  Aims. We estimate the number of pulsars, detectable as continuous
gravitational wave sources with the current and future gravitational-wave
detectors, assuming a simple phenomenological model of evolving non-axisymmetry
of the rotating neutron star.
  Methods. We employ a numerical model of the Galactic neutron star population,
with the properties established by comparison with radio observations of
isolated Galactic pulsars. We generate an arbitrarily large synthetic
population of neutron stars and evolve their period, magnetic field, and
position in space. We use a gravitational wave emission model based on
exponentially decaying ellipticity - a non-axisymmetry of the star, with no
assumption of the origin of a given ellipticity. We calculate the expected
signal in a given detector for a 1 year observations and assume a detection
criterion of the signal-to-noise ratio of 11.4 - comparable to a targeted
continous wave search. We analyze the population detectable separately in each
detector: Advanced LIGO, Advanced Virgo, and the planned Einstein Telescope. In
the calculation of the expected signal we neglect signals frequency change due
to the source spindown and the Earth motion with respect to the Solar
barycentre.
  Results. With conservative values for the neutron stars evolution: supernova
rate once per 100 years, initial ellipticity $\epsilon_{0}$ = 1e-5 with no
decay of the ellipticity $\eta$ = $t_\rm{hub}$ = 1e4 Myr, the expected number
of detected neutron stars is below one: 0.15 (based on a simulation of 10 M
stars) for the Advanced LIGO detector. A broader study of the parameter space
($\epsilon_{0}$ , $\eta$) is presented. With the planned sensitivity for the
Einstein Telescope, and assuming the same ellipiticity model, the expected
detection number is: 26.4 pulsars during a 1-year long observing run.
