Adjoint-based shape optimisation for viscothermal acoustic flow in inkjet printheads

A drop-on-demand inkjet printhead is a narrow channel containing a piezo-electric actuator and a small orifice. Ink is pumped continuously through the channel. When the actuator pulses, it pushes a droplet out of the orifice. After each pulse, acoustic reverberations remain in the channel until they decay due to viscous and thermal dissipation, or propagate out of the channel. If the next droplet is demanded before the reverberations have sufficiently died away, it can differ from previous droplets, reducing print quality. We formally split the compressible Navier-Stokes equations into (i) an incompressible steady flow and (ii) a viscothermal acoustic flow. We useA drop-on-demand inkjet printhead is a narrow channel containing a piezo-electric actuator and a small orifice. Ink is pumped continuously through the channel. When the actuator pulses, it pushes a droplet out of the orifice. After each pulse, acoustic reverberations remain in the channel until they decay due to viscous and thermal dissipation, or propagate out of the channel. If the next droplet is demanded before the reverberations have sufficiently died away, it can differ from previous droplets, reducing print quality. We formally split the compressible Navier-Stokes equations into (i) an incompressible steady flow and (ii) a viscothermal acoustic flow. We use adjoint method to derive the shape sensitivity of (i) the incompressible flow pressure drop and (ii) the acoustic decay rate in Hadamard form, and combine the sensitivities with the CAD representation of the channel's geometry. We use the method of moving asymptotes for shape optimization of a generic geometry and increase the decay rate by 50% while keeping the pressure drop constant.