modified model based on standard k − ω [15][16][17]. The model proposed in [15] was originally developed for turbomachinery, the model from [17] is for flow around airfoils.…”