Skip to main content
SpringerLink
Log in

Effects of Fire Parameters on Critical Velocity in Curved Tunnels: A Numerical Study and Response Surface Analysis

  • Published:
Fire Technology Aims and scope Submit manuscript

Abstract

Fire accidents are more likely to occur in tunnels with different curves, aspect ratios, and slopes due to the land’s geographical characteristics. A three-dimensional computational fluid dynamics code with curvilinear grids fitted to the body was used to simulate a variety of fire locations releasing heat at a rate of 5 MW–60 MW in a tunnel with a turning radius of 100 m–1500 m, an aspect ratio of 0.5–2, and a slope between – 10% and 10%. Using the Design of Experiments (DOE) method coupled with numerical simulations, 32 3D numerical models were constructed and a second-order critical velocity model was generated. Analysis of critical velocity was performed based on Response Surface Methodology (RSM) and multifactor curve plots were drawn for effective parameters. The results showed that the critical velocity was proportional to one-third power of the heat release rate. It was also observed that the critical velocity increased gradually as the fire source moved from the tunnel’s center to its walls. Furthermore, the critical velocity decreased with increasing the aspect ratio. Results showed that the critical velocity increased with increasing the tunnel turning radius. Moreover, tunnels with negative slopes have a higher critical velocity than horizontal tunnels without slopes. Finally, by defining the parameters in non-dimensional form, a new modified form was derived for critical velocity calculation (R2 = 0.98). A critical velocity of 1.24 m/s–5.21 m/s was calculated based on five parameter values in this study. Furthermore, other straight and curved tunnel models confirmed the formula’s predictions.

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

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11
Figure 12
Figure 13
Figure 14
Figure 15
Figure 16
Figure 17
Figure 18

Similar content being viewed by others

Abbreviations

ANOVA:

Analysis of variance

CCD:

Central composite design

DOE:

Design of experiment

RSM:

Response surface method

A:

Tunnel cross-section area \(({{\text{m}}}^{2})\)

Cp :

Specific heat at constant pressure (J/kgK)

AR:

Aspect ratio (dimensionless)

g:

Gravity acceleration (m2/s)

h:

Smoke layer thickness (m)

H:

Tunnel height (m)

HRR:

Heat release rate (MW)

HRRC :

Convective part of the heat release rate (MW)

HRR*:

Non-dimensional form of the heat release rate (dimensionless)

\({{\text{HRR}}}_{{\text{a}}}^{*}\) :

Asymptotic \({{\text{HRR}}}^{*}\) (dimensionless)

HD :

Tunnel hydraulic diameter (m)

Lf :

Flame height (m)

\({\dot{{\text{m}}}}_{{\text{s}}}\) :

Mass flux of smoke \(({\text{kg}}/{\text{s}})\)

\({{\text{P}}}_{{\text{s}}}\) :

Static pressure (Pa)

\({\Delta {\text{P}}}_{{\text{stack}}}\) :

Stack pressure (Pa)

\({\Delta {\text{P}}}_{{\text{total}}}\) :

Total pressure difference (Pa)

\({{\text{P}}}_{{\text{d}}}\) :

Dynamic pressure (Pa)

\({{\text{Q}}}_{{\text{H}}}\) :

Heat of combustion (\({\text{MJ}}/{\text{kg}}\))

R:

Tunnel radius (m)

S:

Tunnel slope (%)

\({{\text{T}}}_{0}\) :

Ambient air temperature (K)

\({{\text{T}}}_{{\text{f}}}\) :

Gas temperature (K)

\(\Delta {\text{T}}\) :

Temperature difference between the smoke layer and airflow (K)

\({{\text{u}}}^{+}\) :

Non-dimensional tangential velocity (dimensionless)

V:

Ventilation air velocity (m/s)

\({{\text{V}}}_{{\text{C}}}\) :

Critical velocity (m/s)

\({{\text{V}}}_{{\text{C}}0}\) :

Critical velocity of the horizontal tunnel (m/s)

\({{\text{V}}}_{{\text{CS}}}\) :

Critical velocity of the slopped tunnel (m/s)

\({{\text{V}}}_{{\text{CS}}}\) :

Critical velocity of the slopped tunnel (m/s)

\({{\text{V}}}_{{\text{min}}}\) :

Minimum critical velocity (m/s)

\({{\text{V}}}_{{\text{max}}}\) :

Maximum critical velocity (m/s)

\({{\text{V}}}_{{\text{C}}}^{*}\) :

Non-dimensional form of the critical velocity (dimensionless)

\({{\text{V}}}_{{\text{min}}}^{*}\) :

Non-dimensional minimum critical velocity (dimensionless)

\({{\text{V}}}_{{\text{max}}}^{*}\) :

Non-dimensional maximum critical velocity (dimensionless)

W:

Tunnel width (m)

\({{\text{x}}}_{{\text{i}}}\) :

Variable factor

\({{\text{x}}}_{{\text{j}}}\) :

Variable factor

\({{\text{X}}}_{{\text{r}}}\) :

Radiation fraction (dimensionless)

y:

Second-order model

\(\Delta {\text{y}}\) :

Grid size (m)

\({{\text{Y}}}_{{\text{s}}}\) :

Soot yield (%)

\({{\text{y}}}^{+}\) :

Non-dimensional distance from the wall (dimensionless)

\(\Delta\) :

Fire transverse location (dimensionless)

\({\upbeta }_{0}\) :

Constant coefficient

\({\upbeta }_{{\text{i}}}\) :

Linear coefficient

\({\upbeta }_{{\text{ii}}}\) :

Second-order coefficient

\({\upbeta }_{{\text{ij}}}\) :

Interaction coefficient

\(\in\) :

Error term

\(\uptheta\) :

Longitudinal inclination of a tunnel (degree)

\({\uprho }_{0}\) :

Ambient air density \(({\text{kg}}/{{\text{m}}}^{3})\)

References

  1. Kazemipour A, Afshin H, Farhanieh B (2015) A comprehensive study on the critical ventilation velocity in tunnels with different geometries. Int J Vent 14(3):303–320

    Google Scholar 

  2. Tang F, McNamee M, Xu T, Zhang X, Deng L, Hu L (2024) Study of the smoke toxicity characteristics in an inclined tunnel. Fire Saf J 142:8

    Article  Google Scholar 

  3. Xu Q, Zhou X, Zhang J, Yang L (2011) Study on numerical simulation for the distribution of carbon monoxide in one closed-end tunnel fire. J Appl Fire Sci 21:299–311

    Article  Google Scholar 

  4. Vianello C, Fabiano B, Palazzi E, Maschio G (2012) Experimental study on thermal and toxic hazards connected to fire scenarios in road tunnels. J Loss Prev Process Ind 25(4):718–729

    Article  CAS  Google Scholar 

  5. Lee SR, Ryou HS (2005) An experimental study of the effect of the aspect ratio on the critical velocity in longitudinal ventilation tunnel fires. J Fire Sci 23(2):119–138

    Article  CAS  Google Scholar 

  6. Vauquelin O, Wu Y (2006) Influence of tunnel width on longitudinal smoke control. Fire Saf J 41(6):420–426

    Article  Google Scholar 

  7. Li YZ, Ingason H (2017) Effect of cross section on critical velocity in longitudinally ventilated tunnel fires. Fire Saf J 91:303–311

    Article  Google Scholar 

  8. Liu C, Lu S, Zhang R, Yang H, Cheng X, Zhang H (2017) The effect of aspect ratios on critical velocity in tunnel fires. Fire Sci Technol: 925–931

  9. Zhang T, Wang G, Li J, Huang Y, Zhu K, Wu K (2021) Experimental study of back-layering length and critical velocity in longitudinally ventilated tunnel fire with various rectangular cross-sections. Fire Saf J 126:12

    Article  Google Scholar 

  10. Li YZ, Fan CG, Ingason H, Lönnermark A, Ji J (2016) Effect of cross section and ventilation on heat release rates in tunnel fires. Tunn Undergr Space Technol 51:414–423

    Article  Google Scholar 

  11. Lee SR, Ryou HS (2006) A numerical study on smoke movement in longitudinal ventilation tunnel fires for different aspect ratio. Build Environ 41(6):719–725

    Article  Google Scholar 

  12. Ko G, Kim S, Ryou H (2010) An experimental study on the effect of slope on the critical velocity in tunnel fires. J Fire Sci 28:27–47

    Article  Google Scholar 

  13. Chow WK, Wong KY, Chung WY (2010) Longitudinal ventilation for smoke control in a tilted tunnel by scale modeling. Tunn Undergr Space Technol 25(2):122–128

    Article  Google Scholar 

  14. Chow WK, Gao Y, Zhao JH, Dang JF, Chow CL, Miao L (2015) Smoke movement in tilted tunnel fires with longitudinal ventilation. Fire Saf J 75:14–22

    Article  Google Scholar 

  15. Zoghi H, Jafari S, Farhanieh B, Afshin H, Kazemipour A (2021) Smoke extraction improvement of mid-tunnel shaft by a slim board beneath the shaft and bevel-angle connection. Tunn Undergr Space Technol 118:20

    Article  Google Scholar 

  16. Riess I, Bettelini M, Brandt R (2001) Smoke extraction in tunnels with considerable slope. In: International Conference Safety in Road and Rail Tunnels. Madrid, pp. 503–512

  17. Li J-m, Li Y, Cheng CH, Chow WK (2019) A study on the effects of the slope on the critical velocity for longitudinal ventilation in tilted tunnels. Tunn Undergr Space Technol: 262–267

  18. Atkinson GT, Wu Y (1996) Smoke control in sloping tunnels. Fire Saf J 27(4):335–341

    Article  Google Scholar 

  19. Tang F, Cao Z, Palacios A, Wang Q (2018) A study on the maximum temperature of ceiling jet induced by rectangular-source fires in a tunnel using ceiling smoke extraction. Int J Therm Sci 127:329–334

    Article  Google Scholar 

  20. Ji J, Tan T, Gao Z, Wan H, Zhu J, Ding L (2019) Numerical investigation on the influence of length–width ratio of fire source on the smoke movement and temperature distribution in tunnel fires. Fire Technol 55(3):963–979

    Article  Google Scholar 

  21. Zhong W, Li Z, Wang T, Liang T, Liu Z (2015) Experimental study on the influence of different transverse fire locations on the critical longitudinal ventilation velocity in tunnel fires. Fire Technol 51(5):1217–1230

    Article  Google Scholar 

  22. Ji J, Fan CG, Zhong W, Shen XB, Sun JH (2012) Experimental investigation on influence of different transverse fire locations on maximum smoke temperature under the tunnel ceiling. Int J Heat Mass Transf 55(17):4817–4826

    Article  Google Scholar 

  23. Wang F, Wang M (2016) A computational study on effects of fire location on smoke movement in a road tunnel. Tunn Undergr Space Technol 51:405–413

    Article  CAS  Google Scholar 

  24. Wu Y, Bakar MZA (2000) Control of smoke flow in tunnel fires using longitudinal ventilation systems—a study of the critical velocity. Fire Saf J 35(4):363–390

    Article  Google Scholar 

  25. Danziger NH, Kennedy WD (1982) Longitudinal ventilation analysis for the Glenwood Canyon Tunnels. In: Proceedings of the fourth international symposium aerodynamics and ventilation of vehicle tunnels. York, pp. 169–186

  26. The National Fire Protection Association (2023) NFPA 502, Standard for road tunnels, bridges, and other limited access highways. Quincy

  27. Oka Y, Atkinson GT (1995) Control of smoke flow in tunnel fires. Fire Saf J 25(4):305–322

    Article  Google Scholar 

  28. Palazzi E, Currò F, Fabiano B (2005) A study on road tunnel fires using hazmat, with emphasis on critical ventilation velocity. Process Saf Environ Prot 83(5):443–451

    Article  CAS  Google Scholar 

  29. Khattri SK, Log T, Kraaijeveld A (2021) A novel representation of the critical ventilation velocity for mitigating tunnel fires. Tunn Undergr Space Technol 112:103853

    Article  Google Scholar 

  30. Li YZ, Lei B, Ingason H (2010) Study of critical velocity and backlayering length in longitudinally ventilated tunnel fires. Fire Saf J 45(6):361–370

    Article  Google Scholar 

  31. Savalanpour H, Farhanieh B, Afshin H (2021) Proposing a general formula to calculate the critical velocities in tunnels with different cross-sectional shapes. Tunn Undergr Space Technol 110:16

    Article  Google Scholar 

  32. Kunsch JP (2002) Simple model for control of fire gases in a ventilated tunnel. Fire Saf J 37(1):67–81

    Article  Google Scholar 

  33. Kazemipour A, Afshin H, Farhanieh B (2016) Numerical-analytical assessment of fire and ventilation interaction in longitudinally ventilated tunnels using jet fans. Heat Transfer Eng 38(5):523–537

    Article  ADS  Google Scholar 

  34. Wang F, Wang M, Carvel R, Wang Y (2017) Numerical study on fire smoke movement and control in curved road tunnels. Tunn Undergr Space Technol 67:1–7

    Article  Google Scholar 

  35. Zhang S, Yang H, Yao Y, Zhu K, Zhou Y, Shi L, Cheng X (2017) Numerical investigation of back-layering length and critical velocity in curved subway tunnels with different turning radius. Fire Technol 53(5):1765–1793

    Article  Google Scholar 

  36. Lu K, Xia K, Shi C, Yang M, Wang J, Ding Y (2021) Investigation on the tunnel curvature effect upon the ceiling temperature of tunnel fires: a numerical simulation. Fire Technol 57(6):2839–2858

    Article  Google Scholar 

  37. Jafari S, Farhanieh B, Afshin H (2023) Numerical investigation of critical velocity in curved tunnels: parametric study and establishment of new model. Tunn Undergr Space Technol 135:18

    Article  Google Scholar 

  38. Xu Z, Zhou D, Tao H, Zhang X, Hu W (2022) Investigation of critical velocity in curved tunnel under the effects of different fire locations and turning radiuses. Tunn Undergr Space Technol 126:11

    Article  Google Scholar 

  39. Pan R, Hostikka S, Zhu G, Wang X, Liu X, Wang W, Lan M (2023) Experimental investigation and numerical simulation of transverse heat flux attenuation during fire in utility tunnel. Tunn Undergr Space Technol 142:105411

    Article  Google Scholar 

  40. Savalanpour H, Farhanieh B, Afshin H (2019) Numerical simulation to investigate the induced buoyant flow characteristics caused by intensive heat in complex curvilinear geometries. Heat Transfer-Asian Research 48(3):835–853

    Article  Google Scholar 

  41. Katopodes ND (2019) Chapter 8—Turbulent flow. Free-surface flow. Butterworth–Heinemann, pp 566–650

    Chapter  Google Scholar 

  42. Cong W, Shi L, Shi Z, Peng M, Yang H, Zhang S, Cheng X (2020) Effect of train fire location on maximum smoke temperature beneath the subway tunnel ceiling. Tunn Undergr Space Technol 97:10

    Article  Google Scholar 

  43. Feng S, Li Y, Hou Y, Li J, Huang Y (2020) Study on the critical velocity for smoke control in a subway tunnel cross-passage. Tunn Undergr Space Technol 97:12

    Article  Google Scholar 

  44. Gannouni S, Maad RB (2015) Numerical study of the effect of blockage on critical velocity and backlayering length in longitudinally ventilated tunnel fires. Tunn Undergr Space Technol 48:147–155

    Article  Google Scholar 

  45. McDermott RJ (2009) FDS wall flows Part I: straight channels. US Department of Commerce, National Institute of Standards and Technology

  46. Massachusetts Highway Department, and Federal Highway Administration (1995) Memorial tunnel fire test ventilation program. Commonwealth of Massachusetts, Central Artery/Tunnel Project

  47. Mégret O, Vauquelin O (2000) A model to evaluate tunnel fire characteristics. Fire Saf J 34(4):393–401

    Article  Google Scholar 

  48. Haghighat A, Luxbacher K (2019) Determination of critical parameters in the analysis of road tunnel fires. Int J Min Sci Technol 29(2):187–198

    Article  Google Scholar 

  49. Ingason H, Li YZ, Lönnermark A (2015) Scaling technique. Tunnel fire dynamics. Springer, New York, pp 473–504

    Chapter  Google Scholar 

  50. Ingason H, Li YZ, Lönnermark A (2015) Smoke stratification. Tunnel fire dynamics. Springer, New York, pp 321–332

    Chapter  Google Scholar 

  51. Miloua H, Azzi A, Wang H (2011) Evaluation of different numerical approaches for a ventilated tunnel fire. J Fire Sci 29:403–429

    Article  CAS  Google Scholar 

  52. Linstrom P (2021) NIST chemistry webBook-NIST standard reference database number 69. National Institute of Standards and Technology

    Google Scholar 

  53. Guo Q, Li YZ, Ingason H, Yan Z, Zhu H (2023) Numerical study on thermally driven smoke flow characteristics in long tunnels under natural ventilation. Int J Therm Sci 192:108379

    Article  Google Scholar 

  54. Kevin M, Randall M, Craig W, Glenn F (2013) Fire dynamics simulator users guide, 6th edn. Special Publication (NIST SP), National Institute of Standards and Technology, Gaithersburg

  55. Orloff L, De Ris J (1982) Froude modeling of pool fires. Symp (Int) on Combust 19(1):885–895

    Article  Google Scholar 

  56. McCaffrey BJ (1983) Momentum implications for buoyant diffusion flames. Combust Flame 52:149–167

    Article  ADS  CAS  Google Scholar 

  57. Tian X, Liu C, Zhong M (2021) Numerical and experimental study on the effects of a ceiling beam on the critical velocity of a tunnel fire based on virtual fire source. Int J Therm Sci 159:10

    Article  Google Scholar 

  58. Corp TD (1976) Subway environmental design handbook: principles and applications, vol I. Urban Mass Transit Administration, Washington, DC

    Google Scholar 

  59. AASHTO (2017) Road tunnel design and construction guide specifications, p. 280

  60. Bassan S (2015) Sight distance and horizontal curve aspects in the design of road tunnels vs. highways. Tunn Undergr Space Technol 45:214–226

    Article  Google Scholar 

  61. Thien Khieu H, Lee YM, Kim JT, Ryou HS (2020) Numerical study of the effects of the jet fan speed, heat release rate and aspect ratio on smoke movement in tunnel fires. Energies 13(5):16

    Article  Google Scholar 

  62. Li YZ, Ingason H, Jiang L (2018) Influence of tunnel slope on smoke control. RISE Research Institutes of Sweden

    Google Scholar 

  63. Chow WK, Gao Y, Zhao JH, Dang JF, Chow NCL (2016) A study on tilted tunnel fire under natural ventilation. Fire Saf J 81:44–57

    Article  Google Scholar 

  64. Weng M-c, Lu X-l, Liu F, Du C-x (2016) Study on the critical velocity in a sloping tunnel fire under longitudinal ventilation. Appl Therm Eng 94:422–434

    Article  Google Scholar 

  65. Yi L, Xu Q, Xu Z, Wu D (2014) An experimental study on critical velocity in sloping tunnel with longitudinal ventilation under fire. Tunn Undergr Space Technol 43:198–203

    Article  Google Scholar 

  66. Cheong M, Spearpoint M, Fleischmann C (2008) Using the peak heat release rate to determine the fire risk level of road tunnels. Proc Inst Mech Eng Part O—J Risk Reliab 222:595–604

    Google Scholar 

  67. Carvel RO (2004) Fire size in tunnels, Doctor of Philosophy. Heriot-Watt University, School of the Built Environment: 335.

  68. Lemaire T, Kenyon Y (2006) Large scale fire tests in the second benelux tunnel. Fire Technol 42(4):329–350

    Article  Google Scholar 

  69. Shipp M, Spearpoint M (1995) Measurements of the severity of fires involving private motor vehicles. Fire Mater 19(3):143–151

    Article  CAS  Google Scholar 

  70. Ingason H, Gustavsson S, Dahlberg MD (1994) Heat release rate measurements in tunnel fires. SP Swedish National Testing and Research Institute, Sweden

    Google Scholar 

  71. Montgomery D (2013) Design and analysis of experiments, 8th edn. John Wiley & Sons Inc

    Google Scholar 

  72. Shen X, Zhang G, Bjerg B (2012) Investigation of response surface methodology for modelling ventilation rate of a naturally ventilated building. Build Environ 54:174–185

    Article  Google Scholar 

  73. Box GE, Hunter WH, Hunter S (1978) Statistics for experimenters. John Wiley and Sons, New York

    Google Scholar 

  74. Box G, Draper N (2007) Response surfaces, mixtures, and ridge analyses, 2nd edn. John Wiley and Sons

    Book  Google Scholar 

  75. Li YZ, Ingason H (2018) Discussions on critical velocity and critical Froude number for smoke control in tunnels with longitudinal ventilation. Fire Saf J 99:22–26

    Article  Google Scholar 

  76. Simpson TW, Poplinski JD, Koch PN, Allen JK (2001) Metamodels for computer-based engineering design: survey and recommendations. Eng Comput 17(2):129–150

    Article  Google Scholar 

  77. Hinkelmann K, Kempthorne O (2007) Design and analysis of experiments, 2nd edn. John Wiley & Sons Inc

    Google Scholar 

  78. Jankovic A, Chaudhary G, Goia F (2021) Designing the design of experiments (DOE)—an investigation on the influence of different factorial designs on the characterization of complex systems. Energy Build 250:17

    Article  Google Scholar 

  79. Peddada SD, Umbach DM, Harris S (2012) Statistical analysis of gene expression studies with ordered experimental conditions. In: Chakraborty R, Rao CR, Sen P (eds) Handbook of statistics. Elsevier, pp 39–66

    Google Scholar 

  80. Voinovich D, Campisi B, Phan-Tan-Luu R (2009) Experimental design for mixture studies: comprehensive chemometrics. Elsevier, Oxford, pp 391–452

    Google Scholar 

  81. Cox DR, Donnelly CA (2011) Principles of applied statistics. Cambridge University Press, Cambridge

    Book  Google Scholar 

  82. Vukoslavčević PV, Šekularac MB (2022) Critical review of the common methods to determine the buoyancy-chimney effects in longitudinally-ventilated traffic tunnel fires. Adv Mech Eng 14(5):13

    Article  Google Scholar 

  83. Jiang L, Xiao M (2022) Effect of tunnel slope on the critical velocity of densimetric plumes and fire plumes in ventilated tunnels. Tunn Undergr Space Technol 123:10

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Center of Excellence in Energy Conversion, Sharif University of Technology, Tehran, Iran

    Saeid Jafari, Bijan Farhanieh & Hossein Afshin

Authors
  1. Saeid Jafari
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bijan Farhanieh
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hossein Afshin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hossein Afshin.

Ethics declarations

Conflict of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Additional information

Publisher's Note

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

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jafari, S., Farhanieh, B. & Afshin, H. Effects of Fire Parameters on Critical Velocity in Curved Tunnels: A Numerical Study and Response Surface Analysis. Fire Technol (2024). https://doi.org/10.1007/s10694-024-01548-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10694-024-01548-2

Keywords

Search

Navigation