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TECHNICAL PAPERS

# Effects of Weak Free Stream Nonuniformity on Boundary Layer Transition

[+] Author and Article Information
Jonathan H. Watmuff

School of Aerospace, Mechanical and Manufacturing Engineering,  RMIT University, Melbourne, Australia

J. Fluids Eng 128(2), 247-257 (Apr 04, 2005) (11 pages) doi:10.1115/1.2169813 History: Received April 30, 2004; Revised April 04, 2005

## Abstract

Experiments are described in which well-defined weak Free Stream Nonuniformity (FSN) is introduced by placing fine wires upstream of the leading edge of a flat plate. Large amplitude spanwise thickness variations form in the boundary layer as a result of the interaction between the steady laminar wakes from the wires and the leading edge. The centerline of a region of elevated layer thickness is aligned with the centerline of the wake in the freestream and the response is shown to be remarkably sensitive to the spanwise length-scale of the wakes. The region of elevated thickness is equivalent to a long narrow low speed streak in the layer. Elevated Free Stream Turbulence (FST) levels are known to produce randomly forming arrays of long narrow low speed streaks in laminar boundary layers. Therefore the characteristics of the streaks resulting from the FSN are studied in detail in an effort to gain some insight into bypass transition that occurs at elevated FST levels. The shape factors of the profiles in the vicinity of the streak appear to be unaltered from the Blasius value, even though the magnitude of the local thickness variations are as large as 60% of that of the undisturbed layer. Regions of elevated background unsteadiness appear on either side of the streak and it is shown that they are most likely the result of small amplitude spanwise modulation of the layer thickness. The background unsteadiness shares many of the characteristics of Klebanoff modes observed at elevated FST levels. However, the layer remains laminar to the end of the test section $(Rx≈1.4×106)$ and there is no evidence of bursting or other phenomena associated with breakdown to turbulence. A vibrating ribbon apparatus is used to examine interactions between the streak and Tollmien-Schlichting (TS) waves. The deformation of the mean flow introduced by the streak is responsible for substantial phase and amplitude distortion of the waves and the breakdown of the distorted waves is more complex and it occurs at a lower Reynolds number than the breakdown of the $K$-type secondary instability that is observed when the FSN is not present.

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## Figures

Figure 1

Spanwise profiles of mean velocity and background unsteadiness for wakes generated by wires located in test section, measured 63.5mm upstream of leading edge: (a) and (d)d=25.4μm (case 2T); (b) and (e)d=50.8μm (case 4T); (c) and (f)d=101.6μm (case 5T)

Figure 13

Pseudoflow contour surfaces and contour lines of wave amplitude, uϕ∕U1, and background unsteadiness, u″/U1, for R=837.5. (a) K-type instability in base flow, (b) Same ribbon amplitude, but with FSN, d=101.5μm wire in test section (case 5T). For uϕ∕U1, dark surfaces: uϕ∕U1=−5.0%, light surfaces: uϕ∕U1=+5.0%, line contours, CR=±19.5%, from ±0.5%, with CI=1.0% (zero level not shown). For u″/U1, contour surface; u″/U1=+2.0%, line contours, CR=5.0%, CI=0.5%. Contour lines shown in the plane y=0.65mm. CR is contour range and CI is contour increment.

Figure 14

Pseudoflow visualization of contour surface of the total phase-averaged velocity, (U+uϕ)∕U1=0.4 corresponding to conditions in Fig. 1. (a) FSN, case 5T, showing fine-scale motions, and (b) base flow, with evidence of Λ-shaped loop resulting from K-type instability.

Figure 2

Spanwise velocity profiles of wakes generated by wires located upstream of contraction, measured 63.5mm upstream of leading edge: Undisturbed flow; d=50.8μm (case 1U); d=101.6μm (case 2U); d=152.4μm (case 3U); d=254μm (case 4U); and d=559μm (case 5U)

Figure 3

Spanwise uniformity of base-flow Blasius boundary layer in plane x=1.05m, R(=Rx1∕2)=837.5: (a) displacement thickness, δ1; (b) shape factor, H; (c) contours of mean velocity, U∕U1; (d) contours of background unsteadiness, u′/U1

Figure 4

Effect of low speed streak introduced by FSN. Case 2T, d=25μm wire, spanwise plane at R=641(x=0.615m): (a) contours of mean velocity, U∕U1; (b) contours of background unsteadiness, u′/U1; (c) power spectra with and without streak

Figure 5

Characteristics of low speed streaks introduced by FSN generated by wires located in the test section. Measurements in plane at x=1.05m, R=837.5: (a)d=25.4μm (case 2T); (b)d=50.8μm (case 4T); (c)d=101.6μm (case 5T). Lines η=2.3 correspond to the Blasius layer.

Figure 6

Characteristics of low speed streaks introduced by FSN generated by wires located upstream of contraction. Measurements in plane x=1.05m, R=837.5: (a)d=50.8μm (case 1U); (b)d=254μm (case 4U); and (c)d=559μm (case 5U). Lines η=2.3 correspond to the Blasius layer.

Figure 7

Modulation of the Blasius boundary layer with spanwise thickness variation but constant shape factor, H: (a) base flow; (b) modulation of magnitude; (c) modulation of spanwise position

Figure 8

Streamwise development of the spanwise variation of displacement thickness. Wires located in the test section: (a)d=25.4μm (case 2T); (b)d=50.8μm (case 4T); (c)d=101.6μm (case 5T). Wires located upstream of contraction: (d)d=50.8μm (case 1U); (e)d=254μm (case 4U); and (f)d=559μm (case 5U). Lines shown in range 15<z<20 indicate corresponding Blasius values, i.e., δ1=1.7208(vx∕U1)1∕2.

Figure 9

Development of minimum and maximum of spanwise displacement thickness variation. (a) Wires located in test section: d=25.4μm (case 2T), d=50.8μm (case 4T) and d=101.6μm (case 5T). (b) Wires located upstream of contraction: d=50.8μm (case 1U), d=254μm (case 4U), and d=559μm (case 5U).

Figure 10

Growth of peak background disturbance levels. (a) Wires located in test section: d=25.4μm (case 2T), d=50.8μm (case 4T), and d=101.6μm (case 5T). (b) Wires located upstream of contraction: d=50.8μm (case 1U), d=254μm (case 4U), and d=559μm (case 5U).

Figure 11

Interaction of small-amplitude TS waves with disturbance generated by the d=50.8μm wire located in the test section (case 4T). Contours of rms wave amplitude, u∕U1, in the spanwise plane, with increasing R (streamwise distance). Ribbon amplitude adjusted to ensure 0.1<u∕U1<0.5%. (a)R=659.0, umax=0.44%; (b)R=707.8, umax=0.30%; (c)R=837.5, umax=0.22%; (d)R=913.8, umax=0.11%; (e)R=1017.5, umax=0.20%, (umax defines legend).

Figure 12

Plan view of pseudo-flow contour surfaces of wave amplitude, uϕ∕U1, and contour lines of uϕ∕U1 and background unsteadiness u″/U1 for R=837.5. (a) K-type instability in base flow. (b) Same ribbon amplitude, but with FSN, d=101.5μm wire in the test section (case 5T). Dark surfaces: uϕ∕U1=−2.5%. Light surfaces: uϕ∕U1=+2.5%. Contour lines in plane y=1.2mm. For uϕ∕U1, CR=±6.25%, CI=0.5%, black lines are positive and gray lines negative levels. For u″/U1, CR=±0.60%, CI=0.05%. CR is contour range and CI is the contour increment.

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