Two-phase discharge flow prediction in safety valves

Safety Relief Valves (SRV) are necessary elements in the protection of any pressurised system and the prediction of the expected discharge flows is an important consideration for the valve sizing to ensure that rupture pressures do not occur. The high speed flows that occur inside the SRV are complex particularly when a two-phase flow is involved and lead to a less capable protection device which result in larger valves compared to single phase flows. In this paper the ability of a CFD based two phase mixture model to predict the critical flows of air and water through a safety valve is examined. An industrial refrigeration safety relief valve of ¼” inlet bore size has been tested experimentally over a pressure range of 6-15 barg and air mass qualities from 0.1-1 when discharging to near atmospheric conditions for a fully open condition. A two-dimensional mixture model consisting of mixture mass, momentum, and energy equations, combined with a liquid mass equation and the standard k- ε turbulence model for mixture turbulent transport has been used to predict the two phase flows through the valve. The mixture model results have been compared with the Homogenous Equilibrium Model (HEM) commonly used for in valve sizing in non flashing two phase flow conditions. The accuracy of the models over the two phase flow range are quantified and discussed

Metastability of Certain Intermittent Maps

We study an intermittent map which has exactly two ergodic invariant densities. The densities are supported on two subintervals with a common boundary point. Due to certain perturbations, leakage of mass through subsets, called holes, of the initially invariant subintervals occurs and forces the subsystems to merge into one system that has exactly one invariant density. We prove that the invariant density of the perturbed system converges in the $L^1$-norm to a particular convex combination of the invariant densities of the intermittent map. In particular, we show that the ratio of the weights in the combination equals to the limit of the ratio of the measures of the holes.Comment: 19 pages, 2 figure

Linear response in the intermittent family: differentiation in a weighted C0C^0-norm

We provide a general framework to study differentiability of SRB measures for one dimensional non-uniformly expanding maps. Our technique is based on inducing the non-uniformly expanding system to a uniformly expanding one, and on showing how the linear response formula of the non-uniformly expanding system is inherited from the linear response formula of the induced one. We apply this general technique to interval maps with a neutral fixed point (Pomeau-Manneville maps) to prove differentiability of the corresponding SRB measure. Our work covers systems that admit a finite SRB measure and it also covers systems that admit an infinite SRB measure. In particular, we obtain a linear response formula for both finite and infinite SRB measures. To the best of our knowledge, this is the first work that contains a linear response result for infinite measure preserving systems.Comment: Final version. To appear in DCDS-

Prediction of two-phase flow through a safety relief valve

Safety relief valves are necessary elements in any pressurised system. The flow inside the safety relief valve shows a number of interesting, yet complicated, features especially when a two-phase flow is involved. Consequently, developing an efficient and accurate means for predicting the safety relief valve performance and understanding the flow physics is a demanding objective. In this article, the ability of a two-phase mixture model to predict the critical flows of air and water through a safety valve is examined. An industrial refrigeration safety relief valve of ¼” inlet bore size has been tested experimentally over a pressure range of 6–15 barg and air mass qualities from 0.23 to 1 when discharging to near atmospheric conditions for a range of valve lift positions. A two-dimensional mixture model consisting of mixture mass, momentum and energy equations, combined with a liquid mass equation and the standard k-e turbulence model for mixture turbulent transport has been used to predict the two-phase flows though the valve. The mixture model results have been compared with the homogenous equilibrium model and the homogenous non-equilibrium model adopted by the ISO standard. It has been shown that the mixture model can be used satisfactorily to predict the mass flows for the above conditions. Overall, the accuracy of the two-phase air mass flow for given inlet liquid flow rates can be predicted to within 15%

Escape Rates Formulae and Metastability for Randomly perturbed maps

We provide escape rates formulae for piecewise expanding interval maps with `random holes'. Then we obtain rigorous approximations of invariant densities of randomly perturbed metabstable interval maps. We show that our escape rates formulae can be used to approximate limits of invariant densities of randomly perturbed metastable systems.Comment: Appeared in Nonlinearity, May 201