  We present the results of a search for long-duration gravitational-wave
transients in the data from the Advanced LIGO second observation run; we search
for gravitational-wave transients of $2~\text{--}~ 500$~s duration in the $24 -
2048$\,Hz frequency band with minimal assumptions about signal properties such
as waveform morphologies, polarization, sky location or time of occurrence.
Targeted signal models include fallback accretion onto neutron stars, broadband
chirps from innermost stable circular orbit waves around rotating black holes,
eccentric inspiral-merger-ringdown compact binary coalescence waveforms, and
other models. The second observation run totals about \otwoduration~days of
coincident data between November 2016 and August 2017. We find no significant
events within the parameter space that we searched, apart from the
already-reported binary neutron star merger GW170817. We thus report
sensitivity limits on the root-sum-square strain amplitude $h_{\mathrm{rss}}$
at $50\%$ efficiency. These sensitivity estimates are an improvement relative
to the first observing run and also done with an enlarged set of
gravitational-wave transient waveforms. Overall, the best search sensitivity is
$h_{\mathrm{rss}}^{50\%}$=$2.7\times10^{-22}$~$\mathrm{Hz^{-1/2}}$ for a
millisecond magnetar model. For eccentric compact binary coalescence signals,
the search sensitivity reaches
$h_{\mathrm{rss}}^{50\%}$=$9.6\times10^{-22}$~$\mathrm{Hz^{-1/2}}$.
