A numerical simulation of a single-reed instrument with a pressure chamber is conducted to examine the interaction among the flow, reed oscillation, and acoustic propagation. The flow and acoustic fields are predicted using the three-dimensional compressible Navier-Stokes equations, whereas the one-dimensional dynamic beam equation is solved for reed oscillation. The deforming geometry in the aeroacoustic field is expressed by the volume penalization method as an immersed boundary technique. The results showed that the waveforms of the tip opening and far-field acoustic spectra agreed well with those measured experimentally. The three-dimensional flow configuration near the tip opening was visualized, and the measurement of the instantaneous volume flow rate at the tip opening revealed that 30%-40% of the total flow rate passed through the side opening. The spectral tendencies of the time derivatives of the flow rate for different tip openings were consistent with that of the far-field sound, indicating that the slope of the flow rate waveform significantly affects the generated sound's harmonics.