Monopile Depth Sizing of Fixed Offshore Wind Turbines on Indian Territorial Waters: Dynamic Analysis of Towers Under Wind and Ocean Loads
Authors: Basak Souvik , Datta Nabanita 
Published: September 2023

Abstract
A semi-analytical dynamic analysis of the monopile tower of an offshore wind turbine is presented. The linearly tapered, hollow, steel tower (with circular cross-section) is modeled as a Euler-Bernoulli cantilever beam with a tip mass, which is partially submerged in water, and partially embedded in the sea-bed as a monopile. The total tower length depends on the water depth at the location, the blade length, and the soil characteristics. The blade length, and hence, the swept area also influences the power captured (rated power) and hence, the nacelle (machinery) weight, which acts as a vertical compressive load on the tower. First, the tower is analyzed for its natural frequencies, which depends on several design parameters: tower geometry, tip mass, the depth of submergence, and depth of the monopile. A parametric study of free vibration is done for the tip mass, depth of submergence in water, and the depth of soil embedment. The tip mass adds to the kinetic inertia and the compressive load, decreasing the natural frequencies. The “added mass” or fluid inertia of the surrounding water (fluid radiation pressure in phase with the flexural acceleration) reduces the natural frequencies. The soil around the embedded monopile is modeled as a distribution of parallel translational springs, which restricts the horizontal motion and increases the natural frequencies. The variation of these frequencies, generated by the energy-based Rayleigh-Ritz method in MATLAB, are analyzed as a function of these parameters, to draw and optimize guidelines for structural design. The non-uniform beam mode-shapes are also generated by the weighted superposition of the admissible function (uniform cantilever beam mode shapes). This is followed by the quantification of the various loads: (i) Wind loads (constant load, turbulence, gust, and vortex-shedding), and (ii) ocean loads (current, waves, and vortex-shedding). First, the quasi-static responses (to the steady wind and ocean current loads) are analyzed to generate the quasi-static stresses. This is followed by the frequency domain analysis for the response to and random waves (Pierson-Moskowitz spectrum). Using the normal mode superposition principle, the dynamic stress amplitudes are generated to establish the safety factors. The depth of the monopile is optimized to withstand the maximum stresses, and also to avoid resonance with the dynamic loads. Since India has started looking into the expansion of the nascent offshore wind industry, a case study is done for a promising location on the Indian Territorial waters. The Gulf of Kutch (off the coast of Gujarat) has a strong wind potential. The location (22.5 N, 70 E), which is north of the industrial city of Jamnagar, is chosen for this study of the optimization of the monopile depth. The average wind speed here is about 6.5 m/s, which gives a design wind speed of about 9 m/s, at 50 m agl. For a 1 MW rated power of one offshore wind turbine, the blade radius is 40 m, requiring a dry tower height of about 80 m. The water depth in the Gulf of Kutch is about 30 m, and the sub-sea soil is rocky. The current speed in this region is a maximum of about 0.8 m/s in the SW monsoon season. Considering all of this, the monopile depth optimization process is detailed and design recommendations are given.