Wind Tunnel Measurements of Surface Shear Stress on an Isolated Dune Downwind a Bridge

Abstract

As part of a comprehensive environmental assessment of the Dun-Gel railway project located in Dunhuang city, Gansu Province, China, a wind tunnel experiment was proposed to predict surface shear stress changes on a sand dune when a bridge was built upstream it. The results show that the length of the wall shear stress shelter region of a bridge is about 10 times of the bridge height (H). In the cases that the interval of the bridge and sand dune (S) is less than 5 H, normalized wall shear stress on the windward crest is decreased from 1.75 (isolated dune) to 1.0 (S = 5.0 H, measured downwind bridge pier) and 1.5 (S = 5.0 H, measured in the middle line of two adjacent bridge piers). In addition, the mean surface shear stress in the downstream zone of the sand dune model is reduced by the bridge pier and is increased by the bridge desk. As for the fluctuation of surface shear stress ($\zeta$) on the windward crest, $\zeta$ decreases from 1.3 (in the isolated dune case) to 1.2 (in the case S = 5.0 H, measured just downwind the pier) and increases from 1.3 (in the isolated dune case) to 1.6 (in the cases S = 5.0 H, in the middle of two adjacent piers). Taking the mean and fluctuation of surface shear stress into consideration together, we introduce a parameter $\psi$ ranging from 0 to 1. A low value indicates deposition and a high value indicates erosion. On the windward slope, the value of $\psi$ increases with height (from 0 at toe to 0.98 at crest). However, in the cases of S = 1.5 H, $\psi$ is decreased by the bridge in the lower part of the sand dune at y = 0 and is increased at y = L/2 compared with the isolated dune case. In other cases, the change of $\psi$ on the windward slope is not as prominent as in the case of S = 1.5 H. Downstream the sand dune, erosion starts in a point that exists between x = 10 H and 15 H in all cases.

1. Introduction

Railways in arid and semiarid regions in Western China suffer from sand hazards [1,2,3]. On one hand, wind-blown sand movement could bury rail tracks, attack railway power systems and roll over the trains. On the other hand, railway structures such as high subgrades, bridges and windbreak walls are huge enough to perturb airflow over the nearby sand dunes, which are stable and moving regularly under initial airflow conditions [4,5,6]. Therefore, it is important to study how the railway structures change the shape and moving patterns of sand dunes in the neighborhood. In previous studies, particular attention has been paid to the effects of wind-blown sands on the railways and subgrades [5,6,7,8], however, the effects of railways on the wind-blown sand, especially on the sand dunes movement, are not well explored. Based on the bridge engineering of the Dun-Gel railway in a sand valley, we observed and characterized the surface shear stress on the sand dunes downwind of a bridge in the wind tunnel.

Sand particle deposition and erosion processes are closely related to the threshold friction velocity of sand entrainment [9,10,11,12,13,14]. Many studies have shown the relationships between surface shear stress acting on the ground and sand entrainment [15,16,17]. To understand the formation and migration of dunes, one first needs to know the stationary wind stress exerted on a given sand topography [18]. Using the visualization techniques to investigate the flow structures around the roughness elements, researchers have shown that vortex strongly governs the pattern and magnitude of surface shear stress at the presence of roughness elements [13]. Hence, it is important to study the fluctuation of surface shear stress.

This study is a part of a comprehensive environmental assessment of the Dun-Gel railway project located in Dunhuang city, Gansu Province, China (Figure 1). Located in the northwest of China, Gansu lies between latitude 32°11′–42°57′ north and longitude 92°13′–108°46′ east, with a total area of 425,800 km². The terrain of Gansu province is long and narrow, and the landform is complex and diverse, including mountains, plateaus, flat rivers, river valleys, deserts and gobi. The climate type of Gansu is mainly temperate continental arid climate. Our purpose is to study how the railway structures affect the shape and moving patterns of sand dunes in the neighborhood by investigating the shear stress on the sand dune surface, which determines the deposition or erosion of the sand dune surface. In this study, spatial variation in the surface shear stress was measured directly by mounting Irwin sensors at numerous discrete points on the sand dune model [19]. The relationship between the surface shear stress on the sand dune and the position of the bridge was analyzed. By analyzing spatial variation changes of surface shear stress on and downstream of the sand dune model, the erosion and deposition zones were identified. Moreover, future changes in the shape and moving patterns of the sand dunes can be predicted.

2. Methods

2.1. Experimental Setup

The experiment was carried out in a multi-functional environment wind tunnel of Lanzhou University. This open-return blow-down low-speed wind tunnel was 22 m long (only for work section) with a cross-section of 1.45 m × 1.3 m [20]. The roughness element in front of the wind tunnel was used to accelerate the development of the boundary layer, which was about 0.2 m thick in the measurement section. The topographic map was measured with an unmanned aerial vehicle, and the dispersion between the crest and the windward slope foot was 10 m, the height of the bridge in front of the sand dune was 12 m. The crests of sand dunes in Figure 1 were parallel to the bridge, suggesting that the prevailing wind direction and dune movement direction were perpendicular to the bridge. In these types of studies, the Reynolds similarity was always unsatisfied because the roughness height in the wind tunnel was 1–2 orders smaller than that in the atmosphere boundary layer. As a result, researches have to neglect the Reynolds similarity [21,22,23].

Figure 2 shows the schematic of the models and the coordinate system used in this study. Roughness elements were placed 6 m upstream of the working section to generate a turbulent boundary layer. The plywood model of the sand dune was 10 cm in height (H) and 100 cm in width. The steel model of the bridge was 12 cm in height (H’) and 36 cm between two adjacent piers (L). The scale between models and real dimensions of dune and bridge is 1:100. To observe the changes of surface stress on the sand dune when the bridge was installed and moved upstream, the distance between the bridge and the sand dune (S) was set as 1.5 H, 3.0 H, 5.0 H, 10.0 H and 20.0 H, respectively. A pitot tube was used to measure the profile of flow speed. Irwin sensors were mounted on the ground and sand dune models, which were to measure surface shear stress.

2.2. Surface Shear Stress Sensor

Irwin sensor is a simple omnidirectional pressure meter that determines the friction velocity without the requirement of alignment by measuring the near-surface vertical pressure differential, which can be used to estimate the surface shear stress in the complex flow [24,25]. It has been used successfully in aeolian sand researches in both lab [13,21,22,26] and field [27,28] to explore the relationship between shear stress and sand transport potential in complex, nonuniform airflow. Many studies have confirmed that the sensor can be simply calibrated [24,29] and is applicable to measure the surface shear stress on a sand dune downwind a bridge in the wind tunnel experiment.

Based on the Irwin empirical function, the friction velocity prepared to calibrate the 34 Irwin sensors was determined using the velocity profile technique. As shown in Equation (1), the calibration of one sensor is [29]:

$$\frac{u_{*}h}{v}=a+b{\left(\frac{\Delta p{h}^2}{\rho v^2}\right)}^n$$

(1)

where h is the height of the obstacle, $v$ stands for kinematic viscosity. The calibration coefficients we used is an averaged result of 34 Irwin sensors. The parameter “$a$” equals 3.86, “$b$” equals 0.11 and “n” equals 0.52. The calibration result is accurate enough for the wind velocity within 2 m s⁻¹ and 18 m s⁻¹ [29]. The friction velocity $u_{*}$ can be converted to shear stress using $\tau =\rho u_{*}^2$.

Figure 3 is the schematic of installation of sensors over the sand dune. In brief, 34 Irwin sensors were used stream-wise. Among them, 8 were set on the windward slope, 5 were set on the leeward slope, 3 were mounted upwind the dune, and 18 were mounted downwind the dune. The measuring position changed three times along the y-axis at y = 0 cm, 6 cm (L/6) and 18 cm (L/2), respectively. One sensor was set at 17.5 H upwind the model to detect the shear stress on a bare surface (${\tau }_0$) for a reference value to normalize surface shear stress (${\tau }^{\prime }=\left({\tau }_x-{\tau }_0\right)/{\tau }_0$). The bridge model, sand dune model and the stream-wise wind velocity were symmetric to the centerline of the wind tunnel. Therefore, the distribution of shear stress on the sand dune was also symmetrically distributed with the centerline.

2.3. Procedure of Wind Tunnel Experiment

The wind tunnel experiment was carried out according to the following steps:

• Before the experiment, we measured the approaching wind velocity and friction velocity on a flat wooden floor with a pitot tube and an Irwin sensor. Figure 4 shows the profile of flow speed and the surface shear stress vary with increasing time. The fitting results are listed in

  Table 1. The fitting results of wind tunnel experiments.

  	Velocity Profile Technique:		Irwin Sensor Results:
  ${\mathit{u}}_0$	${\mathit{u}}_{*\mathit{a}}$	${\mathit{\tau }}_{\mathit{a}}$	${\mathit{u}}_{*\mathit{b}}$	${\mathit{\tau }}_{\mathit{b}}$	${\mathit{\sigma }}_{\mathit{\tau }\mathit{b}}$
  8 m s−1	0.267 m s−1	0.086 N m2	0.261 m s−1	0.082 N m2	0.022 N m2
  12 m s−1	0.389 m s−1	0.182 N m2	0.381 m s−1	0.174 N m2	0.035 N m2
  15 m s−1	0.465 m s−1	0.260 N m2	0.464 m s−1	0.259 N m2	0.054 N m2

  $u_0$ (m s⁻¹) is free-stream wind velocity, $u_{*a}$ (m s⁻¹) is the friction wind velocity computed in profile technique, ${\tau }_a$ (N m²) is the shear stress computed in profile technique, FF. $u_{*b}$ (m s⁻¹) is the friction velocity measured by an Irwin sensor, ${\tau }_b$ (N m²) is the average shear stress measured by an Irwin sensor and ${\sigma }_{\tau b}$ (N m²) is the standard deviation of the shear stress measured by an Irwin sensor.

  .
• Installed the model of sand dune in the wind tunnel. The Irwin sensors were mounted at position shows in Figure 3. Turned on the fan and measured the surface shear stress over 3 min. The free-stream wind velocities were set as 8 m s⁻¹, 12 m s⁻¹ and 15 m s⁻¹, which made the wind velocities at the height of the bridge surface consistent with field actuality (Figure 4).
• Turned off the fan and installed the model of bridge 1.5 H upwind the sand dune model. Restarted the fan and set to the same target speed in Step 2.
• Turned off the fan and changed the position of the bridge model. Restarted the fan and set to the same target speed in Step 2.
• Moved the position of Irwin sensors in the y-direction and started from Step 1 for the next run.

3. Results

3.1. Changes in Averaged Surface Shear Stress

Figure 5 shows the spatial variability of the mean value of normalized surface shear stress (${\tau }^{\prime }$) on the sand dune and downstream it. The windward slope, leeward slope and the crest of the sand dune can be easily recognized in the graphs. It should be noted that for saving the space, the distance between the bridge and the sand dune, S, in the graphs was not in actual scale. Figure 5a shows that in the isolated dune case, wall shear stress increased on the windward slope compared with that on the flat surface. Near the crest of the windward slope, ${\tau }^{\prime }$ was the highest and equals 1.5. In addition, a zone with negative ${\tau }^{\prime }$ was formed between x = 2.5 H and 10 H, corresponding to the backward velocity of the airflow (reattachment region was marked in Figure 5a with green lines). When x reaches 20 H, the magnitude of ${\tau }^{\prime }$ approaches 0, indicating that wall shear stress was no more affected by the sand dune. In Figure 5b–f, although bridge reduces wall shear stress on the windward slope, the magnitude of ${\tau }^{\prime }$ on the windward crest was still high (ranges from 1.25 to 1.5). Moreover, the bridge did not affect the shear stress on the leeward slope dramatically, that is, the change of shear stress on the leeward slope was no more than 5% compared with the isolated case at the same positions. In the cases of S = 1.5 H, 3.0 H and 5.0 H, wall shear stress between x = 5 H and 10 H is affected by the bridge pier and desk. That is, the wall shear stress measured at 5 H < x < 10 H, y = L/2 is higher than that measured at 5 H < x < 10 H, y = 0. Moreover, wall shear stress downwind the sand dune is not affected by the bridge in the case of S = 10.0 H and 20.0 H.

To analyze the change of normalized surface shear stress quantitatively, Figure 6 shows normalized surface shear stress (${\tau }^{\prime }$) as a function of the interval distance (S) and stream-wise position. Figure 6a shows the variation of the normalized surface shear stress (${\tau }^{\prime }$) along the centerline (y = 0). Compared with the isolated dune case, the surface shear stress on the windward slope was reduced due to shelter of the pier (except at the two points at the beginning of the windward slope). When the free-stream wind velocity $u_0$ was 15 m s⁻¹, the ${\tau }^{\prime }$ on the windward crest decreased by 20.4%, 28.2%, 31.7%, 6.4% and 0.5%, corresponding to the cases of S = 1.5 H, 3.0 H, 5.0 H, 10.0 H and 20.0 H respectively. In the case that S equals 20.0 H, the shelter effect of the wall shear stress almost disappears. The shelter region length of the wall shear stress is between 10 and 20 times the bridge height, which is longer than that of a cylinder. We attribute this to the coeffects from the bridge pier and desk.

Figure 6b shows the variation of the normalized surface shear stress (${\tau }^{\prime }$) along y = L/2 with the free-stream wind velocity $u_0=15\mathrm{m}/\mathrm{s}$. Compared with the isolated dune case, shear stress on the crest decreases by 11.4%, 9.1%, 12.0%, 0.5% and −2.3%, corresponding to the cases of S = 1.5 H, 3.0 H, 5.0 H, 10.0 H and 20.0 H. In the downwind area of the sand dune, the shear stress shows some increase from x = 2.5 H to 15 H compared with the isolated dune case. At the downstream position of x = 20 H, the shear stress became stable and almost equaled the free-steam value.

3.2. Changes in the Fluctuation of Surface Shear Stress

To study the fluctuation of the shear stress measured on the sand dune, a normalized parameter $\zeta$ for the standard deviation of shear stress was defined as follows [13]:

$$\zeta =\frac{\sqrt{{\overline{{\tau }_z^{\prime }}}^2}}{\sqrt{{\overline{{\tau }_0^{\prime }}}^2}}$$

(2)

where $\sqrt{{\overline{{\tau }_z^{\prime }}}^2}={\sigma }_{\tau z}$ is the standard deviation of the surface shear stress when the model was installed, and $\sqrt{{\overline{{\tau }_0^{\prime }}}^2}={\sigma }_{\tau 0}$ is the standard deviation of the surface shear stress measured on the flat floor.

Figure 7 shows the variation in the normalized standard deviation of the surface shear stress $\zeta$ with free-stream wind velocity equaled 15 m s⁻¹. On the windward crest, magnitude of $\zeta$ equals 1.35 in the isolated dune case. However, in the cases that S = 1.5 H, 3.0 H and 5.0 H, parameter $\zeta$ measured at the position of y = 0 and L/2 shows some different trends. That is, on the windward crest, wall shear fluctuation at y = 0 is decreased compared with the isolated dune case. Quantitatively, equals 1.2 in the case of S = 1.5 H while $\zeta$ equals 1.35 in the isolated dune case. Downstream the sand dune, wall shear fluctuation measured both at y = 0 and L/2 is lower than the isolated case between x = 5 H to 10 H. However, wall shear fluctuation at y = L/2 is higher than at y = 0. That is, the bridge shows some restraint on the wall shear fluctuation downwind the sand dune and the restraint effect of the bridge pier is greater than that of the bridge desk. In addition, the influence from bridge and sand dune almost disappears at x = 15 H. In the cases that S equals 10.0 H and 20.0 H, $\zeta$ calculated on and downwind the sand dune shows little divergence at y = 0 and L/2 and the trend is very closed to the isolated case and this feature is very prominent in the case that S = 20.0 H.

4. Discussion

The threshold friction velocity is a key parameter to estimate the deposition and erosion potential of the ground. Some experiments show a higher threshold friction velocity than the calculation results using the Bagnold’s empirical equation [30]. We calculated the fluid threshold skin friction velocity as:

$$u_{\tau \tau }=u_{*t}+2\sigma \left(u_{\tau }\right)$$

(3)

where $u_{*t}$ was 0.29 m s⁻¹ in our experiment [31]. The standard deviation $\sigma \left(u_{\tau }\right)$ = 0.048 m s⁻¹ at 15 m/s was determined from skin friction velocity variations measured with Irwin sensors on the smooth wooden floor. As a result, $u_{\tau \tau }$ in our study was 0.387 m s⁻¹ and the threshold shear stress ${\tau }_t$ equaled 0.179 Pa.

To assess the local dominance of erosion and deposition mechanisms, a threshold parameter of fraction time $\psi$ was proposed [14], which represents the fraction of time when friction velocity exceeds the threshold parameter.

$$\psi \left(x,y\right)=\frac{\Delta t\left[\tau \left(t,x,y\right)>{\tau }_t\right]}{T}$$

(4)

where $\Delta t$ is the time period during which the shear stress $\tau$ is larger than the threshold shear stress ${\tau }_t$, and T represents the total time. As defined $\psi =1$ indicates an erosion zone, $\psi =0$ indicates a deposition zone, and $0<\psi <1$ indicates both erosion and deposition are both possible. Specifically, for $\psi <0.5$, deposition dominates the local net and for $\psi >0.5$, erosion dominates.

Figure 8 shows the spatial distribution of $\psi$ at the free-stream wind velocity $u_0=15{\mathrm{m}\mathrm{s}}^{-1}$ in our experiment. In the isolated dune case, the value of $\psi$ increased from 0 at the windward toe to 0.98 at the windward crest, indicating that the erosion rate increases with height on the windward slope. On the leeward and downwind the sand dune (0 < x < 10 H), the values of $\psi$ are less than 0.5, indicating that deposition happened in this region. In the case of S = 1.5 H, the value of $\psi$ is decreased by the bridge pier and increased by the bridge desk in the lower part of the windward slope. That is, the value of $\psi$ between x = -5 and -2.5 decreases at y = 0 and increases at y = L/2 compared with the isolated dune case. For instance, the value of $\psi$ is 0.42 at x = −2.5, y = 0 and the value of $\psi$ is 0.65 at x = −2.5, y = L/2, decreased and increased compared with the value of 0.5 in the isolated dune case. In the cases of S = 3.0 H, 5.0 H, 10.0 H and 20.0 H, the change of $\psi$ on the windward slope is not as prominent as in the case of S = 1.5 H. On the leeward slope, $\psi$ in this region always kept low magnitudes that are lower than 0.3, indicating that the incoming sand particles deposit no matter where the bridge was set. Downstream the sand dune, in the cases of S = 1.5 H, 3.0 H and 5.0 H, $\psi$ is decreased at y = 0 and increased at y = L/2 compared with the isolated dune case. However, the value of $\psi$ exceed 0.5 at x = 15 H almost in all cases. That is, between x = 0 and x = 15 H, deposition domains the sand movement and downwind x = 15 H, erosion domains the sand movement. In the cases of S = 10.0 H and 20.0 H, the trend of $\psi$ is similar to the isolated dune case, especially when S = 20.0 H.

Many wind tunnel experiments for shear stress measurement on the sand dune and around buildings have been done for engineering applications [32]. However, results on the influence of a building on sand terrain are still lacking. To the authors’ knowledge, the study of wind erosion patterns downstream a bridge has not been proposed yet. The results in the present study not only provides predictions on sand dune moving after a bridge which is built upstream, but also confirms the viewpoints that the size of the sand drifts is very sensitive to the frontage of the upwind collecting area, which is accordant with the comment proposed [9]. Our research on surface shear stress can play an important role in railway construction items, and can give some guidance on future research about the moving pattern of sand dunes affected by building upstream.

5. Conclusions

We used 34 Irwin sensors to measure the surface shear stress on a sand dune model that is downstream a bridge model immersed in a fully developed turbulent boundary layer in a wind tunnel. The results showed that the averaged wall shear stress on the windward crest of the sand dune is decreased by the bridge in the cases of S = 1.5 H, 3.0 H and 5.0 H. The decrease ratio obtained at y = 0 is greater than that obtained at y = L/2.

The bridge also affected the fluctuation of surface shear stress on the sand dune. In the case of S = 1.5 H, 3.0 H and 5.0 H, the fluctuation of surface shear stress at the windward crests decreased at y = 0 and is increased at y = L/2 compared with the isolated dune case. Downstream the sand dune, the restraint effect of the bridge pier on the wall shear fluctuation is greater than that of the bridge desk.

The fraction time parameter $\psi$ used in the study to assess the local dominance of erosion and deposition mechanisms indicated strong erosion on the windward slope. The value of $\psi$ increases with height on the windward slope of an isolated sand dune. However, in the cases of S = 1.5 H, $\psi$ is decreased by the bridge in the lower part of the sand dune at y = 0 and is increased at y = L/2 compared with the isolated dune case. In other cases, the change of $\psi$ on the windward slope is not as prominent as in the case of S = 1.5 H. Downstream the sand dune, erosion starts in a point between x = 10 H and 15 H in all cases. However, differences in the value of $\psi$ downwind the sand dune indicates the erosion rate can be different.

Last to be acknowledged, wind tunnel experiments of geometrically similar models cannot fulfill the Reynolds similarity. To get more precise results, the next study we concentrate on the field observation of shear stress and sand flux so that erosion patterns on the sand dune downstream a bridge. The simple assumption in this paper will be improved.