In order to correctly predict tube cross section time-smoothed velocity distribution, friction factor and mass transfer behavior, two models for turbulent flow in circular tubes based on classical Prandtl mixing lengt...In order to correctly predict tube cross section time-smoothed velocity distribution, friction factor and mass transfer behavior, two models for turbulent flow in circular tubes based on classical Prandtl mixing length theory and a modified mixing length were established. The results show that the modified mixing length includes the introduction of a damping function for the viscous sublayer and the second-order derivative to approximate eddy velocity. The calculated dimensionless time-smoothed velocity from the model based on Prandtl mixing length is much better than the result from the concept of eddy viscosity. The calculated eddy viscosity from the model based on modified mixing length is much better than the result from the model based on the classical Prandtl mixing length theory. And the friction factor calculated from the model based on the modified mixing length agrees well with the reported empirical relationships.展开更多
This research used the common decomposition of the velocity and pressure in an average part and a fluctuating part, for high Reynolds number, of the Navier-Stokes equation, which leads to the classic problem of turbul...This research used the common decomposition of the velocity and pressure in an average part and a fluctuating part, for high Reynolds number, of the Navier-Stokes equation, which leads to the classic problem of turbulent closure. The Prandtl’s mixing length model, based on the Boussinesq hypothesis and traditionally used for free shear flows, was chosen and adapted for internal flows to solve the closure problem. For channel flows, Johann Nikuradse proposed a model for the Prandtl mixing length. In the present paper, which has an academic character, the authors made a return to the model of the mixing length of Prandtl and the model of Nikuradse, to solve turbulent flows inside a plane channel. It was possible to develop an ordinary differential model for the velocity in the direction of the flow whose solution occurs computationally in a simple but extremely accurate way when compared with Direct Numerical Simulation databases. For the viscous stress on the wall, it was possible to determine the exact mathematical solution of the ordinary differential equation. It is a model of great academic value and even to be used as reference for verification of computational codes destined to the solution of complete numerical and computational models.展开更多
An improved model to calculate the length of the mixing chamber of the ejector was proposed on the basis of the Fano flow model,and a method to optimize the structures of the mixing chamber and diffuser of the ejector...An improved model to calculate the length of the mixing chamber of the ejector was proposed on the basis of the Fano flow model,and a method to optimize the structures of the mixing chamber and diffuser of the ejector was put forward.The accuracy of the model was verified by comparing the theoretical results calculated using the model to experimental data reported in literature.Variations in the length of the mixing chamber L_(m) and length of the diffuser L_(d) with respect to variations in the outlet temperature of the ejector T_(c),outlet pressure of the ejector p_(c),and the expansion ratio of the pressure of the primary flow to that of the secondary flow p_(g)/p_(e) were investigated.Moreover,variations in L_(m) and L_(d) with respect to variations in the ratio of the diameter of the throat of the motive nozzle to the diameter of the mixing chamber d_(g0)/d_(c3) and ratio of the outlet diameter of the diffuser to the diameter of themixing chamber d_(c)/d_(c3) were investigated.The distribution of flow fields in the ejector was simulated.Increasing L_(m) and d_(c3) reduced T_(c) and p_(c).Moreover,reducing p_(g)/p_(e) or d_(g0)/d_(c3) reduced T_(c) and p_(c).The length of the mixed section L_(m2),which was determined on the basis of the Fano flow model,increased as pg increased and decreased as d_(c3) increased.The mixing length L_(m1),which was considered the primary flow expansion,showed the opposite trend with that of L_(m2).Moreover,Ld increased as p_(g)/p_(e) and d_(c)/d_(c3) increased.When the value of d_(c) was 1.8 to 2.0 times as high as that of dc3,the semi-cone angle of the diffuser ranged between 6°and 12°.At a constant dc/dc3,decreasing T_(c) and pc increased Ld.展开更多
We will give an overview of results obtained by our reactive fluid model. It is characterised as a fluid model where all moments with sources in the experiment are kept. Furthermore, full account is taken for the high...We will give an overview of results obtained by our reactive fluid model. It is characterised as a fluid model where all moments with sources in the experiment are kept. Furthermore, full account is taken for the highest moments appearing in unexpanded denominators also including full toroidicity. It has been demonstrated that the strength of zonal flows is dramatically larger in reactive fluid closures than in those which involve dissipation. This gives a direct connection between the fluid closure and the level of excitation of turbulence. This is because zonal flows are needed to absorb the inverse cascade in quasi 2D turbulence. This also explains the similarity in structure of the transport coefficients in our model with a reactive closure in the energy equation and models which have a reactive closure because of zero ion temperature such as the Hasegawa-Wakatani model. Our exact reactive closure unifies several well-known features of tokamak experiments such as the L-H transition, internal transport barriers and the nonlinear Dimits upshift of the critical gradient for onset of transport. It also gives transport of the same level as that in nonlinear gyrokinetic codes. Since these include the kinetic resonance this confirms the validity of the thermodynamic properties of our model. Furthermore, we can show that while a strongly nonlinear model is needed in kinetic theory a quasilinear model is sufficient in the fluid description. Thus our quasilinear fluid model will be adequate for treating all relevant problems in bulk transport. This is finally confirmed by the reproduction by the model of the experimental power scaling of the confinement time Te ~ P-2/3. This confirms the validity of our reactive fluid model. This also gives credibility to our ITER simulations including the H-mode barrier. A new result is here, that alpha heating strongly reduces the slope of the H-mode barrier. This should significantly reduce the effects of ELM＇s.展开更多
基金Project(20736009) supported by the National Natural Science Foundation of ChinaProject(07JJ6017) supported by the Natural Science Foundation of Hunan Province, China
文摘In order to correctly predict tube cross section time-smoothed velocity distribution, friction factor and mass transfer behavior, two models for turbulent flow in circular tubes based on classical Prandtl mixing length theory and a modified mixing length were established. The results show that the modified mixing length includes the introduction of a damping function for the viscous sublayer and the second-order derivative to approximate eddy velocity. The calculated dimensionless time-smoothed velocity from the model based on Prandtl mixing length is much better than the result from the concept of eddy viscosity. The calculated eddy viscosity from the model based on modified mixing length is much better than the result from the model based on the classical Prandtl mixing length theory. And the friction factor calculated from the model based on the modified mixing length agrees well with the reported empirical relationships.
文摘This research used the common decomposition of the velocity and pressure in an average part and a fluctuating part, for high Reynolds number, of the Navier-Stokes equation, which leads to the classic problem of turbulent closure. The Prandtl’s mixing length model, based on the Boussinesq hypothesis and traditionally used for free shear flows, was chosen and adapted for internal flows to solve the closure problem. For channel flows, Johann Nikuradse proposed a model for the Prandtl mixing length. In the present paper, which has an academic character, the authors made a return to the model of the mixing length of Prandtl and the model of Nikuradse, to solve turbulent flows inside a plane channel. It was possible to develop an ordinary differential model for the velocity in the direction of the flow whose solution occurs computationally in a simple but extremely accurate way when compared with Direct Numerical Simulation databases. For the viscous stress on the wall, it was possible to determine the exact mathematical solution of the ordinary differential equation. It is a model of great academic value and even to be used as reference for verification of computational codes destined to the solution of complete numerical and computational models.
文摘An improved model to calculate the length of the mixing chamber of the ejector was proposed on the basis of the Fano flow model,and a method to optimize the structures of the mixing chamber and diffuser of the ejector was put forward.The accuracy of the model was verified by comparing the theoretical results calculated using the model to experimental data reported in literature.Variations in the length of the mixing chamber L_(m) and length of the diffuser L_(d) with respect to variations in the outlet temperature of the ejector T_(c),outlet pressure of the ejector p_(c),and the expansion ratio of the pressure of the primary flow to that of the secondary flow p_(g)/p_(e) were investigated.Moreover,variations in L_(m) and L_(d) with respect to variations in the ratio of the diameter of the throat of the motive nozzle to the diameter of the mixing chamber d_(g0)/d_(c3) and ratio of the outlet diameter of the diffuser to the diameter of themixing chamber d_(c)/d_(c3) were investigated.The distribution of flow fields in the ejector was simulated.Increasing L_(m) and d_(c3) reduced T_(c) and p_(c).Moreover,reducing p_(g)/p_(e) or d_(g0)/d_(c3) reduced T_(c) and p_(c).The length of the mixed section L_(m2),which was determined on the basis of the Fano flow model,increased as pg increased and decreased as d_(c3) increased.The mixing length L_(m1),which was considered the primary flow expansion,showed the opposite trend with that of L_(m2).Moreover,Ld increased as p_(g)/p_(e) and d_(c)/d_(c3) increased.When the value of d_(c) was 1.8 to 2.0 times as high as that of dc3,the semi-cone angle of the diffuser ranged between 6°and 12°.At a constant dc/dc3,decreasing T_(c) and pc increased Ld.
文摘We will give an overview of results obtained by our reactive fluid model. It is characterised as a fluid model where all moments with sources in the experiment are kept. Furthermore, full account is taken for the highest moments appearing in unexpanded denominators also including full toroidicity. It has been demonstrated that the strength of zonal flows is dramatically larger in reactive fluid closures than in those which involve dissipation. This gives a direct connection between the fluid closure and the level of excitation of turbulence. This is because zonal flows are needed to absorb the inverse cascade in quasi 2D turbulence. This also explains the similarity in structure of the transport coefficients in our model with a reactive closure in the energy equation and models which have a reactive closure because of zero ion temperature such as the Hasegawa-Wakatani model. Our exact reactive closure unifies several well-known features of tokamak experiments such as the L-H transition, internal transport barriers and the nonlinear Dimits upshift of the critical gradient for onset of transport. It also gives transport of the same level as that in nonlinear gyrokinetic codes. Since these include the kinetic resonance this confirms the validity of the thermodynamic properties of our model. Furthermore, we can show that while a strongly nonlinear model is needed in kinetic theory a quasilinear model is sufficient in the fluid description. Thus our quasilinear fluid model will be adequate for treating all relevant problems in bulk transport. This is finally confirmed by the reproduction by the model of the experimental power scaling of the confinement time Te ~ P-2/3. This confirms the validity of our reactive fluid model. This also gives credibility to our ITER simulations including the H-mode barrier. A new result is here, that alpha heating strongly reduces the slope of the H-mode barrier. This should significantly reduce the effects of ELM＇s.
