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FLOW CONTROL OF A CIRCULAR CYLINDER BY PERMEABLE SPLITTER PLATE WITH DIFFERENT POROSITIES AND ANGLE VALUES

Year 2024, Volume: 44 Issue: 1, 89 - 102, 03.06.2024
https://doi.org/10.47480/isibted.1494122

Abstract

Flow control of bluff bodies has been studied extensively to eliminate adverse effects of wake flow such as vibration and acoustic noise or resonance. The circular cylinder has been studied as the bluff body since it is basic geometry and has been used in engineering applications such as heat exchanger tubes, power transmission lines, chimney stacks, bridges, radio telescopes, power lines, offshore drilling rigs etc. In this study, a permeable splitter plate was located at various downstream locations to control the wake flow of the cylinder. All experiments were carried out in a large-scale closed-loop water channel in the Fluid Mechanics Laboratory at Cukurova University. PIV was used to measure the instantaneous velocity vector field in the wake region of the cylinder at Reynolds number Re=5000, which is based on the cylinder diameter, D. Four different splitter plate angle values (θ =0°; 15°; 30°; 45°), three different porosity values (ε=0.30; 0.50; 0.70) were investigated. The porosity (ε) of the separator plates is defined as the ratio of the total hole area to the plate surface area. All lengths are nondimensionalized by dividing by the cylinder diameter and shown with the * index. The splitter plate length kept to constant during the experiment as ls*=1. The distance between the leading edge of the splitter plate and the cylinder (lg*) is variable due to the rotation of the separator plate at certain angles in the flow direction. To overcome this, the distance between the splitter plate rotation axis and the cylinder was taken as a parameter and shown with the **. The gap between splitter plate midpoint and cylinder (lg**) kept to constant during the experiments as lg**=1.5. When the plates are rotated, the cross-section parallel to the flow decreases, which increases the interaction between the boundary layers. Since the permeable separator plates prevent the interaction of the boundary layers formed in the flow around the cylinder, the effect of the permeable separator plates increases in the downstream regions where the interaction of the boundary layers increases. Thus, the fluctuations are reduced, and a more stabilized trail flow occurs downstream of the cylinder. It was observed that the vortex formation was delayed with the increase of the separator plate angle. In this study, the effect of the separator plate angle and the effect of the plate permeability were clearly observed.

References

  • Adrian, Ronald J. 1991. «Particle-Imaging Techniques for Experimental Fluid Mechanics.» Annual Review of Fluid Mechanics, 261-304. doi:https://doi.org/10.1146/annurev.fl.23.010191.001401.
  • Bao, Y., ve J. Tao. 2013. «The passive control of wake flow behind a circular cylinder by parallel dual plates.» Journal of Fluids and Structures, 201-219. doi:https://doi.org/10.1016/j.jfluidstructs.2012.11.002.
  • Blevins, R. D. 1985. «The effect of sound on vortex shedding from cylinders.» J. of Fluid Mech., 217-237. doi:https://doi.org/10.1017/S0022112085002890.
  • Cardell, G. S. 1993. Flow Past a Circular Cylinder with a Permeable Wake Splitter Plate. Dissertation (Ph.D.),. California Institute of Technology. doi:10.7907/25C5-1150.
  • Chen, WL., H Li, ve H. Hu. 2014. «An experimental study on a suction flow control method to reduce the unsteadiness of the wind loads acting on a circular cylinder.» doi:https://doi.org/10.1007/s00348-014-1707-7.
  • Favier, J., A. Dauptain, D. Basso, ve A. Bottaro. 2009. «Passive separation control using a self-adaptive hairy coating.» J Fluid Mech, 451-483. doi:10.1017/S0022112009006119.
  • Gao, Dong-Lai, Guan-Bin Chen, Ye-Wei Huang, Wen-Li Chen, ve Hui Li. 2020. «Flow characteristics of a fixed circular cylinder with an upstream splitter plate: On the plate-length sensitivity.» Experimental Thermal and Fluid Science. doi:https://doi.org/10.1016/j.expthermflusci.2020.110135.
  • Ghadimi, Parviz, Saman Kermani, Sabra Razughi, ve Rahim Zamanian. 2013. «Aerodynamic and Acoustical Analysis of Flow around a Circular Cylinder in a Channel and Parametric Study on the Effects of a Splitter Plate on the Generated Vibration and Noise.» Applied Mathematics and Physics, 1-5. doi:https://doi.org/10.12691/amp-1-1-1.
  • Gozmen, Bengi, Huseyin Akilli, and Besir Sahin. 2013. "Passive control of circular cylinder wake in shallow flow." Measurement (46): 1125-1136. doi:http://dx.doi.org/10.1016/j.measurement.2012.11.008.
  • Guilmineau, P. Q. E. 2002. «A numerical simulation of vortex shedding from an oscillating circular cylinder.» J. Fluid Struct., 773-794. doi:https://doi.org/10.1006/jfls.2002.0449.
  • Huseyin Akilli, Besir Sahin, N. Filiz Tumen,. 2005. «Suppression of vortex shedding of circular cylinder in shallow water by a splitter plate.» Flow Measurement and Instrumentation, 211-219. doi:https://doi.org/10.1016/j.flowmeasinst.2005.04.004.
  • Jong-Yeon Hwang, Kyung-Soo Yang, Seung-Han Sun. 2003. «Reduction of flow-induced forces on a circular cylinder using a detached splitter plate.» Physics of Fluids, 1 8: 2433-2436. doi:https://doi.org/10.1063/1.1583733.
  • Kwon, K., & Choi, H. 1996. «Control of laminar vortex shedding behind a circular cylinder using splitter plates.» Physics of Fluids, 479-486. doi:https://doi.org/10.1063/1.868801.
  • Lecordier, J. C., L. Hamma, ve P. Parantheon. 1991. «The control vortex shedding behind heated cylinders at low Reynolds numbers.» Exp. in Fluids, 224-229. doi:https://doi.org/10.1007/BF00190392.
  • Lee, Jinmo, ve Donghyun You. 2013. «Study of vortex-shedding-induced vibration of a flexible splitter plate behind a cylinder.» Physics of Fluids. doi:https://doi.org/10.1063/1.4819346.
  • Matsumoto, Masaru, Michio Hashimoto, Tomomi Yagi, Tomoyuki Nakase, ve Kouji Maeta. 2008. «Steady Galloping/Unsteady Galloping And Vortex-Induced Vibration Of Bluff Bodies Associated With Mitigation Of Karman Vortex Shedding.» BBAA VI International Colloquium on:Bluff Bodies Aerodynamics & Applications. Milano.
  • Oruc, V., M. Akar, Akilli, H. A., ve B. Sahin. 2013. «Suppression of asymmetric flow behavior downstream of two side-by-side circular cylinders with a splitter plate in shallow water.» Measurement: Journal of the International Measurement Confederation, 442-455. doi:https://doi.org/10.1016/j.measurement.2012.07.020.
  • Ozgoren, Muammer. 2006. «Flow structure in the downstream of square and circular cylinders.» Flow Measurement and Instrumentation, 225-235. doi:https://doi.org/10.1016/j.flowmeasinst.2005.11.005.
  • Ozgoren, Muammer, Engin Pinar, Besir Sahin, ve Huseyin Akilli. 2011. «Comparison of flow structures in the downstream region of a cylinder and sphere.» International Journal of Heat and Fluid Flow, 1138-1146. doi:https://doi.org/10.1016/j.ijheatfluidflow.2011.08.003.
  • Ozkan, G.M., E Firat, ve H. Akilli. 2017. «Control of vortex shedding using a screen attached on the separation point of a circular cylinder and its effect on drag.» J. Fluids Eng. Transactions ASME, July. doi:https://doi.org/10.1115/1.4036186.
  • Pinar, Engin, Gokturk M. Ozkan, Tahir Durhasan, Muhammed M. Aksoy, ve Besir Sahin Huseyin Akilli. 2015. «Flow structure around perforated cylinders in shallow water.» Journal of Fluids and Structures, 52-63. doi:https://doi.org/10.1016/j.jfluidstructs.2015.01.017.
  • Raffel, M., Christian Willert, Steve Wereley, ve Juergen. Kompenhans. 2007. Particle Image Velocimetry. Springer.
  • Reza-zadeh, S. 2013. «Investigation of fluid flow around a cylinder with EHD actuation on inclined plates behind the cylinder.» In Proceedings of the 2013 International Conference on Applied Mathematics and Computational Methods in Engineering., 212-217.
  • Roshko, A. 1954. «On the drag and shedding frequency of two-dimensional bluff bodies.» NACA Technical Note 3169, 1-30. doi:https://doi.org/10.1.1.477.979.
  • Roshko, Anatol. 1952. On the development of turbulent wakes from vortex streets. Dissertation (Ph.D.),. California Institute of Technology. doi:10.7907/4WDN-9807.
  • Sahin, Serdar, Tahir Durhasan, Engin Pinar, ve Huseyin Akilli. 2021. «Experimental study on passive flow control of circular cylinder via perforated splitter plate.» Wind and Structures, 613-621. doi:10.12989/WAS.2021.32.6.613.
  • Tabatabaeian, S., Mirzaei, M., Sadighzadeh, A., Damideh, V., & Shadaram, A. 2015. «Experimental Study of the Flow Field around a Circular Cylinder Using Plasma Actuators.» J. Applied Fluid Mechanics, 291-299. doi:https://doi.org/10.18869/acadpub.jafm.67.221.21459.
  • Teksin, S., ve S. Yayla. 2016. «Effects of Flexible Splitter Plate in the Wake of a Cylindrical Body.» Journal of Applied Fluid Mechanics, 3053-3059. doi:10.29252/jafm.09.06.25564.
  • Weier, T., G. Gerbeth, G. Mutschke, E. Platacis, ve O. Lielausis. 1998. «Experiments on cylinder wake stabilization in an electrolyte solution by means of electromagnetic forced localized on the cylinder surface.» Exp. Therm Fluid Sci., 84-91. doi:https://doi.org/10.1016/S0894-1777(97)10008-5.
  • Westerweel, J. 1993. Digital particle image velocimetry: Theory and application, PhD Thessis. Delft University Press.
  • Xiao, Q., Sun, K., Liu, H., & Hu, J. 2011. «Computational study on near wake interaction between undulation body and a D-section cylinder.» Ocean Engineering, 3: 673-683. doi:https://doi.org/10.1016/j.oceaneng.2010.12.017.
  • Zhou, X., J. Wang, ve Y. Hu. 2019. «Experimental investigation on the flow around a circular cylinder with upstream splitter plate.» J Vis (Tokyo), 683-695. doi:10.1007/s12650-019-00560-x.

FARKLI GÖZENEKLİLİK VE AÇI DEĞERLERİNE SAHİP GEÇİRGEN AYIRICI PLAKA İLE DAİRESEL BİR SİLİNDİRİN AKIŞ KONTROLÜ

Year 2024, Volume: 44 Issue: 1, 89 - 102, 03.06.2024
https://doi.org/10.47480/isibted.1494122

Abstract

Titreşim ve akustik gürültü veya rezonans gibi iz akışının olumsuz etkilerini ortadan kaldırmak için batık gövdelerin akış kontrolü kapsamlı bir şekilde incelenmiştir. Isı eşanjör boruları, enerji nakil hatları, egzoz bacaları, köprüler, radyo teleskoplar, enerji hatları, açık deniz sondaj kuleleri vb. birçok mühendislik uygulamalarında kullanılan, silindir gövdenin iz akışını kontrol etmek için çeşitli art iz konumuna geçirgen bir ayırıcı plaka yerleştirilmiştir. Tüm deneyler, Çukurova Üniversitesi Akışkanlar Mekaniği Laboratuvarı'ndaki büyük ölçekli bir kapalı devre su kanalında, PIV kullanılarak, silindir çapına (D) bağlı olarak Re=5000'de gerçekleştirilmiştir. Dört farklı ayırıcı plaka açısı (θ =0°; 15°; 30°; 45°), üç farklı gözeneklilik (ε=0.30; 0.50; 0.70) incelenmiştir. Ayırıcı plakaların geçirgenliği (ε) plaka üzerindeki toplam delik alanının, plaka toplam alanına oranı olarak belirlenmiştir. Tüm değişkenler silindir çapına (D) bölünerek boyutsuzlaştırılmış ve * indisi ile gösterilmiştir. Ayırıcı plaka uzunluğu da deney sırasında ls*=1 olarak sabit tutulmuştur. Ayırıcı plaka ile silindir arasındaki mesafe, ayırıcı plakanın art iz eksenine göre açısı değişken olduğundan sabit değildir. Bunun üstesinden gelebilmek için silindir ile ayırıcı plaka dönme ekseni arasındaki mesafe ele alınmış ve ** indisi ile gösterilmiştir. Ayırıcı plaka orta noktası ile silindir (lg**) arasındaki boşluk, deneyler boyunca lg**=1.5 olarak sabit tutulmuştur. Plakalar döndürüldüğünde akışa paralel kesit azalmakta, bu da sınır tabakalar arasındaki etkileşimi artırmaktadır. Geçirgen ayırıcı plakalar, silindir etrafındaki akışta oluşan sınır tabakaların etkileşimini engellediğinden, sınır katmanların etkileşiminin arttığı ardıl bölgelerde geçirgen ayırıcı plakaların etkisi artmaktadır. Böylece dalgalanmalar azalmakta ve silindirin akış aşağısında daha kararlı bir iz akışı oluşmaktadır. Ayırıcı plaka açısının artmasıyla çevrinti oluşumunun geciktiği gözlenmiştir. Bu çalışmada ayırıcı plaka açısının etkisi ve plaka geçirgenliğinin etkisi net bir şekilde gözlemlenmiştir.

References

  • Adrian, Ronald J. 1991. «Particle-Imaging Techniques for Experimental Fluid Mechanics.» Annual Review of Fluid Mechanics, 261-304. doi:https://doi.org/10.1146/annurev.fl.23.010191.001401.
  • Bao, Y., ve J. Tao. 2013. «The passive control of wake flow behind a circular cylinder by parallel dual plates.» Journal of Fluids and Structures, 201-219. doi:https://doi.org/10.1016/j.jfluidstructs.2012.11.002.
  • Blevins, R. D. 1985. «The effect of sound on vortex shedding from cylinders.» J. of Fluid Mech., 217-237. doi:https://doi.org/10.1017/S0022112085002890.
  • Cardell, G. S. 1993. Flow Past a Circular Cylinder with a Permeable Wake Splitter Plate. Dissertation (Ph.D.),. California Institute of Technology. doi:10.7907/25C5-1150.
  • Chen, WL., H Li, ve H. Hu. 2014. «An experimental study on a suction flow control method to reduce the unsteadiness of the wind loads acting on a circular cylinder.» doi:https://doi.org/10.1007/s00348-014-1707-7.
  • Favier, J., A. Dauptain, D. Basso, ve A. Bottaro. 2009. «Passive separation control using a self-adaptive hairy coating.» J Fluid Mech, 451-483. doi:10.1017/S0022112009006119.
  • Gao, Dong-Lai, Guan-Bin Chen, Ye-Wei Huang, Wen-Li Chen, ve Hui Li. 2020. «Flow characteristics of a fixed circular cylinder with an upstream splitter plate: On the plate-length sensitivity.» Experimental Thermal and Fluid Science. doi:https://doi.org/10.1016/j.expthermflusci.2020.110135.
  • Ghadimi, Parviz, Saman Kermani, Sabra Razughi, ve Rahim Zamanian. 2013. «Aerodynamic and Acoustical Analysis of Flow around a Circular Cylinder in a Channel and Parametric Study on the Effects of a Splitter Plate on the Generated Vibration and Noise.» Applied Mathematics and Physics, 1-5. doi:https://doi.org/10.12691/amp-1-1-1.
  • Gozmen, Bengi, Huseyin Akilli, and Besir Sahin. 2013. "Passive control of circular cylinder wake in shallow flow." Measurement (46): 1125-1136. doi:http://dx.doi.org/10.1016/j.measurement.2012.11.008.
  • Guilmineau, P. Q. E. 2002. «A numerical simulation of vortex shedding from an oscillating circular cylinder.» J. Fluid Struct., 773-794. doi:https://doi.org/10.1006/jfls.2002.0449.
  • Huseyin Akilli, Besir Sahin, N. Filiz Tumen,. 2005. «Suppression of vortex shedding of circular cylinder in shallow water by a splitter plate.» Flow Measurement and Instrumentation, 211-219. doi:https://doi.org/10.1016/j.flowmeasinst.2005.04.004.
  • Jong-Yeon Hwang, Kyung-Soo Yang, Seung-Han Sun. 2003. «Reduction of flow-induced forces on a circular cylinder using a detached splitter plate.» Physics of Fluids, 1 8: 2433-2436. doi:https://doi.org/10.1063/1.1583733.
  • Kwon, K., & Choi, H. 1996. «Control of laminar vortex shedding behind a circular cylinder using splitter plates.» Physics of Fluids, 479-486. doi:https://doi.org/10.1063/1.868801.
  • Lecordier, J. C., L. Hamma, ve P. Parantheon. 1991. «The control vortex shedding behind heated cylinders at low Reynolds numbers.» Exp. in Fluids, 224-229. doi:https://doi.org/10.1007/BF00190392.
  • Lee, Jinmo, ve Donghyun You. 2013. «Study of vortex-shedding-induced vibration of a flexible splitter plate behind a cylinder.» Physics of Fluids. doi:https://doi.org/10.1063/1.4819346.
  • Matsumoto, Masaru, Michio Hashimoto, Tomomi Yagi, Tomoyuki Nakase, ve Kouji Maeta. 2008. «Steady Galloping/Unsteady Galloping And Vortex-Induced Vibration Of Bluff Bodies Associated With Mitigation Of Karman Vortex Shedding.» BBAA VI International Colloquium on:Bluff Bodies Aerodynamics & Applications. Milano.
  • Oruc, V., M. Akar, Akilli, H. A., ve B. Sahin. 2013. «Suppression of asymmetric flow behavior downstream of two side-by-side circular cylinders with a splitter plate in shallow water.» Measurement: Journal of the International Measurement Confederation, 442-455. doi:https://doi.org/10.1016/j.measurement.2012.07.020.
  • Ozgoren, Muammer. 2006. «Flow structure in the downstream of square and circular cylinders.» Flow Measurement and Instrumentation, 225-235. doi:https://doi.org/10.1016/j.flowmeasinst.2005.11.005.
  • Ozgoren, Muammer, Engin Pinar, Besir Sahin, ve Huseyin Akilli. 2011. «Comparison of flow structures in the downstream region of a cylinder and sphere.» International Journal of Heat and Fluid Flow, 1138-1146. doi:https://doi.org/10.1016/j.ijheatfluidflow.2011.08.003.
  • Ozkan, G.M., E Firat, ve H. Akilli. 2017. «Control of vortex shedding using a screen attached on the separation point of a circular cylinder and its effect on drag.» J. Fluids Eng. Transactions ASME, July. doi:https://doi.org/10.1115/1.4036186.
  • Pinar, Engin, Gokturk M. Ozkan, Tahir Durhasan, Muhammed M. Aksoy, ve Besir Sahin Huseyin Akilli. 2015. «Flow structure around perforated cylinders in shallow water.» Journal of Fluids and Structures, 52-63. doi:https://doi.org/10.1016/j.jfluidstructs.2015.01.017.
  • Raffel, M., Christian Willert, Steve Wereley, ve Juergen. Kompenhans. 2007. Particle Image Velocimetry. Springer.
  • Reza-zadeh, S. 2013. «Investigation of fluid flow around a cylinder with EHD actuation on inclined plates behind the cylinder.» In Proceedings of the 2013 International Conference on Applied Mathematics and Computational Methods in Engineering., 212-217.
  • Roshko, A. 1954. «On the drag and shedding frequency of two-dimensional bluff bodies.» NACA Technical Note 3169, 1-30. doi:https://doi.org/10.1.1.477.979.
  • Roshko, Anatol. 1952. On the development of turbulent wakes from vortex streets. Dissertation (Ph.D.),. California Institute of Technology. doi:10.7907/4WDN-9807.
  • Sahin, Serdar, Tahir Durhasan, Engin Pinar, ve Huseyin Akilli. 2021. «Experimental study on passive flow control of circular cylinder via perforated splitter plate.» Wind and Structures, 613-621. doi:10.12989/WAS.2021.32.6.613.
  • Tabatabaeian, S., Mirzaei, M., Sadighzadeh, A., Damideh, V., & Shadaram, A. 2015. «Experimental Study of the Flow Field around a Circular Cylinder Using Plasma Actuators.» J. Applied Fluid Mechanics, 291-299. doi:https://doi.org/10.18869/acadpub.jafm.67.221.21459.
  • Teksin, S., ve S. Yayla. 2016. «Effects of Flexible Splitter Plate in the Wake of a Cylindrical Body.» Journal of Applied Fluid Mechanics, 3053-3059. doi:10.29252/jafm.09.06.25564.
  • Weier, T., G. Gerbeth, G. Mutschke, E. Platacis, ve O. Lielausis. 1998. «Experiments on cylinder wake stabilization in an electrolyte solution by means of electromagnetic forced localized on the cylinder surface.» Exp. Therm Fluid Sci., 84-91. doi:https://doi.org/10.1016/S0894-1777(97)10008-5.
  • Westerweel, J. 1993. Digital particle image velocimetry: Theory and application, PhD Thessis. Delft University Press.
  • Xiao, Q., Sun, K., Liu, H., & Hu, J. 2011. «Computational study on near wake interaction between undulation body and a D-section cylinder.» Ocean Engineering, 3: 673-683. doi:https://doi.org/10.1016/j.oceaneng.2010.12.017.
  • Zhou, X., J. Wang, ve Y. Hu. 2019. «Experimental investigation on the flow around a circular cylinder with upstream splitter plate.» J Vis (Tokyo), 683-695. doi:10.1007/s12650-019-00560-x.
There are 32 citations in total.

Details

Primary Language Turkish
Subjects Computational Methods in Fluid Flow, Heat and Mass Transfer (Incl. Computational Fluid Dynamics)
Journal Section Research Article
Authors

Serdar Şahin 0000-0002-6451-3329

Tahir Durhasan 0000-0001-5212-9170

Engin Pınar 0000-0002-7484-8616

Hüseyin Akıllı 0000-0002-5240-8441

Publication Date June 3, 2024
Published in Issue Year 2024 Volume: 44 Issue: 1

Cite

APA Şahin, S., Durhasan, T., Pınar, E., Akıllı, H. (2024). FARKLI GÖZENEKLİLİK VE AÇI DEĞERLERİNE SAHİP GEÇİRGEN AYIRICI PLAKA İLE DAİRESEL BİR SİLİNDİRİN AKIŞ KONTROLÜ. Isı Bilimi Ve Tekniği Dergisi, 44(1), 89-102. https://doi.org/10.47480/isibted.1494122
AMA Şahin S, Durhasan T, Pınar E, Akıllı H. FARKLI GÖZENEKLİLİK VE AÇI DEĞERLERİNE SAHİP GEÇİRGEN AYIRICI PLAKA İLE DAİRESEL BİR SİLİNDİRİN AKIŞ KONTROLÜ. Isı Bilimi ve Tekniği Dergisi. June 2024;44(1):89-102. doi:10.47480/isibted.1494122
Chicago Şahin, Serdar, Tahir Durhasan, Engin Pınar, and Hüseyin Akıllı. “FARKLI GÖZENEKLİLİK VE AÇI DEĞERLERİNE SAHİP GEÇİRGEN AYIRICI PLAKA İLE DAİRESEL BİR SİLİNDİRİN AKIŞ KONTROLÜ”. Isı Bilimi Ve Tekniği Dergisi 44, no. 1 (June 2024): 89-102. https://doi.org/10.47480/isibted.1494122.
EndNote Şahin S, Durhasan T, Pınar E, Akıllı H (June 1, 2024) FARKLI GÖZENEKLİLİK VE AÇI DEĞERLERİNE SAHİP GEÇİRGEN AYIRICI PLAKA İLE DAİRESEL BİR SİLİNDİRİN AKIŞ KONTROLÜ. Isı Bilimi ve Tekniği Dergisi 44 1 89–102.
IEEE S. Şahin, T. Durhasan, E. Pınar, and H. Akıllı, “FARKLI GÖZENEKLİLİK VE AÇI DEĞERLERİNE SAHİP GEÇİRGEN AYIRICI PLAKA İLE DAİRESEL BİR SİLİNDİRİN AKIŞ KONTROLÜ”, Isı Bilimi ve Tekniği Dergisi, vol. 44, no. 1, pp. 89–102, 2024, doi: 10.47480/isibted.1494122.
ISNAD Şahin, Serdar et al. “FARKLI GÖZENEKLİLİK VE AÇI DEĞERLERİNE SAHİP GEÇİRGEN AYIRICI PLAKA İLE DAİRESEL BİR SİLİNDİRİN AKIŞ KONTROLÜ”. Isı Bilimi ve Tekniği Dergisi 44/1 (June 2024), 89-102. https://doi.org/10.47480/isibted.1494122.
JAMA Şahin S, Durhasan T, Pınar E, Akıllı H. FARKLI GÖZENEKLİLİK VE AÇI DEĞERLERİNE SAHİP GEÇİRGEN AYIRICI PLAKA İLE DAİRESEL BİR SİLİNDİRİN AKIŞ KONTROLÜ. Isı Bilimi ve Tekniği Dergisi. 2024;44:89–102.
MLA Şahin, Serdar et al. “FARKLI GÖZENEKLİLİK VE AÇI DEĞERLERİNE SAHİP GEÇİRGEN AYIRICI PLAKA İLE DAİRESEL BİR SİLİNDİRİN AKIŞ KONTROLÜ”. Isı Bilimi Ve Tekniği Dergisi, vol. 44, no. 1, 2024, pp. 89-102, doi:10.47480/isibted.1494122.
Vancouver Şahin S, Durhasan T, Pınar E, Akıllı H. FARKLI GÖZENEKLİLİK VE AÇI DEĞERLERİNE SAHİP GEÇİRGEN AYIRICI PLAKA İLE DAİRESEL BİR SİLİNDİRİN AKIŞ KONTROLÜ. Isı Bilimi ve Tekniği Dergisi. 2024;44(1):89-102.