Hybrid numerical - experimental holographic fluid interferometry

Fluid holography enables effective analysis of high speed flow problems, high frequency vibrations of micro-scale components and fluids in dosing and contacting units, high speed processes taking place in biological and chemical microsystems. The investigation of the high frequency vibrations of the fluid is an important problem in the design of various devices. Though the production stage of the interferograms is technically not extremely complicated, the interpretation of the produced fringes faces a number of mathematical and numerical problems. That is related with the complex geometry of the phase-shifting media. Under such circumstances the density can change along the line of sight, and the density is no longer proportional to phase. Therefore, development of hybrid numerical - experimental fluid holographic methods is important both for the interpretation of experimental results and for the analysis of systems in the virtual environments by generating realistic interferograms. In this paper the method of holographic interferometry is used for the analysis of the two-dimensional fluid problem. FEM analysis techniques are based on the approximation of nodal displacements (not the volumetric strains) via the shape functions. Conventional FEM would require unacceptably dense meshing for producing sufficiently smooth images. Therefore the technique for smoothing of the generated images representing the distribution of the volumetric strains and calculated from the displacement distribution is developed. The smoothing technique is based on conjugate approximation used for the calculation of nodal values of stresses and enables to obtain the images of better quality on a coarse mesh by using the displacement formulation for the calculation of the eigenmodes.