Study on similarity parameters of divert-jet interaction in supersonic and hypersonic flows
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摘要:
针对超/高超声速锥-柱-裙拦截弹轨控喷流干扰问题，通过数值求解三维Navier-Stokes方程，分析了冷/热喷干扰差异的原因，结合飞行条件与风洞实验条件开展了相似参数研究，获得了适用于轨控喷流干扰力/力矩模拟的相似参数。研究表明：冷/热喷流质量/能量流量的差别、冷/热喷管几何参数的差别及燃气热喷流的化学反应影响共同造成了冷/热喷干扰的差别，且前两种因素的影响较化学反应更大；不考虑化学反应影响，模拟总压比、动量比、总焓比的空气喷流获得的力干扰因子、轨控偏移量在
Ma =3～8、H =20 km与Ma =7、H =20～40 km条件均与燃气喷流符合良好；地面风洞实验条件使用模拟总压比、动量比、总焓比的空气或氦气喷流模拟飞行条件热喷，获得的力干扰因子与轨控偏移量模拟误差均较以往冷喷模拟明显减小。Abstract:Considering the issue of divert-jet interaction in supersonic and hypersonic cone-cylinder-flare interceptor missiles, a numerical solution of the three-dimensional Navier-Stokes equations was employed to analyze the reasons for the differences between cold and hot jet interaction. A study on similarity parameters was conducted by combining flight conditions and wind tunnel experiment conditions, and similarity parameters suitable for simulating the force and moment of divert jet interaction were obtained. Research indicated that the differences in cold and hot jet interaction attributed to variations in mass/energy flow rates between cold and hot jets, differences in the geometric parameters of cold and hot nozzles, and the chemical reactions in the hot gas jet. Among these, the first two factors had a more significant impact on the interaction characteristics than the chemical reaction effects. Under the premise of neglecting chemical reaction effects, the force interaction factors and the shift amount of jet force center obtained through air jet simulations using equivalent total pressure ratio, momentum ratio, and total enthalpy ratio demonstrated good agreement with the combustion gas jet results across conditions of Mach number 3—8 at 20 km altitude and Mach number 7 at 20—40 km altitude. When employing air or helium jets matching total pressure ratio, momentum ratio, and total enthalpy ratio to simulate hot jet conditions in ground wind tunnel tests, the simulation errors for both force interaction factors and the shift amount of jet force center were significantly reduced compared with conventional cold jet simulation methods.
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图 8 不同网格模拟的压力分布对比
Figure 8. Comparison of pressure distribution with different grid simulations
图 9 不同来流马赫数下的冷/热喷干扰气动结果
Figure 9. Aerodynamic results of cold and hot jet interaction at different incoming Mach numbers
图 11 不同飞行高度下的冷/热喷气动结果
Figure 11. Aerodynamic results of cold and hot jet interaction at different flight altitudes
图 12 不同来流马赫数下的不同相似参数喷流模拟结果
Figure 12. Simulation results of jet with different similarity parameters at different incoming Mach numbers
图 15 不同相似参数模拟结果随飞行高度变化规律
Figure 15. Aerodynamic characteristics simulated by different similarity parameters at different flight altitudes
图 16 Ma∞=3地面模拟与飞行条件对比
Figure 16. Ground simulation and flight conditions comparison at Ma∞=3
图 18 Ma∞=3, α=0°条件缩比模型壁面0°子午线压力分布
Figure 18. Scale model wall pressure distribution of 0° meridian at Ma∞=3, α=0°
图 19 Ma∞=5地面模拟与飞行条件对比
Figure 19. Ground simulation and flight conditions comparison at Ma∞=5
表 1 喷流参数
Table 1. Jet parameters
喷流 p0j/MPa pj/kPa T0j/K γj Rj/（J/（kg· K）） 热喷 4 133.3 3200 1.257 400 冷喷 2.869 133.3 293 1.4 287 
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表 2 不同网格气动力/力矩计算结果
Table 2. Aerodynamic force and moment results of different grids
网格 Fx/N Fy/N Mz/（N·m） 网格1 1352.32 −164.77 67.29 网格2 1358.44 −169.15 70.04 网格3 1361.66 −170.25 76.58 网格4 1361.64 −170.11 77.15
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表 3 不同来流马赫数下冷/热喷干扰相似参数
Table 3. Similarity parameters of cold and hot jet interaction under different incoming Mach numbers
Ma∞ $ {{{{\dot m}_{\text{j}}}} /{{{\dot m}_\infty }}} $ $ {{{h_{0{\text{j}}}}} / {{h_{0\infty }}}} $ $ {\dot E_{\text{j}}}/{\dot E_\infty } $ 热喷 冷喷 热喷 冷喷 热喷 冷喷 3 0.217 0.928 10.27 0.483 2.233 0.448 4 0.163 0.696 6.849 0.322 1.117 0.224 5 0.130 0.557 4.795 0.225 0.625 0.126 6 0.109 0.464 3.508 0.165 0.381 0.077 7 0.093 0.398 2.664 0.125 0.248 0.050 8 0.082 0.348 2.084 0.098 0.170 0.034
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表 4 空气喷流参数
Table 4. Air jet parameters
模拟参数 喷管 p0j/MPa T0j/K γj pjMj2/103 （kg·m/s2） 压力比、动量比 冷喷 2.896 293 5.01 压力比、动量比、质量流量比 冷喷 2.896 5346 5.01 压力比、动量比、总焓比 冷喷 2.869 6231 5.01 总压比、动量比 热喷 4.000 293 5.02 总压比、动量比、质量流量比 热喷 4.000 4791 5.02 总压比、动量比、总焓比 热喷 4.000 6231 5.02
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表 5 不同喷流相似参数
Table 5. Similarity parameters of different jets
模拟参数 $ {{{p_{\text{j}}}} /{{p_\infty }}} $ $ {{{h_{0{\text{j}}}}} / {{h_{0\infty }}}} $ $ {{{{\dot m}_{\text{j}}}} / {{{\dot m}_\infty }}} $ $ {\dot E_{\text{j}}}/{\dot E_\infty } $ 热喷 24.11 2.663 0.093 0.248 压力比、动量比 24.11 0.125 0.398 0.050 压力比、动量比、质量流量比 24.11 2.285 0.093 0.213 压力比、动量比、总焓比 24.11 2.663 0.086 0.230 总压比、动量比 18.18 0.125 0.377 0.047 总压比、动量比、质量流量比 18.18 2.057 0.093 0.192 总压比、动量比、总焓比 18.18 2.663 0.082 0.218
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表 6 风洞条件
Table 6. Wind tunnel conditions
Ma∞ p0/MPa p∞/Pa T0/K T∞/K 3 0.4 10889.47 293 104.64 5 2 3780.08 375 62.5
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表 7 地面模拟喷流条件
Table 7. Ground simulated jet conditions
工况 介质 模拟参数 Fj/N p0/MPa T0/K Ma∞=3，H=15 km 空气 压力比、动量比 145.12 2.583 293 空气 总压比、动量比、总焓比 141.82 3.596 3009 氦气 总压比、动量比 137.84 3.590 293 氦气 总压比、动量比、总焓比 137.84 3.590 582 Ma∞=5，H=20 km 空气 压力比、动量比 110.18 1.961 293 空气 总压比/动量比、总焓比 107.66 2.730 1798 氦气 总压比、动量比 104.62 2.725 293 氦气 总压比、动量比、总焓比 104.62 2.725 348
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表 8 Ma∞=3喷流干扰相似参数
Table 8. Jet interaction similarity parameters at Ma∞=3
喷流 模拟参数 $ {{{h_{0{\text{j}}}}} / {{h_{0\infty }}}} $ $ {{{{\dot m}_{\text{j}}}}/{{{\dot m}_\infty }}} $ $ {\dot E_{\text{j}}}/{\dot E_\infty } $ 热喷 10.27 0.099 1.019 空气 压力比、动量比 1.0 0.295 0.295 空气 总压比、动量比、总焓比 10.27 0.087 0.895 氦气 总压比、动量比 5.17 0.110 0.568 氦气 总压比、动量比、总焓比 10.27 0.078 0.801
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表 9 Ma∞=5喷流干扰相似参数
Table 9. Jet interaction similarity parameters at Ma∞=5
喷流 模拟参数 $ {{{h_{0{\text{j}}}}} / {{h_{0\infty }}}} $ $ {{{{\dot m}_{\text{j}}}} /{{{\dot m}_\infty }}} $ $ {\dot E_{\text{j}}}/{\dot E_\infty } $ 热喷 4.794 0.130 0.625 空气 压力比、动量比 0.781 0.299 0.234 空气 总压比、动量比、总焓比 4.795 0.114 0.548 氦气 总压比、动量比 4.041 0.111 0.450 氦气 总压比、动量比、总焓比 4.795 0.102 0.491
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