稀薄气体动力学的非线性耦合本构方程理论及验证
收稿日期: 2014-08-14
修回日期: 2014-10-29
网络出版日期: 2014-11-02
基金资助
韩国国家自然科学基金 (2012-R1A2A2A02-046270)
Nonlinear coupled constitutive relations and its validation for rarefied gas flows
Received date: 2014-08-14
Revised date: 2014-10-29
Online published: 2014-11-02
Supported by
National Research Foundation of Korea (2012-R1A2A2A02-046270)
作为一种新兴的气体动力学本构方程理论体系,非线性耦合本构方程(NCCR)理论的创新之处在于黏性应力和热传导中抛弃了广义牛顿定律和傅里叶热传导定律,而是考虑熵条件从Boltzmann方程直接推导出了黏性应力和热传导非线性耦合输运方程即NCCR模型。NCCR模型在连续区域与广义牛顿定律和傅里叶热传导定律一致, 但是在稀薄区域其非线性关系逐渐增强,即NCCR模型大大扩展了应力-应变和热传导-温度梯度的本构关系,为稀薄气体流动模拟提供了新的途径。为解决NCCR模型强非线性难题,发展了混合模态间断伽辽金求解NCCR和流动守恒方程的数值算法,成功避免了NCCR边界条件高阶量赋值的难题。并对典型亚声速、超声速NACA0012翼型绕流、高超声速圆柱绕流、极高马赫数圆柱绕流、微尺度激波-涡干涉、连续稀薄渐变算例、方腔流动进行了数值计算和验证。结果表明,在稀薄区域,NCCR模型准确捕捉到了流场信息,吻合于蒙特卡罗直接模拟(DSMC)或实验结果,包括:压力分布、速度分布、温度分布、壁面热流等。对圆柱绕流的进一步研究发现NCCR在低努森数下与Navier-Stokes方程结果相同,随着努森数升高两者差距逐渐扩大且在高努森数下NCCR吻合于DSMC和实验结果,从侧面证明了基于NCCR理论用同一套方程解决连续稀薄耦合流动的可能性。
肖洪 , 商雨禾 , 吴迪 , 师羊羊 . 稀薄气体动力学的非线性耦合本构方程理论及验证[J]. 航空学报, 2015 , 36(7) : 2091 -2104 . DOI: 10.7527/S1000-6893.2014.0300
Being the new constitutive equations for gas flow, the innovation of nonlinear coupled constitutive relations (NCCR)lies in the transport equations of viscous stress and thermal conduction, which are derived from Boltzmann equations by consideration of the entropy and expressed in terms of nonlinear coupled functions. In the continuum state, the NCCR shows linear relations in viscous stress and thermal conduction which is the same as the classical Navier-Stokes equations using Newtonian law of viscosity and the Fourier law of heat conduction. And, in the rarefied state, the relations of viscous stress and thermal conduction become more nonlinear. So, the constitutive relations are extended greatly by NCCR. To solve the high nonlinear of NCCR equations, mixed modal discontinues Galerkin method is proposed in solving the conservation laws with NCCR in which the setting of viscous stress and heat flux on the solid wall are avoided. Numerical study and validations are conducted in subsonic, supersonic and hypersonic gas flows around a cylinder, NACA0012 airfoil and cavity flow. Investigations show that NCCR can capture detailed flow properties which include pressure distribution, contour of velocity, density and temperature, as well as heat flux in solid wall and the NCCR data are closed to those of direct simulation of Monto Carlo (DSMC) or experiment while Navier-Stokes fails. Furthermore, numerical studies on gas flow around a cylinder also show that NCCR results are the same as that of Navier-Stokes in continuum state and the difference becomes to be distinguished with Knudsen number increasing. It can be concluded that NCCR provides a new method to solve continuum-rarefied gas flows.
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