The plane wall jet

Underlying Flow Regime 3-10 © copyright ERCOFTAC 2004

Description

Preface

The underlying flow regime (UFR) the plane wall jet - documented here is of major importance in many engineering applications, such as film cooling and the automobile demister, but it is also an important generic flow in itself.

After a review of the existing literature, starting with the work of Launder and Rodi (1981, 1983), where the deficiencies of the experimental data for the turbulent wall jet were obvious, a test case for this UFR is chosen, which has been specifically designed to produce high-quality turbulence data for CFD model validation (Karlsson et al. (1993a,b) and Eriksson et al. (1997, 1998, 2002). A synthesis of the work is given in the PhD thesis of Eriksson (2003). The resulting data set is included in the ERCOFTAC data base and has been a test case at two ERCOFTAC/IAHR Workshops on Refined Turbulence Modelling (Paris 1996, Delft 1997). Proceedings from the workshops are available from the editors and through the homepage www.ercoftac.org.

Introduction

A wall jet may be formally defined as "a shear flow directed along a wall where, by virtue of the initially supplied momentum, at any station, the streamwise velocity over some region within the shear flow exceeds that in the external stream" (Launder and Rodi, 1981). The most well-known everyday example of a wall jet is probably the automobile demister where it is used for heat and mass transfer modifications. (That is, to keep the windscreen free from mist and/or ice.) There are numerous other engineering applications of the wall jet in essentially different areas. Some examples are the film-cooling of the liner walls of gas-turbine combustion chambers and of the leading stages of the turbine itself, submerged bottom outlets in hydropower dams,the flow from the main circulation pumps of internal type in boiler water nuclear reactors and room ventilation concepts.

The wall jet is usually thought of as a two-layer shear flow, where the inner layer (from the wall to y_m, the position of maximum velocity) is qualitatively similar to the conventional turbulent boundary layer, while the outer layer (extending from y_m to the outer edge of the flow) resembles that of a free jet. The flow situation is sketched in Figure 1. The interaction of the two layers naturally modifies them as compared to the generic flows. Some examples are: The growth rate of the wall jet is considerably lower (~ 30%) than that of the plane free jet. The displacement of the position of zero shear stress from the position of maximum velocity, where it would occur in a free jet, to about two-thirds y_m. The shear stress in the wall region drops off much more quickly than in a boundary layer. The turbulence intensities are higher in the inner layer of the wall jet, including the limiting values at the wall. How this basic combination of wall-bounded flow and free shear flow behaves, and how the two layers interact to determine the development of the wall jet, is of interest also from a more fundamental point of view.

The wall jet also provides the experimentalist with all the challenges he may wish for. There one finds small scales, large gradients, wall effects, high local turbulence intensity and large anisotropy of the turbulence in the inner layer, and large turbulence intensities (asymptotically - infinite) in the outer layer.

Figure 1. Configuration and nomenclature for the plane wall jet.

Review of UFR studies and choice of test case

The literature on wall jets is extensive, almost immense. Twenty years ago, at the time of the cornerstone reviews by Launder and Rodi (1981, 1983), well over two hundred experimental studies had been published. There were, however, at that time still a lot of unknowns and unresolved issues in relation to the turbulent wall jet.

Launder and Rodi (1981, 1983) summarized the work on turbulent wall jets up to 1980. They pointed to, among other issues, the measurement of the wall shear stress, ω_w, as a vexing problem, the lack of definitive data sets on and , and that none of the few sets of near-wall (y <y_m) data for was convincing. Figure 2, taken from Launder and Rodi (1981), illustrates the amount of spread in the then existing turbulence data. Moreover, turbulence data for the very near-wall region were non-existent.

Further work relating to the plane jet in still surroundings was published during the 1980´s, Nizou (1981), Nizou et al. (1986)[1] , Schneider (1987, 1994), Kobayashi & Fujisawa (1982) and Fujisawa & Kobayashi (1987). Notable here is the work of Schneider, who was the first to use laser-Doppler velocimetry (LDV) for turbulence measurements in the turbulent wall jet. His measurements indicated significantly higher values of over the whole flow and significantly higher values of in the outer region, as compared to earlier hot-wire data. He attributed this to problems connected with the use of hot wires in regions with instantaneous flow reversals.

Because of the persisting gaps in the knowledge of the turbulent wall jet, the work by Karlsson and Eriksson was initiated around 1990. It was explicitly aimed at producing high-quality turbulence data, with special attention to the near-wall region. A secondary objective was to provide a data set suitable for validation of numerical simulations. LDV was the obvious choice for measurement technique due to its superiority when taking turbulence data close to a wall, and its potential to yield accurate results even in very high turbulence intensity flows.


a)	b)

Figure 2. Profiles of lateral normal stress (a) and turbulent shear stress (b) across the turbulent wall jet in stagnant surroundings. From Launder & Rodi (1981).

Two major experimental studies were published during the course of that work. Wygnanski et al. (1992) and Abrahamsson (1997) both used hot-wire anemometry (HWA) to study the wall jet in stagnant surroundings. The experiment by Abrahamsson had similar inlet conditions to, and was closely coordinated with, the work by Eriksson, with an almost continuous exchange of results.

The test case chosen for closer analysis here is the one reported by Karlsson et al.(1993 a,b), and Eriksson et al., (1997, 1998, 2002), Eriksson & Karlsson (2000, 2001), and Eriksson (2000, 2002). Most papers and a summary can be found in the PhD thesis of Eriksson (2003). The papers are based on results from two experiments in one and the same test rig. The first set of measurements covered a comparatively long interval in streamwise position but were restricted to two velocity components, meaning that the turbulent kinetic energy could not be determined. The resulting data set was reported in Eriksson et al. (1998) and Karlsson et al. (1993a, 1993b), and are available in the ERCOFTAC Data Base [2] . These data were used as a test case in the ERCOFTAC/IAHR Workshops on Refined Turbulence Modelling in Paris, 1996 and in Delft, 1997.

The repeat experiment was designed and performed to supplement the first data set with three-component measurements at a few streamwise positions in the developed region of the flow. It was also designed to achieve very high spatial resolution for improved near-wall data. Results from the repeat experiment have been reported in e.g. Eriksson & Karlsson (2000), Eriksson & Karlsson (2001) and Eriksson et al. (2002).

Results from the two experiments were compared to measurements obtained in the test rig of Abrahamsson (1997) using various hot-wire techniques: stationary, pulsed and flying. Using the LDV technique as a standard, the results were interpreted to understand the limitations of hot-wire techniques in high intensity turbulent shear flows, Eriksson et al. (2002).

Contributors: Jan Eriksson; Rolf Karlsson - Vattenfall Utveckling AB