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A scaling law for the recirculation zone length behind a bluff body in reacting flows

Published online by Cambridge University Press:  22 July 2019

James C. Massey Open the ORCID record for James C. Massey [Opens in a new window] ,
Ivan Langella  and
Nedunchezhian Swaminathan Open the ORCID record for Nedunchezhian Swaminathan [Opens in a new window]
James C. Massey*
Affiliation:
Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK
Ivan Langella*
Affiliation:
Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK
Nedunchezhian Swaminathan
Affiliation:
Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK
*
†Email address for correspondence: : [email protected], [email protected]
†Email address for correspondence: : [email protected], [email protected]
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Abstract

The recirculation zone length behind a bluff body is influenced by the turbulence intensity at the base of the body in isothermal flows and also the heat release and its interaction with turbulence in reacting flows. This relationship is observed to be nonlinear and is controlled by the balance of forces acting on the recirculation zone, which arise from the pressure and turbulence fields. The pressure force is directly influenced by the volumetric expansion resulting from the heat release, whereas the change in the turbulent shear force depends on the nonlinear interaction between turbulence and combustion. This behaviour is elucidated through a control volume analysis. A scaling relation for the recirculation zone length is deduced to relate the turbulence intensity and the amount of heat release. This relation is verified using the large eddy simulation data from 20 computations of isothermal flows and premixed flames that are stabilised behind the bluff body. The application of this scaling to flames in an open environment and behind a backward facing step is also explored. The observations and results are explained on a physical basis.

JFM classification

Reacting Flows: Combustion Reacting Flows: Turbulent reacting flows Wakes/Jets: Wakes
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 875 , 25 September 2019 , pp. 699 - 724
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Copyright
© 2019 Cambridge University Press 

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Footnotes

‡

Present address: Department of Aeronautical and Automotive Engineering,Loughborough University, Loughborough LE11 3TU, UK.

References

Ahmed, I. & Swaminathan, N. 2013 Simulation of spherically expanding turbulent premixed flames. Combust. Sci. Technol. 185 (10), 1509–1540.10.1080/00102202.2013.808629Google Scholar
Ahmed, I. & Swaminathan, N. 2014 Simulation of turbulent explosion of hydrogen-air mixtures. Intl J. Hydrog. Energy 39 (17), 9562–9572.10.1016/j.ijhydene.2014.03.246Google Scholar
Ahmed, U., Doan, N. A. K., Lai, J., Klein, M., Chakraborty, N. & Swaminathan, N. 2018 Multiscale analysis of head-on quenching premixed turbulent flames. Phys. Fluids 30, 105102.10.1063/1.5047061Google Scholar
Anand, M. S., Zhu, J., Connor, C. & Razdan, M. K. 1999 Combustor flow analysis using an advanced finite-volume design system. In Vol. 2: Coal, Biomass and Alternative Fuels; Combustion and Fuels; Oil and Gas Applications; Cycle Innovations. ASME. Turbo Expo: Power for Land, Sea, and Air.Google Scholar
Bai, X.-S. & Fuchs, L. 1994 Modelling of turbulent reacting flows past a bluff body: assessment of accuracy and efficiency. Comput. Fluids 23 (3), 507–521.10.1016/0045-7930(94)90016-7Google Scholar
Bill, R. G. Jr. & Tarabanis, K. 1986 The effect of premixed combustion on the recirculation zone of circular cylinders. Combust. Sci. Technol. 47 (1–2), 39–53.10.1080/00102208608923863Google Scholar
Bradbury, L. J. S. 1976 Measurements with a pulsed-wire and a hot-wire anemometer in the highly turbulent wake of a normal flat plate. J. Fluid Mech. 77 (3), 473–497.10.1017/S0022112076002218Google Scholar
Calvert, J. R. 1967 Experiments on the low-speed flow past cones. J. Fluid Mech. 27 (2), 273–289.10.1017/S002211206700031XGoogle Scholar
Carmody, T. 1964 Establishment of the wake behind a disk. Trans. ASME J. Basic Engng 86 (4), 869–880.10.1115/1.3655980Google Scholar
Castro, I. P. & Robins, A. G. 1977 The flow around a surface-mounted cube in uniform and turbulent streams. J. Fluid Mech. 79 (2), 307–335.10.1017/S0022112077000172Google Scholar
Chakroun, N. W., Shanbhogue, S. J., Kewlani, G., Taamallah, S., Michaels, D. & Ghoniem, A. F. 2017 On the role of chemical kinetics modeling in the les of premixed bluff body and backward-facing step combustors. In 55th AIAA Aerospace Sciences Meeting. AIAA 2017-1572.Google Scholar
Chen, Z., Ruan, S. & Swaminathan, N. 2017 Large eddy simulation of flame edge evolution in a spark-ignited methane-air jet. Proc. Combust. Inst. 36 (2), 1645–1652.10.1016/j.proci.2016.06.023Google Scholar
Chen, Z. X., Langella, I., Swaminathan, N., Stöhr, M., Meier, W. & Kolla, H. 2019a Large eddy simulation of a dual swirl gas turbine combustor: flame/flow structures and stabilisation under thermoacoustically stable and unstable conditions. Combust. Flame 203, 279–300.10.1016/j.combustflame.2019.02.013Google Scholar
Chen, Z. X., Swaminathan, N., Stöhr, M. & Meier, W. 2019b Interaction between self-excited oscillations and fuel-air mixing in a dual swirl combustor. Proc. Combust. Inst. 37 (2), 2325–2333.10.1016/j.proci.2018.08.042Google Scholar
Chigier, N. A. & Beer, J. M. 1964 Velocity and static-pressure distributions in swirling air jets issuing from annular and divergent nozzles. Trans. ASME J. Basic Engng 86 (4), 788–796.10.1115/1.3655954Google Scholar
Chowdhury, B. R. & Cetegen, B. M. 2017 Experimental study of the effects of free stream turbulence on characteristics and flame structure of bluff-body stabilized conical lean premixed flames. Combust. Flame 178, 311–328.10.1016/j.combustflame.2016.12.019Google Scholar
Darbyshire, O. R. & Swaminathan, N. 2012 A presumed joint pdf model for turbulent combustion with varying equivalence ratio. Combust. Sci. Technol. 184 (12), 2036–2067.10.1080/00102202.2012.696566Google Scholar
Davies, T. W. & Beér, J. M. 1971 Flow in the wake of bluff-body flame stabilizers. Symp. (Intl) Combust. 13 (1), 631–638.10.1016/S0082-0784(71)80065-6Google Scholar
Doan, N. A. K., Swaminathan, N. & Chakraborty, N. 2017 Multiscale analysis of turbulence-flame interaction in premixed flames. Proc. Combust. Inst. 36 (2), 1929–1935.10.1016/j.proci.2016.07.111Google Scholar
Dunstan, T. D., Minamoto, Y., Chakraborty, N. & Swaminathan, N. 2013 Scalar dissipation rate modelling for large eddy simulation of turbulent premixed flames. Proc. Combust. Inst. 34 (1), 1193–1201.10.1016/j.proci.2012.06.143Google Scholar
Durao, D. F. G. & Whitelaw, J. H. 1978 Velocity characteristics of the flow in the near wake of a disk. J. Fluid Mech. 85, 369–385.10.1017/S0022112078000683Google Scholar
Echekki, T. & Mastorakos, E. 2011 Turbulent Combustion Modelling: Advances, New Trends and Perspectives. Springer.10.1007/978-94-007-0412-1Google Scholar
Ferziger, J. H. & Perić, M. 2002 Computational Methods for Fluid Dynamics, 3rd edn. Springer.10.1007/978-3-642-56026-2Google Scholar
Fiorina, B., Baron, R., Gicquel, O., Thevenin, D., Carpentier, S. & Darabiha, N. 2003 Modelling non-adiabatic partially premixed flames using flame-prolongation of ILDM. Combust. Theor. Model. 7 (3), 449–470.10.1088/1364-7830/7/3/301Google Scholar
Fuchs, H. V., Mercker, E. & Michel, U. 1979 Large-scale coherent structures in the wake of axisymmetric bodies. J. Fluid Mech. 93 (1), 185–207.10.1017/S0022112079001841Google Scholar
Fureby, C. & Möller, S. I. 1995 Large-Eddy Simulation of Reacting Flows Applied to Bluff-Body Stabilized Flames. AIAA J. 33 (12), 2339–2347.10.2514/3.12989Google Scholar
Gao, Y., Chakraborty, N. & Swaminathan, N. 2014 Algebraic closure of scalar dissipation rate for large eddy simulations of turbulent premixed combustion. Combust. Sci. Technol. 186 (10–11), 1309–1337.10.1080/00102202.2014.934581Google Scholar
Gao, Y., Chakraborty, N. & Swaminathan, N. 2015 Dynamic closure of scalar dissipation rate for large eddy simulations of turbulent premixed combustion: a direct numerical simulations analysis. Flow Turbul. Combust. 95 (4), 775–802.10.1007/s10494-015-9631-3Google Scholar
Germano, M., Piomelli, U., Moin, P. & Cabot, W. H. 1991 A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A Fluid Dyn. 3 (7), 1760–1765.10.1063/1.857955Google Scholar
Gupta, A. L., Lilley, D. G. & Syred, N. 1984 Swirl Flows. Abacus Press.Google Scholar
Hong, S., Shanbhogue, S. J. & Ghoniem, A. F. 2015 Impact of fuel composition on the recirculation zone structure and its role in lean premixed flame anchoring. Proc. Combust. Inst. 35 (2), 1493–1500.10.1016/j.proci.2014.05.150Google Scholar
Humphries, W. & Vincent, J. H. 1976a Experiments to investigate transport processes in the near wakes of disks in turbulent air flow. J. Fluid Mech. 75 (4), 737–749.10.1017/S0022112076000505Google Scholar
Humphries, W. & Vincent, J. H. 1976b Near wake properties of axisymmetric bluff body flows. Appl. Sci. Res. 32 (6), 649–669.10.1007/BF00384126Google Scholar
Kariuki, J., Dawson, J. R. & Mastorakos, E. 2012 Measurements in turbulent premixed bluff body flames close to blow-off. Combust. Flame 159 (8), 2589–2607.10.1016/j.combustflame.2012.01.005Google Scholar
Kee, R. J., Grcar, J. F., Smooke, M. D., Miller, J. A. & Meeks, E.1985. PREMIX: A FORTRAN program for modeling steady laminar one-dimensional premixed flames. Tech. Rep. 143. Sandia National Labs.Google Scholar
Klein, M., Sadiki, A. & Janicka, J. 2003 A digital filter based generation of inflow data for spatially developing direct numerical or large eddy simulations. Comput. Phys. 186 (2), 652–665.10.1016/S0021-9991(03)00090-1Google Scholar
Kolla, H., Rogerson, J. W., Chakraborty, N. & Swaminathan, N. 2009 Scalar dissipation rate modeling and its validation. Combust. Sci. Technol. 181 (3), 518–535.10.1080/00102200802612419Google Scholar
Kolla, H. & Swaminathan, N. 2010 Strained flamelets for turbulent premixed flames II: Laboratory flame results. Combust. Flame 157 (7), 1274–1289.10.1016/j.combustflame.2010.03.016Google Scholar
Langella, I.2016. Large eddy simulation of premixed combustion using flamelets. PhD thesis, University of Cambridge.10.1080/00102202.2016.1195824Google Scholar
Langella, I., Chen, Z. X., Swaminathan, N. & Sadasivuni, S. K. 2018a Large-eddy simulation of reacting flows in industrial gas turbine combustor. J. Propul. Power 34 (5), 1269–1284.10.2514/1.B36842Google Scholar
Langella, I., Doan, N. A. K. & Swaminathan, N. 2018b Study of subgrid-scale velocity models for reacting and nonreacting flows. Phys. Rev. Fluids 3, 054602.10.1103/PhysRevFluids.3.054602Google Scholar
Langella, I. & Swaminathan, N. 2016 Unstrained and strained flamelets for LES of premixed combustion. Combust. Theor. Model. 20 (3), 410–440.10.1080/13647830.2016.1140230Google Scholar
Langella, I., Swaminathan, N., Gao, Y. & Chakraborty, N. 2015 Assessment of dynamic closure for premixed combustion large eddy simulation. Combust. Theor. Model. 19 (5), 628–656.10.1080/13647830.2015.1080387Google Scholar
Langella, I., Swaminathan, N., Gao, Y. & Chakraborty, N. 2017 Large eddy simulation of premixed combustion: sensitivity to subgrid scale velocity modeling. Combust. Sci. Technol. 189 (1), 43–78.10.1080/00102202.2016.1193496Google Scholar
Langella, I., Swaminathan, N. & Pitz, R. W. 2016a Application of unstrained flamelet SGS closure for multi-regime premixed combustion. Combust. Flame 173, 161–178.10.1016/j.combustflame.2016.08.025Google Scholar
Langella, I., Swaminathan, N., Williams, F. A. & Furukawa, J. 2016b Large-eddy simulation of premixed combustion in the corrugated-flamelet regime. Combust. Sci. Technol. 188 (9), 1565–1591.10.1080/00102202.2016.1195824Google Scholar
Libby, P. A. & Williams, F. A.(Eds) 1980 Turbulent Reacting Flows. Springer.10.1007/3-540-10192-6Google Scholar
Libby, P. A. & Williams, F. A.(Eds) 1994 Turbulent Reacting Flows. Academic Press.Google Scholar
Lilly, D. K. 1992 A proposed modification of the Germano subgrid-scale closure method. Phys. Fluids A Fluid Dyn. 4 (3), 633–635.10.1063/1.858280Google Scholar
Massey, J. C., Chen, Z. X. & Swaminathan, N. 2019 Lean flame root dynamics in a gas turbine model combustor. Combust. Sci. Technol. 191 (5–6), 1019–1042.10.1080/00102202.2019.1584616Google Scholar
Michaels, D., Shanbhogue, S. J. & Ghoniem, A. F. 2017 The impact of reactants composition and temperature on the flow structure in a wake stabilized laminar lean premixed CH4/H2/air flames; mechanism and scaling. Combust. Flame 176, 151–161.10.1016/j.combustflame.2016.10.007Google Scholar
Minamoto, Y., Aoki, K., Tanahashi, M. & Swaminathan, N. 2015 DNS of swirling hydrogen-air premixed flames. Intl J. Hydrog. Energy 40 (39), 13604–13620.10.1016/j.ijhydene.2015.08.049Google Scholar
Nandula, S. P.2003. Lean premixed flame structure in intense turbulence: Rayleigh/Raman/LIF measurements and modeling. PhD thesis, Vanderbilt University.Google Scholar
Nandula, S. P., Pitz, R. W., Barlow, R. S. & Fiechtner, G. J. 1996 Rayleigh/Raman/LIF measurements in a turbulent lean premixed combustor. In 34th AIAA Aerospace Sciences Meeting and Exhibit. AIAA 96-0937.Google Scholar
Pan, J. C., Vangsness, M. D. & Ballal, D. R. 1992 Aerodynamics of bluff-body stabilized confined turbulent premixed flames. Trans. ASME J. Engng Gas Turbines Power 114 (4), 783–789.10.1115/1.2906657Google Scholar
Pan, J. C., Vangsness, M. D., Heneghan, S. P. & Ballal, D. R. 1991a Laser diagnostic studies of bluff-body stabilized confined turbulent premixed flames. In Spring Technical Meeting 1991: Combustion Fundamentals and Applications, pp. 379–384. Combustion Institute, Central States Section.Google Scholar
Pan, J. C., Vangsness, M. D., Heneghan, S. P. & Ballal, D. R. 1991b Scalar measurements in bluff body stabilized flames using cars diagnostics. In Vol. 3: Coal, Biomass and Alternative Fuels; Combustion and Fuels; Oil and Gas Applications; Cycle Innovations. ASME. Turbo Expo: Power for Land, Sea, and Air.Google Scholar
Peters, N. 2000 Turbulent Combustion. Cambridge University Press.10.1017/CBO9780511612701Google Scholar
Poinsot, T. & Veynante, D. 2012 Theoretical and Numerical Combustion, 3rd edn. Available at: http://elearning.cerfacs.fr/combustion/onlinePoinsotBook/buythirdedition/index.php.Google Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.10.1017/CBO9780511840531Google Scholar
Roberts, J. B. 1973 Coherence measurements in an axisymmetric wake. AIAA J. 11 (11), 1569–1571.10.2514/3.50632Google Scholar
Ruan, S., Swaminathan, N. & Darbyshire, O. 2014 Modelling of turbulent lifted jet flames using flamelets: A priori assessment and a posteriori validation. Combust. Theor. Model. 18 (2), 295–329.10.1080/13647830.2014.898409Google Scholar
Ruan, S., Swaminathan, N., Isono, M., Saitoh, T. & Saitoh, K. 2015 Simulation of premixed combustion with varying equivalence ratio in gas turbine combustor. J. Propul. Power 31 (3), 861–871.10.2514/1.B35517Google Scholar
Rydén, R., Eriksson, L.-E. & Olovsson, S. 1993 Large eddy simulation of bluff body stabilised turbulent premixed flames. In Vol. 3A: General. ASME. Power for Land, Sea, and Air.Google Scholar
Shanbhogue, S. J., Sanusi, Y. S., Taamallah, S., Habib, M. A., Mokheimer, E. M. A. & Ghoniem, A. F. 2016 Flame macrostructures, combustion instability and extinction strain scaling in swirl-stabilized premixed CH4/H2 combustion. Combust. Flame 163, 494–507.10.1016/j.combustflame.2015.10.026Google Scholar
Spalding, D. B. 1971 Mixing and chemical reaction in steady confined turbulent flames. Symp. (Intl) Combust. 13 (1), 649–657.10.1016/S0082-0784(71)80067-XGoogle Scholar
Speth, R. L. & Ghoniem, A. F. 2009 Using a strained flame model to collapse dynamic mode data in a swirl-stabilized syngas combustor. Proc. Combust. Inst. 32 (2), 2993–3000.10.1016/j.proci.2008.05.072Google Scholar
Swaminathan, N. & Bray, K. N. C. 2005 Effect of dilatation on scalar dissipation in turbulent premixed flames. Combust. Flame 143 (4), 549–565.10.1016/j.combustflame.2005.08.020Google Scholar
Swaminathan, N. & Bray, K. N. C.(Eds) 2011 Turbulent Premixed Flames. Cambridge University Press.10.1017/CBO9780511975226Google Scholar
Swaminathan, N., Xu, G., Dowling, A. P. & Balachandran, R. 2011 Heat release rate correlation and combustion noise in premixed flames. J. Fluid Mech. 681, 80–115.10.1017/jfm.2011.232Google Scholar
Taylor, A. M. K. P.1982 Confined isothermal and combusting flows behind axisymmetric baffles. PhD thesis, Imperial College London.Google Scholar
Taylor, A. M. K. P. & Whitelaw, J. H. 1984 Velocity characteristics in the turbulent near wakes of confined axisymmetric bluff bodies. J. Fluid Mech. 139, 391–416.10.1017/S0022112084000410Google Scholar
Uberoi, M. S. & Freymuth, P. 1970 Turbulent energy balance and spectra of the axisymmetric wake. Phys. Fluids 13 (9), 2205–2210.10.1063/1.1693225Google Scholar
Van Doormaal, J. P. & Raithby, G. D. 1984 Enhancements of the simple method for predicting incompressible fluid flows. Numer. Heat Transfer 7 (2), 147–163.10.1080/01495728408961817Google Scholar
Winterfeld, G. 1965 On processes of turbulent exchange behind flame holders. Symp. (Intl) Combust. 10 (1), 1265–1275.10.1016/S0082-0784(65)80261-2Google Scholar
Wright, F. H. 1959 Bluff-body flame stabilization: Blockage effects. Combust. Flame 3, 319–337.10.1016/0010-2180(59)90035-5Google Scholar