Peak Expiratory Flow Meter

Research Article

Time-averaged velocity and scalar fields of the flow

Southampton So17 1Bj, United Kingdom

Received: XX 2021; Revised: XX XX 2021; Accepted: XX XX 2021 Keywords: mixing and dispersion, wakes, turbulent boundary layers, urban fluid dynamics, mixing enhancement, turbulence

Abstract

We examine the characteristics of mean flow and scalar concentration characteristics of a turbulent boundary layer flow impinging on a cluster of tall obstacles (which can also be interpreted as a porous obstruction). The cluster is created with a group of cylinders of diameter 𝑑and height ℎarranged in a circular patch of diameter 𝐷.The solidity of the patch/obstruction is defined by 𝜙(the total planar area covered by cylinders), which is systematically varied (0.098 ≤𝜙≤1) by increasing the number of cylinders in a patch (𝑁𝑐). A point source is placed at ground level upstream of the patch and its transport around the patch is examined. Time-averaged velocity and scalar fields, obtained from simultaneous planar PIV-PLIF (particle image velocimetry-planar laser-induced fluorescence) measurements, reveal that the characteristics of wake and flow above porous patches are heavily influenced by 𝜙.

In particular, we observe that the horizontal and vertical extent of the wake and scalar concentration downstream of the patches decreases and increases with 𝜙, respectively. Here, the recirculation bubble is shifted closer to the trailing edge of the patches as 𝜙increases, limiting the flow from convecting downstream, decreasing the scalar concentration and virtually ‘extending’ the patch in streamwise direction. As the bubble forms in the trailing edge, vertical bleeding increases and hence the concentration increases above patch where the cylinders appear to be ‘extend’ vertically towards the freestream.

Impact Statement

Canopy flow covers extensive phenomena encountered in both nature and engineering applications. The characteristics of canopies (also referred to as porous obstructions) is known to affect the mixing, momentum, and scalar (e.g. mass and heat) exchange processes in the flow. Examples include flow around urban areas, wind/tidal farms, patches of roughness in ship hulls, in-line heat-exchangers among various others. In almost all these applications, the patch of obstacles/roughness are typically characterised by its geometric properties such as solidity (frontal and plan) or porosity and it is important to understand the flow/scalar characteristics as well as transport processes for varied geometric parameters. For instance, an urban canopy with given distribution of buildings and a pollutant source at ground level could result in different wake/dispersion characteristics depending on the frontal or plan solidity of distribution. This study attempts to carry out simplified experiments that will enable us to understand the intricacies of scalar-momentum transport around such canopies and allow us to build useful models for engineering design and/or prediction for engineering and environmental flows.

Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.

E1-2

D. D. Wangsawijaya, C. Nicolai, and B. Ganapathisubramani

1. Introduction

Canopy flow refers to a scenario where a boundary layer develops over and around a porous sur- face/obstruction. Examples of such phenomenon are abound in both nature and engineering applications, including but not limited to: flows past aquatic and terrestrial vegetations, atmospheric boundary lay- ers developing over forests, clusters of tall buildings in cities, and wind/tidal farms, which consist of arrays of wind/tidal turbines. These obstructions are known to affect the scalar, momentum, and energy transport process in the flow within the canopy and downstream of the canopies. Aquatic vegetations, for example, provide shielding (Kemp et al., 2000), affect the sediment formation and erosion (De Lan- gre, 2008; Nepf, 2012a,b; Tinoco and Coco, 2016), and also carbon sequestration in coastal ecosystems (Lei and Nepf, 2021). Urban and vegetation canopies induce coherent, multi-scale turbulent motions in the atmospheric boundary layer (Katul et al., 1997; Kanda, 2006; Huang et al., 2009a,b, 2011; Li and Bou-Zeid, 2011), which governs flow mixing, momentum, heat and mass exchange within the layer (Raupach and Thom, 1981; Finnigan, 2000; Poggi et al., 2004), including pollutants and other chem- ical compounds (Poggi et al., 2006; Aristodemou et al., 2018). While the configuration and tuning of turbines in wind/tidal farms are vital in maximising power output (Vennell, 2011; Myers and Bahaj, 2012), they may also alter the meteorological pattern and ecosystem of the installation sites. For exam- ple, installation of wind turbines has been shown to affect the heat distribution and humidity of the surrounding air (Baidya Roy et al., 2004; Rajewski et al., 2016), while wakes generated by tidal turbines can potentially modify sedimentation process and bacterial population in estuarine waters (Ahmadian et al., 2012). Considering its extensive industrial applications and environmental impacts, understanding the transport mechanism of the flow surrounding porous obstructions is, therefore, essential.

Previous studies on porous obstructions (such as examples given above) typically involved some simplifications from real-life conditions. The obstruction may be simplified as an array of cylinders mounted on an isolated patch with an incoming flow upstream of the cylinders (illustrated in figure 1).

Numerical simulations and experiments have been conducted on the flow surrounding such cylindrical array (Ball et al., 1996; Nepf et al., 1997; Nepf, 1999; White and Nepf, 2003; Tanino and Nepf, 2008; Nicolle and Eames, 2011; Rominger and Nepf, 2011; Chen et al., 2012; Zong and Nepf, 2012; Chang and Constantinescu, 2015; Chang et al., 2017), where the cylinders are as tall as, or protruding from, a free surface, as commonly observed in emergent aquatic vegetations. Here, the flow is dominated by Kármán vortex street in wall-normal axis trailing behind the cylinders and thus can be considered two- dimensional (Taddei et al., 2016; Nicolai et al., 2020). A more general approach is to fully submerge the cylinders in the flow such that ℎ≪𝛿(figure 1b). Studies have been conducted for cylinders attached to a bottom wall (as in figure 1b, see also Chen et al., 2013; Taddei et al., 2016; Nicolai et al., 2020) and/or suspended from a free surface (Plew, 2011; Tseung et al., 2016; Zhou and Venayagamoorthy, 2019). In either cases, the patch is considered as 3-D, as flow mixing occurs on the sides of, downstream of, and above the body. Taddei et al. (2016); Zhou and Venayagamoorthy (2019); Nicolai et al. (2020) have identified three mechanisms in which the flow may escape (‘bleed’) from a fully submerged porous obstruction: (i) the lateral bleeding from the interior of the patch to the sides (spanwise direction, see figure 1a), (ii) the trailing edge bleeding, which is responsible in the formation of wake downstream of the body (figure 1a), and (iii) the vertical bleeding, in which the flow escapes from the interior to the top surface of the patch and towards the freestream (figure 1b).

It has been reported that the solidity of a porous obstruction is a critical parameter in determining drag (Nepf, 1999; Taddei et al., 2016; Chang et al., 2017; Zhou and Venayagamoorthy, 2019), the structure of wake formed by the obstruction (Ball et al., 1996; Nicolle and Eames, 2011; Zong and Nepf, 2012; Chen et al., 2012; Chang and Constantinescu, 2015; Chang et al., 2017; Zhou and Venayagamoorthy, 2019; Nicolai et al., 2020), scalar dispersion (Nepf et al., 1997; White and Nepf, 2003; Tanino and Nepf, 2008), and sediment disposition (Chen et al., 2012; Chang and Constantinescu, 2015). For the cylindrical array shown in figure 1, the solidity is measured in terms of the planar area covered by cylinders per total surface, 𝜙≡𝑁𝑐(𝑑/𝐷)2 (also commonly referred to as the solid volume fraction), where 𝑁𝑐is the number of cylinders in a circular patch, 𝐷is the diameter of the circular patch, and 𝑑is

E1-3

Figure 1. Illustrations of (a) lateral and trailing edge bleeding, and (b) vertical bleeding of cylindrical arrays on a circular patch. 𝑈𝑏𝑙is the incoming boundary-layer velocity, whose thickness is 𝛿𝑏𝑙, and ℎ is the height of the cylinders.

the diameter of the cylinder (see figure 2a,d for graphical descriptions of 𝐷and 𝑑). It has been observed by Nicolle and Eames (2011); Taddei et al. (2016); Zhou and Venayagamoorthy (2019) that total drag of the patch 𝐶𝐷increases with the increasing 𝜙then drops for a solid obstruction (𝜙= 1, figure 2d). Higher patch solidity also yields shorter and taller wake (in streamwise and wall-normal direction, respectively, see Nicolai et al., 2020) in the trailing edge, and increases both lateral and vertical bleeding (Zhou and Venayagamoorthy, 2019, see also figure 1). Further, it has been reported in Nicolle and Eames (2011) that at low 𝜙(𝜙< 0.05) each cylinder in an array behaves as a single obstruction, and as the solidity increases to 𝜙> 0.15 the cylindrical array behaves closer to a solid obstruction whose size is equal to that of the patch (𝜙= 1, figure 2d). Within the range of moderate solidity (0.05 ≤𝜙≤0.15), suppression of vortex street formation downstream of 2-D porous patches has been observed. In its place is a steady wake (constant velocity) region, which is a consequence of flow bleeding. Zong and Nepf (2012) and Chen et al. (2012) showed that the streamwise length of this steady wake region scales on 𝐶𝐷𝑎𝐷, where 𝑎is the frontal area per unit volume 𝑎≡𝑁𝑐𝑑/(0.25𝜋𝐷2). Similarly, scaling by 𝐶𝐷𝑎𝑏and 𝐶𝐷𝑎ℎhave also been observed in Rominger and Nepf (2011) for a square patch and Chen et al. (2013) for a fully submerged patch, respectively, where 𝑏is the half-width of the patch.

Although the characteristics of the wake and drag of a porous obstruction shown in figure 1 have been discussed in details for both 2-D and 3-D patches, an element that is still missing from these analyses is the intricacy between bleeding and scalar transport in 3-D porous patches. So far, discussions about scalar transport are limited to lateral and longitudinal dispersion in 2-D patches (White and Nepf, 2003; Tanino and Nepf, 2008), sediment deposition (Chen et al., 2012; Tinoco and Coco, 2016), qualitative flow visualisation using dye injection (Ball et al., 1996; Rominger and Nepf, 2011; Zong and Nepf, 2012), and non-simultaneous velocity and scalar measurements due to limitations of the experimental facilities (Nepf, 1999; Tanino and Nepf, 2008). Here, a 3-D porous patch serves as a more realistic model of urban landscapes, vegetation canopies, and wind farms, which are typically subsumed within the atmospheric boundary layer. Inclusion of scalar measurements (in addition to the velocity components) has many potential benefits, for example: in air pollution studies, where one might consider cluster of densely populated urban landscape as a porous obstruction and the pollutant as scalar, or in studies about sediment disposition in ocean beds.

In this study we aim to address the following question: given a point source of scalar located at ground level just upstream of 3-D porous patches, what are the flow and scalar characteristics in the wake and above the patches for various solidities? To answer this question, we conduct a parametric study of turbulent boundary layers impinging on an array of cylinders mounted on a circular patch (see figure 1).

A point source upstream of the patch is created by releasing a passive fluorescent dye. The solidity 𝜙is

E1-4

D. D. Wangsawijaya, C. Nicolai, and B. Ganapathisubramani varied by systematically increasing the number of cylinders in the patch, such that 0.098 ≤𝜙≤1. This covers both medium and high solidity range described in Nicolle and Eames (2011). The axis system (𝑥, 𝑦, 𝑧) corresponds to the streamwise, wall-normal, and spanwise direction, respectively. Simultaneous planar PIV-PLIF measurements in 𝑥–𝑦plane provide the instantaneous streamwise–wall-normal velocity components 𝑢and 𝑣, respectively, and scalar concentration field 𝑐, which can be decomposed further into their time-average and fluctuation about the mean

(1)

It should be noted that due to the choice of the measurement plane, discussion about flow bleeding in the current study is limited only to the trailing edge and vertical bleeding (figure 1).

2.1. Test Cases

section has the size of 6250 mm × 1200 mm (length × width). In all measurements, the water level is kept constant at 600 mm and the freestream velocity is set to 𝑈∞≈0.45 ms−1. A circular patch with a diameter (𝐷) of 100 mm is mounted on the floor of the tunnel at 5500 mm downstream of the test section entrance, which corresponds to the patch Reynolds number 𝑅𝑒𝐷≡ 𝑈∞𝐷/𝜈≈4.5 × 104, where 𝜈= 1.0035 × 10−6 m2s−1 is the kinematic viscosity of water at 20◦C. The patch constitutes an array of rigid cylinders, each has the diameter of 𝑑= 5 mm and height ℎ= 30 mm (figures 1b and 2a,d). The cylinders are arranged along concentric, evenly-spaced circles whose axis is at the centre of the circular patch, such that the distance between two consecutive cylinders is constant within the patch (see figures 2a–c). The solidity of the patch is parametrically varied by gradually increasing the number of cylinders 𝑁𝑐while keeping 𝐷and 𝑑constant. Table 1 and figures 2(a–c) show three different circular patches: C39, C64, C133, which correspond to 𝑁𝑐= 39, 64, 133, which cover a range of patch density of 0.1 ≲𝜙≲0.33 (2.5 ≲𝑎𝐷≲8.5). A solid obstruction case, i.e. a cylinder covering the entire circular patch (such that 𝑁𝑐= 1 and 𝜙= 1), is included in addition to the porous cases as case ‘CS’ in table 1 and figure 2(d). The solid cylinder in case CS has an equal height ℎto the cylinder arrays in other test cases.

2.2. Validation with smooth-wall turbulent boundary layer A smooth-wall turbulent boundary layer (‘TBL’) case is first tested to validate PIV measurements in the present study. The measurement is conducted in the same test section as other test cases by removing the circular patch. This flow has the Reynolds number (based on momentum thickness 𝜃) of 𝑅𝑒𝜃≡𝜃𝑈∞/𝜈≈3000 and friction Reynolds number 𝑅𝑒𝜏≡𝛿𝑏𝑙𝑈𝜏𝑏𝑙/𝜈≈1500, where 𝛿𝑏𝑙= 82 ± 3%

√︁

𝜏0/𝜌= 0.019 ± 2% ms−1 is the friction velocity for this case, 𝜏0 is the wall shear stress, and 𝜌= 998.12 kg m−3 is the density of water at 20◦C. Figure 2(e) shows the profiles of mean streamwise velocity 𝑈+ ≡𝑈/𝑈𝜏𝑏𝑙and the variance of velocity fluctuations

𝑢′𝑢′+ ≡𝑢′𝑢′/𝑈2

𝜏𝑠as functions of wall-normal location 𝑦+ ≡𝑦𝑈𝜏𝑠/𝜈, where subscript ‘+’ denotes viscous scaling and the viscous lengthscale 𝜈/𝑈𝜏𝑠= 0.053 mm. The logarithmic region of the mean velocity collapses to the line 1/𝜅log 𝑦+ + 𝐴, where 𝜅= 0.41 is the von Kármán constant and the 𝐴= 5.0 is the log-law shift (Schlichting and Gersten, 2017). The variance 𝑢′𝑢′ is in good agreement with that obtained from direct numerical simulation (DNS) of Sillero et al. (2014) at 𝑅𝑒𝜃= 4000.

Note that the DNS results presented in figure 2(e) are filtered according to the spatial resolution of the PIV measurements (Lee et al., 2016), ∆𝑥+ × ∆𝑦+ = 15 × 15 in streamwise and wall-normal directions, respectively.



Table 1. List of cylinder array test cases. 𝑁𝑐is the number of cylinders in a patch, 𝑑and 𝐷are the diameters of the cylinders and the patch, respectively, ℎis the height of the cylinders, 𝜙is patch solidity, and 𝑎is the frontal area per unit volume. ‘PIV’ and ‘PLIF’ columns show the availability of PIV and PLIF images of each test case. The last three columns show the availability of those images in each FOV.

Figure 2. Illustration of cylinder array test cases: (a) C39, (b) C64, (c) C133, and (d) the solid case (CS) in 𝑥–𝑧plane (top view), 𝑑is cylinder diameter and 𝐷is the circular patch diameter. (e) Mean streamwise velocity 𝑈+ (◦) and variance of velocity fluctuation 𝑢′𝑢′+ (•) of the smooth-wall turbulent boundary-layer (TBL) case as functions of wall-normal location 𝑦+ at 𝑅𝑒𝜃≈3000, where 𝜃is the

) Is The Dns Results Of

Sillero et al. (2014) at 𝑅𝑒𝜃= 4000, filtered according to the spatial resolution of the PIV measurements (Lee et al., 2016). Data are downsampled for clarity. 2.3. Particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) For simultaneous planar PIV and PLIF measurements, the measurement domain is located in the streamwise–wall-normal (𝑥–𝑦) plane, slicing the centerline of the circular patch (figure 3) and illuminated by Nd:YAG 100 mJ pulsed laser. The measurement domain is created by combining 3 successive experiments in field-of-view (FOV) 1, FOV 2, and FOV 3, which extends downstream of the circular patch. Dashed lines in figure 3 illustrate these FOVs and the overlaps between each FOV. It should be noted that although the PIV and PLIF measurements are conducted simultaneously in each FOV, these measurements are not conducted simultanenously between FOV 1, 2 and 3. PIV and PLIF images are recorded first in FOV 1, then the cameras and optics are traversed downstream to form FOV 2, then FOV 3. Measurements are conducted in all three FOVs for the cylindrical array cases (C39, C64, and C133), and only the first two FOVs for the baseline cases (CS and TBL, see table 1).

E1-6

D. D. Wangsawijaya, C. Nicolai, and B. Ganapathisubramani Figure 3. Contours of instantaneous (a) streamwise velocity 𝑢/𝑈ℎ/2 and (b) scalar concentration 𝑐/𝐶𝑠 (in logarithmic scale) of case C39, obtained from (a) PIV and (b) PLIF measurements, respectively, where 𝑈ℎ/2 is the incoming velocity at half-height of the cylinders. Dashed lines show the extent of FOV 1, 2 and 3. Black rectangles illustrate the cylinder array of height ℎmounted on a circular patch. The origin 𝑥= 0 is at the centre of the patch and 𝑦= 0 is on the floor of the tunnel. Measurement data are not available in the hatched regions (between the cylinders). In (b), blue arrow shows the location of the scalar point source.

In each FOV, PIV images are recorded by a pair of 4 MP CMOS cameras, equipped with wavelength filters to filter out the PLIF signal. As many as 3000 image pairs are acquired for each case at the rate of 4 Hz, which corresponds to the boundary-layer turnover rate of 𝑇𝑈∞/𝛿𝑏𝑙= 1.4. The timing between

A Pair Of Piv Images Is ∼1 Ms (𝑡+ ≡∆𝑡𝑈2

𝜏𝑏𝑙/𝜈≈0.32). Image cross-correlation and post-processing of the resulting velocity vectors are conducted using a commercial software (DaVis, LaVision GmbH), with the final window size of 24 × 24 pixels (50% overlap) and image pixel size of 15 pixels/mm, which corresponds to the spatial resolution of ∆𝑥+ ×∆𝑦+ = 15×15 for case TBL. Each FOV has the size of 253 mm ×126 mm (𝑥× 𝑦), which approximately extends 2.5 times the patch diameter (2.5𝐷) in streamwise and 4ℎin height. When the three FOVs are stitched together, the total length in 𝑥is 689 mm (6.89𝐷).

For PLIF measurements, a point source is created upstream of the circular patch by injecting Rho- damine 6G dye solution (Schmidt number 𝑆𝑐≈2500) to the flow at the rate of 30 cc/min. The dye is supplied by gravity through a thin tube (3 mm diameter) embedded at the floor of the tunnel at 45◦ angle. The tube is located at 125 mm upstream from the centre the patch (𝑥/𝐷= 1.25, see figure 3b).

PLIF images are acquired using a 5.5 MP 16-bit sCMOS camera equipped with a wavelength filter to block all light except the PLIF signal (Vanderwel and Tavoularis, 2014). To reduce the uncertainty of the scalar concentration measurements, the laser power is recorded at each pulse by an in-line power energy monitor. To maximise the signal-to-noise ratio of the scalar concentration, the concentration of the dye solution at point source 𝐶𝑠is varied based on the location of the FOV relative to the point source. For FOV 1 (closest to the point source), 𝐶𝑠= 0.3 mg/L, while for FOV 2 and FOV 3, 𝐶𝑠= 10 mg/L. The measured scalar concentration presented in this study is normalised by 𝐶𝑠.

E1-7

Figure 4. Contours of time-averaged streamwise velocity 𝑈/𝑈∞of case: (a) C39, (b) C64, (c) C133, and (d) CS. Lines are the time-averaged spanwise vorticity Ω𝑦𝐷/𝑈ℎ/2 with the following contour levels:

) And 0.4, 0.8, ..., 1.6 (

). Figure 5. Contours of time-averaged scalar concentration 𝐶/𝐶𝑠(in logarithmic scale) of case: (a) C39, (b) C64, (c) C133, and (d) CS. Lines are the time-averaged wall-normal velocity 𝑉/𝑈ℎ/2 with the

). Measurement Data

are not available in the hatched regions.

Related Journal Articles & DOI Links

Selected peer-reviewed publications relevant to 12 Lead ECG Acquisition. Click the DOI to access the full paper (may require institutional access).

Why Choose Us?

Bangalore guidance for robotics, Spectre and autonomous systems projects.