Uncertainty Research Of Natural Convection Heat Transfer Under Periodic Stochastic Boundary Condition

In recent years,the flow and heat transfer in cavity with periodic boundary conditions occupy a relatively important position in the field of engineering.The numerical calculation of fluid flow and heat transfer under deterministic conditions has undergone rapid development.However,due to various uncertainties in practical engineering,the numerical simulation of fluid flow and heat transfer can better reflect the real situation of actual engineering.Monte Carlo method is based on statistical sampling of probability and statistics theory.This method does not need to change the computational fluid dynamics code.Therefore,when there is a random change of periodic boundary conditions on the wall of square cavity,Monte-Carlo stochastic finite element method is used to analyze the influence of natural convection heat transfer characteristics.The following conclusions are drawn:(1)Based on Monte-Carto stochastic finite element method,an uncertainty analysis method for natural convection heat transfer process in square cavity under periodic random boundary conditions is developed.This method uses Karhunen-Loeve to discretize the periodic random boundary conditions of the input field,and uses Latin hypercube sampling method to obtain the random samples of the periodic boundary conditions.The average and standard deviation of the random output fields in the physical model are analyzed by numerical statistical method.Based on the designed calculation algorithm and programming flow,the MATLAB stochastic finite element program under periodic random boundary conditions is obtained.(2)Based on the above-mentioned MATLAB calculation program,the random perturbations affecting the uncertainty of natural convection heat transfer in a square cavity are analyzed.The main influencing parameters include:correlation length and variance of periodic boundary conditions,Rayleigh number and periodic number.The results show that the temperature field and the flow field have the same distribution as the temperature field and the flow field of the random output field when the boundary conditions remain unchanged.When Rayleigh number increases gradually,the average Nu number in the square cavity increases gradually;when variance increases gradually,the average Nu number in the square cavity increases gradually;when correlation length decreases,the average Nu number in the square cavity increases gradually;variance has greater influence than correlation length;and when period number decreases,the average Nu number in the square cavity increases gradually.That is to say,the increase of correlation length of periodic boundary conditions,the decrease of variance of periodic boundary conditions,the increase of Rayleigh number and the decrease of periodic number all enhance the natural convection heat transfer capacity in the square cavity.(3)Based on the above-mentioned MATLAB calculation program,the program code for the study of the uncertainty of natural convection heat transfer in square cavity under double periodic random boundary conditions is developed.The results show that the existence of periodic random perturbation has a great influence on the distribution of temperature field and flow field in square cavity.With the decrease of the period number,the flow in square cavity is obviously affected.The area where the distribution of random field changes in square cavity gradually increases,and the Nu number in square cavity gradually increases.