Abstract
A key limitation of Reynolds-Average Navier-Stokes (RANS) simulation of mixing and reaction in turbulent flows is the lack of resolution of small-scale structure and associated unsteadiness. Various subgrid models formulated in state space have been developed to complement the RANS solution in this regard. We here introduce a physical-space formulation that captures unsteady advective and diffusive processes at all scales of the turbulent flow. The approach is a 3D construction based on the Linear Eddy Model (LEM), involving three orthogonally intersecting arrays of 1D LEM domains, and coupled so as to capture the 3D character of fluid trajectories. To illustrate the model performance of the 3D LEM-based formulation, here termed LEM3D, multi-stream mixing in a turbulent round jet is simulated using measured mean-flow properties as input. Comparison to scalar cross-correlation coefficients and other measured properties of this mixing configuration indicate that the LEM3D approach, in conjunction with flow properties that are provided by steady-state models, is a useful representation of complex turbulent mixing processes that would otherwise be difficult to capture within a steady-state CFD framework.
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Kerstein, A.R.: A linear-eddy model of turbulent scalar transport and mixing. Combust. Sci. Technol. 60, 391–421 (1988)
Kerstein, A.R.: Linear-eddy modelling of turbulent transport, part 6. Microstructure of diffusive scalar mixing fields. J. Fluid Mech. 231, 361–394 (1991)
Kerstein, A.R.: Linear-eddy modelling of turbulent transport, part 7. Finite-rate chemistry and multi-stream mixing. J. Fluid Mech. 240, 289–313 (1992)
McMurtry, P.A., Gansauge, T.C., Kerstein, A.R., Krueger, S.K.: Linear eddy simulations of mixing in a homogeneous turbulent flow. Phys. Fluids A 5, 1023–1034 (1993)
McMurtry, P.A., Menon, S., Kerstein, A.R.: A linear eddy sub-grid model for turbulent reacting flows: Application to hydrogen-air combustion. Proc. Combust. Inst. 24, 271–278 (1992)
McMurtry, P.A., Menon, S., Kerstein, A.R.: Linear eddy modeling of turbulent combustion. Energy Fuels 7, 817–826 (1993)
Menon, S,. Calhoon, J.W.H.: Subgrid mixing and molecular transport modeling in a reacting shear layer. Proc. Combust. Inst. 26, 59–66 (1996)
Chakravarthy, V.K., Menon, S.: Subgrid modeling of turbulent premixed flames in the flamelet regime. Flow Turbul. Combust. 65, 133–161 (2000)
Sankaran, V., Menon, S.: Subgrid combustion modeling of 3-D premixed flames in the thin-reaction-zone regime. Proc. Combust. Inst. 30, 575–582 (2005)
Goldin, G.M., Menon, S., Calhoon, J.W.H.: A linear eddy mixing model for steady non-premixed turbulent combustion. AIAA Pap. (95-0379) (1995)
Tong, C., Warhaft, Z.: Passive scalar dispersion and mixing in a turbulent jet. J. Fluid Mech. 292, 1–38 (1995)
Warhaft, Z.: The interference of thermal fields from line sources in grid turbulence. J. Fluid Mech. 144, 363–387 (1984)
Tennekes, H., Lumley, J.L.: A First Course in Turbulence. The MIT Press, Cambridge, MA (1972)
Menon, S., Kerstein, A.R.: The Linear-Eddy model. In: Echekki, T., Mastorakos, E. (eds.) Turbulent Combustion Modeling: Advances, New Trends, and Perspectives, pp. 221–247. Springer, Dordrecht, Germany (2011)
Schmidt, R.C., Kerstein, A.R., McDermott, R.: ODTLES: a multi-scale model for 3D turbulent flow based on one-dimensional turbulence modeling. Comput. Methods Appl. Mech. Eng. 199, 865–890 (2010)
Gonzalez-Juez, E.D., Schmidt, R.C., Kerstein, A.R.: ODTLES simulations in wall-bounded flows. Phys. Fluids 23, 125102 (2011)
Kerstein, A.R., Ashurst, W.T., Wunsch, S., Nilsen, V.: One-dimensional turbulence: vector formulation and application to free shear flows. J. Fluid Mech. 447, 85–109 (2001)
Viswanathan, S., Pope, S.B.: Turbulent dispersion from line sources in grid turbulence. Phys. Fluids 20, 101514 (2008)
Panchapakesan, N.R., Lumley, J.L.: Turbulence measurements in axisymmetric jets of air and helium, Part 1. Air jet. J. Fluid Mech. 246, 197–223 (1993)
Wolfram Research Inc: Mathematica, Version 7.0. Wolfram Research, Inc., Champaign, IL (2008)
Weydahl, T.: A framework for mixing-reaction closure with the Linear Eddy Model. PhD thesis, NTNU Trondheim, Norwegian University of Science and Technology, Department of Energy and Process Engineering. (2010)
Chandrasekhar, S.: Stochastic problems in physics and astronomy. Rev. Mod. Phys. 15, 1–89 (1943)
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Sannan, S., Weydahl, T. & Kerstein, A.R. Stochastic Simulation of Scalar Mixing Capturing Unsteadiness and Small-scale Structure Based on Mean-flow Properties. Flow Turbulence Combust 90, 189–216 (2013). https://doi.org/10.1007/s10494-012-9436-6
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DOI: https://doi.org/10.1007/s10494-012-9436-6