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磁等离子体发动机在深空探测、载人航天等领域具备广阔的应用前景. 发动机的磁喷管单元将离子能量转化为轴向动能, 对磁喷管中等离子体与磁场分离的物理过程开展研究对提升发动机推进效率具有重要意义. 本文建立了针对磁等离子体发动机中磁喷管的流体数值模型, 并在不同入口离子温度、背景磁场条件下开展了数值模拟. 计算结果表明: 等离子体向下游运动的过程中轴向速度增大, 并与磁力线逐渐分离, 绝热性损失分离机制在分离过程中起主导作用; 入口离子温度升高, 离子轴向速度增大, 离子与磁场分离位置更靠上游, 但不会对阻性分离过程产生影响; 背景磁场增强, 下游离子速度减小, 流线与对称轴的夹角减小, 各种分离机制中绝热性损失分离机制仍起主要作用.Magnetoplasma rocket engine has a broad application prospect in the deep space exploration, manned space flight and other space missions. The ion energy is converted into the directed velocity in the magnetic nozzle of the engine. The investigation into the detachment process of the plasma with the magnetic field is of great significance for improving the engine propulsion efficiency. However, there are roughly five kinds of physical mechanisms which can all contribute to the detachment process and make the detachment in the magnetic nozzle quite complicated. Furthermore, the ion temperature is much higher than the electron temperature in the magnetic nozzle of the magnetoplasma rocket engine due to the heating effect of the ion cyclotron resonance stage. As a result, previous numerical model which were based on the assumption of cold ions are unapplicable for the simulation of the engine. In this work, a fluid simulation model is developed which is used for simulating the magnetic nozzle in the magnetoplasma rocket engine. The model includes the electron and the ion of single charge. For the characteristics of the magnetoplasma rocket engine, the ion energy equation is added into the governing equations. In order to analyze the effect of the inertial detachment, the static electric field due to the charge separation is also included. The simulations are performed under the conditions of different inlet ion temperatures and background magnetic fields. The results show that the ion axial velocity gradually increases in the magnetic nozzle and the ion stream lines detach from the magnetic field lines gradually. The loss of adiabaticity is the dominant mechanism in the detachment process. The ion axial velocity increases with the inlet ion temperature rising, and the ion streamlines detach earlier from the magnetic field lines. The resistive diffusion is unaffected by the inlet ion temperature while the detachment interfaces of other three mechanisms all move toward the upstream. With the increase of the background magnetic field, ion axial velocity decreases and the angle included between the streamline and the axis becomes smaller. The loss of adiabaticity is still the dominant physical mechanism when the magnetic field is changed.
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Keywords:
- magnetoplasma rocket engine /
- magnetic nozzle /
- plasma detachment /
- fluid simulation
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图 4 稳态离子参数分布 (a)离子密度; (b)离子温度
Fig. 4. Distribution of the ion parameters in steady state: (a) Ion density; (b) ion temperature.
图 5 稳态离子速度分布 (a) ui, z; (b) ui, r
Fig. 5. Distribution of the ion velocity in steady state: (a) ui, z; (b)ui, r.
图 7 不同分离机制的无量纲参数分布 (a) Rm; (b) α; (c) ζ; (d) βf
Fig. 7. Distribution of the dimensionless parameters with different detachment mechanisms: (a) Rm; (b) α; (c) ζ; (d) βf.
图 8 离子温度分布 (a) Ti, in = 10 eV; (b) Ti, in = 20 eV; (c) Ti, in = 40 eV; (d) Ti, in = 80 eV
Fig. 8. Distribution of the ion temperature: (a) Ti, in = 10 eV; (b) Ti, in = 20 eV; (c) Ti, in = 40 eV; (d) Ti, in = 80 eV.
图 9 离子轴向速度ui, z分布 (a) Ti, in = 10 eV; (b) Ti, in = 20 eV; (c) Ti, in = 40 eV; (d) Ti, in = 80 eV
Fig. 9. Distribution of the ion axial velocity ui, z: (a) Ti, in = 10 eV; (b) Ti, in = 20 eV; (c) Ti, in = 40 eV; (d) Ti, in = 80 eV.
图 10 Ti, in = 40 eV不同分离机制的无量纲参数分布 (a) Rm; (b) α; (c) ζ; (d) βf
Fig. 10. Distribution of the dimensionless parameters with different detachment mechanisms when Ti, in equals to 40 eV: (a) Rm; (b) α; (c) ζ; (d) βf.
图 11 不同Ti, in的α分布 (a) Ti, in = 10 eV; (b) Ti, in = 20 eV; (c) Ti, in = 40 eV; (d) Ti, in = 80 eV
Fig. 11. Distribution of α with different Ti, in: (a) Ti, in = 10 eV; (b) Ti, in = 20 eV; (c) Ti, in = 40 eV; (d) Ti, in = 80 eV
图 12 离子轴向速度ui, z分布 (a) fB = 0.1; (b) fB = 0.4
Fig. 12. Distribution of the ion axial velocity ui, z: (a) fB = 0.1; (b) fB = 0.4.
图 13 fB = 0.1不同分离机制的无量纲参数分布 (a) Rm; (b) α; (c) ζ; (d) βf
Fig. 13. Distribution of the dimensionless parameters with different detachment mechanisms when fB = 0.1: (a) Rm; (b) α; (c) ζ; (d) βf.
表 1 不同物理机制的特征参数
Table 1. Characteristic parameters of the physical mechanisms.
物理机制 无量纲系数 分离判据 绝热性损失分离 $ \alpha = {r_{\text{L}}}\dfrac{{\left| {\nabla B} \right|}}{{\left| B \right|}} $ 不满足$ \alpha \ll 1 $ 阻性扩散分离 $ {R_{\text{m}}} = \dfrac{{\mu L{V_{\text{A}}}}}{\eta } $ $ 1 < {R_{\text{m}}} < 1000 $ 惯性分离 $ G = \dfrac{{{\text{e}}B}}{{{m_{\text{e}}}}}\dfrac{{{\text{e}}B}}{{{m_{\text{i}}}}}\dfrac{{{L^2}}}{{{U^2}}} $ $ \xi = {G^{ - 1/2}}\left| {\dfrac{{\nabla B}}{B}} \right| \approx 0.5 $ 超阿尔芬速度分离 $ {\beta _{\text{f}}} = \dfrac{{\rho {u^2}}}{{{{{B^2}} \mathord{\left/ {\vphantom {{{B^2}} \mu }} \right. } \mu }}} $ $ {\beta _{\text{f}}} > 1 $ 
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表 2 模型几何参数
Table 2. Geometric parameters of the model.
参数 值/m 参数 值/m rend 0.8 dr 0.01 zend 1.2 dz 0.02 r0 0.12 z0 0.2
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