A distributed mathematical model for pressure transient analysis in railway pneumatic brake system

Abstract

A distributed mathematical model consisting of one-dimensional continuity and momentum equations is formulated to simulate the pressure and velocity changes in a pneumatic brake system, which has a common feeder pipe or train pipe connected to a number of brake cylinders. The one-dimensional non-linear partial differential equations for the train pipe and ordinary differential equation for the constant volume brake cylinder are solved to determine the transients due to a step change in pressure at the inlet. The system of non-linear partial differential equations in the model is first reduced to a set of ordinary non-linear differential difference equations and then solved by standard numerical methods. The flow is considered to be either isothermal or reversible adiabatic with friction effects, evaluated using a quasi-steady state approximation. The theoretical results are compared with experimental values and discussed.