(47g) Parametric Study of Rising Jet Diffusion Thermal Plumes.

Understanding the behaviour of a jet diffusion rising plume and hence a proper design of the stack is essential for any chemical process industries from environmental, associate risk and safety view point. While several empirical relations had been developed for thermal jet plumes, the first 1-D model on rising jet thermal plume was proposed by Gupta et al.^1,2, where the temperature and velocity maintains a top-hat profile inside the system for all plume heights. Researchers elaborately shows the counter-effect of buoyancy and inertia force (that is prevalent in rising jet thermal plumes) on plume shape, by identifying the modified Froude number. Later, Rooney and Linden^3,4 classified plumes into Boussinesq and Non-Boussinesq category based on the ratio of plume density to ambient density; the dynamics of which are studied via 1-D models. However, recent studies^5,6 have shown the need to compute surface temperature and velocity of jet plumes apart from its centreline properties to correctly predict the radiant heat effect on distant surrounding elements from the plumes. In the present study, therefore, we have developed a 2-D steady state model under no-wind condition, using conservation laws; solving which plume height, velocity and temperature variation along plume axis and along plume radius are estimated. Prediction of plume geometry variation along plume height shows an initial necking followed by increasing plume diameter along plume height. It is also noted that plume height as function of Froude number (F_r=u/(√(gb_s)) , where u_s = source velocity and b_s = stack radius) increases with increasing stack diameter and decreases with increasing source velocity for all compositions of the plume. However, there is an insignificant change in plume heights with Fr as plume composition changes. For all the compositions, the axisymmetric plume velocity and temperature decrease monotonically both axially and radially.

References:

1. Gupta, A. K., Singh, B. & Kumar, S. Plume Analysis above Finite Size Fire Sources. in Fire Safety Science-Proceedings of the Third International Symposium 445–454
2. Gupta, A. One-Dimensional Mathematical-Modeling of Enclosure Fire Dynamics. Fire Mater. 12, 51–60 (1988).
3. Rooney, G. G. & Linden, P. F. Similarity considerations for non-Boussinesq plumes in an unstratified environment By. J. Fluid Mech. 318, 237–250 (1996).
4. Rooney, G. G. & Linden, P. F. Strongly buoyant plume similarity and ‘small-fire’ ventilation. Fire Saf. J. 29, 235–258 (1997).
5. Sudheer, S. & Prabhu, S. S. V. Characterization of Open Pool Fires and Study of Heat Transfer in Bodies Engulfed in Pool Fires. (2013).
6. Sengupta, A. Optimal Safe Layout of Fuel Storage Tanks Exposed to Pool Fire: One Dimensional Deterministic Modelling Approach. Fire Technology (Springer US, 2019). doi:10.1007/s10694-019-00830-y