Simulating Datacenter Temperature Distribution with OpenFOAM

Paper: Barestrand et al., “Modelling Convective Heat Transfer of Air in a Data Center using OpenFOAM — Evaluation of the Boussinesq Buoyancy Approximation” Published: OpenFOAM Journal, Vol. 3 (2021), doi:10.51560/ofj.v3.59

The Challenge

Reproduce Fig 3 of the paper, the volume-weighted KDE of room temperature in a datacenter, starting from the manuscript PDF and the author’s OpenFOAM case bundle. Run the heavy CFD on a cloud cluster (not the laptop), then analyze the saved fields locally. Cap the SIMPLE solver at 1000 iterations so cloud wall-clock stays under ~60 minutes on a small instance; the KDE shape is the target, not residual convergence.

Prompt 

Reproduce Fig 3 (typical Boussinesq, 62K grid) from the manuscript on
datacenter temperature distribution. Cap the solver at 1000 iterations
so wall clock stays under ~60 min on a small instance. The KDE shape
is what matters, not residual convergence.

Identify the OpenFOAM environment and boundary conditions from
Manuscript.pdf and the case files in the project folder.

Pull all intermediate and final results back into the project folder.

What SciAgent Did

Phase 1: Paper Analysis Read the manuscript and the author-provided case bundle to extract the simulation recipe with no human walkthrough of the physics:

Choice Value Source
Solver buoyantBoussinesqSimpleFoam Manuscript + case files
Turbulence k-epsilon constant/turbulenceProperties
Rack BCs outletMappedUniformInletHeatAddition 0.org/T
Supply T 291.45 K (18.3 C) Manuscript Sec. 2
Grid “c” coarse, 140 mm, Nx=47 x Ny=24 x Nz=50 Manuscript Table
KDE bandwidth covariance_factor = 0.1 kdePlot.py

Phase 2: Stage Modified Case Wrote the coarse blockMeshDict (~56k background cells, ~62k after snappyHexMesh) and a 1000-iteration controlDict. Everything else preserved verbatim from the paper’s steady_incompressible case.

Phase 3: Cloud Compute Stood up a fresh AWS m6i.2xlarge (8 vCPU, 32 GB) cluster on demand and ran the meshing and solver pipeline there with 8-rank MPI:

blockMesh -> surfaceFeatureExtract -> snappyHexMesh -> checkMesh
        -> decomposePar -> buoyantBoussinesqSimpleFoam (parallel)
        -> reconstructPar -> writeCellVolumes -> T, V, logs

1000 SIMPLE iterations completed in 258 s wall-clock. Result fields and logs materialized to the local project folder via S3-backed workspace; cluster torn down afterwards.

Phase 4: Local KDE Analysis Parsed the saved temperature and cell-volume fields (61,927 cells), computed the volume-weighted Gaussian KDE with the paper’s bandwidth (covariance_factor = 0.1), and rendered the plot. Sim and analysis as separate stages means the same fields can be re-analyzed (different bandwidth, different slice) without re-running the solver.

Results

Fig 3 KDE Reproduction

KDE Comparison vs. Paper Fig 3 (“c: 62k” curve)

Metric This run Paper (c: 62k)
Cell count 61,927 ~62,000
T range 290.92 to 302.93 K ~291 to 303 K
Supply T 291.45 K 291.45 K
T_mean (vol-weighted) 296.21 K (23.06 C) ~295 to 296 K
Total domain volume 117.59 m^3 117.6 m^3
KDE integral 117.59 m^3 (self-consistent) -

The KDE shows the multimodal structure expected from a hot-aisle/cold-aisle layout: a sharp cold-supply peak near 291.5 K, an intermediate mixing region, and a warm exhaust peak near 298 K. The qualitative agreement with the paper’s “c: 62k” curve is what the figure tests; residual convergence is intentionally not the gate at this iteration cap.

Mesh Quality (checkMesh)

Metric Value
Cells 61,927
Total volume 117.59 m^3
Max non-orthogonality 48.1 deg
Mean non-orthogonality 4.0 deg
Max skewness 2.75
Mesh OK yes

Validation

Check Status
Solver matches paper PASS
Coarse grid ~62k cells PASS (61,927)
1000-iter cap honored PASS
Boundary conditions match manuscript PASS
KDE shape vs Fig 3 PASS
KDE integral = total volume PASS
Cluster torn down on completion PASS

Generated Artifacts

  • _outputs/fig3_kde.png - Fig 3 reproduction (150 dpi raster)
  • _outputs/fig3_kde.pdf - Fig 3 reproduction (vector)
  • _outputs/fig3_metadata.json - full provenance (n_cells, T range, peak, T_mean, KDE settings, solver, OF version, DOI)
  • _outputs/workspace/fig3_run/T_V.csv - 61,927-row table (T [K], V [m^3])
  • _outputs/workspace/fig3_run/fields/ - T, U, p_rgh, V, k, epsilon, nut, yPlus, turbulence fields
  • _outputs/workspace/fig3_run/logs/ - log_blockMesh, log_snappy, log_checkMesh, log_solver, log_postProcess

Execution

  • Total time: ~50 minutes (cluster launch + meshing + solver + materialization + KDE)
  • Agent turns: 119
  • Solver wall-clock: 258 s for 1000 SIMPLE iterations
  • Services: openfoam-swak4foam-2012 (containerized OpenFOAM v2012 + swak4Foam, run on a SkyPilot AWS m6i.2xlarge cluster, 8-rank MPI)