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Prediction of impinging spray penetration and cone angle under different injection and ambient conditions by means of CFD and ANNs

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Abstract

This paper presents a numerical study on 3D non-reacting isothermal impinging spray penetration and cone angle under different injection pressure and ambient conditions. The selected ambient conditions include different nozzle diameters, injection profiles, backpressure and ambient temperature. Transient Eulerian–Lagrangian multiphase solver in open source software, i.e., OpenFOAM, has been used for modeling fuel discrete phase interacting with compressible gaseous continuous phase. In addition, hybrid breakup model of KH–RT and k–ε have been applied as the standard model in Reynolds averaged Navier–Stokes for liquid fuel core breakup and turbulence modeling, respectively. Numerical results of macroscopic spray characteristics have been validated against the experiment. On the other hand, supervised feed-forward artificial neural networks (ANNs) with back-propagation learning algorithm have been designed to predict the average impinging spray penetration and cone angle under five different injection and ambient conditions. Likewise, 51 different CFD patterns have been used as the input evidence in the selected ANNs. To optimize the learning procedure, Levenberg–Marquardt algorithm has been employed. Based on the iterative algorithm, our optimal ANNs have been selected from 260 different architectures. The selected ANNs are able to predict the impinging penetration length with mean square error (MSE) lower than 0.00097 and correlation coefficient higher than 0.98921. Moreover, the selected ANNs for predicting the spray cone angle have maximum MSE of 0.0004 and minimum correlation coefficient of 0.99439. According to weights and bias of the designed ANNs, two set of equations are proposed for predicting the impinging penetration length and cone angle. Moreover, Based on CFD results, longer impinging penetration length and larger cone angle are achieved using higher injection pressure and ambient temperature and lower backpressure.

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Abbreviations

CFD:

Computational fluid dynamic

ANNs:

Artificial neural networks

HFO:

Heavy fuel oil

SMD:

Sauter mean diameter

RANS:

Reynolds averaged Navier–Stokes

MSE:

Mean square error

RMSE:

Root mean square error

MLA:

Marquardt–Levenberg algorithm

ASOI:

After start of injection

PISO:

Pressure implicit with splitting of operator

SIMPLE:

Semi-implicit method for pressure linked equations

LPT:

Lagrangian particle tracking

DH:

Diameter of nozzle hole [m]

IP:

Injection pressure [MPa]

PRO:

Injection profile

BP:

Backpressure [MPa]

APL:

Averaged penetration length [mm]

ACA:

Averaged cone angle [deg]

KH:

Kelvin–Helmholtz

R :

Correlation coefficient

N :

Number of evidence data

RT:

Rayleigh–Taylor

y + :

Distance to the wall in the wall units

T :

Ambient temperature [K]

T e :

Temperature [K]

T a :

Taylor number

f :

Probable number of droplets per unit volume

r :

Radius [m]

u :

Velocity [m s−1]

t :

Time [s]

\(\dot{y}\) :

The first derivative of y-position

\(\dot{f}_{\text{co}}\) :

Contribution due to the effects of collision of the droplets

\(\dot{f}_{\text{br}}\) :

Contribution due to the effects of droplets breakup

X :

Coordinate in the x-direction [m]

Y :

Coordinate in the y-direction [m]

Z :

Coordinate in the z-direction [m]

We l :

Liquid fuel Weber number

We g :

Gas Weber number

u rel :

Relative speed between droplets and ambient gas [m s−1]

D d :

Diameter of fuel droplet [m]

Re l :

Liquid fuel Reynolds number

r 0 :

Droplet radius before breakup [m]

r c :

Radius of child droplets [m]

Oh :

Ohnesorge number

C D :

Drag coefficient

a :

Droplet acceleration [m s−2]

O i :

Predicted results

b o :

Output layer bias

n j :

The jth neuron of output

r p :

Number of previous layer neurons

b j :

Bias of jth neuron

p i :

Output of ith neuron

r :

Number of neurons

N :

Number of outside evidence

y desired :

Number of reference data as desired values

\(\bar{y}_{desired}\) :

Average of desired values

Zi :

Impinging distance [mm]

ω ij :

Interconnection weight from ith neuron in previous layer to the jth neuron

ω L :

Interconnection weights between last hidden layer with output layer

λ :

Linear transfer function

ϕ n :

Normalized input

Λ KH :

Kelvin–Helmholtz wavelength [m]

Λ RT :

Rayleigh–Taylor wavelength [m]

Ω KH :

Kelvin–Helmholtz growth rate [s−1]

Ω RT :

Rayleigh–Taylor growth rate [s−1]

ρ g :

Gas density [kg m−3]

ρ l :

Liquid fuel density [kg m−3]

τ bu :

Characteristic time [s]

σ :

Surface tension [N m−1]

ν g :

Gas kinematic viscosity [m2 s−1]

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Authors and Affiliations

  1. Department of Marine Technology, Amirkabir University of Technology (Tehran Polytechnic), Hafez Ave, No 424, P.O. Box 15875-4413, Tehran, Iran

    Hashem Nowruzi & Hassan Ghassemi

  2. Department of Mechanical Engineering, Islamic Azad University, Science and Research Branch, Tehran, Iran

    Ebrahim Amini

  3. Department of Mechanical Engineering, Babol Noshirvani University of Technology, Mazandaran, Iran

    Iman Sohrabi-asl

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  1. Hashem Nowruzi
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  2. Hassan Ghassemi
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Correspondence to Hashem Nowruzi.

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Technical Editor: Cezar Negrao.

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Nowruzi, H., Ghassemi, H., Amini, E. et al. Prediction of impinging spray penetration and cone angle under different injection and ambient conditions by means of CFD and ANNs. J Braz. Soc. Mech. Sci. Eng. 39, 3863–3880 (2017). https://doi.org/10.1007/s40430-017-0781-1

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