Performance of Double Pipe Heat Exchanger—Partially Occupied by Metal Foam—Is Better Enhanced Using Robust Adaptive Barrier Function-Based Sliding Mode Control

Numerous thermal practical applications utilize shell and tube heat exchanger appliances to transfer heat energy between hot and cold working fluids. Incorporating metal foam to the outer periphery of inner tube improves the heat transfer process from hot water in the tube side to cold water in the shell side and consequently improves heat exchanger performance. In this study, the integration of use of a porous material together with designing a robust adaptive controller could efficiently regulate the outlet cold water temperature to the desired value. This is achieved with respect to the time required for cold water to reach the desired temperature (settling time) and the amount of hot water volume flow during a certain time span. A barrier function-based adaptive sliding mode controller (BF-based adaptive SMC) is proposed, which requires only the information of temperature measurement of cold water. The stability of BF-based adaptive SMC is proved utilizing Lyapunov function analysis. The effectiveness of proposed controller is verified via numerical results, which showed that the proposed controller could achieve considerable accuracy of cold water temperature using suitable design parameters. In addition, the robustness of controller against variation in inlet temperature is also verified. Another improvement to performance of heat exchanger system is achieved by adding the metal foam of aluminum material on inner pipe perimeter with wide range of metal foam to outer inner pipe diameters ratio (1≤s≤1.8). The results showed that the settling time is significantly reduced which enables outlet cold water to reach the required temperature faster. With respect of the case of non-adding metal foam on inner pipe outer circumference, when s=1.2, the settling time and hot water temperature are reduced by 1/2 and 17.3%, respectively, while for s=1.8, they are decreased by ≤1/20 and 35.3% correspondingly. Accordingly, the required volume flow for hot water is reduced considerably.