Skip to main content

Advertisement

SpringerLink
Log in

High-Reynolds-number effects simulations for wind effects on a cooling tower model in a wind tunnel based on a statistical approach

  • Technical Paper
  • Published:
Journal of the Brazilian Society of Mechanical Sciences and Engineering Aims and scope Submit manuscript

Abstract

The traditional high-Reynolds-number (Re) effects simulation method for wind effects on circular cylindrical models in wind tunnels is fundamentally a trial-and-error practice, which is strongly subjective and laborious. To this end, a mathematically well-founded high-Re effects simulation method is proposed based on the response surface (RS) optimization algorithm in this article. Having the advantages of good considerations of random errors and simplified calculations using the polynomial models, RS method has been widely employed in chemical industry. However, it is seldom employed in physical experiments. Using a case study of Weisweiler cooling tower, it has been proved that model tests using the new high-Re effects simulation method based on RS optimization algorithm can objectively and easily reproduce the mean and the fluctuating wind pressure distributions measured on the spot, and the model-scale spectral characteristics of the wind pressures obtained by using the new high-Re effects simulation method agree well with the full-scale ones. Besides, numerical analyses undertaken on a computational fluid dynamics platform also indicate the validity of the new method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Reprinted from Cheng et al. [1]

Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

Abbreviations

k :

Relative roughness

a :

Rib spacing

b :

Width of the rough zone

e :

Thickness of the rough zone

S A :

Square error caused by uncertain parameter

S e :

Square error caused by experiment

f A :

Dimension of freedom of square error caused by uncertain parameter

f e :

Dimension of freedom of square error caused by experiment

α :

Significance level

F A :

\(\frac{{S_{A} /f_{A} }}{{S_{e} /f_{e} }}\)

y :

Response of the model/outputs of the experiment

x i :

Significant uncertain parameter

β 0, β i, β ij, β ii :

Coefficients in Eq. (3)

R 2 :

Value R2

y R S (j):

Outputs of the RS

\(\overline{y}\) :

Mean of the outputs of the experiment

p :

Design parameter

{f A}:

Analytical structural response vector

{f E}:

Experimental model response vector

VLB :

Lower bound of design space

VUB :

Upper bound of design space

R :

Residual vector

n :

Frequency

a 1(θ), b 1(θ), and β p(θ):

Coefficients in Eqs. (7–9)

α′:

Power law exponent

D :

Diameter of the throat

L u x :

Integral scale of turbulence

θ, θ′:

Circumferential positions

σ p 2 (z, θ):

Mean square of the fluctuating pressure sample

S p (z, θ, n):

Spectra of fluctuating pressures

R f (θ, θ′, n):

Circumferential coherence between fluctuating pressures

β 3 :

Coefficient in Eq. (10) (a constant = 25)

U(δ):

Mean wind speed at the gradient height

δ :

The gradient height

C 2 (θ, θ′):

Coefficient in Eq. (10)

K S :

Equivalent sand roughness

E :

Coefficient in Eq. (12) (a constant = 9.793)

C s :

An empirical dimensionless factor

K S + :

Re roughness

u*:

Friction velocity

υ :

Kinematic viscosity

u + :

\(\frac{u}{{u^{*} }}\)

κ :

Coefficient in Eq. (14) (a constant = 0.42)

y :

Wall distance of the inner-layer grid

y + :

Dimensionless distance normal to the wall surface determined empirically

References

  1. Cheng XX, Zhao L, Ge YJ et al (2017) A comprehensive high Reynolds number effects simulation method for wind pressures on cooling tower models. Wind Struct 24(2):119–144

    Article  Google Scholar 

  2. Cheng XX, Dong J, Han XL et al (2018) Structural health monitoring-oriented finite-element model for a large transmission tower. Intl J Civ Eng 16:79–92

    Article  Google Scholar 

  3. Cheng XX, Peng Y, Khan ZA et al (2019) Beam-end stiffness identification for a structural health monitoring-oriented finite-element transmission tower model using effective optimization techniques. Adv Struct Eng 22(2):364–383

    Article  Google Scholar 

  4. Gölbaşı, D, Buyruk, E, Karabulut, K. (2018). Experimental and numerical research of the flow features around the building pairs with different types. Cumhuriyet Sci J 39 (4) 1089–1106. https://doi.org/10.17776/csj.393304.

  5. Gölbaşı D, Buyruk E, Sahin B, Karabulut K, Alnak DE (2017). Experimental and numerical investigation of the effect of rooftop on the flow characteristic between two buildings. In: 8th international advanced technologies symposium (IATS'17), vol 8, pp 1648–1655, Elazığ-Turkey. ISBN: 978-605-82017-0-5

  6. Goudarzi MA, Sabbagh-Yazdi SR (2008) Modeling wind ribs effects for numerical simulation external pressure load on a cooling tower of KAZERUN power plant-IRAN. Wind Struct 11(6):479–496

    Article  Google Scholar 

  7. Hashish MG, Abu-Sitta SH (1974) Response of hyperbolic cooling towers to turbulent wind. J Struct Div ASCE 100:1037–1051

    Article  Google Scholar 

  8. Huang P, Lin H, Gu M (2020) Wind tunnel investigation of autorotation of plate: the effects of geometry, Reynolds number and rotation direction. J Wind Eng Ind Aerodyn 196:104012

    Article  Google Scholar 

  9. Kargarmoakhar R, Chowdhury AG, Irwin PA (2015) Reynolds number effects on twin box girder long span bridge aerodynamics. Wind Struct 20(2):327–347

    Article  Google Scholar 

  10. Lawson TV (1982) The use of roughness to produce high Reynolds number flow around circular cylinders at lower Reynolds numbers. J Wind Eng Ind Aerodyn 10:381–387

    Article  Google Scholar 

  11. Lee S, Kwon S-D, Yoon J (2014) Reynolds number sensitivity to aerodynamic forces of twin box bridge girder. J Wind Eng Ind Aerodyn 127:59–68

    Article  Google Scholar 

  12. Liu Z, Cao S, Liu H, Hua X, Ishihara T (2020) Effects of Reynolds number in the range from 1.6 × 103 to 1.6 × 106 on the flow fields in tornado-like vortices by LES: a systematical study. J Wind Eng Ind Aerodyn 196:104028

  13. Ma WY, Liu QK, Du XQ, Wei YY (2015) Effect of the Reynolds number on the aerodynamic forces and galloping instability of a cylinder with semi-elliptical cross sections. J Wind Eng Ind Aerodyn 146:71–80

    Article  Google Scholar 

  14. Niemann HJ, Propper H (1975) Some properties of fluctuating wind pressures on a full-scale cooling tower. J Ind Aerodyn 1:349–359

    Article  Google Scholar 

  15. Propper H, Welsch J (1979) Wind pressures on cooling tower shells. In: Proceeding of the fifth international conference on wind engineering, Fort Collins, CO, July 1979

  16. Qiu Y, Sun Y, Wu Y, Tamura Y (2014) Effects of splitter plates and Reynolds number on the aerodynamic loads acting on a circular cylinder. J Wind Eng Ind Aerodyn 127:40–50

    Article  Google Scholar 

  17. Qiu Y, Sun Y, Wu Y, Tamura Y (2014) Modeling the mean wind loads on cylindrical roofs with consideration of the Reynolds number effect in uniform flow with low turbulence. J Wind Eng Ind Aerodyn 129:11–21

    Article  Google Scholar 

  18. Simiu E, Scanlan RH (1996) Wind effects on structures. Wiley, New York

    Google Scholar 

  19. Wang D, Chen C, Hu J, He Z (2020) The effect of Reynolds number on the unsteady wake of a high-speed train. J Wind Eng Ind Aerodyn 204:104233

    Article  Google Scholar 

  20. Wang X, Gu M (2015) Experimental investigation of Reynolds number effects on 2D rectangular prisms with various side ratios and rounded corners. Wind Struct 21(2):183–202

    Article  Google Scholar 

Download references

Acknowledgements

The authors gratefully acknowledge the financial supports from the National Natural Science Foundation of China (Grant No. 51908124) and the China Postdoctoral Science Foundation (Grant No. 2016M601793).

Author information

Authors and Affiliations

  1. School of Civil Engineering, Southeast University, Nanjing, 211189, China

    X. X. Cheng

  2. State Key Laboratory for Disaster Reduction in Civil Engineering, Tongji University, Shanghai, 200092, China

    L. Zhao & Y. J. Ge

Authors
  1. X. X. Cheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Y. J. Ge
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to L. Zhao.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Technical Editor: Daniel Onofre de Almeida Cruz, D.Sc.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cheng, X.X., Zhao, L. & Ge, Y.J. High-Reynolds-number effects simulations for wind effects on a cooling tower model in a wind tunnel based on a statistical approach. J Braz. Soc. Mech. Sci. Eng. 43, 99 (2021). https://doi.org/10.1007/s40430-021-02816-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s40430-021-02816-w

Keywords

Search

Navigation