A Mean Value Model for Unsteady Gas Flows and Heat Transfer in Pipes

Pipes are essential components in engines and therefore models of them are important. For example, the aftertreatment system for modern heavy-duty diesel engines consists of multiple components that are connected using pipes. The temperature in each of these components are important when determining the efficiency of the aftertreatment system and therefore models that accurately describe the temperature in the pipes between the components are important. Here, a dynamic pipe model that combines the adiabatic model of a control volume and that of a stationary one-dimensional flow with heat transfer in a pipe is developed and validated. The resulting model is a quasi-dimensional lumped parameter mean value model containing states for the temperature and pressure of the gas inside the pipe and the temperature of the pipe wall. The model uses the states and convective heat transfer models to calculate pressure at the inlet and outlet as well as temperature at the outlet, in a way that is physically correct under certain conditions. To validate the physical behavior of the model a detailed one-dimensional model is used, and to validate the practical applicability and accuracy of the model data from a passenger car gasoline engine is used to parameterize and validate the model.