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最初机-电模型是针对电磁轨道炮的电磁加速过程提出的，脉冲等离子体推力器（PPT）的工作原理也是通过电磁加速产生元冲量，因此机-电模型是PPT能量转化及元冲量产生机制的主要理论分析工具之一。但是作为PPT放电回路一部分的等离子体通道，其几何形态与目前机-电模型的电流片模型存在明显差异。PPT放电通道在离开推进剂表面向外喷出过程中多呈现弯曲形状，并不断变化，而非平直片状。结合PPT放电通道的实际形态，本文提出了PPT放电通道的二维形态电流片模型，建立基于二维电流片的改进型机-电模型。通过分析放电通道受力情况以及电磁加速过程，推导了PPT羽流的电磁加速动能与放电回路电感量随时间演变函数的关系。针对机-电模型电路方程，提出了分段拟合PPT放电波形获得回路电感量随时间演变函数的算法。形成了基于PPT放电波形分析得到羽流电磁加速动能的计算方案。将改进型机-电模型应用于PPT样机能量转化效率评价，通过分析PPT放电能量转化过程阐释了PPT机-电转化效率低的原因，提出了提高PPT机-电效率的一种探索思路。The primary electro-mechanical model is developed for the acceleration kinetics of electromagnetic railguns. Pulsed plasma thrusters (PPT), whose operation principle is something like that of electromagnetic railguns, generate thrust via electromagnetic acceleration of plasmas. Therefore, the electro-mechanical model serves as a valuable analytical tool to explore the mechanisms of energy conversion and thrust generation of PPTs. In fact, a PPT initiates discharge at its propellant surface and then ejects the discharged channel away to form accelerated plume. During the acceleration, the plasma channel assumes curved shapes, which differ from a flat sheet shape. The curved geometry of PPT discharge channels makes the flat current sheet model used in the present electro-mechanical model be of inherent shortcomings. This paper proposes an 2D curved current sheet model to improve the PPT electro-mechanical model, by referring to the curved morphology of PPT discharge plasma channels. Fig.I shows the schematic of a typical PPT discharge circuit and the curved PPT discharge plasma channel that is indicated as the pink curve $\mathop {ab}\limits^ \wedge $ according to the curved thin current sheet model. Also in Fig.I a current element of the discharge channel is taken arbitrarily to display its instant velocity and the Ampere force element df exerted by the magnetic field induced by the PPT current circuit. The pink dashed curve cdsymbolizes the position of the current sheet at the moment dt later. From the 2D curved current sheet model on, according to the detail shown in Fig.I, the Ampere force on discharge plasma channels and corresponding kinetics can be deduced aiming final kinetic energy of discharge plasma channels. As a result, the relation between the kinetic energy and the inductance of PPT discharge circuit is obtained as expression: ${E_k} = {\int {_0^{{t_{end}}}i(t)} ^2}\frac{{d{L_{eq}}(t)}}{{dt}}dt$. To determine the inductance as a temporal function, an algorithm for the inductance is proposed that employs time-segment fitting of PPT discharge waveforms. Moreover, based on the temporal function of the inductance, PPT discharge waveforms can be simulated using the ODE45 solver of MATLAB with high fitting goodness. So far, a calculation scheme for the kinetic energy of PPT plumes and simulation code for PPT discharge waveforms are setup based on the improved electro-mechanical model. To verify the improved model and the corresponding calculation scheme, a PPT prototype is used via assessing its energy conversion efficiency. The results show that the model enables elucidating the low PPT electro-mechanical efficiency, which is attributed to the partition limitation of PPT energy to electromagnetic acceleration process. Accordingly, a possible exploration routine for elevating PPT electro-mechanical efficiency is suggested.
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Keywords:
- Pulsed plasma thruster /
- Improved electro-mechanical model /
- Electro-mechanical efficiency /
- Plume kinetic energy
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