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    Journals >Journal of Inorganic Materials >Volume 34 >Issue 6 >Page 660 > Article
    • Journal of Inorganic Materials
    • Vol. 34, Issue 6, 660 (2019)
    Simulation of ZrB2 Oxidation Behavior at Constant Temperature Ambient
    Shu-Guang ZHOU1,2, Yi-Jun GUO2,*, and Xiao LIU2
    Author Affiliations
  • 1State Key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, Mianyang 621000, China
  • 2Computational Aerodynamics Institute, China Aerodynamics Research and Development Center, Mianyang 621000, China
    • show less
    DOI: 10.15541/jim20180395 Cite this Article
    Shu-Guang ZHOU, Yi-Jun GUO, Xiao LIU. Simulation of ZrB2 Oxidation Behavior at Constant Temperature Ambient[J]. Journal of Inorganic Materials, 2019, 34(6): 660 Copy Citation Text show less

    Abstract

    Zirconium diboride (ZrB2), a thermal protection material for hypersonic vehicle, has received widespread attention in recent years. Here we advance an oxidation model based on oxidation products (ZrO2 and B2O3) and their morphology at different temperatures to simulate the oxidation behavior of ZrB2. This study further establishes the dynamic equilibrium among formation, evaporation and supplement of B2O3 whose concentration at ambient was assumed to be nonzero. Research results indicate that the advanced model can predict the oxidation behavior of ZrB2 under quasi-static low flow conditions and the simulation results are consistent with the data obtained from sample suspended in wire heater furnace at constant temperature. The porosity has a great influence on the oxidation process, and at the same temperature and oxygen partial pressure, the larger the porosity, the higher the oxidation degree. The oxidation rate controlled by diffusion in the presence of liquid B2O3 film laying outer surface of substrate reduces greatly and the material exhibits the strongest oxidation resistance.

    Keywords

    $JO2=f∏O2-B2O3L(pO2zb−pO2s) =    ∏O2-B2O3hext(pO2a−pO2zb)$

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    ${{\Pi }_{{{\text{O}}_{\text{2}}}\text{-}{{\text{B}}_{\text{2}}}{{\text{O}}_{\text{3}}}}}=0.109\exp \left( -\frac{16724.83}{T} \right)$

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    $p_{{{\text{O}}_{\text{2}}}}^{\text{s}}=2.408\times {{10}^{7}}\exp \left( -\frac{94434.844}{T} \right)$

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    $\frac{\text{d}L}{\text{d}t}=\frac{1}{1-f}\frac{2}{5}{{J}_{{{\text{O}}_{\text{2}}}}}\frac{{{M}_{\text{Zr}{{\text{O}}_{\text{2}}}}}}{{{\rho }_{\text{Zr}{{\text{O}}_{\text{2}}}}}}$

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    $ΓB2O3ext=dnext,B2O3dt=dLdt1−fMZrO2/ρZrO2−    fdLdtρB2O3MB2O3−Jevap(B2O3)$

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    $\frac{\text{d}{{h}_{\text{ext}}}}{\text{d}t}=\Gamma _{{{\text{B}}_{\text{2}}}{{\text{O}}_{\text{3}}}}^{\text{ext}}\frac{{{M}_{{{\text{B}}_{\text{2}}}{{\text{O}}_{\text{3}}}}}}{{{\rho }_{{{\text{B}}_{\text{2}}}{{\text{O}}_{\text{3}}}}}}$

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    ${{h}_{\text{ext}}}={{\left[ \frac{3({{M}_{{{\text{B}}_{\text{2}}}{{\text{O}}_{\text{3}}}}}\Gamma _{{{\text{B}}_{\text{2}}}{{\text{O}}_{\text{3}}}}^{\text{ext}}{{l}_{\text{spec}}}){{\mu }_{{{\text{B}}_{\text{2}}}{{\text{O}}_{\text{3}}}}}}{g\rho _{{{\text{B}}_{\text{2}}}{{\text{O}}_{\text{3}}}}^{2}\sin \left( \phi \right)} \right]}^{{1}/{3}\;}}$

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    ${{R}_{\text{s}}}=L\left( 1-f \right)\frac{{{{M}_{\text{Zr}{{\text{B}}_{\text{2}}}}}}/{{{\rho }_{\text{Zr}{{\text{B}}_{\text{2}}}}}}\;}{{{{M}_{\text{Zr}{{\text{O}}_{\text{2}}}}}}/{{{\rho }_{\text{Zr}{{\text{O}}_{\text{2}}}}}}\;}$

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    $ΔW/A=LρZrO2(1−f)+    (hext+fL)ρB2O3−RsρZrB2$

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    ${{J}_{{{\text{O}}_{\text{2}}}}}=\frac{5}{2}{{\dot{n}}_{\text{Zr}{{\text{O}}_{\text{2}}}}}=\frac{5}{2}{{\dot{n}}_{{{\text{B}}_{\text{2}}}{{\text{O}}_{\text{3}}}}}$

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    $p_{{{\text{B}}_{\text{2}}}{{\text{O}}_{\text{3}}}}^{\text{i}}=1.841\times {{10}^{8}}\exp \left( -\frac{44661.247}{T} \right)$

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    ${{J}_{{{\text{B}}_{\text{2}}}{{\text{O}}_{\text{3}}}}}=f{{D}_{{{\text{B}}_{\text{2}}}{{\text{O}}_{\text{3}}}}}\frac{C_{{{\text{B}}_{\text{2}}}{{\text{O}}_{\text{3}}}}^{\text{i}}-C_{{{\text{B}}_{\text{2}}}{{\text{O}}_{\text{3}}}}^{\text{a}}}{L-{{h}_{\operatorname{int}}}}$

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    $\Gamma _{{{\text{B}}_{\text{2}}}{{\text{O}}_{\text{3}}}}^{\operatorname{int}}={{\dot{n}}_{{{\text{B}}_{\text{2}}}{{\text{O}}_{\text{3}}}}}-{{J}_{{{\text{B}}_{\text{2}}}{{\text{O}}_{\text{3}}}}}$

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    $\frac{\text{d}{{h}_{\operatorname{int}}}}{\text{d}t}=\frac{1}{f}\Gamma _{{{\text{B}}_{\text{2}}}{{\text{O}}_{\text{3}}}}^{\operatorname{int}}\frac{{{M}_{{{\text{B}}_{\text{2}}}{{\text{O}}_{\text{3}}}}}}{{{\rho }_{{{\text{B}}_{\text{2}}}{{\text{O}}_{\text{3}}}}}}$

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    ${{J}_{{{\text{O}}_{\text{2}}}}}=f{{D}_{{{\mathrm{O}}_{2}}}}\frac{C_{{{\text{O}}_{\text{2}}}}^{\text{a}}-C_{{{\text{O}}_{\text{2}}}}^{\text{i}}}{L-{{h}_{\operatorname{int}}}}$

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    ${{J}_{{{\text{O}}_{\text{2}}}}}({{\text{B}}_{\text{2}}}{{\text{O}}_{\text{3}}})=f{{\Pi }_{{{\text{O}}_{\text{2}}}\text{-}{{\text{B}}_{\text{2}}}{{\text{O}}_{\text{3}}}}}\frac{p_{{{\text{O}}_{\text{2}}}}^{\text{i}}-p_{{{\text{O}}_{\text{2}}}}^{\text{s}}}{{{h}_{\operatorname{int}}}}$

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    $\frac{\text{d}L}{\text{d}t}=\left( \frac{1}{1-f} \right){{\dot{n}}_{\text{Zr}{{\text{O}}_{\text{2}}}}}\frac{{{M}_{\text{Zr}{{\text{O}}_{\text{2}}}}}}{{{\rho }_{\text{Zr}{{\text{O}}_{\text{2}}}}}}$

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    ${\Delta W}/{A}\;=L{{\rho }_{\text{Zr}{{\text{O}}_{\text{2}}}}}(1-f)+{{h}_{\operatorname{int}}}f{{\rho }_{{{\text{B}}_{\text{2}}}{{\text{O}}_{\text{3}}}}}-{{R}_{\text{s}}}{{\rho }_{\text{Zr}{{\text{B}}_{\text{2}}}}}$

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    $\ln \frac{{{k}_{2}}}{{{k}_{1}}}=-\frac{{{E}_{a}}}{R}\left( \frac{1}{{{T}_{2}}}-\frac{1}{{{T}_{1}}} \right)$

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    $D1,(2, ⋯, j)=1∑jj≠1(xj/D1−j)xj=nj∑kk≠1nk$

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    ${{D}_{1-2}}=\frac{1.8583\times {{10}^{-7}}{{T}^{{3}/{2}\;}}\sqrt{\left( {1}/{{{M}_{1}}}\; \right)+\left( {1}/{{{M}_{2}}}\; \right)}}{\sigma _{12}^{2}{{\Omega }_{D}}p}$

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    $ΩD=1.06036T∗0.15610+0.193000exp⁡(0.47635T∗)+1.03587exp⁡(1.52996T∗)+1.76474exp⁡(3.89411T∗)$

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    ${{D}_{\text{K}}}=\frac{4}{3}{{\left( \frac{8RT}{\text{ }\!\!\pi\!\!\text{ }M} \right)}^{{1}/{2}\;}}\frac{r}{2}$

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    ${{D}_{\text{eff}}}={{\left( D_{\text{K}}^{-1}+D_{1-2}^{-1} \right)}^{-1}}$

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    ${{J}_{\text{evap,}j}}=\alpha \frac{{{p}_{j}}}{{{(2\text{ }\!\!\pi\!\!\text{ }{{M}_{j}}RT)}^{0.5}}}$

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    Abstract
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    Shu-Guang ZHOU, Yi-Jun GUO, Xiao LIU. Simulation of ZrB2 Oxidation Behavior at Constant Temperature Ambient[J]. Journal of Inorganic Materials, 2019, 34(6): 660
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