  Several binary black holes (BBHs) have been observed using gravitational wave
detectors. For the formation mechanism of BBHs, two main mechanisms, isolated
binary evolution and dynamical formation in dense star clusters, have been
suggested. Future observations are expected to provide more information about
BBH distributions, and it will help us to distinguish the two formation
mechanisms. For the star cluster channel, globular clusters have mainly been
investigated. However, recent simulations have suggested that BBH formation in
open clusters is not negligible. We estimate a local merger rate density of
BBHs originated from open clusters using the results of our $N$-body
simulations of open clusters with four different metallicities. We find that
the merger rate per cluster is the highest for our 0.1 solar metallicity model.
Assuming a cosmic star formation history and a metallicity evolution with
dispersion, we estimate the local merger rate density of BBHs originated from
open clusters to be $\sim 70~{\rm yr}^{-1} {\rm Gpc}^{-3}$. This value is
comparable to the merger rate density expected from the first and second
observation runs of LIGO and Virgo. In addition, we find that BBH mergers
obtained from our simulations can reproduce the distribution of primary mass
and mass ratio of merging BBHs estimated from the LIGO and Virgo observations.
