Adjoint-based optimization for inkjet printing
University of Cambridge
Doctor of Philosophy (PhD)
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Kungurtsev, P. (2020). Adjoint-based optimization for inkjet printing (Doctoral thesis). https://doi.org/10.17863/CAM.79199
In this thesis the flow inside inkjet printhead microchannels is analysed using a two- parameter low Mach number expansion of the compressible Navier–Stokes equations and a reduced order model for the free surface flow inside the inkjet nozzle. The channel flow is separated into equations for an incompressible flow with no acoustic oscillations and equations for thermoviscous acoustic oscillations with no mean flow. This thesis concerns two types of optimal control problems. The optimal control problem of the first type is finding a velocity profile of the piezo-electric actuator that eliminates residual oscillations after a droplet is ejected. The cost function is the sum of the acoustic energy in the channel and the surface energy of the spherical cap of ink at the end of the nozzle at a given time. This problem is approached by obtaining the sensitivity of the total energy inside an inkjet microchannel with respect to boundary forcing using the adjoint method. Using gradient-based optimization algorithms, optimal waveforms are found that minimize the objective value at various final times and for geometries with increasing complexity. Physical interpretation to the optimal waveforms profiles is provided, and the exploited mechanisms are revealed. The optimal control problem of the second type is finding a shape of the inkjet printhead channel that maximises dissipation of the acoustic oscillations, without increasing the pressure drop required to drive the steady flow. Similarly, the adjoint approach is used to obtain the sensitivity of the acoustic flow eigenvalues with respect to boundary deformations in Hadamard form. Knowing the shape sensitivity of the incompressible flow viscous dissipation, the constrained optimization problem is solved to find a design that has the same viscous dissipation for the steady flow but a 40% larger decay rate for the oscillating flow. The final shape is not straightforward and would have been difficult to achieve through physical insight or trial and error. It could be improved further by adapting the parameters that describe the shape, but in this case the improvement would be small. The method is general and could be applied to many different applications in microfluidics. In summary, the methods in this thesis are promising techniques in the design and optimization of inkjet printheads. The discussed numerical techniques and the gained physical understanding can be used to automatically find the optimal design parameters, or, at a minimum, accelerate the experimental trial and error processes.
inkjet printing, adjoint based optimization
This project has received funding from the European Unions Horizon 2020 research and innovation programme under Grant Agreement No. H2020-MSCA-ITN-2015.
European Commission Horizon 2020 (H2020) Marie Sk?odowska-Curie actions (675008)
This record's DOI: https://doi.org/10.17863/CAM.79199
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