Implementation and Assessment of Menterβs Galilean-Invariant Ξ³ Transition Model in OVERFLOW
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Publications and source records attributed to Meelan M. Choudhari.
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Direct numerical simulations (DNS) of favorable-pressure-gradient turbulent boundary layers are presented for a nominal freestream Mach number of 5, with the objective of assessing the limitations of the currently available Reynolds-averaged Navier-Stokes (RANS) models. The favorable pressure gradient is induced by the streamwise curvature of the two-dimensional, planar, convex measurement surface used during experiments at the Texas A&M University. The DNS data shows good comparison with the measured velocity profiles, strain rates, and some, but not all, of the Reynolds-stress components. The discrepancies between the predicted and the measured wall-normal as well as shear stress components are primarily attributed to the lower than actual values inferred from typical PIV measurements of turbulent boundary layers. The DNS data shows a zero or slightly negative Reynolds shear stress in the outer part of the boundary-layer, which is indicative of the decaying turbulent motion under a strong favorable pressure gradient. The DNS data is also compared with the results of RANS computations based on commonly used zero, one, and two equation eddy-viscosity models. The RANS models yield reasonable comparisons with the DNS-based skin friction under zero and weak pressure gradients, but significant discrepancies under a strong pressure gradient. The k-w SST model provided the best overall predictions of skin friction, except in the region where the flow transitions from a favorable to an adverse pressure gradient. While the RANS models examined herein also give good predictions of the Reynolds shear stress under a sufficiently weak pressure gradient, none of those models are able to appropriately capture the reduction in the Reynolds stresses when the flow was subjected to a strong pressure gradient. An a priori assessment of the turbulent heat-flux prediction based on the assumption of a constant turbulent Prandtl number with the DNS data shows that while the constant turbulent Prandtl number model is effective in predicting the wall-normal component of turbulent heat flux, it does not capture the turbulent heat transfer in the streamwise direction for all the pressure gradient cases. The failure of the constant turbulent Prandtl number model highlights a requirement for more advanced models of the turbulent heat flux.
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The dual N-factor method is used to model the boundary-layer transition over the common research model with natural laminar flow (CRM-NLF) aircraft configuration. The flow conditions match selected test conditions from a wind tunnel experiment in the National Transonic Facility at the NASA Langley Research Center. The paper presents a systematic methodology for transition prediction in the presence of a dual shock system and extends the prior capability for iteratively coupled computational fluid dynamics (CFD) predictions to incorporate three-dimensional, transonic wings. The method employs stability computations based on the linear parabolized stability equations (PSE), along with a dual N-factor criterion. The iterative process begins with the fully turbulent Reynolds-averaged-Navier-Stokes (RANS) mean flow solution. For the first iteration, a mean flow solution is calculated with an imposed transition front that aligns with the shock front from the fully turbulent solution. Subsequently, stability computations are performed along a set of streamlines across the wing to calculate the amplification of planar Tollmien-Schlichting (TS) and stationary crossflow (CF) modes. The transition criterion based on the dual N-factor method is used to infer the updated transition front and the process is successively repeated until convergence of the solution. Within three iterations, the predicted fronts for angles of attack of 1.45, 1.98, 2.46 and 2.94 degrees and a mean-aerodynamic-chord Reynolds number equal to 15 million, approach visual convergence in most regions of the studied cases, and the resulting predictions are in good agreement with the transition fronts deduced from measurements of temperature-sensitive paint. Even though surface pressure measurements based on fully-turbulent flow agree well with the measured pressure coefficient distributions, strong viscous-inviscid interaction effects cause significant shifts in the shock locations based on the imposed transition front, underscoring the intrusive nature of static pressure measurements using surface mounted ports on the CRM-NLF configuration.
The linear amplification of modal disturbances that lead to boundary-layer transition in two-dimensional/axisymmetric hypersonic configurations is strongly reduced by the presence of a blunt nosetip, and the mechanisms underlying the observed onset of transition over the cone frustum are currently unknown. Linear nonmodal analysis has shown that both planar and oblique traveling disturbances that peak within the entropy layer experience appreciable energy amplification for moderate to large nosetip bluntness. The present study extends the previous linear analysis by including the nonlinear effects. Specifically, the perturbation form of the 2D, harmonic Navier-Stokes equations (HNSE) are solved with a fully implicit formulation and the Newton-Raphson method. The increased number of degrees of freedom for the nonlinear system presents difficulties for solution strategies based on direct solution of the linearized system. Such difficulties are overcome by using the GMRES iterative method with a preconditioner corresponding to a simplified Jacobian without the cross derivative terms. The HNSE solver is verified by comparing with nonlinear parabolized stability equation (NPSE) results for the nonlinear evolution of planar waves in an incompressible Blasius boundary layer and in a Mach 6 flow over a blunt cone. Finally, nonlinear nonmodal results are presented for planar traveling disturbances over the blunt cone. The nonmodal analysis demonstrates that entropy-layer disturbances generated close to the nose tip can seed the amplification of higher frequency Mackβs second-mode instabilities further downstream.
The Pazy wing, designed as a benchmark for highly flexible wings that experience large deformations, presents intriguing nonlinear phenomena due to its unique geometry with spanwise varying static deformation and low Reynolds number flow conditions. These phenomena include limit cycle oscillation related to laminar separation bubbles, boundary-layer transition, and dynamic stall. The primary focus of this study is to investigate transition behavior on the sagged Pazy wing under static loading by using the shear-stress-transport (SST)-based Langtry-Menter πΈ β πΉππ½π transition model in the NASA OVERFLOW and FUN3D solvers. Based on the steady-state results obtained via different variants of the Langtry-Menter model, we investigate the likely transition behavior over a range of incidence angles. The predicted flowfield on the sagged Pazy wing is strongly three dimensional and the application of turbulence index as a viable indicator of the transition front in such flows is also explored. The study demonstrates the limitations of the Langtry-Menter model when applied to low Reynolds number flows. We introduce a spanwise periodic configuration to simulate a narrow-span section of the Pazy wing, specifically centered on one of the 14 nearly equidistant ribs spanning the wing. The computational results demonstrate that the spanwise periodic configuration provides a straightforward environment for studying transition characteristics as well as demonstrating systematic grid convergence and successful code-to-code comparisons. The research offers useful insights into the transition characteristics of flexible wings under various loading conditions, contributing to the field of aeroelastic simulations.
There has been an increased focus on the overall accuracy and grid convergence of Reynolds-averaged Navier-Stokes (RANS)-based transition models from the recent AIAA and NATO-AVT workshops. Even though satisfactory grid convergence could be achieved for simple two-dimensional flow configurations, it required mesh counts that are substantially larger than those used in typical applications. In this paper, we focus our efforts on understanding how the grid resolution and topology influences the accuracy and convergence of results by studying the Schubauer and Skramstad flat-plate configuration and the NLF-0416 airfoil at an angle of attack equal to five degrees using FUN3D, a second-order finite-volume code. By focusing on these cases, we can analyze both natural and separation-induced transition scenarios. Multiple grid refinement strategies are investigated. First, we determine the relative effectiveness of zonal streamwise refinement in the transition region within structured grids as an alternative to the costly option of globally uniform refinement of a baseline grid. We also complement this zonal technique by globally varying the wall-normal resolution keeping the streamwise resolution fixed. The zonal streamwise refinement can accurately model natural transition in a flat-plate boundary layer and separation-induced transition, but struggles to accurately model natural transition in airfoil flows. A series of unstructured prismatic grids that have similar node counts and viscous wall spacings as the structured hexahedral grids are also tested, and they do not achieve grid convergence until an extremely fine resolution. Last, we employ adjoint-based unstructured grid adaptation in FUN3D to natural and separation-induced transition on the NLF-0416 airfoil. The adjoint-based refinement process converges to the same solution as the baseline family of structured grids, but leads to smaller errors on coarser grids.
There has been an increased focus on the overall accuracy and grid convergence of Reynolds-averaged Navier-Stokes (RANS)-based transition models from the recent AIAA and NATO-AVT workshops. Even though satisfactory grid convergence could be achieved for simple two-dimensional flow configurations, it required mesh counts that are substantially larger than those used in typical applications. In this paper, we focus our efforts on understanding how the grid resolution and topology influences the accuracy and convergence of results by studying the Schubauer and Skramstad flat-plate configuration and the NLF-0416 airfoil at an angle of attack equal to five degrees using FUN3D, a second-order finite-volume code. By focusing on these cases, we can analyze both natural and separation-induced transition scenarios. Multiple grid refinement strategies are investigated. First, we determine the relative effectiveness of zonal streamwise refinement in the transition region within structured grids as an alternative to the costly option of globally uniform refinement of a baseline grid. We also complement this zonal technique by globally varying the wall-normal resolution keeping the streamwise resolution fixed. The zonal streamwise refinement can accurately model natural transition in a flat-plate boundary layer and separation-induced transition, but struggles to accurately model natural transition in airfoil flows. A series of unstructured prismatic grids that have similar node counts and viscous wall spacings as the structured hexahedral grids are also tested, and they do not achieve grid convergence until an extremely fine resolution. Last, we employ adjoint-based unstructured grid adaptation in FUN3D to natural and separation-induced transition on the NLF-0416 airfoil. The adjoint-based refinement process converges to the same solution as the baseline family of structured grids, but leads to smaller errors on coarser grids.
Natural laminar flow technology is a passive laminar flow control (LFC) strategy that seeks to delay the onset of boundary-layer transition (BLT) through shape optimization to reduce the drag of the aerodynamic vehicle. Adjoint-based design optimization for LFC is proposed in an integrated multidisciplinary framework, which includes the computational fluid dynamics (CFD), geometry and grid deformation, and linear stability analysis (LSA) for transition prediction. In particular, the BLT location is predicted using the dual N-factor method that is based on a linear stability theory (LST) eigenvalue problem. The dual N-factor criterion accounts for the amplification of planar Tollmien-Schlichting (TS) and stationary crossflow (CF) boundary-layer instabilities to predict the transition location in three-dimensional boundary-layer flows. The adjoint-based shape optimization procedure is based on an iteratively coupled CFD and LSA methodology to converge the transition location and flow solutions, as well as to calculate the sensitivities of the aerodynamic metrics of interest with respect to the flow and shape design parameters. The RAE 2822 airfoil at 0 and 30 degrees yaw angles, an angle of attack of 0.72 degrees, and subsonic conditions (Mβ = 0.19, Rec = 5.6 Γ 106 ) are used as baseline configurations for design optimization. The angle of attack and the vertical displacement of free-form-deformation control points are used as design variables to reduce the drag coefficient while reaching a specified lift coefficient. The optimized unswept airfoil designs achieve a 30% drag reduction accompanied by a downstream shift of the transition locations over both suction and pressure sides of the airfoil. The initial design iterations for the swept case also show a favorable trend in the drag reduction with transition delay over both sides.
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