Araştırma Makalesi
BibTex RIS Kaynak Göster

Numerical Calculations for the Length of the Transitory Zone in Partially Filled Circular Pipes with Steep Slope

Yıl 2025, Cilt: 28 Sayı: 6, 1865 - 1879, 04.12.2025
https://doi.org/10.2339/politeknik.1521326
https://izlik.org/JA63TB36ML

Öz

Three-dimensional turbulent free-surface flow through smooth and corrugated circular pipes with steep slope is simulated by means of Computational Fluid Dynamics (CFD). For this purpose, the three-dimensional Reynolds Averaged Navier-Stokes equations are solved using the ANSYS Fluent solver, while interface between air and water is calculated using the Volume of Fluid (VOF) method. Effect of inlet conditions regarding the Froude and Reynolds numbers, channel slope and filling ratio on the length of flow development is investigated while both sub-critical and super-critical inlet conditions are considered. Results of the numerical calculations show that uniform open channel flow is guaranteed roughly 110 and 60 diameters downstream the pipe inlet, for smooth and corrugated pipes, respectively. The transitory length shows a tendency to decrease with the Reynolds number, contrary to the entrance length in pipe flow.

Kaynakça

  • [1] Chow, V. T., “Open-channel hydraulics”, McGraw-Hill, New York, (1959).
  • [2] Shah, R. K., and London, A. L., “Laminar Flow Forced Convection in Ducts: A Source Book for Compact Heat Exchanger Analytical Data”, Academic Press, New York, (1978).
  • [3] Patel, R. P., “A note on fully developed turbulent flow down a circular pipe”, Aeronaut. J., 78(758-759), 93-97, (1974).
  • [4] Nezu, I. and Rodi, W., “Open-channel flow measurements with a laser doppler anemometer”, J. Hydraul. Eng., 112(5), 335-355, (1986).
  • [5] Balachandar, R., Blakely, D., Tachie, M., and Putz, G., “A study on turbulent boundary layers on a smooth flat plate in an open channel”, J. Fluids Eng., 123(2), 394-400, (2001).
  • [6] Das, S., Balachandar, R., and Barron, R. M., “Generation and characterization of fully developed state in open channel flow”, Journal of Fluid Mechanics, 934, A35, (2022).
  • [7] Tominaga, A., Nezu, I., Ezaki, K., and Nakagawa, H., “Three-dimensional turbulent structure in straight open channel flows”, J. Hydraul. Res., 27(1), 149-173, (1989).
  • [8] Knight, D. W., “Boundary shear in circular pipes running partially full”, J. Hydraul. Eng., 126(4), 263-275, (2000).
  • [9] Subramanya, K., “Flow in open channels”, McGraw-Hill, New Delhi, India, (1994).
  • [10] Carstens, M. R. and Carter, R. W., “Discussion on “Hydraulics of free overfall” by A. Fathy and M. A. Shaarawi. Proc. Amer. Soc. Civil Eng., 91(HY3), 149-163, (1955).
  • [11] Bos, M. G., “Discharge measurement structures”, 3rd Ed., Publication 20, Int. Institute for Land Reclamation and Improvement/ILRI, Wageningen, The Netherlands, (1989).
  • [12] Ferro, V., “Flow Measurement with Rectangular Free Overfall”, J. Irrig. Drain. Eng., 118(6): 956-964, (1992).
  • [13] Tokyay, N. D., and Yildiz, D., “Characteristics of free overfall for supercritical flows”, Can. J. Civ. Eng., 34(2), 162-169, (2007).
  • [14] Bauer, S.W., and Graf, W.H., “Free overfall as flow measuring device”, Journal of Irrigation and Drainage Division, ASCE, 97(1), 73–83, (1971).
  • [15] Rajaratnam, N., and Muralidhar, D., “End depth for circular channels”, Journal of the Hydraulics Division, 90(2), 99-119, (1964).
  • [16] Kirkgöz, M. S. and Ardiclioglu, M. “Velocity profiles of developing and developed open channel flow”, J. Hydraul. Eng., 123(12), 1099-1105, (1997).
  • [17] Ranga Raju, K. G., Asawa, G. L. and Mishra, H. K., “Flow-Establishment Length in Rectangular Channels and Ducts”, J. Hydraul. Eng., 126(7): 533-539, (2000).
  • [18] Bonakdari, H., Lipeme-Kouyi, G. and Asawa, G. L., “Developing turbulent flows in rectangular channels: A parametric study”, J. Appl. Res. Water Wastewater, 1(2), 53-58, (2014).
  • [19] Wilkerson, G., Sharma, S. and Sapkota, D., “Length for Uniform Flow Development in a Rough Laboratory Flume”, J. Hydraul. Eng., 145(1), 06018018, (2019).
  • [20] Hyman, J. M. “Numerical Methods for Tracking Interfaces”, Physica D, 12(1-3): 396-407. (1984).
  • [21] McKee, S., Tome, M. F., Ferreira, V. G., Cuminato, J. A., Castelo, A., Sousa, F. S. and Mangiavacchi, N. “The MAC Method”, Comput. Fluids, 37: 907-930., (2008).
  • [22] Hirt, C. W., and Nichols, B. D. “Volume of Fluid Method for the Dynamics of Free Boundaries”, J. Comput. Phys., 39: 201-225., (1981).
  • [23] Hirsch, C., “Numerical Computation of Internal and External Flows”, John Wiley & Sons, (1988).
  • [24] Harten, A., “High Resolution Schemes for Hyperbolic Conservation Laws”, J. Comput. Phys., 49(3): 357-393, (1983).
  • [25] Muzaferija, S., Peric M., Sames, P. and Schelin, T., “A Two-fluid Navier-Stokes Solver to Simulate Water Entry”, Proceedings of Twenty-Second Symposium on Naval Hydrodynamics, 277-289, Washington, DC, (1998).
  • [26] Ubbink, O., “Numerical Prediction of Two Fluid Systems with Sharp Interfaces”, PhD Thesis, Imperial College of Science, Technology and Medicine, London, England, (1997).
  • [27] Menter, F. R., “Two-equation Eddy-viscosity Turbulence Models for Engineering Applications”, AIAA J., 32(8): 1598-1605, (1994).
  • [28] Schlichting, H., “Boundary Layer Theory”, McGraw-Hill Book Company, New York, (1979).
  • [29] Durst, F., Ray, S., Ünsal, B. and Bayoumi, O. A., “The Development Lengths of Laminar Pipe and Channel Flows”, J. Fluids Eng., 127(6): 1154-1160, (2005).
  • [30] Ead, S. A., Rajaratnam, N., Katopodis, C. and Ade, F., “Turbulent Open-Channel Flow in Circular Corrugated Culverts”, J. Hydraul. Eng., 126(10): 750-757, (2000).

Kısmen Dolu Yüksek Eğimli Dairesel Borularda Geçiş Bölgesi Uzunluğunun Sayısal Olarak Hesaplanması

Yıl 2025, Cilt: 28 Sayı: 6, 1865 - 1879, 04.12.2025
https://doi.org/10.2339/politeknik.1521326
https://izlik.org/JA63TB36ML

Öz

Yüksek eğimli pürüzsüz ve oluklu dairesel borulardaki üç boyutlu türbülanslı serbest yüzey akışı Hesaplamalı Akışkanlar Dinamiği (HAD) aracılığıyla hesaplanmıştır. Bu amaçla üç boyutlu Reynolds Ortalamalı Navier-Stokes denklemleri ANSYS Fluent yazılımı kullanılarak çözülürken, hava ve su arasındaki arayüzey Volume of Fluid (VOF) yöntemi kullanılarak hesaplanmıştır. Froude ve Reynolds sayıları, kanal eğimi ve doluluk oranına ilişkin giriş koşullarının akış gelişim uzunluğuna etkisi araştırılmış, kritik-altı ve kritik-üstü giriş koşulları göz önünde bulundurulmuştur. Sayısal çözüm sonuçları, dairesel pürüzsüz ve oluklu borular için boru girişinden akım altı yönünde yaklaşık 110 ve 60 çap mesafede üniform açık kanal akışının garanti edilebileceğini göstermektedir.

Kaynakça

  • [1] Chow, V. T., “Open-channel hydraulics”, McGraw-Hill, New York, (1959).
  • [2] Shah, R. K., and London, A. L., “Laminar Flow Forced Convection in Ducts: A Source Book for Compact Heat Exchanger Analytical Data”, Academic Press, New York, (1978).
  • [3] Patel, R. P., “A note on fully developed turbulent flow down a circular pipe”, Aeronaut. J., 78(758-759), 93-97, (1974).
  • [4] Nezu, I. and Rodi, W., “Open-channel flow measurements with a laser doppler anemometer”, J. Hydraul. Eng., 112(5), 335-355, (1986).
  • [5] Balachandar, R., Blakely, D., Tachie, M., and Putz, G., “A study on turbulent boundary layers on a smooth flat plate in an open channel”, J. Fluids Eng., 123(2), 394-400, (2001).
  • [6] Das, S., Balachandar, R., and Barron, R. M., “Generation and characterization of fully developed state in open channel flow”, Journal of Fluid Mechanics, 934, A35, (2022).
  • [7] Tominaga, A., Nezu, I., Ezaki, K., and Nakagawa, H., “Three-dimensional turbulent structure in straight open channel flows”, J. Hydraul. Res., 27(1), 149-173, (1989).
  • [8] Knight, D. W., “Boundary shear in circular pipes running partially full”, J. Hydraul. Eng., 126(4), 263-275, (2000).
  • [9] Subramanya, K., “Flow in open channels”, McGraw-Hill, New Delhi, India, (1994).
  • [10] Carstens, M. R. and Carter, R. W., “Discussion on “Hydraulics of free overfall” by A. Fathy and M. A. Shaarawi. Proc. Amer. Soc. Civil Eng., 91(HY3), 149-163, (1955).
  • [11] Bos, M. G., “Discharge measurement structures”, 3rd Ed., Publication 20, Int. Institute for Land Reclamation and Improvement/ILRI, Wageningen, The Netherlands, (1989).
  • [12] Ferro, V., “Flow Measurement with Rectangular Free Overfall”, J. Irrig. Drain. Eng., 118(6): 956-964, (1992).
  • [13] Tokyay, N. D., and Yildiz, D., “Characteristics of free overfall for supercritical flows”, Can. J. Civ. Eng., 34(2), 162-169, (2007).
  • [14] Bauer, S.W., and Graf, W.H., “Free overfall as flow measuring device”, Journal of Irrigation and Drainage Division, ASCE, 97(1), 73–83, (1971).
  • [15] Rajaratnam, N., and Muralidhar, D., “End depth for circular channels”, Journal of the Hydraulics Division, 90(2), 99-119, (1964).
  • [16] Kirkgöz, M. S. and Ardiclioglu, M. “Velocity profiles of developing and developed open channel flow”, J. Hydraul. Eng., 123(12), 1099-1105, (1997).
  • [17] Ranga Raju, K. G., Asawa, G. L. and Mishra, H. K., “Flow-Establishment Length in Rectangular Channels and Ducts”, J. Hydraul. Eng., 126(7): 533-539, (2000).
  • [18] Bonakdari, H., Lipeme-Kouyi, G. and Asawa, G. L., “Developing turbulent flows in rectangular channels: A parametric study”, J. Appl. Res. Water Wastewater, 1(2), 53-58, (2014).
  • [19] Wilkerson, G., Sharma, S. and Sapkota, D., “Length for Uniform Flow Development in a Rough Laboratory Flume”, J. Hydraul. Eng., 145(1), 06018018, (2019).
  • [20] Hyman, J. M. “Numerical Methods for Tracking Interfaces”, Physica D, 12(1-3): 396-407. (1984).
  • [21] McKee, S., Tome, M. F., Ferreira, V. G., Cuminato, J. A., Castelo, A., Sousa, F. S. and Mangiavacchi, N. “The MAC Method”, Comput. Fluids, 37: 907-930., (2008).
  • [22] Hirt, C. W., and Nichols, B. D. “Volume of Fluid Method for the Dynamics of Free Boundaries”, J. Comput. Phys., 39: 201-225., (1981).
  • [23] Hirsch, C., “Numerical Computation of Internal and External Flows”, John Wiley & Sons, (1988).
  • [24] Harten, A., “High Resolution Schemes for Hyperbolic Conservation Laws”, J. Comput. Phys., 49(3): 357-393, (1983).
  • [25] Muzaferija, S., Peric M., Sames, P. and Schelin, T., “A Two-fluid Navier-Stokes Solver to Simulate Water Entry”, Proceedings of Twenty-Second Symposium on Naval Hydrodynamics, 277-289, Washington, DC, (1998).
  • [26] Ubbink, O., “Numerical Prediction of Two Fluid Systems with Sharp Interfaces”, PhD Thesis, Imperial College of Science, Technology and Medicine, London, England, (1997).
  • [27] Menter, F. R., “Two-equation Eddy-viscosity Turbulence Models for Engineering Applications”, AIAA J., 32(8): 1598-1605, (1994).
  • [28] Schlichting, H., “Boundary Layer Theory”, McGraw-Hill Book Company, New York, (1979).
  • [29] Durst, F., Ray, S., Ünsal, B. and Bayoumi, O. A., “The Development Lengths of Laminar Pipe and Channel Flows”, J. Fluids Eng., 127(6): 1154-1160, (2005).
  • [30] Ead, S. A., Rajaratnam, N., Katopodis, C. and Ade, F., “Turbulent Open-Channel Flow in Circular Corrugated Culverts”, J. Hydraul. Eng., 126(10): 750-757, (2000).
Toplam 30 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Akışkan Akışı, Isı ve Kütle Transferinde Hesaplamalı Yöntemler (Hesaplamalı Akışkanlar Dinamiği Dahil)
Bölüm Araştırma Makalesi
Yazarlar

Kenan Kaya 0000-0002-6897-4077

Oktay Ozcan 0000-0003-1619-3305

Gönderilme Tarihi 23 Temmuz 2024
Kabul Tarihi 3 Mart 2025
Erken Görünüm Tarihi 27 Nisan 2025
Yayımlanma Tarihi 4 Aralık 2025
DOI https://doi.org/10.2339/politeknik.1521326
IZ https://izlik.org/JA63TB36ML
Yayımlandığı Sayı Yıl 2025 Cilt: 28 Sayı: 6

Kaynak Göster

APA Kaya, K., & Ozcan, O. (2025). Numerical Calculations for the Length of the Transitory Zone in Partially Filled Circular Pipes with Steep Slope. Politeknik Dergisi, 28(6), 1865-1879. https://doi.org/10.2339/politeknik.1521326
AMA 1.Kaya K, Ozcan O. Numerical Calculations for the Length of the Transitory Zone in Partially Filled Circular Pipes with Steep Slope. Politeknik Dergisi. 2025;28(6):1865-1879. doi:10.2339/politeknik.1521326
Chicago Kaya, Kenan, ve Oktay Ozcan. 2025. “Numerical Calculations for the Length of the Transitory Zone in Partially Filled Circular Pipes with Steep Slope”. Politeknik Dergisi 28 (6): 1865-79. https://doi.org/10.2339/politeknik.1521326.
EndNote Kaya K, Ozcan O (01 Aralık 2025) Numerical Calculations for the Length of the Transitory Zone in Partially Filled Circular Pipes with Steep Slope. Politeknik Dergisi 28 6 1865–1879.
IEEE [1]K. Kaya ve O. Ozcan, “Numerical Calculations for the Length of the Transitory Zone in Partially Filled Circular Pipes with Steep Slope”, Politeknik Dergisi, c. 28, sy 6, ss. 1865–1879, Ara. 2025, doi: 10.2339/politeknik.1521326.
ISNAD Kaya, Kenan - Ozcan, Oktay. “Numerical Calculations for the Length of the Transitory Zone in Partially Filled Circular Pipes with Steep Slope”. Politeknik Dergisi 28/6 (01 Aralık 2025): 1865-1879. https://doi.org/10.2339/politeknik.1521326.
JAMA 1.Kaya K, Ozcan O. Numerical Calculations for the Length of the Transitory Zone in Partially Filled Circular Pipes with Steep Slope. Politeknik Dergisi. 2025;28:1865–1879.
MLA Kaya, Kenan, ve Oktay Ozcan. “Numerical Calculations for the Length of the Transitory Zone in Partially Filled Circular Pipes with Steep Slope”. Politeknik Dergisi, c. 28, sy 6, Aralık 2025, ss. 1865-79, doi:10.2339/politeknik.1521326.
Vancouver 1.Kaya K, Ozcan O. Numerical Calculations for the Length of the Transitory Zone in Partially Filled Circular Pipes with Steep Slope. Politeknik Dergisi [Internet]. 01 Aralık 2025;28(6):1865-79. Erişim adresi: https://izlik.org/JA63TB36ML
 
TARANDIĞIMIZ DİZİNLER (ABSTRACTING / INDEXING)
181341319013191 13189 13187 13188 18016 

download Bu eser Creative Commons Atıf-AynıLisanslaPaylaş 4.0 Uluslararası ile lisanslanmıştır.