Due to individual unreliable commodity components, failures are common in large-scale distributed storage systems. Erasure codes are widely deployed in practical storage systems to provide fault tolerance with low storage overhead. However, random data distribution (RDD), commonly used in erasure-coded storage systems, induces heavy cross-rack traffic, load imbalance, and random access, which adversely affects failure recovery. In this paper, with orthogonal arrays, we define a Deterministic Data Distribution ($D^3$) to uniformly distribute data/parity blocks among nodes, and propose an efficient failure recovery approach based on $D^3$, which minimizes the cross-rack repair traffic against a single node failure. Thanks to the uniformity of $D^3$, the proposed recovery approach balances the repair traffic not only among nodes within a rack but also among racks. We implement $D^3$ over Reed-Solomon codes and Locally Repairable Codes in Hadoop Distributed File System (HDFS) with a cluster of 28 machines. Compared with RDD, our experiments show that $D^3$ significantly speeds up the failure recovery up to 2.49 times for RS codes and 1.38 times for LRCs. Moreover, $D^3$ supports front-end applications better than RDD in both of normal and recovery states.