A Novel Numerical Method for Simulating Boiling Heat Transfer of Nanofluids

In this paper,a new approach called the Eulerian species method was proposed for simulating the convective and/or boiling heat transfer of nanofluids.The movement of nanoparticles in nanofluids is tracked by the species transport equation,and the boiling process of nanofluids is computed by the Eulerian multiphase method coupled with the RPI boiling model.The validity of the species transport equation for simulating nanoparticles movement was verified by conducting a simulation of nanofluids convective heat transfer.Simulation results of boiling heat transfer of nanofluids were obtained by using the commercial CFD software ANSYS Fluent and compared with experimental data and results from another numerical method(Eulerian three-phase model).Good agreement with experimental data was achieved,and it was proved the Eulerian species method is better than the Eulerian three-phase model since it can give better simulation results with higher accuracy but needs fewer computation resources.

Experimental Study on the Bubble Dynamics of Magnetized Water Boiling

Boiling heat transfer,as an efficient heat transfer approach,that can absorb a large amount of latent heat during the vaporization,is especially suitable for heat transfer occasions with high heat flux demands.Experimental studies show that the surface tension coefficient of pure water can be reduced sharply(up to 25%)when it is magnetized by amagnetic field applied externally.In this paper,magnetized water(MW)was used as the work fluid to conduct boiling heat transfer experiments,to explore the influence of magnetization on the boiling characteristics of pure water.The electromagnetic device was used to magnetize water,and then the MW was used as the work-fluid of boiling heat transfer experiments,the bubble dynamic behavior of the MW boiling was captured by a video camera,and the characteristics andmechanism were analyzed.It was found that at the same conditions,the boiling of MW can produce more vapor bubbles of smaller size than the water without magnetization,which leads to a higher heat-transfer efficiency.This indicates that magnetization can enhance the boiling heat transfer of pure water.Furthermore,the thermal conditions required by magnetized water when the boiling is started are lower than the non-magnetized water boiling,whichmeans the earlier start of nucleate pool boiling when using the MW.

Physics-informed neural networks with residual/gradient-based adaptive sampling methods for solving partial differential equations with sharp solutions

We consider solving the forward and inverse partial differential equations(PDEs)which have sharp solutions with physics-informed neural networks(PINNs)in this work.In particular,to better capture the sharpness of the solution,we propose the adaptive sampling methods(ASMs)based on the residual and the gradient of the solution.We first present a residual only-based ASM denoted by ASMⅠ.In this approach,we first train the neural network using a small number of residual points and divide the computational domain into a certain number of sub-domains,then we add new residual points in the sub-domain which has the largest mean absolute value of the residual,and those points which have the largest absolute values of the residual in this sub-domain as new residual points.We further develop a second type of ASM(denoted by ASMⅡ)based on both the residual and the gradient of the solution due to the fact that only the residual may not be able to efficiently capture the sharpness of the solution.The procedure of ASMⅡis almost the same as that of ASMⅠ,and we add new residual points which have not only large residuals but also large gradients.To demonstrate the effectiveness of the present methods,we use both ASMⅠand ASMⅡto solve a number of PDEs,including the Burger equation,the compressible Euler equation,the Poisson equation over an Lshape domain as well as the high-dimensional Poisson equation.It has been shown from the numerical results that the sharp solutions can be well approximated by using either ASMⅠor ASMⅡ,and both methods deliver much more accurate solutions than the original PINNs with the same number of residual points.Moreover,the ASMⅡalgorithm has better performance in terms of accuracy,efficiency,and stability compared with the ASMⅠalgorithm.This means that the gradient of the solution improves the stability and efficiency of the adaptive sampling procedure as well as the accuracy of the solution.Furthermore,we also employ the similar adaptive sampling technique for the data points of boundary conditions(BCs)if the sharpness of the solution is near the boundary.The result of the L-shape Poisson problem indicates that the present method can significantly improve the efficiency,stability,and accuracy.

Variational inference in neural functional prior using normalizing flows: application to differential equation and operator learning problems

Physics-informed deep learning has recently emerged as an effective tool for leveraging both observational data and available physical laws.Physics-informed neural networks(PINNs)and deep operator networks(DeepONets)are two such models.The former encodes the physical laws via the automatic differentiation,while the latter learns the hidden physics from data.Generally,the noisy and limited observational data as well as the over-parameterization in neural networks(NNs)result in uncertainty in predictions from deep learning models.In paper“MENG,X.,YANG,L.,MAO,Z.,FERRANDIS,J.D.,and KARNIADAKIS,G.E.Learning functional priors and posteriors from data and physics.Journal of Computational Physics,457,111073(2022)”,a Bayesian framework based on the generative adversarial networks(GANs)has been proposed as a unified model to quantify uncertainties in predictions of PINNs as well as DeepONets.Specifically,the proposed approach in“MENG,X.,YANG,L.,MAO,Z.,FERRANDIS,J.D.,and KARNIADAKIS,G.E.Learning functional priors and posteriors from data and physics.Journal of Computational Physics,457,111073(2022)”has two stages:(i)prior learning,and(ii)posterior estimation.At the first stage,the GANs are utilized to learn a functional prior either from a prescribed function distribution,e.g.,the Gaussian process,or from historical data and available physics.At the second stage,the Hamiltonian Monte Carlo(HMC)method is utilized to estimate the posterior in the latent space of GANs.However,the vanilla HMC does not support the mini-batch training,which limits its applications in problems with big data.In the present work,we propose to use the normalizing flow(NF)models in the context of variational inference(VI),which naturally enables the mini-batch training,as the alternative to HMC for posterior estimation in the latent space of GANs.A series of numerical experiments,including a nonlinear differential equation problem and a 100-dimensional(100D)Darcy problem,are conducted to demonstrate that the NFs with full-/mini-batch training are able to achieve similar accuracy as the“gold rule”HMC.Moreover,the mini-batch training of NF makes it a promising tool for quantifying uncertainty in solving the high-dimensional partial differential equation(PDE)problems with big data.