Abstract:Numerical procedures for construction of digital patterns of fringes mimicking fluid holograms are developed. Because conventional finite-element fluid analysis techniques are based on the approximation of nodal displacements, conjugate smoothing of the values of volumetric strain is performed in order to obtain realistic holographic images. Twodimensional fluid oscillations are analyzed using the developed techniques. It is shown that though time-average fluid holography is a powerful optical experimental met… Show more
“…It illuminates the holographic film interfering with the object beam. The phase of the light from the laser beam, ⌿ ͑x , y , t͒, can be expressed as 12,23 ⌿͑x,y,t͒ = 2 ͵ ͓n 0 − n flow ͑x,y,z,t͔͒ dz,…”
Section: Holographic Interferometry Of Fluidsmentioning
Fluid vibrations in axisymmetric geometry according to the first harmonic in the circumferential direction are analyzed. This problem has a practical application in the analysis of transverse vibrations of fluid in an axisymmetric pipe. The numerical model is developed using finiteelement techniques in axisymmetric geometry. Irrotational motions of ideal compressible fluid are analyzed. The finite-element model of the system is based on the approximation of nodal displacements via the shape functions. Thus the field of the amplitudes of the circumferential variation of the volumetric strain is calculated, exploiting conjugate approximation techniques. Obtained volumetric strains are used for the numerical construction of the interference pattern of the vibrating fluid. For this purpose the Abel transform, which is usually exploited in axisymmetric problems, is generalized for problems with circumferential variation of displacements. The obtained interference patterns are used in hybrid experimental-numerical procedures and help to interpret experimental results.
“…It illuminates the holographic film interfering with the object beam. The phase of the light from the laser beam, ⌿ ͑x , y , t͒, can be expressed as 12,23 ⌿͑x,y,t͒ = 2 ͵ ͓n 0 − n flow ͑x,y,z,t͔͒ dz,…”
Section: Holographic Interferometry Of Fluidsmentioning
Fluid vibrations in axisymmetric geometry according to the first harmonic in the circumferential direction are analyzed. This problem has a practical application in the analysis of transverse vibrations of fluid in an axisymmetric pipe. The numerical model is developed using finiteelement techniques in axisymmetric geometry. Irrotational motions of ideal compressible fluid are analyzed. The finite-element model of the system is based on the approximation of nodal displacements via the shape functions. Thus the field of the amplitudes of the circumferential variation of the volumetric strain is calculated, exploiting conjugate approximation techniques. Obtained volumetric strains are used for the numerical construction of the interference pattern of the vibrating fluid. For this purpose the Abel transform, which is usually exploited in axisymmetric problems, is generalized for problems with circumferential variation of displacements. The obtained interference patterns are used in hybrid experimental-numerical procedures and help to interpret experimental results.
The investigation of the high frequency vibrations of the fluid is an important problem in the design of microfluidic devices (periodic microstructures). Laser interferometric methods such as time average holography, high speed double expose holography or laser light diffraction allow to do analysis of high speed fluid flow and dosing or vibration of micro components used in biological and chemical microsystems. Methodology for identification of liquid concentration in the periodic microstructures applying numerical-experimental laser interferometric methods is presented in this paper.
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