CIESC Journal ›› 2021, Vol. 72 ›› Issue (6): 3296-3305.DOI: 10.11949/0438-1157.20201530
• Fluid dynamics and transport phenomena • Previous Articles Next Articles
YIN Xuemei(
),WANG Lei,LIU Yongtao,WU Chao()
Received:2020-10-30
Revised:2021-01-08
Online:2021-06-05
Published:2021-06-05
Contact:
WU Chao
尹雪梅(),王磊,刘永涛,吴超()
通讯作者:
吴超
作者简介:尹雪梅（1979—），女，博士，副教授，基金资助:CLC Number:
YIN Xuemei, WANG Lei, LIU Yongtao, WU Chao. Weighted-sum-of-gray-gases model based on k-distribution for gas mixture[J]. CIESC Journal, 2021, 72(6): 3296-3305.
尹雪梅, 王磊, 刘永涛, 吴超. 适于混合气体基于k分布的灰气体加权和模型[J]. 化工学报, 2021, 72(6): 3296-3305.
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Fig.1 Graphical illustration of the rank correlated theory
| 系数 | j=1 | j=2 | j=3 | j=4 | j=5 |
|---|---|---|---|---|---|
| A1j,1 | 0.8848 | -1.0202 | 0.7944 | 0.1846 | 0.1564 |
| A1j,2 | -0.9493 | 2.6322 | -1.1323 | -0.3050 | -0.2455 |
| A1j,3 | 1.0117 | -1.7960 | 0.5199 | 0.1549 | 0.1094 |
| A1j,4 | -0.2446 | 0.3636 | -0.0769 | -0.0267 | -0.0154 |
| A2j,1 | -1.4184 | 2.2466 | -1.0449 | 0.1484 | 0.0684 |
| A2j,2 | 2.0733 | -4.5500 | 2.2958 | 0.1463 | 0.0345 |
| A2j,3 | -1.5659 | 3.0799 | -1.2987 | -0.1772 | -0.0380 |
| A2j,4 | 0.3665 | -0.6370 | 0.2221 | 0.0420 | 0.0065 |
| A3j,1 | 0.5447 | -0.8849 | 0.4250 | -0.0969 | 0.0121 |
| A3j,2 | -0.8938 | 1.7514 | -0.9582 | 0.0780 | 0.0227 |
| A3j,3 | 0.6108 | -1.1713 | 0.5871 | -0.0036 | -0.0230 |
| A3j,4 | -0.1362 | 0.2431 | -0.1075 | -0.0049 | 0.0055 |
Table 1 Polynomial coefficients for H2O weighting factor
| 系数 | j=1 | j=2 | j=3 | j=4 | j=5 |
|---|---|---|---|---|---|
| A1j,1 | 0.8848 | -1.0202 | 0.7944 | 0.1846 | 0.1564 |
| A1j,2 | -0.9493 | 2.6322 | -1.1323 | -0.3050 | -0.2455 |
| A1j,3 | 1.0117 | -1.7960 | 0.5199 | 0.1549 | 0.1094 |
| A1j,4 | -0.2446 | 0.3636 | -0.0769 | -0.0267 | -0.0154 |
| A2j,1 | -1.4184 | 2.2466 | -1.0449 | 0.1484 | 0.0684 |
| A2j,2 | 2.0733 | -4.5500 | 2.2958 | 0.1463 | 0.0345 |
| A2j,3 | -1.5659 | 3.0799 | -1.2987 | -0.1772 | -0.0380 |
| A2j,4 | 0.3665 | -0.6370 | 0.2221 | 0.0420 | 0.0065 |
| A3j,1 | 0.5447 | -0.8849 | 0.4250 | -0.0969 | 0.0121 |
| A3j,2 | -0.8938 | 1.7514 | -0.9582 | 0.0780 | 0.0227 |
| A3j,3 | 0.6108 | -1.1713 | 0.5871 | -0.0036 | -0.0230 |
| A3j,4 | -0.1362 | 0.2431 | -0.1075 | -0.0049 | 0.0055 |
| 系数 | j=1 | j=2 | j=3 | j=4 | j=5 |
|---|---|---|---|---|---|
| Ca1j,1 | 1.4527×10-5 | 2.5914×10-4 | 5.8007×10-4 | -1.4100×10-3 | -1.1148×10-1 |
| Ca1 j,2 | 6.0925×10-5 | -4.4153×10-4 | -3.3700×10-3 | -1.3810×10-2 | 1.9272×10-1 |
| Ca1 j,3 | -1.9712×10-4 | -2.8330×10-4 | 8.3635×10-4 | 1.1100×10-2 | -1.0364×10-1 |
| Ca1 j,4 | 6.8011×10-5 | 1.0114×10-4 | 7.7633×10-5 | -2.2900×10-3 | 1.8110×10-2 |
| Ca2j,1 | -5.0106×10-5 | -2.7328×10-4 | -7.0262×10-4 | -3.9300×10-3 | 8.9830×10-2 |
| Ca2j,2 | -1.4400×10-5 | 2.6717×10-4 | 3.3400×10-3 | 2.5780×10-2 | -1.5549×10-1 |
| Ca2j,3 | 2.2788×10-4 | 5.7870×10-4 | -3.5251×10-4 | -1.9270×10-2 | 8.0130×10-2 |
| Ca2j,4 | -9.0762×10-5 | -1.6917×10-4 | -2.5547×10-4 | 3.9900×10-3 | -1.3270×10-2 |
| Ca3j,1 | 2.6025×10-5 | 9.4849×10-5 | 2.2372×10-4 | 2.7700×10-3 | -1.5960×10-2 |
| Ca3j,2 | -1.5222×10-5 | -5.0434×10-5 | -8.7092×10-4 | -1.1020×10-2 | 2.4520×10-2 |
| Ca3j,3 | -6.6431×10-5 | -2.3013×10-4 | -8.8588×10-5 | 8.0200×10-3 | -1.0070×10-2 |
| Ca4j,4 | 3.0402×10-5 | 6.4101×10-5 | 1.3331×10-4 | -1.6700×10-3 | 1.2000×10-3 |
| Cb1j,1 | 6.7045×10-4 | -4.0900×10-3 | 5.6300×10-3 | 6.6170×10-2 | 2.7305×100 |
| Cb1 j,2 | -3.8900×10-3 | 6.1400×10-3 | 3.5890×10-2 | 2.2344×10-1 | -3.3582×100 |
| Cb1 j,3 | 6.1600×10-3 | 1.1340×10-2 | 1.2170×10-2 | -1.2287×10-1 | 1.7048×100 |
| Cb1 j,4 | -1.5700×10-3 | -3.2100×10-3 | -6.2200×10-3 | 1.9980×10-2 | -2.9727×10-1 |
| Cb2j,1 | -1.2155×10-4 | 4.4000×10-3 | -8.8100×10-3 | 1.1860×10-2 | -2.7236×100 |
| Cb2j,2 | 3.3500×10-3 | -4.9600×10-3 | -2.2850×10-2 | -3.7177×10-1 | 3.5805×100 |
| Cb2j,3 | -7.0600×10-3 | -1.4730×10-2 | -2.7150×10-2 | 2.1119×10-1 | -1.8779×100 |
| Cb2j,4 | 2.0300×10-3 | 4.0000×10-3 | 9.9400×10-3 | -3.7220×10-2 | 3.3180×10-1 |
| Cb3j,1 | -1.7395×10-4 | -1.3600×10-3 | 3.1700×10-3 | -2.4460×10-2 | 7.8677×10-1 |
| Cb3j,2 | -6.1478×10-4 | 1.1000×10-3 | 2.5900×10-3 | 1.4728×10-1 | -1.0723×100 |
| Cb3j,3 | 2.0600×10-3 | 4.9500×10-3 | 1.2050×10-2 | -8.5390×10-2 | 5.7325×10-1 |
| Cb4j,4 | -6.5632×10-4 | -1.3100×10-3 | -3.8800×10-3 | 1.5630×10-2 | -1.0211×10-1 |
| Cc1j,1 | -3.5400×10-3 | 1.2710×10-2 | 2.8130×10-2 | 1.6931×10-1 | -7.0774×10-1 |
| Cc1 j,2 | 7.9300×10-3 | -3.1440×10-2 | 4.8150×10-2 | -1.4053×10-1 | 1.2303×100 |
| Cc1 j,3 | -3.9400×10-3 | 2.8060×10-2 | -5.4800×10-2 | 2.2850×10-2 | -7.3256×10-1 |
| Cc1 j,4 | 6.2133×10-4 | -6.2400×10-3 | 1.2550×10-2 | 8.5822×10-4 | 1.5340×10-1 |
| Cc2j,1 | 5.4500×10-3 | -2.1340×10-2 | -5.6110×10-2 | -1.5847×10-1 | 1.4189×100 |
| Cc2j,2 | -1.2200×10-2 | 5.4900×10-2 | -2.5720×10-2 | 1.4353×10-1 | -2.4827×100 |
| Cc2j,3 | 6.2100×10-3 | -4.6900×10-2 | 5.5760×10-2 | -2.7450×10-2 | 1.4445×100 |
| Cc2j,4 | -9.9408×10-4 | 1.0210×10-2 | -1.4370×10-2 | 1.0100×10-3 | -2.8973×10-1 |
| Cc3j,1 | -2.0200×10-3 | 8.3200×10-3 | 2.5290×10-2 | 4.5770×10-2 | -5.7282×10-1 |
| Cc3j,2 | 4.5400×10-3 | -2.1790×10-2 | -3.5800×10-3 | -4.9550×10-2 | 1.0218×100 |
| Cc3j,3 | -2.3400×10-3 | 1.8300×10-2 | -1.3190×10-2 | 1.5250×10-2 | -5.9589×10-1 |
| Cc4j,3 | 3.7721×10-4 | -3.9500×10-3 | 4.0600×10-3 | -2.2100×10-3 | 1.1821×10-1 |
Table 2 Polynomial coefficients for H2O absorption coefficients
| 系数 | j=1 | j=2 | j=3 | j=4 | j=5 |
|---|---|---|---|---|---|
| Ca1j,1 | 1.4527×10-5 | 2.5914×10-4 | 5.8007×10-4 | -1.4100×10-3 | -1.1148×10-1 |
| Ca1 j,2 | 6.0925×10-5 | -4.4153×10-4 | -3.3700×10-3 | -1.3810×10-2 | 1.9272×10-1 |
| Ca1 j,3 | -1.9712×10-4 | -2.8330×10-4 | 8.3635×10-4 | 1.1100×10-2 | -1.0364×10-1 |
| Ca1 j,4 | 6.8011×10-5 | 1.0114×10-4 | 7.7633×10-5 | -2.2900×10-3 | 1.8110×10-2 |
| Ca2j,1 | -5.0106×10-5 | -2.7328×10-4 | -7.0262×10-4 | -3.9300×10-3 | 8.9830×10-2 |
| Ca2j,2 | -1.4400×10-5 | 2.6717×10-4 | 3.3400×10-3 | 2.5780×10-2 | -1.5549×10-1 |
| Ca2j,3 | 2.2788×10-4 | 5.7870×10-4 | -3.5251×10-4 | -1.9270×10-2 | 8.0130×10-2 |
| Ca2j,4 | -9.0762×10-5 | -1.6917×10-4 | -2.5547×10-4 | 3.9900×10-3 | -1.3270×10-2 |
| Ca3j,1 | 2.6025×10-5 | 9.4849×10-5 | 2.2372×10-4 | 2.7700×10-3 | -1.5960×10-2 |
| Ca3j,2 | -1.5222×10-5 | -5.0434×10-5 | -8.7092×10-4 | -1.1020×10-2 | 2.4520×10-2 |
| Ca3j,3 | -6.6431×10-5 | -2.3013×10-4 | -8.8588×10-5 | 8.0200×10-3 | -1.0070×10-2 |
| Ca4j,4 | 3.0402×10-5 | 6.4101×10-5 | 1.3331×10-4 | -1.6700×10-3 | 1.2000×10-3 |
| Cb1j,1 | 6.7045×10-4 | -4.0900×10-3 | 5.6300×10-3 | 6.6170×10-2 | 2.7305×100 |
| Cb1 j,2 | -3.8900×10-3 | 6.1400×10-3 | 3.5890×10-2 | 2.2344×10-1 | -3.3582×100 |
| Cb1 j,3 | 6.1600×10-3 | 1.1340×10-2 | 1.2170×10-2 | -1.2287×10-1 | 1.7048×100 |
| Cb1 j,4 | -1.5700×10-3 | -3.2100×10-3 | -6.2200×10-3 | 1.9980×10-2 | -2.9727×10-1 |
| Cb2j,1 | -1.2155×10-4 | 4.4000×10-3 | -8.8100×10-3 | 1.1860×10-2 | -2.7236×100 |
| Cb2j,2 | 3.3500×10-3 | -4.9600×10-3 | -2.2850×10-2 | -3.7177×10-1 | 3.5805×100 |
| Cb2j,3 | -7.0600×10-3 | -1.4730×10-2 | -2.7150×10-2 | 2.1119×10-1 | -1.8779×100 |
| Cb2j,4 | 2.0300×10-3 | 4.0000×10-3 | 9.9400×10-3 | -3.7220×10-2 | 3.3180×10-1 |
| Cb3j,1 | -1.7395×10-4 | -1.3600×10-3 | 3.1700×10-3 | -2.4460×10-2 | 7.8677×10-1 |
| Cb3j,2 | -6.1478×10-4 | 1.1000×10-3 | 2.5900×10-3 | 1.4728×10-1 | -1.0723×100 |
| Cb3j,3 | 2.0600×10-3 | 4.9500×10-3 | 1.2050×10-2 | -8.5390×10-2 | 5.7325×10-1 |
| Cb4j,4 | -6.5632×10-4 | -1.3100×10-3 | -3.8800×10-3 | 1.5630×10-2 | -1.0211×10-1 |
| Cc1j,1 | -3.5400×10-3 | 1.2710×10-2 | 2.8130×10-2 | 1.6931×10-1 | -7.0774×10-1 |
| Cc1 j,2 | 7.9300×10-3 | -3.1440×10-2 | 4.8150×10-2 | -1.4053×10-1 | 1.2303×100 |
| Cc1 j,3 | -3.9400×10-3 | 2.8060×10-2 | -5.4800×10-2 | 2.2850×10-2 | -7.3256×10-1 |
| Cc1 j,4 | 6.2133×10-4 | -6.2400×10-3 | 1.2550×10-2 | 8.5822×10-4 | 1.5340×10-1 |
| Cc2j,1 | 5.4500×10-3 | -2.1340×10-2 | -5.6110×10-2 | -1.5847×10-1 | 1.4189×100 |
| Cc2j,2 | -1.2200×10-2 | 5.4900×10-2 | -2.5720×10-2 | 1.4353×10-1 | -2.4827×100 |
| Cc2j,3 | 6.2100×10-3 | -4.6900×10-2 | 5.5760×10-2 | -2.7450×10-2 | 1.4445×100 |
| Cc2j,4 | -9.9408×10-4 | 1.0210×10-2 | -1.4370×10-2 | 1.0100×10-3 | -2.8973×10-1 |
| Cc3j,1 | -2.0200×10-3 | 8.3200×10-3 | 2.5290×10-2 | 4.5770×10-2 | -5.7282×10-1 |
| Cc3j,2 | 4.5400×10-3 | -2.1790×10-2 | -3.5800×10-3 | -4.9550×10-2 | 1.0218×100 |
| Cc3j,3 | -2.3400×10-3 | 1.8300×10-2 | -1.3190×10-2 | 1.5250×10-2 | -5.9589×10-1 |
| Cc4j,3 | 3.7721×10-4 | -3.9500×10-3 | 4.0600×10-3 | -2.2100×10-3 | 1.1821×10-1 |
| 系数 | j=1 | j=2 | j=3 | j=4 | j=5 |
|---|---|---|---|---|---|
| A1j,1 | 1.4267 | -1.3301 | 0.0237 | 0.4738 | 0.4058 |
| A1j,2 | -2.4743 | 3.4068 | 0.6890 | -0.9611 | -0.6604 |
| A1j,3 | 1.5439 | -2.1186 | -0.5574 | 0.7503 | 0.3818 |
| A1j,4 | -0.2849 | 0.4046 | 0.1227 | -0.1723 | -0.0701 |
| A2j,1 | -1.4833 | 2.2795 | 0.3667 | -0.6377 | -0.5252 |
| A2j,2 | 3.5964 | -5.2272 | -1.2490 | 1.7389 | 1.1408 |
| A2j,3 | -2.2363 | 3.3840 | 0.9880 | -1.3834 | -0.7522 |
| A2j,4 | 0.4312 | -0.6674 | -0.2262 | 0.3139 | 0.1484 |
| A3j,1 | 0.2596 | -0.6805 | -0.1602 | 0.3727 | 0.2083 |
| A3j,2 | -1.1125 | 1.7652 | 0.5775 | -0.8318 | -0.3984 |
| A3j,3 | 0.7745 | -1.2087 | -0.4517 | 0.6182 | 0.2677 |
| A3j,4 | -0.1574 | 0.2457 | 0.1027 | -0.1366 | -0.0544 |
Table 3 Polynomial coefficients for CO2 weighting factor
| 系数 | j=1 | j=2 | j=3 | j=4 | j=5 |
|---|---|---|---|---|---|
| A1j,1 | 1.4267 | -1.3301 | 0.0237 | 0.4738 | 0.4058 |
| A1j,2 | -2.4743 | 3.4068 | 0.6890 | -0.9611 | -0.6604 |
| A1j,3 | 1.5439 | -2.1186 | -0.5574 | 0.7503 | 0.3818 |
| A1j,4 | -0.2849 | 0.4046 | 0.1227 | -0.1723 | -0.0701 |
| A2j,1 | -1.4833 | 2.2795 | 0.3667 | -0.6377 | -0.5252 |
| A2j,2 | 3.5964 | -5.2272 | -1.2490 | 1.7389 | 1.1408 |
| A2j,3 | -2.2363 | 3.3840 | 0.9880 | -1.3834 | -0.7522 |
| A2j,4 | 0.4312 | -0.6674 | -0.2262 | 0.3139 | 0.1484 |
| A3j,1 | 0.2596 | -0.6805 | -0.1602 | 0.3727 | 0.2083 |
| A3j,2 | -1.1125 | 1.7652 | 0.5775 | -0.8318 | -0.3984 |
| A3j,3 | 0.7745 | -1.2087 | -0.4517 | 0.6182 | 0.2677 |
| A3j,4 | -0.1574 | 0.2457 | 0.1027 | -0.1366 | -0.0544 |
| 系数 | j=1 | j=2 | j=3 | j=4 | j=5 |
|---|---|---|---|---|---|
| Ca1j,1 | -2.1346×10-6 | 3.0944×10-6 | -9.9047×10-6 | -2.0258×10-5 | -1.3820×10-2 |
| Ca1 j,2 | 2.0523×10-6 | -8.3230×10-6 | 1.6965×10-5 | 1.6867×10-5 | 1.4270×10-2 |
| Ca1 j,3 | -4.1126×10-7 | 4.7522×10-6 | -9.4011×10-6 | -1.0106×10-5 | -4.3900×10-3 |
| Ca1 j,4 | -1.9147×10-8 | -7.7584×10-7 | 7.1000×10-7 | -3.4980×10-6 | 3.1485×10-4 |
| Ca2j,1 | 3.1527×10-6 | -2.7374×10-6 | 1.7002×10-5 | 7.3932×10-5 | 2.4810×10-2 |
| Ca2j,2 | -5.1497×10-6 | 6.3237×10-6 | -3.2280×10-5 | -1.1467×10-4 | -2.9270×10-2 |
| Ca2j,3 | 2.6358×10-6 | -3.0626×10-6 | 1.6725×10-5 | 3.5196×10-5 | 1.0140×10-2 |
| Ca2j,4 | -4.6573×10-7 | 3.7623×10-7 | -1.1889×10-6 | 1.1072×10-5 | -9.0835×10-4 |
| Ca3j,1 | -1.1690×10-6 | 5.4402×10-7 | -6.5155×10-6 | -4.0532×10-5 | -1.0560×10-2 |
| Ca3j,2 | 2.4121×10-6 | -1.0845×10-6 | 1.2580×10-5 | 6.9330×10-5 | 1.3560×10-2 |
| Ca3j,3 | -1.4576×10-6 | 3.1435×10-7 | -6.2868×10-6 | -2.1240×10-5 | -5.1100×10-3 |
| Ca4j,4 | 2.8945×10-7 | 2.2746×10-8 | 3.9130×10-7 | -4.9317×10-6 | 5.3185×10-4 |
| Cb1j,1 | 2.8246×10-4 | 1.0410×10-4 | 5.3400×10-3 | -1.0399×10-1 | -2.3653×10-1 |
| Cb1 j,2 | -4.7958×10-4 | -2.1082×10-5 | -1.2850×10-2 | 2.5333×10-1 | 9.2246×100 |
| Cb1 j,3 | 2.6229×10-4 | -2.0643×10-5 | 1.3190×10-2 | -1.2216×10-1 | -7.9741×100 |
| Cb1 j,4 | -4.6586×10-5 | 6.7543×10-6 | -2.9100×10-3 | 1.9360×10-2 | 1.7702×100 |
| Cb2j,1 | -3.6666×10-4 | 2.1257×10-5 | -7.1800×10-3 | 1.7230×10-1 | -1.2033×100 |
| Cb2j,2 | 6.5304×10-4 | -1.8580×10-4 | 1.8080×10-2 | -4.6343×10-1 | -7.4848×100 |
| Cb2j,3 | -3.6572×10-4 | 1.5027×10-4 | -1.8410×10-2 | 3.1051×10-1 | 9.2801×100 |
| Cb2j,4 | 6.5961×10-5 | -3.1910×10-5 | 4.0300×10-3 | -6.3420×10-2 | -2.3737×100 |
| Cb3j,1 | 1.2060×10-4 | -3.6365×10-5 | 2.5000×10-3 | -6.4540×10-2 | 1.0061×100 |
| Cb3j,2 | -2.2373×10-4 | 1.0089×10-4 | -6.4700×10-3 | 1.8504×10-1 | 7.9907×10-1 |
| Cb3j,3 | 1.2780×10-4 | -7.1441×10-5 | 6.5300×10-3 | -1.4168×10-1 | -2.4745×100 |
| Cb4j,4 | -2.3342×10-5 | 1.4438×10-5 | -1.4200×10-3 | 3.1210×10-2 | 7.5152×10-1 |
| Cc1j,1 | 4.7752×10-5 | 3.6201×10-5 | -3.4314×10-5 | -1.3040×10-2 | -1.1141×100 |
| Cc1 j,2 | -5.7228×10-5 | -3.8790×10-5 | 8.4780×10-4 | 3.2570×10-2 | 2.9181×100 |
| Cc1 j,3 | 2.1488×10-5 | 2.3765×10-5 | -6.9175×10-4 | -2.2300×10-2 | -1.9768×100 |
| Cc1 j,4 | -2.4853×10-6 | -5.4831×10-6 | 1.6133×10-4 | 4.4900×10-3 | 3.9774×10-1 |
| Cc2j,1 | -5.9376×10-5 | -1.4947×10-6 | 2.6459×10-4 | 2.2800×10-2 | 1.4207×100 |
| Cc2j,2 | 7.6586×10-5 | -1.2064×10-5 | -1.5400×10-3 | -5.7320×10-2 | -3.8688×100 |
| Cc2j,3 | -2.8896×10-5 | 5.4855×10-7 | 1.1800×10-3 | 4.0710×10-2 | 2.7450×100 |
| Cc2j,4 | 3.0725×10-6 | 1.6754×10-6 | -2.6775×10-4 | -8.5100×10-3 | -5.7258×10-1 |
| Cc3j,1 | 1.8059×10-5 | -8.8123×10-6 | -1.3903×10-4 | -9.0500×10-3 | -4.2846×10-1 |
| Cc3j,2 | -2.4188×10-5 | 1.7065×10-5 | 6.2168×10-4 | 2.3050×10-2 | 1.2267×100 |
| Cc3j,3 | 8.7157×10-6 | -6.4827×10-6 | -4.6106×10-4 | -1.6790×10-2 | -9.1186×10-1 |
| Cc4j,3 | -7.5436×10-7 | 4.6804×10-7 | 1.0393×10-4 | 3.5900×10-3 | 1.9666×10-1 |
Table 4 Polynomial coefficients for CO2 absorption coefficients
| 系数 | j=1 | j=2 | j=3 | j=4 | j=5 |
|---|---|---|---|---|---|
| Ca1j,1 | -2.1346×10-6 | 3.0944×10-6 | -9.9047×10-6 | -2.0258×10-5 | -1.3820×10-2 |
| Ca1 j,2 | 2.0523×10-6 | -8.3230×10-6 | 1.6965×10-5 | 1.6867×10-5 | 1.4270×10-2 |
| Ca1 j,3 | -4.1126×10-7 | 4.7522×10-6 | -9.4011×10-6 | -1.0106×10-5 | -4.3900×10-3 |
| Ca1 j,4 | -1.9147×10-8 | -7.7584×10-7 | 7.1000×10-7 | -3.4980×10-6 | 3.1485×10-4 |
| Ca2j,1 | 3.1527×10-6 | -2.7374×10-6 | 1.7002×10-5 | 7.3932×10-5 | 2.4810×10-2 |
| Ca2j,2 | -5.1497×10-6 | 6.3237×10-6 | -3.2280×10-5 | -1.1467×10-4 | -2.9270×10-2 |
| Ca2j,3 | 2.6358×10-6 | -3.0626×10-6 | 1.6725×10-5 | 3.5196×10-5 | 1.0140×10-2 |
| Ca2j,4 | -4.6573×10-7 | 3.7623×10-7 | -1.1889×10-6 | 1.1072×10-5 | -9.0835×10-4 |
| Ca3j,1 | -1.1690×10-6 | 5.4402×10-7 | -6.5155×10-6 | -4.0532×10-5 | -1.0560×10-2 |
| Ca3j,2 | 2.4121×10-6 | -1.0845×10-6 | 1.2580×10-5 | 6.9330×10-5 | 1.3560×10-2 |
| Ca3j,3 | -1.4576×10-6 | 3.1435×10-7 | -6.2868×10-6 | -2.1240×10-5 | -5.1100×10-3 |
| Ca4j,4 | 2.8945×10-7 | 2.2746×10-8 | 3.9130×10-7 | -4.9317×10-6 | 5.3185×10-4 |
| Cb1j,1 | 2.8246×10-4 | 1.0410×10-4 | 5.3400×10-3 | -1.0399×10-1 | -2.3653×10-1 |
| Cb1 j,2 | -4.7958×10-4 | -2.1082×10-5 | -1.2850×10-2 | 2.5333×10-1 | 9.2246×100 |
| Cb1 j,3 | 2.6229×10-4 | -2.0643×10-5 | 1.3190×10-2 | -1.2216×10-1 | -7.9741×100 |
| Cb1 j,4 | -4.6586×10-5 | 6.7543×10-6 | -2.9100×10-3 | 1.9360×10-2 | 1.7702×100 |
| Cb2j,1 | -3.6666×10-4 | 2.1257×10-5 | -7.1800×10-3 | 1.7230×10-1 | -1.2033×100 |
| Cb2j,2 | 6.5304×10-4 | -1.8580×10-4 | 1.8080×10-2 | -4.6343×10-1 | -7.4848×100 |
| Cb2j,3 | -3.6572×10-4 | 1.5027×10-4 | -1.8410×10-2 | 3.1051×10-1 | 9.2801×100 |
| Cb2j,4 | 6.5961×10-5 | -3.1910×10-5 | 4.0300×10-3 | -6.3420×10-2 | -2.3737×100 |
| Cb3j,1 | 1.2060×10-4 | -3.6365×10-5 | 2.5000×10-3 | -6.4540×10-2 | 1.0061×100 |
| Cb3j,2 | -2.2373×10-4 | 1.0089×10-4 | -6.4700×10-3 | 1.8504×10-1 | 7.9907×10-1 |
| Cb3j,3 | 1.2780×10-4 | -7.1441×10-5 | 6.5300×10-3 | -1.4168×10-1 | -2.4745×100 |
| Cb4j,4 | -2.3342×10-5 | 1.4438×10-5 | -1.4200×10-3 | 3.1210×10-2 | 7.5152×10-1 |
| Cc1j,1 | 4.7752×10-5 | 3.6201×10-5 | -3.4314×10-5 | -1.3040×10-2 | -1.1141×100 |
| Cc1 j,2 | -5.7228×10-5 | -3.8790×10-5 | 8.4780×10-4 | 3.2570×10-2 | 2.9181×100 |
| Cc1 j,3 | 2.1488×10-5 | 2.3765×10-5 | -6.9175×10-4 | -2.2300×10-2 | -1.9768×100 |
| Cc1 j,4 | -2.4853×10-6 | -5.4831×10-6 | 1.6133×10-4 | 4.4900×10-3 | 3.9774×10-1 |
| Cc2j,1 | -5.9376×10-5 | -1.4947×10-6 | 2.6459×10-4 | 2.2800×10-2 | 1.4207×100 |
| Cc2j,2 | 7.6586×10-5 | -1.2064×10-5 | -1.5400×10-3 | -5.7320×10-2 | -3.8688×100 |
| Cc2j,3 | -2.8896×10-5 | 5.4855×10-7 | 1.1800×10-3 | 4.0710×10-2 | 2.7450×100 |
| Cc2j,4 | 3.0725×10-6 | 1.6754×10-6 | -2.6775×10-4 | -8.5100×10-3 | -5.7258×10-1 |
| Cc3j,1 | 1.8059×10-5 | -8.8123×10-6 | -1.3903×10-4 | -9.0500×10-3 | -4.2846×10-1 |
| Cc3j,2 | -2.4188×10-5 | 1.7065×10-5 | 6.2168×10-4 | 2.3050×10-2 | 1.2267×100 |
| Cc3j,3 | 8.7157×10-6 | -6.4827×10-6 | -4.6106×10-4 | -1.6790×10-2 | -9.1186×10-1 |
| Cc4j,3 | -7.5436×10-7 | 4.6804×10-7 | 1.0393×10-4 | 3.5900×10-3 | 1.9666×10-1 |
Fig.2 Radiative heat flux for Case 1
Fig.3 Radiative source term for Case 1
| 模型 | γmax/% | γaverage/% | δmax/% | δaverage/% |
|---|---|---|---|---|
| RC-WSGG | 9.57 | 4.26 | 14.69 | 6.75 |
| Guo 2015 | 10.14 | 5.10 | 27.61 | 10.14 |
| Dorigon 2013 | 6.11 | 2.72 | 16.84 | 8.87 |
| Cassol 2014 | 8.99 | 3.81 | 14.66 | 7.78 |
| Guo 2021 | 7.65 | 3.95 | 23.24 | 9.46 |
| Bordbar 2014 | 13.6 | 6.82 | 21.65 | 10.37 |
Table 5 Maximum and average relative errors of the different WSGG models for Case 1
| 模型 | γmax/% | γaverage/% | δmax/% | δaverage/% |
|---|---|---|---|---|
| RC-WSGG | 9.57 | 4.26 | 14.69 | 6.75 |
| Guo 2015 | 10.14 | 5.10 | 27.61 | 10.14 |
| Dorigon 2013 | 6.11 | 2.72 | 16.84 | 8.87 |
| Cassol 2014 | 8.99 | 3.81 | 14.66 | 7.78 |
| Guo 2021 | 7.65 | 3.95 | 23.24 | 9.46 |
| Bordbar 2014 | 13.6 | 6.82 | 21.65 | 10.37 |
Fig.4 Radiative heat flux for Case 2
Fig.5 Radiative source term for Case 2
| 误差 | γmax/% | γaverage/% | δmax/% | δaverage/% |
|---|---|---|---|---|
| RC-WSGG | 5.56 | 2.88 | 23.25 | 10.46 |
| Guo 2015 | 25.3 | 12.59 | 69.44 | 22.55 |
| Dorigon 2013 | 22.19 | 12.33 | 61.81 | 18.39 |
| Cassol 2014 | 12.79 | 6.64 | 14.74 | 9.32 |
| Guo 2021 | 13.94 | 4.72 | 45.71 | 17.35 |
| Bordbar 2014 | 16.22 | 6.17 | 49.43 | 16.39 |
Table 6 Maximum and average relative errors of the different WSGG models for Case 2
| 误差 | γmax/% | γaverage/% | δmax/% | δaverage/% |
|---|---|---|---|---|
| RC-WSGG | 5.56 | 2.88 | 23.25 | 10.46 |
| Guo 2015 | 25.3 | 12.59 | 69.44 | 22.55 |
| Dorigon 2013 | 22.19 | 12.33 | 61.81 | 18.39 |
| Cassol 2014 | 12.79 | 6.64 | 14.74 | 9.32 |
| Guo 2021 | 13.94 | 4.72 | 45.71 | 17.35 |
| Bordbar 2014 | 16.22 | 6.17 | 49.43 | 16.39 |
Fig.6 Radiative heat flux for Case 3
Fig.7 Radiative source term for Case 3
| 误差 | γmax/% | γaverage/% | δmax/% | δaverage/% |
|---|---|---|---|---|
| RC-WSGG | 3.96 | 1.69 | 5.51 | 2.46 |
| Guo 2015 | 13.75 | 11.24 | 19.72 | 4.80 |
| Dorigon 2013 | 48.86 | 23.20 | 71.54 | 28.79 |
| Cassol 2014 | 25.63 | 13.36 | 31.87 | 17.65 |
| Guo 2021 | 5.01 | 3.29 | 5.90 | 3.48 |
| Bordbar 2014 | 14.86 | 6.91 | 7.61 | 4.19 |
Table 7 Maximum and average relative errors of the different WSGG models for Case 3
| 误差 | γmax/% | γaverage/% | δmax/% | δaverage/% |
|---|---|---|---|---|
| RC-WSGG | 3.96 | 1.69 | 5.51 | 2.46 |
| Guo 2015 | 13.75 | 11.24 | 19.72 | 4.80 |
| Dorigon 2013 | 48.86 | 23.20 | 71.54 | 28.79 |
| Cassol 2014 | 25.63 | 13.36 | 31.87 | 17.65 |
| Guo 2021 | 5.01 | 3.29 | 5.90 | 3.48 |
| Bordbar 2014 | 14.86 | 6.91 | 7.61 | 4.19 |
Fig.8 Radiative heat flux for Case 4
Fig.9 Radiative source term for Case 4
| 误差 | γmax/% | γaverage/% | δmax/% | δaverage/% |
|---|---|---|---|---|
| RC-WSGG | 17.17 | 12.64 | 20.26 | 5.95 |
| Guo 2015 | 6.81 | 3.26 | 9.43 | 3.02 |
| Dorigon 2013 | 19.24 | 8.29 | 12.63 | 7.76 |
| Cassol 2014 | 21.26 | 10.33 | 17.63 | 9.74 |
| Guo 2021 | 20.1 | 9.75 | 9.70 | 5.59 |
| Bordbar 2014 | 16.69 | 7.29 | 11.90 | 7.39 |
Table 8 Maximum and average relative errors of the different WSGG models for Case 4
| 误差 | γmax/% | γaverage/% | δmax/% | δaverage/% |
|---|---|---|---|---|
| RC-WSGG | 17.17 | 12.64 | 20.26 | 5.95 |
| Guo 2015 | 6.81 | 3.26 | 9.43 | 3.02 |
| Dorigon 2013 | 19.24 | 8.29 | 12.63 | 7.76 |
| Cassol 2014 | 21.26 | 10.33 | 17.63 | 9.74 |
| Guo 2021 | 20.1 | 9.75 | 9.70 | 5.59 |
| Bordbar 2014 | 16.69 | 7.29 | 11.90 | 7.39 |
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