Simulation of the phonatory flow-structure interaction has been conducted in a three-dimensional, tubular shaped laryngeal model that has been designed with a high level of realism with respect to the human laryngeal anatomy. A non-linear spring-based contact force model is also implemented for the purpose of representing contact in more general conditions, especially those associated with three-dimensional modeling of phonation in the presence of vocal fold pathologies. The model is used to study the effects of a moderate (20%) vocal-fold tension imbalance on the phonatory dynamics. The characteristic features of phonation for normal as well as tension-imbalanced vocal folds, such as glottal waveform, glottal jet evolution, mucosal wave-type vocal-fold motion, modal entrainment, and asymmetric glottal jet deflection have been discussed in detail and compared to established data. It is found that while a moderate level of tension asymmetry does not change the vibratory dynamics significantly, it can potentially lead to measurable deterioration in voice quality.