Spectral Monte Carlo simulation of collimated solar irradiation transfer in a water-filled prismatic louver

Yaomin Cai; Zhixiong Guo

doi:10.1364/AO.57.003021

Applied Optics
Vol. 57,
Issue 12,
pp. 3021-3030
(2018)
•https://doi.org/10.1364/AO.57.003021

Spectral Monte Carlo simulation of collimated solar irradiation transfer in a water-filled prismatic louver

Yaomin Cai and Zhixiong Guo

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Yaomin Cai and Zhixiong Guo, "Spectral Monte Carlo simulation of collimated solar irradiation transfer in a water-filled prismatic louver," Appl. Opt. 57, 3021-3030 (2018)

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- Atmospheric and Oceanic Optics
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About this Article
History
- Original Manuscript: February 9, 2018
- Revised Manuscript: March 15, 2018
- Manuscript Accepted: March 15, 2018
- Published: April 13, 2018

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Abstract

The Monte Carlo model was developed to simulate the collimated solar irradiation transfer and energy harvest in a hollow louver made of silica glass and filled with water. The full solar spectrum from the air mass 1.5 database was adopted and divided into various discrete bands for spectral calculations. The band-averaged spectral properties for the silica glass and water were obtained. Ray tracing was employed to find the solar energy harvested by the louver. Computational efficiency and accuracy were examined through intensive comparisons of different band partition approaches, various photon numbers, and element divisions. The influence of irradiation direction on the solar energy harvest efficiency was scrutinized. It was found that within a 15° polar angle of incidence, the harvested solar energy in the louver was high, and the total absorption efficiency reached 61.2% under normal incidence for the current louver geometry.

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Photons #	Elements #	Bands #	CPU Time (s)
$10^{6}$	7140	7	27.67
$10^{7}$			279.69
$10^{8}$			2727.08
$10^{9}$			27,269.25
$10^{8}$	1086	7	2812.14
	4032		2810.30
	7140		2727.08
	11,130		2796.67
$10^{8}$	7140	1	206.75
		3	1334.52
		7	2727.08
		20	8217.14
		40	18,707.81

Bands	Wavelength	$n_{glass}$	$n_{water}$	$α_{glass}$ ( $m^{- 1}$ )	$α_{water}$ ( $m^{- 1}$ )	$σ_{water}$ ( $m^{- 1}$ )	Weight (%)
1	280–4000 nm	1.5216	1.3307	35.0864	381.3735	0.000165	100
3	280–400 nm	1.5429	1.3421	102.5293	0.009	0.1929	4.575
	400–700 nm	1.5261	1.3338	3.734	0.06265	0.0074	43.77
	700–4000 nm	1.5122	1.3247	47.735	2994.58	0.0016	51.655
7	280–400 nm	1.5429	1.3421	102.5293	0.1929	0.009	4.575
	400–548 nm	1.53	1.336	4.92	0.0276	0.032	21.288
	548–700 nm	1.522	1.3316	12.823	0.008	0.2641	21.643
	700–850 nm	1.5178	1.3294	34.1597	2.4007	0.0026	16.195
	850–1100 nm	1.5143	1.3268	54.6798	32.3981	0.0013	16.673
	1100–1530 nm	1.5104	1.323	52.0098	435.3489	0.000165	10.088
	1530–4000 nm	1.501	1.3148	54.7049	16225.8	0.000006	9.538
20	280–400 nm	1.5429	1.3421	102.5293	0.1929	0.009	4.575
	400–450 nm	1.5343	1.338	6.5916	0.0403	0.0503	6.149
	450–500 nm	1.5299	1.336	4.4101	0.0258	0.0294	7.776
	500–530 nm	1.5271	1.3344	3.8295	0.0292	0.0156	4.559
	530–566 nm	1.5253	1.3332	5.049	0.0468	0.014	5.509
	566–600 nm	1.5236	1.3323	7.9275	0.1323	0.009	5.021
	600–650 nm	1.5219	1.3315	12.9215	0.276	0.0077	7.199
	650–700 nm	1.5203	1.3307	19.3064	0.4348	0.0048	6.72
	700–750 nm	1.5189	1.33	26.3851	2.0035	0.00368	6.001
	750–800 nm	1.5177	1.3293	34.9274	2.3347	0.00323	5.316
	800–850 nm	1.5167	1.3287	42.8651	2.9598	0.002497	4.878
	850–930 nm	1.5156	1.3278	50.5189	7.4352	0.00175	6.651
	930–1000 nm	1.5142	1.3267	56.3405	39.1301	0.00114	3.556
	1000–1100 nm	1.5131	1.3258	58.0337	54.3222	0.001	6.465
	1100–1200 nm	1.5117	1.3245	57.1924	90.3071	0.000544	3.152
	1200–1300 nm	1.5106	1.3233	54.0033	410.1431	0.000165	4.305
	1300–1530 nm	1.5086	1.3205	42.4921	893.4837	0.0001	2.631
	1530–1700 nm	1.5063	1.3166	29.3908	731.7093	0.0001	4.017
	1700–3000 nm	1.5004	1.3005	30.3508	12595	$1.43 E - 05$	4.78
	3000–4000 nm	1.4729	1.3972	351.6867	125250	$5.74 E - 06$	0.74
40	280–370 nm	1.5459	1.3436	175.3724	0.2741	0.0814	2.465
	370–400 nm	1.5392	1.3402	12.6989	0.0928	0.075	2.11
	400–418 nm	1.5362	1.3387	6.6426	0.0509	0.0477	2.146
	418–434 nm	1.5343	1.338	6.9023	0.0387	0.039	1.899
	434–450 nm	1.5326	1.3373	6.2805	0.0315	0.032	2.243
	450–466 nm	1.5312	1.3367	4.8093	0.0272	0.0295	2.541
	466–484 nm	1.5298	1.336	4.4557	0.0251	0.029	2.871
	484–500 nm	1.5286	1.3353	3.9545	0.025	0.029	2.509
	500–514 nm	1.5276	1.3347	3.7208	0.027	0.0191	2.227
	514–530 nm	1.5267	1.3341	3.9284	0.0311	0.0157	2.451
	530–548 nm	1.5259	1.3336	4.4105	0.037	0.014	2.807
	548–566 nm	1.525	1.333	5.2975	0.0506	0.013	2.767
	566–582 nm	1.524	1.3325	7.1211	0.0848	0.011	2.437
	582–600 nm	1.5232	1.3322	8.6563	0.1751	0.00907	2.674
	600–618 nm	1.5225	1.3318	10.7808	0.2491	0.0077	2.675
	618–634 nm	1.5218	1.3315	13.2685	0.2821	0.007	2.328
	634–650 nm	1.5213	1.3312	15.3588	0.3052	0.00655	2.334
	650–666 nm	1.5208	1.3309	17.1635	0.3492	0.006	2.248
	666–682 nm	1.5203	1.3307	19.4444	0.417	0.0055	2.3
	682–700 nm	1.5198	1.3305	21.2542	0.5357	0.005	2.313
	700–724 nm	1.5192	1.3302	24.1409	1.8999	0.0045	2.941
	724–750 nm	1.5186	1.3298	28.5397	2.103	0.0042	3.034
	750–776 nm	1.518	1.3295	32.8266	2.5025	0.0037	2.618
	776–800 nm	1.5174	1.3292	36.9404	2.174	0.0033	2.714
	800–824 nm	1.5169	1.3288	40.8048	2.3352	0.0032	2.359
	824–850 nm	1.5164	1.3285	44.7769	3.5392	0.0023	2.511
	850–874 nm	1.516	1.3282	48.0565	4.9536	0.002	2.296
	874–896 nm	1.5156	1.3279	50.5921	6.0801	0.0018	2.017
	896–930 nm	1.5151	1.3275	52.8901	11.06	0.0016	2.292
	930–1000 nm	1.5142	1.3267	56.3405	39.1301	0.00114	3.473
	1000–1050 nm	1.5134	1.3261	57.8741	45.9067	0.0012	3.404
	1050–1100 nm	1.5128	1.3255	58.219	64.093	0.0008	2.928
	1100–1200 nm	1.5117	1.3245	57.1924	90.3071	0.00054	3.056
	1200–1250 nm	1.5109	1.3236	55.0663	266.7723	0.00025	2.215
	1250–1300 nm	1.5103	1.3229	52.8308	568.2748	0.00017	2.006
	1300–1530 nm	1.5086	1.3205	42.4921	893.4837	0.0001	2.557
	1530–1700 nm	1.5063	1.3166	29.3908	731.7093	0.0001	3.886
	1700–2050 nm	1.5037	1.3111	27.3	2343.7	0.00006	2.043
	2050–3000 nm	1.4979	1.2924	32.6871	20446	0.000012	2.593
	3000–4000 nm	1.4729	1.3972	351.6867	125250	$5.70 E - 06$	0.712

Photons #	Elements #	Bands #	CPU Time (s)
$10^{6}$	7140	7	27.67
$10^{7}$			279.69
$10^{8}$			2727.08
$10^{9}$			27,269.25
$10^{8}$	1086	7	2812.14
	4032		2810.30
	7140		2727.08
	11,130		2796.67
$10^{8}$	7140	1	206.75
		3	1334.52
		7	2727.08
		20	8217.14
		40	18,707.81

Bands	Wavelength	$n_{glass}$	$n_{water}$	$α_{glass}$ ( $m^{- 1}$ )	$α_{water}$ ( $m^{- 1}$ )	$σ_{water}$ ( $m^{- 1}$ )	Weight (%)
1	280–4000 nm	1.5216	1.3307	35.0864	381.3735	0.000165	100
3	280–400 nm	1.5429	1.3421	102.5293	0.009	0.1929	4.575
	400–700 nm	1.5261	1.3338	3.734	0.06265	0.0074	43.77
	700–4000 nm	1.5122	1.3247	47.735	2994.58	0.0016	51.655
7	280–400 nm	1.5429	1.3421	102.5293	0.1929	0.009	4.575
	400–548 nm	1.53	1.336	4.92	0.0276	0.032	21.288
	548–700 nm	1.522	1.3316	12.823	0.008	0.2641	21.643
	700–850 nm	1.5178	1.3294	34.1597	2.4007	0.0026	16.195
	850–1100 nm	1.5143	1.3268	54.6798	32.3981	0.0013	16.673
	1100–1530 nm	1.5104	1.323	52.0098	435.3489	0.000165	10.088
	1530–4000 nm	1.501	1.3148	54.7049	16225.8	0.000006	9.538
20	280–400 nm	1.5429	1.3421	102.5293	0.1929	0.009	4.575
	400–450 nm	1.5343	1.338	6.5916	0.0403	0.0503	6.149
	450–500 nm	1.5299	1.336	4.4101	0.0258	0.0294	7.776
	500–530 nm	1.5271	1.3344	3.8295	0.0292	0.0156	4.559
	530–566 nm	1.5253	1.3332	5.049	0.0468	0.014	5.509
	566–600 nm	1.5236	1.3323	7.9275	0.1323	0.009	5.021
	600–650 nm	1.5219	1.3315	12.9215	0.276	0.0077	7.199
	650–700 nm	1.5203	1.3307	19.3064	0.4348	0.0048	6.72
	700–750 nm	1.5189	1.33	26.3851	2.0035	0.00368	6.001
	750–800 nm	1.5177	1.3293	34.9274	2.3347	0.00323	5.316
	800–850 nm	1.5167	1.3287	42.8651	2.9598	0.002497	4.878
	850–930 nm	1.5156	1.3278	50.5189	7.4352	0.00175	6.651
	930–1000 nm	1.5142	1.3267	56.3405	39.1301	0.00114	3.556
	1000–1100 nm	1.5131	1.3258	58.0337	54.3222	0.001	6.465
	1100–1200 nm	1.5117	1.3245	57.1924	90.3071	0.000544	3.152
	1200–1300 nm	1.5106	1.3233	54.0033	410.1431	0.000165	4.305
	1300–1530 nm	1.5086	1.3205	42.4921	893.4837	0.0001	2.631
	1530–1700 nm	1.5063	1.3166	29.3908	731.7093	0.0001	4.017
	1700–3000 nm	1.5004	1.3005	30.3508	12595	$1.43 E - 05$	4.78
	3000–4000 nm	1.4729	1.3972	351.6867	125250	$5.74 E - 06$	0.74
40	280–370 nm	1.5459	1.3436	175.3724	0.2741	0.0814	2.465
	370–400 nm	1.5392	1.3402	12.6989	0.0928	0.075	2.11
	400–418 nm	1.5362	1.3387	6.6426	0.0509	0.0477	2.146
	418–434 nm	1.5343	1.338	6.9023	0.0387	0.039	1.899
	434–450 nm	1.5326	1.3373	6.2805	0.0315	0.032	2.243
	450–466 nm	1.5312	1.3367	4.8093	0.0272	0.0295	2.541
	466–484 nm	1.5298	1.336	4.4557	0.0251	0.029	2.871
	484–500 nm	1.5286	1.3353	3.9545	0.025	0.029	2.509
	500–514 nm	1.5276	1.3347	3.7208	0.027	0.0191	2.227
	514–530 nm	1.5267	1.3341	3.9284	0.0311	0.0157	2.451
	530–548 nm	1.5259	1.3336	4.4105	0.037	0.014	2.807
	548–566 nm	1.525	1.333	5.2975	0.0506	0.013	2.767
	566–582 nm	1.524	1.3325	7.1211	0.0848	0.011	2.437
	582–600 nm	1.5232	1.3322	8.6563	0.1751	0.00907	2.674
	600–618 nm	1.5225	1.3318	10.7808	0.2491	0.0077	2.675
	618–634 nm	1.5218	1.3315	13.2685	0.2821	0.007	2.328
	634–650 nm	1.5213	1.3312	15.3588	0.3052	0.00655	2.334
	650–666 nm	1.5208	1.3309	17.1635	0.3492	0.006	2.248
	666–682 nm	1.5203	1.3307	19.4444	0.417	0.0055	2.3
	682–700 nm	1.5198	1.3305	21.2542	0.5357	0.005	2.313
	700–724 nm	1.5192	1.3302	24.1409	1.8999	0.0045	2.941
	724–750 nm	1.5186	1.3298	28.5397	2.103	0.0042	3.034
	750–776 nm	1.518	1.3295	32.8266	2.5025	0.0037	2.618
	776–800 nm	1.5174	1.3292	36.9404	2.174	0.0033	2.714
	800–824 nm	1.5169	1.3288	40.8048	2.3352	0.0032	2.359
	824–850 nm	1.5164	1.3285	44.7769	3.5392	0.0023	2.511
	850–874 nm	1.516	1.3282	48.0565	4.9536	0.002	2.296
	874–896 nm	1.5156	1.3279	50.5921	6.0801	0.0018	2.017
	896–930 nm	1.5151	1.3275	52.8901	11.06	0.0016	2.292
	930–1000 nm	1.5142	1.3267	56.3405	39.1301	0.00114	3.473
	1000–1050 nm	1.5134	1.3261	57.8741	45.9067	0.0012	3.404
	1050–1100 nm	1.5128	1.3255	58.219	64.093	0.0008	2.928
	1100–1200 nm	1.5117	1.3245	57.1924	90.3071	0.00054	3.056
	1200–1250 nm	1.5109	1.3236	55.0663	266.7723	0.00025	2.215
	1250–1300 nm	1.5103	1.3229	52.8308	568.2748	0.00017	2.006
	1300–1530 nm	1.5086	1.3205	42.4921	893.4837	0.0001	2.557
	1530–1700 nm	1.5063	1.3166	29.3908	731.7093	0.0001	3.886
	1700–2050 nm	1.5037	1.3111	27.3	2343.7	0.00006	2.043
	2050–3000 nm	1.4979	1.2924	32.6871	20446	0.000012	2.593
	3000–4000 nm	1.4729	1.3972	351.6867	125250	$5.70 E - 06$	0.712

Abstract

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Equations (24)

Applied Optics