Effect of wall heat transfer on shock-tube test temperature at long times

When performing chemical kinetics experiments behind reflected shock waves at conditions of lower temperature ( \u3c 1,000 K), longer test times on the order of 10-20 ms may be required. The integrity of the test temperature during such experiments may be in question, because heat loss to the tube walls may play a larger role than is generally seen in shock-tube kinetics experiments that are over within a millisecond or two. A series of detailed calculations was performed to estimate the effect of longer test times on the temperature uniformity of the post-shock test gas. Assuming the main mode of heat transfer is conduction between the high-temperature gas and the colder shock-tube walls, a comprehensive set of calculations covering a range of conditions including test temperatures between 800 and 1,800 K, pressures between 1 and 50 atm, driven-tube inner diameters between 3 and 16.2 cm, and test gases of N(2) and Ar was performed. Based on the results, heat loss to the tube walls does not significantly reduce the area-averaged temperature behind the reflected shock wave for test conditions that are likely to be used in shock-tube studies for test times up to 20 ms (and higher), provided the shock-tube inner diameter is sufficiently large ( \u3e 8cm). Smaller diameters on the order of 3 cm or less can experience significant temperature loss near the reflected-shock region. Although the area-averaged gas temperature decreases due to the heat loss, the main core region remains spatially uniform so that the zone of temperature change is limited to only the thermal layer adjacent to the walls. Although the heat conduction model assumes the gas and wall to behave as solid bodies, resulting in a core gas temperature that remains constant at the initial temperature, a two-zone gas model that accounts for density loss from the core to the colder thermal layer indicates that the core temperature and gas pressure both decrease slightly with time. A full CFD solution of the shock-tube flow field and heat transfer at long test times was also performed for one typical condition (800 K, 1 atm, Ar), the results of which indicate that the simpler analytical conduction model is realistic but somewhat conservative in that it over predicts the mean temperature loss by a few Kelvins. This paper presents the first comprehensive study on the effects of long test times on the average test gas temperature behind the reflected shock wave for conditions representative of chemical kinetics experiments