Numerical investigation and experimental validation of nonlinear constitutive models with solving algorithms in continuum flows
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摘要:
结合数值模拟和风洞试验技术，在高超声速连续流条件下对非线性耦合本构关系（NCCR）模型和由量纲分析推导得到的简化广义动力学（SGH）模型开展研究。基于小型高超声速风洞试验系统，在不同来流条件下对类HB2（hypervelocity ballistic model 2）标模和钝锥模型的气动力和物面压力进行了风洞试验测量。同时在三维有限体积框架下，分别采用分裂算法和耦合算法的NCCR模型、SGH模型对试验工况下的标模开展数值计算。结果表明：NCCR模型和SGH模型得到的气动力系数和物面压力均与Navier-Stokes（NS）方程解一致，并与风洞试验数据吻合较好；采用分裂算法的NCCR模型在类HB2头部膨胀拐角处预测的摩阻/热流系数明显低于NS方程解，而采用耦合算法的NCCR模型解与NS方程基本一致。计算结果和实验数据对比表明，NCCR模型和SGH模型在高超声速连续流中的准确性得到充分验证，此外，NCCR模型的分裂算法在三维高速流动中的适用性需进一步完善。
Abstract:Combined with numerical simulation and wind tunnel test technology, the nonlinear coupled constitutive relations (NCCR) model and the simplified generalized hydrodynamic (SGH) model derived by dimensional analysis in hypersonic continuum flows were studied. Based on the hypersonic wind tunnel test system, the aerodynamic force and surface pressure of the type hypervelocity Ballistic 2 (HB2) standard model and the blunt cone were measured under different flow conditions. Meanwhile, under the three-dimensional finite volume framework, the NCCR model with decomposed and undecomposed algorithm and SGH model were used for numerical investigation of the flight models under the test conditions. Result showed that, the aerodynamic force and surface pressure obtained by NCCR model and SGH model were consistent with the solutions of Navier-Stokes (NS) equations as well as the data measured in the wind tunnel. However, the friction/heat flux coefficients predicted by NCCR model with decomposed algorithm at the expansion corner of head of type HB2 were lower than those of NS equations, while the NCCR model with undecomposed algorithm was consistent with NS solver. The computational results and experimental data showed that the accuracy of NCCR model and SGH model in hypersonic continuous flow was validated, and the applicability of decomposed algorithm of NCCR model in three-dimensional high-speed flows shall be further improved.
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图 3 类HB2气动力系数随攻角
$\alpha $ 变化（$M{a_\infty } = 5$ ）Figure 3. Aerodynamic coefficients of type HB2 model versus angle of attack （
$M{a_\infty } = 5$ ）
图 4 类HB2标模实验纹影图（
$ M{a}_{\infty }=5$ 、α =0°）Figure 4. Experimental schlieren photographs of type HB2 model （
$ M{a}_{\infty }=5 $ , α=0°）
图 5 温度云图和流线对比（
$ M{a}_{\infty }=5 $ 、α=0°）Figure 5. Comparisons of temperature contour and streamline （
$ M{a}_{\infty }=5 $ , α=0°）
图 6 沿驻点线（
$X$ 方向）密度、局部克努森数（$K{n_{{\rm{GLL}}}}$ ）、温度和马赫数分布（$M{a}_{\infty }=5$ 、α=0°）Figure 6. Density,
$ K{n_{{\rm{GLL}}}} $ , temperature, and Mach number along the stagnation line （$ M{a}_{\infty }=5 $ , α=0°, X direction）
图 7 类HB2标模物面系数分布（
$ M{a}_{\infty }=5$ 、α=0°）Figure 7. Surface coefficients of type HB2 model （
$ M{a}_{\infty }=5 $ , α=0°）
图 8 钝锥物面压力分布（
$M{a_\infty } = 5$ ）Figure 8. Surface pressure distribution f blunt cone （
$M{a_\infty } = 5$ ）
图 9 沿驻点线（
$X$ 方向）密度、局部克努森数、温度和马赫数分布（$ M{a}_{\infty }=7 $ 、α=0°）Figure 9. Density,
$K{n_{{\rm{GLL}}}}$ , temperature, and$Ma$ along the stagnation line （$ M{a}_{\infty }=7 $ , α=0°, X direction）
图 10 钝锥物面系数分布（
$ M{a}_{\infty }=7 $ 、α=0°）Figure 10. Surface coefficients of blunt cone （
$ M{a}_{\infty }=7 $ , α=0°）表 1 ϕ120 mm高超声速风洞性能参数
Table 1. Performance parameters of ϕ120 mm hypersonic wind tunnel
风洞参数 数值及详情 来流马赫数范围 5～7 喷管出口直径/${\rm{mm}}$ 120 来流最大总温/${\rm{K}}$ 500 总压范围/${\rm{MPa}}$ 0.1～1.0 工作时间t/${\rm{s}}$ ≥15 
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表 2 类HB2标模的试验条件
Table 2. Experimental conditions for type HB2 model
参数 工况编号 1 2 3 4 5 马赫数 5 5 5 5 5 攻角/（°） −4 −2 0 2 4 总压/${\rm{kPa}}$ 451 401 494 346 401 总温/${\rm{K}}$ 415 417 410 402 417 静压/${\rm{Pa}}$ 852 758 934 654 758 静温/${\rm{K}}$ 69.2 69.5 68.3 67.0 69.5 壁温/${\rm{K}}$ 300 300 300 300 300 速度/（${\rm{m/s}}$） 834 836 829 820 836
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表 3 钝锥的试验条件
Table 3. Experimental conditions for the blunt cone
参数 工况编号 1 2 3 4 5 6 7 8 9 10 马赫数 5 5 5 5 5 7 7 7 7 7 攻角/（$^ \circ $） −10 −5 0 5 10 −10 −5 0 5 10 总压/${\rm{kPa}}$ 573 648 603 707 666 1429 1403 1388 1403 1410 总温/${\rm{K}}$ 505 504 500 474 511 505 499 480 493 494 静压/${\rm{Pa}}$ 1082 1224 1140 1335 1259 345 339 335 339 341 静温/${\rm{K}}$ 84.1 84.0 83.3 78.9 85.1 46.8 46.2 44.5 45.6 45.8 壁温/${\rm{K}}$ 300 300 300 300 300 300 300 300 300 300 速度/（${\rm{m/s}}$） 919 919 915 891 925 960 953 936 948 950
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