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Yumurta Kesitli Atıksu Borularının Akış Performansının Star CCM+ Hesaplamalı Akışkanlar Dinamiği Programı ile Doğrulanması

Year 2025, EARLY VIEW, 1 - 1
https://doi.org/10.2339/politeknik.1651243

Abstract

Yumurta kesitli boru hatlarının hidrolik değerlendirmelerinin dairesel kesitlere göre daha az olması sebebiyle akış performansları literatürde çok fazla bulunmamaktadır. Bu çalışmada “Experimental and Numerical Analysis of Egg-Shaped Sewer Pipes Flow Performance” adlı makaledeki deneysel ve HAD (Hesaplamalı akışkanlar dinamiği) (Ansys CFX) sonuçlarının akış performansları farklı bir yazılım ile karşılaştırılmıştır. Star CCM+, türbülanslı akış problemlerinin çözümünde kullanılan multidisipliner bir yazılım olup, doğruluğunun ortaya konması ve atıksu hidrolik analizlerinde kullanılmasının yaygınlaşması hedeflenmiştir. Deney seti, H:385 mm, R:110 mm boyutlarındaki boru hattı yumurta kesitli geometri olup, 11 m uzunluğunda %0,2 eğimlidir. SolidWorks ile deney düzeneği oluşturularak, Star CCM+ yazılımına aktarılmıştır. Yazılımda sınır koşulları, iki fazlı (su + hava) akış ve fizik şartları deneysel verilerinden yararlanılarak simüle edilmiştir. Farklı su yüksekliklerinde, h/H = 0,2, 0,3, 0,4 ve 0,5 olmak üzere işletme çalışması yapılmıştır. Belirlenen akış performans değerleri olan; deşarjlar, hız değerleri, reynolds sayıları, kayma gerilmeleri ve boru hattı orta kesit hız dağılımları deneysel ve Ansys CFX yazılımı ile karşılaştırılmıştır. Karşılaştırma sonuçlarına göre Star CCM+ yazılımında; h/H=0,20’de maksimum hızda %8,80, ortalama hız ile deşarjda %3,10 ve kayma gerilmesinde -%2,60’lık fark görülmüştür. h/H=0,30’da maksimum hızda -%3,40, ortalama hız ile deşarjda %7,40 ve kayma gerilmesinde %1,50’lik fark oluşmuştur. h/H=0,40’da maksimum hızda %5,00 fark, ortalama hız ile deşarjda %2,60 ve kayma gerilmesinde %2,50’lik fark meydana gelmiştir. h/H=0,50’de ise maksimum hızda %17,00 fark, ortalama hız ile deşarjda %2,60 fark ve kayma gerilmesinde %0,20’lik fark oluşmuştur. Bu değerlendirmelere göre, deneysel akış performans değerleri ile Star CCM+ sonuçları benzerlik göstermiştir. Böylece Star CCM+ programının akışkanların akış performans değerlendirmelerinde kullanılabileceği sonucuna varılmıştır.

References

  • [1] Regueiro-Picallo, M., Naves, J., Anta, J., Puertas, J. and Suárez, J., “Experimental and Numerical Analysis of Egg-Shaped Sewer Pipes Flow Performance”, Water, 8:1-9, (2016).
  • [2] Li, Z., Liu, S., Zhang, Q., Zhang, Z., “Analytical buckling scheme of a functionally graded porous liner reinforced by nanocomposites encased in an egg-shaped pipe”, Engineering Structures, 310: 1-11, (2024).
  • [3] Boot J.C., Naqvi M.M., Gumbel J.E., “A new method for the structural design of flexible liners for gravity pipes of egg-shaped cross section: theoretical considerations and formulation of the problem” Thin Walled Structures, 85:411-418, (2014).
  • [4] Bonakdari, H., Larrarte, F., “Experimental and numerical investigation on self-cleansing and shear stress in sewers”, Sewer Operation and Maintenance conference, Wien, Austria, (2006).
  • [5] Ashley R. M., Bertrand-Krajewski J. L., Hvitved-Jacobsen T. and Verbanck M., “Solid in sewers”, IWA Publishing, London, (2004).
  • [6] Alfadhli, I., Yang, S. and Sivakumar, M., (2013). “Velocity distribution in non-uniform/unsteady flows and the validity of log law”, SGEM 2013: 13th International Multidisciplinary Scientific Geoconference, Bulgaria, 425-432, (2013).
  • [7] Girolami, L., Sherwood, J. D. and Charru, F., “Dynamics of a slowly-varying sand bed in a circular pipe”, International Journal of Multiphase Flow, 81:113- 129, (2016).
  • [8] Turian, R.M. , Hsu, F.L. , Ma, T.W., “Estimation of the critical velocity in pipeline flow of slurries”, Powder Technology, 51: 35–47, (1987).
  • [9] Zemlyanaya, N.V., Gulyakin, A.V., “Analysis of Causes of Non-Uniform Flow Distribution in Manifold Systems with Variable Flow Rate along Length”, IOP Conference Series: Materials Science and Engineering, Chelyabinsk, Russian Federation, (2017).
  • [10] Zeghadnia, L., Djemili, L., Houichi, L., “Analytic Solution for The computation of Flow Velocity and Water Surface Angle for drainage and Sewer networks: Case of Pipes arranged in series”, International Journal of Hydrology Science and Technology, 4:58-67, (2014).
  • [11] Chow V.T, “Open channel hydraulics”, Mc Graw-Hill College, New York, (1959).
  • [12] Henderson F.M., “Open Channel Flow”, Macmillan Books, New York, (1966).
  • [13] Metcalf and Eddy, Tchobanoglou G., “Wastewater engineering: collection and pumping of Wastewater”, McGraw-Hill College, New York (1981).
  • [14] Ji, H.Y., Yoo, S.S., Koo, D.D., and Kang, J.H., “Analysis of the flow performance of the complex cross-section module to reduce the sedimentation in a combined sewer pipe”, Water, 12:1-13 (2020).
  • [15] Carlier, M., Gaston, R., “Hydraulique générale et appliquée”, Eyrolles, Paris,(1980).
  • [16] Hager, W.H., “Wastewater hydraulics theory and practice”, Springer Science and Business Media, New York, (2010).
  • [17] Polanský, J., “Experimental investigation of slurry flow”, University of Leeds, https://home. zcu. cz/~ rcermak/opvk_htt/VY_02_05. pdf [Erişim: Şubat, 2025].
  • [18] Kim, C., Lee, M., Han, C., “Hydraulic transport of sand-water mixtures in pipelines Part I. Experiment”, Journal of Mechanical Science and Technology, 22: 2534-2541, (2008).
  • [19] Wu, H., Huang, Y., Chen, L., Zhu, Y., Li, H., “Shape optimization of egg-shaped sewer pipes based on the nondominated sorting genetic algorithm (NSGA-II)”, Environmental Research, 204: 1–10, (2022).
  • [20] Yang, N., Wang, W., Ge, W., Li, J., “CFD simulation of concurrent-up gas–solid flow in circulating fluidized beds with structure-dependent drag coefficient”, Chemical Engineering Journal, 96: 71–80, (2003).
  • [21] Ranjbari, P., Ebrahimi, M., Ein-Mozaffari, F., Upreti, S., Lohi, A., “A critical review of the coupled CFD–DEM method for the simulation of two-phase liquid–solid systems”, Powder Technology, 454: 1-28, (2025).
  • [22] Bak, j., Doan, M.L., Park, S., Jeong, J.J., Yun, B., “Local two-group bubble size model for adiabatic air–water flow in a large diameter pipe using CFD code”, Case Studies in Thermal Engineering, Volume 64: 1-17, (2024).
  • [23] Ding, W., Chen, R., Tian, W., Qiu, S., Su, G.H., “Numerical investigation of dynamic characteristics of debris bed formation based on CFD-DEM method”, Annals of Nuclear Energy, 180: 1-10, (2023).
  • [24] Eom, J.H., Ra, I.S., Tak, G.Y., Tiep, N.H., Jeong, H.Y., Jung, J.H., An, S.M., “STAR-CCM+ simulation of debris bed formation in the unheated DEFCON-S experiment”, Annals of Nuclear Energy, 206: 1-8, (2024).
  • [25] Okyay, G., “Utilization of CFD tools in the design process of a Francis türbine”, Yüksek Lisans Tezi, Orta Doğu Teknik Üniversitesi, Fen Bilimleri Enstitüsü, (2010).
  • [26] Taşar, B., Üneş, F., Gemici, E., Varçin, H., “Numerical simulation of channel flow using submerged vane in river arrangements”, 2021 Air and Water – Components of the Environment Conference Proceedings, March 2021, Cluj-Napoca, Romania, (2021).
  • [27] Özdemir, Y.C., “Farklı Açılardaki Batık Kanat Yapılarının Hesaplamalı Akışkanlar Dinamiği ile İncelenmesi”, Yüksek Lisans Tezi, İskenderun Teknik Üniversitesi, Fen Bilimleri Enstitüsü, (2023).
  • [28] Aydın, M.C., “Alttan alışlı dolusavak havalandırıcıların CFD analizi”, Doktora Tezi, Fırat Üniversitesi, Fen Bilimleri Enstitüsü, (2005).
  • [29] Gimbun J., Chuah T. G., Fakhru’l-Razi A., Choong, T. S. Y., “The influence of temperature and inlet velocity on cyclone pressure drop: a CFD study”, Chemical Engineering and Processing, 44, 7-12, (2005).
  • [30] Cici İ., Dursun Ö. F., “Sayısal Model Yardımıyla Farklı Havalandırıcı Tiplerin Venturi Havalandırma Performansı Üzerindeki Etkilerinin İncelenmesi”, El-Cezerî Fen ve Mühendislik Dergisi, 9: 96-112, (2022).
  • [31] Cinosi, N., Walker, S.P., Bluck, M.J.,Issa, R., “CFD simulation of turbulent flow in a rod bundle with spacer grids (MATIS-H) using STAR-CCM+”, Nuclear Engineering and Design, 279: 37–49, (2014).
  • [32] Guo, J.; Mohebbi, A.; Zhai, Y.; Clark, S.P., “Turbulent velocity distribution with dip phenomenon in conic open channels”, Journal Hydraulic Research, 53: 73–82, (2015).
  • [33] Agbodemegbea, V.Y., Chenga, X., Akaho, E.H.K., Allote F.K.A., “Correlation for cross-flow resistance coefficient using STAR-CCM+ simulation data for flow of water through rod bundle supported by spacer grid with split-type mixing vane”, Nuclear Engineering and Design, 285: 134-149, (2015).
  • [34] Yi, L., Gang, W., Pan, N., Wang, W., Mo, S., “Fluid-Structure Coupled Analysis of the Transient Thermal Stress in an Exhaust Manifold, Fluid Dynamics and Materials Processing”, Fluid Dynamics and Materials Processing, 19: 2777-2790, (2023).
  • [35] Sugiyama, K., Ii, S., Takeuchi, S., Takagi, S., Matsumoto, Y., “A full Eulerian finite difference approach for solving fluid-structure coupling problems”, Journal of Computational Physics, 230: 596-627, (2011).
  • [36] Li, B., Cui, Y., Fu, Y., Deng, K., Tian, Y., “Marine diesel exhaust manifold failure and life prediction under high-temperature vibration, Proceedings of the Institution of Mechanical Engineers”, Journal of Mechanical Engineering Science, 236: 6180-6191, (2022).
  • [37] Pawińska, A., Piasecki, A., Dadas, N., Hożejowska, S., Piasecka, M., “Homotopy Perturbation Method with Trefftz Functions and Simcenter STAR-CCM+ used for the Analysis of Flow Boiling Heat Transfer”, Acta Mechanica et Automatica, 18: 233-243, (2024).

Verification of the Flow Performance of Egg-Section Wastewater Pipes with Star CCM+ Computational Fluid Dynamics Program

Year 2025, EARLY VIEW, 1 - 1
https://doi.org/10.2339/politeknik.1651243

Abstract

Due to the fact that hydraulic evaluations of egg-shaped pipe sections are less common than those of circular sections, their flow performance is not widely documented in the literature. In this study, the experimental and CFD (Computational Fluid Dynamics) (Ansys CFX) results from the article titled “Experimental and Numerical Analysis of Egg-Shaped Sewer Pipes Flow Performance” were compared with flow performance using a different software. Star CCM+ is a multidisciplinary software used to solve turbulent flow problems, and the aim is to demonstrate its accuracy and promote its use in wastewater hydraulic analyses. The experimental setup consists of an egg-shaped pipe geometry with dimensions H: 385 mm and R: 110 mm, and a length of 11 m with a 0.2% slope. The experimental setup was created using SolidWorks and transferred to the Star CCM+ software. In the software, boundary conditions, two-phase (water + air) flow, and physical conditions were simulated using experimental data. Operational tests were conducted at different water levels, with h/H = 0.2, 0.3, 0.4, and 0.5. The determined flow performance values, including discharges, velocity values, Reynolds numbers, shear stresses, and pipe line mid-section velocity distributions, were compared with experimental data and Ansys CFX software. According to the comparison results, in the Star CCM+ software, at h/H = 0.20, there was an 8.80% difference in maximum velocity, a 3.10% difference in average velocity and discharge, and a -2.60% difference in shear stress. At h/H=0.30, there was a difference of -3.40% in maximum velocity, 7.40% in average velocity at discharge, and 1.50% in shear stress. At h/H=0.40, there was a difference of 5.00% in maximum velocity, 2.60% in average velocity at discharge, and 2.50% in shear stress. At h/H=0.50, there was a 17.00% difference at maximum speed, a 2.60% difference at average speed during discharge, and a 0.20% difference in shear stress. According to these evaluations, experimental flow performance values and Star CCM+ results were similar. Thus, it was concluded that the Star CCM+ program can be used for evaluating the flow performance of fluids.

References

  • [1] Regueiro-Picallo, M., Naves, J., Anta, J., Puertas, J. and Suárez, J., “Experimental and Numerical Analysis of Egg-Shaped Sewer Pipes Flow Performance”, Water, 8:1-9, (2016).
  • [2] Li, Z., Liu, S., Zhang, Q., Zhang, Z., “Analytical buckling scheme of a functionally graded porous liner reinforced by nanocomposites encased in an egg-shaped pipe”, Engineering Structures, 310: 1-11, (2024).
  • [3] Boot J.C., Naqvi M.M., Gumbel J.E., “A new method for the structural design of flexible liners for gravity pipes of egg-shaped cross section: theoretical considerations and formulation of the problem” Thin Walled Structures, 85:411-418, (2014).
  • [4] Bonakdari, H., Larrarte, F., “Experimental and numerical investigation on self-cleansing and shear stress in sewers”, Sewer Operation and Maintenance conference, Wien, Austria, (2006).
  • [5] Ashley R. M., Bertrand-Krajewski J. L., Hvitved-Jacobsen T. and Verbanck M., “Solid in sewers”, IWA Publishing, London, (2004).
  • [6] Alfadhli, I., Yang, S. and Sivakumar, M., (2013). “Velocity distribution in non-uniform/unsteady flows and the validity of log law”, SGEM 2013: 13th International Multidisciplinary Scientific Geoconference, Bulgaria, 425-432, (2013).
  • [7] Girolami, L., Sherwood, J. D. and Charru, F., “Dynamics of a slowly-varying sand bed in a circular pipe”, International Journal of Multiphase Flow, 81:113- 129, (2016).
  • [8] Turian, R.M. , Hsu, F.L. , Ma, T.W., “Estimation of the critical velocity in pipeline flow of slurries”, Powder Technology, 51: 35–47, (1987).
  • [9] Zemlyanaya, N.V., Gulyakin, A.V., “Analysis of Causes of Non-Uniform Flow Distribution in Manifold Systems with Variable Flow Rate along Length”, IOP Conference Series: Materials Science and Engineering, Chelyabinsk, Russian Federation, (2017).
  • [10] Zeghadnia, L., Djemili, L., Houichi, L., “Analytic Solution for The computation of Flow Velocity and Water Surface Angle for drainage and Sewer networks: Case of Pipes arranged in series”, International Journal of Hydrology Science and Technology, 4:58-67, (2014).
  • [11] Chow V.T, “Open channel hydraulics”, Mc Graw-Hill College, New York, (1959).
  • [12] Henderson F.M., “Open Channel Flow”, Macmillan Books, New York, (1966).
  • [13] Metcalf and Eddy, Tchobanoglou G., “Wastewater engineering: collection and pumping of Wastewater”, McGraw-Hill College, New York (1981).
  • [14] Ji, H.Y., Yoo, S.S., Koo, D.D., and Kang, J.H., “Analysis of the flow performance of the complex cross-section module to reduce the sedimentation in a combined sewer pipe”, Water, 12:1-13 (2020).
  • [15] Carlier, M., Gaston, R., “Hydraulique générale et appliquée”, Eyrolles, Paris,(1980).
  • [16] Hager, W.H., “Wastewater hydraulics theory and practice”, Springer Science and Business Media, New York, (2010).
  • [17] Polanský, J., “Experimental investigation of slurry flow”, University of Leeds, https://home. zcu. cz/~ rcermak/opvk_htt/VY_02_05. pdf [Erişim: Şubat, 2025].
  • [18] Kim, C., Lee, M., Han, C., “Hydraulic transport of sand-water mixtures in pipelines Part I. Experiment”, Journal of Mechanical Science and Technology, 22: 2534-2541, (2008).
  • [19] Wu, H., Huang, Y., Chen, L., Zhu, Y., Li, H., “Shape optimization of egg-shaped sewer pipes based on the nondominated sorting genetic algorithm (NSGA-II)”, Environmental Research, 204: 1–10, (2022).
  • [20] Yang, N., Wang, W., Ge, W., Li, J., “CFD simulation of concurrent-up gas–solid flow in circulating fluidized beds with structure-dependent drag coefficient”, Chemical Engineering Journal, 96: 71–80, (2003).
  • [21] Ranjbari, P., Ebrahimi, M., Ein-Mozaffari, F., Upreti, S., Lohi, A., “A critical review of the coupled CFD–DEM method for the simulation of two-phase liquid–solid systems”, Powder Technology, 454: 1-28, (2025).
  • [22] Bak, j., Doan, M.L., Park, S., Jeong, J.J., Yun, B., “Local two-group bubble size model for adiabatic air–water flow in a large diameter pipe using CFD code”, Case Studies in Thermal Engineering, Volume 64: 1-17, (2024).
  • [23] Ding, W., Chen, R., Tian, W., Qiu, S., Su, G.H., “Numerical investigation of dynamic characteristics of debris bed formation based on CFD-DEM method”, Annals of Nuclear Energy, 180: 1-10, (2023).
  • [24] Eom, J.H., Ra, I.S., Tak, G.Y., Tiep, N.H., Jeong, H.Y., Jung, J.H., An, S.M., “STAR-CCM+ simulation of debris bed formation in the unheated DEFCON-S experiment”, Annals of Nuclear Energy, 206: 1-8, (2024).
  • [25] Okyay, G., “Utilization of CFD tools in the design process of a Francis türbine”, Yüksek Lisans Tezi, Orta Doğu Teknik Üniversitesi, Fen Bilimleri Enstitüsü, (2010).
  • [26] Taşar, B., Üneş, F., Gemici, E., Varçin, H., “Numerical simulation of channel flow using submerged vane in river arrangements”, 2021 Air and Water – Components of the Environment Conference Proceedings, March 2021, Cluj-Napoca, Romania, (2021).
  • [27] Özdemir, Y.C., “Farklı Açılardaki Batık Kanat Yapılarının Hesaplamalı Akışkanlar Dinamiği ile İncelenmesi”, Yüksek Lisans Tezi, İskenderun Teknik Üniversitesi, Fen Bilimleri Enstitüsü, (2023).
  • [28] Aydın, M.C., “Alttan alışlı dolusavak havalandırıcıların CFD analizi”, Doktora Tezi, Fırat Üniversitesi, Fen Bilimleri Enstitüsü, (2005).
  • [29] Gimbun J., Chuah T. G., Fakhru’l-Razi A., Choong, T. S. Y., “The influence of temperature and inlet velocity on cyclone pressure drop: a CFD study”, Chemical Engineering and Processing, 44, 7-12, (2005).
  • [30] Cici İ., Dursun Ö. F., “Sayısal Model Yardımıyla Farklı Havalandırıcı Tiplerin Venturi Havalandırma Performansı Üzerindeki Etkilerinin İncelenmesi”, El-Cezerî Fen ve Mühendislik Dergisi, 9: 96-112, (2022).
  • [31] Cinosi, N., Walker, S.P., Bluck, M.J.,Issa, R., “CFD simulation of turbulent flow in a rod bundle with spacer grids (MATIS-H) using STAR-CCM+”, Nuclear Engineering and Design, 279: 37–49, (2014).
  • [32] Guo, J.; Mohebbi, A.; Zhai, Y.; Clark, S.P., “Turbulent velocity distribution with dip phenomenon in conic open channels”, Journal Hydraulic Research, 53: 73–82, (2015).
  • [33] Agbodemegbea, V.Y., Chenga, X., Akaho, E.H.K., Allote F.K.A., “Correlation for cross-flow resistance coefficient using STAR-CCM+ simulation data for flow of water through rod bundle supported by spacer grid with split-type mixing vane”, Nuclear Engineering and Design, 285: 134-149, (2015).
  • [34] Yi, L., Gang, W., Pan, N., Wang, W., Mo, S., “Fluid-Structure Coupled Analysis of the Transient Thermal Stress in an Exhaust Manifold, Fluid Dynamics and Materials Processing”, Fluid Dynamics and Materials Processing, 19: 2777-2790, (2023).
  • [35] Sugiyama, K., Ii, S., Takeuchi, S., Takagi, S., Matsumoto, Y., “A full Eulerian finite difference approach for solving fluid-structure coupling problems”, Journal of Computational Physics, 230: 596-627, (2011).
  • [36] Li, B., Cui, Y., Fu, Y., Deng, K., Tian, Y., “Marine diesel exhaust manifold failure and life prediction under high-temperature vibration, Proceedings of the Institution of Mechanical Engineers”, Journal of Mechanical Engineering Science, 236: 6180-6191, (2022).
  • [37] Pawińska, A., Piasecki, A., Dadas, N., Hożejowska, S., Piasecka, M., “Homotopy Perturbation Method with Trefftz Functions and Simcenter STAR-CCM+ used for the Analysis of Flow Boiling Heat Transfer”, Acta Mechanica et Automatica, 18: 233-243, (2024).
There are 37 citations in total.

Details

Primary Language Turkish
Subjects Numerical Modelization in Civil Engineering
Journal Section Research Article
Authors

Esin Acar 0000-0002-3926-2804

Early Pub Date September 28, 2025
Publication Date October 13, 2025
Submission Date March 4, 2025
Acceptance Date July 28, 2025
Published in Issue Year 2025 EARLY VIEW

Cite

APA Acar, E. (2025). Yumurta Kesitli Atıksu Borularının Akış Performansının Star CCM+ Hesaplamalı Akışkanlar Dinamiği Programı ile Doğrulanması. Politeknik Dergisi1-1. https://doi.org/10.2339/politeknik.1651243
AMA Acar E. Yumurta Kesitli Atıksu Borularının Akış Performansının Star CCM+ Hesaplamalı Akışkanlar Dinamiği Programı ile Doğrulanması. Politeknik Dergisi. Published online September 1, 2025:1-1. doi:10.2339/politeknik.1651243
Chicago Acar, Esin. “Yumurta Kesitli Atıksu Borularının Akış Performansının Star CCM+ Hesaplamalı Akışkanlar Dinamiği Programı Ile Doğrulanması”. Politeknik Dergisi, September (September 2025), 1-1. https://doi.org/10.2339/politeknik.1651243.
EndNote Acar E (September 1, 2025) Yumurta Kesitli Atıksu Borularının Akış Performansının Star CCM+ Hesaplamalı Akışkanlar Dinamiği Programı ile Doğrulanması. Politeknik Dergisi 1–1.
IEEE E. Acar, “Yumurta Kesitli Atıksu Borularının Akış Performansının Star CCM+ Hesaplamalı Akışkanlar Dinamiği Programı ile Doğrulanması”, Politeknik Dergisi, pp. 1–1, September2025, doi: 10.2339/politeknik.1651243.
ISNAD Acar, Esin. “Yumurta Kesitli Atıksu Borularının Akış Performansının Star CCM+ Hesaplamalı Akışkanlar Dinamiği Programı Ile Doğrulanması”. Politeknik Dergisi. September2025. 1-1. https://doi.org/10.2339/politeknik.1651243.
JAMA Acar E. Yumurta Kesitli Atıksu Borularının Akış Performansının Star CCM+ Hesaplamalı Akışkanlar Dinamiği Programı ile Doğrulanması. Politeknik Dergisi. 2025;:1–1.
MLA Acar, Esin. “Yumurta Kesitli Atıksu Borularının Akış Performansının Star CCM+ Hesaplamalı Akışkanlar Dinamiği Programı Ile Doğrulanması”. Politeknik Dergisi, 2025, pp. 1-1, doi:10.2339/politeknik.1651243.
Vancouver Acar E. Yumurta Kesitli Atıksu Borularının Akış Performansının Star CCM+ Hesaplamalı Akışkanlar Dinamiği Programı ile Doğrulanması. Politeknik Dergisi. 2025:1-.