Study on the formation and development of the white layer in the erosive propellant gas

Abstract

To investigate the formation and development characteristics of the white layer on a gun exposed to erosive and high-temperature propellant gas, an experiment was conducted, and a transient model comprising chemical reactions was established. The numerical results showed a close agreement with the experiment, with a maximum error of 8%. The results suggest that the development of the white layer is primarily influenced by surface carburization under experimental conditions. Moreover, the carbon content and thickness of the white layer monotonically increase, displaying a logarithmic relationship with erosion time. The carbon content is the highest on the surface and decreases rapidly with depth. Furthermore, the growth rate of the white layer is found to correlate positively with the temperature of the propellant gas. When the temperature approaches the melting point of cementite, the surfaces of the samples become softened, leading to an enhanced diffusion rate of carbon to the deep layers. This phenomenon promotes cementite formation, accelerating the white layer’s development.

Appendix

1.1 Notation

a(S):

coefficient related to carbon content

a _j(M):

coefficient of the effect of M on the third-body reaction j

${A}_j^f$ :

pre-exponential factor of reaction j

A _surf :

area of the specimen surface

c _g :

concentration of the gas mixture

c _i :

concentration of component i

c _{surf − Fe} :

concentrations of Fe on the surface

${c}_{\textrm{surf}-F{\textrm{e}}_3C}$ :

concentrations of Fe₃C on the surface

C _p :

specific heat capacity

C _pf :

specific heat capacity of total fluid component

C _pi :

specific heat capacity of component i

C _ps :

specific heat capacity of steel

d :

thickness of sample

${D}_{c_0}$ :

initial diffusion coefficient of carbon

D _C :

diffusion coefficient of carbon

D _i :

diffusion coefficient of components except for carbon

E ^f :

activation energy of reaction

E _c :

activation energy of the carbonization

h _g :

convection heat transfer coefficient between the gas and the wall

h _i :

enthalpy of reactant/generator i

h _w :

thickness of the white layer

H _j :

reaction heat of reaction j

k _eff :

equivalent thermal conductivity coefficient of samples

k _f :

thermal conductivity coefficient of total fluid component

k _g :

propellant gas thermal conductivity coefficient

k _i :

thermal conductivity coefficient of component i

${k}_j^f$ :

reaction rate constant of reaction j

k _s :

thermal conductivity coefficient of steel

M _i :

molar mass of component i

n _C :

total quantity of C element per unit area inside the sample

p _g :

gas pressure around the sample

Pr:

Plante number

Q _react :

heat released/absorbed in reactions

R ₀ :

universal gas constant

R _i :

chemical reaction rate

${R}_{F{e}_3C}$ :

Fe₃C generation rate in the sample

r _j :

reaction rate of reaction j

Re:

Reynolds number

S :

carbon content of the sample

t :

time in calculation

T :

reaction temperature

T _g :

temperature of the gas

T _w :

surface temperature of the specimen

v _ij :

stoichiometric number of component i in reaction j

v _D :

carbon diffusion rate on the surface

V _r :

cell volume

x :

coordinate in calculation

θ _f :

volume fraction of total fluid component

θ _i :

volume fraction of component i

θ _s :

volume fraction of steel

ρ :

density

ρ _f :

density of total fluid component

ρ _s :

density of steel

ω _i :

mass fraction of component i