Numerical Investigation Of Thermomagnetic Convection Based On The Lattice Boltzmann Method And Fast Prediction Based On POD Method

In the last few decades,advances in superconducting magnets technology have turned natural convection under magnetic field into a new research focus which has received widespread attention.Numerical simulation based on lattice Boltzmann method(LBM)has also been seen as one of the most effective and valuable means of investigating and researching practical engineering problems.However,there are no relevant researches focused on thermomagnetic convection of paramagnetic fluid utilizing LBM,so it is of great necessity for investigators to study the current problem using lattice Boltzmann method.A fast method of flow prediction is also essential to overcome the shortcomings of numerical investigations based on LBM,such as slow computation speed,long computing time,etc.In present work,thermomagnetic convection of paramagnetic fluid is numerically simulated using lattice Boltzmann method,and a fast prediction method based on proper orthogonal decomposition(POD)is also developed correctly.Main contents and conclusions in present research are as follows:(1)The algorithm and program code based on LBM are currently developed and employed to simulate the thermomagnetic convection of paramagnetic fluid in square cavity,in the presence of an inhomogeneous magnetic field.Flow structure,isotherms and heat transfer performance are compared carefully for various magnetic force numbers under both non-gravitational and gravitational condition.Results show that under the non-gravitational condition,the flow presents a completely symmetric two-cellular structure,consisting of an anticlockwise vortex and a clockwise one;Under the gravitational condition,a weak clockwise flow emerges at first,and then,an approximately symmetric stratification phenomenon occurs when the magnetic field is strong enough.In addition,the heat transfer is more efficient under gravity effect only in weak magnetic field,while opposite situation happens once ?Ra reaches to 1×105 or more.(2)LBM is utilized to study the transient natural convection of paramagnetic fluid under the influence of magnetic field.Transient characteristics at initial moment,quasi-steady and steady state are closely analyzed and compared for changing magnetic force numbers.Results show that at initial moment,the effect of magnetic buoyancy force is relatively insignificant and light bulb shaped curves on isotherms can be easily observed when magnetic field is relatively strong;As time evolves,isotherms travel towards the cold wall and vortexes also begin to grow and move to the center of enclosure.Under the non-gravitational condition,flow structure and isotherms are completely symmetric about the horizontal central line;While in gravitational environment,the symmetry no longer exists.(3)The algorithm and program code of Proper Orthogonal Decomposition method are developed as well to solve the current problem.POD modes solved by current algorithm are adopted in the reconstruction of the flow,and the computational errors of streamline function and temperature are less than 1%.Thus,validity and correctness of this fast prediction method are proved in present research.Besides,this reduced-order analysis method is nearly 120 times faster,therefore,the time advantage is pretty obvious.