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Frozen core-annular flow model for effervescent atomizer

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Abstract

This research consists in the development of a frozen core-annular flow model to estimate the physical variables of the fluids at the exit orifice of the effervescent atomizer. The model is validated through experimental results of the mean thickness of the ligaments, obtaining excellent estimates for GLR ≥ 1.0%. The model is used to simulate five operating conditions in 17 effervescent atomizers. The results obtained show that the geometric variables defining the atomizer design have no significant influence on the estimated physical variables. The estimated physical variables are: (a) gas volume fraction, (b) dimensionless two-phase pressure, (c) dimensionless gas temperature, (d) dimensionless two-phase density, (e) liquid velocity, (f) gas velocity, and (g) liquid thickness. The ranges for the velocity and thickness of the liquid are [7.976, 26.892 m/s] and [165, 641 µm], respectively. Finally, a dimensionless model is established to estimate the integral Sauter mean diameter (ID32) of the spray droplets. The dimensionless model is characterized by having R2 = 0.734 and RMSE = 3.165, so it is considered good for making future predictions.

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Abbreviations

A :

Area (m2)

\(\overline{c}_{{\text{v,L}}}\) :

Mean specific heat at constant volume for the liquid (kJ/(kg*K))

\(\overline{c}_{{\text{p,G}}}\) :

Mean specific heat at constant pressure for the gas (kJ/(kg*K))

d :

Diameter (mm)

e :

Number of exit orifices of atomizer (–)

E :

Energy transfer (kJ)

g :

Gravity acceleration (m/s2)

GLR:

Mass ratio of gas and liquid flow rates (–)

h :

Specific enthalpy (kJ/kg)

ID32 :

Integral Sauter mean diameter (µm)

\(\dot{m}\) :

Mass flow rate (kg/s)

\(\overrightarrow {n}\) :

Unit normal vector for the control surface

N :

Scalar or vector quantity in relation to the entire control volume

p :

Polytropic index (–)

P :

Absolute pressure (Pa)

P Atm :

Atmospheric pressure (Pa)

\(\dot{Q}\) :

Total volumetric flow rate (m3/s)

\(\dot{q}\) :

Volumetric flow rate in a specific exit orifice of atomizer (m3/s)

Re:

Reynolds number (–)

R G :

Gas constant (kPa*m3/(kg*K))

S :

Surface

sr:

Slip ratio (–)

T :

Temperature (K)

t :

Time (s)

u :

Specific internal energy (kJ/kg)

\(\overrightarrow {V}\) :

Velocity vector

V :

Velocity scalar (m/s)

\(\overline{V}\) :

Mean velocity (m/s)

We:

Weber number (–)

η :

Variable for studying a scalar or vector quantity (N) in the control volume

ρ :

Density (kg/m3)

α :

Volume fraction (–)

β :

Kinetic energy coefficient (–)

γ :

Liquid surface tension (kg/s2)

µ :

Viscosity (kg/(m*s))

π P :

Ratio of the pressure in a position to the pressure in the storage tank (–)

π T :

Ratio of the temperature in a position to the temperature in the storage tank (–)

π ρ :

Ratio of the density in a position to the density of the two-phase mixture using the densities in their respective storage tanks (–)

∀ :

In the context of the use of the Reynolds transport theorem, it expresses volume, and in the context of some condition for a certain determined variable, it has the meaning of the logical symbol ∀

e Thi :

Thickness of the liquid in the atomizer exit orifice (µm)

L:

Refers to the liquid

LT:

Refers to the liquid storage tank

P,L:

Refers to the pressure of the liquid

T,L:

Refers to the temperature of the liquid

L,k :

Refers to liquid at the exit orifice number “k” of atomizer

L,exi:

Refers to liquid in the exit orifice of the core-annular flow

P,L,exi:

Refers to the liquid pressure in the exit orifice of the core-annular flow

T,L,exi:

L,exi: Refers to the liquid temperature in the exit orifice of the core-annular flow

G:

Refers to the gas

GT:

Refers to the gas storage tank

P,G:

Refers to the pressure of the gas

T,G:

Refers to the temperature of the gas

G,k :

Refers to gas at the exit orifice number “k” of atomizer

G,exi:

Refers to gas in the exit orifice of the core-annular flow

P,G,exi:

Refers to the gas pressure in the exit orifice of the core-annular flow

T,G,exi:

Refers to the gas temperature in the exit orifice of the core-annular flow

P,exi:

Refers to the pressure in the exit orifice of the core-annular flow

Heat:

Refers to the transfer of energy by heat

Work:

Refers to the transfer of energy by shaft work

i:

Refers to the diameter of the interface

i,ato:

Refers to the diameter of the interface for any exit orifice of the atomizer

i,exi:

Refers to the diameter of the interface at the exit orifice of the core-annular flow

i,k :

Refers to the diameter of the interface at the exit orifice number “k” of the atomizer

o:

Refers to the largest diameter transversal to the core-annular flow

o,ato:

Refers to the exit diameter for any exit orifice of the atomizer

o,exi:

Refers to the exit diameter in the exit orifice of the core-annular flow

o,k :

Refers to the exit diameter in the exit orifice number “k” of the atomizer

T:

Refers to the storage tank

T-P:

Refers to two-phase flow

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Acknowledgements

This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior—Brasil (CAPES)—Finance Code 001.

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Authors and Affiliations

  1. Chemistry and Energy Department, Engineering School, São Paulo State University (UNESP), Campus of Guaratinguetá, São Paulo, SP, CEP 12510-410, Brazil

    Jordan Amaro & João A. de Carvalho Jr

  2. Department of Mechanical Engineering, Federal University of Rio Grande Do Sul (UFRGS), Porto Alegre, RS, CEP 90050-170, Brazil

    Andrés Z. Mendiburu

  3. Combustion, Propulsion and Energy Laboratory, Technological Institute of Aeronautics (ITA), São José dos Campos, SP, CEP 12228-900, Brazil

    Leila Ribeiro dos Santos

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  1. Jordan Amaro
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  2. Andrés Z. Mendiburu
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  4. João A. de Carvalho Jr
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Correspondence to Jordan Amaro.

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Technical Editor: Erick Franklin.

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Amaro, J., Mendiburu, A.Z., dos Santos, L.R. et al. Frozen core-annular flow model for effervescent atomizer. J Braz. Soc. Mech. Sci. Eng. 44, 452 (2022). https://doi.org/10.1007/s40430-022-03681-x

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  • DOI: https://doi.org/10.1007/s40430-022-03681-x

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