Direct numerical simulations of a reacting mixing layer with chemical heat release

We theoretically and numerically investigate the effect of temperature dependent density and viscosity on turbulence in channel flows. First, a mathematical framework is developed to support the validity of the semi-local scaling as proposed based on heuristic arguments by Huang, Coleman, and Bradshaw ["Compressible turbulent channel flows: DNS results and modelling," J. Fluid Mech. 305, 185-218 (1995)]. Second, direct numerical simulations (DNS) of turbulent channel flows with different constitutive relations for density and viscosity are performed to assess and validate the semi-local scaling for turbulent statistics. The DNS database is obtained by solving the low-Mach number approximation of the Navier-Stokes equation. Finally, we quantify the modulation of turbulence due to changes in fluid properties. In the simulations, the fluid is internally heated and the temperature at both channel walls is fixed, such that the friction Reynolds number based on wall quantities is Re τ = 395 for all cases investigated. We show that for a case with variable density ρ and viscosity µ, but constant semi-local Reynolds number Re * τ ≡  (ρ/ρ w )/(µ/µ w )Re τ (where bar and subscript w, denote Reynolds averaging and averaged wall quantity, respectively), across the whole channel height, the turbulent statistics exhibit quasi-similarity with constant property turbulent flows. For cases where Re * τRe τ across the channel, we found that quasi-similarity is maintained for cases with similar Re * τ distributions, even if their individual mean density and viscosity profiles substantially differ. With a decrease of Re * τ towards the channel center (Re * τ < Re τ ), we show that the anisotropy increases and the pre-multiplied stream-wise spectra reveal that this increase is associated with strengthening of the large scale streaks in the buffer layer. The opposite effect is observed when Re * τ increases towards the channel center. The present results provide an effective framework for categorizing turbulence modulation in wall-bounded flows with variable property effects, and can be applied to any Newtonian fluid that is heated or cooled. C 2015 AIP Publishing LLC. [http://dx

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“…The pressure correction scheme is based on the projection method. 29 The validation of the numerical approach is discussed in Appendix A.…”

Section: A Governing Equations and Computational Approachmentioning

confidence: 99%

Semi-local scaling and turbulence modulation in variable property turbulent channel flows

et al. 2015

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“…The first step is to express all of the dependent variables in terms of a low Mach number expansion [22], i.e. the pressure is written as…”

Section: Low Mach Number Expansionsmentioning

confidence: 99%

Improved Boundary Conditions for the DNS of Reacting Subsonic Flows

Prosser

2010

Flow Turbulence Combust

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In this paper, we develop a method of prescribing time dependent boundary conditions for reacting flows. The method builds on earlier results, and derives from a linearization of the flow field around a base state. The base state is specified in terms of the flow dilatation, and we establish a general expression for the dilatation in reacting flows at low Mach number. This expression is then used to derive acoustically transparent boundary conditions. The utility of the approach is demonstrated via a number of laminar flame calculations, ranging in complexity from single step chemistry to a multi-step methane mechanism. The accuracy of the resulting solutions is found to be superior to those obtained using other means.

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“…The stiff-split scheme developed in [2] is based on a projection method [48][49][50][51][52][53][54][55] for reacting flow. The formulation, which follows the construction outlined in [1], assumes an open 2D domain and relies on a second-order centered finite-difference discretization of the equations of motion.…”

Section: Numerical Schemementioning

confidence: 99%

A numerical scheme for modelling reacting flow with detailed chemistry and transport.

Knio

Najm²,

Paul³

2003

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An efficient projection scheme is developed for the simulation of reacting flow with detailed kinetics and transport. The scheme is based on a zero-Mach-number formulation of the compressible conservation equations for an ideal gas mixture. It is a modified version of the stiff operator-split scheme developed by Knio, Najm & Wyckoff (1999, J. Comput. Phys. 154, 428). Similar to its predecessor, the new scheme relies on Strang splitting of the discrete evolution equations, where diffusion is integrated in two half steps that are symmetrically distributed around a single stiff step for the reaction source terms. The diffusive half-step is integrated using an explicit single-step, multistage, Runge-Kutta-Chebyshev (RKC) method, which replaces the explicit, multi-step, fractional sub-step approach used in the previous formulation. This modification maintains the overall second-order convergence properties of the scheme and enhances the efficiency of the computations by taking advantage of the extended real-stability region of the RKC scheme. Two additional efficiency-enhancements are also explored, based on an extrapolation procedure for the transport coefficients and on the use of approximate Jacobian data evaluated on a coarse mesh. By including these enhancement schemes, performance tests using 2D computations with a detailed C 1 C 2 methane-air mechanism and a detailed mixture-averaged transport model indicate that speedup factors of about 15 are achieved over the previous split-stiff scheme.3

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Direct numerical simulations of a reacting mixing layer with chemical heat release

Cited by 221 publications

References 12 publications

Semi-local scaling and turbulence modulation in variable property turbulent channel flows

Semi-local scaling and turbulence modulation in variable property turbulent channel flows

Improved Boundary Conditions for the DNS of Reacting Subsonic Flows

A numerical scheme for modelling reacting flow with detailed chemistry and transport.

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