**2. Experimental Set-Up**

In this study, a channel flow facility at the University of Liverpool has been utilised to carry out the experimental investigation. The same facility has been used earlier by Whalley et al. [23,24] and Agrawal et al. [27,28,29], and is shown here in Figure 1. The channel-flow facility is a rectangular duct consisting of 6 stainless steel modules and a test section. The test section is connected downstream of five stainless steel modules. Each module is of length 1.2 m and the test section has a length of 0.25 m. The width (*w*) and half-height (*h*) of the duct are 0.298 m and 0.0125 m, respectively, giving an aspect ratio (*w*/2*h*) of 11.92. The modules are constructed in such a manner as to ensure a hydraulically smooth transition between the modules.

**Figure 1.** Schematic of channel-flow flow facility (not to scale).

The working fluid is stored in a stainless steel header tank of capacity about 500 L. A Mono type E101 progressive cavity pump is used to circulate the fluid via the tank in a closed loop. The flow loop also consists of an additional mixing loop which provides an opportunity for having lower flow rates. Three pulsation dampers are situated just after the pump, which helps in damping any pulsations in the flow before entering the channel. A Promass Coriolis flow meter is installed in the return loop to measure the mass flow rate (*m*˙ ) of the fluid. This enables the bulk velocity (*Ub*) to be determined by the relation *Ub* = *m*˙ /(*ρA*), where *A* is the cross-sectional area of the channel and *ρ* is the density of the working fluid. A platinum resistance thermometer (PRT) is present in the last module of the channel which is used to measure the temperature of the working fluid. The PRT is powered by an Agilent 34,970 A switch unit, which provides temperature readings with a resolution of 0.01 ◦C. Throughout this study, only Newtonian fluids are used as working fluids. These are water–glycerol

mixtures of different concentrations where glycerol is used to increase the viscosity to get to lower Reynolds number. For example, while studying the flow for *Re<sup>τ</sup>* ≥ 180, water is used as the working fluid and while studying low Reynolds number flow (*Re<sup>τ</sup>* = 70), a 65% : 35% by weight glycerol–water mixture is used as the working fluid. The density of the working fluid is measured using an Anton Paar DMA 35 N density meter. The shear viscosity of the working fluid is measured using an Anton Paar MCR 302 rheometer. A cone and plate geometry is employed to measure shear viscosity for shear rate (*γ*˙ ,*s*−1) ranging from 10−<sup>2</sup> to 102.

Pressure-drop measurements are conducted using a Druck LPX-9381 low-differential pressure transducer, which has a working range of 5 kPa with an accuracy of ±5 Pa. A Baratron differential pressure transducer made by MKS is used to regularly calibrate the Druck pressure transducer. Instantaneous wall shear stress and velocity measurements are carried out using a hot-film anemometry (HFA) system and a laser Doppler velocimetry (LDV) system, respectively, in the test section. The sideand top-walls of the test section are made of borosilicate glass to provide optical access for the LDV measurements. A Dantec FiberFlow laser system is employed for velocity measurements which uses a 300 mW argon-ion continuous wave laser. Up to two component velocity measurements have been carried out thus requiring two pairs of laser beams of different wavelengths: blue (488 nm) and green (515.5 nm). A Bragg cell is utilised to resolve the directional ambiguity of the velocity of seeding particles by giving a frequency shift of 40 MHz to one of the laser beams. The laser beams are emitted using a transmitting optics (or laser head) which provides a beam separation of 51.5 mm and a focal length of 160 mm in air. The crossing of two beams of the same colour creates a measurement volume of 24 μm diameter and 150 μm length in air. The transmitting optics is placed on a traverse which allows movement of the measurement volume in all three directions. For the seeding particles, generally, natural particles present in the working fluid (for example, supply water) are found to be sufficient to obtain a good data rate. In cases where the natural seeding particles are found to be low, for example, when the working fluid has a high concentration of glycerol, Timiron Supersilk MP-1005, having an average size of 5 μm, are added to the working fluid. In this study, both single component and two-component velocity measurements have been carried out. In the case of two-component velocity measurements, the data are acquired in co-incident mode. This mode samples both velocity components of the same seeding particle simultaneously in the measurement volume. The LDV is operated in a forward-scatter mode and the typical data rate is around 100–500 Hz. The light scattered from the seeding particle enters the photodetector (receiving optics) which splits the laser beams based on the wavelengths. The laser beams then pass to the photomultiplier tubes (PMTs) which sends the Doppler frequencies to the flow processor, burst spectrum analyzer (BSA)-F50, made by Dantec Dynamics. The signals are converted to the corresponding velocity signals using the inbuilt signal processors in the flow processor.

Calculation of RSS requires simultaneous measurements of streamwise and wall-normal velocities, but the wall-normal velocity measurements cannot be made close to the bottom wall because of the cut-off of the laser beams [30], and therefore some modifications to the transmitting optics of the LDV set-up are made. The first modification is to rotate the laser head by 45◦ about the spanwise axis to get closer to the bottom wall, similarly to as previously done by Melling and Whitelaw [31], Walker and Tiederman [32] and Günther et al. [33]. Streamwise (*U*) and wall-normal (*V*) velocity components are recovered based on the coordinate transformation equation, as shown below.

$$
\begin{bmatrix} \mathcal{U} \\ \mathcal{V} \end{bmatrix} = \begin{bmatrix} \cos 45^{\circ} & \sin 45^{\circ} \\ -\sin 45^{\circ} & \cos 45^{\circ} \end{bmatrix} \begin{bmatrix} \mathcal{U}\_1 \\ \mathcal{U}\_2 \end{bmatrix} . \tag{1}
$$

Here, *U*<sup>1</sup> and *U*<sup>2</sup> are the velocity components measured by blue and green beams, respectively. This modification makes the minimum vertical height where the measurement of the wall-normal velocity component can be made reduced by a factor of 1/ <sup>√</sup>2. Next, an external LD1613-N-BK7 biconcave lens, made by Thorlabs, is placed in front of the laser head to increase the focal length of

the laser beams. This lens has a diameter of 25.4 mm and a focal length of 100 mm. Increasing the focal length enables the measurement volume to go further into the test section from the side-wall. Therefore, if the aim is to measure at the same spanwise location in the test section, the laser head needs to be moved further back from the side-wall. This modification enables the laser beams to be closer to each other when they enter through the side-wall. The measurement volume can get closer to the bottom wall as the laser beams get closer to each other. Thus, the two-component velocity measurements can be carried out closer to the bottom-wall after the addition of a biconcave lens. The lens is connected on a lens mount which is attached to an optical post. The optical post is then attached to the traverse of the transmitting optics. Therefore, the entire lens system can be traversed with the transmitting optics. It is important that both pairs of laser beams are aligned properly to the external lens. This alignment is checked based on the high data rate of the LDV signal in co-incident mode and validating the time-averaged RSS profile against available DNS data at the same Reynolds number. By making these two modifications, the two-component velocity measurements can be conducted for *y*/*h* ≥ 0.3 at a spanwise location of *z*/*h* = 5 in the channel-flow facility.

In this study, constant temperature anemometry (CTA) is employed for measuring the instantaneous wall shear stress by utilising the commercially available 55R48 glue-on hot-films probes (made by Dantec Dynamics). The hot-film sensor has a physical spanwise length (Δ*z*) of 0.9 mm. In inner units, this corresponds to Δ*z*<sup>+</sup> = 18 for *Re<sup>τ</sup>* = 250. In this study, the effect of measurement resolution issues due to sensor sizes are thought to be negligible as Ligrani and Bradshaw [34] considered a sensor length of about <sup>Δ</sup>*z*<sup>+</sup> <sup>20</sup> <sup>−</sup> 25 to be acceptable to make well-resolved turbulence measurements. In order to attach the sensor to the channel wall, removable Delrin plugs are designed and fabricated inhouse. The hot-film probes are glued on these plugs and these plugs are then inserted into the bottom wall of the test section. We ensure that the hot-films are flush with the bottom wall of the test section. A detailed description of the mounting process for the hot-film probes in the present channel has been provided in Agrawal [35]. The probe is powered by a Dantec StreamLine Pro velocimetry system. The bridge ratio and the overheat ratio of the anemometer are set at 10 and 1.1, respectively. The typical frequency response of the anemometer, against the square-wave generator is found to be around 10–30 kHz, which is generally considered sufficient for turbulence measurements [36]. The output voltage signal from the anemometer is then digitized using a 14-Bit USB6009 Multifunction A/D converter, made by National Instruments. After A/D converter, the signal is acquired using the CTA application software, StreamWare Pro, installed on the computer. In the case of simultaneous measurements of velocity and wall shear stress, the digitised voltage is sampled by the BSA flow processor which helps in the acquisition of time-synchronised velocity and wall shear stress data. The voltage output signals from the anemometer is converted to instantaneous wall shear stress signals using calibration against the mean pressure-drop obtained from the pressure transducer. The same procedure for the hot-film calibration as discussed in Agrawal et al. [27,28] has been conducted here.

In CTA, all the changes in the fluctuations in voltage output from the anemometer should be representative of fluctuations in the flow. Therefore, any change in voltage output due to thermal and non-thermal drifts need to be minimised. To minimise the thermal drift, an open-loop copper cooling coil is added to the overhead tank and the main supply water is used to control the temperature of the working fluid. Using this set-up, the temperature of the working fluid could be controlled to the precision of ±0.01 ◦C for the entire experimental run of the day (typically about 6–8 h). Non-thermal drifts are also observed which are generally caused due to the contamination of the hot-films [37]. A novel nonlinear regression technique, as discussed in Agrawal et al. [28], has been employed to recover the wall shear stress signals from the drifted voltage signal.

Experiments are conducted for five Reynolds numbers: *Reτ* = 70, 85, 120, 180 and 250 and for each Reynolds number, wall shear stress and velocity data are acquired simultaneously in the measurement test section using HFA and LDV, respectively, at a location of *z*/*h* = 5 and *x*/*h* = 496. As discussed in Agrawal et al. [27], the spanwise location of *z*/*h* = 5 is observed to be devoid of side-wall effects. Velocity acquisition is realised at various wall-normal locations, where each wall-normal location is sampled for 2 h at a typical data rate of around 300–400 Hz. Table 1 shows the Reynolds numbers, corresponding wall-normal locations studied and the parameters measured in this work. For *Reτ* = 70 and 85, both streamwise and wall-normal velocity components are measured simultaneously with the wall shear stress. These particular measurements have been conducted to study the RSS behaviour during the low- and high-drag events. For other Reynolds numbers, due to experimental limitations, only streamwise velocity measurements have been executed along with the wall shear stress because the near peak region of the RSS could not be measured for higher Reynolds numbers as this moves physically closer to the wall at higher Reynolds numbers where the LDV beams lose optical access.


**Table 1.** Reynolds numbers and various wall-normal locations studied. Parameters measured for each Reynolds numbers are also shown.

The procedure described by Kline and McClintock [38] has been employed here to conduct an uncertainty analysis of the measured and calculated variables. The employed channel-flow facility is carefully machined to provide negligible relative uncertainties (~0.15%) in the channel dimensions (*w* and *h*) and the length between the pressure tappings, *l*. The pressure transducer has an accuracy of ±5 Pa, and therefore the relative uncertainty in the mean wall shear stress is Δ*τw*/*τ<sup>w</sup>* = 1–3%. The density meter has a quoted accuracy of ±1 kg/m3. This gives a relative uncertainty in the density of the working fluid of Δ*ρ*/*ρ* = 0.09%. The relative uncertainty in the viscosity (*μ*) measurement of the working fluid using the rheometer is Δ*μ*/*μ* = 2%. The relative uncertainty in the friction velocity (*u<sup>τ</sup>* = *τw*/*ρ*) is Δ*uτ*/*u<sup>τ</sup>* = 0.5–1.5%. This gives an uncertainty in the friction Reynolds number (*Re<sup>τ</sup>* = *uτh*/*ν*) measurement of Δ*Reτ*/*Re<sup>τ</sup>* = 2–2.5%. The major sources of error in LDV data are due to velocity gradient broadening, velocity bias effect or fringe distortion [39]. These combined effects, in general, give the relative uncertainties in the mean velocity of 2–3% and the turbulent intensities of 4–6%. In inner units, the relative uncertainties in the mean velocities and turbulent intensities are Δ*U*+/*U*<sup>+</sup> = 2–3.5% and Δ*uv*+/*uv*<sup>+</sup> = 4–7%. Here, *u* and *v* represent streamwise velocity fluctuation and wall-normal velocity fluctuation, respectively. The LDV transmitting optics traverse has a precision of 0.001 mm, providing a relative uncertainty in the wall-normal position (*y*) measurement, close to the wall (*y* = 0.5 mm), to be Δ*y*/*y* = 0.2%. In inner units, at this wall-normal location, *y*<sup>+</sup> has an uncertainty of Δ*y*+/*y*<sup>+</sup> = 2–2.5%.

In this study, two different ways of averaging the measured variables are carried out: time-averaging and conditional-averaging. To differentiate between these two averages the following nomenclature are used: an overbar indicates a time-averaged quantity (e.g., *U*), and an overbar with an *L* or *H* superscripts indicates the conditionally-averaged quantity for low- and high-drag events (e.g., *U<sup>L</sup>* , *UH*), respectively. Similarly, friction velocities are calculated using two different wall shear stress: time-averaged wall shear stress (*uτ*) and conditionally-averaged wall shear stress (*u<sup>τ</sup> <sup>L</sup>*, *u<sup>τ</sup> <sup>H</sup>*). Based on these definitions of the friction velocities, the wall-normal locations are also normalised in three different ways: *y*<sup>+</sup> = *yuτ*/*ν*, *y*+*<sup>L</sup>* = *yu<sup>τ</sup> <sup>L</sup>*/*ν* and *y*+*<sup>H</sup>* = *yu<sup>τ</sup> <sup>H</sup>*/*ν*.
