Abstract
A new model for flow though rapidly expanding ducts is proposed. Experiments by others have shown that unsteady flows deviate from quasi steady behavior, in particular that rapidly increasing (ie impulsive) flows exhibit less flow separation than equivalent steady flows. This unsteady effect is analyzed here from the perspective of pressure recovery. This approach differs from others as it does not directly involve tuning flow area coefficients. Three common models for flow in expanding ducts are presented and described, namely the isentropic flow model, the constant pressure (or equal pressure) model and the momentum equation model. A fourth model is developed using the energy equation. The model is called the deceleration model and contains a term for the local acceleration of the flow in order to account for the unsteadiness of the flow. The four alternative models are then compared to experimental results for a single flow pulse through ducts with rapid increase in area. The deceleration model performs the best of all the models although the momentum model is also generally good. Finally the four alternative models are compared to one another in a full simulation of a two stroke engine with a tuned exhaust pipe. The differences between the models results are small though not insignificant. It is hoped that the insights presented here stimulate further thinking on the issue and yield improvement in 1D gas dynamics simulations of difficult-to-model regions such as diffusers, valves, throttles, ports, and multi pipe junctions.
Keywords: 1D gas dynamics, unsteady, flow separation, pressure recovery