Two-dimensional direct numerical simulation of spray flames - Part 1: Effects of equivalence ratio, fuel droplet size and radiation, and validity of flamelet model

doi:10.1016/j.fuel.2012.08.044

Fuel

Volume 104, February 2013, Pages 515-525

https://doi.org/10.1016/j.fuel.2012.08.044 Get rights and content

Abstract

The effects of equivalence ratio, fuel droplet size, and radiation on jet spray flame are investigated by means of two-dimensional direct numerical simulation (DNS). In addition, the validity of an extended flamelet/progress-variable approach (EFPV), in which heat transfer between droplets and ambient fluid including radiation is exactly taken into account, is examined. n-decane (C₁₀H₂₂) is used as liquid spray fuel, and the evaporating droplets’ motions are tracked by the Lagrangian method. The radiative heat transfer is calculated using the discrete ordinate method with S₈ quadrature approximation. The results show that the behavior of jet spray flame is strongly affected by equivalence ratio and fuel droplet size. The general behavior of the jet spray flames including the heat transfer between droplets and ambient fluid with radiation effect can be captured by EFPV.

Highlights

► We investigate effects of equivalence ratio, fuel droplet size, and radiation. ► Contribution of premixed flame increases as fuel droplet size decreases. ► Heat transfer between droplets and ambient fluid is captured by flamelet model.

Introduction

Spray combustion is utilized in a number of engineering applications such as energy conversion and propulsion devices. It is therefore necessary to predict the spray combustion behavior precisely when designing and operating equipment. However, since spray combustion is a complex phenomenon in which the dispersion of the liquid fuel droplets, their evaporation, and the chemical reaction of the fuel vapor with the oxidizer take place interactively at the same time, the underlying physics governing these processes has not been well understood.

Recently, the spray combustion behavior has been studied by direct numerical simulations (DNSs) [1], [2], [3], [4], [5], [6], [7], [8] or large-eddy simulations (LESs) [9], [10], [11], [12]. However, since these computations are still so expensive that the effects of the changes in combustion conditions such as equivalence ratio, fuel droplet size and ambient pressure on the spray combustion behavior have not been sufficiently discussed yet. Moreover, in most of these studies, radiative heat transfer was neglected or significantly simplified, because the computation of radiation further increases the computational cost. Watanabe et al. [5] studied the effects of radiation on the spray flame characteristics and soot formation by performing a two-dimensional DNS of spray flames formed in a laminar counterflow, in which the radiative interaction between the gas and dispersed droplets is taken into account, and found that the radiative heat transfer strongly affects the spray flame and soot formation behaviors. However, since the radiation effect is discussed only on the spray flames formed in a laminar counter flow, there remains uncertainty as to how the radiative heat transfer affects the characteristics of jet spray flames.

In LES and RANS (Reynolds-Averaged Navier–Stokes) simulations of gaseous combustions, flamelet models [13], [14] have been widely used as the turbulent combustion model. However, in the original flamelet model in which the energy equation is not solved in the physical space, not only the radiative heat transfer but also convective heat transfer between the gas and droplets for the spray combustion cannot be taken into account. Recently, Ihme and Pitsch [12] extended the flamelet/progress-variable approach [15] (referred to as FPV, in this paper) to account for the radiative heat transfer, and investigated the effects of radiation on the gas temperature and NO formation on LES of Sandia flame D and a realistic aircraft engine. However, they considered the radiation only in the gas phase using the optically thin approximation [16] and still neglected the heat transfer between droplets and ambient fluid including radiation.

The purpose of this study is therefore to investigate the effects of equivalence ratio, fuel droplet size, ambient pressure and radiation on the spray combustion behavior by means of two-dimensional DNS of spray jet flames. In addition, FPV coupled with the radiation model, which can account for the heat transfer between droplets and ambient fluid including radiation, (referred to as EFPV, in this paper) is proposed and validated by comparing with the results using the direct combustion model based on the Arrhenius formation (referred to as ARF, in this paper). n-decane (C₁₀H₂₂) is used as liquid spray fuel, and the evaporating droplets’ motions are tracked by the Lagrangian method. The radiative heat transfer is calculated using the discrete ordinate method [17] with S₈ quadrature approximation. The present paper provides the first part of two investigations. In this part 1, the effects of equivalence ratio, fuel droplet size and radiation on the spray combustion behavior are investigated. In addition, the validity of EFPV in various equivalence-ratio and fuel-droplet-size conditions and in the presence of the radiation are examined. In part 2 [18], the effect of ambient pressure on the spray combustion behavior and the validity of EFPV in high-pressure condition will be discussed. Originally, combustion models such as FPV are intended for use in connection with SGS models for LES or RANS of the carrier gaseous phase. However, in order to avoid discussion of the effect of the SGS contributions on numerical accuracy, a numerical method using fine resolution without the SGS models is chosen here. In these papers, we simply call this method DNS, regardless of the combustion model.

Section snippets

Numerical methods for ARF and EFPV

In ARF, the Arrhenius formation is directly solved in the physical space as well as the flow field. In EFPV, on the other hand, the Arrhenius formation is solved in generating a lookup table called flamelet library. Therefore, the detailed spray combustion behavior is investigated based on ARF, and the validity of EFPV is discussed by comparing with the results obtained by ARF.

The set of governing equations of the carrier gaseous phase and dispersed droplets phase for ARF and EFPV are described

Effects of equivalence ratio and fuel droplet size (without radiation)

Table 1 shows the equivalence ratio, ϕ, and the maximum value of non-dimensional initial droplet diameter, D_max, of the cases performed under the condition without the radiation in this study and the general features of these spray flames. The values at where ϕ and D_max intersect indicate the contributions of the premixed flame to the sum of the premixed and diffusion flames at a certain moment in the upstream (0 ⩽ x ⩽ 0.5) and downstream (3.0 ⩽ x ⩽ 3.5) regions, P_p, estimated by $P_{p} = \frac{\int {\dot{ω}}_{p} (x, y) dxdy}{\int \dot{ω} (x, y}$

Conclusions

The effects of equivalence ratio, fuel droplet size, and radiation on jet spray flames were investigated by means of two-dimensional direct numerical simulation (DNS). In addition, the validity of an extended flamelet/progress-variable approach (EFPV), in which heat transfer between droplets and ambient fluid including radiation was exactly taken into account, is examined. n-decane (C₁₀H₂₂) was used as liquid spray fuel, and the evaporating droplets’ motions were tracked by the Lagrangian

Acknowledgements

The authors are grateful to Dr. Yuya Baba of Earth Simulator Center, Japan Agency for Marine-Earth Science Technology (JAMSTEC) and Mr. Yutaka Yano of Kyoto University for many useful discussions. A portion of this research was supported by the grant for “Strategic Program-Research Field No. 4: Industrial Innovations” from the Ministry of Education, Culture, Sports, Science, and Technology (MEXT)’s ”Development and Use of Advanced, High-Performance, General-Purpose Supercomputers Project”.

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Citation Excerpt :
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Two-dimensional direct numerical simulation of spray flames - Part 1: Effects of equivalence ratio, fuel droplet size and radiation, and validity of flamelet model

Abstract

Highlights

Introduction

Section snippets

Numerical methods for ARF and EFPV

Effects of equivalence ratio and fuel droplet size (without radiation)

Conclusions

Acknowledgements

Combust Flame

Combust Flame

Combust Flame

Combust Flame

Proc Combust Inst

Combust Flame

Prog Energy Combust Sci

Combust Flame

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Int J Heat Mass Transfer

J Comput Phys

J Comput Phys