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Improving Mixing Design with Advance Simulation
- Ravindra Aglave (Ph.D.) Director, Chemical Process IndustryCD-adapco
Mixing can be defined as the reduction in homogeneity of concentration, temperature, or phase. In industry, the application of mixing is wide ranging: from blending in tanks, to gas dispersion in liquids; suspension of solids in liquids; and liquid-liquid dispersions. This article explains how advance simulation help improve the mixing design and scale-up the process.

Mixing occurs over a large range of length scales, as macro level phenomena of stirring and shearing drive micro level processes such as mass transfer or temperature or shear dependent property change. In turn, these micro level phenomena drive molecular diffusion and reaction. Understanding mixing in its entirety is challenging, due to these wide ranging scales.

Each new stirred reactor system needs a scale-up rule that is derived from lab scale and pilot scale experiments after looking at a range of possible operating and design conditions. Process engineers rely heavily on measurements, experience and rule of thumb to carry out design and scale-up of mixing tanks or stirred tank reactors. However, although “tried and tested” each of these approaches has significant drawbacks in terms of either the cost or the accuracy of the results that they provide. Computational Fluid Dynamics (CFD) is increasingly providing a more cost effective and accurate alternative to these established techniques.

Simulation for Design and Scale-up
Traditionally, use of CFD in simulation of mixing in stirred vessel has been characterised by several hurdles. These hurdles and the recent advancements addressing them are described below. Due to these difficulties, the number of simulations cases that are carried out for a given stirred vessel has historically been limited, so that the full benefit of carrying out parametric variations of design and operating conditions cannot be leveraged in the design process and cannot consequently complement the experimental work in a valuable manner.

The CFD simulation process involves four basic steps viz.: geometry creation, mesh generation, setting boundary and initial conditions and finally post-processing. Of all these steps, the first two have historically been the most expensive that requires manual intervention from an engineer. However, in recent years the process has been streamlined in commercial CFD tools that have been specifically created to handle computational geometries - much more complex than mixers (i.e. the underhood of an automobile, or the undercowl of a gas turbine). This development means the effect of a geometric parameter can be studied much more quickly and will be limited only by the computing resource available. As the industry invests more in ever-cheapening computing resources, even this limitation can be overcome easily.

Automating the Mesh Generation Process
The quality and reliability of the results from the simulation depend on the quality of the underlying computational mesh for a given geometry and flow characteristic.

In the past engineers attempted to create meshes using structured hexahedral computational cells; however, this approach usually failed to capture the full geometrical detail of the impellers, and they were forced to use simplified methods such as momentum sources to account for the motion of the impeller. Tetrahedral meshes, however, suffer from a few disadvantages such as large number of cells for a given volume and risk of highly skewed cells in small angles around the impeller blades.

A modern development is so called “polyhedral” meshes that are made from computational cells with an arbitrary number of faces, typically 14-16 faces per cell, as opposed to 4 faces in a tetrahedral mesh. Like tetrahedral meshes, polyhedral meshes can accommodate complex shapes. However, the numbers of cells required are much lower resulting in faster mesh creation and, since each cell communicates with so many neighbours, solution times are significantly reduced. Due to the polyhedral nature of the cells, they rarely run into bad quality cells or skewed cells. They can be combined with prismatic cells near walls to capture boundary effects.

Sliding Meshes
All the mentioned approaches are good for “steady state” type approached that are suitable when the impeller-baffle interaction is not important or weak. More often than not, the interaction is not weak or there are other unsteady effects that are important. In such instances, the sliding mesh or Rigid Body Motion (RBM) approach or a moving/deforming mesh approach can be used. Creating an excellent mesh that gives stable and accurate results requires manual work that slows the turnaround time and causes loss in value of simulation. Automatic meshing of geometries can be quick, but is fraught with the risk of creating unreasonable and/or bad quality meshes. Considering the conflicting approaches of automatic meshing and the slow process of completely manual meshing, an unique and more fundamental approach is needed.

Overset Meshing a Key Enabler
The overset or chimera mesh methodology has existed for a number of years but has become available commercially only recently. It marks a paradigm shift in simulations involving motion of a body relative to another body. All unsteady state stirred vessels simulations require the motion of an inner zone consisting of the impellers. In this method, a background mesh is created for the stationary/non-moving domain and one or more overlapping grids are created for the moving zone. It has the advantage over other meshing methods is that the two zones can be meshed independently giving more flexibility in refining the grid. Moreover, during the motion, an initial good quality mesh still remains the way it is, especially in the sharp angle regions of the impeller because no remeshing is necessary at each time step. This also reduces the computational expense. There is no loss of information as all the grids are implicitly coupled.

Simulation of other complex mixing equipment such as twin-screw extruders, helical mixers can vastly benefit from the overset mesh technique. These equipment typically have more than one moving element with elements having overlapping or entangled motion.

Rigorous Parametric Studies & Model Based Optimisation
Optimisation of a mixing tank design generally is carried out using experiments and observations of quality of mixing. However, numbers of experiments that can be carried out are always limited or cannot cover the entire design space. Therefore, a selected design may not represent the most optimum configuration, mathematically speaking.

Design space exploration use parameterised geometry and automatic meshing methods to explore the entire design space where impeller blade dimensions, number, pitch angles, number of sets etc can be varied to explore how they affect one or more key metrics of mixing such as power density distribution, mixing time or residence time distribution. The resulting Pareto front can help a process engineer choose from various design alternatives. Alternately, optimisation algorithms that plug into the design space exploration study can be employed to select a best design for a given set of single or multiple cost functions e.g as minimising the mixing time while keeping a narrow residence time distribution.

The Human Factor of Success with Simulations
The most important aspect of a CFD simulation of a stirred vessel is interpretation of the results in a manner that is amenable for practical use. Practical experience gives expertise to discern between a feasible/successful design and infeasible or unsuccessful design.

The key to utility of CFD simulation is how a velocity, turbulence or other variable resolved by the Navier- Stokes equation can be translated in to a set of practical evaluation and decision making metrics. Such work demands that engineering performing simulations and carrying out experimental/scale-up work very closely in developing such workflows. Basic understanding of simulation process, easy to use simulation tools, good training, commitment and patience can reveal larger gains in improving this most common problem type in the chemical industry.

A wizard or a simplified setup front end that can perform basic engineering design and follow it up with a complete CFD analysis can ease the learning curve for process engineers who would like to deploy CFD in their engineering process.

Summary and Outlook:
Some of the recent advances in simulation technology can address these hurdles, thereby increasing the frequency and accuracy of the simulations to contribute with a higher value to the scale-up process. Engineers and managers also should consider that a large computation today is several orders of magnitude less expensive than it was a decade ago whereas the cost of experimentation has increased. The skill to set up of a stirred vessel simulation, post-simulation analysis and integrating it into routine engineering design and scale-up process is the need of the future for a process design engineer.

Automation of the setup process, including the ability to seamlessely import CAD geometries, automated but reliable and reasonably mesh generation are some of the capabilities being added to commercial codes that can help a process design engineer acquire these skills rapidly.