Bidirectional monte carlo method for thermal radiation transfer in participating medium

Xiaofeng Zhang; Qing Ai; Kuilong Song; Heping Tan; Xiaofeng Zhang; Qing Ai; Kuilong Song; Heping Tan

doi:10.3934/energy.2021029

AIMS Energy

2021, Volume 9, Issue 3: 603-622. doi: 10.3934/energy.2021029

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Bidirectional monte carlo method for thermal radiation transfer in participating medium

1.
Harbin Institute of Technology, 92 West DaZhi Street, Harbin, 150001, China
2.
Chinese Academy of Sciences, Shanghai, 201200, China

Received: 09 March 2021 Accepted: 05 May 2021 Published: 03 June 2021

A bidirectional Monte Carlo (BDMC) method based on reversibility of bundle trajectory and reciprocity of thermal radiative energy exchange was developed to solve radiative heat transfer in absorbing and scattering medium. Two types of sampling models were introduced into the Monte Carlo (MC) simulation, namely the equivalent sampling and the weight sampling, respectively. Mathematical formula for the sampling models and the statistical calculation of sampling bundles were derived. Furthermore, the reciprocity error correlation of radiative exchange factors between the BDMC method and the traditional Monte Carlo (TMC) method were demonstrated and analyzed. Radiative heat transfer in a two-dimensional rectangular domain with absorbing and scattering media was solved by using both the BDMC method and the TMC method. Radiative exchange factors and radiative equilibrium temperature profiles predicted by the BDMC method were compared with those predicted by the TMC method. The performance parameter P, defined to evaluate the performance of MC methods, was computed and compared between the BDMC and the TMC methods. The results showed the superiority of BDMC method compared with the TMC method for radiative heat transfer, in addition, the weight sampling was proved to be more flexible than the equivalent sampling in the BDMC method.
- bidirectional mote carlo method,
- participating medium,
- thermal radiation transfer
Citation: Xiaofeng Zhang, Qing Ai, Kuilong Song, Heping Tan. Bidirectional monte carlo method for thermal radiation transfer in participating medium[J]. AIMS Energy, 2021, 9(3): 603-622. doi: 10.3934/energy.2021029

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Abstract

A bidirectional Monte Carlo (BDMC) method based on reversibility of bundle trajectory and reciprocity of thermal radiative energy exchange was developed to solve radiative heat transfer in absorbing and scattering medium. Two types of sampling models were introduced into the Monte Carlo (MC) simulation, namely the equivalent sampling and the weight sampling, respectively. Mathematical formula for the sampling models and the statistical calculation of sampling bundles were derived. Furthermore, the reciprocity error correlation of radiative exchange factors between the BDMC method and the traditional Monte Carlo (TMC) method were demonstrated and analyzed. Radiative heat transfer in a two-dimensional rectangular domain with absorbing and scattering media was solved by using both the BDMC method and the TMC method. Radiative exchange factors and radiative equilibrium temperature profiles predicted by the BDMC method were compared with those predicted by the TMC method. The performance parameter P, defined to evaluate the performance of MC methods, was computed and compared between the BDMC and the TMC methods. The results showed the superiority of BDMC method compared with the TMC method for radiative heat transfer, in addition, the weight sampling was proved to be more flexible than the equivalent sampling in the BDMC method.

References

[1]	Farmer JT, Howell JR (1998) Comparison of monte carlo strategies for radiative transfer in participating media. Adv Heat Transfer 31: 333-429. doi: 10.1016/S0065-2717(08)70243-0
[2]	Evans TM, Urbatsch TJ, Lichtenstein H, et al. (2003) A residual monte carlo method for discrete thermal radiative diffusion. J Comput Phys 189: 539-556. doi: 10.1016/S0021-9991(03)00233-X
[3]	Zhou HC, Chen DL, Cheng Q (2004) A new way to calculate radiative intensity and solve radiative transfer equation through using the monte carlo method. J Quant Spectrosc Radiat Transfer 83: 459-481. doi: 10.1016/S0022-4073(03)00031-1
[4]	Xia XL, Ren DP, Tan HP (2006) A curve monte carlo method for radiative heat transfer in absorbing and scattering gradient-Index medium. Numer Heat Transfer, Part B 50: 181-192. doi: 10.1080/10407790500459387
[5]	Wang A, Modest MF (2007) Spectral monte carlo models for nongray radiation analyses in inhomogeneous participating media. Int J Heat Mass Transfer 50: 3877-3889. doi: 10.1016/j.ijheatmasstransfer.2007.02.018
[6]	Mazumder S (2019) Application of a variance reduction technique to surface-to-surface monte carlo radiation exchange calculations. Int J Heat Mass Transfer 131: 424-431. doi: 10.1016/j.ijheatmasstransfer.2018.11.050
[7]	Hsu PF, Farmer JT (1997) Benchmark solutions of radiative heat transfer within nonhomogeneous participating media using the monte carlo and YIX method. J Heat Transfer 119: 185-188. doi: 10.1115/1.2824087
[8]	Ruan LM, Tan HP (2002) Solutions of radiative heat transfer in three-dimensional inhomogeneous, scattering media. J Heat Transfer 124: 985-988. doi: 10.1115/1.1495519
[9]	Hohn RH (1998) The monte carlo method in tadiative heat transfer. J Heat Transfer 120: 547. doi: 10.1115/1.2824310
[10]	Lu Z, Zhang D (2003) On importance sampling monte carlo approach to uncertainty analysis for flow and transport in porous media. Adv Water Resour 26: 1177-1188. doi: 10.1016/S0309-1708(03)00106-4
[11]	Wang X (2000) Improving the rejection sampling method in quasi-monte carlo methods. J Comput Appl Math 114: 231-246. doi: 10.1016/S0377-0427(99)00194-6
[12]	Peplow DE, Verghese K (2000) Differential sampling for the monte carlo practitioner. Prog Nucl Energy 36: 39-75. doi: 10.1016/S0149-1970(99)00024-4
[13]	Xia XL, Ren DP, Dong SK, et al. (2004) Radiative heat flux characteristics of coupled heat transfer in tubes and comparison of random sampling modes. J Eng Thermophys 25: 287-289.
[14]	Walters DV, Buckius RO (1992) Rigorous development for radiation heat transfer in nonhomogeneous absorbing, emitting and scattering media. Int J Heat Mass Transfer 35: 3323-3333. doi: 10.1016/0017-9310(92)90219-I
[15]	Cherkaoui M, Dufresne JL, Fournier R, et al. (1996) Monte carlo simulation of radiation in gases with a narrow-band model and a net-exchange formulation. J Heat Transfer 118: 401-407. doi: 10.1115/1.2825858
[16]	Cherkaoui M, Dufresne JL, Fournier R, et al. (1998) Radiative net exchange formulation within one-dimensional gas enclosures with reflective surfaces. Trans Am Soc Mech Eng 120: 275-278.
[17]	De Lataillade A, Dufresne JL, El Hafi M, et al. (2002) A net-exchange monte carlo approach to radiation in optically thick systems. J Quant Spectrosc Radiat Transfer 74: 563-584. doi: 10.1016/S0022-4073(01)00272-2
[18]	Eymet V, Fournier R, Blanco S, et al. (2005) A boundary-based net-exchange monte carlo method for absorbing and scattering thick media. J Quant Spectrosc Radiat Transfer 19: 27-46. doi: 10.1016/j.jqsrt.2004.05.049
[19]	Lionel Tessé, Francis Dupoirieux, Bernard Zamuner, et al. (2002) Radiative transfer in real gases using reciprocal and forward monte carlo methods and a correlated-k approach. Int J Heat Mass Transfer 45: 2797-2814. doi: 10.1016/S0017-9310(02)00009-1
[20]	Modest MF (2003) Backward monte carlo simulations in radiative heat transfer. J Heat Transfer 125: 57-62. doi: 10.1115/1.1518491
[21]	Lu XD, Hsu PF (2004) Reverse monte carlo method for transient radiative transfer in participating media. J Heat Transfer 126: 621-627. doi: 10.1115/1.1773587
[22]	Tan HP, Shuai Y, Dong SK (2005) Analysis of rocket plume base heating by using backward monte-carlo method. J Thermophysics Heat Transfer 19: 125-127. doi: 10.2514/1.10519
[23]	Shuai Y, Dong SK, Tan HP (2005) Simulation of the infrared radiation characteristics of high-temperature exhaust plume including particles using the backward monte carlo method. J Quant Spectrosc Radiat Transfer 195: 231-240. doi: 10.1016/j.jqsrt.2004.11.001
[24]	Lu X, Hsu PF (2005) Reverse monte carlo simulations of light pulse propagation in nonhomogeneous media. J Quant Spectrosc Radiat Transfer 93: 349-367. doi: 10.1016/j.jqsrt.2004.08.029
[25]	Kovtanyuk AE, Botkin ND, Hoffmann KH (2012) Numerical simulations of a coupled radiative-conductive heat transfer model using a modified monte carlo method. Int J Heat Mass Transfer 55: 649-654. doi: 10.1016/j.ijheatmasstransfer.2011.10.045
[26]	Soucasse L, Rivière P, Soufiani A (2013) Monte carlo methods for radiative transfer in quasi-isothermal participating media. Eurotherm Semin Comput Thermal Radiat Participating Media IV 128: 34-42.
[27]	Ruan LM, Qi H, Liu LH, et al. (2004) The radiative transfer in cylindrical medium and partition allocation method by overlap regions. J Quant Spectrosc Radiat Transfer 86: 343-352. doi: 10.1016/j.jqsrt.2003.08.011
[28]	Shuai Y, Zhang HC, Tan HP (2008) Radiation symmetry test and uncertainty analysis of monte carlo method based on radiative exchange factor. J Quant Spectrosc Radiat Transfer 109: 1281-1296. doi: 10.1016/j.jqsrt.2007.10.001
[29]	Yang WJ (1995) Radiative heat transfer by the monte carlo method. Adv Heat Transf 27: 45-91. doi: 10.1016/S0065-2717(08)70315-0
[30]	Dupoirieux F, Tessé L, Avila S, et al. (2006) An optimized reciprocity monte carlo method for the calculation of radiative transfer in media of various optical thicknesses. Int J Heat Mass Transfer 49: 1310-1319. doi: 10.1016/j.ijheatmasstransfer.2005.10.009
[31]	Ruan LM, Tan HP, Yan YY (2002) A monte carlo method applied to the medium with nongray absorbing-emitting-anisotropic scattering particles and gray approximation. Numer Heat Transfer, Part A 42: 253-268. doi: 10.1080/10407780290059530
[32]	Howell JR, Mengüç MP, Daun K, et al. (2020) Thermal radiation heat transfer. Boca Raton: CRC Press. doi: 10.1201/9780429327308

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