Investigation of turbulent transport in an axisymmetric sudden expansion

Abstract

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

Turbulent flow of viscoelastic liquids through an axisymmetric sudden expansion

“…That 'other parameter' may be, as was the case with backward-facing steps [1,2], the maximum turbulence intensity at separation, although the available data in the literature is less conclusive in the axisymmetric case than it is for flow over a backward-facing step. For example, the large differences in reattachment length x R for the very similar inlet turbulence intensity and expansion ratio of Gould et al (x R = 8 step heights) [6] and Pereira and Pinho (x R = 10 step heights) [7], may be due to different boundary-layer thicknesses. The maximum turbulence intensities for all the results reported in the literature show that u > w > v .…”

An experimental study of two flows through an axisymmetric sudden expansion

“…Studies in which velocities were not measured (for example Runchal 1971, Baughn et al 1984 and studies in which the sudden expansion was followed by a contraction, as in a combustor (for example, Drewry 1978, Yang andYu 1983) are excluded from this table. Most notable in Table 1 is the work done by Durrett et al (1988), Gould et al (1990) and Stevenson et al (1984) who used LDV to measure mean velocities and turbulence quantities in several axisymmetric configurations. Table 1.…”

“…Axisymmetric expansion Durrett et al (1988) 3.61 8.4 9 8.4 Freeman (1975) 4.41 1.6 0.91 8.8 Gould et al (1990) 4.0 5.6 0.16 ~8 Ha Minh and Chassaing (1979) 4.0 7.2 0.30 >8.6 Khezzar et al (1985) 3.06 1.5 0.45 9.3 Moon and Rudinger (1977) 2.04 0.6 ? 8.5 Stevenson et al (1984) 3.51 3.6 9 > 8 Present datum flow 3.52 3.5 0.21 10.7…”

Methods for Prediction of High-Speed Reacting Flows in Aerospace Propulsion

“…The code was first validated against relevant data and then used to simulate the dump combustor. The results were then compared with available experimental data from Gould et al [174,175].…”