以非正交網格方法模擬軸對稱熱電漿流場

Modeling of Axisymmetric Thermal Plasma Flow Using a Non-orthogonal Grid Approach

黃偉祐(Wei-You Huang)

指導教授 ： 趙修武

國立臺灣大學/工學院/工程科學及海洋工程學研究所/碩士(2021年)

https://doi.org/10.6342/NTU202104517

摘要

本研究建立以貼壁非正交網格求解以磁流體動力模型描訴的軸對稱熱電漿流場的數值方法。本研究以有限體積法離散連續方程式、動量方程式、能量方程式和紊流模型，流場內的電流分佈由安培定律求得，磁場則是利用歐姆定律求得。流場中速度與壓力的耦合關係以SIMPLE法加以拆解，以隱式計算方法聯立求解離散後的流場統御方程式。本研究探討Step以及Horn設計根式非傳輸型火炬在氮氣流量範圍25至95 SLM以及工作電流範圍40至90 A的電漿火炬特性。根式火炬陰極位置假設固定於負電極處，陽極位置則是利用實驗電壓加以推估。Step及Horn 電漿火炬設計的出口平均軸向速度分別約為80至120 m/s以及20至80 m/s，出口平均溫度則皆介於3000至5000 K之間。Step及Horn 電漿火炬設計的出口平均軸向速度分別正比於工作電流的0.587次方及1.504次方，以及分別正比於流量的0.3796次方及0.019次方。出口平均溫度則是正比於流量的-0.4694次方及-0.4376次方，以及分別正比於工作電流的0.3389次方及0.4038次方。

關鍵字

電漿火炬 ； 氮氣 ； 熱電漿 ； 非傳輸型 ； 直流電 ； 非正交網格 ； 磁流體動力模型

並列摘要

This study proposes a numerical approach to model axisymmetric thermal plasma flows using body-fitted and non-orthogonal grids. The continuity, momentum, energy equations along with the k-ε turbulence model are discretized by a finite volume method. The current is calculated from Ampere’s law and the interpolated current density is used to calculate the magnetic field governed by Ohm’s law. A SIMPLE approach is used for decoupling velocity and pressure where the discretized governing equations are solved for field variables via a SIP solver. Two rod-type non-transferred torch designs, i.e., Step and Horn, are modeled at the flow rate of Nitrogen ranging from 25 to 95 SLM alongside the working current varying from 40 to 90 A. The cathode position is presumed stationary in a root-type torch and the anode position is fixed by satisfying the measured voltage drop. The axial velocity is predicted about 80 to 160 m/s and 20 to 80 m/s at the outlet of Step and Horn torches, respectively. The gas temperature is estimated about 3000 to 5000 K at the outlet of Step and Horn torches. The mean axial velocity at the outlet for both torches grows with the working current and flow rate. For the working current, an exponent of 0.587 is found for Step design and 1.504 is forecasted for Horn one. For the flow rate, an exponent of 0.3796 is found for Step design and 0.019 is forecasted for Horn one. The mean temperature at the outlet declines with the flow rate but grows with the working current. For the flow rate, an exponent of -0.4694 is found for Step design and -0.4376 is forecasted for Horn one. For the working current, an exponent of 0.3389 is found for Step design and 0.4038 is forecasted for Horn one.

並列關鍵字

Plasma Torch ； Nitrogen ； Thermal Plasma ； Non-transferred ； Direct Current ； Non-orthogonal Grid ； Magnetohydrodynamic Model

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