Effects of confinement, geometry, inlet velocity profile, and Reynolds number on the asymmetry of opposed-jet flows
Abstract
The opposed-jet counterflow configuration is widely used to measure fundamental flame properties that are essential targets for validating chemical kinetic models. The main and key assumption of the counterflow configuration in laminar flame experiments is that the flow field is steady and quasi-one-dimensional. In this study, experiments and numerical simulations were carried out to investigate the behavior and controlling parameters of counterflowing isothermal air jets for various nozzle designs, Reynolds numbers, and surrounding geometries. The flow field in the jets’ impingement region was analyzed in search of instabilities, asymmetries, and two-dimensional effects that can introduce errors when the data are compared with results of quasi-one-dimensional simulations. The modeling involved transient axisymmetric numerical simulations along with bifurcation analysis, which revealed that when the flow field is confined between walls, local bifurcation occurs, which in turn results in asymmetry, deviation from the one-dimensional assumption, and sensitivity of the flow field structure to boundary conditions and surrounding geometry. Particle image velocimetry was utilized and results revealed that for jets of equal momenta at low Reynolds numbers of the order of 300, the flow field is asymmetric with respect to the middle plane between the nozzles even in the absence of confining walls. The asymmetry was traced to the asymmetric nozzle exit velocity profiles caused by unavoidable imperfections in the nozzle assembly. The asymmetry was not detectable at high Reynolds numbers of the order of 1000 due to the reduced sensitivity of the flow field to boundary conditions. The cases investigated computationally covered a wide range of Reynolds numbers to identify designs that are minimally affected by errors in the experimental procedures or manufacturing imperfections, and the simulations results were used to identify conditions that best conform to the assumptions of quasi-one-dimensional modeling.
Keywords
Counterflow configuration Numerical simulations Quasi- one-dimensional modeling BifurcationPreview
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Notes
Acknowledgements
The Air Force Office of Scientific Research (Grant No. FA9550-15-1-0409) supported this work under the technical supervision of Dr. Chiping Li. The numerical simulations were carried out using the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation Grant Number TG-CTS140012. The authors would like to gratefully acknowledge the assistance of Dr. Vyaas Gururajan for his feedback and technical support with the numerical simulations.
References
- 1.Carpioa, J., Liñán, A., Sánchez, A.L., Williams, F.A.: Aerodynamics of axisymmetric counterflowing jets. Combust. Flame 177, 137–143 (2017)CrossRefGoogle Scholar
- 2.Tamir, A.: Impinging-Stream Reactors: Fundamentals and Applications. Elsevier, Beer-Sheva (2014)Google Scholar
- 3.Park, O., Veloo, P.S., Burbano, H., Egolfopoulos, F.N.: Studies of premixed and non-premixed hydrogen flames. Combust. Flame 162(4), 1078–1094 (2015)CrossRefGoogle Scholar
- 4.Won, S.H., Jiang, B., Diévart, P., Sohn, C.H., Ju, Y.: Self-sustaining n-heptane cool diffusion flames activated by ozone. Proc. Combust. Inst. 35(1), 881–888 (2015)CrossRefGoogle Scholar
- 5.Burrell, R.R.: Studies of methane counterflow flames at low pressures. Doctor of Philosophy Thesis, Mechanical Engineering, University of Southern California, Los Angeles, California (2017)Google Scholar
- 6.Carbone, F., Gomez, A.: The structure of toluene-doped counterflow gaseous diffusion flames. Combust. Flame 159(10), 3040–3055 (2012)CrossRefGoogle Scholar
- 7.Kee, R.J., Miller, J.A., Evans, G.H., Dixon-Lewis, G.: A computational model of the structure and extinction of strained, opposed flow, premixed methane-air flames. Proc. Combust. Inst. 22(1), 1479–1494 (1988)CrossRefGoogle Scholar
- 8.Chelliah, H.K., Law, C.K., Ueda, T., Smooke, M.D., Williams, F.A.: An experimental and theoretical investigation of the dilution, pressure and flow-field effects on the extinction condition of methane-air-nitrogen diffusion flames. Proc. Combust. Inst. 23(1), 503–511 (1990)CrossRefGoogle Scholar
- 9.Kim, Y.M., Kim, H.-J.: Multidimensional effects on structure and extinction process of counterflow nonpremixed hydrogen-air flames. Combust. Sci. Technol. 137(1–6), 51–80 (1998)CrossRefGoogle Scholar
- 10.Frouzakis, C.E., Lee, J., Tomboulides, A.G., Boulouchos, K.: Two-dimensional direct numerical simulation of opposed-jet hydrogen-air diffusion flame. Proc. Combust. Inst. 27(1), 571–577 (1998)CrossRefGoogle Scholar
- 11.Mittal, V., Pitsch, H., Egolfopoulos, F.N.: Assessment of counterflow to measure laminar burning velocities using direct numerical simulation. Combust. Theory Model. 16(3), 419–433 (2012)CrossRefMATHGoogle Scholar
- 12.Sarnacki, B.G., Esposito, G., Krauss, R.H., Chelliah, H.K.: Extinction limits and associated uncertainties of nonpremixed counterflow flames of methane, ethylene, propylene and n-butane in air. Combust. Flame 159(3), 1026–1043 (2012)CrossRefGoogle Scholar
- 13.Niemann, U., Seshadri, K., Williams, F.A.: Accuracies of laminar counterflow flame experiments. Combust. Flame 162(4), 1540–1549 (2015)CrossRefGoogle Scholar
- 14.Johnson, R.F., VanDine, A.C., Esposito, G.L., Chelliah, H.K.: On the axisymmetric counterflow flame simulations: is there an optimal nozzle diameter and separation distance to apply quasi one-dimensional theory? Combust. Sci. Technol. 187(1–2), 37–59 (2015)CrossRefGoogle Scholar
- 15.Burrell, R.R., Zhao, R., Lee, D.J., Burbano, H., Egolfopoulos, F.N.: Two-dimensional effects in counterflow methane flames. Proc. Combust. Inst. 36(1), 1387–1394 (2016)CrossRefGoogle Scholar
- 16.Ansari, A., Egolfopoulos, F.N.: Flame ignition in the counterflow configuration: reassessing the experimental assumptions. Combust. Flame 174, 37–49 (2016)CrossRefGoogle Scholar
- 17.Fox, J.L., Morgan, G.W.: On the stability of some flows of an ideal fluid with free surfaces. Q. Appl. Math. 11(4), 439–465 (1952)MathSciNetCrossRefMATHGoogle Scholar
- 18.Rolon, J.C., Veynante, D., Martin, J.P.: Counter jet stagnation flows. Exp. Fluids 11(5), 313–324 (1991)CrossRefGoogle Scholar
- 19.Pawlowski, R.P., Salinger, A.G., Shadid, J.N., Mountziaris, T.J.: Bifurcation and stability analysis of laminar isothermal counterflowing jets. J. Fluid Mech. 551, 117–139 (2006)MathSciNetCrossRefMATHGoogle Scholar
- 20.Ciani, A., Kreutner, W., Frouzakis, C.E., Lust, K., Coppola, G., Boulouchos, K.: An experimental and numerical study of the structure and stability of laminar opposed-jet flows. Comput. Fluids 39(1), 114–124 (2010)CrossRefMATHGoogle Scholar
- 21.Li, W.F., Sun, Z., Liu, H.F., Wang, F.C., Yu, Z.: Experimental and numerical study on stagnation point offset of turbulent opposed jets. Chem. Eng. J. 138(1), 283–294 (2008)CrossRefGoogle Scholar
- 22.Li, W.F., Yao, T.L., Wang, F.C.: Study on factors influencing stagnation point offset of turbulent opposed jets. AIChE J. 56(1), 2513–2522 (2010)CrossRefGoogle Scholar
- 23.Li, W.F., Yao, T.L., Liu, H.F., Wang, F.C.: Experimental investigation of flow regimes of axisymmetric and planar opposed jets. AIChE J. 57(6), 1434–1445 (2011)CrossRefGoogle Scholar
- 24.Fotache, C.G., Kreutz, T.G., Zhu, D.L., Law, C.K.: An experimental study of ignition in nonpremixed counterflowing hydrogen versus heated air. Combust. Sci. Technol. 109(1–6), 373–393 (1995)CrossRefGoogle Scholar
- 25.Seiser, R., Seshadri, K., Piskernik, E., Linán, A.: Ignition in the viscous layer between counterflowing streams: asymptotic theory with comparison to experiments. Combust. Flame 122(3), 339–349 (2000)CrossRefGoogle Scholar
- 26.Hammond, D.A., Redekopp, L.G.: Local and global instability properties of separation bubbles. Eur. J. Mech. B Fluids 17(2), 145–164 (1998)MathSciNetCrossRefMATHGoogle Scholar
- 27.Cherubini, S., Robinet, J., De Palma, P.: The effects of non-normality and nonlinearity of the Navier–Stokes operator on the dynamics of a large laminar separation bubble. Phys. Fluids 22(1), 014102 (2010)CrossRefMATHGoogle Scholar
- 28.Feran, R.M., Mullin, T., Cliffe, K.A.: Nonlinear flow phenomena in a symmetric sudden expansion. J. Fluid Mech. 221, 596–608 (1990)Google Scholar
- 29.Amantini, G., Frank, J.H., Gomez, A.: Experiments on standing and traveling edge flames around flame holes. Proc. Combust. Inst. 30(1), 313–321 (2005)CrossRefGoogle Scholar
- 30.Amantini, G., Frank, J.H., Smooke, M.D., Gomez, A.: Computational and experimental study of steady axisymmetric non-premixed methane counterflow flames. Combust. Theory Model. 11(1), 47–72 (2007)CrossRefMATHGoogle Scholar
- 31.Strogatz, S.T.: Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering. Westview Press, Philadelphia (2014)MATHGoogle Scholar
- 32.Kostiuk, L.W., Bray, K.N.C., Cheng, R.K.: Experimental study of premixed turbulent combustion in opposed streams. Part I—Nonreacting flow field. Combust. Flame 92(4), 377–395 (1993)CrossRefGoogle Scholar
- 33.Pellett, G., Isaac, K., Humphreys, W., Garttrell, L., Roberts, W., Dancey, C., Northam, G.: Velocity and thermal structure, and strain-induced extinction of 14 to 100% hydrogen-air counterflow diffusion flames. Combust. Flame 112(4), 575–592 (1998)CrossRefGoogle Scholar
- 34.Stan, G., Johnson, D.A.: Experimental and numerical analysis of turbulent opposed impinging jets. AIAA J. 39(10), 1901–1908 (2001)CrossRefGoogle Scholar
- 35.Kostiuk, L.W., Bray, K.N.C., Cheng, R.K.: Experimental study of premixed turbulent combustion in opposed streams. Part II—reacting flow field and extinction. Combust. Flame 92(4), 396–409 (1993)CrossRefGoogle Scholar
- 36.Ogawa, N., Maki, H.: Studies on opposed turbulent jets: influences of a body on the axis of opposed turbulent jets. Bull. JSME 29(255), 2872–2877 (1986)CrossRefGoogle Scholar
- 37.Ogawa, N., Maki, H., Hijikata, K.: Studies on opposed turbulent jets: impact position and turbulent component in jet center. JSME Int. J. 35(2), 205–211 (1992)Google Scholar
- 38.Scribano, G., Bisetti, F.: Reynolds number and geometry effects in laminar axisymmetric isothermal counterflows. Phys. Fluids 28(12), 123605 (2016)CrossRefGoogle Scholar
- 39.Lindstedt, R.P., Luff, D.S., Whitelaw, J.H.: Velocity and strain-rate characteristics of opposed isothermal flows. Flow Turbul. Combust. 74(2), 169–194 (2005)CrossRefGoogle Scholar
- 40.Dong, Y., Vagelopoulos, C.M., Spedding, G.R., Egolfopoulos, F.N.: Measurement of laminar flame speeds through digital particle image velocimetry: mixtures of methane and ethane with hydrogen, oxygen, nitrogen, and helium. Proc. Combust. Inst. 29(2), 1419–1426 (2002)CrossRefGoogle Scholar
- 41.Hughes, I., Hase, T.: Measurements and Their Uncertainties: A Practical Guide to Modern Error Analysis. Oxford University Press, New York (2010)MATHGoogle Scholar
- 42.Lutz, A.E., Kee, R.J., Grcar, J.F., Rupley, F.M.: OPPDIF: A FORTRAN Program for Computing Opposed-Flow Diffusion Flames. Sandia National Laboratories, Livermore (1997)CrossRefGoogle Scholar
- 43.Weller, H.H., Tabor, G., Jasak, H., Fureby, C.: A tensorial approach to computational continuum mechanics using object-oriented techniques. Comput. Phys. 12(6), 620–631 (1998)CrossRefGoogle Scholar
- 44.Chen, K.K., Rowley, C.W., Stone, H.A.: Vortex dynamics in a pipe T-junction: recirculation and sensitivity. Phys. Fluids 27(3), 034107 (2015)CrossRefGoogle Scholar
- 45.Chen, K.K., Rowley, C.W., Stone, H.A.: Vortex breakdown, linear global instability and sensitivity of pipe bifurcation flows. J. Fluid Mech. 815, 257–294 (2017)MathSciNetCrossRefMATHGoogle Scholar
- 46.Issa, R.I.: Solution of the implicitly discretized fluid flow equations by operator-splitting. J. Comput. Phys. 62(1), 40–65 (1986)MathSciNetCrossRefMATHGoogle Scholar
- 47.Courant, R., Friedrichs, K., Lewy, H.: On the partial difference equations of mathematical physics. IBM J. 11(2), 215–234 (1967)MathSciNetCrossRefMATHGoogle Scholar
- 48.Armijo, L.: Minimization of functions having Lipschitz continuous first partial derivatives. Pac. J. Math. 16(1), 1–3 (1966)MathSciNetCrossRefMATHGoogle Scholar
- 49.Kelley, C.T.: Iterative Methods for Linear and Nonlinear Equations. Society for Industrial and Applied Mathematics, Philadelphia (1995)CrossRefMATHGoogle Scholar
- 50.Saad, Y., Schultz, M.H.: GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 7(3), 856–869 (1986)MathSciNetCrossRefMATHGoogle Scholar
- 51.Tuckerman, L., Barkley, D.: Bifurcation analysis for time steppers. In: Doedel, E., Tuckerman, L.S. (eds.) Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems, pp. 453–466. Springer, New York (2000)CrossRefGoogle Scholar
- 52.Trefethen, L.N., Bau III, D.: Numerical Linear Algebra. SIAM, Philadelphia (1997)CrossRefMATHGoogle Scholar
- 53.Korusoy, E., Whitelaw, J.H.: Inviscid, laminar and turbulent opposed flows. Int. J. Numer. Methods Fluids 46(11), 1069–1098 (2004)CrossRefMATHGoogle Scholar
- 54.Gresho, P.M., Sani, R.L.: On pressure boundary conditions for the incompressible Navier–Stokes equations. Int. J. Numer. Methods Fluids 7(10), 1111–1145 (1987)CrossRefMATHGoogle Scholar
- 55.Godrèche, C., Manneville, P., Castaing, B.: Hydrodynamics and Nonlinear Instabilities. Cambridge University Press, Cambridge (2005)Google Scholar
- 56.Oh, C.B., Hamins, A., Bundy, M., Park, J.: The two-dimensional structure of low strain rate counterflow nonpremixed-methane flames in normal and microgravity. Combust. Theory Model. 12(2), 283–302 (2008)CrossRefMATHGoogle Scholar
- 57.Fletcher, C.A.J.: Computational Techniques for Fluid Dynamics 1: Fundamental and General Techniques. Springer, Berlin (1988)CrossRefMATHGoogle Scholar