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A direct-forcing IB-LBM implementation for thermal radiation in irregular geometries

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Abstract

Radiative heat transfer in two-dimensional irregular geometries is analyzed using a direct-forcing immersed boundary-lattice Boltzmann method (IB-LBM) in participating media. In this paper, the radiative transfer equation (RTE) is discretized by the lattice Boltzmann method, which Yi et al. (Phys Rev E 94(2):023312, 2016) have recently presented. The D2Q9 scheme is used to solve the lattice Boltzmann equation (LBE) and the quadrature scheme \({S}_{\text{N}}\) to discrete the angular space. The irregular geometries’ boundaries are simulated by Immersed Boundary Method (IBM). The effect of boundaries that do not match the computational nodes is determined by adding a radiation density term to the LBE. Radiative heat flux distribution for different extinction coefficients are compared with the results obtained from the blocked-off domain method (BOM), embedded boundary method (EBM), and body-fitted grid method (BFM). Compared to the BFM, the proposed method has perfect accuracy, and for all considered problems, the average percent relative error in the estimation of radiative heat flux is between 0.4 and 9.8%. The results show that IBM can solve the difficulties of simulating curved boundaries efficiently. It is found that IB-LBM has been able to solve the problem of thermal radiation in irregular geometries for media with any optical depth.

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Abbreviations

\(I\) :

Radiation intensity (W m−2 sr−1)

\(r\) :

Location vector \(\left( {\text{m}} \right)\)

\(s\) :

Unit direction vector

\(F\) :

Force (kg m s−2)

\({{S}}\) :

Source of thermal radiation

\(f\) :

Particle distribution function

\(T\) :

Temperature \(\left( {\text{K}} \right)\)

\(G\) :

Incident radiation (W m−2)

\(e\) :

Discrete particle velocity (m s−1)

\(c_{{\text{s}}}\) :

Sound speed

\(U\) :

Speed vector

\(t\) :

Time \(\left( {\text{s}} \right)\)

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

Radiation intensity

\(I_{{\text{b}}}\) :

Black body intensity

\(M\) :

Number of discrete directions

\(h\) :

Eulerian mesh width

\(D\) :

Interface function

\(\vec{x}_{\text{ij}}\) :

Eulerian position

\(\vec{x}_{{{\text{bou}}}}\) :

Lagrangian position

\(\beta\) :

Extinction coefficient \(\left( {{\text{m}}^{ - 1} } \right)\)

\(\mu\),\({ }\eta\), \(\xi\) :

Directional cosines in x, y, and z

\(\tau\) :

Relaxation time

\(\alpha\) :

Thermal diffusivity (m2 s−1)

\(\sigma\) :

Stefan–Boltzmann constant \(\left( { = 5.67 \times 10^{ - 8} {\text{ W}}\, {\text{m}}^{ - 2} \,{\text{K}}^{ - 4} } \right)\)

\(\omega\) :

The equilibrium distribution function’s masses

\(\overline{\omega }\) :

The source term distribution function’s masses

\(\phi\) :

Dirac delta function

\({\Delta }s\) :

Arc length of the boundary segment

\({\text{bou, b}}\) :

Boundary

\({\text{w}}\) :

Wall

\({\text{k}}\) :

Discrete direction for DOM

\({\text{d}}\) :

Desired

\({\text{i}}\) :

Discrete direction for LBM

\({\text{eq}}\) :

Equilibrium

\({\text{noQ}}_{{\text{R}}}\) :

No radiation density source

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Birjand, Birjand, Iran

    Mahdi Abaszadeh & Ali Safavinejad

  2. Department of Energy, Institute of Science and High Technology and Environmental Sciences, Graduate University of Advanced Technology, Kerman, Iran

    Hossein Amiri

  3. Department of Mechanical Engineering, University of Bojnord, Bojnord, Iran

    Amin Amiri Delouei

Authors
  1. Mahdi Abaszadeh
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  2. Ali Safavinejad
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  3. Hossein Amiri
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  4. Amin Amiri Delouei
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Correspondence to Amin Amiri Delouei.

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Abaszadeh, M., Safavinejad, A., Amiri, H. et al. A direct-forcing IB-LBM implementation for thermal radiation in irregular geometries. J Therm Anal Calorim 147, 11169–11181 (2022). https://doi.org/10.1007/s10973-022-11328-1

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