Navier–Stokes simulations in gappy PIV data

Velocity measurements conducted with particle image velocimetry (PIV) often exhibit regions where the flow motion cannot be evaluated. The principal reasons for this are the absence of seeding particles or limited optical access for illumination or imaging. Additional causes can be laser light reflections and unwanted out-of-focus effects. As a consequence, the velocity field measured with PIV contains regions where no velocity information is available, that is gaps. This work investigates the suitability of using the unsteady incompressible Navier–Stokes equations to obtain accurate estimates of the local transient velocity field in small gaps; the present approach applies to time-resolved two-dimensional experiments of incompressible flows. The numerics are based on a finite volume discretization with partitioned time-stepping to solve the governing equations. The measured velocity distribution at the gap boundary is taken as time-varying boundary condition, and an approximate initial condition inside the gap is obtained via low-order spatial interpolation of the velocity at the boundaries. The influence of this I.C. is seen to diminish over time, as information is convected through the gap. Due to the form of the equations, no initial or boundary conditions on the pressure are required. The approach is evaluated by a time-resolved experiment where the true solution is known a priori. The results are compared with a boundary interpolation approach. Finally, an application of the technique to an experiment with a gap of complex shape is presented.