A METHOD FOR EVALUATION OF ACROSS-WIND RESPONSE OF A CIRCULAR CHIMNEY INCLUDING LOCK-IN EFFECTS AND COMPARISON WITH ACI CODE OF PRACTICE

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1 The Eighth Asia-Pacific Conference on Wind Engineering, December 10 14, 2013, Chennai, India A METHOD FOR EVALUATION OF ACROSS-WIND RESPONSE OF A CIRCULAR CHIMNEY INCLUDING LOCK-IN EFFECTS AND COMPARISON WITH ACI CODE OF PRACTICE S.Arunachalam 1, N.Lakshmanan 2, G.Ramesh Babu 3. 1 Director, Wind Engg. Applications Centre, JUET, Guna, India, sarunacha@yahoo.co.in (Formerly Chief Scientist, CSIR-SERC, Chennai), sarunacha@yahoo.co.in 2 Formerly Director, CSIR-SERC, Chennai, India 3 Principal Scientist, CSIR-SERC, Chennai, India ABSTRACT An empirical method for evaluating the across wind response of a tall circular chimney was earlier proposed by authors and a closed form solution was developed for computing the across wind tip deflection. Based on closer review of our earlier equation, it was realized that the suggested equation for computing the overall modal lift force needs to be modified in order to appropriately account for the correlation of forces, and the modification can be brought in the form of a correction factor. After incorporating the correction factor, the across-wind response values are in good agreement with corresponding values obtained by using ACI , when applied to three typical chimney examples. Keywords: Circular Chimneys, Across Wind Response, Vortex Shedding Introduction The method developed by Vickery and Basu (1983) for evaluating the across-wind response of a circular chimney is currently widely recommended in many international codes of practice including Indian Code IS:4998(1992), although there is no complete theoretical method presently available (Simiu and Scanalan 1996). Research efforts are still continuing to better explain the influence of Reynolds number and turbulence intensity on various aerodynamic parameters such as rms lift coefficient, spectral bandwidth, correlation length, and Strouhal number. Some of the methods proposed in the literature include those by Ruscheweyh (1989), ESDU(1996),Arunachalam et al., (2011), and Flaga (2010). Based on research at CSIR-Structural Engineering Research Centre(CSIR-SERC), Chennai, the authors (2010,2011) have earlier proposed that the increased response can still be predicted with the use of structural damping only, with the condition that the suggested method for the nonlock-in region requires suitable modification of the force spectrum in the lock-in region. A closed form solution for the normalised across-wind tip deflection has been thus developed and presented by authors (2011). In this paper it is reviewed and examined the earlier equation proposed and improved it to include a correction in the expression for evaluating the spectrum of overall generalized across-wind force due to vortex shedding. With this correction, when applied to three typical chimney examples, a good agreement is obtained on the value of across wind base bending moment computed, based on our method and also by using ACI code Proc. of the 8th Asia-Pacific Conference on Wind Engineering Nagesh R. Iyer, Prem Krishna, S. Selvi Rajan and P. Harikrishna (eds) Copyright c 2013 APCWE-VIII. All rights reserved. Published by Research Publishing, Singapore. ISBN: doi: /

2 Background The authors in an earlier paper (2011) have proposed an empirical method for evaluating the spectrum of mode generalised across wind force, in the non-lock-in region. By introducing a non-dimensional parameter of fact, the across wind force spectrum due to lock-in excitation has also been proposed. Further, the following are the five assumptions, made under the lock-in regime. (i) (ii) Only the top 1/3 rd region of the chimney contributes to the vortex shedding forces and in this region the vortices are assumed to be fully correlated under lock-in. The effect of correlation of vortices in the lower 2/3 rd region is assumed to be insignificant. The variation in turbulence intensity in the top 1/3 rd region is assumed to be small and hence in this region, I z1 = I z2 = I zref and I zref is conveniently assumed equal to turbulence intensity at 5H/6 above ground. (iii) In the lock-in region, since the shedding frequency, f sh gets locked into the natural frequency of the chimney, f o, we assume, f sh, z1 = f sh, z2 = f o. (iv) The spectral bandwidth, B in the non-lock-in region is reduced by a factor fact in the lock-in-region and the new bandwidth is (B. fact ). Thus it is equivalent to stating that during lock-in region, the eddies are more concentrated with their frequencies in a narrow region centered around the natural frequency, f o. (v) Similarly, in the top 1/3 rd height of the chimney, the variation in diameter of the chimney is assumed small, and hence D z1 = D z2 = D e, where D e is the average diameter of the top 1/3 rd height of the chimney. The spectrum of overall generalized across wind force due to vortex shedding alone was shown to be given by (Arunachalam 2011): where is the mass density of air, V ref is the mean reference velocity at height, z ref ; D e is the effective diameter at 5/6H; H is the height of the chimney; B is the spectral bandwidth; I 5H/6 is the turbulence intensity at height, 5H/6z; and are the power law exponent values of mean velocity profile and fundamental mode shape respectively. Using the relation, (1) (2) 114

3 where and, (3) the variance of modal lift force, from Eq. (1) can be written as: (4) (5) Based on the principles of random vibration theory, using mechanical admittance function, and with only structural damping,, the variance of the across wind response can be derived from Eq. (5). Thus we have, (6) where variance of tip deflection in across wind direction due to vortex shedding and H(f) is the mechanical admittance function. Eq. (6) can be approximated as (7) Since when y >> x, (which is justified as discussed later), we have Eq. (7) approximated as, Where is the structural damping, or convenience. (8) say for Considering second term in Eq.(8), which is the response from eddies with frequencies centered around fo, we get from Eq. (1), 115

4 (9) Since the generalized mass, G i is given by,, where It can be shown through simplification that, = m ei = equivalent mass, and (10) where P is given by (11) (12) where S is the Strouhal number, (13) Consider First term in Eq. (8), which is the response due to vortex shedding form eddies with frequencies well away from natural frequency, f o,, Using Eq. (1), we get, Since the function (14) is symmetric around fo we can write that (15) (16) 116

5 It can be shown that (17) Net response, (18) (19) Where (20) Thus the response is a function of me α, β,η,,s,i 2 5H/6 ρde, fact, B Discussions and conclusions Based on the formulation presented in this paper, the following important observations can be made: (i) The normalized tip deflection is inversely dependent on the mass damping parameter 2m e given as a product of and 2 a De (ii) It is believed that the value of the RMS lift coefficient, C L, V only due to vortex shedding, taking the value of 0.089, being independent of Reynolds number regime, covering both wind tunnel and full scale experiments, primarily contributes to the strength of this predictive model. The value of has been basically proposed by the author based on the earlier wind tunnel experiments reported in the literature and has been validated with several boundary layer wind tunnel and full-scale experimental data reported in the literature. With more test data becoming available, the preciseness of value of 0.45 for the parameter fact can be improved [Arunachalam and Lakshmanan, 2010] (iii) Eq. (19) can be further extended to compute the peak across wind bending moment as given by: H Mac ˆ 2, base 2f g mzdz z (21) o y o (iv) It may be noted that in this method, only the mode generalized across-wind force spectrum in the lock-in region is suitably modified, whereas from damping point of view, only structural damping is used (instead of the concept of a negative aerodynamic damping as adopted in Vickery & Basu model [Simiu and Scanlan, 1996]. 117

6 (v) Based on a closer review of above Eq. (19), we realized that the suggested equation for computing the overall modal lift force needs to be modified to appropriately take into account the correlation of vortex forces, and the modification can be brought in the form of a correction factor. A closer examination of the above equation revealed that with the assumption of top one third height of the chimney significantly contributing to the vortex shedding phenomenon, as considered here and also as generally agreed in the literature, it is more appropriate that the limits of integration in Eq.(4), shall be changed from (0 to H), to (2H/3 to H) when computing spectrum of overall modal lift force. This results in a correction factor of, to be applied to the rms across-wind tip deflection. Besides, in order to compare the predicted across-wind base bending moment with corresponding value obtained using ACI code , the value of Strouhal number, S is assumed to be the same as recommended in the ACI code. Similarly, since in the proposed method only the structural damping is required, a value of is assumed and this is in agreement with IS: With these modifications, when Eq. (19) is applied to three typical chimney examples,a good agreement is obtained as shown in Table. 1 on the values of across wind base bending moment computed, based on authors proposed method and also by using ACI code (2008).(The chimneyswhich are denoted as Chm1 and Chm2 in the Table- 1,are taken from the numerical examples referred in pages 353 and 355 of the test book authored by Simiu and Scanlan, 1996). References ACI-307,(2008), Standard Practice for the design and construction of cast-in place reinforced concrete chimneys, American Concrete Institute, Detroit, USA. Arunachalam, S. (2011), Studies on Across-Wind Load and Response of a Circular Chimney including Lock-in Effects In the proc of 13th International Conference on Wind Engineering 2011, Amsterdam. Arunachalam, S. and N. Lakshmanan, (2010), Modelling of Across-Wind Force and Response of a Circular Chimney including Lock-in-Effects, Journal of Wind and Engineering, V 7, No. 2, ESDU (1996) Response of structures due to vortex shedding, ESDU Item No , London, UK. Flaga, A., (2010) Code approaches to vortex shedding and own model, Engineering Structures,32, Indian Standard IS:4998 (Part 1)-1992, Criteria for design of concrete chimneys. BIS,New Delhi. Ruscheweyh, H. (1989) Codification of vortex excited vibrations Proceedings of 2 nd Asia-Pacific symposium on Wind Engineering, Beijing,China, Simiu, E., and Scanlan, R.H. (1996), Wind effects on structures, Wiley-Inter-science, New York Vickery, B.J. and Basu, R.I., (1983), Across-wind vibrations of structures of circular cross-section. Part.1. J. Ind. Aerodyn ;12(1):49-74.Part.II.J.IndAerodyn ;12(1):

7 Table: 1 Comparison of Across Wind Base Bending Moment Values ACI Code Authors method Parameter Chm1 Chm2 Chm3 Parameter Chm1 Chm2 Chm3 h(m) H(m) d(u)(m) D (5/6) (m) F1(A) mei/(rho*d (5/6) *D (5/6) ) Strouhal No f 0 (Hz) fo (Hz) Beta Vcr(m/s) Zeta V_zcr(m/s) Strouhal No I I (5/6H) F1(B) B CL Fact V_bar(m/s) P beta_s sigy/de beta_a Corr.factor deflection B sigy,corr (m) beta_s+beta_a G BM integral value h/du+ce (N m) 4.32E E E+08 Ma(Nm) 5.64E E E+08 Base BM,corr (Nm) 6.23E E E

Simplified Analytical Model for Across-Wind Response of Chimneys Around Critical Wind Velocity Regions

The Eighth Asia-Pacific Conference on Wind Engineering, December 1 14, 213, Chennai, India Simplified Analytical Model for Across-Wind Response of Chimneys Around Critical Wind Velocity Regions N. Lakshmanan