Analytical analysis of single-stage pressure relief valves

摘要

The article presents an explicitly straightforward formulation of the stationary and dynamic behaviour of a pressure relief valve (PRV). This includes an analytical solution for the static p-Q-characteristic, the step and harmonic response and a stability criterion using elementary operations only. It also mathematically proves the intrinsic connection between the gradient of the static p-Q-characteristic and the stability. Thus, the new method offers four main advantages. First, it is several orders of magnitude faster because it is not necessary to solve the differential equation system numerically. Secondly, the user does not require any special knowledge or advanced calculation tools - a simple spreadsheet program is sufficient. Thirdly, sensitivity and robustness analyses can be carried out easily due to explicitly known dependencies. Last but not least, the understanding of a PRV is improved by directly knowing the influence of each parameter. The method was tested and verified by comparison with conventional nonlinear numerical simulations using independent test cases.