## 2 Wind Tunnel Apparatus, Equipment, and Test Conditions
### Flat-Plate Model  
During the tests, a riblet surface attached to the surface of a flat aluminum plate was investigated. The setup of the flat-plate model, which had an effective span length of 650 mm, a chord length of 900 mm, and a thickness of 10.8 mm, is shown in Figure 1. An array of disk-shaped roughness elements (a product of CAD-CUT Inc.) were used, each element being 0.29 mm high with a diameter of 1 mm. The array was attached to the test model surface 20 mm downstream of the leading edge at intervals of 2.54 mm in the spanwise direction. The location from the leading edge (\(x=20\) mm) where the disk roughness was located will be referred to as a virtual origin in the evaluation process of the reduction of skin friction drag in a later section. The disk roughness was used to trip the boundary layer. The roughness height was determined to be 50% of the assumed laminar boundary layer thickness, given by \(\delta_{laminar}(x)\cong 5.0 xRe_{x}^{-1/2}\)[25].  
Figure 2 shows the details of the leading edge of the flat-plate model. The effect of the shape of the leading edge on the evolution of the boundary layer profile is discussed later in this section.  
Figure 3 shows the shape factor (\(H_{12}\)), which is the ratio between the displacement thickness (\(6\"\)) and the momentum thickness (\(\theta\)), at several stations from the leading edge measured by using the pitot-rake (described in a later section). The displacement thickness and the momentum thickness are expressed in Equation (1) and Equation (2), respectively. Those values were based on the velocity profile in the boundary layer measured by pitot rake. The shape factor (\(H_{12}\)) is also expressed as Equation (3) and was used to evaluate the flow state in the boundary layer. In general, in the turbulent  
Figure 1: Schematic illustration of the flat-plate test model installed at the center of the wind tunnel duct.  
boundary layer, the higher that \(H_{12}\) is, the stronger the adverse pressure gradient. The value of \(H_{12}\) would typically be 1.3 to 1.4 for a fully developed turbulent boundary layer:  
\[\delta^{*}=\int_{0}^{\infty}\!\!\left(1-\frac{U(z)}{U_{\infty}}\right)\!dz, \tag{1}\]  
\[\theta=\int_{0}^{\infty}\frac{U(z)}{U_{\infty}}\!\left(1-\frac{U(z)}{U_{\infty }}\right)\!dz, \tag{2}\]  
\[H_{12}=\frac{\text{Displacement Thickness}}{\text{Momentum Thickness}}=\frac{ \delta^{*}}{\theta}. \tag{3}\]  
In Figure 3, the horizontal axis is the Reynolds number based on the measurement location from the leading edge and the freestream velocity. Three plots obtained at three different measurement locations (\(x\!/\!x_{chord}\) = 1/2, 2/3, and 0.94 or \(x\) = 450, 600, and 850 mm, respectively) are plotted for comparison. As seen in Figure 3, \(H_{12}\) lies approximately 1.4 for a Reynolds number range of \(6.0\times 10^{5}\) to \(4.0\times 10^{6}\), which corresponds to a freestream velocity range of 25 to 80 m/s downstream 450 mm (\(x\!/\!x_{chord}\) = 1/2). Therefore, the primary measurement using the hot-wire anemometry was implemented at \(x\) = 600 mm (\(x\!/\!x_{chord}\) = 2/3) from the leading edge.