The complex three-way interaction between airflow, tissue, and sound, for asymmetric vocal fold vibration, is not well understood. Current modeling efforts are not able to explain clinical observations where drastic differences in sound production are often observed, with no noticeable differences in the vocal fold kinematics. To advance this understanding, an acoustical model for voiced sound generation in the presence of asymmetric intraglottal flows is developed. The source model operates in conjunction with a wave reflection analog propagation scheme and an asymmetric flow description within the glottis. To enable comparison with prior work, the source model is evaluated using a well-studied two-mass vocal fold model. The proposed source model is evaluated through acoustic measures of interest, including radiated sound pressure level, maximum flow declination rate, and spectral tilt, and also via its effects on the vocal fold dynamics. The influence of the model, in comparison to the standard symmetric Bernoulli flow description, results in an increased transfer of energy from the fluid to the vocal folds, increased radiated sound pressure level and maximum flow declination rate, and decreased spectral tilt. These differences are most pronounced for asymmetric vocal fold configurations that mimic unilateral paresis and paralysis, where minor kinematic changes can result in significant acoustic and aerodynamic differences. The results illustrate that fluid effects arising from asymmetric glottal flow can play an important role in the acoustics of pathological voiced speech.