Axisymmetric buoyant far-field plume in a quiescent unstratified environment

Underlying Flow Regime 1-06

Best Practice Advice

The key physics to be captured in this UFR is the self-similar behaviour of a spreading axisymmetric buoyant plume.

The flow can be treated as axisymmetric.
For a grid-independent resolution of the George et al. [3] plume, at least (40 × 100) grid nodes should be used in the (radial × axial) directions. At least 10 nodes should be used radially to resolve the plume source.
Discretization schemes should be at least second-order accurate.
For further advice on boundary conditions, see Test Case

Use of the standard k – ε model with or without the common Standard Gradient Diffusion Hypothesis (SGDH) for the production term due to buoyancy, G, will probably result in overprediction of the centreline mean parameters, and underprediction of the spreading rate of the plume.
To obtain more accurate plume predictions with a k – ε model, use the Generalized Gradient Diffusion Hypothesis (GGDH) instead of the Standard Gradient Diffusion Hypothesis (SGDH). More refined models have been suggested which could further improve model predictions, see for example Hossain & Rodi.
Do not neglect the buoyancy source term in the &epsilon-equation as this can lead to problems with numerical stability.
If you are considering only the far-field region of a buoyant plume, where density differences are small, the Boussinesq approximation can be used. If, however, your flow domain includes the region nearer the source of buoyancy where density differences are appreciable, avoid using the Boussinesq approximation.
For cases where buoyancy is not as strong as in a plume, in the limit of a non-buoyant axisymmetric jet, be aware of the limitations of the standard k – ε model. The spreading rate of a non-buoyant round jet is 15% lower than for a two-dimensional, plane jet. However, the standard k – ε model predicts the spreading rate for round jets to be 15% higher than for the plane jets.