Assessment of Numerical and Modeling Errors of RANS-based Transition Models for Low-Reynolds Number 2-D Flows based Transition Models
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Development of Physics-Based Transition Models for Unstructured-Mesh CFD Codes Using Deep Learning Models
Predicting transition locations over a vehicle surface is of fundamental importance for many engineering applications. With the transition information, the Reynolds-averaged Navier-Stokes (RANS) computations can turn on the turbulence model at the right locations so that drag, lift and other aerodynamic quantities can be accurately predicted. In contrast to the popularity of RANS-based transition modeling in which transition onset is governed by the turbulence equations, physics-based transition models that account for instability waves within the boundary layer, thus more compliant to flow physics, only gained more attention in recent years. This paper describes the development of a new physics-based transition model based on either the linear stability theory (LST) or parabolized stability equations (PSE). The model is designed to communicate with a structured or unstructured-mesh RANS solver back and forth in order to more accurately compute transition fronts over a three-dimensional body. In the developed model, the Python suite of interface codes in conjunction with the LASTRAC software can be executed autonomously to produce transition onset locations for a given laminar or RANS-computed transitional state. In addition, as a proof of concept, the tool set consists of a deep learning neural network model that has been designed and trained to predict instability wave evolutions inside the boundary layer for various instability wave mechanisms across a selected speed range. A machine-learned intelligent profile interpolation model has also been devised to enable reliable instability-wave spectra predictions with just a few points in the mean flow profiles.
Transition Modeling↗
Implementation and Verification of the SST-𝜸 and SA-AFT Transition Models in FUN3D
The transition modeling capability in the NASA unstructured FUN3D suite of codes has been augmented by incorporating two additional transport-equation-based transition models, namely, the 𝜸 transition model coupled with Menter’s 2003 Shear-Stress Transport (SST) turbulence model and Coder’s Amplification Factor Transport (AFT) transition model combined with the Spalart-Allmaras (SA) turbulence model. Both of these models, SST-𝜸 and SA-AFT, are used to compute transition characteristics of several test cases from the literature. The selected test cases cover a range of transition scenarios including bypass transition over a flat plate (ERCOFTAC T3A and T3A- flow configurations), transition in the presence of separation bubbles (NLF-0416 airfoil at selected angles of attack), and natural transition due to Tollmien-Schlichting instabilities (flat-plate experiment by Schubauer and Klebanoff). To address the urgent need for model verification as highlighted in recent workshops on transition modeling, the drag, lift, surface pressure, and skin-friction coefficients from the FUN3D solutions for a sequence of meshes are compared with the results obtained with the same models implemented in the NASA structured grid flow solver OVERFLOW. Comparisons between the local and global surface coefficients from the FUN3D and OVERFLOW solvers for all test cases resulted in good agreement for the finest meshes.
Verification↗
Assessment and Improvement of RANS-based Transition Models based on Experimental Data of the Common Research Model with Natural Laminar Flow
Transition models based on auxiliary transport equations augmenting the Reynolds-averaged Navier-Stokes (RANS) framework often rely upon the correlations that were derived from a limited number of low-speed experiments and do not account for all of the transition mechanisms and/or their variation with the significant flow parameters. Available data from a recent experiment in the National Transonic Facility at the NASA Langley Research Center are used to assess the current transition modeling capability in NASA's OVERFLOW 2.2o code for a swept wing configuration at transonic cruise conditions. Specifically, the OVERFLOW solutions are used together with detailed stability analysis of the boundary layer flow over the new Common Research Model with Natural Laminar Flow (CRM-NLF) to evaluate the accuracy and the robustness of the transport-equation-based transition models, with the goal of proposing improvements that would help to strengthen the physical basis of these models for the important class of flows involving the combined effects of crossflow and flow compressibility. Results highlight the significant underprediction of the laminar flow extent within the inboard region of the wing, wherein the onset of transition may be attributed to a gradual amplification of Tollmien-Schlichting instabilities.
Boundary layer transition↗
Comparison of two transition models
Two transition functions, one given by Arnal, Coustols and Juillen and the other by Narasimha, are incorporated into a boundary layer program along with an otherwise conventional Baldwin-Lomax turbulence model. Calculations are performed for incompressible flow past a flat plate and compressible flow past a sharp cone at Mach 6 from the leading edge through transition to the fully turbulent state. Results from these calculations are compared with the available experimental data.
Dinavahi, Surya P. G.↗
Assessment of Numerical and Modeling Errors of RANS based Transition Models for Low-Reynolds Numbers 2-D Flows
In this paper we report the outcome of selected workshops organized as part of the NATO Applied Vehicle Technology (AVT)-313 activity Incompressible Laminar-to-Turbulent Flow Transition Study that focused on assessing the numerical and modeling accuracy of the γ−Reθ and γ transition models coupled to the k−ω Shear-Stress Transport (SST) two-equation eddy-viscosity model. Three different test cases involving nominally 2D flow configurations were selected: flow over a flat plate with two different levels of turbulence intensity at the inlet; flow around the Eppler 387 foil at a Reynolds number of 3×10^5 and angles of attack of 1 deg. and 7 deg. flow around the NACA 0015 foil at a Reynolds number of 1.8×10^5 and angles of attack of 5 deg. and10 deg. The flat plate flow conditions correspond to natural and by-pass transition, whereas the other two test cases include laminar separation bubbles that lead to separation-induced transition. For each test case, the selected quantities of interest include both integral and local flow quantities. Geometrically similar grids with a wide range of grid refinement ratios were generated for each of the test cases to allow the estimation of numerical uncertainties for all quantities of interest selected for this study. Several RANS flow solvers were used, employing common grids with the same boundary conditions and mathematical models. Therefore, it is possible to analyze the consistency of the results, i.e., to check if the intervals defined by the different numerical solutions with their respective uncertainties overlap with each other. Modeling errors can also be addressed for the selected flow quantities that have experimental data available. However, the experimental information available in these cases is not sufficient to guarantee that experiments and simulations are performed with the same settings. Nonetheless, the available experimental data is sufficient to guarantee that modeling errors are significantly reduced with the use of the transition models when compared to simulations performed using only the k−ω SST model.
CFD Modeling↗
Assessment of RANS-based Transition Models based on Experimental Data of the Common Research Model with Natural Laminar Flow
Transition models based on auxiliary transport equations augmenting the Reynolds-averaged Navier-Stokes (RANS) framework often rely upon transition correlations that were derived from a limited number of low-speed experiments and these models often fail to account for all of the relevant transition mechanisms and/or the variation in those mechanisms with respect to changes in the significant flow parameters. Available data from a recent experiment on the Common Research Model with Natural Laminar Flow (CRM-NLF) in the National Transonic Facility at the NASA Langley Research Center are used to assess the current transition modeling capability in NASA's OVERFLOW 2.3b solver for a swept wing configuration with nonzero taper and transonic cruise conditions. Specifically, the OVERFLOW solutions are used to evaluate the accuracy and robustness of the transport-equation-based transition models. Results highlight that the Spalart-Allmaras-based amplification factor transport (AFT-2017b) equation model and Menter’s shear-stress transport equation (SST2003)-based Langtry-Menter transition models (either with or without the modeling of crossflow transition) significantly underpredict the reported extent of laminar flow region over the entire span of the wing, irrespective of which instability mechanism(s) is expected to dominate the onset of the transition process. We show that the transition correlations underlying these models fail to account for the stabilizing effect of compressibility on the Tollmien-Schlichting transition, which is likely to be a major contributor to the underprediction of the laminar flow region on the CRM-NLF. The SST-2003-based Langtry-Menter model also appears to inaccurately predict the chordwise pressure variation along the majority of the wing span at all the flow conditions studied herein, due to how the turbulence intensity levels were enforced in the computations and how that was interfering with the functioning of the underlying turbulence model within the boundary layer. The AFT and Langtry-Menter models appear to be sensitive to the level of the freestream turbulence intensity, but the degree of sensitivity varies across the models.
CFD modeling↗
Toward Verification of the γ-Reθt Transition Model in OVERFLOW and FUN3D
The results of an ongoing assessment of the transition modeling capability in NASA's OVERFLOW and FUN3D programs are presented, with a focus on the Langtry-Menter γ-Reθt transition model in combination with the shear-stress transport (SST) turbulence model. While the effect of numerics and boundary conditions on the accuracy and iterative convergence of RANS solutions for fully turbulent flows has been well documented, especially in the context of canonical flow configurations, the same cannot be said for transport-equation-based transition models coupled with RANS-based turbulence models. Given the criticality of transition modeling for new aircraft design and optimization, there has been a renewed focus on the accuracy of such transition models and their inconsistent implementation across different flow solvers as seen from the AIAA and NATO-AVT workshops. In this work, we aim to establish the verification of such models via these two well established CFD codes with different numerics. The goal is to produce high-quality data, such as grids, solutions, and other auxiliary data, that may be utilized for code verification by others in the CFD community. As a first step, the work reported here is focused on the Langtry-Menter transition model as applied to two simple 2D configurations, namely the flat plate, and the NLF-0416, respectively. The paper also highlights how the boundary conditions and baseline turbulence model can affect the solutions from the SST-based Langtry-Menter transition model. A preliminary evaluation of the automatic mesh adaption capabilities of these solvers and potential benefits for flow configurations involving a mix of laminar, transitional, and fully turbulent flows is also reported.
CFD Modeling↗
Implementation and Assessment of Menter’s Galilean-Invariant γ Transition Model in OVERFLOW
With an increased emphasis on greener air transports and sustainable aviation, the modeling of laminar-to-turbulent boundary layer transition is anticipated to have an added significance, particularly in the applications related to laminar flow technology. However, unmanned aerial vehicles, crewed reentry vehicles, and ground-to-flight extrapolation all benefit from transition models. Because no single transition model is ideal for the complete spectrum of applications, it is useful to incorporate a variety of models in general-purpose CFD solvers, such as the NASA OVERFLOW Overset CFD code. While the Langtry-Menter 𝛄 − 𝑹𝒆 𝛉𝒕 model, currently available in OVERFLOW, has been widely used for CFD predictions of flows with laminar, transitional, and turbulent boundary layers, it does not possess the Galilean invariance property, a desirable attribute for rotorcraft applications. To help overcome that limitation, we have recently implemented Menter's baseline version of the SST-based γ transition model, along with a Galilean invariant stationary crossflow extension within OVERFLOW (version 2.3e). An initial assessment of the newly implemented model has been carried out using 2D benchmark cases including flat plates and the NLF-0416 airfoil, addressing several transition scenarios ranging from bypass transition due to freestream turbulence, natural transition via Tollmien-Schlichting instabilities, and transition due to a laminar separation bubble. The crossflow extension has been applied to the infinite swept NLF(2)-0415 wing and the 6:1 prolate spheroid. Wherever possible, the results were obtained on a sequence of meshes to ascertain the grid convergence behavior, which has been evaluated through global metrics such as force coefficients as well as local values of the skin-friction coefficient at selected points near and within the transition region. Overall, the model appears to be correctly implemented and the results show promise for further development using the framework of the γ transition model.
CFD modeling↗
Implementation of a Transition Model in a NASA Code and Validation Using Heat Transfer Data on a Turbine Blade
The purpose of this report is to summarize and document the work done to enable a NASA CFD code to model laminar-turbulent transition process on an isolated turbine blade. The ultimate purpose of the present work is to down-select a transition model that would allow the flow simulation of a variable speed power turbine to be accurately performed. The flow modeling in its final form will account for the blade row interactions and their effects on transition which would lead to accurate accounting for losses. The present work only concerns itself with steady flows of variable inlet turbulence. The low Reynolds number k- model of Wilcox and a modified version of the same model will be used for modeling of transition on experimentally measured blade pressure and heat transfer. It will be shown that the k- model and its modified variant fail to simulate the transition with any degree of accuracy. A case is thus made for the adoption of more accurate transition models. Three-equation models based on the work of Mayle on Laminar Kinetic Energy were explored. The three-equation model of Walters and Leylek was thought to be in a relatively mature state of development and was implemented in the Glenn-HT code. Two-dimensional heat transfer predictions of flat plate flow and two-dimensional and three-dimensional heat transfer predictions on a turbine blade were performed and reported herein. Surface heat transfer rate serves as sensitive indicator of transition. With the newly implemented model, it was shown that the simulation of transition process is much improved over the baseline k- model for the single Reynolds number and pressure ratio attempted; while agreement with heat transfer data became more satisfactory. Armed with the new transition model, total-pressure losses of computed three-dimensional flow of E3 tip section cascade were compared to the experimental data for a range of incidence angles. The results obtained, form a partial loss bucket for the chosen blade. In time the loss bucket will be populated with losses at additional incidences. Results obtained thus far will be discussed herein.
Ameri, Ali A.↗
Implementation of Two Local Correlation-Based Transition Models in OVERFLOW 2.3e
Accurate prediction of the laminar-to-turbulent boundary layer transition is highlighted as a vital component of NASA's CFD Vision 2030 Study. With an increased emphasis on greener air transports and sustainable aviation, transition modeling is anticipated to have an added significance, particularly in the applications related to laminar flow technology. However, unmanned aerial vehicles, crewed reentry vehicles, and ground-to-flight extrapolation all benefit from transition models. It is useful to incorporate a variety of models in CFD solvers because there isn't a single transition model that is ideal for the complete spectrum of applications. While the Langtry-Menter γ–Reθt model has been widely used for CFD predictions of flows with laminar, transitional, and turbulent boundary layers, it does not meet the criteria for Galilean invariance, a desirable attribute for rotorcraft applications. To help overcome that limitation, we have implemented Menter's SST-based γ transition model within NASA’s OVERFLOW Overset CFD code (version 2.3e). In addition, an SA-based implementation of the Langtry-Menter γ–Reθt transition model has also been implemented in view of the increased robustness of the SA-turbulence model for external aerodynamic applications. An initial assessment of the implemented models has been carried out using benchmark 2D test cases involving flat plates and the NLF-0416 airfoil, focusing on bypass, Tollmien-Schlichting, and laminar separation bubble-induced transition scenarios. In comparison to the Langtry-Menter γ–Reθt model, both models were found to produce increased computation efficiency, principally as a result of the decrease from four to three auxiliary transport equations. Results from the initial analysis will be presented, along with additional details pertaining to the deployment of these models.
CFD modeling↗
Implementation and Validation of a Laminar-to-Turbulent Transition Model in the Wind-US Code
A bypass transition model has been implemented in the Wind-US Reynolds Averaged Navier-Stokes (RANS) solver. The model is based on the Shear Stress Transport (SST) turbulence model and was built starting from a previous SST-based transition model. Several modifications were made to enable (1) consistent solutions regardless of flow field initialization procedure and (2) fully turbulent flow beyond the transition region. This model is intended for flows where bypass transition, in which the transition process is dominated by large freestream disturbances, is the key transition mechanism as opposed to transition dictated by modal growth. Validation of the new transition model is performed for flows ranging from incompressible to hypersonic conditions.
Denissen, Nicholas A.↗
Exploring the Langtry-Menter Transition Model for High Speed Applications Using FUN3D
A series of Reynolds-averaged Navier-Stokes (RANS) simulations were performed using the FUN3D flow solver to explore the capabilities of the Langtry-Menter Shear-Stress Transport (LM-SST) transition model for predicting transition for aircraft inlet applications. Two geometries were simulated: a zero-pressure-gradient flat plate and an axisymmetric cone exposed to hypersonic flow. In addition to the transition-sensitized LM-SST model investigations, simulations were run with the one-equation Spalart-Allmaras (SA) and the two-equation Menter Shear-Stress Transport (SST-V) RANS models in fully turbulent mode to identify the natural RANS model transition behavior as a function of Mach number when executed in fully turbulent mode. The flat plate simulations showed that (1) the transition model was able to predict rapid transition at a freestream Mach number of 0.2, which is expected but (2) the predicted transition location moved downstream as the freestream Mach number was increased for the simulations that used the SST-V turbulence model. The latter is significant as it is usually assumed that one- and two-equation turbulence models will produce fully turbulent flow very near the boundary layer origin. The flat plate simulation freestream Mach number trend was confirmed with simulations using the Wind-US code, which also saw a similar trend when employing the SA turbulence model. For the axisymmetric cone simulations, the transition location was highly sensitive to the inflow turbulence levels. This is significant as the prediction of the transition location is crucial when trying to predict inlet performance, especially for hypersonic vehicle applications. It was also noted that the predicted transition location for the cone when using the SST-V turbulence model agreed well with the predicted transition location from the equivalent zero-pressure-gradient flat plate case.
Transition Model↗
Exploring the Langtry-Menter Transition Model for High Speed Applications Using FUN3D
A series of Reynolds-averaged Navier-Stokes (RANS) simulations were performed using the FUN3D flow solver to explore the capabilities of the Langtry-Menter Shear-Stress Transport (LM-SST) transition model for predicting transition for aircraft inlet applications. Two geometries were simulated: a zeropressure-gradient flat plate and an axisymmetric cone exposed to hypersonic flow. In addition to the transition-sensitized LM-SST model investigations, simulations were run with the one-equation SpalartAllmaras (SA) and the two-equation Menter Shear-Stress Transport (SST-V) RANS models in fully turbulent mode to identify the natural RANS model transition behavior as a function of Mach number when executed in fully turbulent mode. The flat plate simulations showed that (1) the transition model was able to predict rapid transition at a freestream Mach number of 0.2, which is expected but (2) the predicted transition location moved downstream as the freestream Mach number was increased for the simulations that used the SST-V turbulence model. The latter is significant as it is usually assumed that one- and two-equation turbulence models will produce fully turbulent flow very near the boundary layer origin. The flat plate simulation freestream Mach number trend was confirmed with simulations using the Wind-US code, which also saw a similar trend when employing the SA turbulence model. For the axisymmetric cone simulations, the transition location was highly sensitive to the inflow turbulence levels. This is significant as the prediction of the transition location is crucial when trying to predict inlet performance, especially for hypersonic vehicle applications. It was also noted that the predicted transition location for the cone when using the SST-V turbulence model agreed well with the predicted transition location from the equivalent zero-pressure-gradient cold wall flat plate case.
Transition Model↗
Recent Progress on Rans-Based Transition Model Verification
The current efforts to assess and improve the Reynolds-averaged Navier-Stokes (RANS)-coupled transition models in the NASA FUN3D and OVERFLOW codes are summarized in this study. The first AIAA Transition Modeling Workshop and the NATO AVT-313 Transition Workshop both emphasized the need for code verification for transport equations based transition models as a top priority. We discuss the methods used for the model verification, the resulting grid families, the flow solutions, and other supporting information collected with at least two established NASA flow solvers, namely, FUN3D and OVERFLOW. These results, which will be uploaded onto the NASA Turbulence Modeling Resource, should assist other members of the computational fluid dynamics (CFD) community in verifying their own implementations of various transition models, such as the Langtry-Menter (LM2009) model, the one-equation γ model, and Coder’s amplification factor transport (AFT) model. Grid convergence is assessed using both global and local flow metrics of interest such as lift and drag as well as local skin-friction coefficients. We also explore the anisotropic unstructured metric-based adaptive mesh refinement library known as refine with the NASA FUN3D solver to determine if this capability can achieve the same accuracy as handcrafted structured grids with a significantly smaller node count and to learn the characteristics of the resulting grid distribution, especially in the vicinity of the transition zone.
Transition↗
Recent Progress on RANS-Based Transition Model Verification
The current efforts to assess and improve the Reynolds-averaged Navier-Stokes (RANS)-coupled transition models in the NASA FUN3D and OVERFLOW codes are summarized in this study. The first AIAA Transition Modeling Workshop and the NATO AVT-313 Transition Workshop both emphasized the need for code verification for transport equations based transition models as a top priority. We discuss the methods used for the model verification, the resulting grid families, the flow solutions, and other supporting information collected with at least two established NASA flow solvers, namely, FUN3D and OVERFLOW. These results, which will be uploaded onto the NASA Turbulence Modeling Resource, should assist other members of the computational fluid dynamics (CFD) community in verifying their own implementations of various transition models, such as the Langtry-Menter (LM2009) model, the one-equation γ model, and Coder’s amplification factor transport (AFT) model. Grid convergence is assessed using both global and local flow metrics of interest such as lift and drag as well as local skin-friction coefficients. We also explore the anisotropic unstructured metric-based adaptive mesh refinement library known as refine with the NASA FUN3D solver to determine if this capability can achieve the same accuracy as handcrafted structured grids with a significantly smaller node count and to learn the characteristics of the resulting grid distribution, especially in the vicinity of the transition zone.
RANS↗
Evaluation of Transport-Equations-Based Transition Models for High-Speed Boundary Layers Using OVERFLOW
Accurate modeling of laminar-turbulent transition is crucial for the design of hypersonic flight systems. However, the current transition models used in production CFD codes are insufficient for high-speed flows. Many extensions to low-speed models have been suggested; however, a thorough verification and validation effort is needed before these models can be used in design settings. Challenges include potentially missing details of the model implementation requirements and/or a complete specification of the input parameters needed to replicate the test findings. A meaningful assessment of the generalization capability of these models is also hindered by a lack of information regarding the specific flow configurations and associated grids employed for model calibration. As a key first step toward model verification, we present an independent assessment of two recently proposed models for high-speed transition, namely, a model within the SST-𝛾 framework and a model based on the SST-𝛾 – 𝜈 𝐿 equations. These models are implemented in the NASA OVERFLOW 2.3e solver and their performance in predicting first mode, second mode, and crossflow transition has been evaluated for several test cases in the supersonic and hypersonic regimes. Besides the test cases employed by the model developers, which could have also been used for model calibration, the present assessment includes supplementary configurations that contribute to an unbiased assessment of the models. The outcomes presented in this study indicate the potential for the models to be applied to high-speed flight configurations. Key steps toward future improvements to these models are also outlined.
CFD↗
A Correlation-Based Transition Model using Local Variables: Model Formation - Part 1
A new correlation-based transition model has been developed, which is based strictly on local variables. As a result, the transition model is compatible with modern computational fluid dynamics (CFD) approaches, such as unstructured grids and massive parallel execution. The model is based on two transport equations, one for intermittency and one for the transition onset criteria in terms of momentum thickness Reynolds number. The proposed transport equations do not attempt to model the physics of the transition process (unlike, e.g., turbulence models) but from a framework for the implementation of correlation-based models into general-purpose CFD methods.
Menter, F. R.↗