A strong wind prediction model for the railway operation based on the onsite measurement and the numerical simulation

Transcription

1 A strong wnd predcton for the ralway operaton based on the onste measurement and the numercal smulaton Yayo Msu a, Atsush Yamaguch b, and Takesh Ishhara c a Dsaster Preventon Research Laboratory, East Japan Ralway Company, Kta, Satama, Satama, JAPAN, msu@brdge.t.u-tokyo.ac.jp b Department of Cvl Engneerng, School of Engneerng, The Unversty of Tokyo Buyo, Tokyo, JAPAN, atsush@brdge.t.u-tokyo.ac.jp c Department of Cvl Engneerng, School of Engneerng, The Unversty of Tokyo Buyo, Tokyo, JAPAN, shhara@brdge.t.u-tokyo.ac.jp ABSTRACT: In ths study, a predcton method for the strong gust was proposed, whch can take the effect of not only local terran but also meteorologcal condtons nto account. Predcted maxmum gust by ths method shows good agreement wth the measurement. In addton, a tme seres based method for the predcton of the frequency of strong wnd n a control secton was proposed. Predcted frequency of strong wnd shows good agreement wth the measurement, whle the conventonal methods underestmate or overestmate the frequency. Fnally, proposed methods were appled to the regulaton of the tran operaton, consderng wnd drecton and wnd fence. The frequency of the regulaton of the tran operaton at a 6km test secton decreases from 0.16% to 0.11% when the wnd drecton s consdered and further decreases to 0.08% when the wnd fence s nstalled. 1 INTRODUCTION Ralway operators regulate tran operaton and nstall wnd fences as countermeasures aganst the strong wnd. The assessment of the strong wnd along ralway tracks s mportant for the adequate mplementaton of these countermeasures. Cléon et al. (2002) estmated the strong wnd along ralway track from measured wnd speed at one ste and the numercal smulaton, whch takes the effect of local terran nto account. Based on the estmated wnd speed, they calculated the frequency of occurrence of strong wnd n control sectons by assumng the occurrences of the strong wnd at dfferent sub-sectons are ndependent each other. However, the gust event s not only affected by local terran but also by meteorologcal patterns. In addton, the assumpton that the occurrences of the strong wnd events between dfferent sub-sectons are ndependent s not always satsfed when the length of the sub-sectons becomes short. In ths study, a predcton method for the maxmum three second gust along ralway track s proposed, n whch the onste measurement data at one ste and mesoscale smulaton nested n global analyss data are used. Then, a predcton method for the frequency of strong wnd events n control secton s proposed, whch can consder the correlaton between the strong wnd events at dfferent sub-sectons. Fnally, proposed methods are appled to the tran regulaton, consderng the wnd drecton and the wnd fence.

2 2 A STRONG WIIND PREDICTION METHOD BASED ON THE ONSITE MEASUREMENT AND THE NUMERICAL SIMULATION 2.1 Predcton method of maxmum three second gust Ths secton explans a predcton method of the maxmum three second gust, n whch the effects of local terran and the meteorologcal phenomena on the wnd speed and the wnd drecton are taken nto account. The flow chart of the proposed method s shown n Fgure 1. Numercal smulaton by the mesoscale meteorologcal, RAMS (Pelke et al., 1992) s carred out to obtan the one year tme seres of mean wnd speed and wnd drecton wth 1km resoluton. These tme seres data are downscaled to the reference ste where the anemometer s nstalled and the predcton stes where the wnd speed and drecton are to be estmated by the mcroscale wnd predcton, MASCOT (Ishhara et al., 2003) wth the Dynamcal Statstcal Downscalng Approach (Yamaguch et al., 2003). The wnd speed rato and the changes n wnd drecton between the reference ste and the predcton stes are calculated as functons of wnd drecton from the smulated tme seres. The wnd speeds at the predcton stes are estmated by multplyng the wnd speed rato to the measured wnd speed at reference ste. The wnd drectons at the predcton stes are also estmated by addng the change n wnd drecton to the measured wnd drecton at reference ste. The gust factor s calculated as a functon of wnd drecton from the estmated turbulence ntensty by the mcroscale wnd predcton and the maxmum gust s estmated by multplyng the gust factor to the tme seres of the predcted mean wnd speed at the predcton stes. Onste measurement Numercal smulaton Measured mean wnd speed and drecton at the reference ste Tme seres of mean wnd speed and drecton at the reference ste and the predcton stes Wnd speed rato C(θ) Change n wnd drecton D(θ) Turbulence ntensty I(θ) Tme seres of the mean wnd speed u and drectonθ at predcton stes Gust factor C R (θ) Tme Tme seres seres of of the the maxmum gust gust at at predcton stes stes Fgure 1. The flow chart of the proposed method In ths study, the wnd speed rato C ( θ ref ) and the change n wnd drecton D ( θ ref ) between the two stes are assumed to be functons of the wnd drecton θ ref obtaned by the numercal smulaton. The wnd speed rato and the change n the wnd drecton are estmated by the least square method as shown n Equatons (1) and (2). C( θ ( ) 2 ref ) = argmn uref ( t) C( θref ) uste ( t) (1) C( θ ) D( θ ) t ( ) 2 ref ref ste D( θref ) = argmn θ () t + D( θ ) θ () t (2) t

3 where u ref ( t) and θ ref ( t) are the wnd speed and drecton at the reference ste where the anemometer s nstalled and u ste ( t) and θ ste ( t) are those at the predcton stes. The one mnute averaged wnd speed u ste and the drecton θ ste at any pont along the ralway are calculated from the one mnute averaged wnd speed u ref and the drecton θ ref at the reference ste, and predcted wnd speed rato C ( θ ref ) and the change n wnd D θ as follows: drecton ( ref ) uste () t uref () t C( θref ) = (3) () t () t D( ) θ = θ + θ (4) ste ref ref The three-second maxmum gust ûste ( ) multplyng the gust factor R ( ste ) t at the predcton ste can be calculated by G θ to the predcted mean wnd speed, and the gust factor can be estmated by multplyng the peak factor k p to the turbulence ntensty Iu ( θste ) obtaned by the mcroscale wnd predcton. ( ) () () R( θ ) () p u( θste) uˆ t = u t G = u t 1+ k I (5) ste ste ste ste In ths study, the peak factor k p s estmated by the formula proposed by Ishzak (1983). 1 T kp = ln, T = 60sec, t = 3sec (6) 2 t 2.2 Predcton of a strong wnd event Proposed method s verfed by usng the feld measurement data at fve measurement ponts along a ralway lne as shown n Fgure 2. The measurements were carred out for one year from February 2004 to January Gust wnd speeds wth 4Hz samplng rate were recorded, whch are equvalent to one second averaged value accordng to three-cup anemometers. Here, the measurement ste No.3 s assumed to be the reference ste and the other stes are assumed to be predcton stes for the verfcaton. Total secton length 3.01km ste 5 ste 4 Sub-secton5 (0.57km) Staton ste 1 ste 2 ste 3 Sub-secton 2 (0.62km) Sub-secton 1 (0.90km) Sub-secton 4 (0.55km) Sub-secton 3 (0.44km) Fgure 2. Fve measurement stes and the vrtual secton and sub-sectons Fgure 3 (a) shows the maxmum gust at ste No. 2 on 25th of January The predcted wnd gust by the proposed method wth the onste measurement and the numercal smulaton shows good agreement wth the measurement, whle that only by the numercal smulaton cannot capture the strong wnd event, even though the annual mean wnd speed

4 s predcted well by Dynamcal Statstcal Downscalng Approach. The underestmaton of strong wnd events s due to the aton of the current mesoscale for the predcton of the down slope wnd, a famous local weather system n a mountanous regon. Fgure 3 (b) shows the annual frequency dstrbuton of maxmum gust at No.2 obtaned by the measurement and by the proposed method. The proposed method slghtly underestmates the frequency at wnd speed more than 20m/s. The reason of ths underestmaton can be supposed to be the dfference of the averaged tme of gust,.e., the three second averaged gust s used n the proposed method, whle measurement s estmated to be the one second averaged gust. 20 Measurement 100 Measurement 15 Numercal Smulaton Proposed Method 10 Proposed Method /1/ /1/26 gust (m/s) (a) Tme seres of maxmum wnd speed n 1 mnute (b) Annual frequency dstrbuton of maxmum gust Fgure 3. Comparson of the strong gust between the predcted and the measured maxmum gust at ste No.2 Maxmum Wnd Speed (m/s) Frequency (%) 3 PREDICTION METHOD OF MAXIMUM GUST FREQUENCY IN CONTROLLED SECTION In order to evaluate the cost performance of the countermeasures of strong wnd such as nstallaton of wnd fences and tran regulaton, t s necessary to accurately predct the frequency of the strong wnd. In ths secton, a tme seres based method to predct the frequency of strong wnd s proposed and two exstng methods based on probablstc densty functons are nvestgated by comparng wth the measurement. 3.1 Predcton method of strong wnd frequency n a control secton The smplest method for the predcton of the frequency of occurrence of strong wnd n a control secton s to assume that measured wnd at one measurement pont can represent wnds n the secton, that s, to assume that wnds have the complete correlaton n the control secton for the tran regulaton. In ths method, the frequency of the strong wnd that exceeds the regulaton wnd speed u can be estmated as follows: ( obs ) P = P u > u (7) where P s the frequency of the strong wnd n the control secton and uobs s the wnd speed at measurement ste. The dsadvantage of ths method s that strong wnd events that occur at the pont other than the measurement ste cannot be ncluded. In order to account for the varatons of wnd speed n the control secton due to the local terran, Cléon (2002) proposed a predcton method n whch the control secton s dvded nto number of sub-sectons as shown n Fgure 4 and t s assumed that there s no correlaton between the wnd speeds n sub-sectons. The frequency of the strong wnd P n the control secton can be estmated as follows:

5 P P u u (8) = 1 1 ( > ) where u s the wnd speed n sub-secton and s estmated by Eq. (5), n whch the observed wnd speeds and drectons at the measurement ste are used as shown n Secton 2.1. The advantage of ths method s that the frequency of the strong wnd P can be calculated analytcally and the varatons of wnd speed n the control secton can be taken nto account. The frequency of the strong wnd assessed by ths method could be overestmated f the strong wnds n dfferent sub-sectons correlated each other. Snce these two methods explaned above are based on the probablty densty functon of wnd speeds at the ste, they can be called the Probablty Densty Functon based Method (PDFM). Regulaton secton Staton u 3 u 2 u 1 u n Measurement ste u Sub-secton () Fgure 4. The regulaton secton and sub-sectons Staton In order to accurately estmate the frequency of the occurrence of the strong wnd, a Tme Seres based Method (TSM) s proposed, whch can consder the correlaton between the wnd speeds n dfferent sub-sectons by usng tme seres of wnd speeds and drectons at sub-sectons. The frequency of strong wnd can be estmated as follows: ( max( ) ) P = P u > u (9) 3.2 Effect of the correlaton of wnd speeds and ntervals of the sub-secton The frequences of the strong wnd are affected by the correlaton of wnds as descrbed above. A vrtual secton whose dstance s about 3km wth fve sub-sectons s consdered as shown n Fgure 2. The ste No. 3 s used as the reference ste and the wnd speed at the other stes are estmated by usng the method proposed n Secton 2 and the frequency of occurrence of the strong wnd event s estmated by usng the three methods descrbed above. Fgure 5 (a) shows the frequency of strong wnd exceeds 25m/s estmated by the three methods. The frequency of the strong wnd event estmated from all the measurement data s denoted as measurement. The predcted frequency of the strong wnd by the TSM shows good agreement wth the measurement. On the other hand, the predcted frequency by the PDFM wth complete correlaton assumpton s underestmated due to the gnorance of the strong wnd at the stes where the anemometers are not nstalled and the predcted frequency by the PDFM wth no correlaton assumpton s overestmated due to the double countng of the strong wnds whch correlate each other. The nterval of the sub-secton also affects the predcted frequency of the strong wnd. In order to nvestgate the effect of the nterval, the frequences of the strong wnd are calculated by three methods for dfferent ntervals of the sub-sectons n a test secton whose dstance s about 6km as shown n Fgure 5 (b). The frequency estmated by the proposed method TSM s almost constant when the ntervals are less than 200m and slghtly decreases as the ntervals ncrease, whle the frequency predcted wth no correlaton as-

6 sumpton ncreases rapdly when the ntervals are less than 1,000m and shows unrealstc values. In the mountanous countres such as Japan, the ntervals of the sub-secton have to be less than 200m and the method wth no correlaton assumpton overestmates the frequency of the strong wnd remarkably. Although the method wth no correlaton assumpton s applcable f the local terran s moderate and the ntervals can be set long, the proposed method consderng the correlaton between the strong wnds s applcable to the complex terran. In order to fnd an nterval-ndependent value for the predcted frequency of strong wnd by the proposed method, the predcted frequency s expressed as a functon of the length of the nterval as follows: P = Cr + C (10) C2 1 3 where r s the length of the nterval and parameters C 1, C 2, C 3 are decded by usng 9 the frequences of the strong wnd obtaned by proposed method as C 1 = 3.04, 3 C 2 = 1.75, C 3 = The nterval-ndependent value s obtaned when the nterval of the sub-secton approaches zero. Table 1 shows the predcton errors of the predcted frequences by three dfferent methods. The absolute value of the predcton errors by the proposed method are less than or equal to 2% when the length of ntervals are less than 200m, whle the predcton errors by the method wth no correlaton assumpton ncrease rapdly and shows mnmum absolute value of 18.2% when the length of ntervals s equal to 1000m. The predcton errors by the method wth complete correlaton assumpton are constant value and reach to -49.1% n the mountanous regon. (a) Frequency of the strong gust (%) Complete correlaton No correlaton Proposed method 0.06 Measurement (b) Frequency of the strong gust (%) Complete correlaton No correlaton Proposed method Interval of the sub-secton (m) Fgure 5. Frequency of strong wnd over 25m/s (a)for the vrtual secton wth 3km (b) for the test secton wth 6km Table 1. The predcton errors n the frequency of the strong wnd The nterval of the sub-secton 50m 100m 200m 400m 1000m 2000m Complete correlaton -49.1% -49.1% -49.1% -49.1% -49.1% -49.1% No correlaton % 522.5% 217.5% 94.2% -18.2% -32.9% Proposed method -1.5% -1.7% -2.0% -6.6% -32.9% -32.9% 4 TRAIN REGULATION COSIDERING THE WIND DIERCTION AND WIND FENCE As the crtcal wnd speed of the tran overturnng changes consderably dependng on wnd drectons and a wnd fence, an effcent tran regulaton s expected by consderng these factors. Ima et al. (2002) proposed a tran regulaton consderng the wnd drectonal effect and showed a good result. In ths secton, the effects of the tran regulaton consderng

7 the wnd drecton and the wnd fence are examned based on the crtcal wnd speed of the tran overturnng. 4.1 The outlne of the regulaton of the tran operaton To take the wnd drectonal effect of the crtcal wnd speed nto account, wnd drecton factor Cc ( φ, V) s defned as follows: WC( φdnger, V) Cc ( φ, V) = (11) WC ( φ, V) where Wc ( φ, V) s the crtcal wnd speed of the tran overturnng, whch s a functon of the relatve angle φ between the ralway drecton and the wnd drecton as well as the tran speed V. φ DANGER s the angle at whch the crtcal wnd speed of the overturnng has the smallest value,.e. the most dangerous drecton. The crtcal wnd speed of the tran overturnng used n ths study was calculated by the method proposed by Hbno and Ishda (2003) as shown n Fgure 6. The crtcal wnd speeds are low at the relatve angle between about 40 and 110 degree and go up remarkably as the angle decreases or ncreases regardless of the tran speed. (a) Tran Wnd drecton θ Wnd The angle of ralway α Relatve angle of wnd to the tran φ= θ - α (b) Crtcal wnd speed of overturnng Wc (m/s) Relatve angle of wnd to the tran φ (degree) 120km/h 100km/h 70km/h Fgure 6. (a) Defnton of the wnd drecton and (b) the crtcal wnd speed of the tran overturnng wth the wnd drecton To take the effect of the wnd fence nto account, a wnd fence factor C f ( φ ) s also defned as follows: C ( φ ) = ( C sn φ) + ( C cos φ ) (12) 2 2 f n r where C n = 0.83 and C r = 1.0 are the wnd reducton factors for the wnd component perpendcular and parallel to the wnd fence respectvely. The frequency of the regulaton of the tran operaton can be calculated by substtuton of the derved wnd speed to Equaton (9) as follows: { () } ˆste φ * P = P max u t C (, V) > u (13) where C (, V) * φ s a factor representng ether the wnd drecton factor Cc ( φ, V) or the product of the wnd drecton factor and the wnd fence factor, and s multpled to the maxmum gust ûste () t derved by proposed method n Secton 2 to consder effects of the wnd drecton and the wnd fence. In ths study, the tran speed V s assumed to be 120km/h.

8 4.2 Effects of the wnd drecton and the wnd fence on the tran regulaton The frequences of the tran regulaton consderng the wnd drecton and the wnd fence n the 6km test secton are shown n Fgure 7. The frequency decreases from 0.16% to 0.11%, when the wnd drecton s consdered and the frequency further decreases to 0.08% when the wnd fences are nstalled n the test secton. It s obvous that the frequency of the tran regulaton wll be decreased wth the equvalent safety by consderng the effect of wnd drecton and the wnd fence. Frequency of suspenson of tran operaton (%) Conventonal method Consder wnd drecton Consder wnd drecton and fence 0 Fgure 7. The frequency of the strong gust over regulaton wnd speed, 25m/s 5 CONCLUSION In ths study, predcton methods for the strong wnd and ts frequency along ralway are proposed and appled to a tran regulaton, consderng wnd drecton and wnd fence. Followng results are obtaned. 1) A predcton method for the strong gust was proposed, whch can take the effect of not only local terran but also meteorologcal condtons nto account and predcted maxmum gust by ths method shows good agreement wth the measurement. 2) A tme seres based method for the predcton of the frequency of strong wnd n a control secton was proposed. The predcted frequency by the proposed method shows good agreement wth the measurement, whle the conventonal methods underestmates or overestmates the frequency. 3) The frequency of the regulaton of the tran operaton at the 6km test secton decreases from 0.16% to 0.11% when the wnd drecton s consdered and further decreases to 0.08% when the wnd fence s nstalled. 6 REFERENCE Cléon L. M., Parrot M., TRAN-HA S., 2002, Les vents traversers sur la LGV Médterranée, Revue Générale des Chemns de Fer,. (In French) Hbno Y., Ishda H., 2003, Statc Analyss on Ralway Vehcle Overturnng under Crosswnd, RTRI Report, Vol.17, No.4, Ima T., Fuj T., Tanemoto K., Shmamura T., Maeda T., Ishda H., Hbno Y., 2002, New tran regulaton method based on wnd drecton and velocty of natural wnd aganst strong wnds, Journal of Wnd Engneerng and Industral Aerodynamcs 90, Ishhara T., Yamaguch A., Fujno Y., 2003, A nonlnear MASCOT development and applcaton, Proc. of 2003 European Energy Conference and Exhbton, T1.8, 1-7 Ishzak H., 1983, Wnd Profles, Turbulence Intenstes and Gust Factors for Desgn n-typhoon-prone Regons, Journal of Wnd Engneerng and Industral Aerodynamcs 13, Pelke, R. A., Cotton, W. R., Walko, R. L., Tremback, C. J., Lyons, W. A., Grasso, L. D., Ncholls, M. E., Moran, M. D., Wesley, D. A., Lee, T. J. and Copeland, J. H., 1992, A comprehensve meteorologcal ng system RAMS, Meteorology Atmospherc Physcs, 49, Yamaguch A., Ishhara T., 2003, Dynamcal Statstcal Downscalng Approach for wnd assessment, Proc. of 2003 European Energy Conference and Exhbton, T1.1, 1-5