Abstract
When performing chemical kinetics experiments behind reflected shock waves at conditions of lower temperature (<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 N2 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 (>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.
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Amadio A.D., Crofton M.W., Petersen E.L.: Test-time extension behind reflected shock waves using CO2−He and C3H8−He driver mixtures. Shock Waves 16, 157–165 (2006)
de Vries J., Petersen E.L.: Autoignition of methane-based fuel blends under gas turbine conditions. Proc. Combust. Inst. 31, 3163–3171 (2007)
Davidson D.F., Hanson R.K.: Recent advances in shock tube/ laser diagnostic methods for improved chemical kinetics measurements. Shock Waves 19, 271–283 (2009)
Hong Z., Pang G.A., Vasu S.S., Davidson D.F., Hanson R.K.: The use of driver inserts to reduce non-ideal pressure variations behind reflected shock waves. Shock Waves 19, 113–123 (2009)
Hong Z., Davidson D.F., Hanson R.K.: Contact surface tailoring condition for shock tubes with different driver and driven section diameters. Shock Waves 19, 331–336 (2009)
Bromberg R.: Use of the shock tube wall boundary layer in heat transfer studies. Jet Propuls. 26, 737–740 (1956)
Hartunian R.A., Russo A.L., Marrone P.V.: Boundary-layer transition and heat transfer in shock tubes. J. Aerosp. Sci. 27, 587–594 (1960)
Mirels, H.: Laminar boundary layer behind shock advancing into stationary fluid. NACA TN 3401 (1955)
Mirels, H.: Boundary layer behind shock or thin expansion wave moving into stationary fluid. NACA TN 3712 (1956)
Wilson G.J., Sharma S.P., Gillespie W.D.: Time-dependent simulation of reflected-shock/boundary layer interaction in shock tubes. In: Brun, R., Dumitrescu, L.Z. (eds) Shock Waves @Marseille I-Proceedings of the 19th International Symposium on Shock Waves, pp. 439–444. Springer, Berlin (1995)
Nishida, M., Lee, M.G.: Reflected shock side boundary layer interaction in a shock tube. In: Hornung, H.G., Shepherd, J.E., Sturtevant, B. (eds.), Proceedings of the 20th International Symposium on Shock Waves, vol. I, pp. 705–710. World Scientific, New York (1996)
Goldsworthy F.A.: The structure of a contact region, with application to the reflexion of a shock from a heat-conducting wall. J. Fluid Mech. 5, 164–176 (1959)
Sturtevant B., Slachmuylders E.: End-wall heat-transfer studies on the trajectory of a reflected shock wave. Phys. Fluids 7, 1201–1207 (1964)
Baganoff D.: Experiments on the wall-pressure history in shock-reflexion processes. J. Fluid Mech. 23, 209–228 (1965)
Hanson, R.K.: Study of gas-solid interaction using shock-wave reflection. In: Stollery, J.L., Gaydon, A.G., Owen, P.R. (Eds.), Shock Tube Research-Proceedings of the Eighth International Shock Tube Symposium, paper 58. Chapman and Hall, London (1971)
Eckert E.M., Drake R.: Analysis of Heat and Mass Transfer. McGraw-Hill, New York (1972)
Luikov A.V.: Analytical Heat Diffusion Theory. Academic Press, New York (1968)
Petersen E.L., Rickard M.J.A., Crofton M.W., Abbey E.D., Traum M.J., Kalitan D.M.: A facility for gas- and condensed-phase measurements behind shock waves. Meas. Sci. Tech. 16, 1716–1729 (2005)
White F.M.: Viscous Fluid Flow, 2nd edn. McGraw-Hill, New York (1991)
Key, R.J., Rupley, F.M., Miller, J.A., Coltrin, M.E., Grcar, J.F., Meeks, E., Moffat, H.K., Lutz, A.E., Dixon-Lewis, G., Smooke, M.D., Warnatz, J., Evans, G.H., Larson, R.S., Mitchell, R.E., Petzold, L.R., Reynolds, W.C., Caracotsios, M., Stewart, W.E., Glarborg, P., Wang, C., Adigun, O.: Chemkin Collection, Release 3.6. Reaction Design, San Diego (2000)
Driscoll, J.F., Khatib-Shahidi, B., Liu, T., Nicholls, J.A., Patel, V.: Shock tube study of the ignition and combustion of aluminum. AIAA Paper 84-1201 (1984)
Teshima K., Deguchi M., Takahashi N.: Thermal boundary layer effects on mass sampling from a shock tube. Jpn. J. Appl. Phys. 23, 118–123 (1984)
Lamnaouer, M., Kassab A.J., Divo E., Petersen E.L.: Time accurate simulations of shock propagation and reflection in an axi-symmetric shock tube. AIAA Paper 2010-0926 (2010)
de Vries J., Aul C., Barrett A., Lambe D., Petersen E.L.: Shock-tube development for high-pressure and low-temperature chemical kinetics experiments. In: Hannemann, K., Seiler, F. (eds) Shock Waves: 26th International Symposium on Shock Waves, pp. 171–176. Springer, Berlin (2009)
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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.
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Frazier, C., Lamnaouer, M., Divo, E. et al. Effect of wall heat transfer on shock-tube test temperature at long times. Shock Waves 21, 1–17 (2011). https://doi.org/10.1007/s00193-010-0282-y
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DOI: https://doi.org/10.1007/s00193-010-0282-y