Laser-Doppler measurements were conducted in a plane turbulent wall jet at a Reynolds number based on inlet velocity, Re0, of 9600. The initial development as well as the fully developed flow was studied. Special attention was given to the near-wall region, including the use of small measuring volumes and the application of specific near-wall data corrections, so that wall shear stresses were determined directly from the mean velocity gradient at the wall using only data bellow y+=4. It was possible to resolve the inner peak in the streamwise turbulence intensity as well as the inner (negative) peak in the shear stress.
The basic flow field that we have tried to obtain is the two-dimensional wall jet on a plane surface, and more specifically "the plane wall jet in still air" according to the terminology used by LR81. There are, however, variations also on this subsection of the wall jet. These variations concern the design of the wall above the inlet. This wall is usually either a thin lip or an "infinite" vertical wall as in the present experiment. The latter design is simpler to treat computationally, since it, together with a "no inflow" upper boundary, results in a single, well-defined inflow boundary with known boundary conditions. It was therefore chosen here, in spite of the inevitable return flow that this configuration generates, a return flow which far downstream of the nozzle changes the character of the jet. An important criterion in the experimental design was that the spatial resolution should be sufficiently high to allow the wall shear stress to be determined directly from mean velocity measurements. This imposes an upper limit on the ratio of measuring control volume diameter to viscous length scale, but a high enough inlet Re-number must also be retained to allow comparisons with earlier studies. Once water was chosen as the working fluid, due to the absence of seeding problems in low-speed water flows, these considerations led to the present combination of slot width and inlet velocity.
The test facility is shown in Fig. It consists of a large tank into which a jet discharges. The tank is 7 m long and its width is 1.45 m. One of the side walls is made of glass, as well as the bottom. (Using a glass bottom improves the conditions for near-wall measurements, since its smoothness minimises the diffuse surface reflections. (Johnson and Brown 1990).) The slot height was measured with water in the tank, by a diver. The results showed the slot height to be 9.6 + 0.1 mm over most of the slot width. Given the uncertainties involved, this is consistent with an indirect determination of the slot height using the volumetric flow rate. Consequently, b = 9.6 mm will be used in the following analysis, giving a jet width-to-height ratio of 151. This was considered large enough to obtain good two-dimensionality. A large contraction (Morel 1975) with a turbulence-reducing screen inserted is used to produce a fairly flat mean velocity profile at the inlet. A weir upstream of the contraction keeps the upstream water level constant, and the flow velocity through the slot is set by an adjustable weir at the downstream end at the tank. This reference velocity is determined as
where Dh is the difference in height between the upstream and downstream free surfaces.
The inlet velocity, U0, was set as close as possible to 1 m/s, corresponding to a water depth downstream of the inlet of about 1.4 m. For this water depth, the influence of the re-circulating flow on the growth rate of the jet was negligible for the first 150 slot heights.
Using water of approximately room temperature, one obtains a nominal inlet Re-number
which is sufficiently high to be comparable to previous experimental studies, e.g. Bradshaw & Gee (1960) and Tailland and Mathieu (1967).
The LDV hardware consisted of a modified TSI two-colour system. The system was modified
as to increase the beam expansion ratio to 8.5 by including an extra beam expansion
module. An upper-central beam arrangement was used to measure the normal velocity
component (V). A front lens with a focal distance of 750 mm was- used, in ord&r to
reach the centreline of the tank. The measuring volume sizes were (0.73 × 0.05) mm
(streamwise velocity component 488 nm) and (1.60 × 0.05) mm (normal velocity
component - 514.5 nm), respectively. Silicon carbide particles with a mean diameter
of 1.5 ~m was used to uniformly seed the flow.
With the exception of the positions closest to the wall, where only the streamwise
velocity component was measured, all measurements were made in coincidence mode;
i£r-rtquirtng -the bursts in channel 1 and channel 2 to arrive within a certain,
pre-determined time interval. Shift frequencies were chosen such that all likely flow
angles were measured with equal probability (Whiffen 1975; Buchhave 1975, 1979), while
still staying away from the filter limits.
Extensive Pitot-tube measurements, spanwise profiles at several heights and numerous vertical profiles at different spanwise positions, were made at the slot (x = 0) to check for symmetry and spanwise variations. Part of the inlet velocity profile was also measured using LDV, to better resolve the boundary layer and to get turbulence data. LDV measurements, streamwise and spanwise profiles, were also taken immediately downstream of the slot. Extensive spanwise measurements were made at several streamwise positions in order to check the two-dimensionality of the flow. Based on these spanwise measurements, it was decided to make the main measurements series approximately halfway between the centreline and the glass wall. The flow conditions in that spanwise position were identical to those at the centreline within the measurement accuracy. The main measurement series were taken at the following streamwise positions: x=50, 100, 200, 400, 700,1000, 1500, 2000 mm. For the sake of simplicity, we will refer to these positions as x/b = 5, 10, 20, 40, 70, 100, 200, although the actual dimensionless distance was about 4% larger. In figures showing the streamwise development of a quantity, the correct x/b will be used. Measurements stopped at x/b = 200 because the flow was losing its wall-jet character. This issue will be discussed later on.
The vertical profiles of the main measurement series were taken in order from x/b = 5 and downstream. Dh and the water temperature, T>sub>0>, was checked regularly, in order to detect any drift in inlet velocity or inlet Re-number. There was essentially no change in U0 or Re0 during the individual profiles. There were, however, small variations between the different profiles due to a 3% variation in the boundary conditions, i.e. Re0. Where relevant, all velocities have been normalised to the same inlet velocity by multiplying with [U0(x=0)/U0(x=X)].
The position of the wall, y = 0, was estimated by observing the output signal from the counter, i.e. after amplifying and filtering, on an oscilloscope. The "wall signal" is very characteristic. The distance from this preliminary wall position ; was then measured by a dial gauge. Finally, the wall distance was adjusted after the measurements by shifting the velocity curve up or down to make it pass through origin. This was relatively simple due to the linear relation. The necessary adjustments typically were of the order of 0.02 mm.
The inlet conditions were determined using Pitot tube and LDV-measurements. Mean velocity profiles from Pitot tube measurements, taken at several spanwise positions at and around the spanwise position finally chosen for the main measurements, showed no visible differences in the maximum velocity. There were, however, small differences in the length of the flat parts of the profiles. These are consistent with the earlier statement of a +0.1 mm variation in slot height. The variation in the spanwise velocity distribution at y = 4.5 mm was less than ±0.25%.
LDV measurements of the lower part of the inlet velocity profile were made in order to resolve the boundary layer and to obtain information on the turbulence levels. The boundary layer thickness, defined as U= 0.99 Umax, is 1.4 mm. The turbulence intensity in the flat part of the profile is less than 1%. No corrections for gradient broadening has been applied to the turbulence measurements, meaning that the peak in turbulence intensity in the boundary layer is exaggerated. We thus have a fairly flat inlet velocity profile with a mean velocity which is uniform in the spanwise direction within ±0.25%. The flow is laminar and the laminar boundary layers along the walls have a thickness 1.4 mm.
Persistent spanwise variations of the thickness of the wall jet were noted. These variations are probably associated with the small variation (1%) in slot height. All subsequent measurements were however made at a spanwise position where "average properties" of the wall jet were prevailing.
