Single and multiphase CFD approaches for modelling partially baffled stirred vessels: comparison of experimental data with numerical predictions

Whilst the use of CFD to study mixing vessels is now common-place, there are still many specialised applications that are yet to be addressed. Here we present CFD and PIV results for a hydrodynamic study of a partially baffled vessel with a free surface. The standard k.ε and SSG Reynolds Stress turbulence models are used and the numerical predictions of the mean flow field are compared with experimental data for single phase modelling. At low rotation rates a flat free surface is observed and the flow is simulated using a single phase model, whilst at high rotation rates an Eulerian–Eulerian multiphase model is used to capture the free surface location, even under conditions when gas is drawn down to the impeller. It is shown that there are significant transient effects that mean many of the “rules of thumb” that have been developed for fully baffled vessels must be revisited. In particular such flows have central vortices that are unsteady and complex, transient flow-induced vortical structures generated by the impeller–baffle interactions and require a significant number of simulated agitator rotations before meaningful statistical analysis can be performed. Surprisingly, better agreement between CFD and experimental data was obtained using the k.ε than the SSG Reynolds stress model. The multiphase inhomogeneous approach used here with simplified physics assumptions gives good agreement for power consumption, and with PIV measurements with flat and deformed free surfaces, making this affordable method practical to avoid the erroneous modelling assumption of a flat free surface often made in such cases

An experimental and CFD study of liquid jet injection into a partially baffled mixing vessel: a contribution to process safety by improving the quenching of runaway reactions

Thermal runaway remains a problem in the process industries with poor or inadequate mixing contributing significantly to these incidents. An efficient way to quench such an uncontrolled chemical reaction is via the injection of a liquid jet containing a small quantity of a very active inhibiting agent (often called a stopper) that must be mixed into the bulk of the fluid to quench the reaction. The hazards associated with such runaway events mean that a validated computational fluid dynamics (CFD) model would be an extremely useful tool. In this paper, the injection of a jet at the flat free surface of a partially baffled agitated vessel has been studied both experimentally and numerically. The dependence of the jet trajectory on the injection parameters has been simulated using a single-phase flow CFD model together with Lagrangian particle tracking. The comparison of the numerical predictions with experimental data for the jet trajectories shows very good agreement. The analysis of the transport of a passive scalar carried by the fluid jet and thus into the bulk, together with the use of a new global mixing criterion adapted for safety issues, revealed the optimum injection conditions to maximise the mixing benefits of the bulk flow pattern

An experimental and computational study of the vortex shape in a partially baffled agitated vessel

The vortex shape in a non-standard partially baffled agitated vessel in the form of a glass-lined, under-baffled stirred vessel has been investigated using both experimental and numerical approaches for an air/water system for different rotation speeds of the agitator. A simple and flexible experimental strategy was developed for determination of the time-averaged location of the unstable free surface using a process involving superimposition of images. CFD simulations were made to predict the vortex shape by using an Eulerian–Eulerian multiphase model coupled with a homogenous turbulence model. The simplifying assumptions of a constant bubble size, a constant drag coefficient and use of the k–ε turbulence model were made. An assessment of the capability of the numerical method to predict the vortex shape was carried out through comparison between experimental data and numerical results. Considering for comparison purposes a water isosurface volume fraction equal to 0.9, to account for the existence of air/water mixture present at the interface in the experiments, instead of the classical value of 0.5, gave very good agreement with the experimental data

Transient hydrodynamics and free surface capture of an under-baffled stirred tank during stopping

The transient hydrodynamics and the free surface shape have been numerically predicted by CFD for an under-baffled agitated vessel during the stopping phase of the agitator, including the inertial period after the agitator has completely stopped. The simulations were carried out in a fully transient manner using a gas/liquid inhomogeneous two phase flow model coupled with a k–1 turbulence model. The time dependence of the system studied reveals that the history of the fluid evolution during the impeller slowing phase determines the instantaneous results, implying that the resulting hydrodynamics cannot be determined via a classical steady-state approach. The numerical prediction of the free surface shape during stopping is in agreement with experimental data

Exact wavefunctions for excitations of the nu=1/3 fractional quantum Hall state from a model Hamiltonian

We study fractional quantum Hall states in the cylinder geometry with open boundaries. By truncating the Coulomb interactions between electrons we show that it is possible to construct infinitely many exact eigenstates including the ground state, quasiholes, quasielectrons and the magnetoroton branch of excited states.Comment: 7 pages, 3 figures, longer published versio

Jet injection studies for partially baffled mixing reactors: a general correlation for the jet trajectory and jet penetration depth

This paper is devoted to the analysis of the jet trajectories, obtained using computational fluid dynamics (CFD), at two different scales (laboratory and industrial) with application to quenching of runaway reactions. One of the goals was to describe how the jet penetrates the fluid in the stirred vessel and to build an easy to use correlation for research and industrial purposes. A model of the jet trajectory based on the analogy with a jet in a cross-flow has been used to predict the jet trajectory at the pilot and industrial scales. The correlation, built using a statistical analysis, has shown that the jet in a cross-flow model performs very well to describe the jet trajectories. A very interesting conclusion is that the correlation constants were found to be independent of scale. Finally, the authors proposed a definition of the penetration depth and use it in its dimensionless form to predict how the jet penetrates in the industrial vessel with the current injection conditions

A Note on Easy and Efficient Computation of Full Abelian Periods of a Word

Constantinescu and Ilie (Bulletin of the EATCS 89, 167-170, 2006) introduced the idea of an Abelian period with head and tail of a finite word. An Abelian period is called full if both the head and the tail are empty. We present a simple and easy-to-implement $O(n\log\log n)$-time algorithm for computing all the full Abelian periods of a word of length $n$ over a constant-size alphabet. Experiments show that our algorithm significantly outperforms the $O(n)$ algorithm proposed by Kociumaka et al. (Proc. of STACS, 245-256, 2013) for the same problem.Comment: Accepted for publication in Discrete Applied Mathematic