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Modeling and Simulation of a Shock Driving Gas Jet Laden with Dense Extinguishant Particles Through a Tube with a Tail Nozzle

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Abstract

In this study, we proposed a new concept of shock wave driving fire extinguishing system (SWDES), which works using a pulsed shock-induced gas-particle jet. We conducted modeling and simulations of shock-induced gas-particle jets through a rectangular tube with a tail nozzle based on a dense discrete phase model. A corrected drag model was developed to take into account gas compressibility and particle volume fraction effects. The aerodynamic and collision forces imposed on particles were determined by a point particle force model and an improved spring-dashpot model, respectively. Based on the validation of numerical method against a previous experiment, a parametric study was performed to explore the effects of type of tail nozzle, incident shock Mach number Ms, initial particle volume fraction φp, and particle size dp on the dimensionless streamwise average velocity vpx,a/us, velocity inhomogeneity ξvp and dispersity of particles ψp. We revealed that the evolution process of the gas-particle jet consists of the first transmitted shock-induced stage and the second pressure-induced stage of gas jet, and identified penetration, spreading and breakup types of pulsed gas-particle jets suited for fire suppression of correspondingly three types of flames.

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Abbreviations

c :

Local sound speed

C 1 :

Turbulence model parameter

C 1ε :

Turbulence model constant

C 2 :

Turbulence model constant

c 2 :

Post-incident shock sound speed

C 3 ε :

Turbulence model constant

C D :

Drag coefficient

C DC :

Clift drag coefficient

C DP :

Parmar drag coefficient

CFL :

Courant number

C M :

Pressure-gradient force coefficient

C p :

Particle specific heat

c pg :

Gas specific heat at constant pressure

d p :

Particle diameter

D p :

Effective diameter of a particle parcel

e g * :

Specific total energy

\(e_{i}^{mn}\) :

Pre-collisional unit relative velocity component between the mth and nth particle parcels

e ij :

Identity matrix component

F am,i :

Added-mass force component

F f p ,i :

Overall aerodynamic force component

F pg,i :

Pressure-gradient force component

\(F_{pp,i}^{n}\) :

Overall collisional force component imposed on the nth particle

\(F_{pp,i}^{mn}\) :

Collisional force component on the mth particle parcel by the nth particle parcel

F qs,i :

Quasi-steady force component

f v :

Correction factor of particle volume fraction

G b :

Turbulent kinetic energies related to the average buoyancy

\(G_{fp}^{n}\) :

Rate of work on the nth particle parcel caused by the aerodynamic force

G k :

Turbulent kinetic energies related to the average velocity gradient

I :

Total number of particles

k :

Turbulent kinetic energy

K :

Spring constant

k ef f :

Effective thermal conductivity

L :

Total number of all the lth particle parcels in contact with the nth particle parcel

L a :

Length of acceleration section

L e :

Side length of nozzle exit

L f :

Distance from the channel inlet to the upstream side of particle curtain

L j :

Length of tail nozzle

L l :

Length of outside flow field

L p :

Initial width of particle curtain

L s :

Side length of rectangular channel

L t :

Wall thickness

L w :

Width of outside flow field

m p :

Mass of a single particle

M p :

Particle Mach number

M s :

Shock Mach number

n :

Number of particle parcels within the current cell

N :

Total number of particle parcels

N p :

Number of real particles represented by one particle parcel

Nu:

Nusselt number

p 1 :

Initial pressure downstream the incident shock wave

Pr:

Prandtl number

\(Q_{fp}^{n}\) :

Rate of heat transfer to the nth particle parcel from the gas

Q gp :

Gas convective heat transfer to a particle

Rep :

Particle Reynolds number

S ij :

Mean strain rate component

t :

Time

T 1 :

Initial temperature downstream the incident shock wave

T g :

Gas temperature

T p :

Particle temperature

v 2 :

Post-incident shock gas velocity

v g,i :

Gas velocity component

\(v_{i}^{mn}\) :

Pre-collisional relative velocity component between the mth and nth particle parcels

V p :

Volume of a single particle

v p ,i :

Particle velocity component

\(v_{px}^{n}\) :

Streamwise velocity of the nth particle

v px,a :

Streamwise average velocity

xp,i :

i-Direction position coordinate of the particle

Y M :

Contribution of pulsating expansion to the total dissipation rate

\(y_{p}^{n}\) :

y Coordinate of the nth particle

y + :

Dimensionless wall distance

\(z_{p}^{n}\) :

z Coordinate of the nth particle

v g :

Gas velocity vector

v mn :

Relative velocity vector between the mth and nth particle parcels

v p :

Particle velocity vector

γ :

Ratio of gas specific heats

δ :

Overlap of the collision pair of particle parcels

Δl min :

Minimum grid size

ε :

Rate of turbulent dissipation

η :

Coefficient of restitution

λ :

Damping coefficient

μ :

Gas dynamic viscosity

μ t :

Turbulent viscosity

ν g :

Gas kinematic viscosity

ξ :

Turbulence model parameter

ξ D :

Denotes the allowable overlap fraction of diameter

ξ vp :

Velocity inhomogeneity

ρ g :

Gas density

ρ p :

Particle density

σ ε :

Turbulence model constant

σ k :

Turbulence model constant

\(\tau_{eff,ij}\) :

Effective stress tensor component

τ g :

Time step of gas phase

\(\tau_{m,ij}\) :

Molecular stress tensor

\(\tau_{t,,ij}\) :

Reynolds stress tensor

φ g :

Gas volume fraction

φ p :

Particle volume fraction

ψ p :

Dispersity of particles

CAFES:

Condensed aerosol-based fire extinguishing system

DDPM:

Dense discrete phase model

DEM:

Distinct elemental method

DFP:

Downstream front of the particle curtain

EW:

Expansion wave

OS:

Oblique shock

SWDES:

Shock wave driving fire extinguishing system

TS:

Transmitted shock

UFP:

Upstream front of the particle curtain

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Acknowledgements

The authors are grateful to the precious suggestions from Prof. Honghui Shi, Dr. Ruoling Dong and Huixia Jia, and the help on figure production from Ms. Sifan Wu, Mr. Jing Wang and Yang Feng.

Funding

This work was supported by the Natural Science Foundation of Zhejiang Province [Grant Number LY17E060006], from the Fundamental Research Funds of Zhejiang Sci-Tech University [Grant Number 2019Q030], and the National Natural Science Foundation of China [Grant Numbers 51876194, 52176048, U1909216].

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  1. School of Mechanical Engineering, Zhejiang Sci-Tech University, 928 Second Avenue, Xiasha Higher Education Zone, Hangzhou, 310018, China

    Lite Zhang, Hao Guan, Zilong Feng, Mengyu Sun & Haozhe Jin

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Zhang, L., Guan, H., Feng, Z. et al. Modeling and Simulation of a Shock Driving Gas Jet Laden with Dense Extinguishant Particles Through a Tube with a Tail Nozzle. Fire Technol 59, 3629–3666 (2023). https://doi.org/10.1007/s10694-023-01481-w

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