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Modeling of sequential reactions during micropyretic synthesis

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Abstract

A numerical model for a two-step sequential micropyretic reaction is reported. Such multiple reactions can take place during micropyretic synthesis of composite materials. The model was developed for the aluminothermic reaction between molybdenum oxide, aluminum, and silicon, which react to give molybdenum disilicide and aluminum oxide. The model was used to obtain the solution for the propagation of the combustion front. The melting of various constituents of reactants and products was incorporated into the model. The effect of the pre-exponential factor and the amount of diluent on the nature of propagation and temperature profile was investigated. Other conditions of propagation and synthesis for general two-step reactions were explored by changing the activation energy and heat release of each sequential reaction. A mapping procedure to characterize the types of sequential reactions is proposed and studied for several aluminothermic type reactions.

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Abbreviations

C p :

specific heat, J/kg K

C pl :

specific heat of liquid phase, J/kg K

N i :

number of moles of componenti

E :

activation energy, J/mole

H :

enthalpy, J/kg

ΔH sl :

latent heat of fusion, J/kg

K 0 :

pre-exponential factor, s−1

K eff :

effective thermal conductivity, W/m K

K Reff :

effective thermal conductivity of reacted products, W/m K

K Ueff :

effective thermal conductivity of unreacted constituents, W/m K

Q :

heat of reaction, J/kg

R:

universal gas constant, J/mole K

T :

temperature, K

T m :

melting point, K

T 0 :

substrate temperature, K

T c :

combustion temperature corresponding to total heat released, K

T′ c :

combustion temperature corresponding to heat of first reaction, K

V f :

volume fraction

V :

propagation velocity, m/s

V 1(T c ):

analytically calculated velocity of first reaction atT c , m/s

V 1,(T c ):

analytically calculated velocity of first reaction atT c , m/s

V 2(T c ):

analytically calculated velocity of second reaction atT c , m/s

W f :

weight fraction

ε :

volume fraction of porosity

ρ :

density, kg/m3

ϕ :

heat release rate, J/m3s

ϕ 1(T c ):

heat release rate of first reaction atT c , J/m3sϕ 1(T′ c ) heat release rate of first reaction atT′ c , J/m3s

ϕ 2(T c ):

heat release rate of second reaction atT c K, J/m3s

ϕ 2(T′ c ):

heat release rate of second reaction atT c K, J/m3s

η :

fraction reacted

n :

new time level

o :

old time level

m :

iteration number

n :

northern side of control volume

N :

northern control volume

P :

center of current control volume

s :

southern side of control volume

S :

southern control volume

1:

first reaction

2:

second reaction

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Authors and Affiliations

  1. University of Cincinnati, 45221-0012, Cincinnati, OH

    J. A. Sekhar (Director, International Center for Micropyretics, and Professor, Department of Materials Science and Engineering)

Authors
  1. V. Subramanian
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  2. M. G. Lakshmikantha
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  3. J. A. Sekhar
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Formerly Graduate Research Assistants, Department of Materials Science and Engineering

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Subramanian, V., Lakshmikantha, M.G. & Sekhar, J.A. Modeling of sequential reactions during micropyretic synthesis. Metall Mater Trans A 27, 961–972 (1996). https://doi.org/10.1007/BF02649764

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  • DOI: https://doi.org/10.1007/BF02649764

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