Entrainment by penetrative convection at low Péclet number (1978)
Type of ContentTheses / Dissertations
Thesis DisciplineCivil Engineering
Degree NameDoctor of Philosophy
PublisherUniversity of Canterbury
AuthorsDenton, Richard Andrewshow all
A theoretical one-dimensional model of interfacial entrainment has been developed which models the temporal behaviour of an initially quiescent, stable temperature stratification heated from below. The specific two-layered stratification, analysed in the thesis, is an inverted model of penetrative convection in the surface layer of a thermal power station cooling pond. At the interface between the uniformly mixed turbulent convection layer and the essentially non turbulent diffusion region, temperature and heat flux are taken to be continuous. However, the partial derivatives of temperature with respect to height and time are assumed to be discontinuous. The rate of rise of the interface is obtained by matching the changes in vertical temperature profile immediately above and below the interface.
The heat transfer above the interface due to penetrating inter facial domes of mixed layer fluid is parameterized by a turbulent diffusivity term and an additional molecular diffusion factor. Both these parameters decrease to zero with increasing height above the interface. However, in this-low Péclet number case, molecular diffusion is found to be significant. It is also found that the "filling" (with heat) of the vertical temperature profile, due to the lower boundary heat flux, makes a major contribution to the rate of rise of the interface. As a result, the turbulent entrainment parameters make a relatively minor contribution.
The empirical relationship for the turbulent diffusivity term, used in the numerical analyses of the model, combines two previously used methods of presenting interfacial entrainment data. It is consistent with data from high Péclet number mechanical stirring grid experiments and also describes the variation of the heat flux ratio k in atmospheric studies.
Laboratory experiments using both steady and unsteady heat flux apparatus were also performed. Good agreement was found between the experimental and numerical analyses.
A review of thermal convection above and below horizontal plates is presented in the appendices. In this review, a graphical form, cq = Nu/Ray⅓ versus log Ra, has been developed. The graphical form allows convection data to be plotted in greater detail than previous methods. It also describes the variation in the heat flux with changes in the convection layer thickness if all other variables are fixed.