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Statistics of particle dispersion in Direct Numerical Simulations of wall-bounded turbulence: results of an international collaborative benchmark test
C. Marchioli, A. Soldati, J. G. M. Kuerten, B. Arcen, A. Taniere, G. Goldensoph, K. D. Squires, M. F. Cargnelutti, L. M. Portela
TL;DR
Published work makes it difficult to assemble a uniform, complete data source for phenomenological studies of turbulent particle dispersion in wall-bounded flows. An international collaboration produced a homogeneous DNS and LPT database and directly compared statistics across codes, revealing how code and simulation choices affect accuracy while retaining quantitative differences.
Problem
Published work makes it difficult to assemble a uniform, complete data source for phenomenological studies of turbulent particle dispersion in wall-bounded flows.
Method
An international collaboration produced a homogeneous source of DNS and LPT data and compared results from different codes under a defined simulation setting.
Results
Direct comparison shows how different codes perform on the same problem and how result accuracy depends on simulation choices.
Takeaways & Limitations
The database supports direct benchmarking of numerical predictions for turbulent particle dispersion in wall-bounded flows.
Takeaways & Limitations
Even when the stated conditions are fulfilled, the statistics can still show non-negligible quantitative differences.
Abstract
from arXiv · showhide
In this paper, the results of an international collaborative test case relative to the production of a Direct Numerical Simulation and Lagrangian Particle Tracking database for turbulent particle dispersion in channel flow at low Reynolds number are presented. The objective of this test case is to establish a homogeneous source of data relevant to the general problem of particle dispersion in wall-bounded turbulence. Different numerical approaches and computational codes have been used to simulate the particle-laden flow and calculations have been carried on long enough to achieve a statistically-steady condition for particle distribution. In such stationary regime, a comprehensive database including both post-processed statistics and raw data for the fluid and for the particles has been obtained. The complete datasets can be downloaded from the web at http://cfd.cineca.it/cfd/repository/. In this paper, the most relevant velocity statistics (for both phases) and particle distribution statistics are discussed and benchmarked by direct comparison between the different numerical predictions.
1. INTRODUCTION
The paper addresses inconsistent numerical data and methodological uncertainty in particle dispersion studies by coordinating independent DNS/LPT simulations of the same turbulent channel-flow test case. It establishes a homogeneous, comprehensive database for benchmarking numerical approaches and studying particle transport.
- Motivation: Available numerical data for particle dispersion lack uniformity and completeness, while many physical and computational parameters complicate methodological assessment.Relevant factors include particle Stokes and flow Reynolds numbers, interaction models, interpolation, grid resolution, and time stepping.
- Benchmark design: The benchmark asks independent groups to perform DNS of particle dispersion in turbulent channel flow using a common test case.Common base guidelines were provided for the participating groups.
- Database scope: The resulting database includes fluid, particle, and fluid-at-particle-position velocity statistics, particle concentration and deposition, and one- and two-particle dispersion statistics.The listed statistics include means, rms values, higher moments, Reynolds stresses, correlations, diffusivity, displacements, integral time scales, and rms particle dispersion.
- Database scope: Five independent simulations provide both post-processed statistics and raw fluid-field and particle-trajectory data for computing additional statistics.The raw data include fluid velocity evolution and particle position and velocity histories.
- Benchmark purpose: Direct comparisons can assess numerical-code performance and parameter-dependent accuracy, while the database can benchmark or validate engineering particle-dispersion models.The paper also identifies applications to models such as two-fluid Eulerian approaches and future large-eddy simulations.
- Benchmark design: The benchmark targets statistically-developing and statistically-steady particle distributions, with each group requiring eight to ten months to reach stationarity.The combined effort corresponded to about four years on standard production machines.
2. PHYSICAL PROBLEM AND NUMERICAL METHODOLOGY
The benchmark models dilute, heavy, spherical particles in low-Reynolds-number turbulent channel flow using DNS coupled with Lagrangian tracking. A common physical setup is combined with independently chosen numerical schemes and interpolation methods for comparison.
- Physical problem: The benchmark uses Reτ = 150 and bulk Reynolds number Reb = 2100, with bulk velocity ub = 1.65 m s−1.Variables are reported in wall units based on friction velocity, viscosity, and density.
- Physical problem: The reference problem is an incompressible, Newtonian air flow between parallel walls, with periodic streamwise and spanwise boundaries and no-slip walls.The domain has size 4πh × 2πh × 2h, corresponding to 1885 × 942 × 300 wall units.
- Numerical methodology: Base requirements constrain grid spacing relative to the smallest flow scale and specify the common physical test case, while computational details vary among groups.The paper explicitly motivates these variations as a way to evaluate how DNS accuracy depends on numerical choices.
- Particle model: Particles have density ρp = 1000 kg m−3 and are injected under dilute conditions, so particle-particle interactions are neglected.Particles are modeled as pointwise, rigid, and spherical.
- Particle model: Particle motion is integrated from ordinary differential equations using Stokes drag and buoyancy for particles much heavier than the fluid, while gravity is neglected in the base simulation.The drag coefficient is corrected because the particle Reynolds number may not remain small, especially for depositing particles.
- Particle model: Three particle sets with different relaxation times and Stokes numbers are tracked under one-way coupling, so particles do not feed back on the flow.Particles are initially random with velocity equal to the local fluid velocity; long-term dispersion is stated to be insensitive to this initialization.
- Numerical methodology: The benchmark permits distinct DNS solvers, time integrators, particle integrators, and velocity-interpolation schemes across groups.Examples include pseudo-spectral and finite-difference solvers, Runge-Kutta or Heun particle integration, and high-order interpolation.
3. RESULTS
The benchmark compares fluid and particle statistics from multiple numerical approaches, using steady-state particle distributions and density-weighted sampling. Results generally agree for fluid and single-point particle statistics, while near-wall concentration and higher-inertia particle predictions show greater variation.
- Scope and statistical framework: The analysis compares mean and rms velocities, Reynolds stresses, particle concentration profiles, deposition rates, and one- and two-particle statistics across numerical approaches.The paper limits the presented analysis mainly to first- and second-order moments, referring readers to the raw repository for higher-order and two-particle data.
- Scope and statistical framework: Particle statistics represent a statistically steady particle distribution and are computed as density-weighted averages over wall-parallel fluid slabs.Each variable is summed over particles in a sampling volume and divided by the number of particles there, a form useful for model developers.
- Fluid statistics: Fluid rms velocity results agree well overall, although quantitative differences are particularly evident for U′z,rms outside the buffer layer near the channel centerline.The profiles for U′x,rms are described as agreeing rather well, while numerical-method and discretization differences propagate into particle-velocity moments.
- Particle statistics: The simulations require long development times: the steady particle state appears at t+ ≃20000, corresponding to roughly 1000 channel heights and potentially exceeding the hydrodynamic developing length.Accumulated numerical errors in particle motion contribute to deviations among concentration profiles, especially near the wall.
- Particle statistics: Near-wall particle concentration builds up from an initially flat profile, with buildup magnitude depending on Stokes number and profile differences concentrated close to the wall.For St = 1 and St = 5, groups differ quantitatively in near-wall peak values; differences remain for St = 25, while agreement increases with Stokes number in other profile comparisons.
- Interpretation and limitations: The benchmark cannot establish which dataset is best a priori, although the range of concentration predictions can be accepted as a measure of particle wall concentration.Different numerical schemes, grid discretizations, and accumulated errors all contribute to the observed spread.
4. CONCLUSIONS
The benchmark produced a shared DNS/LPT database for turbulent particle dispersion in channel flow, enabling direct comparison of numerical predictions and continued parameter studies. Its results show both practical modeling value and persistent quantitative uncertainty across otherwise compliant simulations.
- Database construction: The international test case assembled a comprehensive database of fluid and particle statistics, including post-processed files and raw instantaneous flow-field and particle position/velocity data.The database was collected under statistically steady particle-distribution conditions and made available through a repository.
- Practical implications: Steady-state particle-distribution data may reduce CPU time by enabling simulations to start from a steady dispersed-phase condition and support closure validation for fully developed particle flow.These benefits are stated within the modeling assumptions used for the benchmark.
- Scientific and modeling use: The database provides a homogeneous DNS and LPT data source for benchmarking numerical methods and validating models of gas-solid interactions in channel flow.Its stated uses include testing new numerical methods and validating theoretical models, including a-posteriori Large-Eddy Simulation models.
- Benchmark comparison: Direct comparison shows how different codes perform on the same defined problem and how result accuracy depends on simulation-parameter choices.The conclusions motivate additional parametric studies that vary one or more simulation parameters to isolate their effects.
- Limitations: Even accurate tools satisfying the simulation requirements can yield non-negligible quantitative differences, and the best prediction for a statistic is not known a priori.The range of wall-concentration predictions is offered as a measure accepted under the study’s modeling assumptions.
- Future work: Future benchmark extensions will vary physical-modeling parameters such as two-way coupling, inter-particle collisions, lift-force models, and sub-grid-scale effects.Further parameter analysis and additional statistical quantities are planned at a later stage.