Using two dimensional Langevin dynamics simulations, we investigate the dynamics of polymer translocation into a fluidic channel with diameter $R$ through a nanopore under a driving force $F$. Due to the crowding effect induced by the partially translocated monomers, the translocation dynamics is significantly altered in comparison to an unconfined environment, namely, we observe a nonuniversal dependence of the translocation time $tau$ on the chain length $N$. $tau$ initially decreases rapidly and then saturates with increasing $R$, and a dependence of the scaling exponent $alpha$ of $tau$ with $N$ on the channel width $R$ is observed. The otherwise inverse linear scaling of $tau$ with $F$ breaks down and we observe a minimum of $alpha$ as a function of $F$. These behaviors are interpreted in terms of the waiting time of an individual segment passing through the pore during translocation.