Radial velocity component measurements in cylindrical tubes have been difficult to make because of optical aberrations introduced by the curved tube wall. This is particularly troublesome in gas flows where refractive index matching techniques cannot be employed. The present investigation utilized a specially designed correction lens system to overcome this problem. As a result it was possible to map the axial and radial velocity behavior in detail for the air flow downstream of a sudden expansion in a cylindrical duct. Quantities measured and derived included mean velocities, turbulence intensities, turbulent kinetic energy and Reynolds stress. The weak secondary recirculation zone existing just below the sudden expansion was clearly identified and mapped. Where possible the measurements were compared with numerical predictions based on a k-ε model.

Simultaneous two-component laser velocimeter measurements were made in the incompressible turbulent flowfield following an axisymmetric sudden expansion. Mean velocities, Reynolds stresses, and triple products were measured and are presented at axial positions ranging from x/H = 0.2-14. A balance of the turbulent kinetic energy in the flow was performed. The production, convection, and diffusion of turbulent kinetic energy were computed directly from the experimental data using central differencing. A specially designed correction lens was employed to correct for optical aberrations introduced by the circular tube. This lens system allowed the accurate simultaneous measurement of axial and radial velocities in the test section. The experimental measurements were compared to predictions generated by a code that employed the k-e turbulence model. Agreement was good for mean axial velocities, turbulent kinetic energy, and turbulent shear stresses. However, the modeled turbulent normal stresses where in poor agreement with the measured values. The modeled diffusion of turbulent kinetic energy was underpredicted in the region between the shear layer and the centerline of the flow giving lower values of turbulent kinetic energy downstream of the potential core than measured. NomenclatureC D = turbulence constant, =0.09 H -step height, 38.1 mm _ _ __ k = turbulent kinetic energy, = (uu + vv + ww)/2 / = mixing length, mm P = time-averaged mean static pressure, N/m 2 p = pressure fluctuation about time-averaged mean, N/m 2 RI = inlet radius of sudden expansion, 38.1 mm R 2 = outlet radius of sudden expansion, 76.2 mm r = radial coordinate direction, ( = 0 at centerline) U = time-averaged mean axial velocity, m/s UQ = inlet reference velocity, 22 m/s u_ -fluctuating axial velocity, m/s up = time-averaged axial velocity-ressure correlation, __ N/m-s uju -time-averaged axial turbulent normal stress, m 2 /s 2 uv = time-averaged turbulent shear stress, m 2 /s 2 uuu = turbulent triple product, mVs 3 uuv -turbulent triple product, mVs 3 uvv = turbulent triple product, mVs 3 V -time-averaged mean radial velocity (positive toward wall), m/s v_ = fluctuating radial velocity, m/s vp = time-averaged radial velocity-pressure correlation, N/ _ m-s vv = time-averaged radial turbulent normal stress, m 2 /s 2 vvv = turbulent triple product, mVs 3 w = fluctuating tangential velocity, m/s ww = time-averaged tangential turbulent normal stress, mVs 2 x = axial coordinate direction y = radial coordinate direction, ( = 0 at centerline) e = dissipation of turbulent kinetic energy, m 2 /s 3 fji = dynamic viscosity, Kg/m-s JLI, = turbulent viscosity, Kg/m-s /Xeff = effective viscosity, Kg/m-s p = fluid density, kg/m 3 o = standard deviation

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This paper presents the results of an extensive study of subsonic separated flows using a laser Doppler velocimeter. Both a rectangular rearward facing step and cylindrical (axisymmetric) sudden expansion geometry were studied. The basic objectives were to resolve the question of whether a velocity bias error does, in fact, occur in LDV measurements in highly turbulent flows of this type and, if so, how it may be eliminated; map the velocity field (mean velocity, turbulence intensity, Reynolds stress, etc.) including the entire recirculation zone; and compare experimental results with numerical predictions based on the k-ε turbulence model. Measurements were carried out using a one-dimensional LDV operating in forward scatter with signal processing by means of a commercial counter-type processor. Results obtained show that velocity bias does occur in turbulent flows and that it can be overcome by proper data acquisition procedures. The results also indicate that the important mean velocity and turbulence quantities can be obtained with reasonable accuracy using a one-dimensional LDV system. Although the k-ε turbulence model provides a good qualitative picture of the flow field, it does not yield a completely adequate quantitative description. Results obtained here illustrate the discrepancies to be expected and provide a basis for further model development.

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