Two-dimensional time-domain numerical investigation of sound-induced flow through an orifice with a diameter 6mm is conducted by using lattice Boltzmann method. Emphasis is placed on characterizing its acoustic damping behaviors. The main damping mechanism is identified as incident waves interact with the shear layers formed at the orifices rims and the acoustic oscillations destabilize the shear layers to form vortex rings. And acoustic energy is converted into vortical energy. To quantify the orifice damping effect, power absorption coefficient is used. It is related to Rayleigh conductivity and describes the fraction of incident acoustical energy being absorbed. Numerical simulations are conducted in time domain by forcing a fluctuating flow with multiple tones through the orifice. This is different from frequency-domain simulations, of which the damping is characterized one frequency at a time. Comparing our results with those from Howe theoretical model, good agreement is observed. In addition, orifice thickness effect on its damping is discussed.