Derivation of entropy production in a fluid flow in a general curvilinear coordinate system

Erik Flídr

doi:10.14311/AP.2023.63.0103

Authors

Erik Flídr Czech Technical University in Prague, Faculty of Mechanical Engineering, Technická 4, 160 00 Prague 6 – Dejvice, Czech Republic

DOI:

https://doi.org/10.14311/AP.2023.63.0103

Keywords:

entropy production, fluid flow, general curvilinear coordinates, linear blade cascade, experimental data

Abstract

The paper deals with the derivation of the entropy production in the fluid flow performed in a general curvilinear coordinate system. The derivation of the entropy production is based on the thermodynamics laws as well as on the balances of mass, momentum, and energy. A brief description of the differential geometry used in general curvilinear coordinates is presented here as well to define the used notation.
The application of this approach is then shown in the evaluation of the entropy production along the suction side of the blade, where the calculation was performed using available experimental data.

Downloads

Download data is not yet available.

References

C. Truesdell. The physical components of vectors and tensors. Journal of Applied Mathematics and Mechanics 33(10–11):345–356, 1953. https://doi.org/10.1002/zamm.19530331005

R. Aris. Vectors, Tensors and the Basic Equations of Fluid Mechanics. Dover Publications, 1989.

V. Ivancevic, T. Ivancevic. Applied Differential Geometry: A Modern Introduction. World Scientific, 2007. https://doi.org/10.1142/6420

S. Surattana. Transformation of the Navier-Stokes equations in curvilinear coordinate system with Mapel. Global Journal of Pure and Applied Mathematics 12(4):3315–3325, 2016.

L. Swungoho, S. Bharat. Governing equations of fluid mechanics in physical curvilinear coordinate system. In Third Mississippi State Conference on Difference Equations and Computational Simulations, pp. 149–157. 1997.

P. Asinari, E. Chiavazzo. Overview of the entropy production of incompressible and compressible fluid dynamics. Meccanica 51:1–10, 2015. https://doi.org/10.1007/s11012-015-0284-z

J. Kvasnica. Termodynamika. SNTL, 1965.

A. Bejan. Entropy generation minimization. CRC Press LCC, 2013.

F. Maršík. Termodynamika kontinua. Academia, 1999.

L. Landau, E. Lifschitz. Fluid Mechanics. Pergamon Press, 1987.

A. Perdichizzi, V. Dossena. Incidence angle and pitch–chord effects on secondary flows downstream of a turbine cascade. Journal of Turbomachinerytransactions of The Asme 115(3):383–391, 1993. https://doi.org/10.1115/1.2929265