Thermal and internal acoustic model of a Helmholtz-type pulse combustion furnace

The primary objectives of the present research were the development and validation of a simplified model to predict the thermal and internal acoustic performance of a pulse combustion furnace. The central component of the model was an acoustic analysis, based on the Helmholtz resonator analogy, which predicts the transient pressures in the pulse combustor and the operating frequency. The other key element of the model is the thermal analysis capability which provides time-mean heat transfer rates and temperatures. This is accomplished through a one-dimensional or zero-dimensional analysis for each of the main furnace components. The acoustic and thermal models are supported by an improved analysis of the gas motion in the tail pipe (based on the wave equation), flapper valve motion and mass flow models, a combustion heat release analysis, and quasi-steady friction models for the pipes of the pulse combustor. This approach minimizes the need for empirical data. The model was validated by two methods: an experimental validation and a parametric study validation. Predictions of the operating parameters were compared to experimental measurements (pressures, frequency, mass flow rates, and temperatures) for a standard furnace and also a prototype furnace. The acoustic model predicted the qualitative behavior of the furnace well; however, the predictions were low for the operating frequency (20% low) and the exhaust decoupler pressure amplitude (30% low). Predictions of the flapper motion in the flapper valve were validated using experimental measurements of the flapper movement. The predictions of the component heat transfer rates were in excellent agreement with the experimental data. The overall model results were in excellent qualitative agreement with the experimental data as demonstrated by comparison of the predicted results and experimental data for operation at reduced input rates. The second validation technique used parametric studies to determine trends in the operating parameters which were then compared to data reported in the literature for pulse combustor experimental studies. The parametric studies were successful in confirming the capability of the model to predict trends in the operating parameters, which was an objective of the present work. Previous acoustic (lumped parameter) models have lacked an evaluation of the pulse combustor thermal performance and have required experimental or empirical inputs; therefore, the present approach is considered to be a useful contribution to simplified pulse combustor modeling