Refraction Effect from Beam Refraction by Annular Wall Window in LDA Applications

The influence of laser beam refraction resulting from the annular wall window on refraction effect is investigated both in a theoretical analysis and laser Doppler anemometry(LDA) using a calibration disc. A mathematical procedure, without any simplifications, describing the propagation of two laser beams through an annular window was established to study the effect of refraction on measuring volume(MV) shift in terms of laser beam half angle, annular window thickness, refractive index of the fluid, and LDA probe location. A test system used for LDA calibration was assembled to study this effect of refraction to fringe distortion. The coefficients of relative motion k_x and k_y, and the velocity bias Δu relative to the real fluid velocity are used to estimate the refraction influence on MV position and velocity bias. Results show that the effect can be ignored within 10°of the half angle. k_x, k_y, and Δu are nearly constant if the thickness of the annular wall window is more than 30mm. The refractive index of the fluid should be matched as near possible with that of the annular wall to minimalize the refractive influence. The velocity bias arising from the change in fringe spacing is smaller than that estimated by the mathematical procedure.