Numerical Study On Flow And Heat Transfer Of Porous Media Based On Non-orthogonal Multi-relaxation LBM

In recent years,porous media have played an important role in many fields such as environment,energy and chemical industry.In detail,porous media can be used in the exploitation of oil and natural gas,storage of hydrogen or carbon dioxide,good adsorption media and effective heat transfer enhancement media,sewage treatment and air purification.The study on internal flow and heat transfer is of great significance in both theory and practice.Based on the wide application of fluid seepage and heat transfer in porous media,with the multi-relaxation lattice Boltzmann model of non-orthogonal matrix,the mesoscopic numerical on the flow and heat transfer in porous media was carried out on the REV scale.Through the research in this paper,people can deepen the understanding of the flow and heat transfer problems in porous media and the research can provide a certain theoretical basis in engineering applications.The main work and conclusions of this paper are as follows:?1?The Boltzmann model with single relaxation and double distributed thermal lattice in porous media was established.The D2Q5 model was used to discrete the temperature field,and the D2Q9 model was used to discrete the flow field.A multi-relaxation lattice Boltzmann model with non-orthogonal matrices of porous media flow was established.By using the non-orthogonal transformation matrix,the corresponding D2Q9 velocity field and D2Q5 temperature field were established,and the multi-relaxation lattice Boltzmann temperature equation was recovered based on Chapman Enskog multi-scale technology.?2?Compared with the conventional multi-relaxation lattice Boltzmann model,the non-orthogonal transformation matrixthis in the model contains the more zero elements,also doesn't have to be normalized,thus it has higher computational efficiency.The flow heat transfer problem was simulated,including three classic examples of Poiseuille flow between hot plates,mixed convection between plates,and natural convection in a square cavity.The feasibility and accuracy of the model were verified by comparing the temperature contour map and flow map and quantitative data.The numerical simulation results showed that the model had better numerical stability and higher efficiency than the existing multi-relaxation lattice Boltzmann model.?3?The multi-relaxation lattice Boltzmann model with the non-orthogonal matrix was constructed used for the flow heat transfer of the nano-fluid in the porous media.And the model was numerically verified with pure water.To further simulate the velocity,temperature and pressure distribution of the nano-fluid porous medium in the two-dimensional square cavity were simulated.The porous media with different volume fraction?0%,3%5%?of Al2O3-water nanofluids in different Ra number?10³¹0⁹?,Da number(10^-210^-6),different particle size of the nanofluids?10 nm,20 nm,30 nm?,porosity?0.4⁰.9?,and different aspect ratio?0.25¹?,and other factors on the natural convection were examined The influence of different parameters were given along the hot wall Nu number and the distribution of wall average Nu number.It showed that the heat transfer was enhanced with the increase of the volume fraction of the nanofluid in a certain range,but the fluid velocity reduces when the volume fraction is large,and the heat transfer capacity is weakened.It is found that the heat transfer reaches the best when the volume fraction is 3%.With the increase of Ra number,Da number and porosity,the average Nu number of the high temperature wall increases and the heat transfer increases.Under the same conditions,the Ra number has a greater influence on the average Nu number of the left wall surface than the Da number.As the particle size of the nanofluid decreases,the average Nu number of the wall increases.In the rectangular cavity,the velocity increases with the increase of the aspect ratio A,and the isotherm bends more obviously with the increase of the aspect ratio.When the aspect ratio is 0.25,the nanofluid with 3%of the low Ra number is greater than the high Ra number on.the degree of enhancement.