LDA measurements in low Reynolds number turbulent boundary layer

Abstract

LDA measurements of the mean velocity 0 in a low Reynolds number turbulent boundary layer allow a direct estimate of the friction velocity U~ from the value of ~O/~y at the wall. The trend of the Reynolds number dependence of O + = O/U~ is similar to the direct numerical simulations of Spalart (1988). I IntroductionA source of difficulty in low R o turbulent boundary layers is the accurate determination of the friction velocity U~. At such Reynolds numbers there is no rigorous basis for the log law, viz. + = x -i In y+ +C(1) (where x and C are constants; standard notation is used) and therefore no reason why low R o effects cannot penetrate well into the buffer layer. Consequently, the use of the Clauser chart technique [which is based on (1)] and of the Preston tube method may not be accurate. Under these conditions, a more direct and reliable estimate of U~ (=--w'rl/2, Tw is the kinematic wall shear stress) from the slope of the mean velocity profile at the wall using the relation rw = v .(2) y=0The use of (2) is prohibitive when a hot wire is used because of the wall conduction problem. Near-wall LDA measurements do not suffer from the same difficulty as hot wire measurements (e.g. Mazumder et al., 1981) and should in principle allow a reasonably accurate estimate of U~ from (2) [e.g. Reischman and Tiederman, 1975;Neiderschulte et al., 1990]. The purpose of this note is to show that U~ can be determined with sufficient accuracy from (2) to allow the effect of R o on 0 + to be assessed. Experimental conditions and procedure Experimental conditionsThe measurements were made in a closed circuit vertical water tunnel which consists of a constant head recirculating two-tank system (a brief description of the tunnel is given in Zhou and Antonia, 1992). The working section has a vertical square cross-section (0.26 m • 0.26 m) with a height of 2 m. All walls of the cross section are transparent (20 mm thick perspex). One of the walls, which is removable, was used as the smooth wall for the present boundary layer study. The maximum value of U1, the free stream velocity, is about 42 cm/s. At this speed, the boundary layers on the working section wall are laminar. Tripping was therefore required to achieve a turbulent regime. Three-dimensional roughness elements (pebbles of about 4.5 mm in height) were glued onto a 30 mm large perspex strip. This strip was recessed into a groove, located approx. 10 cm downstream of the contraction exit, so that the side of the strip onto which the pebbles were glued was flush with the working section wall. The measurement station was located 1,100 mm downstream of the trip. The boundary layer thickness 6 is about 35 mm at this station. Three values of R o (560, 1,033, 1,320) were used. Spalart (1988) reported direct numerical simulation (DNS) results for R o = 300, 670 and 1,410. In the present investigation, it was not possible to achieve Ro values less than about 500. Visualisations of dye injected at the wall and in the flow revealed that the boundary layer was laminar for R o < 500. ...

LDA measurements in a turbulent boundary layer over a d-type rough wall

“…Figure za shows the LDA profile of O/U~ at Ro----11oo, together with the DNS (R0~141o) and calculated distributions. The friction velocity, U~, was deduced from the measured velocity gradient at the wall (see Djenidi and Antonia, 1993 for more details about the method). This has the advantage of avoiding the use of the Clauser chart technique which is not reliable at very low Reynolds numbers where the existence of a universal log law is questionable (Spalart, 1988;Antonia et al, 1991 ).…”

“…Raupach et al, 1991). Most of these difficulties can be overcome with the use of laser-Doppler anemometry (LDA); in particular, quite reliable data can be obtained near a smooth surface (Djenidi and Antonia, 1993;Kadsson and Johansson, 1988;Karlsson, 1993) and measurements can, in principle, be made in the region of flow reversal, thus making the technique suitable for exploring the flow in the roughness canopy. In the present paper, the advantages of the LDA technique are exploited in order to examine in some detail the flow near the roughness canopy and to highlight any differences with the flow over a smooth wall.…”

Numerical Investigations of Instability and Transition in Attached and Separated Shear Layers

“…Re θ = 500. The simulation results for Grids 2 and 3, shown in Figure 5.4, compare favourably with the turbulent kinetic energy budgets computed by Spalart (1988) at Re θ = 670 and the mean velocity profile measured by Djenidi and Antonia (1993) at Re θ = 560. Therefore, these validation studies provide strong evidence that the present study should accurately capture the flow development in the turbulent boundary layer downstream of the separation bubble and the transitioning flow in the bubble where the transient coherent flow structures tend to be of notably-greater spatial and temporal scale.…”

“…The companion study was then repeated with a refined spatial resolution of ∆x + = ∆z + = 3. The simulation results for both grid resolutions compare favourably with the turbulent kinetic energy budgets computed by Spalart (1988) and turbulent velocity profile Djenidi and Antonia (1993). Reprinted with the permission of the American Institute of Physics.…”

“…Reprinted with the permission of the American Institute of Physics. measured by Djenidi and Antonia (1993), as shown in Figure 4.2. This provides evidence that the spatial grid in the current separation-bubble simulation is sufficient to adequately capture the flow development in the turbulent boundary layer downstream of the bubble.…”