Part I of this series asked the question: “What do you do when faced with analysing a shell and tube heat exchanger as in the model shown in Figure 1”? The discussion in Part I revolved around the solution of the ‘internal pipe flow with heat transfer problem’ and how FloEFD can be used as an engineering tool in this regard thanks to the SmartCells™ technology. Let’s take the discussion around the SmartCells technology further then. FloEFD is fully CAD-embedded, and by fully CAD-embedded we don’t mean it is just an interface plug-in to some CAD software. No, we mean that FloEFD is tied directly to the CAD model, literally to the background mathematical definitions that make the CAD geometries look the way they do. So being fully CAD-embedded in this strict sense of the term has a set of serious advantages:
- There is no translation to some intermediate neutral file format, i.e. NO information gets ‘lost in translation’, literally speaking.
- Because of this direct link to the CAD model FloEFD will recognize any solid feature, regardless of size.
- And to top it all, FloEFD will also use such geometric features as curvatures, during the calculation, as illustrated in Figure 2.
Couple the feature from point nr. 3 above with the two-scale wall function employed by FloEFD to calculate the boundary layer and it allows for much coarser meshes to be used to generate reliable and useful results, as demonstrated in Figure 3. The two-scale wall function forms part of the “enhanced turbulence modelling” approach employed by FloEFD. The technology decides automatically if the boundary layer is “thin” or “thick” relative to the characteristic cell size and applies the relevant boundary layer calculation. The result in Figure 3 clearly shows the “thin boundary layer” of the two-scale wall function model at work. Again, as with Part I, if you’ve ever wondered exactly how well FloEFD performs in this regard, perhaps the following observations may be very beneficial.
Part II: External flow over a heated cylinder
So then, what about the flow on the outside of the pipes, i.e. the ‘shell-side’ flow of the heat exchanger in question? To represent the ‘shell-side’ flow we will consider the standard validation example of external flow over a heated cylinder. In this analysis, only the heat transfer behavior is considered, and not the drag, per sé. Again the mesh is set up such that the characteristic number of cells across the diameter was varied incrementally. Consider the graph in Figure 4 which shows the Nusselt number prediction for several mesh densities across a wide range of Reynolds numbers. It is evident from the graph that regardless of the mesh density the FloEFD prediction is very good, always within the scatter of the experimental data, even considering the extremely coarse meshes used in CFD terms, i.e. four to ten cells per diameter. See especially the close-up image showing the four and six cell mesh results. Thus, it is evident then that similar to the internal pipe flow case in Part I, FloEFD is still capable of producing the same level of results for this external flow case with Reynolds numbers ranging across 4 orders of magnitude, all with the same mesh.
The above observations, fortunately, aligns very well with that of the internal flow results from Part I in that one should also be able to generate very useful engineering results for the heat transfer in an external flow, with meshes as coarse as just four characteristic cells across the pipe diameter. It should be stated that it does seem that six characteristic cells per pipe diameter would be more desirable, but for the purposes of this engineering approach, the ‘four cells per diameter’ case would be more than sufficient and will be used when analysing the full heat exchanger in Part III.