Derivation of Dimensionless Governing Equations for Axisymmetric Incompressible Turbulent Flow Heat Transfer Based on Standard k-ϵ Model
Abstract
In this work, equations that govern axisymmetric incompressible turbulent flow for heat transfer calculations are derived assuming constant thermo-physical properties and a specific nondimensionalization scheme. Vector algebra is used for expanding vector form of governing equations in cylindrical coordinate system. Emphasis is on the derivatives of unit vectors according to azimuthal direction. Reynolds decomposition is used for separating time averaged terms and Reynolds Stress terms. Standard k-ϵ turbulence model is selected for solving closure problem due to the Reynolds stresses. Organization of the governing equations after model inputs is done explicitly. Also, parameters that constitute nondimensionalization scheme are given. Evaluations of the complete process are given. Two major aims of the work are presenting necessary equations explicitly and revealing some key steps for reorganization of the equations. It is also aimed to present novel illustrations in order to contribute comprehension of the concepts.
Thanks
This work is derived from Ph.D. thesis of Canli (2020). Canli, E, 2020. Numerical solution of transient conjugated heat transfer in thick walled pipes with turbulent flow, Ph.D Thesis, The Graduate School of Natural and Applied Science of Selçuk University, Konya, Turkey, 142 pages.
References
- Anderson, D.A., Tannehill, J.C., Pletcher, R.H., 1984. Computational Fluid Mechanics and Heat Transfer. USA, Hemisphere publishing corporation, 181-235.
- Anonymous, 2009. ANSYS FLUENT 12.0. Theory Guide. ANSYS, Inc., 4:1-4:58.
- Canli, E., 2020. Numerical solution of transient conjugated heat transfer in thick walled pipes with turbulent flow. Ph.D. Thesis, Selcuk University Institute of Sciences, Konya, Turkey, 153.
- Happel, J., Brenner, H., 2012. Low Reynolds number hydrodynamics: with special applications to particulate media. 1, Springer Science & Business Media, 474-524.
- Jayatilleke, C.L.V., 1966. The influence of Prandtl number and surface roughness on the resistance of the laminar sub-layer to momentum and heat transfer. PhD Thesis, Imperial College of Science and Technology, London, UK, 271.
- Launder, B.E., Spalding, D.B, 1974. The numerical computation of turbulent flows. Computer Methods in Applied Mechanics and Engineering, 3(2), 269-289.
- Moukalled, F., Mangani, L., Darwish, M., 2016. The finite volume method in computational fluid Dynamics. 113, Berlin, Germany, Springer, 9-82.
- Patankar, S., 1980. Numerical heat transfer and fluid flow. London, CRC Press, 25-139.
- Tennekes, H., Lumley, J., 1972. A first course in turbulence. The MIT Press, 149-248.
- Versteeg, H.K., Malalasekera, W., 2007. An introduction to computational fluid dynamics: the finite volume method. Pearson education, 40-281.
Standart k-ϵ Modeli Temelinde Eksenel Simetrik Sıkıştırılamaz Türbülanslı Akış Isı Transferi için Boyutsuz Ana Denklemlerin Türetilmesi
Abstract
Bu çalışmada, sabit termo-fiziksel özellikler kabul edilerek ve belirli bir boyutsuzlaştırma şeması kullanılarak, ısı transferi hesaplamaları için eksenel simetrik sıkıştırılamaz türbülanslı akışı yöneten ana denklemler türetilmiştir. Silindirik koordinat sisteminde ana denklemlerin vektör formlarının açılması için vektör cebri kullanılmıştır. Açısal doğrultuya göre birim vektörlerin türevleri üzerine vurgulama yapılmıştır. Zaman ortalamalı terimler ile Reynolds gerilmeleri terimlerinin ayrılması için Reynolds bileşenlerine ayırma yöntemi kullanılmıştır. Reynolds gerilmelerinden kaynaklanan kapama sorununu çözmek için standart k-ϵ türbülans modeli seçilmiştir. Model girdilerinden sonra ana denklemlerin düzenlenmesi açık olarak verilmiştir. Ayrıca boyutsuzlaştırma şemasını oluşturan parametreler verilmiştir. Bütün sürecin değerlendirmeleri verilmiştir. Çalışmanın iki ana amacı, gerekli denklemlerin açık olarak verilmesi ve denklemlerin düzenlenmesindeki bazı anahtar adımların ortaya konmasıdır. Ayrıca kavramların anlaşılmasına katkı sağlamak için özgün görsellerin sunumu amaçlanmıştır.
Keywords
Eksenel simetrik akış Silindirik koordinatlar k-ϵ Türbülans Modeli Reynolds bileşenlerine ayırma
References
- Anderson, D.A., Tannehill, J.C., Pletcher, R.H., 1984. Computational Fluid Mechanics and Heat Transfer. USA, Hemisphere publishing corporation, 181-235.
- Anonymous, 2009. ANSYS FLUENT 12.0. Theory Guide. ANSYS, Inc., 4:1-4:58.
- Canli, E., 2020. Numerical solution of transient conjugated heat transfer in thick walled pipes with turbulent flow. Ph.D. Thesis, Selcuk University Institute of Sciences, Konya, Turkey, 153.
- Happel, J., Brenner, H., 2012. Low Reynolds number hydrodynamics: with special applications to particulate media. 1, Springer Science & Business Media, 474-524.
- Jayatilleke, C.L.V., 1966. The influence of Prandtl number and surface roughness on the resistance of the laminar sub-layer to momentum and heat transfer. PhD Thesis, Imperial College of Science and Technology, London, UK, 271.
- Launder, B.E., Spalding, D.B, 1974. The numerical computation of turbulent flows. Computer Methods in Applied Mechanics and Engineering, 3(2), 269-289.
- Moukalled, F., Mangani, L., Darwish, M., 2016. The finite volume method in computational fluid Dynamics. 113, Berlin, Germany, Springer, 9-82.
- Patankar, S., 1980. Numerical heat transfer and fluid flow. London, CRC Press, 25-139.
- Tennekes, H., Lumley, J., 1972. A first course in turbulence. The MIT Press, 149-248.
- Versteeg, H.K., Malalasekera, W., 2007. An introduction to computational fluid dynamics: the finite volume method. Pearson education, 40-281.
Details
| Primary Language | English |
|---|---|
| Subjects | Engineering |
| Journal Section | Articles |
| Authors | |
| Publication Date | December 31, 2020 |
| Submission Date | November 4, 2020 |
| Published in Issue | Year 2020 Volume: 20 Issue: 6 |
