Langley Research Center Turbulence Modeling Resource

DNS: Periodic Hills of Parameterized Geometries

Return to: Data from DNS - Intro Page

The data on this page were provided by Sylvain Laizet, and organized by Xuhui Zhou.

For the purpose of deriving data-driven, machine-learning-based turbulence models, existing benchmark datasets are often unsuitable. Data are needed from systematically and continuously varied flow configurations with maximum coverage in the parameter space. To this end, DNS of flows over periodic hills with parameterized geometries have been performed, resulting in a family of flows ranging from incipient to mild and massive separations. The dataset consists of 29 simulations with different geometries, all at a Reynolds number of 5600 (based on hill crest height H and bulk velocity U_b at the crest). The design of the parameterization of the periodic hill geometry is described in the following paper:

• Xiao, H., Wu, J.-L., Laizet, S., and Duan, L., "Flows Over Periodic Hills of Parameterized Geometries: A Dataset for Data-Driven Turbulence Modeling from Direct Simulations," Computers & Fluids, Vol. 200, 104431, 2020, https://doi.org/10.1016/j.compfluid.2020.104431.

Other details regarding the general setup of this test case can be found in Breuer, M., Peller, N., Rapp, C., and Manhart, M., "Flow Over Periodic Hills: Numerical and Experimental Study in a Wide Range of Reynolds Numbers", Computers & Fluids, Vol. 38, No. 2, 2009, pp. 433-457, https://doi.org/10.1016/j.compfluid.2008.05.002.

When the above paper by Xiao et al. was written, only five cases were simulated, with the hill width (L_w) varied.

The 27+2 flow configurations provided here were generated by systematically varying the following parameters of the hill:

• Hill width, L_w
• Length of the bottom flat section, L_f
• Domain height, L_y

Variation of hill width: Five different hill widths were obtained by scaling the width of the baseline hill (i.e., L_w/H = 1.929) by a factor of slope parameter alpha = 0.5, 0.75, 1.0 (baseline), 1.25, and 1.5. Later, the length and height of the channel were also varied, leading to the full 27+2 DNS database presented here:

• Variation of the length of bottom flat section: Three different lengths for the bottom flat section were used with L_f = 2.142, 5.142, and 8.142, leading to total horizontal lengths of the domain equal to L_x/H = 3.858*alpha + 2.142, L_x/H = 3.858*alpha + 5.142, and L_x/H = 3.858*alpha + 8.142.
• Variation of domain height: Three different domain heights were used with L_y/H = 2.024, 3.036, and 4.048.

The DNS data files are given here:

• DNS_29_Periodic_Hills.zip (zipped directory, 1.2 GB)

When unzipped, you will find 29 files with names: alphXX-YYYY-ZZZZ.dat

• XX is the slope parameter with alpha = 0.5, 0.75, 1.0, 1.25, or 1.5.
• YYYY is the streamwise length of the domain with L_x/H = 4.071, 7.071, 10.071 for alpha = 0.5, L_x/H = 6, 9, 12 for alpha=1, L_x/H = 7.929, 10.929, 13.929 for alpha = 1.5, L_x/H = 8.0355 for alpha = 0.75, and L_x/H = 9.9645 for alpha=1.25.
• ZZZZ is the domain height with L_y = 2.024, 3.036, 4.048.

Data loading: Each file alphXX-YYYY-ZZZZ.dat contains (1) x and y coordinates, (2) mean velocity, pressure, dissipation, and vorticity fields, (3) Reynolds stresses and root-mean-square (RMS) pressure fluctuations. Example for loading the data is as follows:

     import numpy as np
     import pandas as pd
     data = np.loadtxt("alph075-80355-3036.dat", skiprows=20)
     df = pd.DataFrame(data, columns = ["x","y","u_mean","v_mean","w_mean","p_mean","dissipation_mean","vorticity_mean",\
                                        "uu","vv","ww","uv","uw","vw","pp"])

The DNS data for these 29 cases have been interpolated to coarse meshes for use in OpenFOAM by Xuhui Zhou, who also organized the dataset shared here. The RANS-resolution data (along with the original DNS data), are available at the GitHub site https://github.com/xiaoh/para-database-for-PIML of Heng Xiao.

The 29 Direct Numerical Simulations (DNS) are performed by solving the forced incompressible Navier-Stokes equations for a fluid with a constant density. A forcing field f(x,t) is used to enforce boundary conditions through an immersed boundary method and to ensure a specified mass flux. The data are collected after a transitional period, from the point when the flow is fully developed. A simulation time step delta t = 0.0005H/U_b is used. For all the calculations, turbulent statistical data have been collected over a time period T = 750H/U_b. Data are averaged in time and in the spanwise direction for which L_z/H = 4.5 is always discretised with n_z = 192. Additional details concerning the code and computational methodology can be found in: Laizet, S. and Lamballais, E., "High-Order Compact Schemes for Incompressible Flows: A Simple and Efficient Method with Quasi-Spectral Accuracy," Journal of Computational Physics, Vol. 228, No 16, pp. 5989-6015, 2009, https://doi.org/10.1016/j.jcp.2009.05.010, Laizet, S., "Incompressible Navier-Stokes Equations Solver with Multiple Scalar Transport Equations," https://github.com/xcompact3d/Incompact3d, and the references found therein.

This new dataset has been used in the following paper: Han, J., Zhou, X.-H., and Xiao, H., "An Equivariant Neural Operator for Developing Nonlocal Tensorial Constitutive Models," https://arxiv.org/abs/2201.01287.
 
 

Return to: Data from DNS - Intro Page

Recent significant updates:
none

Privacy Act Statement

Accessibility Statement

Responsible NASA Official: Ethan Vogel
Page Curator: Clark Pederson
Last Updated: 05/17/2023