Research on the Mathematic Model of Air Valve

Air valve is an important measure of water hammer protection in long water distribution system. Volume of air inflow and outflow, the maximum volume of air inflow, and air mass flow rate are not only relate to prefer choose of air valve type, but effect on the safety of water distribution engineering. So it is important to make a theoretical calculation of air valve precisely. Traditional mathematic model of valve assumes that air inflows and outflows the pipeline by isentropic process, then isothermal variation will occur. Though this model is simple in theory and its programming is easy, its two thermodynamic processes are not incongruous obviously which results in its physical achievement unexplainable theoretically. Because the isentropic process is reversible adiabatic and no heat exchange occurs, but achievement of isotherm process need heat exchange sufficiently. This paper raises a new mathematic model of air valve based on those models reported so far. The new model gives up the hypothesis of isotherm, and proves rationality of this model by mathematical induction. Calculation results of two mathematic models are compared by numerical analysis. This provides scientific basis for precise simulation of air behavior through air valve and prefer choose of air valve type in long distribution system.