# Investigation of Turbulence-Radiation Interactions in Turbulent Flames Using a Hybrid Finite Volume/Monte Carlo Approach

Open Access

- Graduate Program:
- Mechanical Engineering
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- June 13, 2007
- Committee Members:
- Michael F Modest, Committee Chair
- Daniel Connell Haworth, Committee Member
- Paul E Plassmann, Committee Member
- Philip John Morris, Committee Member
- Deborah A Levin, Committee Member

- Keywords:
- gas radiative properties
- flame
- turbulence-radiation interactions
- combustion
- thermal radiation
- composition PDF
- Monte Carlo methods

- Abstract:
- In many turbulent reacting flows it is important to predict radiative heat transfer accurately, since radiation dominates heat transfer at high temperatures. The turbulent fluctuations of temperature and chemical species concentrations have strong effects on radiative intensities, and turbulence-radiation interactions (TRI) create a "closure" problem when the governing partial differential equations are averaged. To avoid this problem, TRI effects are completely neglected in traditional combustion calculations. This has been shown to yield huge errors in the estimation of radiative fluxes. In the recent one or two decades, several approaches have been proposed to take TRI into account. However, virtually all of them have adopted an optically-thin fluctuation approximation to neglect the nonlinear coupling between turbulence and absorption: the so-called "absorption TRI." Therefore, the above problem has not been completely solved. Among those attempts, the most promising approaches are joint-probability-density-function (joint-PDF) methods, which can treat the nonlinear coupling between turbulence and emission exactly: the so-called "emission-TRI." The aim of the present thesis is to extend joint PDF methods to take TRI fully into account and validate the widely adopted optically-thin fluctuation approximation in various turbulent flames. The idea of joint-PDF methods is to treat physical variables as random variables and to solve the joint-PDF transport equation by stochastic methods, in which the actual flow is represented by a large number of stochastic particles carrying their own random variable values and evolving with time. Since each particle is one realization of the joint-PDF, the mean value of any function of those random variables only, such as the chemical source term, can be evaluated exactly by taking the ensemble of particles. The local emission term belongs to this category and, thus, can be evaluated exactly and directly from the particle ensemble. However, the local absorption term involves interactions between the local particle and the energy emitted by all other particles, and can not be obtained from the particle ensemble directly. To solve this problem, a photon Monte Carlo method is proposed in the present thesis to evaluate such interactions, so that the absorption term can be evaluated exactly. In the present study a composition-PDF approach is employed, in which only temperature and species concentrations are treated as random variables. Meanwhile, a hybrid finite-volume/Monte Carlo scheme is adopted, in which the finite-volume method is used to solve for the flow field and the Monte Carlo method is used to solve for the composition joint-PDF for chemical reactions and radiation as discussed earlier. To implement the photon Monte Carlo method in the PDF particle field, special schemes are developed since traditional photon Monte Carlo simulations were developed for continuum media. An adaptive emission scheme is proposed to minimize statistical errors of the photon Monte Carlo method, considering that the particle emission energy may vary several orders of magnitude due to the high inhomogeneity of gases in turbulent flames. The absorption simulation requires that an optical thickness be assigned to each of the particles. Two approaches are discussed, the Point Particle Model (PPM), in which the shape of the particle is not specified, and the Spherical Particle Model (SPM) in which particles are assumed to be spheres with constant radiation properties. Another issue for absorption schemes in particle fields is the influence region of a ray. Two ways of modeling a ray are proposed. In the first, each ray is treated as a standard volume-less line. In the other approach, the ray is assigned a small solid angle, and is thus treated as a cone with a decaying influence function away from its center line. Based on these models, three different interaction schemes between rays and particles are proposed, i.e., Line-SPM, Cone-PPM and Cone-SPM methods. The spectral modeling is important for radiation applications involving participating media. Two approaches for spectral modeling, the line-by-line and full-spectrum k-distribution methods, are developed and compared for general photon Monte Carlo simulations in both continuum media and particle fields. For line-by-line calculations the high-resolution absorption coefficient data are generated for important combustion gases. Based on these data, a high-accuracy compact narrow-band k-distribution database is constructed, from which full-spectrum k-distributions can be efficiently assembled. The random number relations have also been constructed for both spectral models. Although the full-spectrum k-distribution approach is extremely efficient in deterministic solvers for the radiative transfer equation, this advantage is not prominent for photon Monte Carlo solvers. Since the full-spectrum k-distribution approach results in inevitable errors due to the uncorrelatedness of absorption coefficients in combustion gases while the line-by-line approach is exact, the line-by-line approach is more preferable for photon Monte Carlo simulations in combustion applications. TRI effects have been fully taken into account in the investigation of radiative transfer in several turbulent jet flames, including nonluminous flames, such as the Sandia Flame D, artificial flames derived from Flame D, and sooting flames. The effects of different TRI components are investigated. In the nonluminous flames considered in this thesis, it is shown that, to predict the radiation field accurately, emission TRI must be taken into account, while, as expected, absorption TRI is negligible if the total radiation quantities are concerned, but non-negligible for evaluation of local quantities. Generally, the presence of soot greatly increases the optical thickness of flames. As a result, TRI effects are more prominent in sooting flames, as shown in the study of an ethylene flame and its enlarged flame. In the ethylene flame, TRI effects on the temperature distribution are more prominent than in the nonluminous flames. Once again, emission TRI can not be neglected, while the importance of absorption TRI is still minor for overall radiation quantities, though non-negligible for local quantities. This implies that it is still an optically thin flame. However, in optically thick flames, such as the enlarged ethylene flame under investigation, absorption TRI has substantial effects on the flame structure and radiation calculations, and the optically-thin fluctuation approximation is invalid. Strong effects of soot on radiation are also demonstrated, which necessitate a more advanced soot model in future research.