Closed-loop flow separation control in the backward facing step flow using fuzzy-based PID controller

Abstract

Fluid flow around solid bodies from rudimentary to sophisticated, is one of the spotlights in fluid dynamic analysis which includes various phenomena such as flow separation. Flow separation is an important engineering topic which has been considered in various internal and external flow problems leading to pressure drag, loss of lift, stall, pressure recovery losses and vortex shedding leading to significant failure in the resonance frequency domain. The problem which has become benchmark regarding the flow separation and reattachment length is the Backward Facing Step. Despite of having tremendous theoretical, numerical, and experimental studies related to this problem, there have been less value of research regarding the flow control in this geometry. Having reattachment after separation of the flow in this geometry increases the unsteadiness, pressure fluctuations, vibrations and noise disturbances. Among the various actuators employed for ameliorating aforementioned issue, the synthetic jet known actuator has been notified. In the beginning of this study, the sinusoidal synthetic configuration has been investigated, and related equations have been extracted. In order of comparing the results, two cases of studies including without and with jet were studied. In the first part of study, the numerical analysis has been conducted to validate the gathered results from the reference studies in the literature using ANSYS FLUENT. The results have concluded that simulation results had the acceptable agreement with the previously conducted reference studies. In the next step, the main Computational Fluid Dynamics simulation part of this study including the single sinusoidal synthetic jet over the step wall was carried out in three different Reynolds numbers as 200, 300, and 400. Having carried out the simulation related to the with-jet case, discrete transfer function was extracted using systemIdentification toolbox of MATLAB. The transfer function with 5 poles and 4 zeros reached the desirable agreement with the reference data. The achieved transfer function was utilized in the SIMULINK models being designed for testing the various Proportional-Integral-Differential (PID) controller configurations. Three types of conventional, Fuzzy and optimized fuzzy PID controllers were considered for investigation and comparison. Three gains including proportional (Kp ′), integral (α) and derivative (Kd ′) of the PID controller were tuned based on classical Ziegler–Nichols and Fuzzy Inference System (FIS). The results revealed that the fuzzy-PID controller has better efficiency regarding the overshoot, rising time and settling time criteria in comparison with conventional PID controller. To reach the better performance of the fuzzy-PID controller, two methods of genetic algorithm and particle swarm optimization methods were employed. Subsequently, the optimized fuzzy inference system from this method was inserted in the SIMULINK model and optimized fuzzy PID controller was constructed. The comparison between three defined PID controllers (conventional, fuzzy, optimized fuzzy) were conducted using the designed SIMULINK model. The results showed that the least values of overshoot, rising time and settling was belonging to the optimized fuzzy PID controller based on defined cost function criteria. After that, instead of applying the extracted transfer function, ANSYS FLUENT was coupled with SIMULINK. The obtained results revealed that the designed PID controller was able to define a desirable amplitude for the jet where the fluctuation of the drag coefficient has been eliminated and the magnitude of the recirculation length became less than value of the without jet case of study by 17.35 %. Furthermore, eliminating the fluctuations of the drag coefficient leads to less consuming energy of the jet which is the another benefits of the applying optimized fuzzy-PID controller. Finally, the results are investigated in detail considering the underlying physical phenomena around the step wall. In the next step, the main CFD simulation part of this study including the single sinusoidal synthetic jet over the step wall was carried out in three different Reynolds numbers as 200, 300, and 400. Having carried out the simulation related to the with-jet case, discrete transfer function related to the 400 Reynolds number was extracted using systemIdentification toolbox of MATLAB. The transfer function with 5 poles and 4 zeros reached the desirable agreement with the reference data, and validated based on 200 and 300 Reynolds numbers. The achieved transfer function was utilized in the SIMULINK models being designed for testing the various upcoming Proportional-Integral-Differential (PID) controller configurations. Three types of conventional, Fuzzy and optimized fuzzy PID controllers were considered for investigation and comparison. Three gains including proportional (Kp ′), integral (α) and derivative (Kd ′) of the PID controller were tuned based on classical Ziegler–Nichols and Fuzzy Inference System (FIS). The results revealed that the fuzzy-PID controller has better efficiency regarding the overshoot, rising time and settling time criteria in comparison with conventional PID controller. To reach the better performance of the fuzzy-PID controller, two methods of genetic algorithm and particle swarm optimization methods were employed. The tournament selection method based on bisector defuzzification showed the least value of the cost function and Number of Function Evaluation with respect two other selection methods. Subsequently, the optimized fuzzy inference system from this method was inserted in the SIMULINK model and optimized fuzzy PID controller was constructed. The comparison between three defined PID controllers (conventional, fuzzy, optimized fuzzy) were conducted using the designed SIMULINK model. The results showed that the least values of overshoot, rising time and settling was belonging to the optimized fuzzy PID controller based on normalized cost function criteria. After that, instead of applying the extracted transfer function, ANSYS FLUENT was coupled with SIMULINK. The obtained results revealed that the designed PID controller was able to define a desirable amplitude for the jet where the fluctuation of the drag coefficient has been eliminated and the magnitude of the recirculation length became less than value of the without jet case of study by 17.35 %. Additionally, the results depicted that the designed SIMULINK model with considering the optimized fuzzy-PID controller is able to reach the defined drag coefficient being less than the sinusoidal jet without PID case of study. Furthermore, eliminating the fluctuations of the drag coefficient leads to less consuming energy of the jet which is the another benefits of the applying optimized fuzzy-PID controller. Finally, the dimensional analysis of the fluid physical phenomena around the step wall was conducted. The results concluded that the height and width of the secondary vortex for the with sinusoidal jet tuned by optimized fuzzy PID controller is higher than the without-jet case of study.