Mathematical modeling of the interaction between solar radiation and the Earth's atmosphere is formalized by the radiative transfer equation(RTE), whose resolution calls for two-stream approximations among other m...Mathematical modeling of the interaction between solar radiation and the Earth's atmosphere is formalized by the radiative transfer equation(RTE), whose resolution calls for two-stream approximations among other methods. This paper proposes a new two-stream approximation of the RTE with the development of the phase function and the intensity into a third-order series of Legendre polynomials. This new approach, which adds one more term in the expression of the intensity and the phase function, allows in the conditions of a plane parallel atmosphere a new mathematical formulation of γparameters. It is then compared to the Eddington, Hemispheric Constant, Quadrature, Combined Delta Function and Modified Eddington, and second-order approximation methods with reference to the Discrete Ordinate(Disort) method(δ –128 streams), considered as the most precise. This work also determines the conversion function of the proposed New Method using the fundamental definition of two-stream approximation(F-TSA) developed in a previous work. Notably,New Method has generally better precision compared to the second-order approximation and Hemispheric Constant methods. Compared to the Quadrature and Eddington methods, New Method shows very good precision for wide domains of the zenith angle μ 0, but tends to deviate from the Disort method with the zenith angle, especially for high values of optical thickness. In spite of this divergence in reflectance for high values of optical thickness, very strong correlation with the Disort method(R ≈ 1) was obtained for most cases of optical thickness in this study. An analysis of the Legendre polynomial series for simple functions shows that the high precision is due to the fact that the approximated functions ameliorate the accuracy when the order of approximation increases, although it has been proven that there is a limit order depending on the function from which the precision is lost. This observation indicates that increasing the order of approximation of the phase function of the RTE leads to a better precision in flux calculations. However, this approach may be limited to a certain order that has not been studied in this paper.展开更多
In this paper, the radial temperature distributions of the blown CO2 arcs in a model gas circuit breaker were investigated by optical emission spectroscopy methods. The CO2 flows with different flow rates(50, 100 and ...In this paper, the radial temperature distributions of the blown CO2 arcs in a model gas circuit breaker were investigated by optical emission spectroscopy methods. The CO2 flows with different flow rates(50, 100 and 150 1 min^-1) were created to axially blow the arcs burning in a polymethyl methacrylate(PMMA) nozzle. Discharges with different arc currents(200 and 400A) were conducted in the experiment. The absolute intensity method was applied for a carbon ionic line of 657.8 nm to obtain the radial temperature profiles of the arc columns at a cross-section 1 mm above the nozzle. The calibration for the intensity of the CⅡ 657.8 nm line was achieved by the Fowler–Milne method with the help of an oxygen atomic line of 777.2 nm.The highest temperature obtained in the arc center was up to 19 900 K when the arc current was 400 A and the CO2 flow rate was 50 1 min^-1, while the lowest temperature in the arc center was about 15 900 K when the arc current was 200 A and the CO2 flow rate was 150 1min^-1. The results indicate that as the arc current increases, the temperature in the arc center would also increase apparently, and a larger gas flow rate would lead to a lower central temperature in general. It can also be found that the influence of the CO2 flow rate on the arc temperature was much less than that of the arc current under the present experimental conditions. In addition,higher temperature in the arc center would cause a sharper temperature decrease from the central region towards the edge.展开更多
正弦波调制全光纤电流互感器(fiber optical current transformer,FOCT)因具备动态范围大、不与一次主回路连接、绝缘性能好、无铁磁饱和等优点,成为特高压换流站重要的测量设备。但在实际运行过程中,FOCT故障率远高于电磁互感器,而光...正弦波调制全光纤电流互感器(fiber optical current transformer,FOCT)因具备动态范围大、不与一次主回路连接、绝缘性能好、无铁磁饱和等优点,成为特高压换流站重要的测量设备。但在实际运行过程中,FOCT故障率远高于电磁互感器,而光回路故障是最为常见的故障类型。针对此,首先建立FOCT数学模型,提出二次谐波、光强峰值、平均光强应作为重要监测量;在此基础上分析光回路故障对探测器输出信号的影响,提出基于驱动电流及探测器输出信号变化的光回路故障预警方法,通过阈值设置及平均光强趋势判断等辨识真实的光回路故障。最后开展现场试验验证,证明该预警方法的有效性。展开更多
文摘Mathematical modeling of the interaction between solar radiation and the Earth's atmosphere is formalized by the radiative transfer equation(RTE), whose resolution calls for two-stream approximations among other methods. This paper proposes a new two-stream approximation of the RTE with the development of the phase function and the intensity into a third-order series of Legendre polynomials. This new approach, which adds one more term in the expression of the intensity and the phase function, allows in the conditions of a plane parallel atmosphere a new mathematical formulation of γparameters. It is then compared to the Eddington, Hemispheric Constant, Quadrature, Combined Delta Function and Modified Eddington, and second-order approximation methods with reference to the Discrete Ordinate(Disort) method(δ –128 streams), considered as the most precise. This work also determines the conversion function of the proposed New Method using the fundamental definition of two-stream approximation(F-TSA) developed in a previous work. Notably,New Method has generally better precision compared to the second-order approximation and Hemispheric Constant methods. Compared to the Quadrature and Eddington methods, New Method shows very good precision for wide domains of the zenith angle μ 0, but tends to deviate from the Disort method with the zenith angle, especially for high values of optical thickness. In spite of this divergence in reflectance for high values of optical thickness, very strong correlation with the Disort method(R ≈ 1) was obtained for most cases of optical thickness in this study. An analysis of the Legendre polynomial series for simple functions shows that the high precision is due to the fact that the approximated functions ameliorate the accuracy when the order of approximation increases, although it has been proven that there is a limit order depending on the function from which the precision is lost. This observation indicates that increasing the order of approximation of the phase function of the RTE leads to a better precision in flux calculations. However, this approach may be limited to a certain order that has not been studied in this paper.
基金supported by National Natural Science Foundation of China (Nos. 51577145, 51707144 and 51877165)the Key Research and Development Program of Shaanxi Province (No. 2018ZDXM-GY-112)the State Key Laboratory of Electrical Insulation and Power Equipment (No. EIPE19302)
文摘In this paper, the radial temperature distributions of the blown CO2 arcs in a model gas circuit breaker were investigated by optical emission spectroscopy methods. The CO2 flows with different flow rates(50, 100 and 150 1 min^-1) were created to axially blow the arcs burning in a polymethyl methacrylate(PMMA) nozzle. Discharges with different arc currents(200 and 400A) were conducted in the experiment. The absolute intensity method was applied for a carbon ionic line of 657.8 nm to obtain the radial temperature profiles of the arc columns at a cross-section 1 mm above the nozzle. The calibration for the intensity of the CⅡ 657.8 nm line was achieved by the Fowler–Milne method with the help of an oxygen atomic line of 777.2 nm.The highest temperature obtained in the arc center was up to 19 900 K when the arc current was 400 A and the CO2 flow rate was 50 1 min^-1, while the lowest temperature in the arc center was about 15 900 K when the arc current was 200 A and the CO2 flow rate was 150 1min^-1. The results indicate that as the arc current increases, the temperature in the arc center would also increase apparently, and a larger gas flow rate would lead to a lower central temperature in general. It can also be found that the influence of the CO2 flow rate on the arc temperature was much less than that of the arc current under the present experimental conditions. In addition,higher temperature in the arc center would cause a sharper temperature decrease from the central region towards the edge.
文摘正弦波调制全光纤电流互感器(fiber optical current transformer,FOCT)因具备动态范围大、不与一次主回路连接、绝缘性能好、无铁磁饱和等优点,成为特高压换流站重要的测量设备。但在实际运行过程中,FOCT故障率远高于电磁互感器,而光回路故障是最为常见的故障类型。针对此,首先建立FOCT数学模型,提出二次谐波、光强峰值、平均光强应作为重要监测量;在此基础上分析光回路故障对探测器输出信号的影响,提出基于驱动电流及探测器输出信号变化的光回路故障预警方法,通过阈值设置及平均光强趋势判断等辨识真实的光回路故障。最后开展现场试验验证,证明该预警方法的有效性。
