恒星对流k-ω模型的性质研究

发布时间：2019-02-24 20:55

【摘要】：在恒星内部，在效应或者κ效应和Γ效应的作用下，当满足Schwarzschild判据或者Ledoux判据时，就会引发对流。由于在恒星内部粘性系数很小而对流的尺度很大，导致恒星流体的Reynolds数和Rayleigh很高，使得恒星内部的对流是充分发展的湍流运动。太阳是观测和研究的最详细的一颗恒星，其表面的米粒组织、中米粒组织和超米粒组织是太阳内部对流的直接证据。在各种各样的对流理论中，广泛使用的是混合长理论和湍对流理论。混合长理论关于平均流体元的假设极大的简化了恒星对流问题，，这种等效的方法使得使用混合长理论得出的结果大致与大多数观测相符。然而，混合长理论没有考虑对流超射的影响，也无法考虑湍流的扩散、耗散和各向异性。而湍对流理论建立在流体动力学的坚实基础上，能考虑湍流的扩散、耗散和各向异性，能较好的解决对流超射及其元素混合问题。但是这些湍对流理论都没有考虑对流涡胞的作用，为此Li提出了一个新的恒星对流模型。这个恒星对流模型近似估计了对流涡胞的大小，并提出了对流涡胞内流体运动的平均速度剪切模型。然后它指定了湍流的一个宏观长度模型，得到了k ε模型在完全局地平衡态下的稳态解，并发展了一个考虑了湍流扩散的k ω模型。为了将Li提出的k ω模型应用到一般的恒星环境中，有必要研究其中模型参数的物理意义，以便限定它们的取值范围。研究表明，模型参数cμ对湍流的P′eclet数、湍动能、特征时标和特征长度都有影响，除此之外，它还能加快底部对流超射区中湍动能的衰减速率；模型参数cμ与等效混合长参数α都能增加对流传热效率，它们的对数存在线性关系；模型参数cμ和底部对流超射区中湍动能的衰减指数θ之间取对数后也存在一个线性关系。
[Abstract]:In the interior of a star, convection will occur when the Schwarzschild criterion or Ledoux criterion is satisfied under the effects of either 魏 effect or 螕 effect. Because the viscosity coefficient is very small and the scale of convection is very large in the stellar interior, the Reynolds number and Rayleigh of the stellar fluid are very high, which makes the convection in the stellar interior a fully developed turbulent motion. The sun is one of the most detailed stars observed and studied. The surface rice grain tissue, middle rice grain tissue and super rice grain tissue are the direct evidence of the convection in the sun. Among all kinds of convection theories, mixing length theory and turbulent convection theory are widely used. The assumption of the mean fluid element in the mixed length theory greatly simplifies the stellar convection problem. This equivalent method makes the results obtained by using the mixed length theory approximately agree with most observations. However, the mixed length theory does not take into account the influence of convection overshoot, nor the diffusion, dissipation and anisotropy of turbulence. However, the theory of turbulent convection is based on the solid foundation of hydrodynamics, which can consider the diffusion, dissipation and anisotropy of turbulence, and can solve the problem of convective overshoot and its element mixing. However, these turbulent convection theories do not take into account the effect of convective vortices. For this reason, Li proposes a new stellar convection model. The stellar convection model estimates the size of the convective vortex cell approximately and presents an average velocity shear model for the fluid motion in the convective vortex cell. Then it specifies a macroscopic length model of turbulence, obtains the steady state solution of k 蔚 model under completely local equilibrium state, and develops a k 蠅 model considering turbulent diffusion. In order to apply the k 蠅 model proposed by Li to the general stellar environment, it is necessary to study the physical meaning of the model parameters in order to limit their range of values. The results show that the model parameter c 渭 has an effect on the P'eclet number, kinetic energy, characteristic time scale and characteristic length of turbulence. In addition, it can accelerate the attenuation rate of turbulent kinetic energy in the bottom convection overshoot region. Both the model parameter c 渭 and the equivalent mixing length parameter 伪 can increase the heat transfer efficiency, and there is a linear relationship between the logarithm of the model parameter c 渭 and the attenuation exponent 胃 of turbulent kinetic energy in the bottom convection overshoot region.
【学位授予单位】：中国科学院研究生院（云南天文台）
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：P144

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