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Effect of length of two-dimensional obstacles on characteristics of separation and reattachment
Journal of Wind Engineering & Industrial Aerodynamics 178 (2018) 38–48
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Effect of length of two-dimensional obstacles on characteristics of separation and reattachment J. van der Kindere, B. Ganapathisubramani * Faculty of Engineering and the Environment, University of Southampton, Southampton, SO17 1BJ, United Kingdom
A R T I C L E I N F O
A B S T R A C T
Keywords: Separated flow Flow past ribs Particle image velocimetry
The flow over a forward-facing step (FFS) and a backward-facing step (BFS) have been extensively studied separately, but the interaction between both obstacles has received little attention. It is believed the distance between the two faces of the step is a critical parameter governing the overall behaviour of the flow. This could have implication on the effect an obstacle would have on its surroundings, such as wind disturbance, or spread of pollution. Consequently, we investigate in detail the flow over a two-dimensional obstacle (also referred to as a rib), that consists of a FFS followed by a BFS. The flow field in such configuration is a result of the interaction between the multiple separation regions that appear upstream, above and downstream of the ribs. Our experimental model is submerged in a fully turbulent boundary layer (δ=H ¼ 1:37, where δ and H are respectively incoming boundary layer thickness and rib height), and the Reynolds number based on rib height is ReH ¼ 20; 000. Rib length (distance between the two vertical faces) varied between L=H ¼ 0:1 and L=H ¼ 8. In order to describe the general features of such a flow, we carried out flow field velocity and surface pressure measurements. Results show that two trends exist according to the length of the rib. Short ribs (L=H 4) produce one large recirculation region from the leading edge which results in higher levels of large scale turbulence which propagate far downstream. On the contrary, the FFS portion of long ribs (L=H 4) is decoupled from the BFS portion. Two separate shear layers are formed which decay quicker resulting in lower levels of turbulence propagating downstream.
1. Introduction Surface-mounted obstacles in industrial, aeronautical, or civil engineering produce unsteady flows with strong turbulence. These situations may improve flow-mixing properties, stabilize a combustion process, or jeopardize the integrity of buildings and their surroundings. Most previous studies have focussed on the separation and reattachment for forward-facing or backward-facing step flows (FFS and BFS). A twodimensional backward-facing step flow is perhaps the most studied canonical separated flow (Armaly et al., 1983; Lee and Mateescu, 1998; Lee et al., 2004), primarily because it is a major source of drag in automotive and aerospace applications. It contains a separated shear layer which interacts with both the free-stream and a region of reverse flow. This produces a complex feedback mechanism that is a source of pressure loss and noise (Chun and Sung, 1996; Le et al., 1997). In comparison, the forward-facing step flow has been a subject of fewer studies (Sherry et al., 2010; Pearson et al., 2013). This type of configuration has been examined more recently in the context of wind resource assessment near
escarpments and cliffs for normal flow as well as yawed flow configurations (Rowcroft et al., 2016). Despite being very common in nature and engineering applications, the flow field past a two-dimensional rib, which is a combination of forward-facing step followed by a backward-facing step, remains a subject with little documentation. Depending on the distance between the upstream and downstream edges of a rib, the separated flow of the forward-facing step may reattach on top of the rib or merge to different degrees with that of the backward-facing steps. Consequently up to three regions may interact together: upstream, on top, and downstream of the rib (see Fig. 1). As described by authors studying these types of obstacles, instrumentation was a limitation, thus a thorough description of recirculation regions was also limited (Counihan et al., 1974; Arie et al. 1975a, 1975b; Castro, 1979; Moss and Baker, 1980; Bergeles and Athanassiadis, 1983; Castro and Dianat, 1983; Dianat and Castro, 1984; Castro and Haque, 1987; Antoniou and Bergeles, 1988). In flow past ribs, there is a difference between flow past ribs with a reattached flow on the top surface (long ribs), and ribs too short for
* Corresponding author. E-mail addresses: [email protected] (J. van der Kindere), [email protected] (B. Ganapathisubramani). https://doi.org/10.1016/j.jweia.2018.04.018 Received 8 January 2018; Received in revised form 15 April 2018; Accepted 15 April 2018 Available online 29 May 2018 0167-6105/© 2018 Elsevier Ltd. All rights reserved.
J. van der Kindere, B. Ganapathisubramani
Journal of Wind Engineering & Industrial Aerodynamics 178 (2018) 38–48
Fig. 1. General configuration of the flow over ribs illustrating the main parameters of the study.
a range of rib height to boundary layer thickness ratio comparable to Bergeles and Athanassiadis (1983), it is reported that pressure drag coefficient decreases with rib length, and δ=H. For longer ribs, it is reported that the drag coefficient remains relatively unchanged. It can be assumed that for very long ribs, skin friction on the top surface increases viscous drag which is not accounted for in pressure drag. Arie et al. (1975b) supports the first experiment and adds a more detailed overview of surface pressure distribution for two rib lengths (L=H ¼ 2 and L=H ¼ 4). Some trends are highlighted: the pressure drop after the leading edge of the rib is stronger as δ=H decreases, and the pressure on the downstream face is constant at all heights whereas it is not on the upstream face. Finally, the turbulent fluctuations induced by ribs is studied by Arie et al. (1975b) and Antoniou and Bergeles (1988). The mixing process in the wake between the uniform flow above, and the still region downstream of the rib is compared by Arie et al. (1975b) to G€ ortler's theory on a uniform flow mixing with static fluid. The authors quote maximum turbulence intensity being generated at lowest δ=H, and above the top surface of the rib. The exact height of maximum turbulence intensity varies with rib length (y=H ¼ 1:13 for short ribs and y=H ¼ 2:5 for a fence). The deviation is associated with Coanda effects along the top surface. In addition, the authors observe that the disruption caused by ribs requires a long time or distance to return to unperturbed boundary layer characteristics. Indeed, it is still not recovered at 25H downstream of the ribs. Similar findings were made by Castro (1979). Antoniou and Bergeles (1988) studied the far wake of short and long ribs and found the lifespan of perturbations caused by long ribs is comparatively shorter than those caused by short ribs. However, the near-field flow characteristics that could lead to this far field effect remains unresolved. In the current study, the aim is to develop further understanding of the flow over ribs of different lengths. The analysis is focussed on three main topics: the length of each recirculation region as rib length varies, the average surface pressure distribution these ribs yield, and finally the turbulent flow fields in the near-wake of the rib. We investigate the effect of rib length on the fluctuations of these quantities, and identify the causes of established trends.
reattachment to take place on the top surface (short ribs). This type of flow has been examined in the context of an elongated bluff body, where the flow separates at the leading edge and reattaches along the chord of the body before separating once again at the trailing edge. Cherry et al. (1984) examined the flow over an infinite plate with a blunt leading edge and found that large vortices are shed from the leading edge separation bubble, however, there was not associated periodicity. Nakamura and Nakashima (1986) have shown that these vortices will form a staggered vortex-street-like arrangement in the wake of blunt-nosed elongated bodies even with a splitter plate because of the presence of the trailing edge. In these type of flows, the elongation ratio (which is the ratio between length of the body to its thickness) is analogous to the length (L) to height (H) ratio of wall-mounted ribs. Parker and Welsh (1983) performed a detailed study for rectangular cylinders over a wide range of elongation ratios and found that there is no dominant frequency in the wake at high Reynolds numbers. Taylor et al. (2011) showed that larger leading edge separation-reattachment increases the role of the turbulent stresses in the recirculation region. Taylor et al. (2013) found that the changes in the leading edge separation-reattachment create markedly different levels of turbulent kinetic energy and near wake structure. Although there are similarities between elongated bodies and ribs, the presence of a wall that bounds the flow in the wake as well the turbulence in the incoming boundary layer will alter the characteristics of separation and reattachment at the leading edge and the wake of wall-mounted obstacles. In the context of wall-mounted obstacles, Castro (1979) asserts that here is a possibility of a reattachment point on the top if there is sufficient amount of turbulence in the incoming boundary layer, and if the rib is long enough. Bergeles and Athanassiadis (1983) and Arie et al. (1975b) agree and find that the threshold between the presence and absence of a reattachment point on top of the rib is near L=H ¼ 3. Bergeles and Athanassiadis (1983) show that the FFS portion is consistent with an isolated FFS in similar flow conditions without discussing potential effects of Reynolds number and incoming flow. Bergeles and Athanassiadis (1983) describe the presence of two trends in the mean recirculation length (LR ) of the wake region. LR decreases linearly with rib length for short ribs (L=H < 4) from over 11.5H–2.8H and is nearly constant for long ribs (L=H 4) at approximately 3H. The authors note that LR in the wake of long ribs is less than what is commonly found in simple backward-facing steps. Adams and Johnston (1988) quote a typical LR between four and ten times the step height in backward-facing steps, whereas Bergeles and Athanassiadis (1983) quote values of LR in the region of three times the height in the case of ribs. Leclercq et al. (2001) find similar results for a rib with L=H ¼ 10. The argument of strong turbulent flow mixing at the trailing edge of the rib is used to justify the discrepancy between ribs and isolated BFS. Finally, the recirculation region upstream of the rib receives the least amount of attention from aforementioned studies, but it seems to display a nearly constant mean recirculation length (Bergeles and Athanassiadis, 1983). The surface pressure distribution, which defines the largest aerodynamic load on a rib-like structure, was addressed by Arie et al. (1975a). The study provides an overview of the behaviour of ribs immersed in a turbulent boundary layer by investigating the mean pressure drag generated at different inflow conditions, but less emphasis is placed on the effect of rib length. For rib lengths up to L=H ¼ 5, within
2. Experimental arrangement 2.1. Test cases and flow conditions The experiment was carried out at the University of Southampton in an open return wind tunnel with a rectangular test section of 0.9 m 0.6 m 4.35 m. The arrangement is depicted in Fig. 2. Speed in the test section (Ue ) was set to 10 m/s and verified with a pair of Pitot tubes. The experiment was mounted on a smooth false floor to control the incoming boundary layer. It extended 2.35 m upstream of the two-dimensional obstacle, and 1.35 m downstream. The leading edge of the false floor was a thin wedge with a strip of zig-zag tape to trip the boundary layer. In order to control circulation around the floor, a flap was mounted at the trailing edge. It was set at an angle that would suppress separation at the leading edge of the floor. This was verified with surface oil flow visualisation near the leading edge. A synthetic smoke generator was used to seed the flow. The obstacles (referred hereafter as ribs) extended along the entire span of the wind tunnel, thus generating a “two-dimensional” obstacle.
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J. van der Kindere, B. Ganapathisubramani
Journal of Wind Engineering & Industrial Aerodynamics 178 (2018) 38–48
Fig. 2. Illustration of the arrangement in the test section. The ribs are mounted between plates of the false floor which is suspended above the floor of the wind-tunnel.
Statistical two-dimensionality of the flow is expected along the centreline because the ribs aspect ratio (height to span) is over 30 (see Moss and Baker (1980) and Kiya and Sasaki (1983) who studied this matter). In addition, the blockage ratio is less than 7%. The false floor as well as the ribs themselves contained pressure taps for mean pressure measurements (see section 2.2). The ribs are inserted between the upstream and the downstream plates of the false floor. Thus, the number transducers is fixed before and after the obstacles so the total number of transducers varies with rib length. In total, six rib lengths were studied: L=H ¼ 0:1; 1; 2; 4; 6; 8, with streamwise rib length L and height H ¼ 30 mm. In addition, the false floor's boundary layer was measured without obstacle using the full set of instruments in order to quantify the base-flow's properties. The flow conditions are described in Section 2.3. With the given free stream velocity and rib height a representative Reynolds number is obtained: ReH ¼ 20000. In this study, lengths are normalized by rib height, local velocity by mean freestream velocity and the origin of the coordinate system is located at the bottom of the upstream face of the rib.
acquire the mean pressure measurements has an accuracy of 0.12% of full-scale, which represents an uncertainty of 6Pa. Thermal drift is considered negligible since the wind-tunnel lab was pre-heated prior to the measurements. In addition, the sensor was zeroed prior to each measurement. Measurements were performed in a plane near the centreline of the model. At this location, the nominally two-dimensional flow was expected to be span-wise homogeneous from a statistics standpoint. This homogeneity was indeed verified for each case with surface oil flow visualisation techniques as per Maltby (1962) and Smits and Lim (2000). 2.3. Approaching flow conditions To obtain incoming flow properties, separate PIV measurements were carried out over the flat plate without rib. The properties of the incoming flow extracted at x=H ¼ 0 are summarized in Table 1. The incoming turbulent boundary layer exhibits a typical log-law profile of a fully developed turbulent boundary layer with κ ¼ 0:384, and B ¼ 4:17 (Marusic et al., 2013). Fitting the log-law to a velocity profile of the incoming boundary layer with this information allowed us to determine the skin-friction velocity. Turbulence content of the approaching flow is characterized by the turbulence intensity within the boundary layer. Fig. 3 also illustrates the streamwise velocity fluctuation profile of the incoming flow. It indicates the ribs are fully immersed within the turbulent boundary layer. The turbulence intensity at the rib height was approximately 4%.
2.2. Measurements Two techniques were used to measure the flow. Flow field velocity was obtained through low-frequency planar particle image velocimetry (PIV). Mean pressure distribution was obtained through pressure taps on the surface of the model. For PIV measurements, seeding is provided by a Martin Magnum 1200 fog smoke machine, ejecting smoke particles (size 1 μm). Two double cavity Nano L 200-15 PIV lasers from Litron illuminated the particles. A large field of view was required to capture the flow in all three expected recirculation regions. The best compromise found was three LaVision's LX Imager 16 MP PIV cameras in conjunction with Sigma 105 mm F2.8 Macro lenses. The total field of view covered 5:4 X=H 14:5, and 0 Y=H 6. PIV interrogation window size was 16 16 pixel with 50% overlap resulting in a vector spacing of 0:5 mm in both axes. The high fluctuations expected in the flow dictated that a high number of samples were necessary for statistical convergence. Standard deviation values of the velocity in the shear layer of FF and BF steps are typically 30% of the free stream velocity. As a result, 2000 vector fields per case were acquired. While the PIV system acquired velocity information, a second system acquired mean surface pressure measurements from 48 pressure taps located near the intersection of the laser sheet from the PIV system with the models. These are aligned axially with a spacing of 0:5H, the first one at X=H ¼ 8:25. Each pressure tap is made up of a brass tube piercing through the surface of the obstacle. These measure 0.6 mm (innerdiameter), and 0.8 mm (outer-diameter). They are cut flush with the surface and glued in position. On the service side of the model, they are connected through fine silicon tubing (0.6 mm) to a 64-channel Scanivalve ZOC 33/64 pressure sensor. The Scanivalve transducer used to
3. Global trends of the flow with varying rib length 3.1. Average recirculation region dimensions The flow over ribs over varying length produces up to three separation regions. Fig. 4 summarizes the evolution of those recirculation regions. On top, long ribs (L=H ¼ 8, 6) produce three small recirculation regions. The medium length (L=H ¼ 4; 2), ribs show the top and wake regions beginning to merge as they are brought closer to each other. However, their dimensions have not yet significantly grown. At the bottom, the short ribs (L=H ¼ 1, 0.1) show one large recirculation region from the leading edge to the downstream floor. In relative terms the Table 1 Properties of the unperturbed boundary layer at the location of the leading edge of the rib. ReH δ99 =H θ (mm) Reθ Uτ (m/s) Reτ Shape factor
40
20000 1.3 3.75 2400 0.4039 1015 1.4831
J. van der Kindere, B. Ganapathisubramani
Journal of Wind Engineering & Industrial Aerodynamics 178 (2018) 38–48
recirculation region is now much larger than the rib. Computing the exact dimension of each recirculation region highlights two trends which are depicted in Fig. 5. Long ribs produce a recirculation region length above the top surface which is steady at 2:7H, and a wake region which asymptotes to 3:8H. Short ribs on the other hand produce a single recirculation region whose length decreases linearly from 13:3H in case L=H ¼ 0:1 to 4:4H in case L=H ¼ 4. The length of the recirculation bubble for each rib was obtained by measuring the furthest point downstream where U 0. We may compare our experiments where the boundary layer is thicker than the rib δ=H > 1 to those of previous publications such as Bergeles and Athanassiadis (1983) with the opposite situation (δ=H < 1), and Arie et al. (1975b), with δ=H ¼ 1.8. Both previous publications quote a comparable Reynolds number based on step height, thus this isolates
Fig. 3. Mean and turbulence intensity profiles at x=H ¼ 5.
Fig. 4. Mean flow streamlines obtained from PIV data that depicts the organization of the various recirculation regions around ribs of varying length. Top figure shows for L=H ¼ 8, with decreasing value of until L=H ¼ 0.1 at the bottom. The red line in each figure links points where U ¼ 0. The green line shows the dividing streamline of the mean flow that passes through the reattachment point at the wake. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) 41
J. van der Kindere, B. Ganapathisubramani
Journal of Wind Engineering & Industrial Aerodynamics 178 (2018) 38–48
distribution can also be used to identify changes in the recirculation regions of ribs. Fig. 7 represents the results obtained from surface pressure measurements normalized to pressure coefficient: CP ¼
P P∞ 1 ρUe2 2
It is clear from these measurements that rib length significantly affects surface pressure distribution. Starting upstream, CP is nearly identical for every rib. Past the leading edge, the three curves of the long ribs are grouped, whereas those of the shorter three are distinct. The long ribs produce closed recirculation regions along their top surface and therefore the surface pressure distribution along this bubble appears to be independent of rib length. Along the top surface of long ribs, the pressure recovers progressively without any clear indication where the flow might reattach. If the top recirculation region is open (in the case of short ribs), the drop in pressure caused by the recirculation region becomes shallower. From the trailing edge of each rib the pressure drop extends downstream and recovers progressively in a length that is not directly comparable to recirculation length. Nevertheless CP in the wake of ribs appears to recover at a similar rate. Fig. 7b illustrates surface pressure distribution from the trailing edge of each rib downstream past the mean reattachment point. It is normalized as described by Kim et al. (1980) in the case of BFS by
Fig. 5. Length of three recirculation regions compared with Bergeles and Athanassiadis (1983), an isolated FFS Sherry et al. (2010), and an isolated BFS Adams and Johnston (1988).
the effects of incoming boundary layer thickness over the ribs which is a key driver of the flow over forward-facing steps. Fig. 5 juxtaposes the recirculation region lengths measured by Bergeles and Athanassiadis (1983), and the present experiment for front, top and wake regions. Note that the top region does not exist for ribs shorter than L=H ¼ 3. From this plot it is evident that the two trends existing in the recirculation lengths as a function of rib length are also present. In Fig. 5, the front region is represented with circles and is constant throughout the range of rib lengths. When compared with Bergeles and Athanassiadis (1983), the recirculation length of the top region is shorter in this study by approximately 25%. Reviewing the behaviour of an “isolated” forward-facing step reveals that ribs are consistent with forward-facing steps. According to Sherry et al. (2010) the larger δ=H of the present study should indeed yield a smaller recirculation region. On the contrary, one could expect a higher Reynolds number to yield a longer recirculation region since the inertia in the flow is higher and therefore there might be a tendency in the flow to remain separated for a longer streamwise distance. Nevertheless, it appears then that boundary layer thickness dictates recirculation length in the current regime. However, the increased recirculation region length above the rib has a direct impact on the wake region downstream. It is approximately only 55% of the length of the recirculation region of an isolated BFS Adams and Johnston (1988). Unlike the top region, the wake region is consistently longer in the present study than it is in Bergeles and Athanassiadis (1983). Arie et al. (1975b), with δ=H ¼ 1.8 and ReH ¼ 30000, obtain an even longer LR =H ¼ 5. This is illustrated for case L=H ¼ 4 in Fig. 6. Taking into account δ=H ¼ 0:48, and ReH ¼ 26000 for Bergeles and Athanassiadis (1983), a trend defines itself clearly where the longer recirculation region on the top surface produces a flow with effectively less momentum at the trailing edge of the rib thus reattaching sooner.
CP;min CP CP;min In general, the pressure distribution in the wake of each rib matches somewhat the case of an isolated BFS Kim et al. (1980) albeit the distribution for each rib length demonstrates slight variations. The initial part near the trailing edge appears to be similar for all cases. However, the rate of recovery is not similar across the cases as there are differences in the trends. The location at which pressure has plateaued also varies with rib length, the longest rib appears to stabilize 20% further downstream of the mean reattachment point compared to a BFS. As rib length shortens this location reduces and case L=H ¼ 2 has already plateaued 10% earlier than the BFS. Even shorter ribs appear to follow a different pattern where the recovery occurs at the same rate as a BFS, although offset in streamwise position. From pressure measurements, we are able to distinguish the features of recirculation regions of similar ribs. It is clear that long ribs with a closed recirculation region on the top surface produce similar surface pressure distributions. This pressure recovers then at similar rates for the three longest ribs, however they are offset by the location of the trailing edge. Short ribs produce varying pressure drops which recover at varying rates, where in general, the shallower the initial drop, the slower the recovery. Rescaled pressure distribution also show some degree of similarity with isolated BFS. 4. Dimensions of recirculation regions
3.2. Mean surface pressure distribution
The previous sections identified patterns in mean recirculation bubble length, and surface pressure distribution on ribs of varying length. In
In addition to recirculation length from PIV results, surface pressure
Fig. 6. Effect of boundary layer thickness on length of recirculation regions of a rib L=H ¼ 4. The forward and backward-facing steps behave in reverse with variation of incoming boundary layer thickness.- Arie et al. (1975a), - current study, - Bergeles and Athanassiadis (1983). 42
J. van der Kindere, B. Ganapathisubramani
Journal of Wind Engineering & Industrial Aerodynamics 178 (2018) 38–48
Fig. 7. Left: Mean surface pressure distribution. Right: Rescaled wake region pressure distribution as per Kim et al. (1980). xTE corresponds to the streamwise location of the trailing edge of each rib. It is normalized by LR specific to each rib length.
this section, we investigate length, height and area of recirculation bubble in the plane of measurement and how the fluctuations observed in these quantities may vary with rib length. Those fluctuations may be linked to sources of noise, and unsteady loading on engineering applications. In order to determine the height of a recirculation region we locate the highest vector with negative streamwise velocity at each streamwise point of measurement in the region of interest. The y=H coordinates of these vectors are then averaged to obtain a mean recirculation region height per PIV snapshot. To determine area in the PIV plane, we sum the number of vectors with U 0 in each area of interest. The number of vectors is converted to units of area by the size of each vector window ( 0:28 103 H 2 ). This method was first used by Pearson et al. (2013), who compared and validated this method of measuring the instantaneous extent of separation with other methods (including one where the separation can be identified as the location where the wall-shear-stress is zero). It should be noted that in this work, this definition is used to represent the separating and reattaching parts of the flow and comparisons can be made for this definition across the different cases. Fig. 8 contains a summary of average dimensions for all three recirculation regions in each case. The mean values for the front bubble is shown in Fig. 8a, the values for the top bubble (that only exists for the long ribs) is shown in Fig. 8b and the quantities for the wake bubble (whose length begins at the leading-edge for short ribs and begins at the trailing edge for the long ribs) are shown in Fig. 8c. Average height and area follow the same trends as observed in bubble length. Short ribs produce regions with decreasing area, height and length. Long ribs produce wake regions whose length asymptotes to a constant value. The top region remains of nearly constant dimension, as does the front recirculation region. Fig. 9 presents probability distributions of each dimension (area, height and length) of the recirculation region at the top of the long ribs. The distributions are presented relative to the mean dimension presented in Fig. 8b. It is clear from the distribution that the fluctuations of the dimensions about the mean are similar for ribs of length L=H ¼ 4; 6; or 8. These distributions show a mode that is marginally negative, and a long tail on the positive side. This trend appears to be the same for all three dimensions. This indicates that the bubbles are often smaller or shorter than the mean value, but tend to grow far more than they shrink. Therefore, the recirculating flow regions are constrained in how small they can be, but are able to grow in size. The distribution of the recirculation length of L=H ¼ 4 is clipped on the right side because in many instances the bubble extends past the trailing edge suggesting that instantaneously, the top bubble merges with the recirculation region in the wake. The probability distributions of the bubble variations can also be computed for the wake region. As previously, the data can be presented relative to their corresponding mean values in Fig. 8c. Fig. 10 shows contours of variations in different bubble dimensions for different rib
Fig. 8. Average dimensions of recirculation region around ribs of varying length. a. Front region, b. Top region, c. Wake region. AR corresponds to the area in the plane of measurement and HR the height of the recirculation region.
length L=H ¼ 2; 4; 6 and 8. The abscissa in this contour map is the rib length while the ordinate shows the bins of normalized fluctuations. This contour map enables us to compare the fluctuations (relative to the mean) in the recirculation region across different cases. The shortest ribs (L ¼ 0:1H and H) are omitted as the limited PIV field of view was unable to capture the extent of the recirculation in every snapshot. The distribution would be biased without being able to include the longest regions. From the distribution of length, height, and area, it is clear the shortest and longest ribs produce the most steady values. L=H ¼ 4 and 6 produce the widest spread in values of all three dimensions. Up to 50% differences in extremes is observed between L=H ¼ 4, and L=H ¼ 2. The long rib 43
J. van der Kindere, B. Ganapathisubramani
Journal of Wind Engineering & Industrial Aerodynamics 178 (2018) 38–48
Fig. 10. Histogram of wake recirculation region dimensions normalized by their respective mean values as a function of rib length.
Fig. 9. Histograms of each dimension of recirculation regions on top of the longest ribs. Dimensions are normalized by the mean value presented in Fig. 8.
recirculation region. Consequently, we first focus on the state of the flow produced by the top recirculation region before it reaches the wake recirculation regions. In order to do so, we will analyse velocity fluctuations along the top surface of ribs. Fig. 11 shows profiles of streamwise velocity (U) and the turbulent 0 0 kinetic energy (T.K.E ¼ 0:5ðu 2 þ v 2 Þ, which comprises of only two velocity components) computed from PIV velocity normalized by free stream velocity. Three key rib lengths are reported in the results for clarity: short (L=H ¼ 1), medium (L=H ¼ 4), and long (L=H ¼ 8). The vertical profiles are obtained near the leading edge (x=H ¼ 0:5, figures a. and b.), and at the trailing edge (figure c. and d.). Similar to mean surface pressure distribution, velocity profiles near the leading edge (x=H ¼ 0:5) show that medium and long ribs produce identical profiles in mean velocity, and T:K:E:. Both long ribs produce a reversed flow up to 1.15H indicated by the local minimum, an acceleration of the flow up to 1.2 Ue at y=H ¼ 2:25, and peak T:K:E: at y=H ¼ 1:2. The short rib produces reversed flow up to the same height, however the acceleration of the flow is weaker, only up to 1.1 Ue . Peak T:K:E is located at the same height (for all three cases) but is also weaker for short rib by 15% compared to the longer ribs. This could be linked to the pressure drop shown in section 3.2 at the same streamwise location (x=H ¼ 0:5) which was weakest for the short rib.
shows the least relative fluctuation in the wake bubble length across all the cases. This suggests that any fluctuating loads and/or pressure could be lower in the wake region of the longest ribs compared to shorter ones. However for L=H ¼ 4, demonstrates the least steady recirculation region in the wake due to the occasional merging of the top and wake recirculation regions. Finally, there is no real trend that demarcates the long and short ribs in terms of fluctuations in separation region dimensions. This is in contrast to the finding for the mean bubble dimensions. Therefore, once the mean dimensions are isolated, the fluctuations appear to scale with the mean dimensions regardless of the rib length. 5. The resemblance of top recirculation regions of long ribs In the previous section, we showed how the presence of a recirculation region on the top surface may affect the recirculation region of the wake. It is known that variations in size of recirculation regions are the result of the amount of turbulence present in the shear-layer formed on the edge of recirculation regions, the momentum carried by the flow around the recirculation regions, and the scale of the fluctuations in velocity produced by the separation at the sharp corners (Pearson et al., 2013; Awasthi et al., 2014). In this section, we aim to identify features from the top recirculation region that could be present in the wake 44
J. van der Kindere, B. Ganapathisubramani
Journal of Wind Engineering & Industrial Aerodynamics 178 (2018) 38–48
Fig. 11. Top: T:K:E (a.) and velocity (b.) profiles from PIV measurements at the leading edge of three ribs (x=H ¼ 0:5). Bottom: T:K:E (c.) and velocity (d.) profiles at the trailing edge of two long ribs. For comparison, “8, x ¼ 4” corresponds to the profile at x=H ¼ 4 on rib L=H ¼ 8.
Fig. 12 shows contours of T:K:E for three different obstacle lengths (L=H ¼ 8, 4 & 1). All three ribs exhibit a separated shear-layer (that has intense turbulence activity) at the leading edge. Turbulence generated at leading-edge will convect/diffuse downstream and past the trailing edge. At the trailing edge, the backward-facing step-like separation produces a second shear layer, and a second zone of high T:K:E as seen in the figure. This appears to be the case for only the long and medium length ribs. The short rib also displays a second zone of high T:K:E, but, this zone almost appears to be a continuation of the first shear layer, however, there is a drop in T:K:E along the streamwise direction (between the first intense zone near the leading edge and the second intense zone, which is past the trailing edge). It can be clearly seen from this figure that the maximum kinetic energy in the second zone increases with decreasing rib length. Further downstream of long ribs, remnants of two separate shear layers is clearly visible in the turbulent kinetic energy with two local maxima in profiles of kinetic energy. For medium length ribs, these two shear-layers appear to be merged while for the short rib there is no evidence of two shear layers. Antoniou and Bergeles (1988) found that the effect of short ribs was still felt even in the far wake compared to medium and long ribs. This effect could be caused by two factors. First, the short ribs could produce higher levels of turbulent kinetic energy that takes a long time/distance to dissipate. Fig. 12 shows that this may indeed be the case as the highest level of turbulent kinetic energy is present in the wake of the shortest rib. Additionally, the turbulent length scales of the flow generated by the ribs might be different, which, for a given level of turbulent kinetic energy, could lead to different turnover time/distance. The turbulent length scales produced by each rib can be potentially observed in by examining the mode shapes obtained via Proper Orthogonal Decomposition (POD) (Sirovich, 1987). This analysis on the vector fields is not focussed on exposition of the flow structures or to develop reduced-order models for dynamics. Such analyses would need to be exhaustive and detailed and is beyond the scope of the current work. Here, the aim is to use POD mode shapes and energy content as comparative measures to determine the similarities and differences in the energy containing scales across the different cases.
At the trailing-edge of long ribs, we observe that the mean velocity profile is positive throughout, however very different from a flat plate turbulent boundary layer profile. It is clear that the trailing edge of the medium rib, L=H ¼ 4, is closer to the recirculation region at the top since the velocity is lower in the near surface portion of the profile. Furthermore, the peak intensity of T:K:E is greater by over 65% and is located closer to the surface of the rib. Consequently, from a similar amount of turbulence and velocity at the leading edge, the medium rib shows a lower velocity and more turbulent flow at its trailing edge. In addition to the observation that the top region may extend past the trailing edge, this would justify the most unsteady recirculation region dimensions in the wake. It must be observed that the velocity and T:K:E profiles observed at the trailing edge of the medium rib are identical to those measured at x=H ¼ 4 on top of the longest rib, thus indicating that the vicinity of the trailing edge to the top bubble does not affect the flow along the top surface of the medium rib. However, it is clear from the above analysis that the flow reaching the trailing face is highly turbulent and the degree of turbulence varies with rib length. The next section will identify the effects of this changing incoming flow on the wake that develops downstream of the rib. 6. The development of turbulence in the wake of ribs Rib length dictates the state of the flow at the point of separation at the trailing edge. For short ribs, it is dominated by large vortex shedding from the leading edge. For the medium rib, the flow has reattached on the top surface but occasionally stretches into the wake region and produces high turbulence. For the longest rib, the flow is fully reattached on the top surface and subsequently separates again at the trailing-edge. Unlike the top region, the wake region exhibits marked discrepancies between the medium and long ribs. Focussing solely on the top surface, the long and medium rib produced indistinguishable velocity distributions, but only slight changes in surface pressure distribution. In the wake, we may no longer categorize ribs by the closed or open recirculation regions on the top surface as the position of the trailing edge forces a more gradual evolution of the flow. 45
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Journal of Wind Engineering & Industrial Aerodynamics 178 (2018) 38–48
Fig. 12. Organization of T:K:E above three critical rib lengths (L=H ¼ 8; 4; 1 from top to bottom). Contours represent regions of high T:K:E:. Lines represent qualitatively the distribution of T:K:E: within these regions and offers a comparison between cases. The triangular markers indicate the location of mean reattachment points.
The POD modes were computed using the snapshot method (with all 2000 snapshots) where both streamwise and wall-normal velocity fluctuations were used. Fig. 13 shows the cumulative turbulent kinetic energy distribution for all POD modes for each case. Given that we have 2000 vector fields, we will require all 2000 modes to capture all the energy contained in the velocity fluctuations. However, the number of modes required to reach a certain fraction of the kinetic energy will provide an indication on the range of scales required to capture the energy. The fraction of energy captured is not necessarily an important factor here except that the value has to be high enough to be of interest and at the same time it should be low enough such that measurement noise and other PIV related issues (filtering, window size etc) does not affect the results. As a compromise, the number of modes required to capture 50% of the total energy can be compared across the different cases. It can be seen that a larger number of modes is required for longer ribs to capture 50% of the total kinetic energy. For the short, the medium, and the long rib, 25, 28 and 40 modes are required respectively to reproduce 50% of the total fluctuating kinetic energy. This suggests the fluctuations over long ribs are the most complex, requiring more modes to be described. It should be noted that the ordering of the modes in POD is based on the amount of energy captured in a certain mode. Therefore, lowernumbered modes capture larger fraction of the energy. Unlike the Fourier analysis, there is no scale information in the ordering of the modes. However, a comparison of these modes for a similar amount of energy content could give an indication of the scales at which a certain fraction of energy is contained. Fig. 14 represents the first eight POD modes of the three principal rib lengths. The lowest order modes are the most dominant - the ones that produce the largest kinetic energy of the fluctuations. The relative energy content of each mode for each case is given in the figure. POD associates the strongest modes with large patches of velocity fluctuations suggesting the strongest fluctuations are associated with large-scale velocity fluctuations. In addition to the large strong modes, higher-numbered modes appear to be smaller and introduce more localized fluctuations. These POD modes do not show physical
Fig. 13. Cumulative POD energy for each rib length. The dashed line indicates the number of modes required to obtain 50% of the fluctuating T:K:E:, respectively 25, 28 and 40 for L=H ¼ 1, 4, 8.
phenomena, merely the general location where fluctuations occur, and how strong they might be. The longest rib produces pulses of fluctuations which are near its surface and do not expand vertically much in comparison to smaller ribs. The first 8 modes show smaller and smaller trains of fluctuations aligned in the streamwise direction. The medium rib (centre) shows differences with the long rib from mode 3 onwards. In mode 3, we begin to notice that the pulse of high and low velocity are stacked vertically, rather than aligned in the streamwise direction. Higher mode numbers (weaker modes) exhibit fluctuations which expand higher vertically. This is similar to the comparison of T:K:E distribution (Fig. 12) and suggests the fluctuations are developing more and further into the freestream. The first mode of the shortest rib presents one single large velocity pulse where the recirculation region should be. Modes 2,3,4 show trains of smaller pulses aligned with the top of the shear layer. The largest scales of velocity fluctuations are clearly visible here. Furthermore, these occur on the shear layer where they may be swept downstream at high velocity.
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Journal of Wind Engineering & Industrial Aerodynamics 178 (2018) 38–48
Fig. 14. POD modes obtained for three rib lengths. Increasing mode numbers on the left indicate decreasing magnitude of the energy associated with each mode. Blue indicates negative velocity fluctuation and red the opposite. The inset reports the percentage of total energy associated with each mode. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
examine the effect of rib height as well as the rib length. PIV measurements made in the wake region of long ribs indicate that it is affected by rib length. Shorter ribs produce a more steadily separated flow which is affected by rib length. The single large recirculation region follows a linear trend with rib length. The source of the different effects perceived far downstream of each rib is established for the first time. The single shear layer in the wake of the short rib produces turbulence more gradually than the two individual shear layers of long ribs. This leads to larger scale turbulence for short ribs, which persists far downstream of the trailing edge of the rib. However, the turbulent scales are much smaller for longer ribs (despite larger amount of energy) and they tend to breakdown earlier before reaching large downstream distances.
Higher mode numbers show more complex patterns but remain organized. Observing the POD modes of three critical ribs, it is clear that longer ribs produce smaller scale turbulence which inherently dissipates quicker than larger scale fluctuations, despite stronger initial T:K:E: as reported in Fig. 12. Shorter ribs tend to produce predominantly fluctuations of larger scale in the shear layers which subsist longer, thus being more noticeable far downstream of the rib. 7. Conclusions We studied the effect of rib length on the characteristics of flow separation and reattachment in a turbulent boundary layer. PIV measurements provide planar flow field information for the first time in these type of flows and these fields are used to examine the spatial distribution of the separating and reattaching flow structure. Mean flow from the PIV fields confirm previously observed trends on the length of the recirculation bubble. Rib length is the dominating factor in determining whether a closed recirculation region forms on the top surface of the rib. This phenomenon is the cause of two different behaviours observed in ribs of varying length. A closed recirculation region on the top surface (long ribs) dictates that the leading edge region is independent of rib length. This is true in the recirculation region dimensions as well as the velocity and pressure distribution around the leading edge of the rib. It should be noted that these results are valid for one rib height to boundary layer thickness ratio. It is expected that when this ratio is altered, the separation region on the top could be different. This difference could perhaps be attributed to the change in turbulence intensity at rib height for different rib height to boundary layer thickness ratios. Future studies could
Acknowledgements The authors acknowledge the financial support of the European Research Council (ERC Grant agreement No. 277472) and the Leverhulme Trust for the Philip Leverhulme Prize. Appendix A. Supplementary data All data supporting for this study are openly available from the University of Southampton repository at http://doi.org/10.5258/SOTON/ D0496. References Adams, E., Johnston, J., 1988. Flow structure in the near-wall zone of a turbulent separated flow. AIAA J. 26 (8), 932–939. 47
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Journal of Wind Engineering & Industrial Aerodynamics 178 (2018) 38–48 Le, H., Moin, P., Kim, J., 1997. Direct numerical simulation of turbulent flow over a backward-facing step. J. Fluid Mech. 330. Leclercq, D.J., Jacob, M.C., Louisot, A., Talotte, C., 2001. Forward-backward Facing Step Pair: Aerodynamic Flow, Wall Pressure and Acoustic Characterisation, p. 2249. AIAA paper. Lee, I., Ahn, S.K., Sung, H.J., 2004. Three-dimensional coherent structure in a separated and reattaching flow over a backward-facing step. Exp. Fluid 36, 373–383. Lee, T., Mateescu, D., 1998. Experimental and numerical investigation of 2-d backwardfacing step flow. J. Fluid Struct. 12, 703–716. Maltby, R., 1962. Flow Visualization in Wind Tunnels Using Indicators. Technical report, DTIC Document. Marusic, I., Monty, J.P., Hultmark, M., Smits, A.J., 2013. On the logarithmic region in wall turbulence. J. Fluid Mech. 716, R3. Moss, D., Baker, S., 1980. Re-circulating flows associated with two-dimensional steps. Aeronaut. Q. 31, 151–172. Nakamura, Y., Nakashima, M., 1986. Vortex excitation of prisms with elongated rectangular, H and i cross-sections. J. Fluid Mech. 163, 149–169. Parker, R., Welsh, M., 1983. Effects of sound on flow separation from blunt flat plates. Int. J. Heat Fluid Flow 4 (2), 113–127 cited By 82. Pearson, D., Goulart, P., Ganapathisubramani, B., 2013. Turbulent separation upstream of a forward-facing step. J. Fluid Mech. 724, 284–304. Rowcroft, J., Burton, D., Blackburn, H., Sheridan, J., 2016. Siting wind turbines near cliffs–the effect of wind direction. Wind Energy 19 (8), 1469–1484. WE-15-0020.R1. Sherry, M., Lo Jacono, D., Sheridan, J., 2010. An experimental investigation of the recirculation zone formed downstream of a forward facing step. J. Wind Eng. Ind. Aerod. 98 (12), 888–894. Sirovich, L., 1987. Turbulence and the dynamics of coherent structures. part i: coherent structures. Q. Appl. Math. 45 (3), 561–571. Smits, A.J., Lim, T., 2000. Flow Visualization, Techniques and Examples. Taylor, Z., Palombi, E., Gurka, R., Kopp, G., 2011. Features of the turbulent flow around symmetric elongated bluff bodies. J. Fluid Struct. 27 (2), 250–265. Taylor, Z.J., Kopp, G.A., Gurka, R., 2013. Distribution of spanwise enstrophy in the near wake of three symmetric elongated bluff bodies at high Reynolds number. Phys. Fluids 25 (5), 055103.
Antoniou, J., Bergeles, G., 1988. Development of the reattached flow behind surfacemounted two-dimensional prisms. ASME Trans. J. Fluid Eng. 110, 127–133. Arie, M., Kiya, M., Tamura, H., Kanayama, Y., 1975a. Flow over rectangular cylinders immersed in a turbulent boundary layer: Part 1, correlation between pressure drag and boundary-layer characteristics. Bull. JSME 18 (125), 1260–1268. Arie, M., Kiya, M., Tamura, H., Kosugi, M., Takaoka, K., 1975b. Flow over rectangular cylinders immersed in a turbulent boundary layer: Part 2 flow patterns and pressure distributions. Bull. JSME 18 (125), 1269–1276. Armaly, B.F., Durst, F., Pereira, J.C.F., Sch€ onung, B., 1983. Experimental and theoretical investigation of backward-facing step flow. J. Fluid Mech. 127, 473–496. Awasthi, M., Devenport, W.J., Glegg, S.A.L., Forest, J.B., 2014. Pressure fluctuations produced by forward steps immersed in a turbulent boundary layer. J. Fluid Mech. 756, 384–421. Bergeles, G., Athanassiadis, N., 1983. The flow past a surface-mounted obstacle. J. Fluid Eng. 105 (4), 461–463. Castro, I., 1979. Relaxing wakes behind surface-mounted obstacles in rough wall boundary layers. J. Fluid Mech. 93 (04), 631–659. Castro, I., Dianat, M., 1983. Surface flow patterns on rectangular bodies in thick boundary layers. J. Wind Eng. Ind. Aerod. 11 (1), 107–119. Castro, I., Haque, A., 1987. The structure of a turbulent shear layer bounding a separation region. J. Fluid Mech. 179, 439–468. Cherry, N., Hillier, R., Latour, M., 1984. Unsteady measurements in a separated and reattaching flow. J. Fluid Mech. 144, 13–46. Chun, K.B., Sung, H.J., 1996. Control of turbulent separated flow over a backward-facing step by local forcing. Exp. Fluid 21, 417–426. Counihan, J., Hunt, J., Jackson, P., 1974. Wakes behind two-dimensional surface obstacles in turbulent boundary layers. J. Fluid Mech. 64 (03), 529–564. Dianat, M., Castro, I., 1984. Fluctuating surface shear stresses on bluff bodies. J. Wind Eng. Ind. Aerod. 17 (1), 133–146. Kim, J., Kline, S., Johnston, J., 1980. Investigation of a reattaching turbulent shear layer: flow over a backward-facing step. J. Fluid Eng. 102 (3), 302–308. Kiya, M., Sasaki, K., 1983. Structure of a turbulent separation bubble. J. Fluid Mech. 137, 83–113.
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Journal of Wind Engineering & Industrial Aerodynamics journal homepage: www.elsevier.com/locate/jweia
Effect of length of two-dimensional obstacles on characteristics of separation and reattachment J. van der Kindere, B. Ganapathisubramani * Faculty of Engineering and the Environment, University of Southampton, Southampton, SO17 1BJ, United Kingdom
A R T I C L E I N F O
A B S T R A C T
Keywords: Separated flow Flow past ribs Particle image velocimetry
The flow over a forward-facing step (FFS) and a backward-facing step (BFS) have been extensively studied separately, but the interaction between both obstacles has received little attention. It is believed the distance between the two faces of the step is a critical parameter governing the overall behaviour of the flow. This could have implication on the effect an obstacle would have on its surroundings, such as wind disturbance, or spread of pollution. Consequently, we investigate in detail the flow over a two-dimensional obstacle (also referred to as a rib), that consists of a FFS followed by a BFS. The flow field in such configuration is a result of the interaction between the multiple separation regions that appear upstream, above and downstream of the ribs. Our experimental model is submerged in a fully turbulent boundary layer (δ=H ¼ 1:37, where δ and H are respectively incoming boundary layer thickness and rib height), and the Reynolds number based on rib height is ReH ¼ 20; 000. Rib length (distance between the two vertical faces) varied between L=H ¼ 0:1 and L=H ¼ 8. In order to describe the general features of such a flow, we carried out flow field velocity and surface pressure measurements. Results show that two trends exist according to the length of the rib. Short ribs (L=H 4) produce one large recirculation region from the leading edge which results in higher levels of large scale turbulence which propagate far downstream. On the contrary, the FFS portion of long ribs (L=H 4) is decoupled from the BFS portion. Two separate shear layers are formed which decay quicker resulting in lower levels of turbulence propagating downstream.
1. Introduction Surface-mounted obstacles in industrial, aeronautical, or civil engineering produce unsteady flows with strong turbulence. These situations may improve flow-mixing properties, stabilize a combustion process, or jeopardize the integrity of buildings and their surroundings. Most previous studies have focussed on the separation and reattachment for forward-facing or backward-facing step flows (FFS and BFS). A twodimensional backward-facing step flow is perhaps the most studied canonical separated flow (Armaly et al., 1983; Lee and Mateescu, 1998; Lee et al., 2004), primarily because it is a major source of drag in automotive and aerospace applications. It contains a separated shear layer which interacts with both the free-stream and a region of reverse flow. This produces a complex feedback mechanism that is a source of pressure loss and noise (Chun and Sung, 1996; Le et al., 1997). In comparison, the forward-facing step flow has been a subject of fewer studies (Sherry et al., 2010; Pearson et al., 2013). This type of configuration has been examined more recently in the context of wind resource assessment near
escarpments and cliffs for normal flow as well as yawed flow configurations (Rowcroft et al., 2016). Despite being very common in nature and engineering applications, the flow field past a two-dimensional rib, which is a combination of forward-facing step followed by a backward-facing step, remains a subject with little documentation. Depending on the distance between the upstream and downstream edges of a rib, the separated flow of the forward-facing step may reattach on top of the rib or merge to different degrees with that of the backward-facing steps. Consequently up to three regions may interact together: upstream, on top, and downstream of the rib (see Fig. 1). As described by authors studying these types of obstacles, instrumentation was a limitation, thus a thorough description of recirculation regions was also limited (Counihan et al., 1974; Arie et al. 1975a, 1975b; Castro, 1979; Moss and Baker, 1980; Bergeles and Athanassiadis, 1983; Castro and Dianat, 1983; Dianat and Castro, 1984; Castro and Haque, 1987; Antoniou and Bergeles, 1988). In flow past ribs, there is a difference between flow past ribs with a reattached flow on the top surface (long ribs), and ribs too short for
* Corresponding author. E-mail addresses: [email protected] (J. van der Kindere), [email protected] (B. Ganapathisubramani). https://doi.org/10.1016/j.jweia.2018.04.018 Received 8 January 2018; Received in revised form 15 April 2018; Accepted 15 April 2018 Available online 29 May 2018 0167-6105/© 2018 Elsevier Ltd. All rights reserved.
J. van der Kindere, B. Ganapathisubramani
Journal of Wind Engineering & Industrial Aerodynamics 178 (2018) 38–48
Fig. 1. General configuration of the flow over ribs illustrating the main parameters of the study.
a range of rib height to boundary layer thickness ratio comparable to Bergeles and Athanassiadis (1983), it is reported that pressure drag coefficient decreases with rib length, and δ=H. For longer ribs, it is reported that the drag coefficient remains relatively unchanged. It can be assumed that for very long ribs, skin friction on the top surface increases viscous drag which is not accounted for in pressure drag. Arie et al. (1975b) supports the first experiment and adds a more detailed overview of surface pressure distribution for two rib lengths (L=H ¼ 2 and L=H ¼ 4). Some trends are highlighted: the pressure drop after the leading edge of the rib is stronger as δ=H decreases, and the pressure on the downstream face is constant at all heights whereas it is not on the upstream face. Finally, the turbulent fluctuations induced by ribs is studied by Arie et al. (1975b) and Antoniou and Bergeles (1988). The mixing process in the wake between the uniform flow above, and the still region downstream of the rib is compared by Arie et al. (1975b) to G€ ortler's theory on a uniform flow mixing with static fluid. The authors quote maximum turbulence intensity being generated at lowest δ=H, and above the top surface of the rib. The exact height of maximum turbulence intensity varies with rib length (y=H ¼ 1:13 for short ribs and y=H ¼ 2:5 for a fence). The deviation is associated with Coanda effects along the top surface. In addition, the authors observe that the disruption caused by ribs requires a long time or distance to return to unperturbed boundary layer characteristics. Indeed, it is still not recovered at 25H downstream of the ribs. Similar findings were made by Castro (1979). Antoniou and Bergeles (1988) studied the far wake of short and long ribs and found the lifespan of perturbations caused by long ribs is comparatively shorter than those caused by short ribs. However, the near-field flow characteristics that could lead to this far field effect remains unresolved. In the current study, the aim is to develop further understanding of the flow over ribs of different lengths. The analysis is focussed on three main topics: the length of each recirculation region as rib length varies, the average surface pressure distribution these ribs yield, and finally the turbulent flow fields in the near-wake of the rib. We investigate the effect of rib length on the fluctuations of these quantities, and identify the causes of established trends.
reattachment to take place on the top surface (short ribs). This type of flow has been examined in the context of an elongated bluff body, where the flow separates at the leading edge and reattaches along the chord of the body before separating once again at the trailing edge. Cherry et al. (1984) examined the flow over an infinite plate with a blunt leading edge and found that large vortices are shed from the leading edge separation bubble, however, there was not associated periodicity. Nakamura and Nakashima (1986) have shown that these vortices will form a staggered vortex-street-like arrangement in the wake of blunt-nosed elongated bodies even with a splitter plate because of the presence of the trailing edge. In these type of flows, the elongation ratio (which is the ratio between length of the body to its thickness) is analogous to the length (L) to height (H) ratio of wall-mounted ribs. Parker and Welsh (1983) performed a detailed study for rectangular cylinders over a wide range of elongation ratios and found that there is no dominant frequency in the wake at high Reynolds numbers. Taylor et al. (2011) showed that larger leading edge separation-reattachment increases the role of the turbulent stresses in the recirculation region. Taylor et al. (2013) found that the changes in the leading edge separation-reattachment create markedly different levels of turbulent kinetic energy and near wake structure. Although there are similarities between elongated bodies and ribs, the presence of a wall that bounds the flow in the wake as well the turbulence in the incoming boundary layer will alter the characteristics of separation and reattachment at the leading edge and the wake of wall-mounted obstacles. In the context of wall-mounted obstacles, Castro (1979) asserts that here is a possibility of a reattachment point on the top if there is sufficient amount of turbulence in the incoming boundary layer, and if the rib is long enough. Bergeles and Athanassiadis (1983) and Arie et al. (1975b) agree and find that the threshold between the presence and absence of a reattachment point on top of the rib is near L=H ¼ 3. Bergeles and Athanassiadis (1983) show that the FFS portion is consistent with an isolated FFS in similar flow conditions without discussing potential effects of Reynolds number and incoming flow. Bergeles and Athanassiadis (1983) describe the presence of two trends in the mean recirculation length (LR ) of the wake region. LR decreases linearly with rib length for short ribs (L=H < 4) from over 11.5H–2.8H and is nearly constant for long ribs (L=H 4) at approximately 3H. The authors note that LR in the wake of long ribs is less than what is commonly found in simple backward-facing steps. Adams and Johnston (1988) quote a typical LR between four and ten times the step height in backward-facing steps, whereas Bergeles and Athanassiadis (1983) quote values of LR in the region of three times the height in the case of ribs. Leclercq et al. (2001) find similar results for a rib with L=H ¼ 10. The argument of strong turbulent flow mixing at the trailing edge of the rib is used to justify the discrepancy between ribs and isolated BFS. Finally, the recirculation region upstream of the rib receives the least amount of attention from aforementioned studies, but it seems to display a nearly constant mean recirculation length (Bergeles and Athanassiadis, 1983). The surface pressure distribution, which defines the largest aerodynamic load on a rib-like structure, was addressed by Arie et al. (1975a). The study provides an overview of the behaviour of ribs immersed in a turbulent boundary layer by investigating the mean pressure drag generated at different inflow conditions, but less emphasis is placed on the effect of rib length. For rib lengths up to L=H ¼ 5, within
2. Experimental arrangement 2.1. Test cases and flow conditions The experiment was carried out at the University of Southampton in an open return wind tunnel with a rectangular test section of 0.9 m 0.6 m 4.35 m. The arrangement is depicted in Fig. 2. Speed in the test section (Ue ) was set to 10 m/s and verified with a pair of Pitot tubes. The experiment was mounted on a smooth false floor to control the incoming boundary layer. It extended 2.35 m upstream of the two-dimensional obstacle, and 1.35 m downstream. The leading edge of the false floor was a thin wedge with a strip of zig-zag tape to trip the boundary layer. In order to control circulation around the floor, a flap was mounted at the trailing edge. It was set at an angle that would suppress separation at the leading edge of the floor. This was verified with surface oil flow visualisation near the leading edge. A synthetic smoke generator was used to seed the flow. The obstacles (referred hereafter as ribs) extended along the entire span of the wind tunnel, thus generating a “two-dimensional” obstacle.
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J. van der Kindere, B. Ganapathisubramani
Journal of Wind Engineering & Industrial Aerodynamics 178 (2018) 38–48
Fig. 2. Illustration of the arrangement in the test section. The ribs are mounted between plates of the false floor which is suspended above the floor of the wind-tunnel.
Statistical two-dimensionality of the flow is expected along the centreline because the ribs aspect ratio (height to span) is over 30 (see Moss and Baker (1980) and Kiya and Sasaki (1983) who studied this matter). In addition, the blockage ratio is less than 7%. The false floor as well as the ribs themselves contained pressure taps for mean pressure measurements (see section 2.2). The ribs are inserted between the upstream and the downstream plates of the false floor. Thus, the number transducers is fixed before and after the obstacles so the total number of transducers varies with rib length. In total, six rib lengths were studied: L=H ¼ 0:1; 1; 2; 4; 6; 8, with streamwise rib length L and height H ¼ 30 mm. In addition, the false floor's boundary layer was measured without obstacle using the full set of instruments in order to quantify the base-flow's properties. The flow conditions are described in Section 2.3. With the given free stream velocity and rib height a representative Reynolds number is obtained: ReH ¼ 20000. In this study, lengths are normalized by rib height, local velocity by mean freestream velocity and the origin of the coordinate system is located at the bottom of the upstream face of the rib.
acquire the mean pressure measurements has an accuracy of 0.12% of full-scale, which represents an uncertainty of 6Pa. Thermal drift is considered negligible since the wind-tunnel lab was pre-heated prior to the measurements. In addition, the sensor was zeroed prior to each measurement. Measurements were performed in a plane near the centreline of the model. At this location, the nominally two-dimensional flow was expected to be span-wise homogeneous from a statistics standpoint. This homogeneity was indeed verified for each case with surface oil flow visualisation techniques as per Maltby (1962) and Smits and Lim (2000). 2.3. Approaching flow conditions To obtain incoming flow properties, separate PIV measurements were carried out over the flat plate without rib. The properties of the incoming flow extracted at x=H ¼ 0 are summarized in Table 1. The incoming turbulent boundary layer exhibits a typical log-law profile of a fully developed turbulent boundary layer with κ ¼ 0:384, and B ¼ 4:17 (Marusic et al., 2013). Fitting the log-law to a velocity profile of the incoming boundary layer with this information allowed us to determine the skin-friction velocity. Turbulence content of the approaching flow is characterized by the turbulence intensity within the boundary layer. Fig. 3 also illustrates the streamwise velocity fluctuation profile of the incoming flow. It indicates the ribs are fully immersed within the turbulent boundary layer. The turbulence intensity at the rib height was approximately 4%.
2.2. Measurements Two techniques were used to measure the flow. Flow field velocity was obtained through low-frequency planar particle image velocimetry (PIV). Mean pressure distribution was obtained through pressure taps on the surface of the model. For PIV measurements, seeding is provided by a Martin Magnum 1200 fog smoke machine, ejecting smoke particles (size 1 μm). Two double cavity Nano L 200-15 PIV lasers from Litron illuminated the particles. A large field of view was required to capture the flow in all three expected recirculation regions. The best compromise found was three LaVision's LX Imager 16 MP PIV cameras in conjunction with Sigma 105 mm F2.8 Macro lenses. The total field of view covered 5:4 X=H 14:5, and 0 Y=H 6. PIV interrogation window size was 16 16 pixel with 50% overlap resulting in a vector spacing of 0:5 mm in both axes. The high fluctuations expected in the flow dictated that a high number of samples were necessary for statistical convergence. Standard deviation values of the velocity in the shear layer of FF and BF steps are typically 30% of the free stream velocity. As a result, 2000 vector fields per case were acquired. While the PIV system acquired velocity information, a second system acquired mean surface pressure measurements from 48 pressure taps located near the intersection of the laser sheet from the PIV system with the models. These are aligned axially with a spacing of 0:5H, the first one at X=H ¼ 8:25. Each pressure tap is made up of a brass tube piercing through the surface of the obstacle. These measure 0.6 mm (innerdiameter), and 0.8 mm (outer-diameter). They are cut flush with the surface and glued in position. On the service side of the model, they are connected through fine silicon tubing (0.6 mm) to a 64-channel Scanivalve ZOC 33/64 pressure sensor. The Scanivalve transducer used to
3. Global trends of the flow with varying rib length 3.1. Average recirculation region dimensions The flow over ribs over varying length produces up to three separation regions. Fig. 4 summarizes the evolution of those recirculation regions. On top, long ribs (L=H ¼ 8, 6) produce three small recirculation regions. The medium length (L=H ¼ 4; 2), ribs show the top and wake regions beginning to merge as they are brought closer to each other. However, their dimensions have not yet significantly grown. At the bottom, the short ribs (L=H ¼ 1, 0.1) show one large recirculation region from the leading edge to the downstream floor. In relative terms the Table 1 Properties of the unperturbed boundary layer at the location of the leading edge of the rib. ReH δ99 =H θ (mm) Reθ Uτ (m/s) Reτ Shape factor
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20000 1.3 3.75 2400 0.4039 1015 1.4831
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Journal of Wind Engineering & Industrial Aerodynamics 178 (2018) 38–48
recirculation region is now much larger than the rib. Computing the exact dimension of each recirculation region highlights two trends which are depicted in Fig. 5. Long ribs produce a recirculation region length above the top surface which is steady at 2:7H, and a wake region which asymptotes to 3:8H. Short ribs on the other hand produce a single recirculation region whose length decreases linearly from 13:3H in case L=H ¼ 0:1 to 4:4H in case L=H ¼ 4. The length of the recirculation bubble for each rib was obtained by measuring the furthest point downstream where U 0. We may compare our experiments where the boundary layer is thicker than the rib δ=H > 1 to those of previous publications such as Bergeles and Athanassiadis (1983) with the opposite situation (δ=H < 1), and Arie et al. (1975b), with δ=H ¼ 1.8. Both previous publications quote a comparable Reynolds number based on step height, thus this isolates
Fig. 3. Mean and turbulence intensity profiles at x=H ¼ 5.
Fig. 4. Mean flow streamlines obtained from PIV data that depicts the organization of the various recirculation regions around ribs of varying length. Top figure shows for L=H ¼ 8, with decreasing value of until L=H ¼ 0.1 at the bottom. The red line in each figure links points where U ¼ 0. The green line shows the dividing streamline of the mean flow that passes through the reattachment point at the wake. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) 41
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distribution can also be used to identify changes in the recirculation regions of ribs. Fig. 7 represents the results obtained from surface pressure measurements normalized to pressure coefficient: CP ¼
P P∞ 1 ρUe2 2
It is clear from these measurements that rib length significantly affects surface pressure distribution. Starting upstream, CP is nearly identical for every rib. Past the leading edge, the three curves of the long ribs are grouped, whereas those of the shorter three are distinct. The long ribs produce closed recirculation regions along their top surface and therefore the surface pressure distribution along this bubble appears to be independent of rib length. Along the top surface of long ribs, the pressure recovers progressively without any clear indication where the flow might reattach. If the top recirculation region is open (in the case of short ribs), the drop in pressure caused by the recirculation region becomes shallower. From the trailing edge of each rib the pressure drop extends downstream and recovers progressively in a length that is not directly comparable to recirculation length. Nevertheless CP in the wake of ribs appears to recover at a similar rate. Fig. 7b illustrates surface pressure distribution from the trailing edge of each rib downstream past the mean reattachment point. It is normalized as described by Kim et al. (1980) in the case of BFS by
Fig. 5. Length of three recirculation regions compared with Bergeles and Athanassiadis (1983), an isolated FFS Sherry et al. (2010), and an isolated BFS Adams and Johnston (1988).
the effects of incoming boundary layer thickness over the ribs which is a key driver of the flow over forward-facing steps. Fig. 5 juxtaposes the recirculation region lengths measured by Bergeles and Athanassiadis (1983), and the present experiment for front, top and wake regions. Note that the top region does not exist for ribs shorter than L=H ¼ 3. From this plot it is evident that the two trends existing in the recirculation lengths as a function of rib length are also present. In Fig. 5, the front region is represented with circles and is constant throughout the range of rib lengths. When compared with Bergeles and Athanassiadis (1983), the recirculation length of the top region is shorter in this study by approximately 25%. Reviewing the behaviour of an “isolated” forward-facing step reveals that ribs are consistent with forward-facing steps. According to Sherry et al. (2010) the larger δ=H of the present study should indeed yield a smaller recirculation region. On the contrary, one could expect a higher Reynolds number to yield a longer recirculation region since the inertia in the flow is higher and therefore there might be a tendency in the flow to remain separated for a longer streamwise distance. Nevertheless, it appears then that boundary layer thickness dictates recirculation length in the current regime. However, the increased recirculation region length above the rib has a direct impact on the wake region downstream. It is approximately only 55% of the length of the recirculation region of an isolated BFS Adams and Johnston (1988). Unlike the top region, the wake region is consistently longer in the present study than it is in Bergeles and Athanassiadis (1983). Arie et al. (1975b), with δ=H ¼ 1.8 and ReH ¼ 30000, obtain an even longer LR =H ¼ 5. This is illustrated for case L=H ¼ 4 in Fig. 6. Taking into account δ=H ¼ 0:48, and ReH ¼ 26000 for Bergeles and Athanassiadis (1983), a trend defines itself clearly where the longer recirculation region on the top surface produces a flow with effectively less momentum at the trailing edge of the rib thus reattaching sooner.
CP;min CP CP;min In general, the pressure distribution in the wake of each rib matches somewhat the case of an isolated BFS Kim et al. (1980) albeit the distribution for each rib length demonstrates slight variations. The initial part near the trailing edge appears to be similar for all cases. However, the rate of recovery is not similar across the cases as there are differences in the trends. The location at which pressure has plateaued also varies with rib length, the longest rib appears to stabilize 20% further downstream of the mean reattachment point compared to a BFS. As rib length shortens this location reduces and case L=H ¼ 2 has already plateaued 10% earlier than the BFS. Even shorter ribs appear to follow a different pattern where the recovery occurs at the same rate as a BFS, although offset in streamwise position. From pressure measurements, we are able to distinguish the features of recirculation regions of similar ribs. It is clear that long ribs with a closed recirculation region on the top surface produce similar surface pressure distributions. This pressure recovers then at similar rates for the three longest ribs, however they are offset by the location of the trailing edge. Short ribs produce varying pressure drops which recover at varying rates, where in general, the shallower the initial drop, the slower the recovery. Rescaled pressure distribution also show some degree of similarity with isolated BFS. 4. Dimensions of recirculation regions
3.2. Mean surface pressure distribution
The previous sections identified patterns in mean recirculation bubble length, and surface pressure distribution on ribs of varying length. In
In addition to recirculation length from PIV results, surface pressure
Fig. 6. Effect of boundary layer thickness on length of recirculation regions of a rib L=H ¼ 4. The forward and backward-facing steps behave in reverse with variation of incoming boundary layer thickness.- Arie et al. (1975a), - current study, - Bergeles and Athanassiadis (1983). 42
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Journal of Wind Engineering & Industrial Aerodynamics 178 (2018) 38–48
Fig. 7. Left: Mean surface pressure distribution. Right: Rescaled wake region pressure distribution as per Kim et al. (1980). xTE corresponds to the streamwise location of the trailing edge of each rib. It is normalized by LR specific to each rib length.
this section, we investigate length, height and area of recirculation bubble in the plane of measurement and how the fluctuations observed in these quantities may vary with rib length. Those fluctuations may be linked to sources of noise, and unsteady loading on engineering applications. In order to determine the height of a recirculation region we locate the highest vector with negative streamwise velocity at each streamwise point of measurement in the region of interest. The y=H coordinates of these vectors are then averaged to obtain a mean recirculation region height per PIV snapshot. To determine area in the PIV plane, we sum the number of vectors with U 0 in each area of interest. The number of vectors is converted to units of area by the size of each vector window ( 0:28 103 H 2 ). This method was first used by Pearson et al. (2013), who compared and validated this method of measuring the instantaneous extent of separation with other methods (including one where the separation can be identified as the location where the wall-shear-stress is zero). It should be noted that in this work, this definition is used to represent the separating and reattaching parts of the flow and comparisons can be made for this definition across the different cases. Fig. 8 contains a summary of average dimensions for all three recirculation regions in each case. The mean values for the front bubble is shown in Fig. 8a, the values for the top bubble (that only exists for the long ribs) is shown in Fig. 8b and the quantities for the wake bubble (whose length begins at the leading-edge for short ribs and begins at the trailing edge for the long ribs) are shown in Fig. 8c. Average height and area follow the same trends as observed in bubble length. Short ribs produce regions with decreasing area, height and length. Long ribs produce wake regions whose length asymptotes to a constant value. The top region remains of nearly constant dimension, as does the front recirculation region. Fig. 9 presents probability distributions of each dimension (area, height and length) of the recirculation region at the top of the long ribs. The distributions are presented relative to the mean dimension presented in Fig. 8b. It is clear from the distribution that the fluctuations of the dimensions about the mean are similar for ribs of length L=H ¼ 4; 6; or 8. These distributions show a mode that is marginally negative, and a long tail on the positive side. This trend appears to be the same for all three dimensions. This indicates that the bubbles are often smaller or shorter than the mean value, but tend to grow far more than they shrink. Therefore, the recirculating flow regions are constrained in how small they can be, but are able to grow in size. The distribution of the recirculation length of L=H ¼ 4 is clipped on the right side because in many instances the bubble extends past the trailing edge suggesting that instantaneously, the top bubble merges with the recirculation region in the wake. The probability distributions of the bubble variations can also be computed for the wake region. As previously, the data can be presented relative to their corresponding mean values in Fig. 8c. Fig. 10 shows contours of variations in different bubble dimensions for different rib
Fig. 8. Average dimensions of recirculation region around ribs of varying length. a. Front region, b. Top region, c. Wake region. AR corresponds to the area in the plane of measurement and HR the height of the recirculation region.
length L=H ¼ 2; 4; 6 and 8. The abscissa in this contour map is the rib length while the ordinate shows the bins of normalized fluctuations. This contour map enables us to compare the fluctuations (relative to the mean) in the recirculation region across different cases. The shortest ribs (L ¼ 0:1H and H) are omitted as the limited PIV field of view was unable to capture the extent of the recirculation in every snapshot. The distribution would be biased without being able to include the longest regions. From the distribution of length, height, and area, it is clear the shortest and longest ribs produce the most steady values. L=H ¼ 4 and 6 produce the widest spread in values of all three dimensions. Up to 50% differences in extremes is observed between L=H ¼ 4, and L=H ¼ 2. The long rib 43
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Journal of Wind Engineering & Industrial Aerodynamics 178 (2018) 38–48
Fig. 10. Histogram of wake recirculation region dimensions normalized by their respective mean values as a function of rib length.
Fig. 9. Histograms of each dimension of recirculation regions on top of the longest ribs. Dimensions are normalized by the mean value presented in Fig. 8.
recirculation region. Consequently, we first focus on the state of the flow produced by the top recirculation region before it reaches the wake recirculation regions. In order to do so, we will analyse velocity fluctuations along the top surface of ribs. Fig. 11 shows profiles of streamwise velocity (U) and the turbulent 0 0 kinetic energy (T.K.E ¼ 0:5ðu 2 þ v 2 Þ, which comprises of only two velocity components) computed from PIV velocity normalized by free stream velocity. Three key rib lengths are reported in the results for clarity: short (L=H ¼ 1), medium (L=H ¼ 4), and long (L=H ¼ 8). The vertical profiles are obtained near the leading edge (x=H ¼ 0:5, figures a. and b.), and at the trailing edge (figure c. and d.). Similar to mean surface pressure distribution, velocity profiles near the leading edge (x=H ¼ 0:5) show that medium and long ribs produce identical profiles in mean velocity, and T:K:E:. Both long ribs produce a reversed flow up to 1.15H indicated by the local minimum, an acceleration of the flow up to 1.2 Ue at y=H ¼ 2:25, and peak T:K:E: at y=H ¼ 1:2. The short rib produces reversed flow up to the same height, however the acceleration of the flow is weaker, only up to 1.1 Ue . Peak T:K:E is located at the same height (for all three cases) but is also weaker for short rib by 15% compared to the longer ribs. This could be linked to the pressure drop shown in section 3.2 at the same streamwise location (x=H ¼ 0:5) which was weakest for the short rib.
shows the least relative fluctuation in the wake bubble length across all the cases. This suggests that any fluctuating loads and/or pressure could be lower in the wake region of the longest ribs compared to shorter ones. However for L=H ¼ 4, demonstrates the least steady recirculation region in the wake due to the occasional merging of the top and wake recirculation regions. Finally, there is no real trend that demarcates the long and short ribs in terms of fluctuations in separation region dimensions. This is in contrast to the finding for the mean bubble dimensions. Therefore, once the mean dimensions are isolated, the fluctuations appear to scale with the mean dimensions regardless of the rib length. 5. The resemblance of top recirculation regions of long ribs In the previous section, we showed how the presence of a recirculation region on the top surface may affect the recirculation region of the wake. It is known that variations in size of recirculation regions are the result of the amount of turbulence present in the shear-layer formed on the edge of recirculation regions, the momentum carried by the flow around the recirculation regions, and the scale of the fluctuations in velocity produced by the separation at the sharp corners (Pearson et al., 2013; Awasthi et al., 2014). In this section, we aim to identify features from the top recirculation region that could be present in the wake 44
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Journal of Wind Engineering & Industrial Aerodynamics 178 (2018) 38–48
Fig. 11. Top: T:K:E (a.) and velocity (b.) profiles from PIV measurements at the leading edge of three ribs (x=H ¼ 0:5). Bottom: T:K:E (c.) and velocity (d.) profiles at the trailing edge of two long ribs. For comparison, “8, x ¼ 4” corresponds to the profile at x=H ¼ 4 on rib L=H ¼ 8.
Fig. 12 shows contours of T:K:E for three different obstacle lengths (L=H ¼ 8, 4 & 1). All three ribs exhibit a separated shear-layer (that has intense turbulence activity) at the leading edge. Turbulence generated at leading-edge will convect/diffuse downstream and past the trailing edge. At the trailing edge, the backward-facing step-like separation produces a second shear layer, and a second zone of high T:K:E as seen in the figure. This appears to be the case for only the long and medium length ribs. The short rib also displays a second zone of high T:K:E, but, this zone almost appears to be a continuation of the first shear layer, however, there is a drop in T:K:E along the streamwise direction (between the first intense zone near the leading edge and the second intense zone, which is past the trailing edge). It can be clearly seen from this figure that the maximum kinetic energy in the second zone increases with decreasing rib length. Further downstream of long ribs, remnants of two separate shear layers is clearly visible in the turbulent kinetic energy with two local maxima in profiles of kinetic energy. For medium length ribs, these two shear-layers appear to be merged while for the short rib there is no evidence of two shear layers. Antoniou and Bergeles (1988) found that the effect of short ribs was still felt even in the far wake compared to medium and long ribs. This effect could be caused by two factors. First, the short ribs could produce higher levels of turbulent kinetic energy that takes a long time/distance to dissipate. Fig. 12 shows that this may indeed be the case as the highest level of turbulent kinetic energy is present in the wake of the shortest rib. Additionally, the turbulent length scales of the flow generated by the ribs might be different, which, for a given level of turbulent kinetic energy, could lead to different turnover time/distance. The turbulent length scales produced by each rib can be potentially observed in by examining the mode shapes obtained via Proper Orthogonal Decomposition (POD) (Sirovich, 1987). This analysis on the vector fields is not focussed on exposition of the flow structures or to develop reduced-order models for dynamics. Such analyses would need to be exhaustive and detailed and is beyond the scope of the current work. Here, the aim is to use POD mode shapes and energy content as comparative measures to determine the similarities and differences in the energy containing scales across the different cases.
At the trailing-edge of long ribs, we observe that the mean velocity profile is positive throughout, however very different from a flat plate turbulent boundary layer profile. It is clear that the trailing edge of the medium rib, L=H ¼ 4, is closer to the recirculation region at the top since the velocity is lower in the near surface portion of the profile. Furthermore, the peak intensity of T:K:E is greater by over 65% and is located closer to the surface of the rib. Consequently, from a similar amount of turbulence and velocity at the leading edge, the medium rib shows a lower velocity and more turbulent flow at its trailing edge. In addition to the observation that the top region may extend past the trailing edge, this would justify the most unsteady recirculation region dimensions in the wake. It must be observed that the velocity and T:K:E profiles observed at the trailing edge of the medium rib are identical to those measured at x=H ¼ 4 on top of the longest rib, thus indicating that the vicinity of the trailing edge to the top bubble does not affect the flow along the top surface of the medium rib. However, it is clear from the above analysis that the flow reaching the trailing face is highly turbulent and the degree of turbulence varies with rib length. The next section will identify the effects of this changing incoming flow on the wake that develops downstream of the rib. 6. The development of turbulence in the wake of ribs Rib length dictates the state of the flow at the point of separation at the trailing edge. For short ribs, it is dominated by large vortex shedding from the leading edge. For the medium rib, the flow has reattached on the top surface but occasionally stretches into the wake region and produces high turbulence. For the longest rib, the flow is fully reattached on the top surface and subsequently separates again at the trailing-edge. Unlike the top region, the wake region exhibits marked discrepancies between the medium and long ribs. Focussing solely on the top surface, the long and medium rib produced indistinguishable velocity distributions, but only slight changes in surface pressure distribution. In the wake, we may no longer categorize ribs by the closed or open recirculation regions on the top surface as the position of the trailing edge forces a more gradual evolution of the flow. 45
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Fig. 12. Organization of T:K:E above three critical rib lengths (L=H ¼ 8; 4; 1 from top to bottom). Contours represent regions of high T:K:E:. Lines represent qualitatively the distribution of T:K:E: within these regions and offers a comparison between cases. The triangular markers indicate the location of mean reattachment points.
The POD modes were computed using the snapshot method (with all 2000 snapshots) where both streamwise and wall-normal velocity fluctuations were used. Fig. 13 shows the cumulative turbulent kinetic energy distribution for all POD modes for each case. Given that we have 2000 vector fields, we will require all 2000 modes to capture all the energy contained in the velocity fluctuations. However, the number of modes required to reach a certain fraction of the kinetic energy will provide an indication on the range of scales required to capture the energy. The fraction of energy captured is not necessarily an important factor here except that the value has to be high enough to be of interest and at the same time it should be low enough such that measurement noise and other PIV related issues (filtering, window size etc) does not affect the results. As a compromise, the number of modes required to capture 50% of the total energy can be compared across the different cases. It can be seen that a larger number of modes is required for longer ribs to capture 50% of the total kinetic energy. For the short, the medium, and the long rib, 25, 28 and 40 modes are required respectively to reproduce 50% of the total fluctuating kinetic energy. This suggests the fluctuations over long ribs are the most complex, requiring more modes to be described. It should be noted that the ordering of the modes in POD is based on the amount of energy captured in a certain mode. Therefore, lowernumbered modes capture larger fraction of the energy. Unlike the Fourier analysis, there is no scale information in the ordering of the modes. However, a comparison of these modes for a similar amount of energy content could give an indication of the scales at which a certain fraction of energy is contained. Fig. 14 represents the first eight POD modes of the three principal rib lengths. The lowest order modes are the most dominant - the ones that produce the largest kinetic energy of the fluctuations. The relative energy content of each mode for each case is given in the figure. POD associates the strongest modes with large patches of velocity fluctuations suggesting the strongest fluctuations are associated with large-scale velocity fluctuations. In addition to the large strong modes, higher-numbered modes appear to be smaller and introduce more localized fluctuations. These POD modes do not show physical
Fig. 13. Cumulative POD energy for each rib length. The dashed line indicates the number of modes required to obtain 50% of the fluctuating T:K:E:, respectively 25, 28 and 40 for L=H ¼ 1, 4, 8.
phenomena, merely the general location where fluctuations occur, and how strong they might be. The longest rib produces pulses of fluctuations which are near its surface and do not expand vertically much in comparison to smaller ribs. The first 8 modes show smaller and smaller trains of fluctuations aligned in the streamwise direction. The medium rib (centre) shows differences with the long rib from mode 3 onwards. In mode 3, we begin to notice that the pulse of high and low velocity are stacked vertically, rather than aligned in the streamwise direction. Higher mode numbers (weaker modes) exhibit fluctuations which expand higher vertically. This is similar to the comparison of T:K:E distribution (Fig. 12) and suggests the fluctuations are developing more and further into the freestream. The first mode of the shortest rib presents one single large velocity pulse where the recirculation region should be. Modes 2,3,4 show trains of smaller pulses aligned with the top of the shear layer. The largest scales of velocity fluctuations are clearly visible here. Furthermore, these occur on the shear layer where they may be swept downstream at high velocity.
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Journal of Wind Engineering & Industrial Aerodynamics 178 (2018) 38–48
Fig. 14. POD modes obtained for three rib lengths. Increasing mode numbers on the left indicate decreasing magnitude of the energy associated with each mode. Blue indicates negative velocity fluctuation and red the opposite. The inset reports the percentage of total energy associated with each mode. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
examine the effect of rib height as well as the rib length. PIV measurements made in the wake region of long ribs indicate that it is affected by rib length. Shorter ribs produce a more steadily separated flow which is affected by rib length. The single large recirculation region follows a linear trend with rib length. The source of the different effects perceived far downstream of each rib is established for the first time. The single shear layer in the wake of the short rib produces turbulence more gradually than the two individual shear layers of long ribs. This leads to larger scale turbulence for short ribs, which persists far downstream of the trailing edge of the rib. However, the turbulent scales are much smaller for longer ribs (despite larger amount of energy) and they tend to breakdown earlier before reaching large downstream distances.
Higher mode numbers show more complex patterns but remain organized. Observing the POD modes of three critical ribs, it is clear that longer ribs produce smaller scale turbulence which inherently dissipates quicker than larger scale fluctuations, despite stronger initial T:K:E: as reported in Fig. 12. Shorter ribs tend to produce predominantly fluctuations of larger scale in the shear layers which subsist longer, thus being more noticeable far downstream of the rib. 7. Conclusions We studied the effect of rib length on the characteristics of flow separation and reattachment in a turbulent boundary layer. PIV measurements provide planar flow field information for the first time in these type of flows and these fields are used to examine the spatial distribution of the separating and reattaching flow structure. Mean flow from the PIV fields confirm previously observed trends on the length of the recirculation bubble. Rib length is the dominating factor in determining whether a closed recirculation region forms on the top surface of the rib. This phenomenon is the cause of two different behaviours observed in ribs of varying length. A closed recirculation region on the top surface (long ribs) dictates that the leading edge region is independent of rib length. This is true in the recirculation region dimensions as well as the velocity and pressure distribution around the leading edge of the rib. It should be noted that these results are valid for one rib height to boundary layer thickness ratio. It is expected that when this ratio is altered, the separation region on the top could be different. This difference could perhaps be attributed to the change in turbulence intensity at rib height for different rib height to boundary layer thickness ratios. Future studies could
Acknowledgements The authors acknowledge the financial support of the European Research Council (ERC Grant agreement No. 277472) and the Leverhulme Trust for the Philip Leverhulme Prize. Appendix A. Supplementary data All data supporting for this study are openly available from the University of Southampton repository at http://doi.org/10.5258/SOTON/ D0496. References Adams, E., Johnston, J., 1988. Flow structure in the near-wall zone of a turbulent separated flow. AIAA J. 26 (8), 932–939. 47
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