The 16th Symposium on Measuring Techniques in Transonic and Supersonic Flow in Cascades and Turbomachines 1 Cambridge, UK September 2002 REYNOLDS STRESS MEASUREMENT WITH A SINGLE COMPONENT LASER DOPPLER ANEMOMETER R.D. Stieger Whittle Laboratory Cambridge University Engineering Department H.P. Hodson Whittle Laboratory Cambridge University Engineering Department ABSTRACT Measurements of the 2D Reynolds stress tensor of a steady or periodic flow may be made using a rotated 1D probe. The use of this technique in LDA measurements is presented showing that the LDA is in fact an ideal instrument for this technique due to its known cosine response with angle. The rotated 1D technique is compared to 2D LDA measurements and it is demonstrated that a 1D system can be used to make 2D Reynolds stress measurements at a fraction of the capital cost. INTRODUCTION The measurement of the full 2D Reynolds Stress tensor typically requires multi-axis anemometry systems. By simultaneously measuring multiple velocity components, it is possible to directly calculate the correlation between the components of velocity fluctuation and thus to calculate the Reynolds Stress tensor. However, if the flow is time invariant, or if it is phase locked, it is possible to combine a series of measurements made at different probe orientations and derive the time averaged or ensemble averaged Reynolds Stress tensor. This has been demonstrated by Fujita and Kovasznay [1], Kuroumaru et al.[2] and Kool et al. [3] who have used the technique in thermal anemometry. The adaptation of the method of Fujita and Kovasznay [1] to Laser Doppler Anemometry (LDA) is detailed here. It is demonstrated that the directional response of LDA makes it most suitable to this form of measurement. Moreover, the range of possible measurements obtainable from a 1D system is greatly enhanced with significant financial savings on equipment purchase. The data collected at multiple probe angles can also be utilised to enhance the mean flow measurements. NOMENCLATURE M measured quantity N number of probe angles S error U mean velocity magnitude i index m fluctuation of measured quantity u streamwise fluctuation v fluctuation normal to stream α angle of probe θ angle between probe and mean flow τ bar passing period ¯ time mean <> ensemble mean DERIVATION The velocity measured by LDA is the component of velocity in the plane of the intersecting beams and normal to the fringe pattern. If the plane of the beams is rotated relative to the instantaneous flow velocity vector (U) as shown in Figure 1, then only the instantaneous component of velocity in the plane of the intersecting beams (M) will be measured according to the cosine relationship ) cos( θ U M = (1) y U u v M M U α θ θ Figure 1: Decomposition of velocity vector. The instantaneous velocity component measured by the LDA (M) can also be written in terms of the mean flow vector ( U ), the instantaneous fluctuation components normal (v) and parallel (u) to the local mean flow and the angle between the probe and the mean flow ( θ ) according to