Shock Waves (2011) 21:1–17 DOI 10.1007/s00193-010-0282-y ORIGINAL ARTICLE Effect of wall heat transfer on shock-tube test temperature at long times C. Frazier · M. Lamnaouer · E. Divo · A. Kassab · E. Petersen Received: 30 September 2009 / Revised: 1 February 2010 / Accepted: 6 September 2010 / Published online: 9 October 2010 © Springer-Verlag 2010 Abstract When performing chemical kinetics experiments behind reflected shock waves at conditions of lower temper- ature (<1,000 K), longer test times on the order of 10–20 ms may be required. The integrity of the test temperature dur- ing 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. Assum- ing 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 condi- tions 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 (>8 cm). Smaller diameters on the order Communicated by R. Hanson. A part of this paper is based on work that was presented at the 26th International Symposium on Shock Waves, Goettingen, Germany, 15–20 July 2007. C. Frazier · E. Petersen (B ) Department of Mechanical Engineering, Texas A&M University, College Station, TX, USA e-mail: epetersen@tamu.edu M. Lamnaouer · E. Divo · A. Kassab Mechanical, Materials and Aerospace Engineering, University of Central Florida, Orlando, FL, USA 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 temper- ature 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 temper- ature 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 sim- pler 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 compre- hensive study on the effects of long test times on the average test gas temperature behind the reflected shock wave for con- ditions representative of chemical kinetics experiments. Keywords Shock tube · Heat transfer · Chemical kinetics · Driver gas tailoring · CFD 1 Introduction Shock-tube experiments have traditionally been performed at short test times (around 1 ms) with the assumption that such a short test time allows the region behind the reflected shock wave to be considered isothermal. Often, high test temperatures greater than about 1,400 K are used to ensure chemical reaction occurs within these short test times and maintain thermal integrity, as lower test temperatures would slow down the chemistry; the longer test times could result 123