‘One-dimensional turbulence’ simulation of turbulent jet diffusion flames: model formulation and illustrative applications
Introduction
The modeling of turbulent combustion processes presents a number of challenges. Turbulent reacting flows are inherently unsteady, three-dimensional, and are characterized by a wide range of length and time scales [1]. An adequate account of the characteristics of turbulent reacting flows must address the turbulence, the chemistry of the reacting mixture, and their coupling. This coupling, usually denoted as ‘turbulence-chemistry interactions,’ is often expressed in the effects of heat release on turbulence through temperature and composition-dependent transport properties, and the enhancement of mixing by turbulence.
A number of approaches have been developed to address turbulence-chemistry interactions in conjunction with traditional turbulence models. They include Laminar Flamelet Models (LFM) [2], Monte-Carlo PDF transport models [3], and Conditional Moment Closure (CMC) [4]. These models are coupled to turbulence models, which compute the velocity field. The turbulence model provides characteristics of the flow (such as kinetic energy and dissipation) to estimate the rate of mixing needed in the transport equations for the scalars. Traditional approaches to turbulence modeling have focused on the larger scales where most of the energy resides and implemented more simplified descriptions of the fine scales. Such strategies have proven to be more difficult to justify in turbulent combustion. The combustion process involves the coupling between fine-scale motions and chemical reactions which involve hundreds of chemical reactions and dozens of species for the simplest hydrocarbons. Mixing models that rely solely on large scale times and lengths represent a critical limitation in existing models of turbulence-chemistry interactions, which are coupled to traditional turbulence modeling approaches.
An alternative strategy, developed by Kerstein [5], is the Linear Eddy Model (LEM). LEM addresses the difficulty of adequately predicting the mixing-reaction coupling at all scales by spatially and temporally resolving the processes of turbulent advection, molecular transport and chemistry on one dimension. The model is based on a mechanistic distinction between advective (stirring) processes and molecular transport and reaction processes. Molecular processes are computed deterministically by solving the unsteady reaction-diffusion equations. Advective processes are implemented stochastically by using triplet-map stirring events which emulate the compressive-strain and rotational folding effects of turbulent eddies [5]. The frequency and the eddy size distribution of the stirring events are prescribed so as to emulate a predefined energy power spectrum and a characteristic turbulent Reynolds number. The model has been successfully implemented for a wide variety of applications involving mixing in shear flows 6, 7, 8.
A recent refinement of this modeling approach is the One-Dimensional Turbulence (ODT) model [9]. ODT is an outgrowth of the LEM modeling strategy of maintaining a distinction between turbulent stirring and molecular diffusion and reaction on a 1D domain. The principal distinction between the two models stems from the solution of one or more components of the velocity vector in ODT, which provides information about the shear field, thereby a mechanism for driving the turbulence. Therefore, in contrast to LEM, which is a ‘mixing model,’ ODT is a self-contained turbulence model.
ODT provides a realistic description of the physics characterizing the coupling of turbulence with molecular transport and chemistry, with obvious cost advantages over multi-dimensional Direct Numerical Simulations. However, the low-dimensional nature of the ODT model limits its application as a stand-alone model to simple isotropic or homogenous flows [9]. Extension to more complex bulk flows may require additional modeling, such as the one implemented in this study, or a coupling of the ODT with multi-dimensional formulations such as Reynolds-Averaged Navier-Stokes (RANS) and Large-Eddy Simulations (LES.) Beyond these limitations, stand-alone ODT remains a valuable tool to understand the role of turbulent mixing and entrainment on chemistry and complement traditional low-dimensional tools on which researchers have long relied to build combustion libraries (e.g., well stirred and partially stirred reactors, planar unstrained, and strained flames). Moreover, various reduction strategies of molecular transport and chemistry may be tested with ODT prior to multidimensional applications.
In this paper, the stand-alone ODT model is applied to two hydrogen-air jet diffusion flames to examine its predictions of (1) entrainment mechanisms, (2) finite-rate chemistry effects, and (3) differential diffusion effects. ODT predictions are validated with experimental measurements.
The paper is organized as follows. First, the model formulation for temporally developing reacting shear flows is outlined. ODT temporal simulations of hydrogen-air jet diffusion flames are presented and compared to measured (spatially developing) jet diffusion flames. ODT predictions of the general flow features are discussed first. Then, comparisons of ODT results with measured axial statistics of temperature and major species are presented to evaluate the ODT representation of entrainment, while finite rate chemistry effects are studied using conditional statistics. Finally, ODT predictions of differential diffusion effects are discussed.
Section snippets
Stand-alone model formulation for temporal simulations of simple reacting shear flows
In the following discussion, we describe the formulation of the ODT model as applied to the temporal simulation of simple reacting mixing layer flows, such as jets and shear layers. Other stand-alone formulations of ODT have been reported in the literature for shear-driven [9] and buoyancy-driven flows [10].
As stated earlier, the ODT model is based on a mechanistic distinction between molecular processes (reaction and diffusion) and turbulent advection in a time-resolved simulation on a 1D
Results and discussion
In this section, the modeling of temporally developing planar reacting jets is described based on the procedure outlined earlier. Because the ODT temporal results are compared to actual experimental data from round jets, it is important to relate the temporal planar evolution of the 1D domain profiles to round-jet spatial evolution. Details of the numerical implementation and the reduced chemical kinetic scheme follow. Finally, ODT computational results are discussed in comparison to existing
Conclusions and implications for modeling in complex reacting flows
A formulation for the simulation of turbulent jet flows using ODT model has been developed. The formulation is implemented for turbulent jet diffusion flames to examine the model predictions of flow entrainment, mixing, and chemistry. The simulations are characterized by full temporal and spatial resolution of the streamwise velocity and thermochemical scalars on a 1D domain. The mechanistic distinction between molecular processes, including molecular diffusion and reaction, and advective
Acknowledgements
This research was supported by the United States Department of Energy, Office of Basic Energy Sciences, Chemical Sciences Division. We would like to thank Dr. Wolfgang Meier and co-workers for making their data accessible to the research community.
References (27)
Prog. Energy Combust. Sci.
(1985)Combust. Flame
(1989)- et al.
Combust. Flame
(1990) - et al.
Combust. Flame
(1999) - Bray, K. N. C., Twenty-Sixth Symp. (International) on Combustion. The Combustion Institute, Pittsburgh, 1996, pp....
- Peters, N., Twenty-First Symp. (International) on Combustion. The Combustion Institute, Pittsburgh, 1988, pp....
Phys. Fluids A
(1993)J. Fluid Mech.
(1991)J. Fluid Mech.
(1990)Combust. Sci. Tech.
(1992)
J. Fluid Mech.
SIAM J. Sci. Stat. Comput.
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