Effect of fringe divergence in fluid acceleration measurement using LDA

레이저 도플러 원리를 이용한 유체 가속도 측정

The laser Doppler technique is well-established as a velocity measurement technique of high precision for flow velocity. Recently, the laser Doppler technique has also been used to measure acceleration of fluid particles. Acceleration is interesting from a fluid mechanics point of view, since the Navier Stokes equations, specifically the left-hand-side, are formulated in terms of fluid acceleration. Further, there are several avenues to estimating the dissipation rate using the acceleration. However such measurements place additional demands on the design of the optical system; in particular fringe non-uniformity must be held below about 0.0001 to avoid systematic errors. Relations expressing fringe divergence as a function of the optical parameters of the system have been given in the literature; however, direct use of these formulae to minimize fringe divergence lead either to very large measurement volumes or to extremely high intersection angles. This dilemma can be resolved by using an off-axis receiving arrangement, in which the measurement volume is truncated by a pinhole in front of the detection plane. In the present study an optical design study is performed for optimizing laser Doppler systems for fluid acceleration measurements. This is followed by laboratory validation using a round free jet and a stagnation flow, two flows in which either fluid acceleration has been previously measured or in which the acceleration is known analytically. A 90 degree off-axis receiving angle is used with a pinhole or a slit.