The Influence of Wall Heat Transfer, Friction, and Condensation on Detonation Tube Performance

Abstract

The authors investigated the influence of heat transfer, friction, and condensation on the performance of a single-pulse detonation tube using a combination of numerical analysis and experiments. Several different 1-D modeling strategies were considered for quantitatively predicting wall heat loss and shear stress. The merits of each approach were evaluated using benchmark results from an axisymmetric, reacting Navier-Stokes model in which the wall losses are directly resolved for a low-pressure (P 1 = 6.67 kPa) model problem. These benchmark results represent the first known attempt at directly modeling wall heat transfer and shear stress behind a multidimensional detonation wave. Comparison of the 1-D models to the benchmark results reveals a Reynolds analogy approach with a constant friction coefficient can be used to simultaneously predict convective heat loss and shear stress at the walls. The 1-D models are extended for use at higher pressure (P 1 = 1 atm) via calibration with experimental heat flux data. Although the magnitude of the wall losses increases at higher initial pressure, the relative influence of these losses on performance diminishes. To rigorously test the developed 1-D models, thrust-wall pressure measurements are recorded for stoichiometric C2H4-O2 detonations in 1.6 m long tubes with 8, 16, and 32 mm diameters. Unheated (293 K) tube wall experiments result in pressure traces showing large deviations from ideal theory. Comparison of measurements with the 1-D wall loss models reveals heat transfer and friction alone are not sufficient to reconcile theory with experiment. Additional experiments are conducted with heated (376 K) tube walls to test whether condensation of water vapor on the facility walls might account for the additional disparity between theory and measurement. Pressure traces from the heated wall experiments start closer to theory at early times and produce 66%, 31%, and 12% more specific impulse (I sp ) than the corresponding cold wall experiments for the 8, 16, and 32 mm diameter tubes, respectively. An approximate condensation model is developed and incorporated into the existing 1-D heat loss and shear stress model. It is shown for the first time that condensation can be the dominant wall loss mechanism leading to substantial performance decrement in large L/D detonation tubes.