Application Of A Fuzzy Control Method In The Numerical Simulation Of Three-dimensional Flow And Heat Transfer Problems

The numerical simulation has become one of important methods to investigate the flow and heat transfer problems.The problems are controlled by continuity,momentum,and energy equations,which are highly nonlinear equations and coupled each other.As a result,it is necessary to solve them by iterating numerically.Due to the complexity of solving process,the under-relaxation factor,which lies between 0 and 1,is needed for the discrete control equations.However,lots of data show that the numerical convergence rate is greatly affected by the initial relaxation factor.In this study,the fuzzy control technology is applied to the three-dimensional SIMPLER and IDEAL algorithms.Both of the convergence rate and robustness are greatly improved.The influence of relaxation factor and computation time are both greatly decreased because the fuzzy control technology can dynamically find the best relaxation factor for current iteration level.The fuzzy control input is the ratio of maximum momentum residual errors between current and previous iterative levels,while the variation of relaxation factor is set to be the fuzzy control output.By simulating several steady incompressible laminar flow cases,it is found that:(1)For fuzzy control method,the convergence rate of is slightly affected by the initial relaxation factor and is always close to the highest convergence rate of the fixed relaxation factor method.It can obtain solutions with high convergence rate even for the most unfavorable initial relaxation factor.For fixed relaxation factor method,however,the convergence rate is only 1.1%-16.4% of the highest convergence rate when the initial relaxation factor is most unfavorable.The convergence rate is greatly affected by the initial relaxation factor.(2)When the initial relaxation factor is near its optimal value,the introduction of fuzzy control method almost doesn't affect the convergence rate.However,the convergence rate is greatly increased by fuzzy method for other relaxation factors.In particular,the convergence rate of fuzzy control method is up to 36 times of fixed relaxation factor method for some most unfavorable relaxation factors.(3)The introduction of fuzzy control method enhances the robustness of SIMPLER and IDEAL algorithms.To be specific,the influnce is greater for SIMPLER algorithm because the IDEAL algorithm is already an efficient and stable numerical method.IDEAL algorithm has a good adaptability to the complicated problem,grid,and so on.Its robustness is superior than the SIMPLER algorithm.