Half of all chemical, pharmaceutical and food production takes place in stirred tanks. This figure is generally believed to be even higher in the food industry, where frequent recipe changes make batch processing the norm for many manufacturers. Basic mixing technology hasn’t changed much for decades, but with everyone trying to squeeze more out of their assets, there are still gains to be made. It’s all about understanding the mixing process better so that engineers can optimise it.
The answer lies in building better models of the process: but should you opt for a physical approach, or might mathematical modelling such as CFD be more effective for your particular application?
Trying to invoke general rules for modelling mixing is fraught with difficulty, because there are so many important factors that can interact to affect the outcome. “Food mixer designs are almost infinitely variable because the applications and products are so variable," says David Brown, head of the Fluid Mixing Processes (FMP) programme, a collaborative research effort at BHRSolutions.
The degree of difficulty can be compounded if the fluids being mixed are non-Newtonian. Newtonian fluids are those that move in direct proportion to the force applied, while non-Newtonian fluids include anything that doesn’t obey this simple rule. Examples include shear thinning liquids (which get runnier the more vigorously they are mixed) or shear thickening liquids (which get stiffer).
In the quest for ever more sophisticated solutions to modelling, it can be easy to overlook more basic approaches. A recent paper from a group of researchers at the University of Dayton, Ohio, is a great example of an inspired piece of successful, low-tech thinking.
“[The journal] Chemical Engineering Science is used to covering research that uses instruments worth hundreds of thousands of dollars. We used ketchup, a plastic bucket and a handsaw," says Dr Bob Wilkens, assistant professor in the Department of Chemical and Materials Engineering.
Ketchup models
Ketchup was an ideal fluid for the experiment, which sought to help the researchers develop a model of mixing in a type of material called a Bingham plastic fluid. These fluids do not start to move until the force on them reaches a critical level known as the yield stress. This means that when an agitator begins to stir ketchup it creates a moving volume surrounded by stationary zones where the yield stress has not been reached. The moving portion is known as a cavern. What Wilkens and his team wanted was a physical model that could help them develop and verify a mathematical formula for the way the shape and size of a cavern varies with mixing speed.
It was a simple misunderstanding that eventually led to the breakthrough. “I told the students that it would be easier to study a cavern if we could freeze it. I meant it conceptually, but they literally stuck it in the freezer," says Wilkens.
First the researchers injected coloured glitter around the agitator in a bucket full of ketchup. They then set the impeller moving at the fastest of the three speeds they planned to test. Next, they injected a second colour of glitter and set the mixer to the medium speed. Last came a third dose of glitter and the slowest of the mixing speeds. They then stuck the entire vessel into a freezer for several days until it was solid. The shapes of the three caverns could clearly be seen by slicing up the resulting ice cube to reveal the distribution of the different types of glitter.
“The results looked like we were cleaning up after a particularly nasty road accident, but you can clearly see the shapes of the caverns," says Wilkens. “In some ways it’s such a trivial technique it seems so obvious once you’ve thought of it. But it’s proved useful and there’ll probably be more work like this."
The resulting mathematical model describes a doughnut-shaped cavern, which grows with the increasing speed of an impeller until it reaches the vessel walls. “We hope it’s a very generic model that can be used with any of these yield stress fluids," says Wilkens.
Physical modelling is not always straightforward, however. Brown says that test rigs should generally be geometrically similar to the process being studied, but the difference in scale between a test rig and the industrial process must be taken into account to produce valid results. “Especially in the case of shear thinning liquids, tests at a small scale need to use the appropriate viscosity so that the Reynolds number [a measure of turbulence] is appropriate. You have to ensure that the flow patterns are the same," says Brown.
FMP’s test facilities include some very large mixing vessels for experimental studies. For unusual requirements, the team also designs and builds its own custom-made rigs. But one of the things that FMP prides itself on is not being tied to one technique or another. If physical modelling is not appropriate, CFD may hold the answer. “We do quite a lot of CFD but there are quite a number of problems where it doesn’t apply," says Brown. “In a fully turbulent flow in Newtonian systems it can be very helpful and cheaper than running physical models. In transitional flows with non-Newtonian fluids, CFD must be approached with caution."
CFD used to be the domain of academic researchers equipped with super computers. Only recently have modern computers made it feasible to produce commercial software to tackle complex flow regimes.
“Quite useful CFD calculations can be done on to today’s desktop computers. The real cost is buying the time of someone who really knows what they’re doing particularly in tricky applications," says Brown. “You can buy CFD packages to help mixing simulations and they can be very helpful but you need a lot of guidance on where it’s appropriate and where it isn’t."
Martin Branagan, account manager for leading CFD vendor Fluent Europe, agrees that expert help is often needed when using computer models to solve complex problems. The company offers comprehensive training to anyone using its software and follows this up with expert support and consultancy services.
“Modelling can only ever be as good as the information you put in," he says. “In the food industry there are lots of complex applications, with parameters like viscosity and density varying with temperature, for example. It all adds to the complexity of the model. Some applications are well characterised and understood and where they’re not we work closely with clients to iron out any problems. Certain applications, such as multiphase flow with gas, liquids and solids, bring in a whole different range of physics, but the maths behind the models is developing all the time."
At its heart CFD relies heavily on Navier Stokes equations, which describe the way in which certain parameters, such as mass, energy or momentum, must be conserved as fluid passes from one tiny volume to the next. According to Branagan, this gives CFD an intrinsic advantage over physical experiments: “The CFD models can define the variables at any point in the flow domain but in real life you can only take point measurements. In addition, the introduction of probes to take the measurements influences the flow, so you’re creating artificial conditions."
Dough kneading model
On the academic front, the search for better numerical models is continuing. There is quite a gap between cutting-edge academic work and the current capability of commercial packages, according to Professor Mike Webster, secretary of the Institute of Non-Newtonian Fluid Mechanics at the University of Wales: “We’ve done work on dough kneading for a consortium of major food companies and we’ve made some serious headway with complex fluids that you wouldn’t expect of commercial software off the shelf."
But Webster says that the non-Newtonian fluids often regarded as problematic for CFD are not intrinsically any more difficult to model than turbulent, Newtonian flow regimes: “You have to study each instance case by case. You can’t really expect to just pick up a CFD tool and abuse it."
Webster is also a principle investigator in the Engineering and Physical Sciences Research Council’s Portfolio Partnership on Complex Fluids and Complex Flows. One of its goals is to establish new numerical simulation tools for the small to large-scale behaviour of complex fluids. “These fluids crop up in all sorts of guises at all sorts of scales. Better tools will be seriously useful for the community," he says. FM
KEY CONTACTS
■ BHRSolutions 01234 750422
■ Fluent Europe 0114 281 8888
■ University of Dayton 001 937 229 1000
■ University of Wales, Swansea 01792 205678