Calculation of added water mass effects for reactor system components

The vibrations of many components of reactor systems such as heat exchanger tubes and rectangular channels are greatly affected by the interaction of these components with the surrounding water. The inertial properties of the water can be represented by an added mass matrix, which is an expression of such interaction. A computational approach is presented, based on the finite element method, for deriving the added mass matrix of complex systems of components. The method is two-dimensional, and is valid for long axial bodies of arbitrary cross section which are defined by a nodal grid. The results are expressed in mass per unit axial length. No account is taken of end leakage and similar effects. The method is based on the successive solutions of Laplace's equation for a number of fundamental boundary conditions (in which each body in turn is given a unit acceleration in two orthogonal directions, one at a time). Examples are given concerning the added mass matrices of well known configurations (for instance, concentric cylinders) in order to demonstrate the accuracy of the method. Examples are also given of more complex configurations involving pipes and channels found in reactors