It is already some time ago when I worked together with DonVK and fluid investigating fin horns and especially finding methods how to simulate them properly with BEM. First, off I would like to mention that this collaboration was one of my highlight “diy” experiences. When three people with their respective strengths work together in a concentrated and constructive manner over a longer period of time this is a very good chance creating something special. It all started exploring the original Yuichi/Arai fin horn design and how to simulate it with BEM.
I had started developing my own fin horns already a few years before, but struggled to simulate these horns accordingly. Especially the individual fins or separate channels and their integration as BEM model at throat and at the end of the fins is tricky. You could either simulate them as individual channels but in this case several interfaces are necessary and you could end up with interface issues (one to many and many to one subdomain). Or the BEM model is one single mesh including the fins but then at fin start and end you encounter very close vertices when the fins are very sharp which is a problem with BEM. At that time more questions than answers left for me and these initial designs ended up in the drawer.
Some time ago I presented the first article about my development of the ALO William Neile horn type and the underlying construction method. Although, most of my previous worksheets use a super ellipse for each 3D layer / spline along the horn axis. To have an alternative option for William Neile horns I have implemented the the necessary math together with evenly distributed Neile parabolas used in this context to build up the horizontal construction wave front. All William Neile (WN) horns based on the super ellipse algorithm will get the extension “SE” in their name.
By varying the Lamé exponent of the super ellipse formula many different shapes from elliptical to almost rectangular are possible. At throat everything always starts with a Lamé exponent of 2 which indicates an ideal ellipse. Of course, if major and minor axis of the ellipse are equal there will results a perfect circle at throat. If major and minor axis differ an ellipse will result. Generally, the major axis is the horizontal plane because it is intended to radiate more broad compared to the vertical plane (minor axis). For higher Lamé exponents of the super ellipse formula the resulting shape will be an almost rectangular spline but a transition function is needed to provide a smooth transition from exponent 2 to higher values along the horn axis. A very similar procedure was already used for my spherical wave horn (SWH) and JMLC worksheets.
This article is about the first making of such a horn by DonVK who much preferred the native elliptical shape and asked for my assistance to optimize a horn for his setup. Finally, we ended by with two horn of different cut-off. This article describes the making of the first smaller version.
Surprisingly, the JMLC articles are constantly among the most read here. My corresponding JMLC worksheets can already be found in the Download section of my webpage since some time. Recently, I got the request that in addition to the existing point cloud export it should also be possible to export splines for each step along the horn axis as many CAD programs can import and loft such splines much more elegant than to mesh a point cloud. Fortunately, I implemented the splines feature already for my William Neile worksheets so it was no big thing to migrate the feature also for the JMLC HVDdiff worksheet.