Hydrodynamics and sediment transport in a meandering channel with a model axial-flow hydrokinetic turbine

Abstract

An investigation into the interactions between a model axial-flow hydrokinetic turbine (rotor diameter, d_T = 0.15 m) and the complex hydrodynamics and sediment transport processes within a meandering channel was carried out in the Outdoor StreamLab research facility at the University of Minnesota St. Anthony Falls Laboratory. This field-scale meandering stream with bulk flow and sediment discharge control provided a location for high spatiotemporally resolved measurements of bed and water surface elevations around the model turbine. The device was installed within an asymmetric, erodible channel cross section under migrating bed form and fixed outer bank conditions. A comparative analysis between velocity and topographic measurements, with and without the turbine installed, highlights the local and nonlocal features of the turbine-induced scour and deposition patterns. In particular, it shows how the cross-section geometry changes, how the bed form characteristics are altered, and how the mean flow field is distorted both upstream and downstream of the turbine. We further compare and discuss how current energy conversion deployments in meander regions would result in different interactions between the turbine operation and the local and nonlocal bathymetry compared to straight channels.

Key Points:

• Local scour is observed near axial-flow turbines in meandering channels
• Axial-flow turbines modify bed form kinematics around meander bend
• Turbine wake follows channel curvature

1 Introduction

Current energy converter (CEC) technologies provide an opportunity to broaden the renewable energy portfolio in an effort to meet local energy demand, reduce carbon footprint, and minimize fossil fuel consumption. Advancing these technologies requires both rapid development and deployment into natural environments of increasing hydrodynamic and morphodynamic complexity. Unfortunately, uncertainty surrounding potential environmental impacts poses a challenge for small companies to adequately address the concerns raised by overseeing agencies during all steps of site development, from environmental permitting to pilot project monitoring. It thus remains critically important for the growth of the CEC industry and for the development of sustainable riverine and coastal communities that researchers elucidate the interactions between single or multiple energy harnessing devices and the surrounding environment, including both ecological and geomorphic response [Bedard, 2008; Polagye et al., 2011; Foufoula-Georgiou et al., 2012]. While a growing effort has been focused on understanding the effects of CEC deployments on fish habitat and population diversity and safety [Copping et al., 2014, 2015; Zydlewski et al., 2015], an often overlooked, key impact area is the morphodynamics of erodible substrates and the connections among sediment transport, hydrodynamics, and the aquatic biota [Shields et al., 2011]. Compared to straight channels with nonerodible beds, natural waterways are characterized by a broad range of large-scale flow structures modulated by bed form evolution and migration as well as by channel curvature and point bar configuration [Kang et al., 2011]. The link between topographic complexity and flow complexity is important to predict the optimal deployment location in terms of mean velocity U (note that the device power production, ) and also in terms of reduced variability of the flow field (limiting unsteady loads on blades, shaft, and support tower of CEC devices). For multiturbine array deployments, the same requirements apply, adding the design parameter of the optimal distance between CEC devices, a criteria based on mean velocity recovery in the wake of the rotor.

Many recent laboratory experiments and simulations have focused on the hydrodynamics of CEC turbines and downstream wake recovery in straight rectangular flumes or tow tanks. For example, Myers and Bahaj [2007], Tedds et al. [2014], and Bachant and Wosnik [2015] characterized the near-wake environment (less than 10 rotor diameters, d_T) while Chamorro et al. [2013] and Stallard et al. [2013] have shown detailed wake recovery up to 15 d_T. Bahaj and Myers [2013] used porous disks to investigate wake recovery up to ≈25 d_T and lateral wake velocity deficit to establish lateral spacing requirements in multiturbine arrays. Neary et al. [2013] reports on the far-field wake of a three-bladed axial-flow turbine (d_T = 0.5 m), showing wake velocity deficit remains at approximately 10–5% up to 35 d_T downstream of the rotor location. Numerically, Kang et al. [2012, 2014] have demonstrated the benefits of using state-of-the-art large eddy simulations for investigating wake characteristics of a full-scale and model axial-flow turbine, and for identifying governing mechanisms of wake meandering, providing new insight into the physics of marine turbines, their performance, and characteristics of the near and far-field wake. Additional numerical work investigated far-field wake effects within multiturbine array configurations [Churchfield et al., 2013; Blackmore et al., 2014; Fallon et al., 2014], demonstrating how numerical approaches are advantageous for investigating many configurations to determine optimal layout of arrays.

Despite some companies targeting man-made flood diversion and irrigation canals for hydrokinetic energy production [Gunawan et al., 2014], in reality, most installations will not occur in rectangular or trapezoidal channels. In fact, for economic viability and long-term energy contribution, hydrokinetic turbine arrays must target tidal and river channels or offshore coastal regions with strong ocean or tidal currents. For axial-flow turbines, (D is the rotor diameter), implying that the channel depth represents the tightest constraint. While providing large cross-sectional area, natural sites are typically characterized by abrupt changes in topography, channel roughness, bed form induced roughness, channel sinuosity, submerged obstacles, and a number of other physical constraints that directly impact the turbulent hydrodynamic environment. These geometric inhomogeneities such as large submerged obstacles (i.e., boulders and rock ledges) or man-made structures (i.e., bridge piers, abutments, and upstream turbines) introduce periodic large-scale coherent eddies that may intersect a turbine's rotor, causing undesired unsteady structure loading and decreased energy production. Recent work by Chamorro et al. [2015] examined the effects such coherent eddies have on turbine performance and wake characteristics using vertically oriented cylinders to introduce eddies of various sizes.

Until recently, investigations into the morphodynamic impact resulting from single and multiturbine arrays remained unstudied. Numerical investigations have been undertaken by Neill et al. [2009, 2012] and Robins et al. [2014], where they investigated the far-field effects of large-scale arrays in areas such as coastal England and the Irish Sea. At this scale, computational costs prohibit studying local effects and allow for generalized representations of each turbine or the turbine array. Regardless, such studies have indicated that large-scale conversion of kinetic energy to electrical energy using hydrokinetic turbine devices will likely alter sediment transport and depositional patterns in the far field. More recently, advancements in computational methods and supercomputing resources have allowed integration of high-resolution hydrodynamic and morphodynamic processes to simulate coupled turbulent flow and sediment transport in natural waterways around rotating hydrokinetic turbines and other hydraulic structures [Yang et al., 2013; Khosronejad et al., 2013].

In the work leading up to this study, a straight channel with an erodible bed was used to investigate the local and far-field effects of axial-flow hydrokinetic turbine(s) on sediment transport, and the role that large-scale migrating bed forms have on turbine performance [Hill et al., 2014, 2016]. These experiments showed only locally enhanced scour and deposition induced by a small-scale turbine. Measurements also indicated how bed form features located within a critical zone approximately 2–3 d_T upstream of the turbine location were able to impact performance as a result of the time varying flow characteristics imposed by (migrating) dune geometry [Best, 2005].

The interactions between axial-flow turbines and meandering channels with asymmetric channel cross-section geometry have yet to be investigated. To address these interactions, a case study was conducted in the Outdoor StreamLab (OSL) research basin at the University of Minnesota's St. Anthony Falls Laboratory (SAFL). The OSL has been the subject of recent research demonstrating novel bed form morphodynamic measurement techniques [Palmsten et al., 2015] and advanced numerical methods capable of simulating turbulent flow and sediment transport in arbitrarily complex channel topography [Kang et al., 2011; Kang and Sotiropoulos, 2011; Kang et al., 2012; Kang and Sotiropoulos, 2012; Khosronejad et al., 2015]. The results of these studies provide key insights into the complex flow patterns and coherent structures occurring within the asymmetric cross section developing in a meandering channel. Of key interest for the present study is the effect of a CEC turbine on the morphodynamics and hydrodynamics of a meandering river, in particular on the longitudinal and transverse sediment transport along the meander point bar, on dune migration and deformation along the meander, and on the variability of the flow impinging on the turbine rotor. The experiments and facility are described in section 2. Results from data collected during the baseline and turbine experiments are presented in sections 3.1 and 3.2, respectively. Finally, discussion (section 4) and concluding remarks (section 5) summarize the interactions among sediment transport, complex flow patterns, and a model hydrokinetic turbine operating in a meandering channel, including implications for development of CEC devices and comparison with results obtained in a straight channel. While the results published in this work do not provide a holistic understanding or predictive model governing these interactions, they provide insight into the complexity axial-flow devices will operate under when installed at full-scale.

2 Experimental Facility

The experiments were conducted in the OSL Riparian Basin research facility located at SAFL at the University of Minnesota (UMN). The OSL is a field-scale meandering stream research facility with control of bulk flow (Q_w) and sediment supply (q_s) rates (Figure 1a). A transportable data acquisition (DAQ) carriage provides researchers the ability to collect high-resolution, spatially referenced data, including channel and floodplain topography, water surface elevation, and three-dimensional (3-D) velocity measurements (Figure 1b). The 40 m by 20 m Riparian Basin, once an emergency spillway for St. Anthony Falls on the Mississippi River, contains the OSL channel, a wide, deep (bankfull conditions) meandering channel (sinuosity, , and average channel bed slope, ). The sand-bed channel (d₅₀ = 0.7 mm coarse sand) has been continuously supplied with Mississippi River water since 2008. The channel banks remain relatively stable through the use of coconut fiber matting and well established vegetation. Coarse sand transports as bed load through the system, bypassing riffle zones comprising coarse cobbles and depositing as point bars on the inside of each meander bend creating the asymmetric channel cross-section topography typical of sand-bed meandering systems. Transported bed load sediment is captured in a downstream settling basin and hydraulically transported upstream to a sediment holding tank, where a variable-speed auger system feeds sediment into the channel at a constant, user-defined rate. In this case, q_s ≈ 6.9 kg/min. The DAQ carriage location is surveyed by a total station Sokkia SET 330R3. Using the DAQ carriage reference points, all data can be converted from local carriage coordinates to global OSL coordinates, providing a method for referencing current data to historic topographic and flow data collected within OSL. Through a series of overlapping DAQ carriage topography data scans, the OSL channel topography was mapped along its entire length in 2010 (Figure 2a). A closer view of the middle meander bed (Figure 2b) highlights locations of the hydrokinetic turbine model, data collections zones, and recently surveyed channel banks during these experiments. The model turbine used in the OSL experiments was a 1:33 scale three-bladed axial-flow turbine with rotor diameter, d_T = 0.15 m and was mounted near the apex of the middle meander bend (Figures 1c and 1d). The turbine was installed in the channel such that the rotor plane was parallel to the channel cross section. Turbine hub height was h_hub = 0.147 m, resulting in an approximate channel blockage ratio of 4%. For additional details on the turbine geometry, operating characteristics, and previous work using the same turbine, the readers are directed toward Hill et al. [2014, 2016].

Figure 1

(a) Photograph of the St. Anthony Falls Laboratory (SAFL) Outdoor StreamLab (OSL). (b) OSL data acquisition (DAQ) carriage used for data collection. (c) Hydrokinetic turbine model (d_T = 0.15 m) mounted near the apex of the middle meander bend. Arrows in photos indicate flow direction.

Figure 2

(a) OSL channel topography mapped in 2010. Location of turbine indicated by red diamond at (X, Y) (19.7 m, 19.3 m). (b) Topography of middle meander bend outlined by the box in Figure 2a showing channel topography from 2010 (light gray contour lines), turbine location (A, red diamond), streamwise sonar transect location (B), spanwise sonar transect location (C), final near-turbine sonar topography zone (D), boundary of DAQ carriage (E) from which sensors were mounted (see Figure 1), and the channel bank edges (F). Flow is from left to right in both images.

For both the baseline and turbine experiments, the bulk flow rate was set to 280 L s⁻¹ (bankfull channel conditions). The OSL channel was run at bankfull conditions for 2 days leading up to the testing period to ensure the channel had reached quasi-equilibrium transport conditions for the flow and sediment supply rates used. Then, the baseline experiment (9 October 2014) ran for approximately 8 h, while the turbine experiment (10 October 2014) ran for approximately 7 h. A sonar transducer repeatedly traversed a streamwise and a cross-stream transect. Referring to Figure 2b, the streamwise transect (B) passed over the top of the turbine (location A) and collected bed elevation data from −2.6 to at Δx = 0.01 m spacing. The cross-stream transect (C) traversed the channel at 1.4 downstream of the turbine and collected bed elevation data from y∕d_T ≈ −6.3 (right bank) to (left bank) at Δy = 0.01 m spacing. The time intervals between sequential transects was Δt ≈ 12.3 and 12.7 s for the streamwise and cross-stream sections, respectively. At the end of both the baseline and turbine experiments, flow was decreased to base flow conditions (Q_w ≈ 25 L s⁻¹), and a sonar patch scan measured ending channel topography for a region within the meander (see monitored area (D) in Figure 2b). Figures 3a and 3b show the final topography from the baseline and turbine experiments, respectively. Note that topographic data in the OSL reference system report elevation above the sea level.

Figure 3

(a) Ending topography after baseline experiment and (b) after turbine (circled) experiment. Flow is from left to right in both images.

A Nortek Vectrino+ acoustic Doppler velocimeter (ADV) was used to measure 3-D velocity at three locations along the same streamwise transect (B) used for time-resolved bed elevation data (Figure 2b). The ADV sampled instantaneous U_i, V_i, and W_i values at the same elevation of the turbine hub height, z_hub = 239.086 m (with the hub height defined with respect to the averaged bed elevation, h_hub = 0.147 m), at streamwise locations x∕d_T = −2.9 (upstream), 0 (turbine), and 4.4 (downstream). Velocity data were collected at 100 Hz for during 45 min at each location. Additionally, a series of cross-stream velocity profiles were collected at hub height in the turbine wake using a moving ADV sampling and averaging method, described in section 3.2.3. The five profiles were located downstream of the turbine from x∕d_T = 1.4–5.4 at 1 d_T streamwise spacing. The ADV was traversed from y∕d_T = −1.5 to 1.2 at a speed of U_adv = 1 mm s⁻¹.

3 Results

3.1 Baseline Experiment

Baseline data were collected to determine bed form characteristics and velocity statistics within the investigated region in the middle meander bend of the OSL. The following presents results on dune geometry, migration, orientation and variability, and mean velocity and turbulent fluctuations before installing the model hydrokinetic turbine in the channel.

3.1.1 Morphodynamics

At the end of the baseline experiment, a rectangular section of the channel bed topography was mapped prior to installing the model turbine (Figure 2b area (D), consistent with the scan in Figure 3a). These data provide channel geometry initial conditions for the turbine experiment. The kinematics of migrating bed forms along the meander bend results in a distortion of bed form geometry with appreciable effects on bed form crest orientation. This distortion largely reflects the channel boundary shear stress imposed on the sediment, and therefore results in varying bed form migration velocities in the cross-stream direction [Dietrich and Smith, 1984]. Acknowledging the curvature of bed form crests, Figure 3 allows for an estimate of the bed form approach angle within a range of approximately 35°–40° with respect to the turbine rotor plane. Channel cross-section variability in depth, bed form height, migrating bed form velocity, and local mean flow velocity results in steady and unsteady loads on turbine components that axial-flow turbines is not subject to in straight, nonerodible channels.

Repeated streamwise and cross-stream bed and water surface elevation scans reveal the range of instantaneous bed surface elevations and provide a method for calculating the mean bed surface over the span of 2 h during cross-stream profile data collection and over 2.25 h during streamwise profile data collection (Figure 4). During the 2 h period of cross-stream profile data collection, 15 bed forms migrated past this location in the meander, as evidenced by the space-time contour illustrated in Figure 5a. The time series of bed elevations at the cross-stream location where the turbine was eventually placed is provided in Figure 6 (location referenced by arrows at in Figure 5), showing bed form heights, , and a bed form crest period of min. Mean flow depth at this location was and maximum cross-sectional channel depth was .

Figure 4

Instantaneous (light gray) and mean bed (solid black) and water surface (solid blue) elevation data in the (top) cross-stream and (bottom) streamwise directions collected during the baseline experiment.

Figure 5

Space versus time contours of the cross-stream sonar bed elevation data from the (a) baseline and (b) turbine experiments. Arrows at 0 indicate the cross-stream location where bed elevation time series data were collected from and plotted in Figure 6.

Figure 6

Bed elevation, z_b, time series comparison between baseline (dotted line) and turbine (solid line) experiments at 1.4 and 0.

Average bed form velocity, , was estimated through cross-correlation analysis of sequential streamwise sonar bed elevation measurements. Spatial correlation coefficients, , were averaged to find a peak correlation coefficient at ( ). Given the time difference, , necessary to complete two sonar passes, the resulting average bed form velocity during baseline experiments was calculated to be m s⁻¹. Using this velocity and the estimated bed form crest periodicity, T_b, the average bed form wavelength along the streamwise transect is λ_b ≈ 0.74 m. These bed form characteristics are quantified for the location at which the turbine was eventually placed. Due to varying bed form kinematic properties from the inner bank of the meander toward the outer bank, λ_b, h_b, and T_b may vary as qualitatively visualized in Figure 5a.

3.1.2 Velocity Characteristics

Asymmetric channel cross-section geometry, migrating bed forms, and channel meandering in the OSL facility create a complex environment with turbulent characteristics affected by both local and nonlocal, steady and unsteady, topographic features. Locally, sediment grain roughness and bed form geometry introduce a strong variability in the streamwise direction, while nonlocal channel geometry such as sinuosity and asymmetric channel cross sections give rise to secondary currents. Recent simulations of turbulent flow through the OSL channel using time-averaged bed topography with no mobile bed forms provide insight into these complex secondary current flow patterns in the OSL channel [Kang et al., 2011]. However, it is likely that the presence of bed forms ( 0.74 m, 0.087 m) migrating through the OSL middle meander contaminates the signature of these secondary currents inducing strong fluctuations in the streamwise-vertical plane. Nonetheless, to characterize the flow in the region where the turbine would be placed, an ADV was placed at three streamwise locations (referred to as upstream, turbine, and downstream locations) to quantify mean and fluctuating 3-D velocity characteristics, correlations between bed elevation and velocity direction and magnitude, and dominant turbulence scales in the flow along the meander. These measurements provide a baseline for comparison to turbine-induced flow modifications.

Table 1 summarizes the mean , standard deviation , turbulent kinetic energy (k), and the integral time and length scales based on the velocity time series autocorrelation function for these three locations at the turbine hub height elevation. Because the ADV coordinate system was referenced to the DAQ carriage and turbine rotor plane and did not follow the curvature of the channel or rotate with the mean streamwise velocity direction, it is also valuable to assess the magnitude and direction of the velocity vector (Figure 7). Using the right-hand rule notation, the ADV coordinate system measured positive streamwise velocities, U, in the downstream direction, positive cross-stream velocities, V, toward the left bank of the OSL channel, and small but positive vertical velocities, W, upward toward the free surface. Positive horizontal angle direction, , indicates departure toward the left (outer) OSL bank, while positive vertical angle direction, θ, indicates departure toward the free surface. Table 2 summarizes the horizontal and vertical angles of the velocity vector at each location. The channel curvature has a small but noticeable effect in the baseline horizontal velocity direction, , switching from positive (toward left outer bank) to negative (toward right inner bank) further downstream. The flow is nearly orthogonal to the channel cross section and turbine rotor plane where the turbine was located.

Figure 7

(a) Schematic of the ADV coordinate system and calculated velocity magnitude and direction (horizontal angle) and θ (vertical angle). (b) Schematic of the relative change in between baseline (subscript, B) and turbine (subscript, T) experiments, summarized in Table 2.

Table 1. Summary of the Mean ( ), Fluctuating (σ_u, σ_v, σ_w), Turbulent Kinetic Energy (k), and the Integral Time ( ) and Length ( ) Scales From the Baseline (B) and Turbine (T) Experiments From Three Locations (US Upstream ( −2.9); Turb. Turbine ( 0.4), and DS Downstream ( 4.4)) at the Same Elevation as the Turbine Hub Height, h_huba

Location	Case	(m s^−1)	(m s^−1)	(m s^−1)	σu (m s^−1)	σv (m s^−1)	σw (m s^−1)	K (m^2 s^−2)	(s)	(m)
US	B	0.658	0.055	−0.018	0.104	0.097	0.077	0.0131	0.069	0.046
	T	0.673	0.109	−0.010	0.078	0.094	0.063	0.0094	0.066	0.044
Turb.	B	0.676	−0.008	−0.006	0.103	0.095	0.074	0.0125	0.067	0.045
	T	n/a	n/a	n/a	n/a	n/a	n/a	n/a	n/a	n/a
DS	B	0.696	−0.060	−0.002	0.096	0.083	0.070	0.0105	0.069	0.048
	T	0.560	−0.027	−0.019	0.129	0.120	0.103	0.0207	0.067	0.037

• ^a Statistics were calculated from 45 min ADV records at each location. No data are available for the Turbine location during the Turbine experiment because the turbine was in the way of the ADV.

Table 2. Summary of the Horizontal ( ), Vertical (θ), and Relative Change in Angle ( ) of the Velocity Magnitude Vector (U_mag) From the Three ADV Locationsa

Location	Case	(°)	θ (°)	(°)
US	B	4.75	−1.46	n/a	0.23	−0.31	0.40
	T	9.09	−2.87	4.34	0.28	−0.04	0.11
Turb.	B	−0.74	−0.44	n/a	0.41	−0.20	0.32
	T	n/a	n/a	n/a	n/a	n/a	n/a
DS	B	−4.94	−0.14	n/a	0.70	−0.66	0.16
	T	−2.87	1.95	2.07	0.43	−0.33	0.05

• ^a Cross-correlation coefficients for lag zero (ρ₀) are summarized from the correlation analysis between bed elevations and velocity magnitude and direction.

Insight into the influence of bed form elevation (z_b) on the local velocity magnitude (U_mag) and direction ( , θ) is illustrated in Figure 8. Simultaneous sonar and ADV measurements provide a 45 min time series of bed form migration and velocity magnitude and direction at each of the three locations. Cross-correlation analysis between the bed elevation time series, , and U_mag, , and θ are plotted in Figure 9, providing an even further understanding into the bed form influence on hydrodynamics where the turbine would be installed. In Figure 9, the cross-correlation function between z_b and θ lags approximately 1.5 min behind the peak correlation of z_b and . Similarly, the peak correlation between z_b and U_mag appears another 1.5 min after the peak between z_b and θ. The distance between peaks in the correlation functions provides an additional estimate for the bed form period. Because the peak correlations range between 0.45 0.6, this indicates a relatively significant local effect on the hydrodynamics due to the bed forms. Table 2 summarizes these correlation coefficients, while further discussion on the implications of these synchronous bed elevation and velocity measurements is discussed in section 4.2.

Figure 8

Forty-five minute time series of velocity magnitude, (top) U_mag, (middle) horizontal (black) and vertical θ (red) angles, and (bottom) bed elevations z_b from the future turbine location during the baseline experiment. Bed elevations were measured 0.13 m downstream of ADV location. Raw data (dotted line) and shifted data (solid line) are presented as though the elevations were collected simultaneously directly under the ADV sampling location. Time series has been shifted using the mean bed form velocity, 0.0016 m s⁻¹ assuming minor bed form geometry distortion under relatively short travel times and lengths.

Figure 9

Temporal cross-correlation curves between the bed elevations and the velocity magnitude and direction time series presented in Figure 8. Data from baseline experiments at the location where the turbine was placed.

To further investigate the streamwise homogeneity of the flow in the region of interest, the integral time scale, , and the integral length scale, of the flow (Table 1) are calculated from the autocorrelation function as

(1)

and

(2)

where is the autocorrelation function, defined as

(3)

where is the instantaneous velocity fluctuation and τ is the time lag. is the local mean velocity.

Spectral analysis of the U, V, and W velocity components at the three locations during baseline experiments provides, in addition to integral scale values discussed above, further evidence that the characteristic turbulent scales were similar throughout the region of interest. Figure 10 illustrates the normalized velocity spectra. Here the mean flow depth at the future turbine location ( 0.306 m) and a turbulent kinetic energy velocity scale, defined as

(4)

were used for normalizing the calculated spectral energy density ( , units of m² s⁻¹).

Figure 10

Velocity spectrum from the ADV measurements under baseline conditions at three locations: upstream (red), future turbine location (black), and downstream (blue). is the calculated energy spectrum (m² s⁻¹). The energy spectra are normalized by the mean flow depth at the location of the turbine during baseline experiments (  = 0.306 m) and the turbulent kinetic energy velocity scale, u_k, from the upstream baseline time series data.

3.2 Turbine Experiment

Following the baseline experiment, a model axial-flow hydrokinetic turbine ( 0.15 m, 0.147 m) was installed near the apex of the middle meander bed approximately half way across the channel cross section in an area where the turbine was exposed to the combined effect of actively migrating dunes, incoming turbulence, and secondary currents. This section highlights results on mean bed topography and both bed form and flow characteristics in the presence of the instream turbine in the OSL meander.

3.2.1 Morphodynamics

Cross-stream and streamwise continuous bed and water surface elevation measurements were collected along the same transects as during the baseline experiment, providing a method for monitoring the change in mean and fluctuating bed elevations induced by the turbine deployment (Figure 11). When compared to the baseline condition in the cross-stream direction (Figure 12), the presence of the turbine resulted in a lowering of the mean bed elevation (scour) between −2.5 2.5 and an increase (deposition) toward the inner bank on the point bar within the meander ( −2.5). This configuration results in a wide scour hole centered on the turbine location due to a slight flow acceleration around the rotor (the cross-section transect is 1.4 d_T downstream of the rotor). The increased planform size of the high momentum region near the outer bank is balanced by a likely reduction in flow velocity in the proximity of the inner bank where deposition is observed. Comparisons between the baseline and turbine experiment standard deviation ( ) values of the bed elevation profiles in the cross-stream direction are also provided in Figure 12. The largest reduction in due to the turbine was observed with the center of the turbine position at 0. In general, stayed consistent between the baseline and turbine experiments inward of the mean bed elevation crossover location at −2.5 (i.e., ), while was substantially decreased in the presence of the turbine elsewhere. As observed in Figures 5, 6, and 11, such decreased variability is due to a reduction in height and wavelength of the incoming bed forms.

Figure 11

Instantaneous (light gray) and mean bed (solid black) and water surface (solid blue) elevation data in the (top) cross-stream and (bottom) streamwise directions collected during the turbine experiment. Turbine rotor area is represented gray circle at 0 in the top figure and by the solid black vertical line at 0 in the bottom figure.

Figure 12

Comparison between the cross-stream mean bed and (top) water surface elevations and (bottom) the standard deviation elevations for the baseline (dashed lines) and turbine (solid lines) experiments. Turbine rotor area is represented by the gray circle in the top figure. The x axis is presented in both dimensional (m) and nondimensional ( ) units. The y axis is presented in both dimensional (m) and nondimensional ( ) units with 0 corresponding to the turbine hub height, h_hub.

Similar comparisons are made between the baseline and turbine experiments streamwise bed and water surface elevation profiles as illustrated in Figure 13. Most notable is the locally enhanced scour induced by the presence of the turbine up to 2 or 3 downstream of the turbine location. Local scour depths reached a maximum of −0.023 m ( 0.15). Downstream from here ( 3 or 4), the mean bed elevation profile asymptotes toward the baseline streamwise mean bed elevation profile. While mean bed elevations between baseline and turbine experiments were similar upstream and farther downstream of the turbine, the variability in bed elevation was consistently observed to be approximately 65% of that measured during the baseline experiment.

Figure 13

Comparison between the streamwise mean bed and (top) water surface elevations and (bottom) the standard deviation elevations for the baseline (dashed lines) and turbine (solid lines) experiments. Turbine rotor area is represented by the vertical solid black line in the top figure. The x axis is presented in both dimensional (m) and nondimensional ( ) units. The y axis is presented in both dimensional (m) and nondimensional ( ) units with 0 corresponding to the turbine hub height, h_hub.

The cross-stream space versus time evolution contour illustrated in Figure 5b and the bed elevation time series data comparison at 1.4 in Figure 6 provide another comparison between the baseline and the turbine-altered morphodynamic characteristics. In general, cross-stream bed form length has decreased, the slope between the inner point bar and the outer bank thalweg is steeper, and the frequency of bed forms has increased while the bed form height is smaller. Distinguishing bed forms is more challenging in the wake region of the turbine at 1.4, yet approximately 17–20 smaller bed forms were observed during the same time period.

3.2.2 Velocity Characteristics

Mean and fluctuating 3-D velocity characteristics in the OSL channel with the turbine are summarized in Table 1. The most noticeable effects of the turbine are in the decrease in the mean streamwise velocity, , the increase in each of the three turbulent fluctuating components (σ_u, σ_v, and σ_w), and the nearly doubling of the turbulent kinetic energy, k, resulting from the ADV measuring at 4.4 in the wake of the turbine. In addition, the cross-stream component, V, at the upstream measurement location nearly doubled when the turbine was in the channel. With this increase in cross-stream velocity, the direction of the mean velocity vector upstream of the turbine was redirected outward by 4.3° toward the outer (left) bank of the OSL channel (Figure 7 and Table 2). The horizontal direction, , in the wake of the turbine was also shifted by 2.1° toward the outer bank of the OSL channel, indicating a straighter trajectory of the velocity magnitude vector at this position in the wake of the turbine compared to the baseline conditions (rather than following the channel curvature).

The characteristic length and time scales of the flow were again calculated using the integral time and length scales and compared to the baseline conditions (Table 1). In general, there were no noticeable modifications to these scales due to the presence of the turbine except in the downstream location in the wake of the turbine. Despite a similar time scale, , the length scale, , is lower due to the substantially lowered local mean streamwise velocity, . An investigation into the turbulent energy spectrum of the flow at the downstream location shows a noticeable increase in energy in all three components, particularly in V and W between 0.7–3 Hz (Figure 14). This broad peak represents the added energy from the turbulent wake of the turbine. Similar to the baseline spectral characteristics shown in Figure 10, the mean flow depth from the baseline experiment at the turbine location ( 0.306 m) and a turbulent kinetic energy velocity scale were used to normalize the spectra.

Figure 14

Comparison among the U, V, and W velocity spectrum from the downstream ADV measurements during the baseline (blue) and turbine (red) experiments. is the calculated energy spectrum (m² s⁻¹). The energy spectra are normalized by the mean flow depth at the location of the turbine during baseline experiments (  = 0.306 m) and the turbulent kinetic energy velocity scale, u_k, from the upstream baseline time series data.

3.2.3 Traversing Wake Measurements

The turbulent wake region of the turbine was also characterized using a moving ADV traverse method, a method similar to that used for collecting moving boat acoustic Doppler current profiler (ADCP) data to characterize the flow field within large rivers [Dinehart and Burau, 2005; Sime et al., 2007; Tsubaki et al., 2012]. Data were collected along five cross-stream transects located at 1.4, 2.4, 3.4, 4.4, and 5.4 downstream of the turbine, spanning from approximately −1.5 to 1.2 in the cross-stream direction. The DAQ carriage moved the ADV in the cross-stream direction at a speed of 0.001 m s⁻¹. The total distance traveled was 0.4 m, resulting in a total sampling duration of 400 s for each profile. Using the estimated bed form velocity, 0.0016 m s⁻¹ and bed form wavelength, 0.74 m, it is assumed that approximately one complete bed form passed during each traverse, therefore providing a minimally adequate representation of the bed-form-averaged turbulent flow field in the wake of the turbine. During postprocessing, the ADV traversing speed, U_adv, was removed from the cross-stream ADV measurements, V. The time series collected during each traverse was averaged and assigned to a lateral position using a moving average window filter. The maximum size of this low-pass filter was determined by the equation

(5)

where n_adv is the maximum number of samples for the low-pass filter window, d_adv is the diameter of the ADV sampling volume, and f_adv is the ADV sampling frequency. In this scenario, 1200 samples. Figure 15 illustrates the application of this low-pass filter to determine (a) the mean streamwise velocity, , and (b) the turbulent fluctuations, , at 1.4. Figure 16 combines the five traverses to illustrate (a) the mean streamwise velocity, , (b) the streamwise standard deviation velocity fluctuations, or σ_u, and (c) the turbulent kinetic energy, k, in the near-wake region of the turbine. The gray-scale bathymetry contour is a “frozen” snapshot of the bed form geometry at the end of the turbine experiment.

Figure 15

Comparison of the collected moving average window data (red, —) and the low-pass filtered data (black, - - -) for (a) the mean streamwise velocity, , and (b) the streamwise velocity fluctuations, , in the wake of the turbine ( 1.4) collected during the ADV moving traverse measurements.

Figure 16

(a) Mean streamwise velocity, , (b) streamwise velocity fluctuations, , and (c) turbulent kinetic energy, k, in the wake of the turbine ( 1.4–5.4) collected during the ADV moving traverse measurements. The model turbine, 0.15 m, is visible in each image at (19.7 m, 19.3 m). Channel topography from the end of the turbine experiment is shown in gray-scale contoured background region. Moving traverse ADV transect locations illustrated by black lines spanning the velocity contour regions.

4 Discussion

4.1 Channel Bathymetry and Sediment Transport

The simultaneous velocity and bed elevation measurements presented in Figure 8 provide useful insight into the dominant flow and bed form characteristics at the turbine location before the actual deployment. While the blockage of the turbine rotor ( 4%) redirects the flow toward the outer (left) bank, this outward and downward shift observed in the bulk flow may be the driving factor to the overall scour experienced by the mean bed observed during the turbine experiment (Figure 12). Similar to results from previous work [Hill et al., 2014, 2016], the presence of the turbine in the OSL meandering channel exhibited locally enhanced scour. Interestingly, the magnitude and extent of local scour is similar to that found by Hill et al. [2014] using the same scale turbine in a straight laboratory channel under both clear water and live bed sediment transport experiments at comparable flow depths (Figure 17). During the OSL experiments, maximum scour depths immediately downstream of the turbine were 0.15 (0.023 m). Unlike the results found from the straight channel, there was no local deposition that occurred between 3 and 7. It is hypothesized that the lack of deposition here is due to the outward mean flow pattern characterizing the turbine wake redirecting sediments toward the outer meander bank where they are transported downstream as a result of increased flow depth and bed shear stress. We acknowledge that the measurements from the OSL only allow observations along two transects, while it is likely that the scour, shear stress distribution, and deposition of the removed sediment is a highly 3-D problem, especially in meandering channels. As local shear stress is increased due to the turbine rotor blockage and flow acceleration beneath the rotor, the sediment is likely to be transported further up onto the point bar (where deposition is indeed observed, Figure 12) or outward toward the thalweg where such sediment is easily swept away downstream.

Figure 17

Comparison between the streamwise mean bed elevation from the OSL turbine experiments and the clear water and live bed experiments presented by Hill et al. [2014].

Initially, the decrease in bed form variability, , estimated from cross-stream sonar measurements and observed to align with the position of the turbine (see Figure 12) was thought to be a local effect in the near-wake region of the turbine. However, this phenomenon was observed along the entire range of the streamwise sonar measurements. Interestingly, a similar phenomenon was observed from experiments in a straight rectangular laboratory channel using the same sized turbine operating in conditions similar to the OSL (similar flow depth, h, bed form height, h_b, turbine hub height, h_hub, etc.) [Hill et al., 2016] (Figure 18). From the straight channel experiments, measurements recorded a decrease in upstream of the turbine location compared to the baseline (no turbine) experiment. Downstream, values recovered to the baseline condition approaching the far-wake region of the turbine, something that was not observed in the OSL meandering channel experiments. This is likely due to the fact that in the meandering channel, the far-wake downstream measurements were beginning to enter the deeper thalweg portion of the channel and any sediment located in this region is likely transported rapidly downstream due to higher bed shear stress [i.e., Kang and Sotiropoulos, 2011] before reforming into appreciable bed forms. However, the similarity in upstream and downstream reduction in bed form values is strikingly similar between the straight and meandering channel experiments. Note that an extended region of reduced bed form variability in height and wavelength is potentially a favorable feature within larger multiturbine deployments because bed form induced turbulence is known to have a strong effect on turbine performance, especially in terms of fluctuating power production and enhanced loads [Hill et al., 2016; Chamorro et al., 2015].

Figure 18

Comparison of the streamwise bed elevation standard deviation values from baseline (dashed) and turbine (solid) experiments in both a straight laboratory channel (red) and the meandering natural channel in the OSL (black).

4.2 Flow Field and Wake Characteristics

Measurements from the ADV at three locations during baseline conditions provide evidence that the region of interest within the OSL channel had fairly homogenous turbulent flow in the streamwise direction. Not only were the turbulent fluctuations and turbulent kinetic energy levels similar (Table 1), but also the velocity spectrum at all three locations collapse onto one another (Figure 10) indicating similar distribution of turbulent kinetic energy across scales. Estimates of the integral time and lengths scales at the three streamwise locations corroborate this finding.

The most insightful measurements and analysis into the flow field (where the turbine was installed) comes from the cross-correlation analysis between bed elevations, z_b, and the velocity magnitudes and directions during the 45 min ADV point measurements. Maximum correlation between z_b and U_mag occurs near a lag 0. Essentially, when the local depth is at a minimum due to an approaching bed form crest, z_b maximum, the confining effect induces an increase in local velocity. When the bed form crest (maximum z_b) is upstream of the ADV sensor, the peak correlation between z_b and θ occurs, preceded by the peak correlation between z_b and when the bed form crest is even further upstream from the ADV. This implies that an approaching dune in the meander bend induces first a horizontal flow diversion, directing the mean velocity toward the outer bank, and then a more local effect on the vertical velocity direction. The turbulent flow field properties above dunes studied over recent decades, summarized nicely by Best [2005], provides an indication as to the physical processes occurring governing these periodic and phase-shifted relationships illustrated in Figure 9. When the maximum correlation between z_b and occurs, the ADV sensor is likely measuring velocities above the stoss side (upstream, low slope side) of the dune where (i) the flow is mostly being dictated by the nonlocal channel geometry, for example the sinuosity of the channel bend and (ii) the velocity magnitude vector maintains a deviation toward the outer (left) bank of the OSL (positive ). The correlation between z_b and is at a minimum when the crest of the dune is beneath the ADV measurement location, indicating negative angles and a deviation of the flow toward the inner bank of the channel, possibly a clue that at this time the flow direction is mostly dictated by the local topography of the dune crest.

In general, flow throughout the meander is complex, especially considering the presence of the moving bed forms that can cause quasiperiodic fluctuations of the local velocity and introduce variability into the velocity spectrum measured, in this case, at hub height h_hub [Singh et al., 2010]. As shown by Chamorro et al. [2015], these periodic fluctuations due to coherent eddies will likely impact the performance and wake structure of an axial-flow device in the channel. Although not quantified here, the stability of the turbine wake visualized in Figure 16 is potentially disrupted by the coherent eddies shed by large-scale bed forms as well as any meander-induced circulating eddy structures convected through the meander bend.

4.3 Applications Within CEC Industry

As the CEC industry advances, proposed project sites will likely be sited in complex topography, mobile sediment and bed forms, and time-varying approach flow (both in terms of direction, magnitude, and length scales). These effects are actively studied and pursued within the wind industry through active yaw and blade pitch mechanisms incorporated into turbine designs. The effects of complex topography on wind turbine performance and wake characteristics are also being investigated through experiments and simulations [Politis et al., 2012; Howard et al., 2014]. As demonstrated by the cross-correlation analysis in Figure 9, the local bed elevation greatly influences the direction and magnitude of the inflow perceived by a device at that location. Possible strategies for maintaining optimal performance of CEC devices is to incorporate in situ monitoring to feed these measurements into advanced control strategies, whether that be through controlled yaw mechanisms, blade pitch control to maximize generator torque or minimize rotor fatigue from unsteady loading, or incorporating turbine designs that are less susceptible to performance deficiencies due to nonorthogonal inflow (i.e., vertical axis cross flow devices). What will remain a challenge, however, especially in curved channels, is where to measure the characteristic inflow velocities. Local morphodynamics can introduce extensive variability that may not be representative of the flow perceived by a device, while individual turbines can also exert an influence on the magnitude and direction of the flow, even up to 3 d_T upstream of the rotor location.

The near-wake measurements provided from the OSL experiments illustrate how axial-flow turbine wake characteristics may vary slightly in meandering, asymmetric channel flow compared to straight, relatively smooth and fully developed turbulent channel flow. This slight curvature visible in the mean streamwise wake velocity and nonsymmetric tip vortex σ_u levels illustrated in Figure 16 indicate that optimal layout of a turbine array within meandering channels, especially those with actively transported bed forms, will likely not rely on a simple uniform Cartesian grid of devices (staggered or aligned). Instead, site-specific bathymetric and hydrodynamic characterization should be considered to optimize multiturbine deployments in these complex environments.

5 Conclusion

This study provides some of the first insight into the morphodynamic impact of an axial-flow hydrokinetic turbine ( 0.15 m) operating in a meandering, asymmetric channel with actively migrating bed forms and secondary currents in turbulent open channel flow. The instream turbine location was defined to (i) experience effects of both migrating dunes and secondary currents, (ii) leave a signature on the erodible bed, (iii) qualitatively expose the turbine to the bulk of the flow (for high energy production) without enhancing erosion mechanisms on the outer bank, and (iv) have a hub height to depth ratio comparable with experiments performed in a straight flume under similar Froude number ( 0.39) and bed form dimensions. The hydrodynamic and morphodynamic impact of the turbine, estimated by simultaneous measurements of velocity and bed elevations, can be summarized in the following:

1. Local (i.e., dunes) and nonlocal (i.e., meander geometry) bathymetry introduced large-scale fluctuations and modified the direction and magnitude of the perceived inflow at the turbine location. Upstream approach velocity orientation was further modified by the turbine, while its wake signature persisted beyond the measurement extent of 5.4, implying zones of higher velocity may concentrate between the wake and the outer bank. Wake velocity recovery is likely accelerated by increased mixing as a consequence of turbulent flow organization along the channel curvature, likely governed by secondary currents.
2. Local mean scour depth of 0.15 was measured downstream of the turbine extending from −2.5 2 in the cross-stream direction and up to 3 in the streamwise direction. This supports previous results indicating individual turbines only locally affect the mean bathymetry of erodible channels. Compared to straight flume experiments, the local turbine scour depth in the meandering channel was 30% lower, while the variability in bed elevation was similarly decreased by 35%. Increased bed form frequency was also observed with the turbine installed. The transverse channel slope increased due to measurable inner bank deposition, implying that sediment is likely swept away in the armored outer bank thalweg rather than forming large-scale migrating bed forms along the banks.

Future experiments should provide more detailed wake characterization, especially in the far wake region of the turbine and further along the meander bend to understand wake statistics in complex topography and curving channels. Additionally, interactions between multiturbine arrays and complex topographic channels requires further investigation, in particular on how to employ site-specific hydrodynamic and bathymetric characterization to address optimal design of single turbine placement, multiturbine arrays, and advanced turbine control strategies for maximizing energy production. Applications of these and future results should be considered by full-scale device developers during CEC site-specific assessment and development.

Notation

b

channel width.

d_adv

ADV sampling volume diameter.

d_T

turbine rotor diameter.

d₅₀

median sediment grain size.

f

sampling frequency.

h

flow depth.

h_adv

ADV sampling volume height.

h_b

bed form height.

h_hub

hub height.

k

turbulent kinetic energy.

n

number of samples.

Q_w

bulk flow rate.

q_s

sediment supply rate.

SI

sinuosity index, or sinuosity.

S_b

channel bed slope.

spectral energy density.

t

time.

T_b

bed form period.

mean streamwise velocity.

U_adv

ADV traversing velocity.

U_b

bed form velocity.

U_mag

velocity magnitude.

streamwise velocity fluctuations.

u_k

turbulent kinetic energy velocity scale.

mean cross-stream velocity.

cross-stream velocity fluctuations.

mean vertical velocity.

vertical velocity fluctuations.

x, X

streamwise coordinate direction.

y, Y

cross-stream coordinate direction.

z, Z

vertical coordinate direction.

z_b

bed surface elevation.

z_hub

hub elevation.

z_w

water surface elevation.

λ_b

bed form wavelength.

integral length scale.

horizontal velocity vector angle (subscripts: B baseline, T turbine).

ρ

correlation coefficient.

σ_i

standard deviation (i = u, v, w or 1, 2, 3).

τ

time step lag.

integral time scale.

θ

vertical velocity vector angle (subscripts: B baseline, T turbine).

Acknowledgments

This work was supported by National Science Foundation (NSF) Career Grant Geophysical Flow Control (Michele Guala), NSF PFI grant IIP-1318201 and the Initiative for Renewable Energy and the Environment (IREE) at the UMN. Many thanks to the graduate students (Toni Calderer, Nick Evans, Mohammad Hajit, Mirko Musa, Gerard Salter, Jon Schwenk, Abby Tomasek, Anne Wilkinson, and Adam Witt) at St. Anthony Falls Laboratory who assisted in recirculating sediment during these Outdoor StreamLab experiments. The data used to create figures and tables in this manuscript are readily available by contacting the corresponding author.