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Adsorption is a retention mechanism of fluid molecules on solid surfaces and presents a wide range of applications, such as fuel storage, refrigeration and separation processes. This work describes the modelling of gas adsorption on porous media and presents an optimisation approach for the design of adsorption systems based on biphasic adsorbent beds by topology optimisation. A comprehensive formulation for the adsorption phenomenon is presented, detailing the derivation of governing equations and respective weak forms and discretisation for the implementation of the finite element method (FEM). A new topology optimisation material model based on offset hyperbolic tangents is introduced. The derivation of sensitivities is presented in detail, based on a transient adjoint problem. A diverse set of optimised adsorbed natural gas (ANG) tanks, considering real material properties of activated carbon and steel, is presented. Results indicate the suitability of the method in optimising the distribution of phases across adsorbent beds and show that biphasic ANG tanks can perform significantly better than traditional tanks.

Adsorption phenomena are encountered in several engineering applications. One of its uses is in the storage and transport of gas in the form of adsorption tanks. The exothermic nature of the adsorption process decreases adsorption capacity presenting an impetus to understand the thermal characteristics of the gas storage process. Studies using mixtures of phase change materials and adsorbents in adsorption tanks demonstrate potential improvements in the adsorption capacity of the tanks. They also show that the distribution of phase change materials and adsorbent are important. Thus, this work presents two approaches for optimising the adsorbent domain. The first is to use a semi-analytic model to determine the best homogeneous material concentration for the adsorbent and phase change material for the vessel composition. The other is to use a 2D axisymmetric model to perform FGM optimisation to distribute material in the tank. Results for both models are presented and discussed for different conditions. The study shows that, for the cylindrical geometry, FGM optimisation is always, at least, marginally better than the homogeneous distribution from the semi-analytic model. However, FGM optimisation demands more computing time increases the complexity of implementation and results assembling. The semi-analytic approach is a possible alternative for optimising adsorption systems with phase change material mixed with adsorbents.

Piezoelectric actuators are in common use for control of distributed parameter systems. We consider the topology optimization of a multiphysic model in piezoelectricity into two spatial dimensions. The topological derivative of a tracking-type shape functional is derived in its closed form for the purpose of shape optimization of piezoelectric actuators. The optimum design procedure is applied to a micromechanism which transforms the electrical energy supplemented via its piezoceramic part into the elastic energy of an actuator. The domain decomposition technique and the Steklov-Poincaré pseudodifferential boundary operator are employed in the asymptotic analysis of the shape functional defined on a part of the boundary of the elastic body under consideration. The new method of sensitivity analysis is general and can be used for shape-topological optimization in a broad class of multiphysics models. Our numerical results confirm the efficiency of the proposed approach to optimum design in multiphysics.

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