Hi,
I’m in the process of building a model of a 3 MW offshore “paper” turbine for our SeaCon project. I thought I would pass on some of my experiences. This first posting is about generating the tower mode shapes using BModes.
The standard BModes executable is hardwired to use 12 analysis elements (nodes). We hope to make this a user-input setting next year. For now, however, you must use 12 or recompile with a different setting. I wanted 21 analysis elements, so I changed mselt to 21 in para.inc and recompiled. When I ran BModes with 21 elements for a symmetrical tower, I got incorrect results. Gunjit did some sleuthing and found that something goes wrong when we had more than 20 elements. Something seems to be hardwired. He is working on that now. He found that BModes worked correctly when using 20 elements, so I recompiled to code to use 20.
The current version of BModes assumes the tower-top mass is at the end of the tower, which is not the case; we hope to fix that next year. To get around that problem, I added 1.631 m of stiff, low-mass section to extend the tower to the tower-top CM. When I requested four modes shapes, BModes generated mode shapes for one fore-aft and three side-to-side tower modes, yet FAST needs two of each. BModes includes a torsional degree of freedom, while FAST does not. To get two fore-aft and two side-to-side tower modes, I increased the tower torsional stiffness by a factor of ten.
I’ve created a spreadsheet that takes the BModes mode shapes and computes polynomials for them, which is what FAST requires. A future version of FAST will accept the digitized mode shapes instead of polynomials.
For the polynomial fit, the workbook renormalized the x values so that the real tower top had a value of 1; otherwise, the x=1 point would be the center of mass for the tower-top mass. The workbook fit the mode shapes generated by BModes to polynomials that have zeros for the zeroth- and first-power terms, which is the case for cantilevered beams (no deflection or slope at the fixed end). The workbook normalizes the polynomials by the sum of the coefficients.
For the second fore-aft mode, the mode shape was two orders of magnitude closer to zero at the true top of the tower than at the maximum-displacement point. Such a huge difference essentially applies a much higher weight to the large-displacement points than to the tower top. This results in a very poor fit for the polynomial at the critical tower-top point. When I normalized the raw points and the polynomial fit so they both went through (1,1), they differed at the maximum-displacement point by about 25%. To get around this problem, I duplicated the 1.0 point over 200 times to add weight to it for the polynomial fit. This resulted in the polynomial passing closer to the 1.0 point. The resulting curve was a much better approximation to the normalized data points.
That’s all for now.
Marshall