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Evaluation of dynamic behavior of a falling porous magnesium particle over the ignition and combustion processes

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Abstract

In this research study, combustion of micron-sized porous magnesium particle which freely falls into an infinite hot oxidizer medium is investigated. To examine the particle behavior during the process, acceleration and all forces acting on it including mass, buoyancy and drag forces are considered. The effects of produced magnesium oxide and both types of porosity consisting of surface and volume porosities are applied in mathematical modeling. The governing equations including magnesium particle mass continuity, linear momentum balance and energy conservation are numerically solved. Afterward, the impacts of important parameters on combustion characteristics are studied. Results show that by considering both types of surface and volume porosities, combustion time decreases compared to the cases in which one of these parameters is employed. With increasing the particle diameter and its porosity factor, velocity and acceleration enhance. Moreover, during the combustion process, mass and drag forces of magnesium oxide and its radius variations have the most effective contributions in total acceleration with the shares of 39.8%, 30.07% and 12.8%, respectively. Also, contribution of magnesium oxide in total acceleration is 4.8 times greater than that of magnesium.

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Abbreviations

\(A_{\text{eff}}\) :

Effective surface area (m2)

a :

Particle acceleration (m s−2)

Bi:

Biot number

\(C_{\text{ox}}\) :

Weight fraction of oxygen in air

\(C_{\text{P}}\) :

Specific heat of particle (J K−1 kg−1)

\(E_{\text{a}}\) :

Activation energy (J kg−1)

\(F_{\text{B}}\) :

Buoyant force (kg m s−2)

\(F_{\text{D}}\) :

Drag force (kg m s−2)

\(\overline{h}_{\text{conv}}\) :

Average of convective heat transfer coefficient (W m−2 K−1)

k :

Thermal conductivity (W m−1 K−1)

K :

Permeability (m2)

m :

Mass (kg)

Mw:

Molecular weight (kg mol−1)

Nu:

Nusselt number

Pe:

Peclet number

Pr:

Prandtl number

\(Q_{\text{Comb}}\) :

Specific heat of magnesium combustion (J kg−1)

r :

Radius (m)

R :

Pore radius (m)

\(r_{{{\text{Mg}},0}}\) :

Magnesium initial radius (m)

Re:

Reynolds number

\(R_{\text{Mg}}\) :

Gas constant for magnesium (J K−1 kg−1)

\(r_{\text{P}}\) :

Particle radius (m)

t :

Time (s)

T :

Temperature (K)

T :

Initial temperature (K)

\(T_{\text{surr}}\) :

Temperature of surrounding (K)

\(T_{\infty }\) :

Temperature of oxidizer medium (K)

V :

Volume (m3)

v :

Velocity (m s−1)

W :

Mass force (kg m s−2)

x :

Location (m)

ε :

Emissivity

\(\upvarepsilon_{\iota }\) :

Defined in Eq. 20

μ :

Dynamic viscosity (m kg−1 s−1)

ρ :

Density (kg m−3)

σ :

Stefan–Boltzmann constant (W m−2 K−4)

τ :

Magnesium burning time (ms)

φ :

Porosity factor

ω :

Reaction rate (kg s−1 m−2)

in:

Input

out:

Output

Mg:

Magnesium

MgO:

Magnesium oxide

com:

Combustion

sys:

System

\(\infty\) :

Oxidizer medium

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  1. School of Engineering, Mechanical Engineering Department, Iran University of Science and Technology, Narmak, Tehran, Iran

    Peyman Maghsoudi & Mehdi Bidabadi

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  1. Peyman Maghsoudi
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Correspondence to Mehdi Bidabadi.

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Maghsoudi, P., Bidabadi, M. Evaluation of dynamic behavior of a falling porous magnesium particle over the ignition and combustion processes. J Therm Anal Calorim 141, 1605–1617 (2020). https://doi.org/10.1007/s10973-020-09759-9

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