Research And Application On High-order Accuracy Difference Based Pseudo-potential MRT Multiphase Flow Lattice Boltzmann Method

Multiphase flow is ubiquitous in nature and industrial and agricultural production.Intensive study of the phenomenon and movement law of multiphase flow under different conditions is very important for improving the production efficiency and safety of industrial and agricultural fields as well as maintaining ecological balance.The lattice Boltzmann method has unique advantages such as clear physical background,natural parallel characteristics,simple algorithm and high calculation efficiency.It has developed into a mainstream multiphase flow numerical simulation research method.Among them,the pseudo-potential model is widely used because it directly describes the interaction mechanism between micro-molecules,which has the advantages of clear physical concepts,high calculation efficiency,and easy implementation.Through further research,this paper finds that the original pseudo-potential model still has some deficiencies in multiphase flow simulation,such as:?1?The density gradient calculation still remains errors,and its calculation accuracy is low;?2?It cannot be applied to a larger gas-liquid phase Numerical simulation of multi-phase flow in the case of density ratio and large temperature interval,so it is poor in robustness;?3?The virtual velocity is too large so as to the stability is weak.Through dada analysis,we find that when using the traditional central difference method algorithm to calculate the density gradient of the pseudo-potential model,there is a large error between the calculation result and the theoretical value.This paper firstly improves the calculation accuracy by introducing a high-order accuracy difference algorithm to calculate the density gradient.Then,by analyzing the effect of relaxation time on the mechanism of the model in the Lattice-Bhatnagar-Gross-Krook?LBGK?and the Multiple-Relaxation-Time lattice Boltzmann model?MRT?,it is found that,in the MRT model,With the increase of the relaxation factor term,the intervention and influence of the relaxation time on the stability of the model simulation can be significantly reduced.Therefore,the LBGK collision operator of the original pseudo-potential model is changed to the MRT collision operator to construct a high-order accuracy difference based pseudo-potential MRT multiphase flow Lattice Boltzmann Method.After the improved model was proposed,its performance was verified through a series of numerical simulation experiments.The experimental results show that the gas-liquid two-phase coexistence density curve simulated by the improved model is in good agreement with the theoretical value obtained by Maxwell's equal-area construction method,and the gas-liquid density ratio under each state equation exceeds 10¹².As for Redlich-Kwong equation of state,the gas-liquid density ratio is up to 10¹⁸.The improved model has also made great progress in reducing the virtual velocity.For different state equations,the maximum virtual velocity does not exceed 0.0015.These simulations show that by introducing a high-order accuracy difference algorithm and an improved model of the MRT collision operator,the calculation accuracy and robustness can be significantly improved,and the virtual velocity can be reduced.To further verify the performance of the improved model,this paper studies the flow characteristics of single and double droplets impinging on the liquid film with the improved model.The numerical experiments of single and double droplets impinging on liquid film were simulated under different parameters such as Reynolds number,gas-liquid density ratio,horizontal distance and impact velocity.The simulation results show that the Reynolds number is a key parameter that affects the spreading radius of the crowned water splash generated by a single droplet impacting the liquid film,the height of the water splash and whether it can produce a secondary droplet splash,and the gas-liquid two-phase density ratio mainly affects.The crest of the crown-shaped water splash.For the double-droplet impinging on the liquid film,the spreading splash in the middle of the two drops collides and merges during the splashing process,forming a vertical upward central jet in vertical and horizontal liquid film.The spreading splash at the left and right ends of the droplet and single spreading splash generated after the droplet hits the liquid film are the same.By increasing the Reynolds number,horizontal distance and impact velocity,the rising speed and rising height of the central jet can be increased,and the water spray on the top of the central jet gradually becomes thinner,and finally the secondary droplet splash phenomenon is overcome by overcoming its surface tension.In addition,if the Reynolds number increasing to5000,due to the full spread of the water droplets between the two droplets,the central jet energy is greater after collision and merger,resulting in the generation of multiple droplets secondary splash phenomenon.The above-mentioned numerical experiments prove that the improved model constructed by introducing the high-order accuracy difference algorithm and the MRT collision operator has shown good performance in the study of practical multiphase flow problems.Moreover,it is suitable for multiphase flow simulation under the condition of higher Reynolds number and larger gas-liquid density ratio.Therefore,it is expected that this model will be more widely used in the field of dynamic multiphase flow numerical simulation of complex fluids.