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The goal of the present study is to develop an optimized skeletal chemical kinetic mechanism for methane combustion, for conditions relevant to dual-fuel marine engines. To this end, a systematic approach is developed, consisting of the following steps: (a) assessment of three widely used detailed mechanisms, by comparing simulation results against three sets of indirect experimental data pertinent to methane combustion, (b) sensitivity analysis, with identification of important reactions (species), (c) selection of one detailed mechanism and production of a skeletal mechanism by means of the simulation error minimization connectivity method, (d) uncertainty analysis of the rate constants of important reactions, and (e) optimization of the skeletal mechanism for the rate constant parameters of the important reactions. The resulting optimized skeletal mechanism, consisting of 28 species and 119 elementary reactions, accurately reproduces experimental data in a wide range of conditions and is an important development for computational fluid dynamics studies in dual-fuel marine engines.

This paper demonstrates an approximation to the numerical solution of the dynamic equilibrium of a catenary riser. The approximant is obtained in the frequency domain when the structure is excited by motions applied at the top. The dynamic equilibrium is formulated mathematically through six nonlinear partial differential equations which involve both geometric and hydrodynamic nonlinearities. The latter are represented by the Morison’s formula. The numerical solution of the six nonlinear differential equations is used to generate spatio-temporal data series for riser bending moments induced by sinusoidal heave motions of various amplitudes and frequencies. The data series are transformed to the frequency domain where a complex singular value decomposition scheme is applied in order to reconstruct the full nonlinear spectrum. The significant harmonics of the riser’s spectrum are then identified as the three lower odd harmonics. The method finally provides a set of orthogonal modes for all significant harmonics; that is, the fundamental, the third and the fifth harmonic of the bending moment in the 2D plane of reference. The nonlinear, frequency-domain modal decomposition proposed is also examined in a typical test case.

A numerical simulation and system identification approach to the dynamic equilibrium of a catenary riser has been developed. A finite DOF representation of the dominant dynamics is constructed using frequency domain identification by applying nonlinear signal theory techniques on response data series when exciting the structure with sinusoidal motions at the top. Data series are obtained through numerical integration of a finite differences simulation model on the basis of the six nonlinear partial differential equations describing the riser dynamics. Dynamic equilibrium is mathematically formulated by the very same equations that implicate both geometric and hydrodynamic nonlinearities; the latter are depicted by Morison’s formula. Thus, spatio-temporal series are generated for riser bending moments induced by sinusoidal heave motions of various amplitudes and frequencies. These data are consequently transformed to the frequency domain where complex Singular Value Decomposition is applied in order to derive the full nonlinear spectrum. The significant harmonics of the riser’s spectrum for the bending moment on the 2D plane of reference are demonstrated to be the three lower odd harmonics and a set of orthogonal modes for these three significant harmonics is derived. The methodology proposed is finally applied to a typical test case for validation.