INSTANTANEOUS VELOCITY AND PRESSURE FEATURES IN A TURBULENT BOUNDARY LAYER

ORGANIZED MOTION: INSTANTANEOUS STRUCTURES
EXPERIMENTAL SET-UP
PRESSURE-VELOCITY INTERACTIONS: TURBULENCE PRODUCTION

Illinois Institute of Technology, Chicago, IL

INSTANTANEOUS VELOCITY AND PRESSURE FEATURES

IN A TURBULENT BOUNDARY LAYER

William de Ojeda

March 1996

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Abstract

Measurements of the instantaneous u-v velocity field in the streamwise-wall normal plane are combined with measurements of pressure time history under and around the velocity field. These are performed in a turbulent boundary layer on a smooth flat plate, over a range of 1500<

<6000. The instantaneous velocity field is resolved using Particle Image Velocimetry from the buffer layer through the log region and into the outer layer, while encompassing approximately 2

in the streamwise direction. A rectangular 13x3 array of microphones extends 1

in the streamwise direction and it is centered under the PIV picture. These are used to record the pressure history simultaneous with the instantaneous velocity field. The combination of instantaneous, spatially resolved, pressure and velocity measurements offers a unique view at turbulence.

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ORGANIZED MOTION: INSTANTANEOUS STRUCTURES

Successful modeling of turbulence relies in understanding the mechanisms responsible for its production. The unfolding of this very difficult process has long been studied, the more widely recognized physical explanations having risen from experimental observations and statistical calculations applied to theory and experiments -e.g. fluid sweep-ejections (Corino and Brodkey, 1967), bursting (Kim et al, 1971). The mathematical difficulty of the turbulent problem has encouraged experimental investigations, often involving single or multiple point measurements of velocity and wall pressure. Studies have found relationships between characteristic pressure and velocity events connected to the production of turbulence.

The work performed herein combines instantaneous, spatially resolved, pressure and velocity measurements. The primary objectives are two fold, and are described below.

To the present date, the relationship found between strong pressure events and the velocity field is non-unique. Fundamentally, they are a result of statistical averaging and are disassociated from the instantaneous, highly irregular nature of turbulence. Only instantaneous and simultaneous images of pressure and velocity over large regions in space can begin to uncover the cause-effect relations.
A great deal of the statistical analysis in turbulent flows has involved single point measurements in the streamwise direction. This fact, which suggests Taylor's hypothesis or frozen flow assumption that the flow convects without change, undermines the physical turbulent structures inferred from these measurements. This study combines the instantaneous velocity features of PIV with a large two dimensional array of closely positioned microphones aligned in the streamwise direction.

Figure 1 44600 byte jpeg

Figure 1 Experimental set-up: PIV instrumentation is shown alongside the pressure transducer array.

EXPERIMENTAL SET-UP

This paper shows illustrations of detailed simultaneous two dimensional velocity and wall pressure fields associated to structures responsible for production of turbulence. The experimental configuration is shown in the above Fig 1.

PRESSURE-VELOCITY INTERACTIONS: TURBULENCE PRODUCTION

Figure 2 385084 byte jpeg

Figure 2 Instantaneous velocity and wall pressure field.

Conditional Averages

Large positive wall pressure peaks often occur in the immediate vicinity of strong shear layers comprised of fluid with momentum deficit followed by fast moving flow (Johansson et al, 1987, Lueptow and Snarsky, 1995). Large negative pressure events have not been so readily associated with a distinctive velocity field.

Instantaneous Structures

An instantaneous velocity field in a turbulent boundary layer at =3950 is shown in Fig 2. Shown are line-averaged-removed fluctuations. Color is based on the streamwise component, showing fast or slow flow with respect to the mean profile. Underneath the velocity field, the corresponding pressure profile is shown. Pressures are normalized with rms. Microphone locations are shown with square symbols.

A large pressure peak coincides with a distinct shear layer spanning across the boundary layer. It is not always so clear, as it is in this present case, to distinguish the main event highlighted in the conditional average. In addition to the main feature, the instantaneous picture shows spots of large vorticity occurring at the interface. These correspond to heads of hairpin and horseshoe vortices proposed by Theodorsen (1955) and later by Head and Bandyopadhyay (1981).

Evolution of Pressure Structures

The current experimental set-up allows to consider the evolution of a given pressure profile and its interaction with the velocity field. This is illustrated in the velocity-pressure sequence of Fig 3. The color contours of pressure mark the convection, rise and breakdown of the pressure structures underneath the two dimensional velocity field. The negative pressure peak, at about -3.5p_rms (x⁺=425) coinciding with the instantaneous picture (t⁺=0) is seen here to be the beginning of a quick but very strong pressure event. On the contrary a smaller positive pressure peak (+2p_rms, x⁺=600, t⁺=0) is the very end of a much longer lasting pressure structure.

Figure 3 371145 byte jpg

Figure 3 Time evolution of wall pressure associated with an instantaneous velocity field.

This and similar pressure patterns were considered by Thomas and Bull (1983) and Dinkelacker et al (1977) as possibly been associated with the burst-sweep cycle. The present realization shows a distinctive shear layer coinciding with the positive pressure peak (not with the stronger negative pressure peak), which gives rise to a localized spot of turbulence production.

Space and time Conditional Averages

Multiple velocity and pressure history sequences give significant insight to the interplay of positive and negative pressure peaks and the flow features responsible for the production of turbulence: a large positive pressure peak preceding in time and space a negative pressure peak would be hidden from one or even a small number of continuos microphones.

A conditional sampling in space and time detecting on large negative pressures, p<-2.5p_rms, is shown in Fig 4. The results of using solely one microphone would correspond to a single vertical line (e.g. x⁺=0). A strong positive pressure peak immediately precedes the negative pressure peak in time. Also preceding in time, the averaging exhibits a positive region displaced downstream. The lack of strength in this positive region indicates that, though organized, there exists a range of convection speeds.

Figure 4 387364 byte jpg

Figure 4 Conditional average field in space and time: detection threshold set to p<-2. 5prms.

REFERENCES

Corino, E. R. and Brodkey, R. S., 1969. J. Fluid Mech., Vol. 37, pp. 1-30.
Dinkelacker, A., Hessel, M., Meier, G. E. A. and Schewe, G., 1977. Pys. Fluids Suppl., S216.
Head, M. R. and Bandyopadhyay, P., 1981. J. Fluid Mech., Vol. 107, pp. 297-338.
Johanson, A. V., Her, J. Y. and Haritonidis, J. H., 1987. J. Fluid Mech. Vol. 175, pp. 119-142.
Kim, H. T., Kline, S. J., Reynolds, W. C., 1971. J. Fluid Mech. , Vol. 50, pp. 133-160.
Snarski S. R. and Lueptow R. M., 1995. J. Fluid Mech. , Vol. 286, pp. 137-171.
Theodorsen, T., 1955. 50 Jahre Grenzschichtforsung, ed. H. Gortier and W. Tollmein, p. 55.
Thomas, A. S. W. and Bull, M. K., 1983. J. Fluid Mech. Vol. 128, pp. 283-322.

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