The purpose of this research is to show that Foaucault pendulum as well as other Coriolis effects, which are normally studied in a rotating coordinate system, can also be analyzed in a fixed reference frame. To this e...The purpose of this research is to show that Foaucault pendulum as well as other Coriolis effects, which are normally studied in a rotating coordinate system, can also be analyzed in a fixed reference frame. To this end, Foucault pendulum and other Coriolis effects are studied in inertial reference frames. The approach is simple, yet rigorous, and the results are exactly the same as those obtained in non-inertial reference frames but without resorting to some of the assumptions that are needed in rotating coordinate systems.展开更多
The theoretical foundation for the modelling of the turbulent pressure\|strain correlations in rotating reference frame is presented. Based on the recently developed materially\|frame indifference principle it is obse...The theoretical foundation for the modelling of the turbulent pressure\|strain correlations in rotating reference frame is presented. Based on the recently developed materially\|frame indifference principle it is observed that most of the existing second\|moment closures violate the Taylor\|Proudman theorem in the limit of rapid rotation. It is shown that the application of the materially\|frame indifference principle gives rise to the formation of a new pressure\|strain correlation model which satisfies the Taylor\|Proudman theorem.展开更多
In order to identify the influence of shape comers on the instantaneous forces in the case of oscillating bodies, the simula- ted flow field is compared for two kinds of cross sections： diamond prism and circular cyl...In order to identify the influence of shape comers on the instantaneous forces in the case of oscillating bodies, the simula- ted flow field is compared for two kinds of cross sections： diamond prism and circular cylinder. For these two flow configurations, the same Reynolds number and a Keulegan-Carpenter are considered. To compute the dynamic flow field surrounding the body, the Navier-Stokes transport equations in a non-inertial reference frame attached to the body are considered. Hence, a source term is added locally to the momentum equation to take into account the body acceleration. The proposed model is solved using the PHOENICS code. For the oscillating circular cylinder, the simulated results are in good agreement with the experimental data availa- ble in the litterature. After validation of this proposed model, flow field for diamond prism is determined. For both bodies, the pro- cess of the vortex formation is similar, with the formation of a recirculation zone in the near-wake containing a symmetric pair of vortices of equal strength and opposite rotation. The length of recirculation zone varies approximately linearly with time. However, the in-line force coefficient of the oscillating diamond prism is found to be greatest, since the recirculation zone is longer compared with that of the oscillating circular cylinder.展开更多
This paper focuses on the development and application of a threedimensional gas-kinetic Bhatnagar-Gross-Krook(BGK)method for the viscous flows in rotating machinery.For such flows,a rotating frame of reference is usua...This paper focuses on the development and application of a threedimensional gas-kinetic Bhatnagar-Gross-Krook(BGK)method for the viscous flows in rotating machinery.For such flows,a rotating frame of reference is usually used in formulating the Navier-Stokes(N-S)equations,and there are two major concerns in constructing the corresponding BGK model.One is the change of the convective velocities in the N-S equations,which can be reflected through modification of the gas streaming velocity.The other one is the necessity to account for the effect of the additional Coriolis and centrifugal forces.Here,a specifically-designed acceleration term is added into the modified Boltzmann equation so that the source effects can be naturally included into the gas evolution process and the resulted fluxes.Under the finitevolume framework,the constructed BGK model is locally solved at each cell interface and then the numerical fluxes can be evaluated.When employing the BGK scheme,it is sometimes found that the calculated spatial derivatives of the initial and equilibrium distribution functions are sensitive to the mesh quality especially in complex rotating flow applications,which may significantly influence flux evaluation.Therefore,an improved approach for computing these slopes is adopted,through which the modeling capability for viscous flows is enhanced.For validation,several numerical examples are presented.The computed results show that the present method can be well applied to a wide range of flows in rotating machinery with favorable accuracy.展开更多
文摘The purpose of this research is to show that Foaucault pendulum as well as other Coriolis effects, which are normally studied in a rotating coordinate system, can also be analyzed in a fixed reference frame. To this end, Foucault pendulum and other Coriolis effects are studied in inertial reference frames. The approach is simple, yet rigorous, and the results are exactly the same as those obtained in non-inertial reference frames but without resorting to some of the assumptions that are needed in rotating coordinate systems.
文摘The theoretical foundation for the modelling of the turbulent pressure\|strain correlations in rotating reference frame is presented. Based on the recently developed materially\|frame indifference principle it is observed that most of the existing second\|moment closures violate the Taylor\|Proudman theorem in the limit of rapid rotation. It is shown that the application of the materially\|frame indifference principle gives rise to the formation of a new pressure\|strain correlation model which satisfies the Taylor\|Proudman theorem.
文摘In order to identify the influence of shape comers on the instantaneous forces in the case of oscillating bodies, the simula- ted flow field is compared for two kinds of cross sections： diamond prism and circular cylinder. For these two flow configurations, the same Reynolds number and a Keulegan-Carpenter are considered. To compute the dynamic flow field surrounding the body, the Navier-Stokes transport equations in a non-inertial reference frame attached to the body are considered. Hence, a source term is added locally to the momentum equation to take into account the body acceleration. The proposed model is solved using the PHOENICS code. For the oscillating circular cylinder, the simulated results are in good agreement with the experimental data availa- ble in the litterature. After validation of this proposed model, flow field for diamond prism is determined. For both bodies, the pro- cess of the vortex formation is similar, with the formation of a recirculation zone in the near-wake containing a symmetric pair of vortices of equal strength and opposite rotation. The length of recirculation zone varies approximately linearly with time. However, the in-line force coefficient of the oscillating diamond prism is found to be greatest, since the recirculation zone is longer compared with that of the oscillating circular cylinder.
基金This work has been supported by the National Natural Science Foundation of China(Grant No.11372135)the National Basic Research Program of China(“973”Project)(Grant No.2014CB046200).
文摘This paper focuses on the development and application of a threedimensional gas-kinetic Bhatnagar-Gross-Krook(BGK)method for the viscous flows in rotating machinery.For such flows,a rotating frame of reference is usually used in formulating the Navier-Stokes(N-S)equations,and there are two major concerns in constructing the corresponding BGK model.One is the change of the convective velocities in the N-S equations,which can be reflected through modification of the gas streaming velocity.The other one is the necessity to account for the effect of the additional Coriolis and centrifugal forces.Here,a specifically-designed acceleration term is added into the modified Boltzmann equation so that the source effects can be naturally included into the gas evolution process and the resulted fluxes.Under the finitevolume framework,the constructed BGK model is locally solved at each cell interface and then the numerical fluxes can be evaluated.When employing the BGK scheme,it is sometimes found that the calculated spatial derivatives of the initial and equilibrium distribution functions are sensitive to the mesh quality especially in complex rotating flow applications,which may significantly influence flux evaluation.Therefore,an improved approach for computing these slopes is adopted,through which the modeling capability for viscous flows is enhanced.For validation,several numerical examples are presented.The computed results show that the present method can be well applied to a wide range of flows in rotating machinery with favorable accuracy.
