Study Of Discrete Unified Gas-kinetic Scheme For Flows Of Binary Gas Mixtures

The multi-scale transport process of binary gas mixtures exists widely in the fields such as greenhouse gas storage,shale gas exploration,and the re-entry of a space shuttle,which has become a common scientific problem in environment,energy and aerospace.Due to the scale effect and the interactions among different gas species,the multi-scale transport mechanisms of binary gas mixtures are very complicated,which bring great challenges to the theoretical and experimental methods.With the development of computing technology and improvement of computer performance,the numerical methods for solving the gas-kinetic model equations have become effective means of studying such problems.One of these methods is the discrete unified gas kinetic scheme(DUGKS)proposed by Guo et al.recently.Due to its asymptotic preserving properties,the DUGKS can be used to solve multi-scale flows effectively.However,the original DUGKS is designed for flows of single-species gas,and studies of binary gas mixtures have not been performed.As a result,in this thesis we extend the DUGKS to flows of binary gas mixtures based on two typical model equations.Then we investigate the multi-scale oscillatory flows of binary gas mixtures.The main work of the thesis includes the following aspects:Firstly,the DUGKS for binary gas mixtures is developed based on the single-relaxation model for multi-species gases.Since the collision term of each species in the mixtures does not satisfy the conservative laws,the half-implicit treatment of the collision term not only shows the interactions between different gas species,but also guarantees the asymptotic preserving(AP)properties of the proposed DUGKS.Several tests are performed to validate the scheme.Results show that the proposed DUGKS for binary gas mixtures is an effective and reliable method for multi-scale high-speed flows,channel flows and shear flows.Secondly,another DUGKS for binary gas mixtures is constructed by solving the McCormack model.Compared to the above single-relaxation model,besides the possibility toreproduce all the transport coefficients,the Mc Cormack model also allows people to use different laws to describe more complicated intermolecular interactions.The multi-scale linear shear flows and heat transfer problems of binary gas mixtures have been performed to validate the accuracy of DUGKS.Due to its AP properties,the DUGKS is much more effective than the DSMC in the near-continuum regime.Thirdly,the oscillatory Couette flow of binary gas mixtures is numerically investigated based on the above proposed DUGKS in the second part.By comparing with those of the single-species cases,the dependencies of penetration depth,the velocity amplitude,and damping force exerted on the oscillating plate on the gas rarefaction conditions and the oscillation parameters are studied over a wide range.Results show that the mixture with a mass ratio of about 2 exhibits similar behaviors with those of a single gas,while the mixture with a molecular mass ratio as large as 32.8 is more sensitive to the molar concentration: in the high-frequency oscillation regime,the amplitudes of velocity and shear stress with a large molar concentration of the light species vary non-monotonously,and local minima of these amplitudes appear between the plates.The distance of these local minima to the oscillating plate is around the order of the molecular mean free path.Finally,the oscillatory cavity flow of binary gas mixtures is studied.The resonance and anti-resonance phenomena are investigated in a wide range of Knudsen numbers and oscillation frequencies.Due to the anti-resonance phenomenon,the damping force on the cavity is even smaller than that of the Couette flow.It is found that the Strouhal numbers,which refer to the oscillation frequency of the lid,for resonance and anti-resonance of the mixture with a mass ratio of about 2 are close to those of the single gas,regardless of the value of molar concentration.However,results of the mixture with the mass ratio up to 32.8show qualitative differences: deviations of the Strouhal numbers for resonance and antiresonance of the mixture from those of the single gas increase with the molar concentration of the light species.Especially when the molar concentration of the light species is much larger than that of the heavy species,the resonance and anti-the resonance can no longer be observed in the near-continuum regime.In summary,we extend the DUGKS to binary gas mixtures on the basis of the two model equations for multi-species gases.Several standard tests are performed to show that,the proposed DUGKS models are effective and reliable for simulating multi-scale flows of binary gas mixtures.The 1D and 2D oscillatory flows are systematically investigated based on the DUGKS developed in the second part.The above work lays a necessary basis for the future work on the transport mechanism of gas mixtures.