Uncertainty Research Of Natural Convection Based On Monte-Carlo Stochastic Finite Element Method

Natural convection study in the closed cavity is a hotspot in the field of computational fluid dynamics and computational heat transfer.Almost all the relevant researchs are adopting deterministic mathematical models,physical parameters and boundary conditions.However,practical flow and heat transfer has many uncertainty elements.Thus the study of heat transfer must consider the influence of those elements theoretically.Monte-Carlo method is the simplest approach to solve uncertainty problems,it has wide application scope,and the program structure writing is comparatively easier than other methods.In present work,heat transfer study of natural convection in a square cavity with random fluctuation boundary conditions,and a porous cavity with uncertain porosity were carried out based on Monte-Carlo stochastic finite element method.The main contents and conclusions in present research are as follows:(1)A Monte-Carlo stochastic finite element method was developed to solve uncertainty propagation of natural convection heat transfer under stochastic boundary condition.The input random parameters were expanded by Karhunen-Loeve expansion and the random samples of boundary condition were generated by Latin sampling method.The flow field and temperature field in the square cavity at different random samples of boundary condition were calculated numerically.The mathematical expectation and variance of stochastic output fields were calculated by sampling statistical method.The stochastic finite element program with Matlab language was written to solve uncertainty propagation of natural convection heat transfer in cavity under stochastic boundary condition based on computational framework.The effects of correlation length and variance of stochastic boundary condition on natural convection uncertainty were analyzed.The results show that the mean temperature field and flow field are basically the same as the deterministic temperature field and flow field.The probability distribution of Nusselt number under stochastic boundary condition is basically presented as normal distribution.The mean Nusselt number increases with the increase of correlation length and variance,the variance has a greater influence to heat transfer of natural convection than correlation length.(2)A Karhunen-Loeve-Monte-Carlo stochastic mathematical model and finite element framework of uncertainty quantification of natural convection in random porous media were developed based on stochastic theory and heat transfer theory in porous media.The momentum equations solved by Brinkmann-Darcy-Forchheimer model,mass and energy conservation equations are utilized in the calculation.The Karhunen-Loeve expansion and Latin sampling method were utilized to represent the input random field,so as to simulate the heat transfer of natural convection in the porous media cavity with stochastic finite element program.The mathematical expectation and standard deviation of stochastic output field were attained.Furthermore,the influence of Darcy number on Nusselt number was analyzed.The results show that the porosity uncertainty has important influence on the natural convection in porous cavity.The flow field and temperature field in random porous media and those under certain condition have some deviations,the standard deviation of Nusselt number increases first and then decreases with the increase of Darcy number.