• Infrared and Laser Engineering
  • Vol. 51, Issue 4, 20210376 (2022)
Mingqi Pang1,2,3,4, Haizheng Liu2,3,4, Daijun Zhang2,3,4, and Zelin Shi1,2,3,4
Author Affiliations
  • 1Department of Automation, University of Science and Technology of China, Hefei 230027, China
  • 2Key Laboratory of Opto-Electronic Information Processing, Chinese Academy of Sciences, Shenyang 110016, China
  • 3Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016, China
  • 4Institutes for Robotics and Intelligent Manufacturing, Chinese Academy of Sciences, Shenyang 110169, China
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    DOI: 10.3788/IRLA20210376 Cite this Article
    Mingqi Pang, Haizheng Liu, Daijun Zhang, Zelin Shi. A numerical study of carbon dioxide radiation and transmission property in high temperature shock layer[J]. Infrared and Laser Engineering, 2022, 51(4): 20210376 Copy Citation Text show less

    Abstract

    CO2 is the main source of radiation noise in mid-infrared and short-infrared detection. The research on radiation and transmission property of CO2 at high temperature is still not clear at present. The absorption effect of CO2 in the shock layer was mainly studied, and the thermal radiation of CO2 and radiation component proportion on the photosensitive surface were analyzed and calculated. The improved tangent-slab approximation method was used to solve the radiative transport equation, and the influences of target and window radiation on the radiation field distribution in the shock layer were considered. Based on this, the radiation and transmission property of shock layer were deduced. Finally, the calculation model of each radiation component and proportion of the photosensitive surface was given. The property of the shock layer of a supersonic missile at an altitude of h=1 km and flight speed of Ma=3-5 was simulated and calculated. The results showed that the transmittance of shock layer in mid-wave bands is lower than that in short-wave band, but shock layer absorption can be ignored in general. The increase of flight speed leads to a broadening of the CO2 radiated noise region to the long-wave direction, and the target signal is submerged seriously by CO2 radiation noise in the band above 4.4 μm under condition of Ma≥4 and h=1 km, the filter with a cutoff wavelength of 4.4 μm is not suitable.
    $ \frac{{{\rm{d}}{L_\lambda }}}{{{\rm{d}}s}} = - k_\lambda ^{'}\left[ {{L_\lambda } - {B_\lambda }\left( T \right)} \right] $(1)

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    $ k_\lambda ^{'}= {k_\lambda }\left[ {1 - {{{\rm{e}}} ^{ - \frac{{{c_2}}}{{\lambda T}}}}} \right] $(2)

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    $ {B_\lambda }\left( T \right) = \frac{{{c_1}}}{{\pi {\lambda ^5}}}{\left( {{{\rm{e}}^{\frac{{{c_2}}}{{\lambda T}}}} - 1} \right)^{ - 1}} $(3)

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    $ \delta \left( x \right) = \int_0^x {k_\lambda ^{'}{\rm{d}}x} $(4)

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    $ Lλ + (x,θ)=Lλ,teδ(x)/cosθ+0xkλ(x)Bλ[T(x)]e(δ(x)δ(x))/cosθdxcosθ $(5)

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    $ Lλ - (x,θ)=Lλ,we(δ(x) - δ(xw))/cosθ+xwxkλ(x)Bλ[T(x)]e(δ(x)δ(x))/cosθdxcosθ $(6)

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    $ δ(xn)=0xnkλ(x)dxk=1n1xkxk+1kλ(x)dx12k=1n1[kλ(xk)+kλ(xk+1)](xk+1xk)$(7)

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    $ \delta \left( {{x_n}} \right) \approx \sum\limits_{k = 1}^{n - 1} {k_\lambda ^{'}\left( {{x_{k,mid}}} \right)} \left( {{x_{k + 1}} - {x_k}} \right) $(8)

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    $ \delta \left( x \right) = {a_k}x + {b_k} $(9)

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    $ Lλ+(xn,θ)=Lλ,teδ(xn)/cosθ+0xnkλ(x)Bλ[T(x)]e(δ(xn)δ(x))/cosθdxcosθ=Lλ,teδ(xn)/cosθ+k=1n1kλ(xk,mid)Bλ[T(xk,mid)]eδ(xn)/cosθxkxk+1eδ(x)/cosθdxcosθ=Lλ,teδ(xn)/cosθ+k=1n1kλ(xk,mid)Bλ[T(xk,mid)]eδ(xn)/cosθakxkxk+1deδ(x)/cosθ=Lλ,teδ(xn)/cosθ+k=1n1kλ(xk,mid)Bλ[T(xk,mid)]eδ(xn)/cosθak(eδ(xk+1)cosθeδ(xk)cosθ)$(10)

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    $Extra \left or missing \right \right. \Rightarrow {a_k} = \frac{{\delta \left( {{x_{k + 1}}} \right) - \delta \left( {{x_k}} \right)}}{{{x_{k + 1}} - {x_k}}} = k_\lambda ^{'}\left( {{x_{k,mid}}} \right) \end{gathered}$(11)

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    $Lλ+(xn,θ)=Lλ,teδ(xn)/cosθ+k=1n1Bλ[T(xk,mid)]eδ(xn)/cosθ(eδ(xk+1)cosθeδ(xk)cosθ)$(12)

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    $Lλ(xn,θ)=Lλ,we(δ(xn)δ(xw))/cosθk=nkmax1Bλ[T(xk,mid)]eδ(xn)/cosθ(eδ(xk+1)cosθeδ(xk)cosθ)$(13)

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    $ Lλ + (xw,θ)=Lλ,teδ(xw)/cosθ+0xwkλ(x)Bλ[T(x)]e(δ(xw)δ(x))/cosθdxcosθ $(14)

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    $ {L_{\lambda ,s}}\left( {{x_w},\theta } \right) = \int_0^{{x_w}} {k_\lambda ^{'}{B_\lambda }\left[ {T\left( {{x^{'}}} \right)} \right]{{\rm{e}}^{ - \left( {\delta \left( {{x_w}} \right) - \delta \left( {{x^{'}}} \right)} \right)/\cos \theta }}\frac{{{\rm{d}}{x^{'}}}}{{\cos \theta }}} $(15)

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    $ Lλ,s(xkmax,θ)=k=1kmax1{Bλ[T(xk,mid)]×eδ(xkmax)/cosθ(eδ(xk+1)cosθeδ(xk)cosθ)} $(16)

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    $ {\tau _{\lambda ,s}} = {{\rm{e}}^{ - \delta \left( {{x_w}} \right)/\cos \theta }} $(17)

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    $ {E_n}(X) = \int_1^\infty {{{\rm{e}}^{ - \xi X}}\frac{{{\rm{d}}\xi }}{{{\xi ^n}}}} $(18)

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    $ M = \int {L\cos \theta {\rm{d}}\Omega } $(19)

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    $ Mλ,t=Lλ,teδ(xw)/cosθcosθdΩ=02π0π2Lλ,teδ(xw)/cosθcosθsinθdθdφ=2πLλ,t01eδ(xw)/cosθcosθdcosθ $(20)

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    $ 01eδ(xw)/cosθcosθdcosθ=1eδ(xw)ξdξξ3=E3(δ(xw)) $(21)

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    $ Mλ,t=2πLλ,tE3(δ(xw))=2E3(δ(xw))πLλ,t $(22)

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    $ {\tau }_{\lambda ,s}=\left\{eδ(xw)/cosθ=eδ(xkmax)/cosθ2E3(δ(xw))=2E3(δ(xkmax))\right. $(23)

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    $ Mλ,s={0xwkλ(x)Bλ[T(x)]e(δ(xw)δ(x))/cosθdxcosθ}cosθdΩ=02π0π2{0xwkλ(x)Bλ[T(x)]e(δ(xw)δ(x))cosθdxcosθ}cosθsinθdθdφ=2π0xw{kλ(x)Bλ[T(x)]01e(δ(xw)δ(x))/cosθdcosθ}dx $(24)

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    $ 01e(δ(xw)δ(x))/cosθdcosθ=1e(δ(xw)δ(x))ξdξξ2=E2(δ(xw)δ(x))$(25)

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    $E2(δ(xw)δ(x))dx=E2(δ(xw)δ(x))d(δ(xw)δ(x))ak=dE3(δ(xw)δ(x))kλ(x)=dE3(δ(xw)δ(x))kλ(x)$(26)

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    $ Mλ,s=2π0xwkλ(x)Bλ[T(x)]E2(δ(xw)δ(x))dx=2π0xwBλ[T(x)]dE3(δ(xw)δ(x))=2πk=1kmax1Bλ[T(xk,mid)]xkxk+1dE3(δ(xkmax)δ(x))=2πk=1kmax1Bλ[T(xk,mid)][E3(δ(xkmax)δ(xk+1))E3(δ(xkmax)δ(xk))] $(27)

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    $ Mλ,s=2πBλ(T)k=1kmax1[E3(δ(xkmax)δ(xk+1))E3(δ(xkmax)δ(xk))]=2πBλ(T)[E3(δ(xkmax)δ(xkmax))E3(δ(xkmax)δ(x1))]=2πBλ(T)[E3(0)E3(δ(xkmax))]=πBλ(T)[12E3(δ(xkmax))] $(28)

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    $ {E_{\lambda ,t}} = {\tau _{\lambda ,w}} \cdot {\tau _{\lambda ,s}} \cdot {L_{\lambda ,t}} \cdot \omega $(29)

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    $ Φλ,t=Eλ,tAoτo=τλ,wτλ,sτoLλ,tωAo $(30)

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    $ {L_{\lambda ,s}}\left( {{x_{{k_{\max }}}},0} \right) = \sum\limits_{k = 1}^{{k_{\max }} - 1} {{B_\lambda }\left[ {T\left( {{x_{k,mid}}} \right)} \right]{{\rm{e}}^{ - \delta \left( {{x_{{k_{\max }}}}} \right)}}} \left( {{{\rm{e}}^{\delta \left( {{x_{k + 1}}} \right)}} - {{\rm{e}}^{\delta \left( {{x_k}} \right)}}} \right) $(31)

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    $ {\varPhi _{\lambda ,s}} = {\tau _{\lambda ,w}} \cdot {\tau _o} \cdot {L_{\lambda ,s}} \cdot \omega \cdot {A_o} $(32)

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    $ {\varPhi _{\lambda ,w}} = {\tau _o} \cdot {L_{\lambda ,w}} \cdot \omega \cdot {A_o} $(33)

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    $ ηλ,t=Φλ,tΦλ,t+Φλ,s+Φλ,w=τλ,wτλ,sLλ,tτλ,wτλ,sLλ,t+τλ,wLλ,s+Lλ,w $(34)

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    $ ηλ,s=Φλ,sΦλ,t+Φλ,s+Φλ,w=τλ,wLλ,sτλ,wτλ,sLλ,t+τλ,wLλ,s+Lλ,w $(35)

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    $ ηλ,w=Φλ,wΦλ,t+Φλ,s+Φλ,w=Lλ,wτλ,wτλ,sLλ,t+τλ,wLλ,s+Lλ,w $(36)

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    Mingqi Pang, Haizheng Liu, Daijun Zhang, Zelin Shi. A numerical study of carbon dioxide radiation and transmission property in high temperature shock layer[J]. Infrared and Laser Engineering, 2022, 51(4): 20210376
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