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
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