Plume Rise Calculations Using a Control Volume Approach and the Damped Spring Oscillator Analogy

The PUFF code was originally written and designed to calculate the rise of a large detonation or deflagration non-continuous plume (puff) in the atmosphere. It is based on a buoyant spherical control volume approximation. The theory for the model is updated and presented. The model has been observed to result in what are believed to be unrealistic plume elevation oscillations as the plume approaches the terminal elevation. Recognizing a similarity between the equations for a classical damped spring oscillator and the present model, the plume rise model can be analyzed by evaluating equivalent spring constants and damping functions. Such an analysis suggests a buoyant plume in the atmosphere is significantly under-damped, explaining the occurrence of the oscillations in the model. Based on lessons learned from the analogy evaluations and guided by comparisons with early plume rise data, a set of assumptions is proposed to address the excessive oscillations found in the predicted plume near the terminal elevation, and to improve the robustness of the predictions. This is done while retaining the basic context of the present model formulation. The propriety of the present formulation is evaluated. The revised model fits the vast majority of the existing data to +/− 25%, which is considered reasonable given the present model form. Further validation efforts would be advisable, but are impeded by a lack of quality existing datasets.