Perturbed turbulent stirred tank flows with amplitude and mode-shape variations Somnath Roy, Sumanta Acharya n Mechanical Engineering Department, Louisiana State University, Baton Rouge, LA 70803, USA article info Article history: Received 14 March 2011 Received in revised form 2 August 2011 Accepted 3 August 2011 Available online 10 August 2011 Keywords: Stirred tank Perturbation Impeller-jet Periodic fluctuations Turbulence Power number abstract Stirred tank (STR) flows at low and moderate Reynolds numbers show poor mixing behavior due to formation of segregated zones inside which both magnitude and fluctuation level of velocity components show lower values compared to the active fluid regime (i.e., impeller jet stream, circulation loops). Active perturbation of the STR flow using a time-dependent impeller rotational speed can potentially enhance mixing by breaking up these segregated unmixed zones and enhancing the turbulence level throughout the tank volume. In the present study, the effect of different perturbation cycles on an unbaffled turbulent stirred tank flow at a moderate Reynolds number (rotational speed N ¼3 rps) is studied using a large-eddy simulation (LES) technique coupled with immersed boundary method (IBM). The perturbation frequency (f) is chosen to correspond to a dominant macro-instability in the flow (f/N ¼0.022). Two different perturbation amplitudes (20% and 66%) and two perturbation shapes (square-wave and sine-wave) are investigated, and changes in the mean flow field, turbulence level and impeller jet spreading are examined. Large-scale periodic velocity fluctuations due to perturbations are noticed to produce large strain rates favoring higher turbulence levels inside the tank. Production of turbulent kinetic energy due to both the mean and periodic component of the velocity field is presented. Fluctuations in power consumption due to perturbation are also calculated, and shown to correlate with the perturbation amplitude. & 2011 Elsevier Ltd. All rights reserved. 1. Introduction Stirred Tank Reactors (STRs) represent over $350 billion of product yield in the U. S chemical industry with nearly $ 10 billion per year lost due to inefficient operation of the mixing devices (Paul et al., 2004). Therefore, improvements in existing technologies can potentially translate to several billion dollars in annual cost savings. Many of these mixing and blending opera- tions (e.g. polymerization, petro-chemical blending) are carried out at laminar and transitional regime due to high viscosity of the working fluids. Hindrance to proper mixing arises due to forma- tion of segregated regions in laminar or moderately low Reynolds number turbulent/transitional stirred tank flows (Dong et al. 1994; Harvey et al., 1996), which acts as barriers to the impel- ler-jet stream allowing unmixed fluid to reside in the tank and increasing the mixing time as well as the amount of byproducts generated in industrial operations. So, the dispersion of the segregated regions via enhanced spreading and mixing out of the impeller jet-stream is one of the primary objectives of studies in mixing enhancement. Aref (1984) and Aref and Balachandar (1986) showed that periodic perturbation sets in chaotic advection in low Reynolds number viscous flows diminishing the sizes of the stagnation zones. Franjione et al. (1989) showed that in lid-driven cavity flows, periodic lid velocity can enhance mixing. For a similar lid- driven cavity flow, Liu et al. (1994) observed that unstable manifolds wrap themselves around the islands preventing forma- tion of segregated low stretching zones. Lamberto et al. (1996) introduced instabilities in the flow field through a time varying rpm of the impeller, and for a sufficient low Reynolds number (Re  9–18) flow, they performed a direct visualization of acid– base-indicator mixture to observe the break-up of the segregated tori structures due to the imposed dynamic perturbations. Yao et al. (1998) also observed an improvement in mixing rate by perturbing the STR flow with a time-varying impeller rotational speed. They also obtained a faster mixing by periodically chan- ging the direction of impeller rotation. Lamberto et al. (2001) demonstrated that with change in rotational speed the stable tori formed during one constant impeller speed breaks up and the unmixed fluid disperses in the outer fluid. Ascanio et al. (2002) studied combined effects of variable rpm and off centered shafts and obtained a high mixing rate. Using impellers mounted on two different off-centered shafts, they obtained a complete break-up of segregated zones. Bar-Ell et al. (1983) and Schneider (1985) Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/ces Chemical Engineering Science 0009-2509/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2011.08.005 n Corresponding author. E-mail address: acharya@LSU.edu (S. Acharya). Chemical Engineering Science 66 (2011) 5703–5722