Leakage Rates Through Complex Crack Paths Using an ODE Method

Abstract

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.

Role of welding residual stress in stainless steel piping with application of the leak-before-break technology

“…In the Henry-Fauske model (Abdollahian and Chexal, 1983;Gill et al, 2015), the parameters of the crack flow path through the wall include the crack opening area (COA), the area ratio of the exit to the entrance of the flow path, the surface roughness of the crack, and the number of crack channel corners. These factors can affect pressure loss during medium leakage.…”

“…For uniform and unbalanced two-phase flow, the Henry-Fauske model is employed for the medium leakage rate analysis (Abdollahian and Chexal, 1983;Gill et al, 2015). In the case of saturated vapor in the piping, the continuity equation of the fluid reads:…”

“…Assuming that an expansion process of vapor is an isoentropy process which follows the thermodynamic equilibrium of ideal gases, Eq. 6 (Abdollahian and Chexal, 1983;Gill et al, 2015) could be derived from Eqs. (3 & (5).…”