Investigation of turbulent reacting mixing processes at high Schmidt numbers in a coaxial jet mixer using OpenFOAM

Turbulent mixing of fluids plays a dominating role in a large number of engineering devices such as combustion chambers, burners, injection systems and heat exchangers. Especially in the context of chemical applications exploration of physical mechanisms of mixing processes is extremely important to control the chemical reactions. Solution of this problem is based on detailed analysis of both hydrodynamics in the mixing device and behaviour of chemical reactions. These two processes are strongly coupled. The aim of this work is the investigation of hydrodynamic and chemical aspects as well as their interactions in turbulent reacting mixing processes at high Schmidt and Reynolds numbers. The mixing device is a classical coaxial jet mixer (see figure 1(a)) consisting of a nozzle of diameter d positioned along the centerline of a pipe of diameter D with the length L. It provides excellent mixing properties due to strong vortices appearing at the jet boundary as a result of the instability of the shear layer. From dimensions analysis it can be shown that the characteristics of the jet mixer depend for the isothermal case on the following parameters: the diameter ratio D/d, the Reynolds number related to the nozzle flow ν / Re d d du = , the Schmidt number Sc and the flow rate ratio , where the jet velocity (nozzle) exceeds the coflow one (pipe). Two following mixing regimes can be observed. The flow similar to a free jet (hereinafter called j-mode) appears if d D V V / d D V V d D / 1 / + < (see [2] and [3]). Otherwise if a strong recirculation zone is created just behind the nozzle (hereinafter called r-mode). The r-mode is often used to accelerate the homogenization of fluids because the recirculation enhances the mixing efficiency drastically so that the homogeneous state is already reached after some pipe diameters downstream of the nozzle. On the contrary the j-mode is more useful to control the progress of chemical reactions. d D V V d D / 1 / + > The mixing of scalars has already been thoroughly investigated both experimentally (LDV, PLIF) and numerically in a number of previous works published by the authors (see, for instance, [12], [5], [9] and [7]) and presented at THMT05 [11] and THMT09 [10] respectively. Despite of efforts in the development of new scalar mixing approaches in the last years, there are only few models available which can (accurately) predict the amount of molecular mixing at varying Schmidt numbers. However, no modeling is needed if using direct numerical simulations but all scales up to the batchelor scale ( ) where the molecular diffusion takes places have to be resolved. Considering flows at high Reynolds numbers and high Schmidt numbers (Sc~1000 for water) a DNS becomes impracticable due to the necessary high grid resolution. In the present study large eddy simulations have been done using an extended dynamic mixed model (DMM) which was also applied to the scalar dynamics of the flow. The DMM contains a special clipping procedure based on Taylor series approximation to improve the stability of LES computations [6]. The simulations were performed in j-mode at 2 / 1 − = Sc B η λ 1000 ~ , 12000 Re Sc d = and 5 / = d D V V . A simple irreversible neutralization reaction of acid and base was chosen as representative reaction case to investigate the turbulence chemistry interaction. The variation of the density and thermal effects can be neglected due to small inlet concentrations of reagents. The chemical closure is modelled in terms of an eddy dissipation concept which slows down the chemical reaction rate whenever it is faster than the micromixing rate. Figure 1(b) shows the profile of the passive scalar (mixture fraction of acid and base) obtained from LES and experiment along the x-axis at the centerline of the pipe. As seen f remains constant in the initial jet region at x/D < 0.6. The interior of the jet contains only acid. The chemical reaction takes place on the boundary between the jet and the coflow. At x/D > 0.6 the mixing arrives the jet centerline and it is completed at x/D > 7 with the formation of a homogeneous mixture. LES prediction for f agrees well with measurements. However, the performed frequency analysis of the passive scalar (see figure 1(c)) doesn't show a spectrum in the viscous-convective sub range