Entrainment dynamics of turbulent forced plume subjected to volumetric heating in a stratified medium

We present an investigation of the entrainment dynamics of a forced plume subjected to volumetric heating using energy-consistent entrainment relations. We decomposed the entrainment coefficient into different components for both unheated and heated plumes. According to the energy-consistent entrainment relations, there are three contributors to the entrainment coefficient, (1) turbulence energy production, (2) buoyancy effects, and (3) departure from self-similarity. In the unstratified medium, turbulence energy production is found to be the primary driver of the entrainment in unheated plumes. In contrast, for the heated plumes, the contribution from the turbulence energy production is reduced, and buoyancy emerged as the dominant factor driving the entrainment within the heat injection zone (HIZ) and beyond. In the stratified medium, the entrainment coefficient for the unheated plume due to the buoyancy effects is negative in the neutral layer. However, volumetric heating leads to additional buoyancy, and thus, the contribution of buoyancy to the entrainment coefficient becomes less negative. As a result, the cumulative entrainment coefficient goes from a negative value (detrainment zone) to a positive value (entrainment zone) toward the end of HIZ. As the stratification strength increases, the contribution from the turbulent production to the entrainment coefficient increases. We also observed that the deviation from expected self-similar behavior was more pronounced as the stratification strength increased. Overall, in both unstratified and stratified environments, the addition of heat decreases contribution due to turbulence production to the entrainment rate, while the contribution from positive buoyancy increases.