Application of L-R Two-Step Euler Method to Micro Ejection of Aluminum
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摘要: 应用三维弹塑性流体力学Lagrangian-Remapping两步欧拉计算方法对铝材料微喷射现象进行了数值模拟研究。计算了Asay实验中表面刻有相同深度、不同夹角沟槽的金属铝微喷射模型，计算得到的微喷物总质量、最大射流速度和实验结果均符合较好。进一步展开了对相同深度、更大夹角范围沟槽微喷射的数值模拟。分析认为喷射最大速度随沟槽角度的增大呈线性下降趋势。同时给出了喷射系数随沟槽角度的变化的拟合关系曲线，看到由于材料强度及沟槽角度变化后造成的波系关系变化的影响，随着沟槽角度增加，喷射系数曲线呈明显非线性发展。Abstract: The 3D elastic-plastic hydrodynamic Lagrangian-Remapping two-step Euler method was used for the micro ejection simulation of aluminum.The micro ejection calculation models have grooves on the aluminum interface with the same depth and different angles, and the numerical results of the micro-jet mass and maximum velocity thus accorded with Asay's experiment results.And then, the micro ejection calculation models with the same groove depth but much larger angle range were calculated.By the analysis of the numerical results, it is showed that the maximum velocity of the micro-jet decreases linearly with the increase of the groove angle, and the curving contour of the ejected factor versus groove angle is given.Because of the influence of metal strength and groove angle on the wave relations, the micro-jet coefficient curve is obviously nonlinear with the groove angle.
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Key words:
- Euler /
- L-R two-step method /
- micro-jet /
- ejected factor
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图 1 表面刻有沟槽的铝板及其剖面计算模型(虚线框内为计算区域)
Figure 1. The grooved Al specimen and simulation model
图 2 t=0.05 μs时刻不同沟槽角度密度图像及喷射物质区(白线内区域)
Figure 2. The numerical results at different groove angles(t=0.05 μs), and the region of microjet aluminum
图 3 θ=90°、45°情况下不同时刻微喷方向速度图像
Figure 3. The microjet velocity at different time with θ=90°, 45°
图 5 随沟槽角度变化的喷射量和最大速度与实验结果对比
Figure 5. Comparison between experimental results of ejected mass and maximum velocity versus groove angle
图 6 t=0.051 μs沟槽角度θ=90°、45°时在沟槽间距l=0.400 mm下的微喷图像
Figure 6. The microjet aluminum with groove space l=0.400 mm and groove angle θ=90°, 45° at t=0.051 μs
图 7 沟槽角度从10°~150°的喷射系数和最大喷射速度
Figure 7. The ejected factor and maximum velocity versus groove angle from 10° to 150°
表 1 6061-T6铝材料计算模型参数
Table 1. The simulation parameters of 6061-T6 aluminum samples
ρ0/(g/cm3) c0/(km/s) S1 S2 S3 γ0 α em Pmin/(GPa) G0/(GPa) Y0/(GPa) 2.7 5.376 1.55 0 0 2.19 1.7 0.88 0.45 27.6 0.276 
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表 2 Euler方法计算喷射量、最大速度和两组实验结果[2]对比
Table 2. Comparison between numerical and experimental results[2] of ejected mass and maximum velocity
Groove
angle/(°)Numerical results
of ejected mass
/(mg/cm2)Experimental results
of ejected mass
/(mg/cm2)Numerical results
of maximum velocity
/(km/s)Experimental results
of maximum velocity
/(km/s)15 1.63 1.46, 1.57 8.8 8.4, 8.6 30 1.60 1.58, 1.60 8.2 8.1, 8.3 45 2.32 2.07, 2.33 7.5 7.2, 7.5 60 2.35 - 7.1 - 75 2.62 - 6.7 - 90 2.92 2.60, 3.06 6.2 6.3
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表 3 不同沟槽角度下的喷射系数和最大喷射速度
Table 3. The ejected factor and maximum velocity at different groove angles
Groove
angle/(°)Ejected
factorMaximum velocity
/(km/s)10 2.640 9.43 15 2.470 8.88 30 1.570 8.16 35 1.330 8.01 40 1.220 7.75 45 1.200 7.57 60 0.920 7.10 75 0.747 6.66 90 0.632 6.20 100 0.585 5.90 110 0.566 5.69 120 0.539 5.23 130 0.423 4.89 140 0.340 4.52 150 0.257 4.16
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