What do you do when faced with analysing a shell and tube heat exchanger as in the model shown in Figure 1? I can already hear you saying “you want to ‘C..F..D’ this thing!? There’s like a thousand meters worth of piping..?” Quite literally in fact, approximately 1km in total with a 1mm wall thickness and a total of 800 bends. Thoughts that run through my mind are; “How big is this mesh going to be? How long is it going to take to solve? I only have a quad core laptop (at least with 32GB of memory which helps)”. And if I were to use anything other than FloEFD I’d also think “with all those bends I’m probably going to have to remodel the piping so that I can HEX-mesh it…or something” It seems overwhelming at first because most of the time us engineers simply don’t have time for all of that, we need answers and we needed them yesterday!
Fortunately, this is exactly where FloEFD starts to make a lot of sense, especially for the internal pipe flow, where the SmartCells™ technology within FloEFD really comes into play. SmartCells will recognize directly from the CAD geometry if it is a pipe or a channel, and decide based on the number of cells across this pipe or channel to apply a textbook or engineering calculation (1D) for the pressure drop and heat transfer when there is insufficient cells across the pipe to numerically resolve the flow. Alternatively, when there is indeed a sufficient number of cells across the pipe, SmartCells will then automatically switch to resolving the flow field (3D) with the numerical grid. But, if you’ve ever wondered exactly how well FloEFD performs in this regard, perhaps the following observations may be very beneficial. Let us start this discussion by looking first of all at solving internal pipe flow with heat transfer in FloEFD.
Part I: Internal pipe flow with heat transfer
See the FloEFD validation example. Let’s consider an example slightly more relevant to the heat exchanger at hand. Figure 2 shows the FloEFD model of a 10-pass pipe layout with internal flow. Heat transfer to the internal fluid is modeled with a Heat Transfer Coefficient applied to the outer wall boundary, to allow for the calculation of conduction through the wall along with the conjugate heat transfer at the fluid-solid interface on the internal pipe surface. Radiation is neglected for this example. The mesh was generated such that the characteristic number of cells across the diameter of the pipe was gradually increased, starting with as little as 2 cells across the pipe diameter up to 6 cells. Figure 3 illustrates the typical Cartesian mesh used. One other very important aspect of the SmartCells technology is “Thin walls” technology which allows the original cartesian cells to be divided into multiple control volumes at the solid-fluid boundaries, such that they can contain either a fluid or solid control volume or a series of both and still calculate the conjugate heat transfer at the solid-fluid interfaces. So you can see in Figure 3 there is no need to generate a ‘body-fitted’ mesh that adapts the mesh to the solid boundaries.
Now let us compare the results from FloEFD with that of the very reliable 1D thermal-hydraulic system solution called Flownex (developed locally here in South Africa). The Flownex model of the same pipe layout is shown in Figure 4. Consider the graph of the total heat transfer as presented in Figure 5. The FloEFD results are displayed with respect to the increasing mesh density and compared to the Flownex result. A band of +10% and -10% of the Flownex result is also shown to add some perspective to the comparison. It runs out that for this example the heat transfer prediction by FloEFD is always within the +/-10% band compared to Flownex, regardless of the mesh density. Quite fascinating really.
It should be noted that I am only showing one example here, but an extensive study of first comparing 1-pass, 2-pass and then 10-pass pipe layouts, with flows at varying Reynolds numbers (as high as Re=600,000 with air at 45m/s), all produced very similar behavior. Consider Figure 6 which shows the expanded study results for 1-pass and 10-pass pipe layouts respectively with air as the fluid at vastly different flow rates. What is so astonishing about these results is the fact that even at much higher velocities FloEFD predicts a total heat transfer still within 10% of the Flownex result for what can only be considered ridiculously coarse meshes in CFD terms. I want to go right out and say that FloEFD is the only CFD solution that will allow you to use the same level of mesh resolution and produce the same level of accuracy across a wide range of Reynolds number flows – I just want to let that sink in for a moment…I will prove and restate this fact in Part II of this series. For the sake of everybody’s curiosity, I want to make the following interesting observation: It seems to me then that the switchover point from the engineering calculation to the fully resolved pure CFD solution happens at around eight to ten cells… Beyond this point, one could see a sudden jump in heat transfer prediction as the mesh resolution is increased, but all the while remaining within the +/-10% band compared to Flownex.
In conclusion, considering the revelations made above, it is evident that one can use FloEFD as an engineering tool for solving internal pipe flow with heat transfer by utilising the SmartCells technology and resolving the pipe cross-section with meshes that are as coarse as 4 to 6 characteristic cells across the diameter. This makes it possible to at least attempt to solve large heat exchanger models with much fewer computer and engineering resources than one would expect with CFD if one can follow the same approach regarding the flow external to the tubes, or the shell-side, which will be investigated in Part II. The full heat exchanger will be discussed in Part III.