Improvement Of The Taylor-series Expansion Method Of Moments Model And Its Application In Nanoparticle-landen Two-phase Flow

Nanoparticle-laden two-phase flows occur in a wide range of natural phenomena and engineering applications,thus receives much attention by scientists.In this work,we performed the theoretical analysis and numerical simulation on TEMOM model for nanoparticle Brownian coagulation.Three aspects are highlighted here:(1)A new analytical solution is first proposed to solve the population balance equation due to Brownian coagulation in the continuum-slip regime.An assumption for a novel variable g(g=m0m2/m12,where m0,m1,and m2 are the first three moments,respectively)is successfully applied in executing a separate variable method for ordinary differential equations of the Taylor expansion method of moments.The sectional method is selected as a reference to verify the new solution.The accuracy between the new solution and Lee et al.analytical solution is mainly compared.The geometric standard deviation of number distribution for the new analytical solution is revealed to be limited to 1.6583.Within the valid range of the geometric standard deviation,the new analytical solution is confirmed to solve the population balance equation undergoing Brownian coagulation with the very nearly same accuracy as Lee et al.analytical solution.For the total particle number concentration,the new solution usually yields higher accuracy.The new solution and Lee et al.analytical solution approximately become one solution as the Knudsen number is smaller than 0.1000.The new solution has the potential to become a competitive analytical solution for solving population balance equation regarding its accuracy and very straightforward derivation.(2)The effect of Taylor expansion order on the accuracy of the Taylor expansion method of moments model in both free molecular regime and continuum-slip regime was studied.The ordinary differential equations for moments with fourth Taylor expansion was firstly derived for fractal-like agglomerates,which was further compared to the existing Taylor expansion method of moments model with third Taylor expansion.We fully confirmed the accuracy of Taylor expansion method of moments with fourth Taylor expansion is less than that with third Taylor expansion,and the scope of application of the Taylor expansion method of moments with fourth Taylor expansion is much limited.The existing Taylor expansion method of moments with third Taylor expansion is finally verified to be the most reliable model for solving population balance equation for agglomerates undergoing Brownian coagulation.(3)The coupling of Taylor expansion method of moments Model to homogeneous isotropic turbulence was studied.We performed a number simulation of the moment equations based on the Taylor expansion method of moments model in homogeneous isotropic turbulence that was frozen and compare the results with the ordinary differential equation which is protected from the turbulence flow.The results show that the rate of change over time of the first three moments on the particle number concentration shows more strongly in the case of the homogeneous isotropic turbulence.