In presently used safety valve sizing standards the gas discharge capacity is based on a nozzle flow derived from ideal gas theory. At high pressures or low temperatures real gas effects can no longer be neglected, so the discharge coefficient corrected for flow losses cannot be assumed constant anymore. Also the force balance and as a consequence the opening characteristics will be affected. In former Computational Fluid Dynamics (CFD) studies valve capacities have been validated at pressures up to 35 bar without focusing on the opening characteristic. In this thesis alternative valve sizing models and a numerical CFD tool are developed to predict the opening characteristics of a safety valve at higher pressures. To describe gas flows at pressures up to 3600 bar and for practical applicability to other gases the Soave Redlich-Kwong real gas equation of state is used. For nitrogen consistent tables of the thermodynamic quantities are generated. Comparison with experiment yielded inaccuracies below 5% for reduced temperatures larger than 1.5. The first alternative valve sizing model is the real-average model that averages between the valve inlet and the nozzle throat at the critical pressure ratio. The second real-integral model calculates small isentropic state changes from the inlet to the final critical state. In a comparison the most simple ideal model performs slightly better than the real-average model and the dimensionless flow coefficient differs less than 3% from the most accurate real-integral nozzle model. Benchmark validation test cases from which field data is available are used to investigate the relevance of the physical effects present in a safety valve and to determine the optimal settings of the CFD code ANSYS CFX. First, 1D Shock tube calculations show that strong shocks cannot be captured without oscillations, but the shock strength in a safety valve flow is small enough to be accurately computed. Second, an axisymmetric nozzle (ISO 9300) model is simulated at inlet pressures up to 200 bar with computed mass flow rate deviations less than 0.46%. Third, a supersonic ramp flow shows a dependency of the location of the separation and reattachment points on the turbulence model, where the first order accurate SST model gives the best agreement with experiment. Fourth, computations of a simplified 2D valve model by F¨ollmer show that reflecting shocks can be accurately resolved. Fifth, a comparison of mass flow rates of a pneumatic valve model results in deviations up to 5% which seems due to a 5% too high stagnation pressure at the disk front. Sixth, the computed safety valve capacities of T¨UV Rheinland Aachen overpredict the measured discharge coefficient by 18%. However, a replication of this experiment at the test facility re8 Summary duces the error to 3%. A clear reason for the large deviation with the reference data cannot be given. Lastly, the computed mass flow rates of a nozzle flow with nitrogen at pressures up to 3500 bar agrees within 5% with experiment. A high-pressure test facility has been constructed to perform tests of safety valves with water and nitrogen at operating pressures up to 600 bar at ambient temperature. The valve disk lift and flow force measurement systems are integrated in a modified pressurized protection cap so that the opening characteristics are minimally affected. The mass flow rates of both fluids are measured at ambient conditions by means of a collecting tank with a mass balance for fluids and through subcritical orifices for gases with inaccuracies of the discharge coefficient of 3 and 2.5%. Reproducible valve tests with water have been carried out at operating pressures from 64 to 450 bar. The discharge coefficient does not depend on the set pressure of the safety valve. The dimensionless flow force slightly increases with disk lift. CFD computations of selected averaged measurement points with constant disk lift show that for smaller disk lifts the mass flow rate is overpredicted up to 41%. Extending the numerical model with the Rayleigh-Plesset cavitation model reduces the errors of the mass flow rates by a factor of two. The reductions in the flow forces range from 35 to 7% at lower disk lifts. Also reproducible valve tests with nitrogen gas at operating pressures from 73 to 453 bar have been conducted. The discharge coefficient is also independent of set pressure. In contrast to the water tests, the dimensionless flow force continually decreases with disk lift. All computed mass flow rates agree within 3.6%. The computed flow forces deviate between 7.8 and 14.7%. An analysis shows that the effects of condensation, transient effects, variation of the computational domain or mechanical wear cannot explain the flow force deviation. The reason partially lies in a larger difference between the set pressure and the opening pressure of the test valve. The flow distribution around the valve spindle is sensitive to the inlet pressure and rounding of sharp edges due to mechanical wear. The cavity of the valve spindle probably causes valve chatter partially observed in the experiments and simulations. In safety valve computations with nitrogen at higher pressures up to 2000 bar and temperatures down to 175 K outside the experimentally validated region the discharge coefficient of all three valve sizing models varies less than 6% compared to the 7 bar reference value at ambient temperature. So the standardized ideal valve sizing model is sufficient for safety valve sizing. The dimensionless force, however, increases with pressure up to 34% so that the valve characteristic is affected. The influence of valve dynamics on steady state performance of a safety valve is studied by extending the CFD tool with deformable numerical grids and the inclusion of Newton’s law applied to the valve disk. The mass flow rate and disk lift are less affected, but a fast rise and collapse of the flow force due to redirection of the bulk flow has been observed during opening. Only dynamic simulations can realistically model the opening characteristic, because these force peaks have not been observed in the static approach. Furthermore, the valve geometry can be optimized without sharp edges or cavities so that redirection of the flow will result in gradual flow force changes. Then, traveling pressure waves will lead to less unstable valve operation.
|Qualification||Doctor of Philosophy|
|Award date||22 Oct 2009|
|Place of Publication||Eindhoven|
|Publication status||Published - 2009|