Leakage Rates Through Complex Crack Paths Using an ODE Method

The geometry of a crack is a fundamental consideration when calculating leakage rates for Leak-before-Break assessments. Carrying out fluid mechanics calculations does not give any additional benefit if there is not enough information on the crack shape. To address this issue, work is being carried out under the R6 development programme to derive a model that couples fluid mechanics and solid mechanics. The aim is to combine complex crack shapes with relatively simple fluid mechanics models and compare with experimental data. Then, the model can be extended to examine various stress distributions, and give indications as to how conservative are the current models. The model is a development of the one presented in a previous PVP paper (Reference 1), and a special case of isothermal gas flow is considered, where the equations reduce to an Ordinary Differential Equation (ODE). This is solved using a Runge-Kutta integration scheme in MATHCAD. A test case is presented based on the crack geometries considered in experiments, and upon comparison with numerical results; it is clear that choosing the correct crack shape is crucial in obtaining accurate predictions of leak rate. The assumed crack openings are rectangular, diamond or elliptical. In addition to this, weld residual stress profiles are postulated, based on experience of welds in piping components. Comparing the numerical simulations with the simplified DAFTCAT model indicates that the more precise ODE method can reduce conservatism in calculation of leak rates.