Validation: 2D coupled Lattice Boltzmann and Finite Difference, Laminar Flow, Heat Transfer.
Overview
Laminar, natural convection inside a concentric annular domain. The inner wall is maintained at a higher temperature than the outer wall, causing buoyancy induced circulation.
Simulation Inputs
| Input | Value |
|---|---|
| Material Properties | Density = incompressible, ideal gas. Kinematic viscosity = 2.081 × 10⁻⁵ m²/s. Thermal conductivity = 0.02967 W/(m·K). Specific heat = 1008 J/(kg·K). |
| Geometry | Radius_inner = 0.0178 m. Radius_outer = 0.04625 m. |
| Boundary Conditions | Buoyancy body force from Boussinesq approximation (g = 9.81 m/s², T₀ = 350 K). Inner wall Ti = 373 K, outer wall To = 327 K. |
Assumptions and Notes
Flow is incompressible, steady and laminar. Fluid density is based on the incompressible gas assumption, and applied using the Boussinesq approximation.
Results
Results plotted along the vertical symmetry line. FlowDeck closely reproduces the Kuehn & Goldstein (1976) measurements [1].
Temperature on the vertical symmetry line
Hover or tap the chart to read the values at any point. Click a legend item to show or hide it. FlowDeck values are at cell centres; the lines are completed with the wall boundary values.
Temperature on the vertical symmetry line: experiment vs FlowDeck
| y (mm) | Experiment T (K) | FlowDeck T (K) | Error (K) |
|---|---|---|---|
| −46.16 | 326.99 | 327.05 | 0.06 |
| −38.49 | 327.38 | 328.19 | 0.81 |
| −34.53 | 327.95 | 328.91 | 0.96 |
| −30.08 | 329.02 | 330.01 | 1.00 |
| −26.13 | 330.67 | 332.10 | 1.43 |
| −23.56 | 333.58 | 335.86 | 2.29 |
| −21.68 | 339.41 | 342.13 | 2.72 |
| −20.59 | 345.82 | 348.44 | 2.62 |
| −19.82 | 352.23 | 354.16 | 1.93 |
| −19.19 | 358.81 | 359.60 | 0.79 |
| −18.51 | 365.48 | 365.99 | 0.51 |
| −17.88 | 373.23 | 369.42 | −3.81 |
| 17.99 | 373.03 | 372.47 | −0.57 |
| 19.91 | 371.31 | 369.78 | −1.53 |
| 22.56 | 367.53 | 366.85 | −0.68 |
| 26.91 | 363.43 | 363.74 | 0.31 |
| 42.11 | 359.12 | 358.06 | −1.07 |
| 43.48 | 355.75 | 352.62 | −3.13 |
| 44.03 | 352.13 | 348.77 | −3.36 |
| 44.53 | 348.42 | 344.53 | −3.88 |
| 44.85 | 344.88 | 341.39 | −3.49 |
| 45.17 | 341.25 | 338.22 | −3.03 |
| 45.49 | 338.20 | 334.86 | −3.35 |
| 46.00 | 331.36 | 331.02 | −0.34 |
Reference Data
- Kuehn, T. H. and Goldstein, R. J., “An experimental and theoretical study of natural convection in the annulus between horizontal concentric cylinders,” Journal of Fluid Mechanics, 74(4), 695–719, 1976. https://doi.org/10.1017/S0022112076002012
Data licence. The model results on this page and in the CSV downloads are published by FlowDeck under the Creative Commons Attribution 4.0 licence (CC BY 4.0). The reference values are from the sources listed under References.