As the UV water treatment industry has matured, increasingly sophisticated tools have helped to bring about a steady improvement in the performance of UV systems. Among these is CFD modelling, which has allowed the complex flow through UV chambers to be understood as never before.

### A numbers game

As anyone who studied fluid mechanics will recall, most of the standard equations that are used to analyse how a system behaves strictly apply only to the case of laminar flow, that ideal but elusive condition when a fluid passes through the system in a uniform stream without causing turbulence or eddy currents. Such a situation rarely occurs in the real world, and most certainly not with the complex geometry and high flow rates inside a UV chamber. These situations require equations which are often impossible to solve exactly, but for which an approximate answer can be obtained using numerical methods.

Numerical (also known as iterative) methods involve repeating a calculation many times, each time using the answer to the previous calculation as the new input value, until the difference in the results from each step is so small that the calculation is said to have converged to give a stable solution. Such an approach demands substantial computing power, something which is now available to virtually everyone. This has led to the burgeoning field of Computational Fluid Dynamics (CFD), a technique widely used in the engineering industry that has now shed valuable new light on the UV treatment of water.

### How it works

A mesh or grid is used to break the system down into manageable chunks within which the mass, momentum and energy can be calculated. The cells in the mesh can then be linked together to give a complete solution for the system. Designing the mesh is the first important decision when building the model. A coarse mesh can be modelled fairly quickly and easily but risks giving an inaccurate solution. A very fine mesh requires longer computing time as more calculations are involved but should give a more accurate solution, although a balance is needed as each calculation inevitably introduces rounding errors.

The UV light from a set of eight lamps inside a chamber can be modelled using a suitable mesh

The next step is to choose a suitable CFD model from the many now available for different flow regimes. A set of suitable boundary conditions also needs to be selected; these conditions constrain the calculations to shorten processing time and reduce the likelihood of the calculation diverging, where the answer never reaches a stable solution. These stages require a certain amount of judgement, intuition and familiarity with real-world conditions and behaviour, which helps to understand whether the selected options give a reasonable comparison with “the truth”. Modelling involves art as well as science.

The real nuts and bolts of the modelling calculation come next. The model is reduced to a series of algebraic equations that are solved iteratively to obtain a set of flow variables for each cell of the mesh. Once the results are calculated, they are usually presented as a contour map or vector plot superimposed on a 2-D representation of the system, which shows how the flow variables vary at each location of the volume being analysed. In cases where a series of time steps are considered, an animation can also be constructed.

The air flow around a motorcycle and rider can be represented by CFD modelling as a coloured vector diagram showing areas of high (red) and low (blue) velocity

### Upsides/downsides

The main advantage of using CFD is that a design can be analysed and optimised without resorting to physical testing, a prolonged and costly business which may itself be subject to errors if not carried out at full scale. Modern computers allow even complex systems to be modelled relatively quickly, and so different designs can be evaluated and compared before anything is manufactured. CFD modelling software also presents the results in a manner that is more accessible and intuitive than graphs or data tables.

As with all modelling techniques, the limitations of CFD must be remembered when analysing the results. Any model is only as good as the data used to construct it; a great deal of work has gone into developing models of different flow regimes but it is unlikely that any of them precisely describe reality. However, after several decades of development, the confidence in CFD modelling has grown and it has been used in many diverse applications such as visualising the air flow around aircraft, calculating the efficiency of cooling fins on heat exchangers and, now, modelling the flow through Hanovia’s UV treatment chambers.

CFD modelling has largely replaced wind tunnels in analysing aircraft and space vehicle design

### UV chamber secrets revealed

In the past, the performance of UV water treatment systems had to be either proven using complicated and expensive tests with biological assays of microorganisms, or extrapolated from very simple calculations of average UV dose. Now, CFD modelling has revealed the various flow paths through a particular chamber and what proportion of the water passes along them. Each flow path has a certain proximity to the UV lamps, and therefore the dose received by a microorganism as it moves along each path can be calculated. A simplified view of the results from such an analysis is shown below, with three different flow paths traced out in the chamber. The calculated UV dose received by microorganisms travelling along each path in mJ/cm^{2} is also shown.

Flow paths and UV doses for a chamber can be derived from CFD modelling

CFD modelling exercises like this have enabled Hanovia to calculate Reduction Equivalent Doses (REDs) for its systems. These doses are directly related to the percentage of the microorganisms that are inactivated by the UV light in the chamber, and are a much more accurate measure of the system’s efficacy than the average doses previously estimated.

By optimising the chamber design in this way, the UV light from the lamp can be used to maximum effect. Armed with CFD modelling, Hanovia can provide greater assurance to itself and its customers about the performance of the systems that it manufactures.

#### Further reading

Appendix D in Ultraviolet Disinfection Guidance Manual for the Final Long Term 2 Enhanced Surface Water Treatment Rule, United States Environmental Protection Agency Report EPA 815-R-06-007, November 2006.

Douglas, J F, et al., Fluid Mechanics, Sixth edition, Prentice Hall, 2011.