Smartphones have recently become a popular platform for deploying the computation-intensive virtual reality (VR) applications, such as immersive video streaming (a.k.a., 360-degree video streaming). One specific challenge involving the smartphone-based head mounted display (HMD) is to reduce the potentially huge power consumption caused by the immersive video. To address this challenge, we first conduct an empirical power measurement study on a typical smartphone immersive streaming system, which identifies the major power consumption sources. Then, we develop QuRate, a quality-aware and user-centric frame rate adaptation mechanism to tackle the power consumption issue in immersive video streaming. QuRate optimizes the immersive video power consumption by modeling the correlation between the perceivable video quality and the user behavior. Specifically, QuRate builds on top of the user's reduced level of concentration on the video frames during view switching and dynamically adjusts the frame rate without impacting the perceivable video quality. We evaluate QuRate with a comprehensive set of experiments involving 5 smartphones, 21 users, and 6 immersive videos using empirical user head movement traces. Our experimental results demonstrate that QuRate is capable of extending the smartphone battery life by up to 1.24X while maintaining the perceivable video quality during immersive video streaming. Also, we conduct an Institutional Review Board (IRB)-approved subjective user study to further validate the minimum video quality impact caused by QuRate.