Research Papers: Energy Conversion/Systems

Large Eddy Simulation for Local Entropy Generation Analysis of Turbulent Flows

[+] Author and Article Information
M. R. H. Sheikhi

Assistant Professor
e-mail: sheikhi@neu.edu

Mehdi Safari

Graduate Research Assistant

Hameed Metghalchi

Fellow ASME
Department of Mechanical and Industrial Engineering,
Northeastern University,
Boston, MA 02115

1Corresponding author.

Contributed by the Advanced Energy Systems Division of ASME for publication in the Journal of Energy Resources Technology. Manuscript received January 11, 2012; final manuscript received August 13, 2012; published online October 19, 2012. Assoc. Editor: Muhammad M. Rahman.

J. Energy Resour. Technol 134(4), 041603 (Oct 19, 2012) (6 pages) doi:10.1115/1.4007482 History: Received January 11, 2012; Revised August 13, 2012

A new methodology is developed for local entropy generation analysis of turbulent flows using large eddy simulation (LES). The entropy transport equation is considered in LES and is solved along with continuity, momentum, and scalar transport equations. The filtered entropy equation includes several unclosed source terms that contribute to entropy generation. The closure is based on the filtered density function (FDF) methodology, extended to include the transport of entropy. An exact transport equation is derived for the FDF. The unclosed terms in this equation are modeled by considering a system of stochastic differential equations (SDEs). The methodology is employed for LES of a turbulent shear layer involving transport of passive chemical species, energy, and entropy. The local entropy generation effects are obtained from the FDF and are analyzed. It is shown that the dominant contribution to entropy generation in this flow is due to combined effects of energy transfer by heat and mass diffusion. The FDF results are assessed by comparing with those obtained by direct numerical simulation (DNS) of the same layer. The FDF predictions show favorable agreements with the DNS data.

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Herwig, H., and Kock, F., 2006, “Local Entropy Production in Turbulent Shear Flows: A Tool for Evaluating Heat Transfer Performance,” J. Therm. Sci., 15(2), pp. 159–167. [CrossRef]
Adeyinka, O. B., and Naterer, G. F., 2004, “Modeling of Entropy Production in Turbulent Flows,” ASME J. Fluids Eng., 126, pp. 893–899. [CrossRef]
Rezac, P., and Metghalchi, H., 2004, “A Brief Note on the Historical Evolution and Present State of Exergy Analysis,” Int. J. Exergy, 1(4), pp. 426–437. [CrossRef]
Nishida, K. T. T., and Kinoshita, S., 2002, “Analysis of Entropy Generation and Exergy Loss During Combustion,” Proc. Combust. Inst., 29(1), pp. 869–874. [CrossRef]
Sezer, I., Altin, I., and Bilgin, A., 2009, “Exergetic Analysis of Using Oxygenated Fuels in Spark-Ignition (SI) Engines,” Energy Fuels, 23(4), pp. 1801–1807. [CrossRef]
Datta, A., 2005, “Effects of Gravity on Structure and Entropy Generation of Confined Laminar Diffusion Flames,” Int. J. Therm. Sci., 44(5), pp. 429–440. [CrossRef]
Stanciu, D., Isvoranu, D., Marinescu, M., and Gogus, Y., 2001, “Second Law Analysis of Diffusion Flames,” Int. J. Appl. Thermodynamics, 4(1), pp. 1–18.
Li, Z. W., Chou, S. K., Shu, C., and Yang, W. M., 2005, “Entropy Generation During Microcombustion,” J. Appl. Phys., 97(8), p. 084914. [CrossRef]
Raghavan, V., Gogos, G., Babu, V., and Sundararajan, T., 2007, “Entropy Generation During the Quasi-Steady Burning of Spherical Fuel Particles,” Int. J. Therm. Sci., 46(6), pp. 589–604. [CrossRef]
Hutchins, T. E., and Metghalchi, M., 2003, “Energy and Exergy Analyses of the Pulse Detonation Engine,” ASME J. Eng. Gas Turbines Power, 125(4), pp. 1075–1080. [CrossRef]
Datta, A., and Som, S., 1999, “Energy and Exergy Balance in a Gas Turbine Combustor,” Proc. Inst. Mech. Eng. Part A, 213(1), pp. 23–32. [CrossRef]
Rakopoulos, C. D., and Giakoumis, E. G., 2006, “Second-Law Analyses Applied to Internal Combustion Engines Operation,” Prog. Energy Combust., 32(1), pp. 2–47. [CrossRef]
Yapici, H., Kayataş, N., Albayrak, B., and Baştürk, G., 2005, “Numerical Calculation of Local Entropy Generation in a Methane-Air Burner,” Energy Convers. Manage., 46(11–12), pp. 1885–1919. [CrossRef]
Lior, N., Sarmiento-Darkin, W., and Al-Sharqawi, H. S., 2006, “The Exergy Fields in Transport Processes: Their Calculation and Use,” Energy, 31(5), pp. 553–578. [CrossRef]
Ugarte, S., and Metghalchi, M., 2005, “Evolution of Adiabatic Availability and Its Depletion Through Irreversible Processes,” Int. J. Exergy, 2(2), pp. 3–13. [CrossRef]
Chavannavar, P., and Caton, J., 2006, “Destruction of Availability (Exergy) Due to Combustion Processes: A Parametric Study,” Proc. Inst. Mech. Eng. Part A, 220(7), pp. 655–668. [CrossRef]
Som, S. K., and Datta, A., 2008, “Thermodynamic Irreversibilities and Exergy Balance in Combustion Processes,” Prog. Energy Combust. Sci., 34(3), pp. 351–376. [CrossRef]
Klausner, J. F., Li, Y., Darwish, M., and Mei, R., 2004, “Innovative Diffusion Driven Desalination Process,” ASME J. Energy Resour. Technol., 126, pp. 219–225. [CrossRef]
Yilbas, B. S., 2002, “Entropy Production During Laser Picosecond Heating of Copper,” ASME J. Energy Resour. Technol., 124, pp. 204–213. [CrossRef]
Sciacovelli, A., and Verda, V., 2010, “Entropy Generation Minimization in a Tubular Solid Oxide Fuel Cell,” ASME J. Energy Resour. Technol., 132, p. 012601. [CrossRef]
Teng, H., Kinoshita, C. M., Masutani, S. M., and Zhou, J., 1998, “Entropy Generation in Multicomponent Reacting Flows,” ASME J. Energy Resour. Technol., 120(3), pp. 226–232. [CrossRef]
Call, F. W., 1998, “Dispersion—An Entropy Generator of Diffusion,” ASME J. Energy Resour. Technol., 120, pp. 149–153. [CrossRef]
Gyftopoulos, E. P., and Beretta, G. P., 1993, “Entropy Generation Rate in a Chemically Reacting System,” ASME J. Energy Resour. Technol., 115, pp. 208–212. [CrossRef]
Datta, A., 2000, “Entropy Generation in a Confined Laminar Diffusion Flame,” Combust. Sci. Technol., 159(1), pp. 39–56. [CrossRef]
Briones, A. M., Mukhopadhyay, A., and Aggarwal, S. K., 2009, “Analysis of Entropy Generation in Hydrogen-Enriched Methane-Air Propagating Triple Flames,” Int. J. Hydrogen Energy, 34(2), pp. 1074–1083. [CrossRef]
Shuja, S. Z., Yilbas, B. S., and Khan, M., 2006, “Entropy Generation in Laminar Jet: Effect of Velocity Profiles at Nozzle Exit,” Heat Mass Transfer, 42(9), pp. 771–777. [CrossRef]
Walsh, E. J., and Hernon, D., 2006, “Unsteady Volumetric Entropy Generation Rate in Laminar Boundary Layers,” Entropy, 8(1), pp. 25–30. [CrossRef]
Walsh, E. J., Mc Eligot, D. M., Brandt, L., and Schlatter, P., 2011, “Entropy Generation in a Boundary Layer Transitioning Under the Influence of Free-Stream Turbulence,” ASME J. Fluids Eng., 133, p. 061203. [CrossRef]
Khan, W. A., and Gorla, R. S. R., 2011, “Second Law Analysis for Free Convection in Non-Newtonian Fluids Over a Horizontal Plate Embedded in a Porous Medium: Prescribed Surface Temperature,” ASME J. Heat Transfer, 133, p. 052601. [CrossRef]
Okong'o, N. A., and Bellan, J., 2010, “Small-Scale Dissipation in Binary-Species, Thermodynamically Supercritical, Transitional Mixing Layers,” Comput. Fluids, 39(7), pp. 1112–1124. [CrossRef]
Shuja, S. Z., Yilbas, B. S., and Budair, M. O., 2001, “Local Entropy Generation in an Impinging Jet: Minimum Entropy Concept Evaluating Various Turbulence Models,” Comput. Meth. Appl. Mech. Eng., 190(28), pp. 3623–3644. [CrossRef]
Stanciu, D., Marinescu, M., and Dobrovicescu, A., 2007, “The Influence of Swirl Angle on the Irreversibilities in Turbulent Diffusion Flames,” Int. J. Thermodyn., 10(4), pp. 143–153.
Pope, S. B., 2000, Turbulent Flows, Cambridge University Press, Cambridge, UK.
Poinsot, T., and Veynante, D., 2005, Theoretical and Numerical Combustion, 2nd ed., R. T. Edwards, Inc., Philadelphia, PA.
Janicka, J., and Sadiki, A., 2005, “Large Eddy Simulation of Turbulent Combustion Systems,” Proc. Combust. Inst., 30, pp. 537–547. [CrossRef]
Peters, N., 2000, Turbulent Combustion, Cambridge University Press, Cambridge, UK.
Menon, S., 2000, “Subgrid Combustion Modelling for Large-Eddy Simulations,” Int. J. Engine Res., 1(2), pp. 209–227. [CrossRef]
Pitsch, H., 2006, “Large-Eddy Simulation of Turbulent Combustion,” Annu. Rev. Fluid Mech., 38, pp. 453–482. [CrossRef]
Piomelli, U., 1999, “Large-Eddy Simulation: Achievements and Challenges,” Prog. Aerosp. Sci., 35, pp. 335–362. [CrossRef]
Givi, P., 2006, “Filtered Density Function for Subgrid Scale Modeling of Turbulent Combustion,” AIAA J., 44(1), pp. 16–23. [CrossRef]
Ansari, N., Jaberi, F. A., Sheikhi, M. R. H., and Givi, P., 2011, “Filtered Density Function as a Modern CFD Tool,” Engineering Applications of CFD, Vol. 1, M. A. R. S.Al-Baghdadi, ed., International Energy and Environment Foundation, Al-Najaf, Iraq, Chap. 1, pp. 1–22.
Williams, F. A., 1985, Combustion Theory, 2nd ed., The Benjamin/Cummings Publishing Company, Menlo Park, CA.
Safari, M., Sheikhi, M. R. H., Janbozorgi, M., and Metghalchi, H., 2010, “Entropy Transport Equation in Large Eddy Simulation for Exergy Analysis of Turbulent Combustion Systems,” Entropy, 12(3), pp. 434–444. [CrossRef]
Sagaut, P., 2005, Large Eddy Simulation for Incompressible Flows, Springer-Verlag, New York, NY.
Sheikhi, M. R. H., Givi, P., and Pope, S. B., 2007, “Velocity-Scalar Filtered Mass Density Function for Large Eddy Simulation of Turbulent Reacting Flows,” Phys. Fluids, 19(9), p. 095106. [CrossRef]
Sheikhi, M. R. H., Givi, P., and Pope, S. B., 2009, “Frequency-Velocity-Scalar Filtered Mass Density Function for Large Eddy Simulation of Turbulent Flows,” Phys. Fluids, 21(7), p. 075102. [CrossRef]
O'Brien, E. E., 1980, “The Probability Density Function (PDF) Approach to Reacting Turbulent Flows,” Turbulent Reacting Flows, Vol. 44, P. A.Libby and F. A.Williams, eds., Springer-Verlag, Heidelberg, Chap. 5, pp. 185–218.
Lundgren, T. S., 1967, “Distribution Functions in the Statistical Theory of Turbulence,” Phys. Fluids, 10(5), pp. 969–975. [CrossRef]
Sheikhi, M. R. H., Drozda, T. G., Givi, P., and Pope, S. B., 2003, “Velocity-Scalar Filtered Density Function for Large Eddy Simulation of Turbulent Flows,” Phys. Fluids, 15(8), pp. 2321–2337. [CrossRef]
Karlin, S., and Taylor, H. M., 1981, A Second Course in Stochastic Processes, Academic Press, New York, NY.
Dopazo, C., 1994, “Recent Developments in PDF Methods,” Turbulent Reacting Flows, P. A.Libby and F. A.Williams, eds., Academic Press, London, England, Chap. 7, pp. 375–474.
Kloeden, P. E., Platen, E., and Schurz, H., 1997, Numerical Solution of Stochastic Differential Equations Through Computer Experiments, Corrected Second Printing Edition, Springer-Verlag, New York, NY.
Colucci, P. J., Jaberi, F. A., Givi, P., and Pope, S. B., 1998, “Filtered Density Function for Large Eddy Simulation of Turbulent Reacting Flows,” Phys. Fluids, 10(2), pp. 499–515. [CrossRef]
Jaberi, F. A., Colucci, P. J., James, S., Givi, P., and Pope, S. B., 1999, “Filtered Mass Density Function for Large Eddy Simulation of Turbulent Reacting Flows,” J. Fluid Mech., 401, pp. 85–121. [CrossRef]
Drummond, J. P., Carpenter, M. H., and Riggins, D. W., 1991, “Mixing and Mixing Enhancement in Supersonic Reacting Flow Fields,” High Speed Propulsion Systems (Progress in Astronautics and Aeronautics), Vol. 137, S. N. B.Murthy and E. T.Curran, eds., American Institute of Aeronautics and Astronautics, Chap. 7, pp. 383–455.
Kennedy, C. A., and Carpenter, M. H., 1994, “Several New Numerical Methods for Compressible Shear-Layer Simulations,” Appl. Num. Math., 14, pp. 397–433. [CrossRef]
Rogers, M. M., and Moser, R. D., 1989, “The Development of Three-Dimensional Temporally-Evolving Mixing Layers,” 7th Symposium on Turbulent Shear Flows, Stanford, CA, pp. 1–6.
Sandham, N. D., and Reynolds, W. C., 1991, “Three-Dimensional Simulations of Large Eddies in the Compressible Mixing Layer,” J. Fluid Mech., 224, pp. 133–158. [CrossRef]
Moser, R. D., and Rogers, M. M., 1993, “The Three-Dimensional Evolution of a Plane Mixing Layer: Pairing and Transition to Turbulence,” J. Fluid Mech., 247, pp. 275–320. [CrossRef]
Gicquel, L. Y. M., Givi, P., Jaberi, F. A., and Pope, S. B., 2001, “Velocity Filtered Density Function for Large Eddy Simulation of a Turbulent Mixing Layer,” DNS/LES-Progress and Challenges, C.Liu, L.Sakell, and R.Herklotz, eds., Greyden Press, Columbus, OH, pp. 327–334.
Vreman, B., Geurts, B., and Kuerten, H., 1997, “Large-Eddy Simulation of the Turbulent Mixing Layer,” J. Fluid Mech., 339, pp. 357–390. [CrossRef]


Grahic Jump Location
Fig. 1

A schematic of the 3D temporally developing mixing layer flow configuration

Grahic Jump Location
Fig. 5

The instantaneous volumetric rate of total entropy generation at t = 80 and z = 0.125 L, predicted by the FDF

Grahic Jump Location
Fig. 4

Cross-stream variation of Reynolds-averaged filtered total entropy generation at t = 80. The solid line denotes the FDF results and the circles denote the filtered DNS data.

Grahic Jump Location
Fig. 3

Cross-stream variation of Reynolds-averaged filtered entropy at t = 80. The solid line denotes the FDF results and the circles denote the filtered DNS data.

Grahic Jump Location
Fig. 2

Cross-stream variation of instantaneous filtered temperature field at t = 80, predicted by (a) FDF and (b) DNS



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