Pressure calculation for flows with moving surface boundaries from particle tracking velocimetry (PTV)
The examples of flow conditions, where an object of a fixed or deformable body moves in a fluid, or the interface between the flow phases instantaneously changes its topology, are numerous in industry and natural sciences. The advent of particle image velocimetry (PIV)  and particle tracking velocimetry (PTV)  enabled the measurement of the instantaneous velocity fields in these types of complicated flow fields. As a next step, several methodologies have been developed in the past decade to calculate the pressure fields from PIV or PTV data [3,4]. These methods were developed based on the assumption of a stationary flow domain, with surface boundaries that are fixed and independent of time. This makes the current pressure calculation methods inapplicable to a flow domain with deformable moving surface boundaries. Also, for most of the two-phase flows, the capillary forces are significant and the pressure drop over the two-phase interface must be considered. Therefore, the current pressure calculators require an improvement in the formulation of the algorithms to account for the deformable volume conditions and the effect of the surface tension force. For the calculation of pressure from sparse PTV velocity data, firstly, a tessellation method is required to interconnect the irregularly spaced vectors in the flow field using a highquality mesh grid. The mesh must be dynamic and adjust itself to the moving boundaries. This tessellation method has already been developed by the current authors . As the next step, equations of motion for a deformable C.V. need to be coupled with the tessellation method to calculate the instantaneous pressures in a two-phase flow field, with a moving interface, which will be the ultimate goal of the current study.
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