Turbulent Boundary Layers
We have concentrated our effort on two challenging areas of turbulent boundary layers: the axisymmetric boundary layer on a long, slender cylinder and the wall pressure beneath a turbulent boundary layer.
Cylindrical Boundary Layers
The boundary layer on a long slender cylinder in axial flow is of interest because of its application to linear towed sonar arrays, a long hose filled with hydrophones that is towed behind a ship or submarine. The turbulent boundary layer that develops on the array generates wall pressure fluctuations that are of the same magnitude as the far-field sound resulting in a noise problem. My doctoral research constituted the first measurements of the turbulent velocity field, as well as the first turbulence event detection for this boundary layer ["The thick, axisymmetric turbulent boundary layer: Mean and fluctuating velocities," with P. Leehey and T. Stellinger, Physics of Fluids, 28:3495-3505, 1985; "The structure of the turbulent boundary layer on a cylinder in axial flow," with J. Haritonidis, Physics of Fluids, 30:2993-3005, 1987; "Computer-aided calibration of X-probes using a look-up table," with K. Breuer and J. Haritonidis, Experiments in Fluids, 6:115-118, 1988]. At Northwestern I expanded my investigation of the turbulent boundary layer on a cylinder in axial flow to the complex problem of relating the stress field at the wall of the cylinder to the turbulent velocity field. This required the design and construction of a low-turbulence, low-noise wind tunnel. Our research has focused on very difficult measurements of the normal and shear stresses on the wall of a cylinder under a turbulent boundary layer.
"Wall pressure and coherent structures in a turbulent boundary layer on a cylinder in axial flow," with S. Snarski, Journal of Fluid Mechanics, 286:137-171, 1995. Based on the simultaneous measurement of the wall pressure and the streamwise velocity in a cylindrical boundary layer, we found that two types of flow structures contribute to fluctuating pressure at the wall: (1) low-frequency, large-scale structures with dynamic significance across the boundary layer, and (2) high-frequency, small-scale disturbances near the wall associated with the production of turbulence that are responsible for large-amplitude, short-duration wall pressure fluctuations. We also provided convincing evidence that both positive and negative wall pressure peaks can be related to the streamwise acceleration near the wall, rather than the streamwise velocity as suggested by several other researchers. It appears that the transverse curvature of the wall of the cylinder acts to enhance the large-scale turbulent motions in the boundary layer compared to the boundary layer on a flat plate, probably as a result of the reduced constraint imposed on the flow by a cylinder that is small with respect to the boundary layer thickness.
"Wall shear stress and velocity in a turbulent, axisymmetric boundary layer," with A. Wietrzak, Journal of Fluid Mechanics, 259:191-218, 1994. We have made the only measurements of the fluctuating wall shear stress on a cylinder in axial flow and one of the few measurements of wall shear stress spectra for any wall-bounded flow. The wall shear stress was measured using a 2.5 mm diameter platinum-rhodium wire mounted flush to the wall. The cooling of the heated wire is a measure of the local fluctuating wall shear stress. Our results indicate that the ratio of the rms to the mean value of the wall shear stress is slighter lower than that for a flat plate. Spectral analysis of the wall shear stress shows that a cylindrical boundary layer contains less energy at lower frequencies and more energy at higher frequencies than other wall-bounded flows. Perhaps most interesting, though, is the detection of cross-flow coherent structures that may be associated with fluid from the outer part of the boundary layer washing over the cylinder. Such structures cannot occur in a boundary layer on a flat plate.
"Normal and shear stresses in the turbulent boundary layer on a cylinder," with H. Nepomuceno, Flow Noise Modeling, Measurement, and Control, ASME NCA-Vol. 19/FED-Vol. 230: 119-128, 1995. We have made simultaneous measurements of the wall shear stress, wall pressure, and streamwise velocity in the boundary layer on a cylinder. These are the first simultaneous measurements of the wall shear stress and the wall pressure in a turbulent boundary layer where the transducers are very closely spaced. Using several event detection and signal analysis techniques we have concluded that the wall shear stress is only weakly related to the wall pressure even though both are strongly related to the streamwise velocity near the wall. Our results also indicate that positive wall pressure peaks are the "fundamental" wall pressure signature associated with the burst cycle.
"Near-wall streaky structure in a turbulent boundary layer on a cylinder," with C. P. Jackson, Physics of Fluids A: Fluid Dynamics, 3:2822-2824, 1991. Our flow visualization of a cylindrical boundary layer provides the first evidence of a near-wall streaky structure similar to that in a planar boundary layer. This streaky structure indicates that the same sort of burst cycle responsible for turbulence production in a planar boundary also plays an important role when the boundary layer has substantial transverse curvature.
- "The turbulent boundary layer on a cylinder in axial flow," AIAA Journal, 28:1705-1706, 1990. This is the most extensive survey of literature on boundary layer on cylinders in axial flow to date. Previous research focused on the integral characteristics of cylindrical boundary layers with very little information about the wall pressure, wall shear stress, and turbulence statistics. In particular, the effect of the transverse curvature of the wall on the structure of turbulence was not investigated prior to the work described in the four preceding papers.
- Current Research: We are beginning a project in which we will make simultaneous measurements of wall pressure at three circumferential positions on a cylinder to determine the spanwise correlation of wall pressure structures in the boundary layer.
Wall Pressure Beneath a Turbulent Boundary Layer
- "Wall pressure events in turbulent wall-bounded flow," Turbulent Flows, ASME FED-188: 65-69, 1994. I have analyzed the space-time development of wall pressure peak events, which can be related to the acceleration of fluid above the wall associated with the ejection-sweep cycle, using the NASA-Ames direct numerical simulation database for turbulent channel flow. A wall pressure event could be tracked in both space and time using the database, a feat that is not possible experimentally. Positive pressure peaks begin as a wave packet consisting of a pair of pressure "humps". The downstream hump eventually dominates and becomes a positive pressure peak. A negative pressure peak begin as a negative hump that grows to become the negative pressure peak. Pressure peak events average about 80 wall units in diameter. They grow and decay over a streamwise distance of about 800 wall units. This study provides the first information about the size, growth and decay, and structure of such events.
- "Local wall pressure gradient events in turbulent wall-bounded flow," Flow Noise Modeling, Measurement, and Control, ASME NCA-Vol. 19/FED-Vol. 230: 75-85, 1995. Based on the dominant terms in the Navier-Stokes equation at the wall, it is evident that a positive streamwise pressure gradient must be associated with an inflectional instantaneous streamwise velocity profile. The fact that an inflectional velocity profile is unstable in the inviscid limit suggests that it may be related to the burst cycle, which is responsible for the generation of most turbulence. I am using the NASA-Ames turbulent wall pressure database to track the spatio-temporal development of large wall pressure gradients. I have found that such events begin as a wave packet. The amplitude of one of the waves overwhelms the other waves, becoming the wall pressure gradient event. The growth and decay of a sharp pressure gradient event is similar to the growth and decay of a composite event made up of negative and positive wall pressure peak events. At the instant of detection, the characteristic wall pressure signature can be related to the lifting up of a horseshoe vortex and the shear layer of the burst cycle.
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"Wall pressure and coherent structures in a turbulent boundary layer on a cylinder in axial flow," with S. Snarski, Journal of Fluid Mechanics, 286:137-171, 1995. Based on the simultaneous measurement of the wall pressure and the streamwise velocity in a cylindrical boundary layer, we found that two types of flow structures contribute to fluctuating pressure at the wall: (1) low-frequency, large-scale structures with dynamic significance across the boundary layer, and (2) high-frequency, small-scale disturbances near the wall associated with the production of turbulence that are responsible for large-amplitude, short-duration wall pressure fluctuations. We also provided convincing evidence that both positive and negative wall pressure peaks can be related to the streamwise acceleration near the wall, rather than the streamwise velocity as suggested by several other researchers. It appears that the transverse curvature of the wall of the cylinder acts to enhance the large-scale turbulent motions in the boundary layer compared to the boundary layer on a flat plate, probably as a result of the reduced constraint imposed on the flow by a cylinder that is small with respect to the boundary layer thickness.
"Wall shear stress and velocity in a turbulent, axisymmetric boundary layer," with A. Wietrzak, Journal of Fluid Mechanics, 259:191-218, 1994. We have made the only measurements of the fluctuating wall shear stress on a cylinder in axial flow and one of the few measurements of wall shear stress spectra for any wall-bounded flow. The wall shear stress was measured using a 2.5 mm diameter platinum-rhodium wire mounted flush to the wall. The cooling of the heated wire is a measure of the local fluctuating wall shear stress. Our results indicate that the ratio of the rms to the mean value of the wall shear stress is slighter lower than that for a flat plate. Spectral analysis of the wall shear stress shows that a cylindrical boundary layer contains less energy at lower frequencies and more energy at higher frequencies than other wall-bounded flows. Perhaps most interesting, though, is the detection of cross-flow coherent structures that may be associated with fluid from the outer part of the boundary layer washing over the cylinder. Such structures cannot occur in a boundary layer on a flat plate.
"Normal and shear stresses in the turbulent boundary layer on a cylinder," with H. Nepomuceno, Flow Noise Modeling, Measurement, and Control, ASME NCA-Vol. 19/FED-Vol. 230: 119-128, 1995. We have made simultaneous measurements of the wall shear stress, wall pressure, and streamwise velocity in the boundary layer on a cylinder. These are the first simultaneous measurements of the wall shear stress and the wall pressure in a turbulent boundary layer where the transducers are very closely spaced. Using several event detection and signal analysis techniques we have concluded that the wall shear stress is only weakly related to the wall pressure even though both are strongly related to the streamwise velocity near the wall. Our results also indicate that positive wall pressure peaks are the "fundamental" wall pressure signature associated with the burst cycle.