In a number of experiments and field tests of point absorbers, snap loads have been identified to cause damage on the mooring cables. Snap loads are basically propagating shock waves, which require special care in the numerical modeling of the mooring cable dynamics. In this paper we present a mooring cable model based on a conservative formulation, discretized using the Runge-Kutta discontinuous Galerkin method. The numerical model is thus well suited for correctly capturing snap loads. The numerical model is verified and validated using analytic and experimental data and the computed results are satisfactory.
A generic point-absorbing wave energy converter is modeled in CFD as a vertical cylinder, moored with a single catenary chain that is fully coupled through a dynamic mooring code. The method of choice is very complete and takes much of the non-linearities in the highly coupled system of the moored body into account. The paper presents numerical results compared with experimental data for surge, heave and pitch motion in both decay tests and regular waves. Further, the wave motion response of the cylinder is computed using both a viscous and a non-viscous formulation as a first attempt to quantify viscous effects. Results show a good match between numerical and experimental results in heave, while the surge and pitch motion are more difficult to reproduce. The mooring load cycle appearance compares well with the experiments in shape but gives higher peak values. Although made at low Keulegan-Carpenter numbers, the simulations show vortical structures due to the heave motion, and the resulting motions are clearly affected by the inclusion or exclusion of viscosity. More test-cases and detailed experimental results are needed for further quantification of the viscous impact on floating point absorbers.
The stability formula for rock slopes under wave attack was revised in Van der Meer (2021), replacing the mean period Tm with the spectral period Tm-1.0. This rewritten formula closely resembles the Modified Van der Meer formula as in the Rock Manual (2007), with differences primarily in coefficients and the use of H2% in the Rock Manual and H1/3 in Van der Meer (2021).
The wave characteristics change significantly in shallow water due to nonlinearities and wave breaking. The result is a significant change in the wave height and period, especially when severe breaking occurs and infragravity waves become significant or even dominate the spectrum. This may lead to very large breaker parameters. At a certain point, existing stability formulas may thus become inaccurate, both the original and the Modified formula for shallow water. The primary objective of this paper is to identify when and where shallow water stability results deviate from established formulas and how these deviations can be described.
The analysis involves an in-depth examination of datasets from Van Gent et al. (2003), Eldrup (2019), and other relevant data to increase the understanding of waves in shallow water and how they affect rock slope stability.
The use of H2% in the Modified Van der Meer formula gives some difficulties as no reliable prediction method is available for that parameter when the relative depth is small, h/Hm0 depth < 1.5. The Van der Meer (2021) formula applies the significant wave height, and it may be chosen as either Hm0 or H1/3. These two parameters are almost identical in deep water for which the formula was derived, but significant differences may occur in shallow water. The application of the Van der Meer formula in shallow water indicates a preference for the use of Hm0 as it describes nonlinear waves better. The main conclusion is that the Van der Meer (2021) formula seems valid much further into the shallow water region than what the Rock Manual (2007) recommends and at least to relative water depths of h/Hm0 deep > 1.5. For shallow water with h/Hm0 depth < 1.5 no systematic trend with the energy period is observed anymore and constant combined stability numbers are given for guidance in preliminary design.
Marine cables are primarily designed to support axial loads. The effect of bending stiffness on the cable response is therefore often neglected in numerical analysis. However, in low-tension applications such as umbilical modeling of ROVs or during slack events, the bending forces may affect the slack regime dynamics of the cable. In this paper, we present the implementation of bending stiffness as a rotation-free, nested local Discontinuous Galerkin (DG) method into an existing Lax–Friedrichs-type solver for cable dynamics based on an hp-adaptive DG method. Numerical verification shows exponential convergence of order P and P + 1 for odd and even polynomial orders, respectively. Validation of a swinging cable shows good comparison with experimental data, and the importance of bending stiffness is demonstrated. Snap load events in a deep water tether are compared with field-test data. The bending forces affect the low-tension response for shorter lengths of tether (200–500 m), which results in an increasing snap load magnitude for increasing bending stiffness. It is shown that the nested LDG method works well for computing bending effects in marine cables.
The paper presents incompressible Navier-Stokes simulations of the dynamics of a floating wave energy converter (WEC) coupled to a high-order finite element solver for cable dynamics. The coupled model has very few limiting assumptions and is capable of capturing the effects of breaking waves, green water loads on the WEC as well as non-linear mooring forces and snap loads, all of which are crucial for correct estimates of the extreme loads acting on the system in violent seas. The cable dynamics model has been developed as a stand-alone library that can be coupled to any body motion solver. In this study the open-source CFD package OpenFOAM has been employed. Preliminary test cases using incident regular Stoke's 5th order waves are presented, both for wave heights corresponding to operational conditions of the WEC as for a more severe condition in survival mode. It is illustrated that the coupled model is able to capture the complicated force propagation in the mooring cables.
In the present paper, the experimental data on wave run-up on slender monopiles from recently published small and large scale tests are reanalyzed using different methods for the wave analysis. The hypothesis is that the post processing has an impact on the results, due to limited depth and highly nonlinear waves in many of the tests. Thus, the identified maximum waves by a zero-down crossing analysis are highly influenced by the reflection analysis method as well as by bandpass filtering. The stagnation head theory with the run-up coefficient is adopted and new coefficients are presented. The hypothesis is verified, and the applied bandpass filter is identified as a large contributor to conservatism in previous studies, as the steep, nonlinear waves that produce the highest run-up can be heavily distorted by the bandpass filter.
Simulation-based analysis estimating both the energy requirement of the entire carbon capture process and the purity of the recovered CO 2 is scarce. The purity of the captured CO 2 is crucial as it must meet a specification before transportation, preventing phase change and damage to the transportation system. This study conducted 31,104 simulations of a monoethanolamine carbon capture plant treating measured flue gas from an existing cement production plant. After capture, the CO 2 is treated through a deoxygenation unit followed by a compression train to fulfill specific quality specifications. Based on the sensitivity analysis, the energy consumption of the post-treatment process decreased with increased purity downstream. Despite this, the total energy consumption was not affected. Moreover, after the two-step purification the CO 2 stream was able to successfully fulfill the specification for NO x, O 2, NH 3, Ar, CO, SO 2. However, failing to meet the H 2O concentration requirements of both considered specifications and the N 2 concentration specified for ship transport. Thus, increasing the post-treatment energy cost or standard adjustments is required for future applications.
The expansion of Carbon Capture, Utilization, and Storage (CCUS) highlights the growing need for carbon dioxide (CO2) pipeline transportation. While pure CO2 is non-corrosive, impurities such as H2O and NO2 create a corrosive environment that risks pipeline integrity. This study investigates how H2O and NO2 concentrations, along with temperature, influence corrosion under CO2 pipeline conditions. The investigation was performed in an autoclave setup emulating a linear velocity of 0.96 m/s at 100 bar and temperatures of 5 °C and 25 °C, testing X52 and GR70, and a more corrosion-resistant 9Cr alloy. The results indicated that the presence of NO2 elevated the corrosion rate compared to scenarios without. Low H2O concentration led to a corrosion rate of up to five times higher at 5 °C, compared to at 25 °C, in the presence of NO2. Low to moderate corrosion was observed for the carbon steels without NO2 and with 70 ppmv H2O at both temperatures. Reducing the H2O concentration below 70 ppmv and removing NO2, while SO2 and O2 are present, will only result in low to moderate corrosion in the carbon steel CO2 pipeline. The corrosion rate for X52 and GR70 was 0.065 mm/y and 0.016 mm/y higher or 5 and 3 times greater, respectively, at 5 °C compared to 25 °C. The study concludes that H2O should be maintained below 70 ppmv and NO2 should be eliminated to prevent severe corrosion. Emphasizing the importance of CO2 specification compliance and the need for further research into CO2 compositions that align with the specifications.
Various sources of harmonic problems in large wind power plants (WPPs) and optimized harmonic mitigation methods are presented in this paper. The harmonic problems such as sources of harmonic emission and amplification as well as harmonic stability are identified. Also modern preventive and remedial harmonic mitigation methods in terms of passive and active filtering are described. It is shown that WPP components such as long HVAC cables and park transformers can introduce significant low-frequency resonances which can affect wind turbine control system operation and overall WPP stability as well as amplification of harmonic distortion. It is underlined that there is a potential in terms of active filtering in modern grid-side converters in e.g. wind turbines, STATCOMs or HVDC stations utilized in modern large WPPs. It is also emphasized that the grid-side converter controller should be characterized by sufficient harmonic/noise rejection and adjusted depending on WPPs to which it is connected.
The typical approach for generating nonlinear waves in physical models involves employing first- or second-order wave theory, requiring a large water depth at the wavemaker. When the prototype bathymetry shows a gentle slope, a large facility is required. However, practical constraints often make this unfeasible, leading to the use of steep transition slopes to obtain sufficient water depth at the generator. Incorporating a transition slope may generate unwanted free waves beyond the transition point, significantly impacting the wave parameters. The presence of these free waves causes the response of the tested structure to deviate from that found in the prototype. This paper offers guidelines for using transition slopes effectively while avoiding the generation of unwanted free waves after the transition point.