A Study Of Statistics Of Passive Scalar Along Inertial Particle Trajectory And Its Dynamical Model

The internal mechanism of the momentum and heat transfer between two-phase in non-isothermal gas-solid flow and their corresponding prediction models are very complex and needed to be studied in depth, so they have been research hot spots of multi-phase flow in recent years.Based on this status quo, three aspects studies of non-isothermal gas/particle flow are carried out in this paper:First of all, by the use of pseudo-spectral method, a passive scalar field with a mean scalar gradient in homogeneous isotropic turbulence was studied. The spatial structure of scalar, the dynamic mechanism of scalar dissipation and other Euler statistics were discussed. Direct numerical simulation results show that: the space structure of the scalar field is nearly Ramp-Cliff and the high-intensity scalar dissipation, which gathered in these Cliff structures, is highly intermittent in space. The strain rate plays the leading role in the form of high-intensity scalar dissipation, however, the vorticity has less direct impact on this formation, but it can rotate these cliff structures to produce scalar gradients, which opposite to the mean scalar gradient, to weaken the effeteness of the latter. In addition, by adopting the topology theory of turbulence, it is found that high-intensity scalar dissipation is mainly formed in the R_a=2√3(Q_a)^1.5/9, Q_A <0, R_a>0 regions, where correspond to flow field with topology of unstable node/saddle/saddle, and this characteristic does not significantly depend on the Pr number of scalar field.Secondly, after the spatial structure of scalar and the dynamical mechanism of scalar dissipation had been understood in the first part, the characteristics of scalar (temperature) along inertial particle are studied based on the point source hypothesis and the influence of parameters of particle and scalar (temperature) on these characteristics had been discussed in detail. The results show that, the scalar variance and scalar dissipation seen by particle show completely different behavior and reach their minimum and maximum at the critical particle of Stokes^l .0, respectively. The correlation coefficients between scalar dissipation and fluid strain rate or vorticity along particle trajectory also show complex behavior with Stokes number. Moreover, the cross heat flux between the particle phase and fluid field have been computed firstly in this paper and found they are monotonically decreasing functions with the particle Stokes number, the heat capacity ratio a and the temperature Pr number; the self-correlation coefficient of temperature along particle trajectory is also reduced with the increasing of particle St number and temperature Pr number, but the heat capacity ratio a has no pronounced effect on the self-correlation.Finally, in the framework of PDF method, the PDF equation of non-isothermal gas/particle flow was systematically derived, which included particle velocity, particle temperature, fluid velocity seen by particle and fluid temperature seen by particle. And then based on the random Langevin model system, a closed PDF equation was gotten and the macro-moment equations were derived. By the use of Rodi's approximation, these moment equations were reasonably simplified to algebraic models. The inertia effect, continuity effect and trajectory-crossing effect had been considered at the same time in the diffusion coefficient of the model of fluid velocity seen by particle and the Lagrangian integral time scale of fluid temperature seen by particle as the input parameter of the diffusion coefficient in the model of fluid temperature seen by particle, was firstly proposed by us. The results show that, the computed values based on this integral time scale, are more closed to the DNS results than those based on the dissipation time scale of fluid flow and Kolmogorov constant, so the integral time scale of fluid temperature seen by particl is recommended as the diffusion coefficien in the follow-up models.