Rip/singularity free cosmology models with bulk viscosity

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(2)q) H by taking into account the decelerating parameter q, and the other model is of the form zeta = zeta(0) + zeta H-1 + zeta H-2(2). We give 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.