Mixing and reaction in turbulent plumes: the limits of slow and instantaneous chemical kinetics

We investigate the behaviour of a reactive plume in the two limiting cases of slow and instantaneous chemical reactions. New laboratory measurements show that, whereas the slow reaction between the source and entrained chemical species takes place within the whole volume of each eddy in the plume, the fast reaction develops preferentially at the periphery of the eddies. We develop a new model that quantifies the mixing of the reactive buoyant fluids at the Batchelor scale and thereby the progress of the fast reaction. We present a series of new experimental results that suggest that a critical distance from the source, $z_{crit}$, exists at which the volume of fluid that is entrained from the ambient is equal to that which is mixed within the plume at the Batchelor scale. For $z>z_{crit}$, only a fraction of the entrained fluid is rapidly mixed and reacts with the plume fluid. The results of the new experiments enable us to quantify the distance from the source at which an instantaneous reaction reaches completion, and show that it can be significantly larger than the distance $L_{s}$ at which the stoichiometric dilution of the plume fluid is achieved. In the limit of an instantaneous reaction, the longitudinal profiles of source chemical concentration in the plume depend on $(z_{crit}/L_{s})^{5/6}$. The predictions of the model are validated against the experimental results, and the profiles of source chemical concentration in the plume for slow and fast reactions are compared.

Experimental study on miscible viscous fingering involving viscosity changes induced by variations in chemical species concentrations due to chemical reactions

When a reactive and miscible less-viscous liquid displaces a more-viscous liquid in a Hele-Shaw cell, reactive miscible viscous fingering takes place. We succeed in showing experimentally how a reactive miscible viscous fingering pattern in a radial Hele-Shaw cell changes when the viscosity of the more-viscous liquid is varied owing to variation in chemical species concentration induced by an instantaneous chemical reaction. This is done by making use of a polymer solution's dependence of viscosity on pH. When the viscosity is increased by the chemical reaction, the shielding effect is suppressed and the fingers are widened. As a result, the ratio of the area occupied by the fingering pattern in a circle whose radius is the length of the longest finger is larger in the reactive case than in the non-reactive case. When the viscosity is decreased by the chemical reaction, in contrast, the shielding effect is enhanced and the fingers are narrowed. These lead to the area ratio being smaller in the reactive case than in the non-reactive case. A physical model to explain this change in the fingering pattern caused by the chemical reaction is proposed.

LB SIMULATION ON COMBUSTION WITH TURBULENCE

In this study, we simulate combustion field by the lattice Boltzmann method. We use a compressible model to describe the behavior of a turbulent non-premixed flame in the mixing layer of two co-flowing streams, one of propane and the other of air. By the assumption of fast-chemistry and unity Lewis number, we adopt the conserved scalar approach to reduce computational costs. In this case, the instantaneous chemical composition of the mixture at a given spatial location is at chemical equilibrium. This is so-called laminar flamelet model where the temperature and concentration are obtained by mixture fraction, which is determined by the degree of mixing of fuel and oxidizer. Results show that a thin flame zone separates two fluids of fuel and oxidizer, and the interaction between flame and a vortex pair is observed.