Hesaplamalı Akışkanlar Dinamiğine Genel Bir Bakış

Nehir Tokgoz; Özge Süfer

doi:10.47495/okufbed.1191498

Derleme

An Overview About Computational Fluid Dynamics

Yıl 2023, Cilt: 6 Sayı: 3, 2392 - 2408, 04.12.2023

Nehir Tokgoz Özge Süfer

https://doi.org/10.47495/okufbed.1191498

Öz

Computational fluid dynamics (CFD) is a science that uses numerical methods, partial differential equations and computational geometry together in the analysis and solution of fluid mechanics problems, and its popularity has been increasing day by day in almost all engineering applications. This discipline, which makes applied mathematics solutions by using powerful computers, allows the realization of optimum designs by modeling heat, mass and momentum transfer as well as the flow structure in all industrial processes where flow is involved, and enables the solution of complex problems with less cost and the simultaneous analysis of multiple parameters. Basically, 3 steps are followed to solve a flow problem with CFD method. First, mathematical equations describing the flow are written, and these equations, which are usually partial differential equations, are discretized to turn into a numerical analogy, and then the flow field is divided into small meshes or elements. In the third step, these equations are solved by using initial and boundary conditions of the defined problem. Three different methods are used when solving equations: (i) finite differences; (ii) finite elements and (iii) finite volumes method. The rapid progress of the software technologies utilized in CFD and the high accuracy and precision of the software, as well as the decrease in costs day by day, have made these programs widely used in visualizing and solving flow problems more effectively and efficiently. In this review paper; the basis, history, methodology, advantages and disadvantages of CFD and the balance equations used during the solution of CFD are mentioned.

Anahtar Kelimeler

Computational fluid dynamics, Heat transfer, Mass transfer, Momentum transfer, Flow problem

Kaynakça

Ali M. H., Mehdi S. N. ve Naik M. Comparative analysis of low velocity vertical axis wind turbine NACA blades at different attacking angles in CFD. Materials Today: Proceedings 2021, (In Press).
Badas M. G., Salvadori L., Garau M., Querzoli G. ve Ferrari S. Urban areas parameterisation for CFD simulation and cities air quality analysis. International Journal of Environment and Pollution 2019; 66(1/2/3): 5.
Basri E. I., Basri A. A., Riazuddin V. N., Shahwir S., Mohammad Z. ve Ahmad K.Computational fluid dynamics study in biomedical applications: a review.International Journal of Fluids and Heat Transfer 2016; 1 (2): 2-14.
Bilen K., Tokgoz N., Solmaz İ. ve Balta T.Thermo-hydraulic performance of tube with decaying swirl flow generators.Applied Thermal Engineering 2022; 200: 117643.
Blocken B. Computational Fluid Dynamics for urban physics: Importance, scales, possibilities, limitations and ten tips and tricks towards accurate and reliable simulations.Building and Environment 2015; 91: 219-245.
Cengel Y. ve Cimbala J. Fluid Mechanics Fundamentals and Applications (SI units): McGraw Hill; 2013.
Chakraborty S. ve Ghosh S. A CFD study on the structural parameters of NACA 2412 airfoil based air-wing using different composite materials. Materials Today: Proceedings 2022; 60: 894-901.
Ding H., Visser F., Jiang Y. ve Furmanczyk M. Demonstration and validation of a 3D CFD simulation tool predicting pump performance and cavitation for industrial applications. ASME Fluids Engineering Division Summer Meeting At: Vail, CO, USA 2009; Volume: 1, Paper No. FEDSM2009-78256, pp. 277-293.
Doering C. R. ve Gibbon J. D. Applied analysis of the Navier-Stokes equations: Cambridge University Press; 1995.
Dutta R., Spence B., Wei X., Dhapare S., Hindle M. ve Longest P.CFD guided optimization of nose-to-lung aerosol delivery in adults: effects of inhalation waveforms and synchronized aerosol delivery.Pharmaceutical research 2020; 37 (10): 1-18.
Fluent I.Fluent 14.5 user guide.Fluent Inc., Lebanon. NH-03766 2002.
Godunov S. ve Bohachevsky I. Finite difference method for numerical computation of discontinuous solutions of the equations of fluid dynamics. Matematičeskij Sbornik 1959; 47 (3): 271-306.
Gurusamy P., Thirupathiraja S., Raj S. H. K. ve Kumar J. L. Experimental investigation and CFD analysis of inlet manifold in Internal combustion engine. Materials Today: Proceedings 2021; 37: 840-843.
Hadavi M. ve Pasdarshahri H. Impacts of urban buildings on microclimate and cooling systems efficiency: Coupled CFD and BES simulations. Sustainable Cities and Society 2021; 67: 102740.
Hassanzadeh R. ve Tokgoz N.Analysis of heat and fluid flow between parallel plates by inserting triangular cross-section rods in the cross-stream plane. Applied Thermal Engineering 2019; 160: 113981.
Inthavong K., Singh N., Wong E. ve Tu J. Clinical and Biomedical Engineering in the Human Nose: A Computational Fluid Dynamics Approach: Springer Nature; 2020.
Jiang J., Li C., Hu Y., Li C., He J., Leng X., Xiang J. ve Ge J. A Novel CFD-based Computed Index of Microcirculatory Resistance (IMR) Derived from Coronary Angiography to Assess Coronary Microcirculation.Computer Methods and Programs in Biomedicine 2022: 106897.
Jurado X., Reiminger N., Vazquez J. ve Wemmert C. On the minimal wind directions required to assess mean annual air pollution concentration based on CFD results.Sustainable Cities and Society 2021; 71: 102920.
Karakas E. S., Tokgöz N., Watanabe H., Aureli M. ve Evrensel C. A. Comparison of transport equation-based cavitation models and application to industrial pumps with inducers. Journal of Fluids Engineering 2022; 144 (1): 011201.
Kumar A. Analysis of heat transfer and fluid flow in different shaped roughness elements on the absorber plate solar air heater duct. Energy Procedia 2014; 57: 2102-2111.
Lax P. D.Weak solutions of nonlinear hyperbolic equations and their numerical computation. Communications on pure and applied mathematics 1954; 7(1): 159-193.
Lemus-Mondaca R. A., Vega-Gálvez A. ve Moraga N. O. Computational simulation and developments applied to food thermal processing. Food Engineering Reviews 2011; 3(3): 121-135.
Li J., Deng Y., Wang Y., Su C. ve Liu X.CFD-Based research on control strategy of the opening of active grille shutter on automobile. Case Studies in Thermal Engineering 2018; 12: 390-395.
Li Z., Deng G., Queutey P., Bouscasse B., Ducrozet G., Gentaz L., Le Touzé D. ve Ferrant P.Comparison of wave modeling methods in CFD solvers for ocean engineering applications. Ocean Engineering 2019; 188: 106237.
Malekjani N. ve Jafari S. M. Simulation of food drying processes by Computational Fluid Dynamics (CFD); recent advances and approaches.Trends in Food Science & Technology 2018; 78: 206-223.
Martínez-Ferrer P. J., Qian L., Ma Z., Causon D. M. ve Mingham C. G. Improved numerical wave generation for modelling ocean and coastal engineering problems. Ocean Engineering 2018; 152: 257-272.
Mirzaei P. A.CFD modeling of micro and urban climates: Problems to be solved in the new decade. Sustainable Cities and Society 2021; 69: 102839.
Moin P. ve Kim J. Tackling turbulence with supercomputers.Scientific American 1997; 276(1): 62-68.
Norton T. ve Sun D.-W. CFD: an innovative and effective design tool for the food industry, In: Food engineering interfaces, Eds: Springer 2010; pp. 45-68.
Norton T., Tiwari B. ve Sun D.-W. Computational fluid dynamics in the design and analysis of thermal processes: a review of recent advances. Critical reviews in food science and nutrition 2013; 53(3): 251-275.
Oberkampf W. L. ve Trucano T. G. Verification and validation in computational fluid dynamics. Progress in Aerospace Sciences 2002; 38(3): 209-272.
Ouyang T., Mo X., Lu Y. ve Wang J. CFD-vibration coupled model for predicting cavitation in gear transmissions.International Journal of Mechanical Sciences 2022: 107377.
Oyinloye T. M. ve Yoon W. B. Application of Computational Fluid Dynamics (CFD) Simulation for the Effective Design of Food 3D Printing (A Review). Processes 2021a; 9(11): 1867.
Oyinloye T. M. ve Yoon W. B. Stability of 3D printing using a mixture of pea protein and alginate: Precision and application of additive layer manufacturing simulation approach for stress distribution. Journal of Food Engineering 2021b; 288: 110127.
Richardson L. F. IX. The approximate arithmetical solution by finite differences of physical problems involving differential equations, with an application to the stresses in a masonry dam.Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character 1911; 210 (459-470): 307-357.
Richardson L. F. Weather Prediction by numerical process: Richardson, Lewis F (ry); With a new introd. by Sydney Chapman: Dover Publ.;1965.
Sadaq S. I., Mehdi S. N., Mehdi S. D. ve Yasear S.Analysis of NACA 0020 aerofoil profile rotor blade using CFD approach.Materials Today: Proceedings 2022.
Sagaut P., Terracol M. ve Deck S. Multiscale and multiresolution approaches in turbulence-LES, DES and Hybrid RANS/LES Methods: Applications and Guidelines: World Scientific; 2013; 448 pages.
Schaldach G., Berger L., Razilov I. ve Berndt H.Computer simulation for fundamental studies and optimisation of ICP spray chambers.ISAS (Institute of Spectrochemistry and Applied Spectroscopy) Current Research Reports, Berlin, Germany 2000.
Sethian J.Computational fluid dynamics.From Desktop to teraflop: Exploiting the US lead in high performance computing. NSF Publications, National Science Foundation, Washington, DC, USA 1993.
Shinde S., Mukhopadhyay S. ve Mukhopadhyay S. Investigation of flow in an idealized curved artery: Comparative study using CFD and FSI with Newtonian and Non-Newtonian fluids. Journal of Mechanics in Medicine and Biology 2022; 22 (02): 2250010.
Smale N., Moureh J. ve Cortella G. A review of numerical models of airflow in refrigerated food applications. International Journal of Refrigeration 2006; 29 (6): 911-930.
Southwell R. Relaxation Methods in Engineering Science. Oxford University Press 1940.
Tokgoz N., Aksoy M. ve Sahin B. Investigation of flow characteristics and heat transfer enhancement of corrugated duct geometries.Applied Thermal Engineering 2017; 118: 518-530.
Tokgoz N., Alıç E., Kaşka Ö. ve Aksoy M. The numerical study of heat transfer enhancement using Al2O3-water nanofluid in corrugated duct application. Journal of Thermal Engineering 2018; 4 (3): 1984-1997.
Tokgoz N.Experimental and numerical investigation of flow structure in a cylindrical corrugated channel.International Journal of Mechanical Sciences 2019; 157: 787-801.
Triscone G., Abdennadher N., Balistreri C., Donzé O., Greco D., Haas P., Haas-Peköz H., Mohamed-Nour T., Munier P. ve Pontelandolfo P.Computational fluid dynamics as a tool to predict the air pollution dispersion in a neighborhood–a research project to improve the quality of life in cities.International Journal of Sustainable Development and Planning 2016; 11 (4): 546-557.
Uddin M. J. ve Yousuf M. S. I.Numerical Simulation of CFD and Fluid-Structure-Interaction (FSI) of Steady Flow in a Stenotic Vessel.Open Journal of Modelling and Simulation 2022; 10(3): 255-266.
Xia B. ve Sun D.-W.Applications of computational fluid dynamics (CFD) in the food industry: a review. Computers and Electronics In Agriculture 2002; 34(1-3): 5-24.
Yue G., Zhang H., Zhao C. ve Luo Z. Proceedings of the 20th International Conference on Fluidized Bed Combustion: Springer Science & Business Media; 2010.
Zhang H., Xia B., Kong F., Li G. ve Cao P. Experimental investigation of cavitation characteristics for a high-speed inducer with a great flow rate. Advances in Mechanical Engineering 2022; 14(3): 16878132221087510.

Hesaplamalı Akışkanlar Dinamiğine Genel Bir Bakış

Yıl 2023, Cilt: 6 Sayı: 3, 2392 - 2408, 04.12.2023

Nehir Tokgoz Özge Süfer

https://doi.org/10.47495/okufbed.1191498

Öz

Hesaplamalı akışkanlar dinamiği (HAD), akışkanlar mekaniği problemlerinin analiz edilmesi ve çözümlenmesi sırasında sayısal yöntemleri, kısmi diferansiyel denklemleri ve hesaplamalı geometriyi bir arada kullanan ve hemen hemen bütün mühendislik uygulamalarında popülerliği günden güne artan bir bilim dalıdır. Güçlü bilgisayarlar kullanarak uygulamalı matematik çözümü yapan bu bilim, akışın söz konusu olduğu bütün endüstriyel proseslerde ısı, kütle ve momentum transferini ve aynı zamanda akış yapısını modelleyerek optimum tasarımların gerçekleşmesine imkân vermekte ve daha az zamanda daha az maliyetle karmaşık problemlerin çözümüne ve birden fazla parametrenin aynı anda incelenmesine olanak sağlamaktadır. Bir akış problemini HAD yöntemiyle çözmek için temelde 3 adım takip edilmektedir. İlk olarak akışı tanımlayan matematiksel denklemler yazılmakta ve genellikle kısmi diferansiyel denklemlerden oluşan bu eşitlikler sayısal bir analojiye dönüştürülmek için ayrıklaştırılmakta (discretization) ve de sonrasında akış alanı küçük ağlara (mesh) veya elemanlara bölünmektedir. Üçüncü adımda ise tanımlanan problemin başlangıç ve sınır şartları kullanılarak bu denklemler çözülmektedir. Denklemler çözülürken üç farklı metot kullanılmaktadır: (i) sonlu farklar; (ii) sonlu elemanlar ve (iii) sonlu hacimler yöntemi. HAD’da kullanılan yazılım teknolojilerinin hızla ilerlemesi ve yazılımların yüksek doğruluk ve hassasiyete sahip olmasıyla beraber maliyetlerinin günden güne azalması, akış problemlerinin görselleştirilmesinde ve problemlerin daha etkili ve verimli çözülmesinde bu programların yaygın bir şekilde kullanılmasını sağlamıştır. Bu derleme çalışmada; HAD’ın temelinden, tarihinden, metodolojisinden, avantajlarından ve dezavantajlarından ve HAD’da çözüm sırasında kullanılan denge denklemlerinden bahsedilmiştir.

Anahtar Kelimeler

Hesaplamalı akışkanlar dinamiği, Isı transferi, Kütle transferi, Momentum transferi, Akış problemi

Kaynakça

Ali M. H., Mehdi S. N. ve Naik M. Comparative analysis of low velocity vertical axis wind turbine NACA blades at different attacking angles in CFD. Materials Today: Proceedings 2021, (In Press).
Badas M. G., Salvadori L., Garau M., Querzoli G. ve Ferrari S. Urban areas parameterisation for CFD simulation and cities air quality analysis. International Journal of Environment and Pollution 2019; 66(1/2/3): 5.
Basri E. I., Basri A. A., Riazuddin V. N., Shahwir S., Mohammad Z. ve Ahmad K.Computational fluid dynamics study in biomedical applications: a review.International Journal of Fluids and Heat Transfer 2016; 1 (2): 2-14.
Bilen K., Tokgoz N., Solmaz İ. ve Balta T.Thermo-hydraulic performance of tube with decaying swirl flow generators.Applied Thermal Engineering 2022; 200: 117643.
Blocken B. Computational Fluid Dynamics for urban physics: Importance, scales, possibilities, limitations and ten tips and tricks towards accurate and reliable simulations.Building and Environment 2015; 91: 219-245.
Cengel Y. ve Cimbala J. Fluid Mechanics Fundamentals and Applications (SI units): McGraw Hill; 2013.
Chakraborty S. ve Ghosh S. A CFD study on the structural parameters of NACA 2412 airfoil based air-wing using different composite materials. Materials Today: Proceedings 2022; 60: 894-901.
Ding H., Visser F., Jiang Y. ve Furmanczyk M. Demonstration and validation of a 3D CFD simulation tool predicting pump performance and cavitation for industrial applications. ASME Fluids Engineering Division Summer Meeting At: Vail, CO, USA 2009; Volume: 1, Paper No. FEDSM2009-78256, pp. 277-293.
Doering C. R. ve Gibbon J. D. Applied analysis of the Navier-Stokes equations: Cambridge University Press; 1995.
Dutta R., Spence B., Wei X., Dhapare S., Hindle M. ve Longest P.CFD guided optimization of nose-to-lung aerosol delivery in adults: effects of inhalation waveforms and synchronized aerosol delivery.Pharmaceutical research 2020; 37 (10): 1-18.
Fluent I.Fluent 14.5 user guide.Fluent Inc., Lebanon. NH-03766 2002.
Godunov S. ve Bohachevsky I. Finite difference method for numerical computation of discontinuous solutions of the equations of fluid dynamics. Matematičeskij Sbornik 1959; 47 (3): 271-306.
Gurusamy P., Thirupathiraja S., Raj S. H. K. ve Kumar J. L. Experimental investigation and CFD analysis of inlet manifold in Internal combustion engine. Materials Today: Proceedings 2021; 37: 840-843.
Hadavi M. ve Pasdarshahri H. Impacts of urban buildings on microclimate and cooling systems efficiency: Coupled CFD and BES simulations. Sustainable Cities and Society 2021; 67: 102740.
Hassanzadeh R. ve Tokgoz N.Analysis of heat and fluid flow between parallel plates by inserting triangular cross-section rods in the cross-stream plane. Applied Thermal Engineering 2019; 160: 113981.
Inthavong K., Singh N., Wong E. ve Tu J. Clinical and Biomedical Engineering in the Human Nose: A Computational Fluid Dynamics Approach: Springer Nature; 2020.
Jiang J., Li C., Hu Y., Li C., He J., Leng X., Xiang J. ve Ge J. A Novel CFD-based Computed Index of Microcirculatory Resistance (IMR) Derived from Coronary Angiography to Assess Coronary Microcirculation.Computer Methods and Programs in Biomedicine 2022: 106897.
Jurado X., Reiminger N., Vazquez J. ve Wemmert C. On the minimal wind directions required to assess mean annual air pollution concentration based on CFD results.Sustainable Cities and Society 2021; 71: 102920.
Karakas E. S., Tokgöz N., Watanabe H., Aureli M. ve Evrensel C. A. Comparison of transport equation-based cavitation models and application to industrial pumps with inducers. Journal of Fluids Engineering 2022; 144 (1): 011201.
Kumar A. Analysis of heat transfer and fluid flow in different shaped roughness elements on the absorber plate solar air heater duct. Energy Procedia 2014; 57: 2102-2111.
Lax P. D.Weak solutions of nonlinear hyperbolic equations and their numerical computation. Communications on pure and applied mathematics 1954; 7(1): 159-193.
Lemus-Mondaca R. A., Vega-Gálvez A. ve Moraga N. O. Computational simulation and developments applied to food thermal processing. Food Engineering Reviews 2011; 3(3): 121-135.
Li J., Deng Y., Wang Y., Su C. ve Liu X.CFD-Based research on control strategy of the opening of active grille shutter on automobile. Case Studies in Thermal Engineering 2018; 12: 390-395.
Li Z., Deng G., Queutey P., Bouscasse B., Ducrozet G., Gentaz L., Le Touzé D. ve Ferrant P.Comparison of wave modeling methods in CFD solvers for ocean engineering applications. Ocean Engineering 2019; 188: 106237.
Malekjani N. ve Jafari S. M. Simulation of food drying processes by Computational Fluid Dynamics (CFD); recent advances and approaches.Trends in Food Science & Technology 2018; 78: 206-223.
Martínez-Ferrer P. J., Qian L., Ma Z., Causon D. M. ve Mingham C. G. Improved numerical wave generation for modelling ocean and coastal engineering problems. Ocean Engineering 2018; 152: 257-272.
Mirzaei P. A.CFD modeling of micro and urban climates: Problems to be solved in the new decade. Sustainable Cities and Society 2021; 69: 102839.
Moin P. ve Kim J. Tackling turbulence with supercomputers.Scientific American 1997; 276(1): 62-68.
Norton T. ve Sun D.-W. CFD: an innovative and effective design tool for the food industry, In: Food engineering interfaces, Eds: Springer 2010; pp. 45-68.
Norton T., Tiwari B. ve Sun D.-W. Computational fluid dynamics in the design and analysis of thermal processes: a review of recent advances. Critical reviews in food science and nutrition 2013; 53(3): 251-275.
Oberkampf W. L. ve Trucano T. G. Verification and validation in computational fluid dynamics. Progress in Aerospace Sciences 2002; 38(3): 209-272.
Ouyang T., Mo X., Lu Y. ve Wang J. CFD-vibration coupled model for predicting cavitation in gear transmissions.International Journal of Mechanical Sciences 2022: 107377.
Oyinloye T. M. ve Yoon W. B. Application of Computational Fluid Dynamics (CFD) Simulation for the Effective Design of Food 3D Printing (A Review). Processes 2021a; 9(11): 1867.
Oyinloye T. M. ve Yoon W. B. Stability of 3D printing using a mixture of pea protein and alginate: Precision and application of additive layer manufacturing simulation approach for stress distribution. Journal of Food Engineering 2021b; 288: 110127.
Richardson L. F. IX. The approximate arithmetical solution by finite differences of physical problems involving differential equations, with an application to the stresses in a masonry dam.Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character 1911; 210 (459-470): 307-357.
Richardson L. F. Weather Prediction by numerical process: Richardson, Lewis F (ry); With a new introd. by Sydney Chapman: Dover Publ.;1965.
Sadaq S. I., Mehdi S. N., Mehdi S. D. ve Yasear S.Analysis of NACA 0020 aerofoil profile rotor blade using CFD approach.Materials Today: Proceedings 2022.
Sagaut P., Terracol M. ve Deck S. Multiscale and multiresolution approaches in turbulence-LES, DES and Hybrid RANS/LES Methods: Applications and Guidelines: World Scientific; 2013; 448 pages.
Schaldach G., Berger L., Razilov I. ve Berndt H.Computer simulation for fundamental studies and optimisation of ICP spray chambers.ISAS (Institute of Spectrochemistry and Applied Spectroscopy) Current Research Reports, Berlin, Germany 2000.
Sethian J.Computational fluid dynamics.From Desktop to teraflop: Exploiting the US lead in high performance computing. NSF Publications, National Science Foundation, Washington, DC, USA 1993.
Shinde S., Mukhopadhyay S. ve Mukhopadhyay S. Investigation of flow in an idealized curved artery: Comparative study using CFD and FSI with Newtonian and Non-Newtonian fluids. Journal of Mechanics in Medicine and Biology 2022; 22 (02): 2250010.
Smale N., Moureh J. ve Cortella G. A review of numerical models of airflow in refrigerated food applications. International Journal of Refrigeration 2006; 29 (6): 911-930.
Southwell R. Relaxation Methods in Engineering Science. Oxford University Press 1940.
Tokgoz N., Aksoy M. ve Sahin B. Investigation of flow characteristics and heat transfer enhancement of corrugated duct geometries.Applied Thermal Engineering 2017; 118: 518-530.
Tokgoz N., Alıç E., Kaşka Ö. ve Aksoy M. The numerical study of heat transfer enhancement using Al2O3-water nanofluid in corrugated duct application. Journal of Thermal Engineering 2018; 4 (3): 1984-1997.
Tokgoz N.Experimental and numerical investigation of flow structure in a cylindrical corrugated channel.International Journal of Mechanical Sciences 2019; 157: 787-801.
Triscone G., Abdennadher N., Balistreri C., Donzé O., Greco D., Haas P., Haas-Peköz H., Mohamed-Nour T., Munier P. ve Pontelandolfo P.Computational fluid dynamics as a tool to predict the air pollution dispersion in a neighborhood–a research project to improve the quality of life in cities.International Journal of Sustainable Development and Planning 2016; 11 (4): 546-557.
Uddin M. J. ve Yousuf M. S. I.Numerical Simulation of CFD and Fluid-Structure-Interaction (FSI) of Steady Flow in a Stenotic Vessel.Open Journal of Modelling and Simulation 2022; 10(3): 255-266.
Xia B. ve Sun D.-W.Applications of computational fluid dynamics (CFD) in the food industry: a review. Computers and Electronics In Agriculture 2002; 34(1-3): 5-24.
Yue G., Zhang H., Zhao C. ve Luo Z. Proceedings of the 20th International Conference on Fluidized Bed Combustion: Springer Science & Business Media; 2010.
Zhang H., Xia B., Kong F., Li G. ve Cao P. Experimental investigation of cavitation characteristics for a high-speed inducer with a great flow rate. Advances in Mechanical Engineering 2022; 14(3): 16878132221087510.

Toplam 51 adet kaynakça vardır.

Ayrıntılar

Birincil Dil	Türkçe
Konular	Gıda Mühendisliği
Bölüm	Derlemeler (REVIEWS)
Yazarlar	Nehir Tokgoz 0000-0001-9264-9971 Özge Süfer 0000-0001-8337-6318
Yayımlanma Tarihi	4 Aralık 2023
Gönderilme Tarihi	19 Ekim 2022
Kabul Tarihi	12 Nisan 2023
Yayımlandığı Sayı	Yıl 2023 Cilt: 6 Sayı: 3

Kaynak Göster

APA	Tokgoz, N., & Süfer, Ö. (2023). Hesaplamalı Akışkanlar Dinamiğine Genel Bir Bakış. Osmaniye Korkut Ata Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 6(3), 2392-2408. https://doi.org/10.47495/okufbed.1191498
AMA	Tokgoz N, Süfer Ö. Hesaplamalı Akışkanlar Dinamiğine Genel Bir Bakış. OKÜ Fen Bil. Ens. Dergisi ((OKU Journal of Nat. & App. Sci). Aralık 2023;6(3):2392-2408. doi:10.47495/okufbed.1191498
Chicago	Tokgoz, Nehir, ve Özge Süfer. “Hesaplamalı Akışkanlar Dinamiğine Genel Bir Bakış”. Osmaniye Korkut Ata Üniversitesi Fen Bilimleri Enstitüsü Dergisi 6, sy. 3 (Aralık 2023): 2392-2408. https://doi.org/10.47495/okufbed.1191498.
EndNote	Tokgoz N, Süfer Ö (01 Aralık 2023) Hesaplamalı Akışkanlar Dinamiğine Genel Bir Bakış. Osmaniye Korkut Ata Üniversitesi Fen Bilimleri Enstitüsü Dergisi 6 3 2392–2408.
IEEE	N. Tokgoz ve Ö. Süfer, “Hesaplamalı Akışkanlar Dinamiğine Genel Bir Bakış”, OKÜ Fen Bil. Ens. Dergisi ((OKU Journal of Nat. & App. Sci), c. 6, sy. 3, ss. 2392–2408, 2023, doi: 10.47495/okufbed.1191498.
ISNAD	Tokgoz, Nehir - Süfer, Özge. “Hesaplamalı Akışkanlar Dinamiğine Genel Bir Bakış”. Osmaniye Korkut Ata Üniversitesi Fen Bilimleri Enstitüsü Dergisi 6/3 (Aralık 2023), 2392-2408. https://doi.org/10.47495/okufbed.1191498.
JAMA	Tokgoz N, Süfer Ö. Hesaplamalı Akışkanlar Dinamiğine Genel Bir Bakış. OKÜ Fen Bil. Ens. Dergisi ((OKU Journal of Nat. & App. Sci). 2023;6:2392–2408.
MLA	Tokgoz, Nehir ve Özge Süfer. “Hesaplamalı Akışkanlar Dinamiğine Genel Bir Bakış”. Osmaniye Korkut Ata Üniversitesi Fen Bilimleri Enstitüsü Dergisi, c. 6, sy. 3, 2023, ss. 2392-08, doi:10.47495/okufbed.1191498.
Vancouver	Tokgoz N, Süfer Ö. Hesaplamalı Akışkanlar Dinamiğine Genel Bir Bakış. OKÜ Fen Bil. Ens. Dergisi ((OKU Journal of Nat. & App. Sci). 2023;6(3):2392-408.