多重网格法在SF_6高压断路器电场与气流场数值计算中应用的研究
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摘要
SF_6高压断路器的介质恢复特性是衡量断路器开断特性的重要依据,介质恢复特性的数值模拟涉及到断路器液压操动机构的输出特性的数值计算,灭弧室电场与气流场的数值计算。本论文研究工作的重点是多重网格法在SF_6断路器电场和气流场数值计算中的应用与研究。
电场数值计算方面
为了易于将多重网格法用于电场和气流场的数值计算,并且使复杂结构的场域的边界得到良好的拟合,研究了分域贴体网格生成技术,分别在物理平面(原场域)上生成分域贴体网格,在规则计算平面上生成分域矩形网格,使电场和气流场的数值计算都在计算平面上进行。
通过坐标变换,推导出计算平面上描述电场分布的数学模型,并将其离散成有限差分格式,将多重网格法与离散格式相结合,给出了一种有限差分+多重网格法的电场数值计算法。
考虑到有限分析法在矩形网格上具有计算精度高的优点,本论文在对传统的有限分析法进行了改进的基础上,为提高数值计算的收敛速度,将多重网格法与改进后的有限分析法相结合,给出了一种有限分析+多重网格法的电场数值计算方法。
流场数值计算方面
通过数学推导,建立了在计算平面上描述非定常、可压缩粘性流体的控制方程及其有限体积法离散格式,并与多重网格法计算格式相结合,给出了对非定常、可压缩粘性流体进行数值模拟的有限体积+多重网格法的流场数值计算法。
为解决非定常、可压缩流动的控制方程中速度-压力梯度耦合问题在数值求解时的难题,采用了交错网格技术和线分步迭代法对离散方程求解,克服了速度-压力梯度耦合问题的计算难点。
应用所开发的计算方法,以550kV SF_6高压断路器灭弧室的气流场为实例,在260mm开距的全开断过程,以1mm为计算步长,对吹弧气体的流动进行了数值模拟,并将数值模拟结果与用国际商用软件FLUENT的计算结果相比较,证明本文所给出的数值计算方法是正确的。
在上述研究成果的基础上,对550kV SF_6高压断路器空载开断和短路开断的介质恢复特性进行了数值模拟。本论文给出的对SF_6断路器的介质恢复特性进行数值模拟的方法是可行的。
The dielectric recovery property of SF_6 high voltage circuit breaker is the basis for judging the breaking performance. The numerical simulation of dielectric recovery property involves the numerical calculation of the output characteristics of the hydrodynamic actuator and the numerical simulation of electric field and gas flow field of arc quenching chamber of SF_6 circuit breaker. The focal point of the thesis is to investigate of the application of the multi-grid method in the electric field calculation and the numerical simulation of gas flow field of arc quenching chamber.
Numerical calculation of electric field
For the sack of making the application of multi-grid method easily and making the boundary of complex structure chamber well fitted, the partition body fitting grid generating technique has been investigated, so that the body fitting grids and rectangle grids are generated in each subregion of physic plane and calculating plane respectively, which makes the electric field calculation and the numerical simulation of gas flow field be able to run in same calculation plane.
Through the coordinate transformation, the mathematical model for describing electric field distribution and its discrete scheme on the calculation plane are deduced, and the multi-grid method is combined with the discrete scheme and a combination of Finite Difference + Multi-grid Method has been developed.
Considering the fact that the finite analytic method possesses the advantage of high precision at the rectangle calculating element, In this thesis, the conventional finite analytic method has been improved and combined with multi-grid method for accelerating the convergence speed, and a finite analytic + multi-grid method for calculating electric field distribution has been developed.
Numerical simulation of gas flow field
Through mathematical deducing, the control equation set and for describing the time dependent compressible viscous flow have been given at the calculating plane. The discrete scheme of those control equations have also been deduced by the finite volume method and combined with multi-grid method which forms a Finite volume + Multi-grid Method for calculating the time dependent compressible viscous flow.
For the sack of solving the hard problems encountered in the numerical simulation of the velocity-pressure gradient coupling problem, the interlock grid technique and the linear distribute iteration method have been adopted. So that those hard problems have been well solved.
Applying this numerical simulation method, the 550kV circuit breaker was taken as numerical calculation example and the gas blast flow during breaking process of 260mm open stroke has been simulated at each 1mm calculating step. The simulation results have been compared with the results calculated by commercial software FLUENT which show that the numerical simulation method given by this thesis is correct.
On the basis of the research results, the numerical simulation of dielectric recovery properties of 550kV circuit breaker under non-load breaking and short circuit breaking have been carried out and discussed. The results show that the numerical method for dielectric recovery property simulation given by this thesis is feasible.
电场数值计算方面
为了易于将多重网格法用于电场和气流场的数值计算,并且使复杂结构的场域的边界得到良好的拟合,研究了分域贴体网格生成技术,分别在物理平面(原场域)上生成分域贴体网格,在规则计算平面上生成分域矩形网格,使电场和气流场的数值计算都在计算平面上进行。
通过坐标变换,推导出计算平面上描述电场分布的数学模型,并将其离散成有限差分格式,将多重网格法与离散格式相结合,给出了一种有限差分+多重网格法的电场数值计算法。
考虑到有限分析法在矩形网格上具有计算精度高的优点,本论文在对传统的有限分析法进行了改进的基础上,为提高数值计算的收敛速度,将多重网格法与改进后的有限分析法相结合,给出了一种有限分析+多重网格法的电场数值计算方法。
流场数值计算方面
通过数学推导,建立了在计算平面上描述非定常、可压缩粘性流体的控制方程及其有限体积法离散格式,并与多重网格法计算格式相结合,给出了对非定常、可压缩粘性流体进行数值模拟的有限体积+多重网格法的流场数值计算法。
为解决非定常、可压缩流动的控制方程中速度-压力梯度耦合问题在数值求解时的难题,采用了交错网格技术和线分步迭代法对离散方程求解,克服了速度-压力梯度耦合问题的计算难点。
应用所开发的计算方法,以550kV SF_6高压断路器灭弧室的气流场为实例,在260mm开距的全开断过程,以1mm为计算步长,对吹弧气体的流动进行了数值模拟,并将数值模拟结果与用国际商用软件FLUENT的计算结果相比较,证明本文所给出的数值计算方法是正确的。
在上述研究成果的基础上,对550kV SF_6高压断路器空载开断和短路开断的介质恢复特性进行了数值模拟。本论文给出的对SF_6断路器的介质恢复特性进行数值模拟的方法是可行的。
The dielectric recovery property of SF_6 high voltage circuit breaker is the basis for judging the breaking performance. The numerical simulation of dielectric recovery property involves the numerical calculation of the output characteristics of the hydrodynamic actuator and the numerical simulation of electric field and gas flow field of arc quenching chamber of SF_6 circuit breaker. The focal point of the thesis is to investigate of the application of the multi-grid method in the electric field calculation and the numerical simulation of gas flow field of arc quenching chamber.
Numerical calculation of electric field
For the sack of making the application of multi-grid method easily and making the boundary of complex structure chamber well fitted, the partition body fitting grid generating technique has been investigated, so that the body fitting grids and rectangle grids are generated in each subregion of physic plane and calculating plane respectively, which makes the electric field calculation and the numerical simulation of gas flow field be able to run in same calculation plane.
Through the coordinate transformation, the mathematical model for describing electric field distribution and its discrete scheme on the calculation plane are deduced, and the multi-grid method is combined with the discrete scheme and a combination of Finite Difference + Multi-grid Method has been developed.
Considering the fact that the finite analytic method possesses the advantage of high precision at the rectangle calculating element, In this thesis, the conventional finite analytic method has been improved and combined with multi-grid method for accelerating the convergence speed, and a finite analytic + multi-grid method for calculating electric field distribution has been developed.
Numerical simulation of gas flow field
Through mathematical deducing, the control equation set and for describing the time dependent compressible viscous flow have been given at the calculating plane. The discrete scheme of those control equations have also been deduced by the finite volume method and combined with multi-grid method which forms a Finite volume + Multi-grid Method for calculating the time dependent compressible viscous flow.
For the sack of solving the hard problems encountered in the numerical simulation of the velocity-pressure gradient coupling problem, the interlock grid technique and the linear distribute iteration method have been adopted. So that those hard problems have been well solved.
Applying this numerical simulation method, the 550kV circuit breaker was taken as numerical calculation example and the gas blast flow during breaking process of 260mm open stroke has been simulated at each 1mm calculating step. The simulation results have been compared with the results calculated by commercial software FLUENT which show that the numerical simulation method given by this thesis is correct.
On the basis of the research results, the numerical simulation of dielectric recovery properties of 550kV circuit breaker under non-load breaking and short circuit breaking have been carried out and discussed. The results show that the numerical method for dielectric recovery property simulation given by this thesis is feasible.
引文
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