Fatigue analysis of jacket support structure for offshore wind turbines

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In the past few decades and up to now, the fossil energy has exerted tremendous impacts on human environments and gives rise to greenhouse effects while the wind power, especially in offshore region, is an attractive renewable energy resource. For offshore fixed wind turbine, stronger foundation like jacket structure has a good applicability for deeper water depth. Journal of Science and Technology in Civil Engineering NUCE 2019 13 (1): 46–59 FATIGUE ANALYSIS OF JACKET SUPPORT STRUCTURE FOR OFFSHORE WIND TURBINES Nguyen Van Vuonga,∗, Mai Hong Quana a Faculty of Coastal and Offshore Engineering, National University of Civil Engineering, 55 Giai Phong road, Hai Ba Trung district, Hanoi, Vietnam Article history: Received 01 October 2018, Revised 19 November 2018, Accepted 31 January 2019 Abstract In the past few decades and up to now, the fossil energy has exerted tremendous impacts on human environments and gives rise to greenhouse effects while the wind power, especially in offshore region, is an attractive renewable energy resource For offshore fixed wind turbine, stronger foundation like jacket structure has a good applicability for deeper water depth Once water depth increases, dynamic responses of offshore wind turbine (OWT) support structures become an important issue The primary factor will be the total height of support structure increases when wind turbine is installed at offshore locations with deeper water depth, in other words the fatigue life of each components of support structure decrease The other one will experience more wind forces due to its large blades, apart from wave, current forces, when makes a comparison with offshore oil and gas platforms Summing up two above reasons, fatigue analysis, in this research, is a crucial aspect for design of offshore wind turbine structures which are subjected to time series wind, wave loads and carried out by aiding of SACS software for model simulation (P-M rules and S-N curves) and Matlab code Results show that the fatigue life of OWT is decreased accordingly by increasing the wind speed acting on the blades, especially with the simultaneous interaction between wind and wind-induced wave Hence, this should be considered in wind turbine design Keywords: offshore wind turbine; Jacket structure; fatigue analysis; P-M rules; S-N curves https://doi.org/10.31814/stce.nuce2019-13(1)-05 c 2019 National University of Civil Engineering Introduction Wind energy has been utilized for mankind in terms of electricity production for thousands of years [1] Wind energy onshore nowadays is a mature industry responsible for meeting a part of the energy needs in countries around the globe In the recent few decades, offshore fixed wind turbines have been all installed in shallow water depth off the coast of Europe (< 30 m) [2], with the typical gravity-based supports of Mono-pile and Tripod structures However, there is strong demand that the application of offshore fixed wind turbine could be extended to deep water where winds are stronger and steadier than on land [3] Once water depth increases, dynamic responses of offshore wind turbine support structures become an important issue Although there is a potential for more wind turbines to be erected in offshore locations in order to achieve a greater wind energy harvest, the access to turbines for maintenance will be restricted Besides, the fatigue analysis of offshore oil and gas platforms have been studied in a comprehensive way for ages, but for wind turbine in general and offshore wind turbine in particular, this issue is still a new field and a restriction to scientists Thus, the objective of ∗ Corresponding author E-mail address: vuongnv@nuce.edu.vn (Vuong, N V.) 46 Vuong, N V., Quan, M H / Journal of Science and Technology in Civil Engineering the article is to analyze fatigue life of components of wind turbine support structure and eventually predict the expected lifetime of OWT xtended to deep water where winds are stronger and The paper is carried out by applying the fatigue knowledge for the offshore wind turbine, any water depth increases, dynamic responses of offshore computing details are conducted by is MATLAB code program and SACS software Applications of the become an important issue Although there a potential method to offshore wind turbine with Jacket support ected in offshore locations in order to achieve a greater structure are illustrated in the following sections up with conclusions and highlights for future research to turbinesand forending maintenance will be restricted Besides, ore oil and gas platforms have been studied in a t for wind turbine general and offshore wind turbine Load in effects analysis of offshore wind turbine a new field and a restriction to scientists Thus, the load yze fatigue2.1 lifeWind of components of wind turbine support he expected lifetime of OWT a Wind profiles and turbulence applying the fatigue knowledge for the offshore wind The wind velocity measured in the field shows variations in space, time and direction and is are conducted by MATLAB code program and SACS composed by two parts: a mean (or slowly variable) and a stochastic part (turbulence) as showing in method to offshore wind turbine with Jacket support Fig The wind up velocity any points of structure is the sum of the average wind velocity and ollowing sections andtotal ending with in conclusions and turbulent wind velocity [4]: (1) {V (z, t)} = {¯v (z)} + {v (t)} hore wind turbine where v¯ (z) is average wind velocity; v(t) is turbulent wind velocity The geometric parameters in Fig conclude: the water mean depth (h), the hub height above the mean water level (H) and the blades length (or rotor radius) (R) Accepting approximately the ed in the field shows variations in space, time and component of the wind according to the Weibull distribution law Weibull probability diswo parts: adynamic mean (or slowly variable) and a stochastic tribution (the so-called probability distribution Rosin-Rammler) is a common form used to describe Fig The total wind velocity in any points of structure occurrence of velocity extreme quantities in meteorology, hydrology and weather forecasts such as floods, elocity andthe turbulent wind [4]: waves and winds In this paper, the Weibull probability distribution is used to calculate the cumulative velocity any velocity; directions.k (1) )} = {v ̅ (z)}frequencies + {v(𝑡)} of wind where U is in wind is the shape parameter; U is the rate parameter The o distribution curve of Weibull function with different wind speed as shown in Fig c) Correlation between significant wave height, period and wind speed Wind blowing time tx,u is in accordance to wind fetch X, and wind velocity u [5], the time to a state of fully developed sea: wind elocity Figure pth (h), n water or rotor imately e wind ribution X0.67 ribution t x,u = 77.23 0.34 0.33 (3) 𝑢 g ribution Significant wave height in n form Figure Wind, accordance wave and current actions Figure Distribution curve of wind speed with windconfiguration velocity u:[14] of Figure Wind, wave and current actions Figure Distribution curve of wind speed ogy, hydrology and weather forecasts such as floods, 𝑢∗ configuration [5] (4) Hz = Ho the Weibull probability distribution is used to calculate g nd velocity in any directions where according b Cumulative distributionto function of wind velocity according to Weibull ribution function of windfrequency velocity Weibull 𝑘 g𝑋 𝑈 m1 H = λ 𝑥 ; 𝑥 = o (2)  U 𝑢k 2 = − exp [− ( ) ] ∗ 𝑈o P (u) = − exp − (2) (5) U0  rate parameter The distribution curve where U is wind velocity; k is the shape parameter; U0 is the m1 = λ1 = 0.0413; ; 𝑢 = √Cd u10 of Weibull function with different wind speed as shown in Fig 2.∗ Zero-crossing average period Tz47 in accordance with wind velocity u: Tz = To where 𝑢∗ g (6) Vuong, N V., Quan, M H / Journal of Science and Technology in Civil Engineering c Correlation between significant wave height, period and wind speed Wind blowing time t x,u is in accordance to wind fetch X, and wind velocity u [6], the time to a state of fully developed sea: X 0.67 (3) t x,u = 77.23 0.34 0.33 u g Significant wave height in accordance with wind velocity u: Hz = H0 u2∗ g where H0 = λ1 xm1 ; x= (4) gX u2∗ (5) Ag g (8) exp (−B ( ) ) λ1 = 0.0413; m𝑓15= ; u∗ = 𝑓UCd u10 𝐻𝑠 𝑈 u: Zero-crossing average period T z in accordance with wind velocity (9) A = 4𝜋 ( ) ; B = 16𝜋 ( ) 𝑔𝑇𝑧 𝑔𝑇𝑧 u∗ where U is wind speed at the (6) T z height = T of 19.5m above sea level; A, B are constants, and P-M spectra with wind speed U19.5 =g15m/s is shown in Fig.5 c) JONSWAP Spectra where (ω − ωm )2 ag ω −4 T = λ(2 xm2) ) γ exp (− (7) (10) Sηη (𝑓) = exp (− ) (2π)4 𝑓 ωm 2σ2 ωm −0.22 λ1 = 𝑋0.751; m2 = 16.04 (11) a = 0.046 ( ) ; ωm = (XU10 )0.38 𝑈10 2.2 Wind-induced wave where X isload fetch; U10 is wind speed at the height of 10m above sea level; γ = 0.3; σ = a Sea-state0.08 model For the by purpose of primarily Waves are generated wind blowing over the analyzing fatigue of offshore surface of the sea and are the major source of loadP-M spectra is posian ing for moststructures, offshore structures At any fixed appropriate model in the study that tion in the open sea, the level of the water surface deals with the state of sea with varies randomly due to the passing waves and may maximum wind speed (generating be modeled as a steadily stochastic process, stanwaves under the infinite wind dard distribution, Ergodic nature [8] The wave fetch) The most glaring difference height H of single wave is normally defined as between JONSWAP and P-M the total range of η(t) in the time interval T beFigure Description of single wave [15] spectrum with the same wind speed Figure Description of single wave [7] tween two consecutive zero up-crossing by η(t), can be seen in Fig Sηη (𝑓) = see Fig Recent research has led to a number of semi-empirical expressions for the form of the spectra S ηη (ω) of water surface elevation η(t), (generally called wave spectra) Two commonly used spectra are the Pierson-Moskowitz (P-M) [9] and the JONSWAP [10] b Pierson-Moskowitz Spectra (P-M Spectra)   Ag2 g S ηη ( f ) = exp −B fU f 4    (8) 48 Figure Pierson-Moskowitz and JONSWAP spectrum Figure P-M spectrum, wind speed u19.5=15m/s ectrum For the purpose of primarily analyzing fatigue of offshore structures, P-M spectra is an appropriate model in the study that Vuong, N V., Quan, M H / Journal of Science and Technology deals with thein Civil stateEngineering of sea with maximum wind speed (generating the infinite wind waves under Hs U A = 4π ; B = 16π (9) fetch) The gT z most glaring difference gT z2 between JONSWAP and P-M where is wind speed at thewave height sea level; A, B are constants, and P-M spectra Figure U Description of single [15]of 19.5 m above spectrum with the same wind speed with wind speed U19.5 = 15 m/s is shown in Fig can be seen in Fig Figure Pierson-Moskowitz and JONSWAP spectrum Figure P-M spectrum, wind speed u19.5=15m/s Figure P-M spectrum, wind speed u19.5 = 15 m/s Figure Pierson-Moskowitz and JONSWAP spectrum 3.1 The fundamental equation of the stochastic dyn Differential equation that describes stochastic   structure system is as 2following:  ω −4  ag2  γ exp − (ω − ωm ) MÜ + CU̇ + (10) KU = F(𝑡) exp (12) − he stochastic dynamic problem c JONSWAP Spectra ibes stochastic oscillation of the offshore fixS ηη ( f ) = Figure Stochastic dynamics of wind turbine in freq d turbine in frequency domain + KU = F(𝑡) Figure ωm 2σ ωm    X −0.22  16.04 a = 0.046  4; ωm = U10 (XU10 )0.38 (2π) f (11) where X is fetch; U10 is wind speed at the height of 10 m above sea level; γ = 0.3; σ = 0.08 For the purpose of primarily analyzing fatigue of offshore structures, P-M spectra is an appropriate model in the study that deals with the state of sea with maximum wind speed (generating waves under the infinite wind fetch) The most glaring difference between JONSWAP and P-M spectrum with the same wind speed can be seen in Fig Stochastic dynamics of wind turbine in frequency domain 3.1 The fundamental equation of the stochastic dynamic problem Differential equation that describes stochastic oscillation of the offshore fix-structure system is as following: M Uă + C U˙ + KU = F (t) (12) 49 Vuong, N V., Quan, M H / Journal of Science and Technology in Civil Engineering where RFF (τ) is correlation function (self-correlation) of the steadily stochastic process (SSP) F(t), performs Fourier integral transformation (complex form) to RFF (τ): ∞ RFF (τ) = S FF (ω) eiωt dω (13) −∞ where S FF (ω) - Spectral density function of SSP F(t), is the Fourier map of the correlation function RFF (τ): ∞ S FF (ω) = JRFF (τ) = 2π RFF (τ) eiωt dω (14) −∞ Formula pairs Eqs.(τ) (13) (14) is called formula(self-correlation) Khinchin – Weinerr of (only SSP), which where RFF isand correlation function theapplicable steadilytostochastic play a pivotal role in the method of solving stochastic dynamical problems Linking to to Eq.R(14), allows process (SSP) F(t), performs Furier integral transformation (complex form) FF (τ): ∞ time-varied correlation function t, to one for frequencyto transform problem to be considered for 𝑖𝜔𝑡 forms of this transform varied density spectral function ω.  Fig describes typical 𝑅𝐹𝐹 (𝜏) = ∫ 𝑆𝐹𝐹 (𝜔) 𝑒  𝑑𝜔 (13) −∞ 3.2 System response in frequency domain where SFF(ω) - Spectral density function of Khinchin – Weiner formula SSPAlso F(t),applying is the Fourier map of the correlation pairs for stochastic process u(t) [11], [noticing that function RFF (τ): ∞ output the input F(t) is SSP, also for U(t) is SSP], 𝑆𝐹𝐹 (𝜔)   =  𝐽𝑅𝐹𝐹 (𝜏)   =   ∫−∞ 𝑅𝐹𝐹 (𝜏) 𝑒 𝑖𝜔𝑡  𝑑𝜔 2𝜋 we have: (14) ∞ iωτ (14) is called Formula (τ) = Eqs (ω) eand Ruupairs dω (15) S uu(13) formula Khinchin−∞– Weinerr (only applicable to SSP), which play ∞ a pivotal role in the method of solving stochastic dynamical S uu (ω) = Ruu (ω) e−iωτ dω (16) problems Linking 2π to Eq (14), allows to transform problem −∞ to be considered for timeApplying correlation theory (or spectral varied correlation function t, totheory) one –for with any theories of SSP into the Eq (16), obtainfrequency-varied density spectral function ω ing important results: Fig describes typical forms of this transform S uu (ω) = |H (iω)|2 S FF (ω) (17) In other words: The output spectral density Figure Description of spectral method (system is equal to input onedomain (load) Figure Description of spectral method 3.2 response) System response in the frequency multiplied by the square of the transfer function Also applying Khinchin – Weiner formula pairs for stochastic process u(t) [9], module (Fig 8) [noticing that the input F(t) is SSP, also for output U(t) is SSP], we have: From Eq (17) determine the average ∞ square (so-called variance) of the response: ∞ 𝑖𝜔𝜏  𝑑𝜔 𝑅𝑢𝑢 (𝜏)  ∞=   ∫ 𝑆𝑢𝑢 (𝜔) 𝑒 σ2u = (ω)∞dω = S uu −∞ |H (iω)|2 S FF (ω) dω (15) (18) −𝑖𝜔𝜏 (16)  ∫ 𝑅 (𝜔) 𝑒  𝑑𝜔 2𝜋 −∞ 𝑢𝑢 where H(iω) - transfer function (complex form) also known as “frequency characteristics” of the Applying correlation theory (or spectral theory) – with any theories of SSP into the system, receiving this equation: Eq (16), obtaining important results: (17) (19) = 𝑆𝑢𝑢 (𝜔)  H=(iω)   |𝐻(𝑖𝜔)|  𝑆𝐹𝐹2(𝜔) K − Mω + iCω In other words: The output spectral density (system response) is equal to the input 50 one (load) multiplied by the square of the transfer function module (Fig 8) From Eq (17) determine the average square (so-called variance) of the response: 𝑆𝑢𝑢 (𝜔)   =0   ∞ 𝜎𝑢2 = ∫ 𝑆𝑢𝑢 (𝜔) 𝑑𝜔 ∞ = ∫ |𝐻(𝑖𝜔)|2  𝑆𝐹𝐹 (𝜔) 𝑑𝜔 (18) A spectrum can be used to recreate a time signal By assuming that the phase is distributed randomly, harmonic waves can be recreated based on the power spec density at each separate frequency, combined with a randomly picked phase angle time series created in this way is never the exact copy of the time series but the spe are theandsame, provided that Engineering the signal is long enough Fig show Vuong, N V., Quan, M H / parameters Journal of Science Technology in Civil inverse conversion from frequency to time domain as well as the normal transform Fatigue analysis from time to frequency domain For both transformations standard algorithm available, the most commonly used is the Fast Fourier Transform (FFT) and its In 4.1 Fourier transformation one (IFFT) [10] A spectrum can be used to recreate a time signal By assuming that the phase angle is distributed randomly, harmonic waves can be recreated based on the power spectrum density at each separate frequency, combined with a randomly picked phase angle The time series created in this way is never the exact copy of the time series but the spectral parameters are the same, provided that Figure Transformation from time series to frequency domain and vice versa the signal is long enough Fig shows the inTransformation time series to spectrum de A time signal canFigure be also7 used to recreate afrom spectrum, the power verse conversion from frequency to time domain frequency domain and vice versa per frequency defined as: as well as the normal transformation from time to (𝑆𝑛 /Δf) = {(𝐴2𝑞 +B frequency domain For both transformations standard algorithms are available, the𝑞2 )𝑇} most commonly 2 used is the Fast Fourier Transform (FFT) its Inverse one (IFFT) as aand function of frequency, where[12] the Fourier coefficients Aq and Bq defined by: A time signal can be also used to recreate a spectrum, the power spectrum density 𝑇 𝑇 per frequency 𝐴𝑞 = ∫ 𝑧(𝑡)cos(2πf𝑞 𝑡)dt and 𝐵𝑞 = ∫ 𝑧(𝑡)sin(2πf𝑞 𝑡)dt defined as: 𝑇 𝑇 When the spectral of frequency, we S n /∆ f = power Aq + B2q T density is plotted as a function (20) obtain a power density spectrum as a function of frequency, where the Fourier coefficients Aq in and Bqseries defined by: 4.2 Fatigue analysis time Fatigue is the process of gradual damage done to materials (mainly is steel mat T when these are subjected to continually changing stresses Due to these stress cha 2 the material slowly deteriorates, initiating Aq = z (t) cos 2π fq t dt and Bq = z (t) sin 2πcracks fq t dtwhich will eventually (21) lead to brea T of the material OffshoreTwind turbines are by default subjected to loads varying in 0 from wind as well as waves This means that the stress response will also offshore wind turbine’s to fatigue When the power spectral density iscontinuously, plotted as making a function of frequency, weresponse will obtain a power The fatigue calculation method for variable stress ranges in the time domain c density spectrum summarized by the flowchart in Fig Calculation of the stresses experienced b 4.2 Fatigue analysis in time series detail being considered under all possible load cases during the lifetime will resul T Fatigue is the process of gradual damage done to materials (mainly is steel material) when these are subjected to continually changing stresses Due to these stress changes, the material slowly deteriorates, initiating cracks which will eventually lead to breaking of the material Offshore wind turbines number of stress Byinfiltering thewind number of stress variations for every arelarge by default subjected to time loadsseries varying time from as well as waves This means that the stress range class, the Miner sum can be calculated to check whether D < 1.0 fat stress response will also vary continuously, making offshore wind turbine’s response to fatigue Figure fatiguecalculation calculation [13] Figure8.8.Flowchart Flowchart of of fatigue [11] Fatigue curve linked between the number of stresses S and the number of stress The fatigue calculation method for variable stress ranges in the time domain can be summarized cycles N is revealed as following: by the flowchart in Fig Calculation of the stresses experienced by the detail being considered −m will result in a large number of stress time series under all possible load cases during lifetime (22) By N the = KS , S>0 51 where K and m are random variables due to inherent physical and statistical uncertainty The value of K can depend on the mean stress Sa in the stress cycles Where K0 is the value of K from tests with zero mean stress and where Su is the ultimate tensile strength Vuong, N V., Quan, M H / Journal of Science and Technology in Civil Engineering Figure Flowchart of fatigue calculation [11] filtering the number of curve stress variations for every range the SMiner can be calculated Fatigue linked between thestress number of class, stresses and sum the number of stress to check whether D fisat revealed < 1.0 as following: cycles N Fatigue curve linked between the number of stresses S and the number of stress cycles N is (22) revealed as following: N = KS −m , S > N = KS −m , S > (22) where K and m are random variables due to inherent physical and statistical where K and m are random due todepend inherentonphysical andstress statistical The value of uncertainty The variables value of K can the mean Sa in uncertainty the stress cycles Where K can depend on the mean stress S in the stress cycles Where K is the value of K from tests with where Su is the ultimate tensile K0 is the value of K froma tests with zero mean stress and zero mean strength stress and where S u is the ultimate tensile strength On the above diagram, index the i is index the number stress of ithstress of structure, the ratiothe of ratio fatigue On the above the diagram, i is the of number ith of structure, of damage D ffatigue theissum of the fatigue damage duefatigue to the number stresses at is calculated damage as Dfat calculated as the sum of the damage of due to the caused numberinofa short sea state stresses caused in a short sea state The magnitude and number of stresses are The magnitude and number of stresses calculated from fatigue data by calculated are from fatigue stress data bystress counting To take all peaks method Tocounting take allmethod peaks into account withoutinto without doubling, the rain-flow doubling, account the rain-flow method resembles rain method resembles rain flowing flowing off a pagoda roof as shown in Fig.off a pagoda roof as shown in Fig When When the stress time series is rotated 90 degrees, thealgorithm stress time the counting starts series is rotated 90 degrees, the counting algorithm starts Figure Description of rainflow method [12] When the method has been performed, the sigFigure Description of rainflow method [14] nal is taken apart in a number of half stress range When the method has been performed, the signal is taken apart in a number of half variations, that is, the rain-flow cycle runs only in stress range variations, that is, the rain-flow cycle runs only in one direction each time one direction each time The mean value of cumulative fatigue damage during year and the maxiThe mean value of cumulative fatigue damage during year and the maximum mean mum meanfatigue fatiguelifetime lifetimeTT maxofofthe thehot hotspot spotare areobtained obtainedas asfollows: follows: max [D] 365 × 24 × 3600 ni D1year = 365x24x3600 𝑛𝑖 ; T max = [D] T0 D1year = ∑i Ni ; Tmax = D1year T0 𝑁𝑖 D1year (23) (23) i where i is investigated stress domain; ni is the number of stress cycles at the ith load; Ni is the numwherethei iscrashes investigated of of stress cycles at the ith load; thenumber duration stress in time series; [D] ber of cycles until occur stress at the domain; ith load; nTi 0isisthe N is the number of cycles until the crashes occur at the ith load; T is the duration of i is permissible fatigue, given in used design standard (for offshore structure [D] = 0.5, from API stress in time series; [D] is permissible fatigue, given in used design standard (for standard) offshore structure [D] = 0.5, from API standard) Results and discussions In this paper, the Offshore Jacket Wind Turbine (OJWT) in water depth of 70 m is modeled for analysis showed in Fig 10 As shown in Fig 10, a full-scale offshore wind turbine model includes7 turbine support, transitions, blades and Jacket support At the top of the support is a MW turbine, the main specifications are listed in Table a Structural dimensions The size of the wind turbine support structure is selected as Fig 11 for the analysis of fatigue damages under the action of sea environment loads such as waves and wind The main dimensions of the entire Jacket support structure with the tower and the wind directions to OJWT are shown in Figs 12 and 13, respectively From top to bottom, the Jacket size is 32 m2 on the seafloor 52 with the tower and the wind directions to OJWT are shown in Figs 12 and 13 respectively From top to bottom, the Jacket N V., Quan, M H / Journal of Science and Technology in Civil Engineering size is 32m2 on Vuong, the seafloor Table Characteristics of offshore wind turbines Power MW Cut-out wind speed 25 support-structure wind m/s Figure 10 3D model of Jacket turbine Cut-in wind speed m/s With regard to the input data of waves and winds, the probability of occurrence of ussions both in theBlade scopenumber of this research is taken in 08 directions 3as shown in Tables -and Null diameter OJWT Meanwhile, m the EachWind direction is 45 indegrees apart before acting on the ffshore Jacket Turbine (OJWT) water depth of 70m is Blade diameter 126 howed in Fig 10 As shown the Figure, are a full-scale offshore prevailing windindirections the South West, East and North East and the wind mspeeds mass top-turbine 120000 kg ludes turbine support, blades andatJacket support At vary from transitions, 0Concentrated m/s to 20 m/s a 5MW turbine, main parameters specifications are listed in Tab b)the Wave sions Table Characteristics of offshore wind turbines nd turbine MW elected as Power of fatigue 25 m/s ion of sea Cut-out wind speed h as waves ons of the structure the wind e shown in spectively the Jacket loor Cut-in wind speed m/s Blade number - Null diameter m Blade diameter 126 m 120000 kg Concentrated mass at top-turbine Figure 10 3D model of Jacket support-structure wind turbine Figure 10.winds, 3D model of Jacket support-structure input data of waves and the probability of occurrence of wind turbine in Tables and s research is taken in 08 directions as shown degrees apart before acting on the OJWT Meanwhile, the ons are the South West, East and North East and the wind speeds m/s Figure 11 Main dimensions of OJWT Figure 11 Main dimensions of OJWT of offshore wind turbines MW 25 m/s m/s - m 126 m 120000 kg Figure 12 Wave directions to OJWT Figure 12 Wave directions to OJWT Figure 13 Tower, Brace and diagonal diameters Table Probability wave directions to OJWT Figure 12 Wave directions to OJWT of occurrence of Figure 13 Tower, Brace and diagonal diameters 0⁰ 45⁰ 90⁰ 135⁰ 180⁰ 225⁰ 270⁰ 315⁰ Wave Figure 11 Main dimensions of OJWT Total Figure 13 Tower, Brace and diagonal diameters directions SW S SE E NE N NW SW Probability of occurrence of wavethe directions to OJWT With regard to theTable input2 data of waves and winds, probability of occurrence of both in the 0⁰ 135⁰ as 180⁰ 315⁰ direction is 45 scope of this research is45⁰ taken in90⁰ 08 directions shown in225⁰ Tables 2270⁰ and Each Probability Wave 0.3012 0.0353 0.046 0.2964 0.0039 0.002 0.0524 Total 1.000 (P) 0.2629 degrees apart before acting on the OJWT Meanwhile, the prevailing wind directions directions SW S SE E NE N NW SW are the South (SW – South West; S – South; SE – South East; E – East; NE – North East; N – 53 Probability North; NW – North West; SW – South West).0.2964 0.0039 0.3012 0.0353 0.046 (P) 0.2629 0.002 0.0524 1.000 c) Wind parameters: Probability of occurrence of wind directions to OJWT (SW – South West; Table S – South; SE – South East; E – East; NE – North East; N – Directions Vuong, N V., Quan, M H / Journal of Science and Technology in Civil Engineering West, East and North East and the wind speeds vary from m/s to 20 m/s b Wave parameters Table Probability of occurrence of wave directions to OJWT 0◦ 45◦ 90◦ 135◦ 180◦ 225◦ 270◦ 315◦ SW S SE E NE N NW SW 0.3012 0.0353 0.046 0.2629 0.2964 0.0039 0.002 0.0524 Wave directions Probability (P) Total 1.000 (SW – South West; S – South; SE – South East; E – East; NE – North East; N – North; NW – North West; SW – South West) c Wind parameters Table Probability of occurrence of wind directions to OJWT Wind Speed Middle (m/s) Value Directions 45 90 0-5 2.50 0.0146 0.0329 - 10 7.50 0.1653 0.0938 10 - 15 12.50 0.1531 0.0036 15 - 20 17.50 0.0098 0.0000 Total 0.3428 0.1303 135 180 225 270 315 360 0.0337 0.0162 0.0000 0.0000 0.0498 0.0375 0.0299 0.0002 0.0000 0.0676 0.0321 0.1603 0.0515 0.0000 0.2439 0.0148 0.0751 0.0361 0.0000 0.1260 0.0054 0.0056 0.0004 0.0000 0.0114 0.0065 0.0116 0.0084 0.0016 0.0282 Total 0.1774 0.5579 0.2533 0.0115 1.0000 After taking the estimation of Weibull Parameters for long term distribution of wind speeds in each direction, the fitted parameters U0 and K are obtained as illustrating in Table The wind data measured in the field is fitted rather precisely with the Weibull distribution function as shown in Fig 14 Table The fitted Weibull parameters for wind distribution Wind Directions Fitted Weibull Parameter 45 90 135 180 225 270 315 U0 K 6.050 2.200 2.750 2.250 2.350 2.150 4.250 2.250 8.250 2.875 6.975 1.475 3.350 1.500 6.725 2.225 d Results After obtaining the results of wind turbine analysis from SACS software under hot-spot stress spectrum as showing in Figs 15 and 16, then utilizes the Fourier transform to convert the hot-spot stress into a time domain for two cases caused by waves and winds as showing in Figs 17 and 18 In the case of wind turbine systems subjected to both waves and winds is going to take a linear combination of two results due to wave and wind in time series, and obtain the combining results as Fig 19 shown 54 Vuong, N V., Quan, M H / Journal of Science and Technology in Civil Engineering o o Figure Long term term distribution distributionofofwind windspeeds speeds– –curve curvefitting fitting– direction – direction Figure 14 14 Long 4545 d) d)Results Results Figure 14 Long term distribution of wind speeds – curve fitting – direction 45 Figure 14 Long term distribution of wind speeds – curve fitting – direction 45◦ d) Results After the results of of wind windturbine turbineanalysis analysisfrom fromSACS SACSsoftware softwareunder under hotAfter obtaining obtaining hoto After obtaining the results of wind turbine analysis from SACS software under hot- Figure 16 Hot-spot stress spectrum (wind induced) Figure 15 Hot-spot stress spectrum (wave induced) spot stress spectrum as showing in Figs 15 and 16, then utilizes the Fourier transform to convert the hotspot stress into a time domain for two cases caused by waves and winds as showing in Figs 17 and 18 In the case of wind turbine systems subjected to both Figureof 16 Hot-spot stress spectrum (wind induced) Figure 16 Hot-spot spectrum (wind induced) Figure Hot-spot spectrum (wave induced) andstress windsspectrum is going(wave to take a linear combination two resultsstress due to wave and Figure15 15.waves Hot-spot induced) Figure 15 Hot-spot stressseries, spectrum (wavethe induced) Figureas16 Hot-spot stress spectrum (wind induced) wind in time and obtain combining results Fig 19 shown spot as showing showing in in Figs Figs.15 15and and16, 16,then thenutilizes utilizesthetheFourier Fouriertransform transform spotstress stress spectrum spectrum to to Fatigue damage at high-concentrated stress points (hotspots) is calculated by convert the the hotspotthestress aa range time domain two bybywaves winds convert hotspot into time(HSSR) domain for two cases and winds evaluating hot-spotinto stress andfor make usecases of this caused ascaused input date forwaves S-N and fatigue curve The stress concentration factors (SCF) is defined as following: showing in in Figs 17 and 18 In to toboth asas showing 18.SCF In the the case caseofofwind windturbine turbinesystems systemssubjected subjected both (24) = HSSR/ Nominal Stress Range waves and and winds winds to take aa linear combination ofof two due andand For all is concentric of the structure system, the SCF coefficient will be taken waves goingmasses take linear combination tworesults results duetotowave wave as 2.0 in this paper windinin time timeCorresponding series, and toobtain the results as Fig shown wind series, obtain the combining combining Fig.1919method shown each hotspot stress in time results series, theasrain-flow is applied here under aiding of MATLAB software so that the rain-flow matrices at Fatigue damage at high-concentrated stress points (hotspots) is iscalculated Fatigue damage high-concentrated stress points (hotspots)different calculatedbyby hotspot points due to wave and wind are obtained without any trouble as shown in Figs evaluating20the the hot-spot stress range and make use of this date for S-N evaluating range (HSSR) (HSSR)due and makeand use thisasasinput input and 21 Finally, the rain-flow matrices to wave windofinteraction can be date for S-N easilyThe obtained in theconcentration same manner andfactors the result(SCF) can be seen in the Fig fatiguecurve curve The isisdefined as22 fatigue stress concentration factors (SCF) defined asfollowing: following: == HSSR/ Nominal Stress Range SCF HSSR/ Nominal Stress Range FigureFigure 17.SCF Hot-spot (wave induced) 17 Hot-spot stress stress in in timetime seriesseries (wave induced) Figure 17 Hot-spot stress in time series (wave induced) (24) (24) For all all concentric concentric masses of taken For of the the structure structuresystem, system,the theSCF SCFcoefficient coefficientwill willbebe taken 2.0inin this this paper paper asas2.0 Corresponding to each hotspot is isapplied Corresponding hotspot stress stressinintime timeseries, series,the therain-flow rain-flowmethod method applied 10 here under aiding of MATLAB software so that the rain-flow matrices at different here under aiding MATLAB software so that the rain-flow matrices at different hotspot points due to wave in in Figs hotspot points due to wave and and wind wind are areobtained obtainedwithout withoutany anytrouble troubleasasshown shown Figs 20 and 21 Finally, the rain-flow matrices due to wave and wind interaction can 20 and 21 Finally, the rain-flow matrices due to wave and wind interaction canbebe easilyobtained obtained in in the the same same Figure manner and the can 18 Hot-spot time series (windbe induced) easily manner andstress theinresult result can beseen seenininthe theFig Fig.22.22 Figure 18 Hot-spot stress in time series (wind induced) Figure 18 Hot-spot stress in time series (wind induced) 55 10 10 Hot-spot stress in time series (wind induced) in Civil Engineering Vuong, N V., Quan,Figure M H.18./ Journal of Science and Technology Figure 19 Hot-spot stress in time series (wave and wind induced) Figure 19 Hot-spot stress in time series (wave and wind induced) Fatigue damage at high-concentrated stress points (hot-spots) is calculated by evaluating the hotspot stress range (HSSR) and make use of this as input date for S-N fatigue curve The stress concentration factors (SCF) is defined as following: SCF = HSSR/Nominal Stress Range (24) For all concentric masses of the structure system, the SCF coefficient will be taken as 2.0 in this paper 11 Figure 20 Rain-flow matrix at hot-spot point due to wave Figure 20 Rain-flow matrix at hot-spot point due to wave Figure 20 cycles Rain-flow matrix hot-spot point Some that areatcounted with the due to wave amplitude and average stress value at the Some cycles that are counted with the Figure 21 Rain-flow matrix at hot-spot point due to wind Figure 21 Rain-flow matrix at hot-spot point Figure 21 Rain-flow matrix at hot-spot point due to wind due to wind hot-spot point can be extracted from the amplitude and average stress stress valueinattime the Corresponding to each rain-flow matrix Thishot-spot type of matrix hasseries, the rain-flow method is applied here under hot-spot point can be extracted from the aiding MATLAB software that the rain-flow beenofwidely applied forsofatigue analysis matrices at different hot-spot points due to wave rain-flow matrix This type of matrix has in Figs 20 and 21 Finally, the rain-flow matrices and wind areof obtained without form, any trouble as shown because its simple time-saved been widely applied for fatigue analysis due to wave and and wind interaction can be easily obtained in the same manner and the result can be seen computing, its expression provides because its simple form, time-saved ingeneral Fig 22.of information on the nature of loads computing, and expression provides [13] mentioned earlier, PalmgrenSomeAs cycles that its are counted with the amplitude and average stress value at the hot-spot point can general information on thematrix nature oftype loads hypothesis assumes thatThis the total beMiner’s extracted from the rain-flow of matrix has been widely applied for fatigue analysis of fatigue damage is calculated taking aand its expression provides general information on [13] As earlier, by Palmgrenbecause of itsmentioned simple form, time-saved computing, linear combination any individual Miner’s thatearlier, the total the naturehypothesis of loads [15].assumes As of mentioned Palmgren-Miner’s hypothesis assumes that the total of cycles The fatigue of at each damage is calculated by structure takingby a linear combination of any individual cycles The fatigue life offatigue fatigue damage is life calculated taking a hot-spot is listed in Tab 5, and below Figure 22 Rain-flow matrix at hot-spot17.5 pointm/s) due to both wave of structure at each hot-spot Tables 5, and (the mean wind velocity: linear combination ofis listed any in individual and wind cycles Thewind fatigue life of structure at each (the mean velocity: 17.5m/s): 56 hot-spot is listed in Tab 5, 65.and below Table Fatigue life of OWT support structure (wave induced) Figure 22 Rain-flow matrix at hot-spot point due to both wave and wind Fatigue life Chord (cm) (year) OD WT Table Fatigue life of OWT support structure (wave induced) 3600 Y 70 829.25 [D] velocity: T (sec)17.5m/s): Node type (theNo mean wind 0.5 Status Ok w matrix at hot-spot point due to wave Vuong, N V., Quan, M H / Journal of Science and Technology in Civil Engineering Figure 21 Rain-flow matrix at hot-spot point due to wind es that are counted with the average stress value at the can be extracted from the ix This type of matrix has applied for fatigue analysis s simple form, time-saved nd its expression provides ation on the nature of loads ntioned earlier, Palmgrenhesis assumes that the total age is calculated by taking a nation of any individual igue life of structure at each d in Tab 5, and below Figure 22 Rain-flow matrix at hot-spot point due to both wave Figure 22 Rain-flow matrix at hot-spot and wind point due to both wave and wind velocity: 17.5m/s): Table 5.structure Fatigue (wave life of induced) OWT support structure (wave induced) Table Fatigue life of OWT support T (sec) Node type No 3600 3600 3600 3600 3600 3600 [D] Y Y Y X X X 0.5 0.5 0.5 0.5 0.5 0.5 Fatigue life Chord (cm) Chord (cm) OD WT T (sec) Node type (year) OD WT 70 829.25 70 Y 561.36 3600 70 3600 70 70 Y 996.15 3600 70 80 Y 937.57 3600 X 80 120 4.5 1005.21 3600 X 120 4.5 120 4.5 1258.02 3600 X 120 4.5 StatusFatigue life Ok (year) Ok 829.25 Ok 561.36 Ok 996.15 Ok 937.57 Ok 1005.21 1258.02 Status Ok Ok Ok Ok Ok Ok Figure Fatigue life of OWT support structure (wind induced) Table 6.(cm) Fatigue life of OWT support Chord Fatigue lifestructure (wind induced) T (sec) Node type Y 1Y Status OD WT (year) Chord (cm) Ok Fatigue life [D] 70 T (sec) Node type 197.81 (year) OD WT Ok 70 151.26 196.2170 0.5 70 3600 Y Ok 197.81 3600 3600 3600 Y No 0.5 0.5 0.5 0.5 0.5 0.5 3600 3600 3600 3600 3600 3600 Y Y X X X Y 70 70 80 120 120 70 2 4.5 4.5 151.26 196.21 12 271.26 306.12 465.32 182.13 Status Ok Ok Ok Ok Ok Ok Ok Apart from the result of mean wind velocity 17.5 m/s, Fig 23 shows the fatigue life curve of OWT due to different velocities, whereas there are mean wind velocities that are greater than the cut-out mean wind velocity 57 0.5 3600 X 80 271.26 0.5 3600 X 120 4.5 306.12 Vuong, 0.5 N V., 3600 120 and Technology 4.5 465.32 Quan, M H /XJournal of Science in Civil Engineering 0.5 3600 Y 70 182.13 Table Fatigue life of OWT support structure (wave and wind induced) Ok Ok Ok Ok Figure Fatigue life of OWT support structure (wave and wind induced) No life life Chord (cm) Chord (cm) Fatigue Fatigue Status Status (year) ODOD WTWT (year) 0.5 3600 Y 70 176.38 Ok 20.5 0.5 3600 3600 YY 70 70 2 132.58 Ok Ok 176.38 30.5 0.5 3600 3600 YY 80 70 2 273.32 Ok Ok 132.58 40.5 0.5 3600 3600 XY 80 80 2 278.51 Ok Ok 273.32 0.5 3600 X 120 4.5 291.46 Ok 0.5 3600 X 80 278.51 Ok 0.5 3600 X 120 4.5 452.96 Ok 291.46 70.5 0.5 3600 3600 YX 70120 4.5 172.34 Ok Ok 0.5Apart from 3600 X 120 4.5 452.96 Ok the result of mean wind velocity 17.5m/s, the Fig 23 shows the fatigue 0.5 3600 Y 70 172.34 Ok life curve of OWT due to different velocities, whereas there are mean wind velocities that are greater than the cut-out mean wind velocity No (sec) [D] [D] T T (sec) Node type Node type Figure 23 Thelife fatigue life of curve of OWT corresponding toto each mean wind velocity Figure 23 The fatigue curve OWT corresponding each mean wind velocity Conclusion To calculate the fatigue life of OJWT, in the scope of the paper, a wind turbine Conclusions model with jacket support structure in the water depth of 70m is utilized All blades, turbine support towermodel that mass To calculate themachine fatigueand lifemachine-support of OJWT, in thetower scopeare ofsimplified the paper,into a wind turbine with jacket is concentrated on top, and is supported by jacket structure In terms of wind data, support structure in the water depth of 70 m is utilized All blades, turbine machine and machineWeibull distribution is used to generate input data for fatigue analysis of OJWT Wind support tower are simplified into support tower that mass is concentrated on top and is supported by jacket structure In terms of wind data, Weibull distribution is used to generate input data for 13 fatigue analysis of OJWT Wind and wind-induced wave loads act on structure in stochastic directions, however, only 08 directions are considered with evenly spaced 45-degree angle to compute fatigue life of each components’ jacket support structure The Airy wave theory is applied for computing the static and dynamic transfer function of wave to support the fatigue analysis, and further study should be utilized different wave theories The results are rather reasonable since the simultaneous interaction between wind and wind-induced wave is considered 58 Vuong, N V., Quan, M H / Journal of Science and Technology in Civil Engineering References [1] Zachary, S (2014) History of wind turbines Renewable Energy World [2] Tempel, J (2002) Offshore wind, to mill or to be milled Delf University of Technology [3] BTM Consult ApS (2005) International wind energy development, world market update 2004, Forecast 2005-2009 IC Christensens Allé 1, DK6950 Ringkøbing, Denmark [4] Jingpeng, H., Zitang, S., Yanxia, L (2012) Simulation of turbulent wind velocity for transmission tower based on auto-Regressive model method School of Civil Engineering, Northeast Dianli University, Jilin, China [5] Petrini, F., Li, H., Bontempi, F (2010) Basis of design and numerical modeling of offshore wind turbines Structural Engineering & Mechanics, 36(5):599–624 [6] U.S Army Corps of Engineers (2006) Coastal engineering manual Part II, EM 1110-2-1100 [7] Mathisen, J., Bitner-Gregersen, E (1990) Joint distributions for significant wave height and wave zeroup-crossing period Applied Ocean Research, 12(2):93–103 [8] Thoft-Cristensen, P., Baker, M J (1982) Structural reliability theory and its applications Spring-Verlag, Berlin Heidelberg, New York [9] Pierson Jr, W J., Moskowitz, L (1964) A proposed spectral form for fully developed wind seas based on the similarity theory of SA Kitaigorodskii Journal of Geophysical Research, 69(24):5181–5190 [10] Hasselmann, K., Barnett, T P., Bouws, E., Carlson, H., Cartwright, D E., Enke, K., Ewing, J A., Gienapp, H., Hasselmann, D E., Kruseman, P., Meerburg, A., Muller, P., Olbers, D J., Richter, K., Sell, W., Walden, H (1973) Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP) Deutsches Hydrographisches Zeitschrift, Hamburg, Reihe A [11] Barltrop, N D P., Adams, A J (1991) Dynamics of fixed marine structures Atkins Oil & Gas Engineering Limited, Epsom, UK [12] Li, Y Q., Dong, S L (2001) Random wind load simulation and computer program for large-span spatial structures Spatial Structures, 7(3):3–11 [13] Matsuiski, M., Endo, T (1969) Fatigue of metals subjected to varying stress Japan Soc Mech Eng [14] Vandijk, G M., Dejonge, J B (1975) Introduction to a fighter aircraft loading standard for fatigue evaluation FALSTAFF, National Aerospace Laboratory, NLR, MP75017U, Amsterdam, Holland [15] Adam, N (2009) Determination of fragments of multi-axial service loading strongly influencing the fatigue of machine components Mechanical Systems and Signal Processing 59 ... load yze fatigue2 .1 lifeWind of components of wind turbine support he expected lifetime of OWT a Wind profiles and turbulence applying the fatigue knowledge for the offshore wind The wind velocity... Characteristics of offshore wind turbines Power MW Cut-out wind speed 25 support- structure wind m/s Figure 10 3D model of Jacket turbine Cut-in wind speed m/s With regard to the input data of waves and winds,... Characteristics of offshore wind turbines nd turbine MW elected as Power of fatigue 25 m/s ion of sea Cut-out wind speed h as waves ons of the structure the wind e shown in spectively the Jacket loor
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