Structure of 2-D and 3-D Turbulent Boundary Layers with Sparsely Distributed Roughness Elements

Abstract

The present study deals with the effects of sparsely distributed three-dimensional elements on two-dimensional (2-D) and three-dimensional (3-D) turbulent boundary layers (TBL) such as those that occur on submarines, ship hulls, etc. This study was achieved in three parts: Part 1 dealt with the cylinders when placed individually in the turbulent boundary layers, thereby considering the effect of a single perturbation on the TBL; Part 2 considered the effects when the same individual elements were placed in a sparse and regular distribution, thus studying the response of the flow to a sequence of perturbations; and in Part 3, the distributions were subjected to 3-D turbulent boundary layers, thus examining the effects of streamwise and spanwise pressure gradients on the same perturbed flows as considered in Part 2. The 3-D turbulent boundary layers were generated by an idealized wing-body junction flow.Detailed 3-velocity-component Laser-Doppler Velocimetry (LDV) and other measurements were carried out to understand and describe the rough-wall flow structure. The measurements include mean velocities, turbulence quantities (Reynolds stresses and triple products), skin friction, surface pressure and oil flow visualizations in 2-D and 3-D rough-wall flows for Reynolds numbers, based on momentum thickness, greater than 7000. Very uniform circular cylindrical roughness elements of 0.38mm, 0.76mm and 1.52mm height (k) were used in square and diagonal patterns, yielding six different roughness geometries of rough-wall surface. For the 2-D rough-wall flows, the roughness Reynolds numbers, + k , based on the element height (k) and the friction velocity ( τ U ), range from 26 to 131. Results for the 2-D rough-wall flows reveal that the velocity-defect law is similar for both smooth and rough surfaces, and the semi-logarithmic velocity-distribution curve is shifted by an amountdepending on the height of the roughness element, showing thatis a function of + k and the wall geometry. For the 3-D flows, the data show that the surface pressure gradient is not strongly influenced by the roughness elements. Higher roughness elements cause greater turbulence intensities near the wall, which cause the pressure-driven mean flow three-dimensionality to propagate or diffuse more rapidly from the wall region. In general, for both 2-D and 3-D rough-wall TBL, the differences between the two roughness patterns (straight and diagonal), as regards the mean velocities and the Reynolds stresses, are limited to about 3 roughness element heights from the wall.For the single elements, the values of + k range from 23 to 92. The study on single elements revealed that the separated shear layers emanating from the top of the elements form a pair of counter rotating vortices that dominate the downstream flow structure. These vortices, termed as the roughness top vortex structure (RTVS), in conjunction with the mean flow, forced over and around the elements, are responsible for the production of large Reynolds stresses in the neighborhood of th...

Application of a Novel Laser-Doppler Velocimeter for Turbulence: Structural Measurements in Turbulent Boundary Layers

“…The geometry of the wing is a 3:2 elliptical nose joined at the maximum thickness to a NACA 0020 airfoil with a maximum thickness of 7.17cm. This particular flow is well-studied by the TBLRG (Devenport and Simpson 1990;Olmen and Simpson 1995;Simpson 1996;Olmen et al 2001a;2001b;Simpson 2001;George 2005). The complex flow includes a meandering separated region very near the junction region of the wing, a highly-unsteady horseshoe vortex that is formed at the leading edge of the wing/body junction, and span-wise pressure gradients that generate stream-wise vorticity and strong three-dimensionality even outside of the attached vortex region.…”

“…The diameter of these cylinders were each 1.98mm with heights of k=0.38mm, 0.76mm, and 1.52mm, corresponding to viscous roughness scales, ku• k+ = -, of k+=23.5, 47.1, and 94.1, respectively. In the discussions to follow, the V Reynolds-averaged velocity statistics for profiles taken at locations of x/d=2.75 on the centerline of the cylinder (z/d=O) will be compared with those of George (2005) to verify the consistency in the flows. To augment the current understanding of this flow, measurements of the velocity auto-and cross-spectra will be considered for the additional information about the frequency of motions that occur in the wakes of these elements.…”

“…This is somewhat unexpected since the approach flow is fully-turbulent, and that may lead one to the conclusion that a deterministic occurrence in frequency is unlikely. The extensive velocity statistics data of George (2005) give some insight into this phenomenon. The large cylinder has a relatively-intense mean vortex, denoted by George as the roughness top vortex structure (RTVS) with its center of rotation at y+=30.…”

Vortex organization in a turbulent boundary layer overlying sparse roughness elements

“…Tomkins (2001) conducted PIV measurements downstream of isolated cylindrical and hemispherical elements immersed in a turbulent boundary layer (H ≈ 0.05 − 0.15δ; H + ≈ 100 − 300) and found vortices to be shed downstream of both element types, though a higher density of spanwise vortex signatures consistent with hairpin-like vortices were noted downstream of the hemisphere relative to the cylinder. Finally, George (2005) studied flow around isolated cylindrical elements immersed below the log layer (y + < 100) of a turbulent boundary layer and found that a horseshoe vortex is formed around the element, with the element wake extending tens of diameters downstream and the downwash of high-speed fluid driven by the counter-rotating legs of the horseshoe vortex increasing the local skin friction.…”

An Experimental Study of Turbulent Boundary Layers Subjected to High Free-Stream Turbulence Effects

“…Pressure measurements over the wind tunnel's centerline were made by using a pitot-static probe (Dwyer Instruments Inc., model 160-12) and a digital manometer (Dwyer Instruments Inc., model 475-0-FM) over a short period of time. As illustrated in Figure 3.39, Pisterman (2004) and George (2005) had a small pressure gradient. In the fall of 2005, the pressure gradient was corrected and set to zero by the current author and Lowe (2006) without the turbulence generator in the test section for a reference speed of 27.5 m/sec.…”