- Research Letter
- Open Access
Wind tunnel measurements of turbulent boundary layer flows over arrays of ribs and cubes
- Ziwei Mo^{1} and
- Chun-Ho Liu^{1}Email authorView ORCID ID profile
https://doi.org/10.1186/s40562-018-0115-x
© The Author(s) 2018
Received: 27 February 2018
Accepted: 18 June 2018
Published: 26 June 2018
Abstract
Understanding the effect of building morphology on the flow aloft is important to the ventilation and pollutant removal in cities. This study examines the dynamics over hypothetical urban areas in isothermal conditions using wind tunnel experiments. Different configurations of rib-type and cube-type arrays are designed to model hypothetical rough urban surfaces. The mean and fluctuating velocities are measured by hot-wire anemometry with X-wire probes. The results show that significant variations of fluctuating velocities and momentum fluxes are clearly observed in the near-wall region, depicting the inhomogeneous flow in response to the presence of roughness elements in the lower part of turbulent boundary layer. Comparing the variables over different rough surfaces, the roof-level fluctuating velocities and momentum fluxes increase with increasing surface roughness. Quadrant analyses and frequency spectra collectively suggest that the fresh air entrainment and aged air removal are enhanced over rougher surfaces. Larger energy-carrying turbulence motions contribute mostly to the more efficient ventilation over urban areas.
Keywords
- Frequency spectra
- Momentum fluxes
- Quadrant analyses
- Turbulent flows
- Wind tunnel laboratory experiments
Background
In the presence of building obstacles in urban areas, the atmospheric boundary layer (ABL) is developed similar to the rough-wall turbulent boundary layer (TBL; Pope 2000). The flow structure and turbulence behavior are highly modified over different types of surface roughness (Jiménez 2004). It is, therefore, important to study the flow characteristics in the TBLs over rough surfaces.
Wind tunnel experiments are commonly performed to examine the turbulent flows over rough surfaces (Raupach et al. 1991). Scaling down the dimensions of realistic urban areas in a wind tunnel offers a cost-effective platform for sensitivity tests with full control of variables and boundary conditions (Cermak 1981). A series of wind tunnel studies have been carried out to demystify the effects of roughness-element configurations on the flows in rough-wall TBLs (Britter and Hanna 2003; Salizzoni et al. 2008; Liu et al. 2015). ABL velocity profiles are examined over arrays of ribs (Salizzoni et al. 2008; Ho and Liu 2017) and arrays of cubes (Cheng and Castro 2002a, b). Some of the aerodynamic parameters, such as displacement height d and roughness length z_{0}, were contrasted over different surface configurations. The effect of roughness elements on the roughness sublayer (RSL) was also investigated (Placidi and Ganapathisubramani 2015). Besides, turbulence structure was characterized by autocorrelation, quadrant analyses as well as spectra over cube-type arrays (Castro et al. 2006). These experimental studies have enriched our understanding of turbulent flows over rough-wall TBLs. However, more wind tunnel results are needed to study the effect of surface configurations on the turbulence behavior and the associated street-level ventilation over urban areas.
In this study, a series of wind tunnel experiments are carried out to examine the flows in the TBLs over rib-type and cube-type arrays. Square aluminum bars and LEGO™ bricks are used to fabricate different configurations of hypothetical urban areas. The profiles of mean wind speeds and turbulence are sampled in each repeating unit of roughness element. The effect of sampling position and rough-surface configurations on the flows is contrasted. Quadrant analyses and frequency spectra are performed as well to elucidate the scale of motions governing the roof-level ventilation mechanism over urban areas.
Methods
Roughness elements
Models of hypothetical urban areas are fabricated by idealized roughness elements in the wind tunnel test section. Two types of rough surfaces are considered in this study, namely, rib-type arrays and cube-type arrays. The rib-type arrays are assembled by square aluminum bars of size l (= 560 mm; long) × h (= 9 mm; wide) × h (= 9 mm; high). The ribs are placed evenly apart in crossflows, spanning the full width of the wind tunnel test section. Ten configurations of rib-type arrays are adopted by adjusting the separation between the ribs w. The roughness-element-height-to-separation (aspect) ratios (AR) are equal to 1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/8, 1/10, 1/12, and 1/15. For the cube-type arrays, roughness elements are assembled by staggering LEGO^{®} bricks on a LEGO^{®} baseboard. The size of each piece of LEGO^{®} brick is l (= 16 mm; long) × l (= 16 mm; wide) × h (= 11.4 mm; high, including the studs at the top). The separation among the LEGO^{®} bricks is varied in the streamwise x direction, covering h:l, h:2l, h:3l, h:4l, h:5l, h:6l, h:7l and h:9l. In addition, the height of cube-type arrays is increased by mounting double (h:4l − D), triple (h:4l − T) and quadruple (h:4l − Q) layers of LEGO^{®} bricks on the h:4l configuration. Examples of the roughness configurations (AR = 1/2, AR = 1/4, h:2l, and h:6l) are shown in Fig. 1b–e. A total of eleven configurations of cube-type array of roughness element are employed in the wind tunnel measurements.
Velocity measurements
Results and discussion
Dynamics over different rough surfaces are analyzed based on the wind tunnel measurements. In the following section, overbar \(\overline{ \bullet }\), angle bracket \(\left\langle \bullet \right\rangle\) and double prime \(\bullet^{\prime\prime}\) (= \(\bullet - \left\langle {\overline{ \bullet } } \right\rangle\)) denote the temporal average, spatial average and fluctuating component, respectively. Temporal average \(\overline{ \bullet }\) is the averaged property during the sampling duration at each point while spatial average \(\left\langle \bullet \right\rangle\) is the averaged property at wall-normal distance z of seven vertical profiles measured at different streamwise positions x.
Turbulent boundary layer parameters
Parameters in the turbulent boundary layers over different rough surfaces
Rough surfaces | h (× 10^{−3} m) | w (× 10^{−3} m) | δ (× 10^{−3} m) | U_{∞} (m s^{−1}) | u_{ * } (m s^{−1}) | C_{ d } (× 10^{−3}) | d (× 10^{−3} m) | z_{0} (× 10^{−3} m) |
---|---|---|---|---|---|---|---|---|
Rib-type arrays | ||||||||
AR = 1/1 | 19 | 19 | 219 | 8.0 | 0.36 | 4.1 | 6.0 | 0.04 |
AR = 1/2 | 19 | 38 | 244 | 8.0 | 0.45 | 6.5 | 6.9 | 0.44 |
AR = 1/3 | 19 | 57 | 248 | 8.4 | 0.52 | 7.6 | 5.9 | 0.63 |
AR = 1/4 | 19 | 76 | 283 | 8.5 | 0.56 | 8.7 | 7.0 | 0.81 |
AR = 1/5 | 19 | 95 | 284 | 8.5 | 0.59 | 9.6 | 6.2 | 1.04 |
AR = 1/6 | 19 | 114 | 294 | 8.5 | 0.60 | 9.9 | 6.1 | 0.98 |
AR = 1/8 | 19 | 152 | 294 | 8.4 | 0.60 | 10.1 | 4.0 | 1.04 |
AR = 1/10 | 19 | 190 | 304 | 9.1 | 0.65 | 10.1 | 8.3 | 0.80 |
AR = 1/12 | 19 | 228 | 304 | 9.1 | 0.67 | 10.8 | 13.6 | 0.85 |
AR = 1/15 | 19 | 285 | 293 | 9.0 | 0.64 | 10.1 | 11.6 | 0.73 |
Cube-type arrays | ||||||||
h:l | 11.4 | 16 | 135 | 10.0 | 0.42 | 3.6 | 5.2 | 0.02 |
h:2l | 11.4 | 32 | 165 | 10.9 | 0.53 | 4.8 | 5.8 | 0.08 |
h:3l | 11.4 | 48 | 165 | 10.8 | 0.54 | 4.9 | 5.3 | 0.09 |
h:4l | 11.4 | 64 | 165 | 10.8 | 0.56 | 5.5 | 5.6 | 0.13 |
h:5l | 11.4 | 80 | 160 | 10.6 | 0.54 | 5.2 | 5.4 | 0.11 |
h:6l | 11.4 | 96 | 165 | 10.6 | 0.54 | 5.1 | 5.3 | 0.10 |
h:7l | 11.4 | 112 | 160 | 10.6 | 0.53 | 5.0 | 5.0 | 0.09 |
h:9l | 11.4 | 144 | 155 | 10.7 | 0.51 | 4.5 | 4.8 | 0.06 |
h:4l − D | 21 | 64 | 190 | 10.8 | 0.60 | 6.3 | 5.8 | 0.23 |
h:4l − T | 30.6 | 64 | 215 | 11.1 | 0.66 | 7.1 | 5.1 | 0.37 |
h:4l − Q | 40.2 | 64 | 219 | 11.2 | 0.70 | 7.9 | 3.6 | 0.52 |
The friction velocity is defined as u_{*} = (τ_{ w }/ρ)^{1/2} where τ_{ w } is the total shear stress on the rough surface and ρ the fluid density. In the wind tunnel measurements, the friction velocity is commonly estimated by the relationship u_{*} (= \(\left\langle {\overline{{u^{\prime\prime}w^{\prime\prime}}} } \right\rangle^{1/2}\)) by averaging the turbulent momentum flux over the entire rough surface (Cheng and Castro 2002a; Salizzoni et al. 2008). Cheng et al. (2007) reported that u_{ * } was underestimated by 25% over staggered arrays of cubical elements based on averaging \(\overline{{u^{\prime\prime}w^{\prime\prime}}}\) in the inertia sublayer (ISL) compared with that of direct drag measurement. In addition, u_{ * } is obtained by assuming it to be the maximum of Reynolds shear stresses in the same studies, and comparable with a corrected estimate value defined as \(\left. {\left( {1 + 0.25} \right) \times \left\langle {\overline{{u^{\prime\prime}w^{\prime\prime}}} } \right\rangle^{1/2} } \right|_{\text{ISL}}\) (Manes et al. 2011; Placidi and Ganapathisubramani 2015; Cheng et al. 2007). In this study, we adopt the conventional method by assuming that u_{*} is equal to the peaked \(\left\langle {\overline{{u^{\prime\prime}w^{\prime\prime}}} } \right\rangle^{1/2}\). Although this would introduce error (within 25% uncertainty) in estimating the value of u_{ * }, the variation pattern of u_{ * } in this study will not be significantly affected as a consistent method is used among the testing cases. The friction velocity u_{ * } over rib-type and cube-type arrays is estimated in the ranges of 0.36–0.67 m s^{−1} and 0.42–0.70 m s^{−1}, respectively (Table 1). Using u_{ * } as the slope, the other two key rough-TBL parameters, roughness length z_{0} and displacement height d, are determined by the best fit of the wind-tunnel-measured mean wind speed profiles to the theoretical logarithmic law of the wall (log law). As shown in Table 1, the displacement height is in the range of 4.1 mm (0.2h) ≤ d ≤ 13.6 mm (0.72h) over the rib-type arrays and 3.6 mm (0.09h) ≤ d ≤ 5.8 mm (0.5h) over the cube-type arrays. The roughness length z_{0} is much smaller, ranging from 0.04 mm (0.002h) to 1.04 mm (0.06h) over rib-type arrays and from 0.02 mm (0.002h) to 0.52 mm (0.013h) over cube-type arrays. Drag coefficient C_{ d } (= 2u _{ * } ^{2} /U _{∞} ^{2} ) is commonly used to measure the aerodynamic resistance for flows over (non-smooth) solid boundaries. It is found to be 4.1 × 10^{−3} ≤ C_{ d } ≤ 10.1 × 10^{−3} over rib-type arrays and 3.6 × 10^{−3} ≤ C_{ d } ≤ 7.9 × 10^{−3} over cube-type arrays.
Velocity profiles
Velocity profiles measured at different positions
Velocity profiles measured over different rough surfaces
Quadrant analyses
Frequency spectra
Conclusions
TBLs over rib- and cube-type arrays are developed in the wind tunnel to examine the flow and turbulence characteristics. For the aerodynamic parameters, a notable trend is observed that roughness length z_{0} increases with increasing drag coefficient C_{ d } while displacement height d varies significantly with increasing C_{ d }. Significant variations of fluctuating velocities and momentum flux are found in the near-wall region, demonstrating the inhomogeneous flows due to the presence of roughness elements in the bottom of TBL. Comparing the velocities over different rough surfaces, it is found that the spatially averaged fluctuating streamwise velocity \(\left\langle {\overline{{u^{\prime\prime}w^{\prime\prime}}} } \right\rangle^{1/2}\), fluctuating vertical velocity \(\left\langle {\overline{{w^{\prime\prime}w^{\prime\prime}}} } \right\rangle^{1/2}\) and momentum flux \(\left\langle {\overline{{u^{\prime\prime}w^{\prime\prime}}} } \right\rangle\) in the near-wall region increase with widening separation among roughness elements, reach a plateau (over rib-type array of AR = 1/8 and cube-type array of h:4l), then finally decrease with further increasing separation between roughness elements. Quadrant analyses and frequency spectra show that the flow entrainment and air removal are enhanced over rougher surfaces. Larger scale motions of turbulence also effectuate roof-level ventilation over urban areas.
Declarations
Author contributions
ZM performed the experiments and drafted the manuscript. CHL performed data interpretation and drafted the manuscript. Both authors read and approved the final manuscript.
Acknowledgements
Not applicable.
Competing interests
The authors declare that they have no competing interests.
Availability of data and materials
The data are available from the corresponding author on reasonable request.
Ethics approval and consent to participate
Not applicable.
Funding
This study is partly supported by the General Research Fund (GRF) 17210115 of The Hong Kong Research Grants Council (RGC).
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Authors’ Affiliations
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