  In this paper we present two concrete models of non-perfect fluid with bulk
viscosity to interpret the observed cosmic accelerating expansion phenomena,
avoiding the introduction of exotic dark energy. The first model we inspect has
a viscosity of the form ${\zeta} = {\zeta}_0 + ({\zeta}_1-{\zeta}_2q)H$ by
taking into account of the decelerating parameter q, and the other model is of
the form ${\zeta} = {\zeta}_0 + {\zeta}_1H + {\zeta}_2H^2$. We give out the
exact solutions of such models and further constrain them with the latest
Union2 data as well as the currently observed Hubble-parameter dataset (OHD),
then we discuss the fate of universe evolution in these models, which confronts
neither future singularity nor little/pseudo rip. From the resulting curves by
best fittings we find a much more flexible evolution processing due to the
presence of viscosity while being consistent with the observational data in the
region of data fitting. With the bulk viscosity considered, a more realistic
universe scenario is characterized comparable with the {\Lambda}CDM model but
without introducing the mysterious dark energy.
