Band Models for Nonisothermal Radiating Gases

F. S. Simmons

doi:10.1364/AO.5.001801

Applied Optics
Vol. 5,
Issue 11,
pp. 1801-1811
(1966)
•https://doi.org/10.1364/AO.5.001801

Band Models for Nonisothermal Radiating Gases

F. S. Simmons

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F. S. Simmons, "Band Models for Nonisothermal Radiating Gases," Appl. Opt. 5, 1801-1811 (1966)

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Abstract

Approximate relations are presented for calculating the mean spectral distribution of the net radiance at the boundary of a nonisothermal gas, given the distributions of temperature, pressure, and composition within the region and the appropriate experimental spectral absorptance data. Experimental data obtained for the 2.7-μ bands of H₂O, in which variations in temperature between 900°K to 1200°K were imposed along a 60-cm path at various pressures, are compared with calculations based on a strongline model. A more general band model expression is proposed for intermediate optical depths.

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Rum	λ (μ)	Q(T₀) (cm^−½)	k(T₀) (cm⁻¹)	${\bar{N}}_{λ}$ [Eq. (3d)] (W-cm⁻² sr⁻¹-μ⁻¹)	${\bar{N}}_{λ}$ [Eq. (3e)] (W-cm⁻² sr⁻¹-μ⁻¹)	${\bar{N}}_{λ}$ (exp) (W-cm⁻² sr⁻¹-μ⁻¹)	$\bar{α}$ (λ)	N_λ (W-cm⁻² sr⁻¹-μ⁻¹)	T_AE (°K)
1123–4		T₀ = 1224°K; ${\bar{N}}_{0}$ = 271 mm; (AF)₀ = 0.067 cm; Y_L = 0.801 cm; $\bar{T}$ = 1224°K
	2.465	0.116	0.053	0.192	0.213	0.246	0.20	1.230	1248
	2.562	0.250	0.100	0.365	0.453	0.499	0.40	1.248	1257
	2.635	0.130	0.052	0.207	0.232	0.321	0.24	1.365	1287
	2.685	0.300	0.130	0.411	0.531	0.523	0.48	1.090	1226
	2.728	0.271	0.106	0.377	0.475	0.482	0.45	1.071	1225
	2.805	0.296	0.127	0.395	0.509	0.492	0.48	1.028	1216
	2.927	0.255	0.106	0.340	0.424	0.393	0.41	0.959	1208
	3.122	0.100	0.036	0.142	0.155	0.131	0.17	0.795	1166
1123–5		T₀ = 1006°K; P₀ = 223 mm; (AF)₀ = 0.061 cm; Y_L = 0.728 cm; $\bar{T}$ = 1007°K
	2.465	0.091	0.040	0.051	0.055	0.077	0.17	0.466	1036
	2.562	0.250	0.100	0.127	0.156	0.204	0.40	0.510	1048
	2.635	0.142	0.055	0.080	0.090	0.134	0.23	0.583	1073
	2.685	0.300	0.130	0.150	0.192	0.217	0.47	0.462	1025
	2.728	0.245	0.094	0.129	0.157	0.200	0.48	0.417	1005
	2.805	0.296	0.127	0.150	0.191	0.215	0.45	0.478	1031
	2.927	0.206	0.086	0.112	0.133	0.133	0.33	0.409	1000
	3.122	0.063	0.022	0.038	0.034	0.034	0.10	0.324	954
1123–6			T₀ = 1005°K; P₀ = 251 mm; (AF)₀ = 0.078 cm
	2.465	0.092	0.040	0.099	0.110	0.213	—	—	—
	2.562	0.250	0.100	0.216	0.280	0.324	—	—	—
	2.635	0.142	0.055	0.134	0.154	0.220	—	—	—
	2.685	0.300	0.130	0.253	0.343	0.354	—	—	—
	2.728	0.245	0.094	0.226	0.294	0.318	—	—	—
	2.805	0.296	0.127	0.253	0.343	0.324	—	—	—
	2.927	0.206	0.086	0.208	0.264	0.253	—	—	—
	3.122	0.063	0.022	0.082	0.087	0.073	—	—	—
1124–4		T₀ = 1222°K; ${\bar{N}}_{0}$ = 398 mm; (AF)₀ = 0.145 cm; Y_L = 1.74 cm; $\bar{T}$ = 1218°K
	2.465	0.116	0.052	0.263	0.305	0.320	0.29	1.122	1246
	2.562	0.250	0.100	0.479	0.653	0.583	0.54	1.078	1216
	2.635	0.130	0.052	0.284	0.335	0.395	0.34	1.145	1237
	2.685	0.300	0.130	0.531	0.767	0.625	0.63	0.993	1203
	2.728	0.271	0.106	0.490	0.684	0.569	0.59	0.965	1196
	2.805	0.296	0.127	0.512	0.735	0.586	0.63	0.930	1189
	2.927	0.255	0.106	0.445	0.610	0.481	0.54	0.890	1186
	3.122	0.100	0.036	0.196	0.222	0.165	0.23	0.703	1133
1124–6		T₀ = 1001 °K; ${\bar{N}}_{0}$ = 329 mm; (AF)₀ = 0.133 cm; Y_L = 1.59 cm; $\bar{T}$ = 1006°K
	2.465	0.091	0.040	0.075	0.084	0.114	0.22	0.518	1055
	2.562	0.250	0.100	0.174	0.235	0.263	0.51	0.516	1050
	2.635	0.142	0.055	0.114	0.135	0.188	0.31	0.606	1082
	2.685	0.300	0.130	0.202	0.289	0.293	0.61	0.480	1033
	2.728	0.245	0.094	0.177	0.237	0.233	0.54	0.432	1011
	2.805	0.296	0.127	0.203	0.288	0.253	0.59	0.429	1010
	2.927	0.205	0.086	0.157	0.201	0.195	0.45	0.433	1011
	3.122	0.064	0.022	0.056	0.060	0.043	0.18	0.242	901
1124–7			T₀ = 1015°K; ${\bar{N}}_{0}$ = 376 mm; (AF)₀ = 0.071 cm
	2.465	0.093	0.041	0.152	0.178	0.224	—	—	—
	2.562	0.250	0.100	0.308	0.447	0.399	—	—	—
	2.635	0.141	0.055	0.199	0.245	0.289	—	—	—
	2.685	0.300	0.130	0.351	0.547	0.428	—	—	—
	2.728	0.246	0.095	0.320	0.470	0.384	—	—	—
	2.805	0.296	0.127	0.352	0.544	0.387	—	—	—
	2.927	0.208	0.087	0.299	0.423	0.319	—	—	—
	3.122	0.064	0.023	0.126	0.143	0.089	—	—	—
1125–3		T₀ = 1234°K; P₀ = 651 mm; (AF)₀ = 0.382 cm; Y_L = 4.61 cm; $\bar{T}$ = 1231°K
	2.465	0.118	0.053	0.414	0.527	0.520	0.40	1.300	1262
	2.562	0.250	0.100	0.682	1.108	0.789	0.69	1.142	1231
	2.635	0.129	0.051	0.434	0.565	0.596	0.50	1.192	1249
	2.685	0.300	0.130	0.734	1.299	0.826	0.80	1.032	1211
	2.728	0.273	0.106	0.691	1.167	0.750	0.78	0.961	1195
	2.805	0.296	0.127	0.708	1.244	0.763	0.80	0.954	1196
	2.927	0.257	0.107	0.633	1.040	0.646	0.70	0.923	1196
	3.122	0.102	0.037	0.312	0.384	0.255	0.34	0.750	1151
1125–4	T₀ = 1004°K; P₀ = 533 mm; (AF)₀ = 0.349 cm; Y_L = 4.17 cm; $\bar{T}$ = 1007°K
	2.465	0.091	0.040	0.113	0.135	0.160	0.34	0.470	1037
	2.562	0.250	0.100	0.239	0.380	0.343	0.72	0.477	1036
	2.635	0.142	0.055	0.166	0.219	0.250	0.49	0.510	1044
	2.685	0.300	0.130	0.270	0.467	0.375	0.81	0.463	1026
	2.728	0.245	0.094	0.243	0.384	0.325	0.75	0.433	1012
	2.805	0.296	0.127	0.271	0.466	0.347	0.79	0.439	1014
	2.927	0.206	0.086	0.220	0.325	0.267	0.65	0.411	1011
	3.122	0.063	0.022	0.086	0.098	0.081	0.28	0.290	933
1125–5			T₀ = 1010°K; P₀ = 597 mm; (AF)₀ = 0.434 cm
	2.465	0.092	0.041	0.199	0.254	0.280	—	—	—
	2.562	0.250	0.100	0.363	0.648	0.488	—	—	—
	2.635	0.142	0.055	0.258	0.358	0.364	—	—	—
	2.685	0.300	0.130	0.401	0.794	0.470	—	—	—
	2.728	0.246	0.094	0.375	0.677	0.453	—	—	—
	2.805	0.296	0.127	0.403	0.791	0.446	—	—	—
	2.927	0.207	0.087	0.356	0.606	0.391	—	—	—
	3.122	0.064	0.023	0.167	0.202	0.165	—	—	—
122–3		T₀ = 1229°K; P₀ = 439 mm; (AF)₀ = 0.175 cm; Y_L = 2.10 cm; $\bar{T}$ = 1229°K
	2.465	0.117	0.053	0.298	0.351	0.372	0.31	1.200	1242
	2.562	0.250	0.100	0.528	0.742	0.677	0.57	1.170	1239
	2.635	0.129	0.051	0.316	0.379	0.456	0.37	1.242	1260
	2.685	0.300	0.130	0.582	0.871	0.713	0.67	1.065	1220
	2.728	0.272	0.106	0.541	0.781	0.640	0.64	1.000	1209
	2.805	0.296	0.127	0.560	0.834	0.654	0.67	0.975	1202
	2.927	0.256	0.107	0.492	0.697	0.537	0.58	0.926	1198
	3.122	0.101	0.037	0.222	0.257	0.192	0.25	0.753	1152
122–4			T₀ = 1019°K; P₀ = 401 mm; (AF)₀ = 0.193 cm
	2.465	0.093	0.041	0.139	0.164	0.201	—	—	—
	2.562	0.250	0.100	0.281	0.418	0.375	—	—	—
	2.635	0.141	0.055	0.185	0.231	0.274	—	—	—
	2.685	0.300	0.130	0.319	0.511	0.400	—	—	—
	2.728	0.247	0.095	0.290	0.435	0.378	—	—	—
	2.805	0.296	0.127	0.319	0.508	0.378	—	—	—
	2.927	0.209	0.088	0.270	0.387	0.309	—	—	—
	3.122	0.065	0.023	0.113	0.128	0.112	—	—	—
122–5			T₀ = 1223°K; P₀ = 414 mm; (AF)₀ = 0.156 cm
	2.465	0.116	0.052	0.224	0.258	0.260	—	—	—
	2.562	0.250	0.100	0.415	0.568	0.518	—	—	—
	2.635	0.130	0.052	0.249	1.296	0.343	—	—	—
	2.685	0.300	0.130	0.460	0.667	0.578	—	—	—
	0.728	0.271	0.106	0.423	0.587	0.504	—	—	—
	2.805	0.296	0.127	0.443	0.640	0.542	—	—	—
	2.927	0.255	0.106	0.381	0.517	0.396	—	—	—
	3.122	0.100	0.036	0.163	0.184	0.126	—	—	—
122–7			T₀ = 1218°K; ${\bar{N}}_{0}$ = 391 mm; (AF)₀ = 0.041 cm
	2.465	0.116	0.052	0.191	0.216	0.244	—	—	—
	2.562	0.250	0.100	0.373	0.491	0.540	—	—	—
	2.635	0.130	0.052	0.222	0.259	0.342	—	—	—
	2.685	0.300	0.130	0.417	0.577	0.587	—	—	—
	2.728	0.270	0.105	0.377	0.501	0.500	—	—	—
	2.805	0.296	0.127	0.402	0.554	0.542	—	—	—
	2.927	0.254	0.106	0.336	0.436	0.400	—	—	—
	3.122	0.099	0.036	0.136	0.150	0.117	—	—	—
122–8			T₀ = 1013°K; P₀ = 393 mm; (AF)₀ = 0.187 cm
	2.465	0.092	0.041	0.144	0.168	0.212	—	—	—
	2.562	0.250	0.100	0.298	0.431	0.425	—	—	—
	2.635	0.141	0.055	0.194	0.239	0.300	—	—	—
	2.685	0.300	0.130	0.340	0.528	0.453	—	—	—
	2.728	0.246	0.095	0.308	0.448	0.399	—	—	—
	2.805	0.296	0.127	0.341	0.526	0.418	—	—	—
	2.927	0.208	0.087	0.285	0.400	0.349	—	—	—
	3.122	0.064	0.023	0.117	0.132	0.120	—	—	—
122–9		T₀ = 1005°K; P₀ = 359 mm; (AF)₀ = 0.158 cm; Y_L = 1.90 cm; $\bar{T}$ = 1005°K
	2.465	0.092	0.040	0.081	0.088	0.113	0.24	0.471	1038
	2.562	0.250	0.100	0.186	0.246	0.260	0.55	0.473	1036
	2.635	0.142	0.055	0.122	0.141	0.176	0.35	0.503	0143
	2.685	0.300	0.130	0.215	0.302	0.293	0.64	0.458	1024
	2.728	0.245	0.094	0.188	0.248	0.240	0.58	0.414	1003
	2.805	0.296	0.127	0.215	0.301	0.269	0.62	0.433	1011
	2.927	0.206	0.086	0.167	0.210	0.186	0.49	0.379	985
	3.122	0.063	0.022	0.060	0.063	0.053	0.18	0.294	936

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Applied Optics