Source-linked AI summary
Flows Over Periodic Hills of Parameterized Geometries: A Dataset for Data-Driven Turbulence Modeling From Direct Simulations
Heng Xiao, Jin-Long Wu, Sylvain Laizet, Lian Duan
TL;DR
The paper addresses inadequate public datasets for training and testing data-driven turbulence models. It presents a periodic-hill dataset with varied slopes and demonstrates its use for machine-learning-based flow prediction.
Problem
Currently available public datasets are inadequate for training and testing data-driven turbulence models, while turbulence understanding and predictive modeling remain difficult.
Method
The paper presents a dataset of flows over periodic hills with various slopes and uses it to train and test data-driven models.
Results
Predictive patterns are observed through all three flows, with machine-learning model performance examined from the separation bubble through reattachment and downstream.
Takeaways & Limitations
The generated dataset and its design methodology support training and testing data-driven turbulence models.
Takeaways & Limitations
The dataset varies Reynolds number but not geometry, limiting its challenge relative to cross-geometry testing.
Abstract
from arXiv · showhide
Computational fluid dynamics models based on Reynolds-averaged Navier--Stokes equations with turbulence closures still play important roles in engineering design and analysis. However, the development of turbulence models has been stagnant for decades. With recent advances in machine learning, data-driven turbulence models have become attractive alternatives worth further explorations. However, a major obstacle in the development of data-driven turbulence models is the lack of training data. In this work, we survey currently available public turbulent flow databases and conclude that they are inadequate for developing and validating data-driven models. Rather, we need more benchmark data from systematically and continuously varied flow conditions (e.g., Reynolds number and geometry) with maximum coverage in the parameter space for this purpose. To this end, we perform direct numerical simulations of flows over periodic hills with varying slopes, resulting in a family of flows over periodic hills which ranges from incipient to mild and massive separations. We further demonstrate the use of such a dataset by training a machine learning model that predicts Reynolds stress anisotropy based on a set of mean flow features. We expect the generated dataset, along with its design methodology and the example application presented herein, will facilitate development and comparison of future data-driven turbulence models.
1. Introduction
The paper identifies inadequate, sparsely distributed public flow databases as a bottleneck for data-driven turbulence modeling and proposes parameterized benchmark data spanning flow conditions and geometries.
- Existing turbulence models have large model-form uncertainties and have seen little development for decades despite unsatisfactory performance across many flows.
- Machine-learning turbulence models are attractive alternatives, but their development is hindered by difficulty incorporating physical knowledge and by a lack of high-quality public training databases.
- Current public databases contain representative but distinctly different configurations, leaving benchmark data sparsely scattered across the parameter space.
- The authors argue that databases for data-driven turbulence modeling should systematically vary flow conditions and geometry to improve parameter-space coverage.
2. Methodology
The study constructs a periodic-hill DNS database by varying hill steepness at Re = 5600, producing flows with different separation regimes and validating the simulations against benchmark results.
- DNS of periodic-hill flows at Re = 5600 varies hill steepness to generate incipiently, mildly, and vastly separated flows.
- Hill geometry is parameterized by scaling its width with α while keeping hill height and the flat section constant.
- The simulations solve the forced incompressible Navier–Stokes equations using the high-order Incompact3d solver with immersed-boundary treatment and incompressibility enforcement.
- Excellent agreement with prior benchmark data is obtained for mean velocity and Reynolds stresses, while the resolved turbulence stresses remain unchanged under tested temporal or spatial coarsening.
3. Data Analysis, Machine Learning, and Interpretation
The DNS dataset is publicly distributed with mean fields, Reynolds stresses, and a methodology for systematically varying flow configurations. Machine-learning examples predict Reynolds-stress anisotropy from mean-flow features, with both models agreeing reasonably well with DNS and larger errors for extrapolation.
- Data analysis: The DNS dataset provides mean pressure and velocity fields plus second-order Reynolds-stress statistics for RANS-based turbulence-model development.The data are available through a public GitHub repository and NASA Turbulence Modeling Portal.
- Machine learning models: The study constructs machine-learning models that map mean-flow features to Reynolds-stress anisotropy using DNS data only.Random forests and fully connected neural networks are used as illustrative models rather than as advocated final turbulence models.
- Predictive performance: Both random forests and neural networks show satisfactory agreement with DNS for interpolation and extrapolation cases.The evaluation uses Barycentric representations at locations in and downstream of the separation bubble.
- Predictive performance: The similar predictive performance of the two models is notable because neural networks are more complex and computationally expensive to train.The authors suggest that the training flows do not exhibit clear intrinsic trends that favor the more complex model.
- Predictive performance: Extrapolation errors are much larger because the predicted α = 1.5 flow has a milder slope and smaller separation bubble than the training flows.Prediction for α = 0.5 is reported as comparable to the interpolation case, where massive separation is represented in the training data.
4. Conclusion
The paper addresses inadequate turbulence-modeling datasets by proposing systematically varied periodic-hill benchmark data and demonstrating its use for predicting Reynolds stress anisotropy.
- 4. Conclusion: The dataset is designed to address the lack of suitable training and testing data for data-driven turbulence models.Existing databases are described as sparse in flow-parameter space and inadequate for model development and evaluation.
- 4. Conclusion: The authors construct benchmark data by systematically varying periodic-hill flow configurations and geometry.The dataset consists of flows over periodic hills with various slopes.
- 4. Conclusion: The dataset is intended to support training and evaluating data-driven models on separated flows.The authors expect it to help developers assess predictive capabilities on separated-flow cases.
- 4. Conclusion: An example application maps mean flow features to Reynolds stress anisotropy using the presented dataset.The conclusion identifies this mapping as an example use of the generated data.
Appendix A. Description of the Hill Geometry
The appendix defines the first periodic-hill geometry with six piecewise third-order polynomial segments in normalized coordinates.
- Appendix A. Description of the Hill Geometry: The first hill geometry is represented by six segments of third-order polynomials.Each segment applies over a specified interval of the normalized horizontal coordinate.
- Appendix A. Description of the Hill Geometry: The six polynomial expressions define the normalized vertical coordinate across successive intervals of the hill.The segment intervals run from [0, 0.3214] through (1.429, 1.929].
- Appendix A. Description of the Hill Geometry: The geometry uses normalized coordinates ˆx = x/H and ˆy = y/H, where H is the reference height.These normalized coordinates are used in the piecewise definitions.
Highlights
The paper addresses the need for systematically varied flow data by performing DNS over periodic hills with varying slopes, generating cases from incipient to massive separation.
- The work identifies systematically varied flow data as needed for data-driven turbulence modeling.
- Direct numerical simulations were performed for periodic hills with varying slopes.
- The dataset spans flows from incipient to massive separations.