Theoretical And Numerical Study On Two-phase Interactions In Gas-particle Turbulence Flows Based On PDF Approach

The fluid-particle interaction in gas-particle two-phase flows is both a hot and troublesome issue.It is generally known that turbulence is a hard nut to crack for researchers,and the problem becomes much more complicated when embedding discrete particles in turbulence.At present,the particle diffusion model is still needs to be further improved.The conventional discrete random walk model cannot reflect the continuous effect of turbulence on particle diffusion,while the generalized Langevin model is often too complex to implement.On the other hand,there is still no general recognized turbulence modification model up to now,the turbulence modification problem is still an open topic.The probability density function(PDF)approach has unique advantages in the study of turbulence flow,and it has been widely used in the fields of combustion,two-phase turbulence,turbulent reaction flow,etc.However,utilizing it in the investigations of fluid-particle interaction problem has not been explored so far.In this paper,a theoretical and numerical study on the interactions between gas and particles is carried out based on the PDF approach.The main contents and results of this paper are as follows:(1)A PIV experimental platform for two-phase backward-facing step flow is designed and set up.The particle dispersion in the complex vortex region is investigated by PIV system,and the two-phase velocity distributions near the reflux region are measured and discussed.It is found that the trend of two-phase velocity distributions is consistent overall,but the particle-velocity profiles are flatter than the air-velocity profiles in the main flow field.On the whole,the particle-velocity profiles are top-hat like,while the air-velocity profiles are straw-hat like.(2)A new particle diffusion langevin model is obtained by means of the unified colored noise approximation(UCNA)method.Then,the PDF transport equation and the corresponding Eulerian and Lagrangian macroscopic equations are deduced then.Compared with the conventional model,there are three features of the present UCNA model:The UCNA langevin model modified the particle relaxation time with the turbulent time scale,which is more able to reflect the continuous action of turbulence on particles,and the model is simple and easy to implement;The Eulerian macroscopic model based on the UCNA method do not need to model the two-phase velocity correlation,and the two-phase correlation term on the basis of UCNA theory coincides with the usual empirical correlation;Compared with the previous Lagrangian macroscopic moment model,the UCNA Lagrangian macroscopic model in this paper can better reflect the effect of turbulence on particle mean velocity and fluctuating velocity.The one-way coupling numerical study with the present particle diffusion model shows that the UCNA model has the advantages of minor calculation and easy to implement.The prediction results of two two-phase backward-facing step flow experiments are reasonable and accurate.(3)On the basis of the micro level Lagrangian equation,two macroscopic models of fluid are obtained in the use of PDF approach:a new turbulence modification model without considering the crossing-trajectory effect and a new turbulence modification model with considering the crossing-trajectory effect.Compared with the traditional Reynolds-averaged model,a new Reynolds stress production term appears in the new turbulence modification model.Most of the previous models need to use additional empirical formulas to describe the increase of Reynolds stress caused by particles,while in present model the 'extra production term' is gained by theoretical deduction.The new term gives a reasonable explanation for the particle's enhancement effect on the turbulence.Furthermore,a new turbulence modulation model is successfully set up with considering the crossing-trajectory effect.The model modified the diffusion and particle source terms of momentum equations,as well as the generation and dissipation terms of turbulent kinetic energy equation.The new model will change into the standard k—? model when the particle relaxation time tends to zero.The present model provides a new explanation for turbulence modification problem.The new turbulence modification model was applied to simulate the wall jet gas-particle turbulence flow,and it found that the simulation results are closer to the experimental data than the results calculated by traditional Reynolds averaged approach.(4)An improved two-phase macroscopic model is established based on two-point PDF,and a comparative study on PDF and Reynolds-averaged approaches is carried on.The theoretical basis,mathematical method,derivation process,the final form of the two models and numerical results of the two approaches are compared and analyzed.On the base of the Navier-Stokes equation for single-phase and two-phase flows,the macroscopic models based on the one-point and two-point PDF,and subsequently,the single-phase and two-phase RANS models are established.By comparison,it is found that the RANS model and PDF macroscopic model are established with similar opinion(obtained macroscopic moment models from microcosmic Navier-Stokes equations),the starting-point and the averaging methods used in the two derivations are equivalent,the single-phase RANS model is in good agreement with the one-point PDF macroscopic model,while the two-fluid RANS model is different from the two-point PDF macroscopic model,additional production terms are arising in the two-phase Reynolds stress equations based on PDF approach.According to the comparative study,one can find that the difference between the two-fluid RANS model and the two-point PDF macroscopic model is caused by two different point of views to the two-phase turbulent flow.The two additional terms are of great significance for explaining the particle dispersion and turbulence modification problems,but they will never be uttered in the RANS model.The two-fluid RANS model and the two-phase PDF macroscopic model are used to simulate a gas-particle turbulent upward pipe flow.Theoretical analysis and simulation results show that the PDF statistical moment model has more advantages in explaining and predicting particle diffusion and turbulence modulation problems.