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Numerical simulation of an ethanol turbulent spray flame with RANS and diffusion combustion model

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Abstract

A detailed numerical simulation of ethanol turbulent spray combustion on a rounded jet flame is presented in this article. The focus is to propose a robust mathematical model with relatively low complexity submodels to reproduce the main characteristics of the coupling between both phases, such as the turbulence modulation, turbulent droplets dissipation, and evaporative cooling effect. A RANS turbulent model is implemented. Special features of the model include an Eulerian–Lagrangian procedure under a fully two-way coupling and a modified flame sheet model with a joint mixture fraction–enthalpy β-PDF. Reasonable agreement between measured and computed mean profiles of temperature of the gas phase and droplet size distributions is achieved. Deviations found between measured and predicted mean velocity profiles are attributed to the turbulent combustion modeling adopted.

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Abbreviations

A P :

Surface area of the droplet

B :

Spalding number

c p :

Sensible specific heat

c P :

Specific sensible heat of the liquid

C d and C g :

Adjustable constants in the equation of mixture fraction variance

C D :

Draft coefficient

C L,S :

Concentration of liquid vapor on surface of the droplet

C L,∞ :

Concentration of liquid vapor on gas phase

C 3ε :

Adjustable parameter

C μ , C1ε , C 2ε :

Adjustable constants of the k–ε Standard model

d p :

Droplet diameter

D :

Diameter of the fuel nozzle

D L,m :

Binary mass diffusion coefficient of vapour of the liquid in air

D ψ :

Diffusive part of the equation

f :

Mixture fraction

f″2 :

Mixture fraction variance

g :

Gravity acceleration vector

g i :

Component in the i direction of the gravitational acceleration

h :

Specific enthalpy or heat transfer coefficient of convection

h fl :

Enthalpy of vaporization of the fuel

k :

Kinetic turbulent energy

k C :

Mass transfer coefficient

k ∞ :

Thermal conductivity of the gas phase

L :

Turbulent integral scale

m P :

Mass of a droplet

Mwl :

Molar mass of the liquid

p :

Gas pressure

\( \bar{p} \) :

Time average of pressure

p sat :

Saturation pressure of the liquid

Pr :

Prandtl number

R :

Universal constant of ideal gases

Re e :

Droplet’s Reynolds number

s :

Stoichiometric oxidant/fuel mass ratio for the global reaction mechanism

Sc :

Schmidt number

\( \tilde{S}_{ij} \) :

Deformation tensor

\( \overline{{S_{{{\text{p}},\psi }} }} \) :

Source term associated with the transport and evaporation of droplets

S ψ :

Extra and source terms of the equation

t :

Time

T :

Temperature of the gas phase

T P :

Temperature of the droplet

T ref :

Reference temperature

u :

Instantaneous velocity vector of the gas phase

\( \tilde{u}_{j} \) :

Density-weighted averaging of the Cartesian component of velocity in j direction

u j ″ :

Density-weighted component of turbulent fluctuation of the velocity in direction j

u P :

Instantaneous velocity vector of the droplet

u Pi :

Instantaneous component of velocity in i direction of the droplet

x j :

Spatial Cartesian coordinate in j direction

X L :

Mole fraction of the liquid vapour

x P :

Displacement vector of the droplet

Y ox,0 :

Maximum mass fraction of oxidant in flame domain

α :

Total number of particles in a cell in the time step of the continuous phase

δij :

Kronecker’s delta operator

Δm p :

Variation of mass of a droplet due to the evaporation

ΔV :

Volume of a cell

Δt :

Time step of dispersed phase

ΔT log :

Logarithmic mean temperature difference, K

ε :

Dissipation of kinetic turbulent energy

μ :

Molecular dynamic viscosity

μ t :

Turbulent viscosity

\( \bar{p} \) :

Time averaged density of the gas mixture

ρ l :

Density of the liquid phase

σ k , σ ε :

Adjustable constants of the k–ε Standard model

σ t :

Turbulent Prandtl/Schmidt number

τ :

Relaxation time scale of a droplet

\(\widetilde{\tau }_{{ij}}\) :

Mean flow stress tensor

ψ :

General variable

\( \gamma \) :

Angle between two adjacent pins in the same cross-section, deg

\( \eta \) :

Pin efficiency, pinned region efficiency, dimensionless

μ :

Air dynamic viscosity, dynamic viscosity, kg/(m s)

ρ :

Air density, kg/m3

e :

Property when a particle enter in a cell

s :

Property when a particle exits from a cell

\( \sim \) :

Favre’s average

\( - \) :

Time average

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Acknowledgments

The authors would like to thank the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) for supporting of this work under the grant ‘‘CAPES-PRÓ-ENGENHARIAS/ESTUDO COMPUTACIONAL E EXPERIMENTAL DE CHAMAS TURBULENTAS DE ETANOL’’— PE004/2008 and, the Laboratory of Environmental and Thermal Engineering (LETE) of the Polytechnic School of the University of Sao Paulo.

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Authors and Affiliations

  1. Laboratory of Environmental and Thermal Engineering, University of São Paulo/EPUSP, São Paulo, SP, 05508-030, Brazil

    Fernando Luiz Sacomano Filho, Newton Kiyoshi Fukumasu & Guenther Carlos Krieger

Authors
  1. Fernando Luiz Sacomano Filho
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  2. Newton Kiyoshi Fukumasu
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  3. Guenther Carlos Krieger
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Correspondence to Fernando Luiz Sacomano Filho.

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Technical Editor: Luis Fernando Silva.

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Sacomano Filho, F.L., Fukumasu, N.K. & Krieger, G.C. Numerical simulation of an ethanol turbulent spray flame with RANS and diffusion combustion model. J Braz. Soc. Mech. Sci. Eng. 35, 189–198 (2013). https://doi.org/10.1007/s40430-013-0029-7

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