Inflow Direction Research Articles

Source apportionment of PM2.5 using dispersion normalized positive matrix factorization (DN-PMF) in Beijing and Baoding, China

Fine particulate matter (PM2.5) samples were collected in two neighboring cities, Beijing and Baoding, China. High-concentration events of PM2.5 in which the average mass concentration exceeded 75 µg/m3 were frequently observed during the heating season. Dispersion Normalized Positive Matrix Factorization was applied for the source apportionment of PM2.5 as minimize the dilution effects of meteorology and better reflect the source strengths in these two cities. Secondary nitrate had the highest contribution for Beijing (37.3 %), and residential heating/biomass burning was the largest for Baoding (27.1 %). Secondary nitrate, mobile, biomass burning, district heating, oil combustion, aged sea salt sources showed significant differences between the heating and non-heating seasons in Beijing for same period (2019.01.10–2019.08.22) (Mann-Whitney Rank Sum Test P < 0.05). In case of Baoding, soil, residential heating/biomass burning, incinerator, coal combustion, oil combustion sources showed significant differences. The results of Pearson correlation analysis for the common sources between the two cities showed that long-range transported sources and some sources with seasonal patterns such as oil combustion and soil had high correlation coefficients. Conditional Bivariate Probability Function (CBPF) was used to identify the inflow directions for the sources, and joint-PSCF (Potential Source Contribution Function) was performed to determine the common potential source areas for sources affecting both cities. These models facilitated a more precise verification of city-specific influences on PM2.5 sources. The results of this study will aid in prioritizing air pollution mitigation strategies during the heating season and strengthening air quality management to reduce the impact of downwind neighboring cities.

Selection criteria for rotor number and rotational direction in arrays of closely spaced Darrieus turbines

Abstract The efficiency gains observed in a pair of closely spaced Darrieus turbines suggest the deployment of multiple turbines as an appealing solution for wind and, particularly, hydrokinetic applications, where the inflow direction is constant. The present study develops some design guidelines for closely spaced hydrokinetic Darrieus turbines by analyzing the trends of both power augmentation and wake development within arrays of multiple rotors, including not only an even number of rotors, which is the usual case in literature, but also an odd one. The analysis is carried out by means of two-dimensional Computational Fluid Dynamics simulations and includes not only the assessment of instantaneous blade forces but also locally sampled flow fields past each blade that allowed the reconstruction of dynamic polar data, contributing to a more comprehensive understanding of the physical mechanisms at play in such compact setups. The study demonstrates a consistent power augmentation mechanism across different layouts, even in the case of an odd number of rotors. This enhancement originates from flow blockage in the mutual interaction areas, favorably altering the inflow angle and subsequently increasing the angle of attack and lift generation. While this mechanism aligns with previous observations on arrays of counter-rotating pairs, its application to multiple turbines introduces complexities due to potential asymmetries in inflow, leading to an uneven power enhancement across turbines within the array. The identified efficiency improvement pattern suggests that maximizing leeward mutual interactions within an array of multiple Darrieus turbines would enhance the overall efficiency of the setup.

A solar rotation signature in cosmic dust: Frequency analysis of dust particle impacts on the Wind spacecraft

Dust particle impacts on the Wind spacecraft were detected with its plasma wave instrument Wind/WAVES. Frequency analysis on the resulting dust impact time series has revealed spectral peaks indicative of a solar rotation signature. We investigated whether this solar rotation signature is embedded in the interplanetary or in the interstellar dust (ISD) and whether it is caused by co-rotating interaction regions (CIRs), by the sector structure of the interplanetary magnetic field (IMF), or by external effects. We performed frequency analysis on different subsets of the data to investigate the origin of these spectral peaks, comparing segments of Wind's orbit when the spacecraft moved against or with the ISD inflow direction and comparing the time periods of the ISD focusing phase and the ISD defocusing phase of the solar magnetic cycle. A superposed epoch analysis of the number of dust impacts during CIRs was used to investigate the systematic effect of CIRs. Case studies of time periods with frequent or infrequent occurrences of CIRs were performed and compared to synthetic data of cosmic dust impacts affected by CIRs. We performed similar case studies for time periods with a stable or chaotic IMF sector structure. The superposed epoch analysis was repeated for a time series of the spacecraft floating potential. Spectral peaks were found at the solar rotation period of $ sim d $ and its harmonics at $13.5\ d $ and $9\ d $. This solar rotation signature may affect both interplanetary and interstellar dust. The appearance of this signature correlates with the occurrence of CIRs but not with the stability of the IMF sector structure. The CIRs cause, on average, a reduction in the number of dust impact detections. Periodic changes of the spacecraft's floating potential were found to partially counteract this reduction by enhancing the instrument's sensitivity to dust impacts; these changes of the floating potential are thus unlikely to be the cause of the solar rotation signature.

Deflected wind field over a two-dimensional steep ridge subjected to yawed inflow

In this study, large-eddy simulations (LES) are performed to investigate the turbulent wake flow of a two-dimensional ridge with cosine-squared cross-section for representative wind direction. The power law index of the mean velocity profile of the approaching turbulent boundary layer is 0.13. The variations of separation bubble, mean and fluctuating velocities, wind deflection angles, speed-up ratio and power spectra density with inflow angle are systematically investigated. One significant horizontal feature of the flow field is that the yawed inflow deflects further when it encounters the two-dimensional ridge. The yaw angles exhibit strong non-linear relationships with the inflow angle, especially at locations influenced by the separation bubble. The length of the separation bubble projected to the plane perpendicular to the ridge gradually decreases with an increasing inflow angle. Meanwhile, the longitudinal mean velocity above the ridge and the vertical mean velocity near the windward side decrease with a higher inflow angle. A lateral mean velocity emerges and strengthens as the inflow angle increases. In addition, peak frequency in the power spectrum of longitudinal velocity rises with increasing inflow angle, accompanied by higher energy concentrations near the peak frequency.

Optimizing Wind Farm Efficiency through Active Yaw Control: A Neural Network-Aided Game Theory Approach

This research investigates the potential of a game-theoretic-based Active Yaw Control (AYC) strategy to enhance power generation in wind farms. The proposed AYC strategy in this study replaces traditional look-up tables with a trained Artificial Neural Network (ANN) that determines the optimal yaw misalignment for turbines under time-varying atmospheric conditions. The study examines a hypothetical 3x2 rectangular arrangement of NREL 5-MW wind turbines. The FAST.Farm simulation tool, utilizing the dynamic wake meandering (DWM) model, is employed to assess both the power performance and structural load on the wind turbines. When tested with two different inflow directions and ambient turbulence (10%), the AYC strategy demonstrated a maximum increase in total power output of 2.6%, although it affected individual turbines differently. It also exhibits an increase in some structural loads, such as tower-top torque, while some components experience a slight reduction in load. The results underscore the effectiveness of the ANN-guided game-theoretic algorithm in improving wind farm power generation by mitigating the negative impact of wake interference, offering a scalable and efficient method for optimizing large-scale wind farm. However, it is essential to evaluate the overall impact of AYC on wind farm efficiency in terms of both Annual Energy Production (AEP) and structural loading under various atmospheric conditions.

LES-based validation of a dynamic wind farm flow model under unsteady inflow and yaw misalignment

This work presents the validation of an extended version of the control-oriented, dynamic wind farm flow solver SPLINTER. The two-dimensional model is applied to use cases of wake steering by yaw misalignment and inflow wind direction variations and the results are compared to large-eddy simulations (LES). While SPLINTER is able to reproduce the antagonal behaviour of decreasing upstream and increasing downstream turbine power under wake deflection, a systematic deviation of the downstream power is detected and quantified, which is connected to underrepresented three-dimensional wake effects. In case of changing inflow wind direction, SPLINTER is capable of computing movement and shape of the bending wakes. The model smooths small-scale turbulent structures and disturbances and does not reproduce wake meandering, but manages to describe the evolution of the mean flow, which is tested by averaging over an ensemble of LES and comparing the resulting flow fields and turbine power time series. Under dynamic inflow conditions, SPLINTER is able to predict at which time intervals and at which rates downstream turbines will be influenced by wakes, which can improve the accuracy of short-term power and load forecasting and enables its application to online model predictive wind farm control.

A correction model for the effect of spanwise flow on the viscous force contribution in BEM and Lifting Line methods

Design optimization and aeroelastic load evaluation for wind turbines are still infeasible for CFD due to computational cost. These tasks are carried out using 3D engineering aerodynamic methods, where the local aerodynamic loads are obtained from tabulated 2D aerodynamic polars, which makes the models fast. With recent developments such as highly flexible blades, coned/prebent/swept blades, the relative inflow direction to the “inner” 2D airfoil section systems can have a significant component in the spanwise direction. The Crossflow Principle (CP) is used to treat the effects of this in a physically consistent manner. Cases dominated by pressure forces are described well with the CP method, but it is shown in the paper that CP fails to describe the part of the forces stemming from the friction forces correctly. It is shown in the paper that the power loss due to friction forces will be underestimated with the crossflow principle for rotors with significantly swept blades or other designs with a significant amount of local crossflow on the blades. The present work presents a simple model to correct the baseline crossflow principle method to take into account also the friction force part in a consistent manner. The model is validated with 3D CFD results on a 2D airfoil section. It is shown that the new model successfully corrects for the addition of the viscous forces due to spanwise flow component. The paper includes examples of the effect of using the model on rotor designs with different amounts of blade sweep simulated using a blade element momentum (BEM) and blade element vortex cylinder (BEVC) methods.

Study on the Evolution Pattern of Complex Topographic Flow Field in Typical Tableland and Hogback Ridge

The flow field in complex mountainous wind farms is highly intricate, affecting the accuracy of wind resource assessments and the reliability of wind turbine operation. In order to study the evolving characteristics of the flow field in typical complex terrains under different inflow wind directions and wind speeds, this paper, based on the open-source software OpenFOAM, adopts a neutral atmospheric boundary layer model combined with Reynolds-averaged turbulence model to construct a high-precision flow field model for complex terrains. The research reveals that this model requires fewer computational resources and can effectively simulate the flow characteristics around complex terrains. Wind resource distribution in tableland terrains and hogback ridge terrains is more influenced by the height of the mountains, and the recovery speed of the wake behind the mountains decreases with a reduction in slope. In hogback ridge terrains, under a wind direction of 0 °, the wind acceleration effect at the top of the hogback ridge is stronger than under a wind direction of 270°, as it experiences more intense compression from the mountains. This paper can provide reference for micro-siting in complex terrain.

A Study on the Scour Surrounding the Fixed Foundation of an Offshore Wind Turbine under Complex Waves, Tidal Currents, and Pile Vibration Conditions

Scouring around the fixed foundations of offshore wind turbines (OWTs) remains a pressing concern within the offshore wind industry, significantly jeopardizing OWT safety. Despite previous efforts, the current understanding of this phenomenon remains incomplete, as various factors related to offshore wind farms and OWT operations can exert intricate influences. To further explore this matter, this paper undertakes a new study to further understand the interplay between monopile vibrations, tidal currents, and sea waves, elucidating their combined impact on scour surrounding an OWT’s foundation. It was found that, besides pile vibration amplitude and frequency, the pile vibration direction can also notably influence the scour around the monopile. Specifically, the most pronounced scour mostly transpires when the monopile undergoes vibrations along the 135° direction relative to the inflow direction. The mildest scour mostly occurs when the pile vibrates along the 90° direction. Additionally, this study reveals that different types of waves, indicated by the ratio of water depth, H, to wavelength, L, also engender varying scour around the monopile. The influence of waves on scour increases with the decrease in the H/L ratio, implying that OWT foundations are more threatened by shallow water waves than by deep water waves.

State-of-Charge Trajectory Planning for Low-Altitude Solar-Powered Convertible UAV by Driven Modes

The conversion efficiency of solar energy and the capacity of energy storage batteries limit the development of low-altitude solar-powered aircrafts in the face of challenging meteorological phenomena in the lower atmosphere. In this paper, the energy planning problem of solar-power convertible unmanned aerial vehicles (SCUAVs) is studied, and a degressive state-of-charge (SOC) trajectory planning method with energy management strategy (EMS) is proposed. The SOC trajectory planning strategy is divided into four stages driven by three modes, which achieves the energy cycle of SCUAV’s long-endurance cruise and multiple hovers without the need to fully charge the battery SOC. The EMS is applied to control the output of solar cell/battery and power distribution for each stage according to three modes. A prediction model based on wavelet transform (WT), long short-term memory (LSTM) networks and autoregressive integrated moving average (ARIMA) is proposed for the weather forecast in the low altitude, where solar irradiance is used for the prediction of solar input power, and the wind and its inflow direction take into account the multi-mode power prediction. Numerical and simulation results indicate that the effectiveness of the proposed SOC trajectory planning method has a positive impact on low-altitude solar-powered aircrafts.

Experimental investigations on water sorptivity in mortars with the use of X-ray micro-CT system

The phenomenon of water sorptivity in prismatic mortar specimens was investigated in this experimental work. This phenomenon is closely linked to material durability. Sorptivity evaluated during a steady stage, combined with exposure conditions can be used for performing service life predictions. Water's initial and secondary sorptivity in unsaturated mortar specimens were measured in laboratory tests following the standard ASTM C 1585–04. The impact of initial porosity on sorptivity was investigated by varying the cement-to-sand ratio (c/s) and the water-to-cement ratio (w/c). In addition, the surface area of water intake was changed which was either vertical or horizontal in orientation. The water distribution in the test specimens was visualized using the 3D X-ray micro-CT system SkyScan 1173 which was a novelty. The mortar sorptivity was found to be highly responsive to the c/s ratio, varying by up to 100%, and to be moderately impacted by the w/c ratio, varying by up to 25% and the surface inflow direction, varying by up to 45%. The sorptivity increased with a decline in the c/s (in agreement with the existing literature data) and w/c ratio (in contrast with the existing literature data). According to micro-CT images, the water distribution in the specimens was found to be non-uniform and larger porosity contributed to the rise in water level but not to the total volume of absorbed water (in contrast to the literature data). The snap-off events were detected ahead of the waterfront.

Wake meandering of wind turbines under dynamic yaw control and impacts on power and fatigue

In this study, we use large-eddy simulation (LES) to investigate the wake-meandering phenomenon within a wind turbine array under dynamic yaw control (DYC) and the effects on power and fatigue. The wind turbine array consists of eight NREL 5-MW reference turbines aligned with the inflow direction. The first turbine in the array is subjected to sinusoidal yaw control with a magnitude of 10∘ and different yaw frequencies. Based on spectral and dynamic-mode-decomposition (DMD) analyses of the flow fields, we find that the wake meandering within the turbine array is significantly amplified when the turbine yaw frequency coincides with the natural wake meandering frequency of the turbine array in the static zero-yaw condition. The resonance of wake meandering accelerates wake recovery and helps the turbine array achieve an optimal power gain (5% with respect to the non-yaw baseline cases). We also find that the fatigue of the turbine array overall increases with the yaw frequency of the first turbine, highlighting the necessity of jointly considering power production and fatigue when applying DYC.

Simulation of natural ventilation for semi-enclosed buildings

Energy-saving buildings have become a topical issue and widely used the energy-saving ventilation design, which aims to maximize the use of natural ventilation while reducing demand on mechanical ventilation. In this research, natural ventilation performance of two different semi-enclosed building layouts, "O" type and "L-L" type, are studied by numerical simulation. According to the simulation results, in the "O" type, the maximum indoor air velocity occurs in building A (orientation facing the inflow direction). The minimum indoor air velocity occurs in building C (orientation facing building A). In the "L-L" type, the maximum indoor air velocity occurs in building A (orientation facing the inflow direction). The minimum indoor air velocity occurs in buildings B and D (orientation parallel to the inflow direction). And air flow field simulation results show that, the "L-L" type exhibits better than the "O" type in natural ventilation. Furthermore, simulation results show that the natural ventilation performance in the room is influenced not only by the building orientation, but also by the window size.

A study on a fixed-bed for Pb(ii) removal by modified alkaline lignin-sodium alginate composite hydrogel.

In this work, alkaline lignin (AL) co-modified with trimercapto-s-triazine trisodium salt (TMT) and sodium alginate (SA) as a matrix were used to create a composite hydrogel for removing heavy metals, specifically divalent lead (Pb) from water. The obtained hydrogel beads were packed into a fixed bed, and then various operating conditions were explored to assess their impact on the efficiency of Pb(ii) removal. The findings indicated that the optimal removal efficiency for Pb(ii) was attained using an inflow rate of 0.159 L min-1, a hydrogel-II filling height of 40 cm, an initial Pb(ii) concentration of 10 mg L-1, and a bottom inflow direction. In the third adsorption-desorption cycle experiment, the breakthrough curve reached equilibrium after 650 min, in which equilibrium time for the initial breakthrough curve was 855 min, indicating that hydrogel-II exhibit good regeneration capability. This work serves as a foundation for practical applications in removing heavy metals from wastewater.

Investigating the bearing performance of the foundation under the combined effects of flood scouring and soaking

Bearing capacity degradation of foundations under the impact of the flood is one of the major reasons responsible for the collapse and damage to the rural buildings, posing a serious threat to the local village societies. Based on a case study of a rural building foundation had been destroyed by flooding. This paper investigated the deterioration process of rural building foundations under the combined effect of dynamic scouring and static soaking caused by flooding. Using the two-dimensional shallow water equation, erosion depth was calculated for different flood velocities. Then, the bearing capacity degradation under the combined scouring-soaking effect was analyzed using the finite element method. Finally, investigating the influence of inflow direction and building group masking on the foundation's bearing capacity. The results indicate that under the combined effect, the bearing capacity of village building foundations decreases by 47.88%, with scouring slightly more impactful than soaking. Inflow angle has minimal effect on bearing performance, while the masking effect of the building group provides better protection for the foundation of rear buildings.

The Influence of Mountain Height and Distance on Shape Factor of Wind Load of Plastic Tunnel

Due to their soft structure and covering material, plastic greenhouses are vulnerable to wind disasters, causing large-scale damage and huge economic losses. The wind load of greenhouses depends on the surface wind pressure distribution, which is different for greenhouses located in valleys from those in plain areas. To study the wind pressure distribution law for various regions of greenhouses built in valleys, mountain and greenhouse models have been built by Computational Fluid Dynamics, in which the length direction of the greenhouse is perpendicular to the valley and the wind direction is parallel to the valley. In the analysis, the verified turbulence model and grid division method are both introduced, and the effect of the height and distance of mountains is considered. According to the distribution law of wind pressure, the greenhouse’s surface is partitioned, and the variation law of the shape factor of wind load on a plastic tunnel is analyzed. Then, the calculation model for the shape factor of the wind load on the greenhouse located in a valley is proposed. The conclusions show that: (a) When the wind inflow direction angle is parallel to the valley, the distribution pattern of wind pressure on the surface of the greenhouse is similar to that on the plain regardless of the distance and height of the mountains, while the values of the wind pressure are greatly affected by the mountain height and distance. The distance between mountains has greater influence than the effect of mountain height. (b) The shape factor of wind load on the suction area of the greenhouse decreases as the distance of mountains increases, while the shape factor on the pressure area of the greenhouse increases with the increase in the distance. It can be seen that the valley effect is non-negligible. The narrower and deeper the valley, the greater the wind pressure effect. (c) When the ratio of the distance between the foot of the mountain and the greenhouse d to the height of the mountain H is less than 5, i.e., d/H &lt; 5, the ratio of the distance to the height has a significant impact on the shape factor of wind load on the greenhouse. When d/H is close to 10, the shape factor of the wind load in the valley area is close to that in the plain area, and the effect of the ratio between the height and the distance is negligible. (d) The proposed calculation model can be used to calculate the effect of mountain height and distance on the shape factor of wind load. The research results can be used in the wind resistance design of plastic greenhouses in valley areas, and can also provide some data support for the revision of the greenhouse structural load code.

Physicochemical characteristics and seasonal variations of PM2.5 in urban, industrial, and suburban areas in South Korea

Among countries that are a part of the Organization for Economic Co-operation and Development, South Korea is the most exposed to PM2.5. Despite the country having implemented various strategies to limit PM2.5 emissions, its concentrations are still high enough to pose serious environmental and health concerns. Herein, we monitored various physiochemical properties of PM2.5 across different regions in South Korea from January 1 to December 31, 2021. Specifically, the study area consisted of the city center, industrial complexes, and suburban areas. Before analyzing dynamics of emissions specific to each site, the Clean Air Policy Support System data for the three areas were compared to elucidate their respective primary emission sources. The particle concentrations for the three areas were 21.8–26.44 µg/m3, with the highest concentrations being observed in March. All the three areas exhibited high ratios of NO3− across all seasons. The particle number concentrations in the three sites were 1.3–1.5 × 107, and the peak points of the concentrations were different in every site: city center (40 nm), industrial complexes (60 nm), and suburban areas (80 nm). We also conducted potential source contribution function and conditional bivariate probability function analyses. These analyses were conducted to determine the inflow direction of the pollution sources for high PM2.5 episodes. For the episodes that occurred in spring and winter, there were no differences in the PM2.5 concentrations between the three sites. Overall, the insights gained from this study offer a framework for developing air-quality management policies in South Korea, specifically in the context of PM2.5 emissions.

Numerical simulation of heat transfer properties of large-sized biomass particles during pyrolysis process

During the pyrolysis process of large particles, the conduction between particles cannot be ignored. In the present work, a numerical simulation model for the pyrolysis of biomass particles was established, which takes into account the conduction within the particles. Based on this model, the temperature distribution inside the particle during the pyrolysis process was determined and the effects of particle size, moisture content, and gas velocity on heat transfer characteristics were analyzed. The results showed that the temperatures at different positions of the particles along the inflow direction were quite different, and the maximum temperature difference inside the particles was about 146.7 K for a particle diameter of 10 mm and a velocity of 0.2 m/s. During the pyrolysis process of biomass particles, there were two peaks of Nusselt number. The increase of moisture content prolonged the pyrolysis time. The pyrolysis.time of particles with moisture content of 15 % was about 1.5 times longer than that of dry particles when the particle diameter was 10 mm. Increasing the particle size decreased the difference between the two peaks and increased the time interval between the two peaks. Increasing the gas velocity can improve the heat transfer, but the effect of too high gas velocity on improving the heat transfer is limited. The present study is of great importance for a detailed understanding of the pyrolysis process of biomass particles.

Experimental investigation of inflow-outflow asymmetry in induced-charge electro-osmosis

Induced-charge electro-osmosis (ICEO) is a research hotspot in bioengineering and analytical chemistry. Inflow-outflow asymmetry of ICEO was reported in the existing literatures, but systematic study on this phenomenon is insufficient. In this experimental study, we found that in strong electric fields, not only the velocity magnitude but also the vortex positions of ICEO are asymmetrical along the inflow and outflow directions because of the pronounced non-uniform surface electrokinetic transport. On the inflow and outflow directions, the amplitudes of velocities are unequal, ICEO maximum velocity positions change depending on the electric field intensity and sodium chloride (NaCl) concentration. Additionally, the distances between vortex centers are different. At NaCl solution concentration of 0.001 mol·L–1, the outflow velocity almost vanishes. The asymmetry rises with the increasing electric field intensity. The new discoveries can direct the application of microscale devices.

The Experimental Study of Dynamic Response of Marine Riser under Coupling Effect of Multiparameter

In order to investigate the dynamic response of a marine riser under the coupling effect of multiparameter, a model experiment of a marine riser was designed and carried out. The main parameters of the model test were divided into riser design parameters and flow field parameters. The riser parameters included the elastic modulus, boundary conditions, and top tension forces, and the flow field parameters were the velocities and wave parameters (wave height and period). The riser materials were aluminum (Al) and polymethyl methacrylate (PMMA), representing the metal riser and fiber-reinforced composite marine riser, respectively, which differ greatly in modulus. Two types of boundary conditions were considered, which were simple supports at both ends (S-S) and simple and fixed supports at each end (S-F). The top tension forces were chosen as 10 N and 30 N, respectively. In terms of the flow velocities, 0.3 m/s and 0.7 m/s were used. For the wave types, the small wave had a period of 1.0 s and a wave height of 5 cm while the large wave had a period of 2.0 s and a wave height of 15 cm. The dynamic response of the riser under 32 different working conditions was studied experimentally, and through the analysis of the experimental data, the effects of various parameters on the dynamic response of the risers were obtained. The results show that the amplitude of the riser was negatively correlated with the elastic modulus, the number of constraints, and the magnitude of the top tension, while it was positively correlated with the flow velocity and wave size. Moreover, the sequences of importance were b3 (flow velocity) &gt; b6 (modulus) &gt; b1 (number of constraints) &gt; b2 (top tension force) &gt; b5 (wave height) &gt; b4 (wave period) for the vibration of the riser in the in-flow direction and b3 (flow velocity) &gt; b1 (number of constraints) &gt; b6 (modulus) &gt; b2 (top tension force) &gt; b5 (wave height) &gt; b4 (wave period) for the vibration of the riser in the cross-flow direction, respectively, according to the multiple linear regression calculation.