Experimental and numerical analysis of the performance and wake of a scale–model horizontal axis marine hydrokinetic turbine

For the last two decades, marine renewable energy resources have gained significant popularity, in parallel to other renewable energy sources such as wind and solar energy. The main knowledge gap with this relatively new renewable energy technology is the lack of well-established benchmarks and validated numerical methodologies for hydrodynamic design and optimization of single and array of turbine/s, particularly at large scales (and Reynolds numbers), to help understanding the underlying physics of the flow field upstream, around and downstream of these devices. Ultimately, these benchmarks and validated methodologies combined with other multi-physics models can be used toward the reduction of both economic and environmental uncertainties, a step that requires predictive models for performance optimization and environmental changes induced by hydrodynamics.

In their seminal work, Couch and Bryden¹ laid out the path to develop energy extraction from tidal energy sources as a large-, economically feasible scale: First, a methodology for reliable resource characterization at proposed tidal sites is needed. Second, a methodology for device performance characterization, which includes environmental changes introduced by Marine Hydrokinetic (MHK) turbines, is required. The main focus of the current work is on the latter: development and validation of numerical methodologies to study the performance and flow field of turbines with further application to address the potential environmental effects of the operating turbines in tidal channels such as turbine–fish² and turbine–sediment interactions.³ A wide spectrum of numerical and experimental studies on the performance and flow field characterization of MHK turbines were summarized by Ng et al.,⁴ noting that at that point, there was no dominant turbine configuration (axial, cross-flow,…) or modeling methodology. Bahaj et al.⁵ experimentally validated the power production from a numerical study of a Horizontal Axis Hydrokinetic Turbine (HAHT) using the actuator disk theory in a RANS steady flow simulation, with data from a large Reynolds number cavitation tunnel. Batten et al.⁶ validated their blade element momentum simulation scheme⁷ for HAHTs, comparing the predicted torque with the measurements in Ref. 5. Blade-Element modeling integrates geometrical (i.e., pitch angle and chord length) and physical variables (i.e., lift and drag coefficients) along the span of the blades to capture the hydrodynamics of the rotating blades unlike Actuator Disk modeling, where the rotor is a thin disk whose only hydrodynamic characteristic is the induction factor.

Several seminal works that propose data and modeling methodologies to better understand and optimize HAHTs^8–13 have appeared in the literature. The U.S. Department of Energy (DOE), in collaboration with the National Renewable Energy Laboratory (NREL), proposed DOE Reference Model 1 (DOE RM1), as an open source design for HAHTs. Lawson et al.¹¹ performed a detailed numerical analysis on this benchmark using RANS in a rotating reference frame (RRF). Good agreement between unsteady and steady simulations was found for the optimal operating condition (TSR = 6.3 and θ_p = 0°), where the flow is fully attached to the turbine blade span. For other operating conditions, unsteady models proved the better choice to provide accurate results in situations where the flow is separated in a significant part of the blade suction surface. Gunawan et al.¹³ performed numerical modeling using the same rotating reference turbine model in a RANS simulation close to the SST k–ω turbulent model. The numerical predictions for the device's thrust and torque coefficients are compared to the experimental values with generally good agreement. Comparison with flow field experimental data, however, was not complete, and the agreement was inconsistent. Kang et al.¹² published the results of an LES simulation of the Gen4 KHPS turbine developed by Verdant Power for the Roosevelt Island Tidal Energy (RITE) project in New York's East River. They compared the near wake mean velocity fields and coherent vortical structures with the limited field data available to validate their numerical model. In more complex formats, Churchfield et al.¹⁴ and Calaf et al.¹⁵ used LES methodologies to investigate flow field and device performances in an array of tidal and wind turbines, respectively.

Insight into the fluid dynamics and energy conversion in HAHTs is obtained using a variety of turbine performance metrics and wake structure data or reduced models. However, there is still a need for comprehensive analysis that combines synchronized experimental performance and wake measurements to characterize the physics of the flow field of a single HAHT with numerical simulations of the energy extraction and flow field around the turbine. This combination would fill the gap in existing details that are difficult or impossible to measure experimentally.

This paper investigates the design, performance, and wake flow field of a single HAHT via detailed comparison between experimental measurements of turbine torque and angular speed, wake flow velocity, and corresponding numerical results, filling the gaps identified in the literature. The experimental setup and its design challenges are briefly described in Sec. II. Section III outlines the simulation methods and the quality assurance for the computational results. In Sec. IV, the experimental measurements are compared against computational results at matched Reynolds numbers (Re = 7.8 × 10⁴–1.4 × 10⁵) and in a wide range of Tip Speed Ratios (TSRs = 5.5–10.33). The agreements and discrepancies between the results and the physics between them are discussed in depth, trying to identify the physics and numerical model that are responsible for them. Section V presents the summary of physical insights gained from the combination of experiments and simulations. Furthermore, discussions and perspectives on the capabilities, limitations, and further potential applications of each numerical model are briefly presented. All the experimental database and simulation files are made public here¹⁶ so that they can be used to validate other engineering design and analysis tools.

Preliminary experimental results obtained from laboratory testing of a 45:1 geometrically-scaled DOE RM1 rotor showed low coefficient of performance (⁠$Cpmaximum≈20%$⁠) compared to design predictions of full-scale DOE RM1 performance of $Cpmaximum≈45%$⁠. These results are shown in Fig. 1. The strong Reynolds number effect on the performance of the NACA 63–family of airfoils used in the full scale DOE–RM1 design, specifically the presence of a laminar separation bubble on the suction side for a wide range of Reynolds numbers between 2 × 10⁴ and 7 × 10⁴, resulted in a significantly decreased lift coefficient and reduced torque by the geometrically scaled blades under the flume testing conditions at the 45:1 scale.¹⁷ 

A new scale model was redesigned and built to operate in the same range of TSRs but matched the performance of the full scale DOE RM 1 at the Reynolds numbers achievable in the laboratory flume. The laboratory-scale rotor was modified to be dynamically (rather than geometrically) similar to the full-scale DOE RM1 rotor, matching the efficiency curve and peak performance TSR of the full-scale DOE RM1, while maximizing chord Reynolds numbers by increasing the chord length (moderately so as to not change the solidity ratio significantly).¹⁸ 

As discussed earlier, the relatively poor performance of the geometrically-scaled rotor was caused by the sharp decrease in hydrofoil performance associated with laminar separation bubbles in this family of airfoils (NACA 63–424, critical Re_chord = 10⁵)¹⁹ and was therefore strongly influenced by both the family of hydrofoils used in the original design (to minimize cavitation) and the operating chord Reynolds number. The redesigned rotor uses the NACA 4415 foil, with a lower critical Reynolds number measured at 7 × 10⁴, and maximizes the chord Reynolds number along the blade, within the constraints of matching the optimum TSR of the full-scale rotor and the maximum rotor diameter that could be tested in the flume at a reasonable blockage ratio. The first plot in Fig. 2 compares the local Reynolds number along the blade span at several free-stream flow speeds for the geometrically scaled DOE RM1 with solid lines and the modified rotor with dashed lines. The second plot in this figure shows that modified rotor efficiency becomes independent of the Reynolds number at different TSRs as the flow speed goes beyond the value of $0.75 ms$⁠. The open-source design code HARP–Opt²⁰ was used with experimental wind tunnel data for the NACA 4415 lift and drag coefficients at appropriate Reynolds numbers, to optimize chord and twist distributions.

The final 45:1 scale model consists of a 0.45 m diameter turbine rotor manufactured on a CNC mill from aluminum and a 0.1 × 1 m cylindrical nacelle. The nacelle contains a torque sensor (TFF325 Futek, Irvine, California), a magnetic encoder (RM22 RLS, Komenda, Slovenia), and a magnetic particle brake (Placid Industries, Lake Placid, NY) used to apply loading on the shaft. The torque sensor and magnetic encoder are wired to an analog–digital converter and acquisition system (PCIe–6341 National Instruments, Austin, Texas) sampled at 1000 Hz. The turbine model is mounted to a vertical post extending from the top of the flume to the nacelle. The turbine design is shown in Fig. 3. More details of the rotor mechanical design, nacelle, instrumentation, and calibration procedure can be found in Ref. 18.

Flume testing was carried out at the Bamfield Marine Science Center, with a width of 1 m, a cross-sectional depth of 0.8 m, and a long test section of 12.3 m. The blockage ratio was 20%. ADV (Vector Nortek, Oslo, Norway) and particle image velocimetry (PIV) (LaVision Gmbh., Goettingen, Germany) systems were used to characterize the flow upstream and in the wake of the turbine within the predefined interrogation windows, aligned parallel to the flow and on the axis of rotation of the turbine, as shown in Fig. 4. PIV data were taken for 60 s at 5 Hz for each imaging location, and the results were processed under the assumption of statistically steady free-stream flow.

In this experiment, the velocity fields 2 diameters upstream of the turbine and at 2, 3, 5, and 7 diameters downstream of the turbine were measured from PIV at vertical-streamwise planes that covered the flow from the centerline to very near the free surface. Figure 4 sketches the position of these imaging windows. These measurements were averaged over the interval of acquisition (60 s) and along the streamwise coordinate inside each PIV domain, that is, for all the measurement points that are at the same distance from the turbine axis of rotation (and the same depth, since the PIV plane is vertical).

The Rotating Reference Frame (RRF) model renders the unsteady problem of flow around turbine rotating blades in (a single) fixed reference frame a steady problem in a rotating reference frame moving around the fixed blades. The effect of rotation is input into the Navier–Stokes equations by adding body forces that represent the inertial effects associated with centrifugal and Coriolis accelerations.²¹ This avoids the complexity and numerical stiffness associated with rotating mesh simulations but requires an axisymmetric domain and periodic boundary conditions.²² 

The boundary conditions in this model are uniform streamwise velocity at the inlet and uniform pressure at the outlet. The outer walls of the domain and nacelle are modeled as slip-free walls, due to the limitation of the RRF model. Blade walls are modeled as no slip wall to capture the generated turbulent boundary layer along it. Periodic boundary conditions are implemented on the planes of symmetry on the bottom of the domain. The blockage ratio of 20% in the experiment is matched by an equivalent axisymmetric geometry of the computational domain.

The RRF computational domain has ≈ 4.7 × 10⁶ structured mesh cells, except for two small regions at the front and back of the nacelle. The mesh resolution around the hydrofoils and along the blade span was based on the results of previous grid resolution studies.²² The numbers of nodes around the airfoil sections of the blade and along the blade span are 152 and 94, respectively, equally spaced. In the radial directions of the C-mesh, 19 nodes were considered with the first 0.5 mm from the blade wall. The distance of the first cell in the boundary layer was calculated for the chord-based Reynolds number of 10⁵ so that the first cell falls between y⁺ = 30 and 300 to capture the turbulent boundary layer along the blade span using the wall function approach. It should be noted that this mesh resolution should be modified for the full-scale simulation as the Reynolds number changes by an order of magnitude.

The Blade Element Model (BEM) simulates the hydrodynamic effect of the turbine rotating blades via body forces placed on a finite disk with the base area equal to the rotor-swept area. Based on the Blade Element Theory, the blade span is divided into thin elements (slices) from root to tip. The Angle of Attack (AOA) and Reynolds number at each element are estimated by solving the RANS equations around the full turbine. Based on the angle of attack and Reynolds number of the flow at each blade element, the lift and drag coefficients are computed, as a function of AOA, from the provided look-up table for the airfoil used in the turbine design (obtained from the RRF simulation described above), and from those coefficients, the lift and drag forces on each of the blade slices are then calculated. These lift and drag forces are then averaged over a full turbine revolution to calculate the value of body forces replacing the turbine rotating blade effect. The flow is updated with these forces, and the process is repeated until a converged solution is attained.²² 

The boundary conditions in this model are uniform streamwise velocity at the inlet and uniform pressure at the outlet. The outer walls of the domain and nacelle are modeled as slip-free walls to be consistent with the RRF. The actual geometry of the experimental flume to match the 20% blockage ratio is used, as there is no requirement of an axisymmetric domain compared to RRF.

The BEM discretization has about 3.6 × 10⁶ cells. Similar to the RRF case, the BEM mesh is structured in most of the computational domains except for the regions immediately upstream and downstream of the nacelle. The concentrations of mesh elements were increased immediately upstream and downstream of the rotor zone to ensure the accurate estimation of the induced incoming flow and turbulent wake generated by the rotor existence.

Figure 5 shows the performance predicted by the RRF and BEM, overlaid with the experimental results. Comparison between the red dashed curve (RRF) and the green dashed curve (BEM) shows that the turbine performances predicted by both the models are consistent, within 2%–6%, for the majority of the TSR range. The BEM simulation predicts a slightly higher performance than the RRF.

Both numerical models predict a peak in efficiency for the scaled model turbine at TSR = 8.17, while the experimental results show peak performance at TSR ≈ 7. For the range of TSRs from 7 to 9.5, the experimental and numerical performance coefficients are in good agreement. Experimental results confirm that as the value of the TSR increases above the peak-performance value, the efficiency of the turbine decreases. Under these TSR conditions, the Angle of Attack (AOA) for the majority of the blade section along the blade span is lower than the peak-lift angle, and thus, the power extracted by the turbine decreases. It should be noted that the RRF model, in which the actual geometry of the blade is modeled, closely matches the experimental results in this range of TSRs. However, the BEM prediction fails at a TSR of 10, with a non-physical drop in performance at TSR = 10.33. At this high non-dimensional rotation rate, the three dimensionality of the flow along the blade span, and especially near the blade tip where most of the torque is produced, becomes dominant. The BEM, unlike the RRF model which predicts the performance well at this limit of the TSR range, cannot accurately calculate the lift and drag forces under three dimensional conditions, and therefore, the performance is modeled poorly for this case.

Moving from this peak towards lower TSR values (TSR = 5.5–7), the performance decreases due to the increase in AOA. The discrepancy in the efficiency between experiments and computations at lower TSR, from 5 to 7, provides an interesting insight into the dynamics of the operation in these conditions and the differences in turbine efficiency predicted computationally versus measured in the laboratory. Figure 5 shows that, in the experiments, the turbine efficiency is almost constant for a wide range of TSR values, with little change in performance from the theoretical peak around 7 to about 5.5. This is counterintuitive: according to the inverse tangent relationship between AOA and TSR (⁠$AOA≈aarc tan(1TSR$⁠)), TSR values lower than the optimum (TSR = 5.5–7) will increase AOA values above the optimal distribution along the blade span and larger AOA values (above the peak-lift angle) should result in flow separation at least partially along the blade span starting from the blade root and eventually stall, as shown in Fig. 6. The efficiency of the turbine, then, would decrease with decreasing TSR.

The Wall Shear Stress (WSS) values, normalized with the case maximum, are used to highlight regions of flow detachment along the blade span at different TSRs in Fig. 6 modeled via RRF. Limited streamlines are superimposed on the WSS color contours in Fig. 6 to further delineate the extent of flow recirculation. As TSR decreases, from bottom right to top left of the figure, the dark blue region of low WSS grows from the root to the tip along the trailing edge of the blade. In this region of low WSS, the flow starts to detach from the blade span and the limited streamlines diverge from each other. Significant separated flow exists from a TSR of 5 to 7 but not from 7 to 10. This view supports the hypothesis that while numerical simulations do not include a mechanism to account for dynamic stall, they predict a decrease in the coefficient of power with decreasing TSR below the optimum value.

Analysis of the experimental time-resolved rotor angular speed shows that as the turbine operates under decreasing TSR conditions, there is a corresponding increase in the amplitude of the fluctuations in the angular velocity. This rapid change in angular speed is equivalent to the periodic changes in the AOA in an oscillating pitching airfoil. Thus, the flow structure along the blade is modified and presents delayed separation compared to that observed at steady AOA,^23,24 and dynamic stall will preserve rotor performance at low TSRs beyond what is theoretically expected or computationally predicted (in the absence of a good dynamic stall model).¹⁸ 

Figure 7 shows the two time series, of the instantaneous rotational velocity measured from the angular encoder, during two runs at the extremes of the TSR range for the turbine (Mean TSR = 5.5 and 10). The rotational speed is normalized with the mean for each time series. At TSR = 10, the rotational speed fluctuations are very small, with Ω_rms ≈ 1% Ω_mean. As the TSR decreases, however, the fluctuations in angular velocity increase in amplitude, with values approaching 10% for the lowest TSR investigated. The TSR = 5 time series, in blue on Fig. 7, shows a few large excursions beyond 3 Ω_rms during the 60-s data acquisition. Our hypothesis is that these large fluctuations in the rotational velocity translate into rapid changes in the AOA along the blade sections. These rapid changes in AOA values would delay flow separation on some parts of the blade,^23,24 compared to the prediction based on the static C_L = f(AOA) curves used for the rotor design and CFD simulation of the flow around the turbine. The resulting effect would be an increased lift in some regions of the blade span that would be separated if the angle of attack was static (the rotational speed of the blades was constant) and therefore an increase in torque and power coefficient over the theoretical and numerical predictions. The efficiency of the turbine remains high in the experiments for low operating TSR values, and so, it performs close to its maximum efficiency. Previously presented and discussed results on the numerically modeled flow field along the suction side of the blade span using the RRF simulation support this hypothesis.

The flow field evolution in the wake of the HAHT is described from the RRF and BEM simulations and experimental measurements. The RRF and BEM results are compared to highlight the applicability of and validity regions for each model. Figure 8 shows the normalized streamwise velocity contours with the free stream velocity (⁠$VyV0$⁠) on a vertical plane parallel to the flow direction. These velocity fields highlight that the free stream flow decelerates due to the turbine induction as it approaches the rotor. The turbine creates a momentum deficit in the flow, as it extracts kinetic energy from the incoming flow, generating a turbulent wake. Comparison between the RRF (top) and BEM (bottom) results shows differences between these two numerical approaches. The RRF simulation captures the inhomogeneous flow field in the near wake region of the turbine (⁠$yr<2D$⁠) accurately. This inhomogeneity is apparent as two cyan blobs of slow flow near the blade tip and near the blade root. Shed vortices are also captured by the RRF close to the blade tip, visible as discrete high speed (dark red) circles. The BEM does not capture these details of the near wake region of the blade since it averages the hydrodynamic effect of the blades across the entire rotor swept area. As a result of this averaging, the inhomogeneity of the near wake is smoothed out in this model. The momentum deficit in the wake region appears as a uniform region that starts close to the blade. The same process of azimuthal averaging is responsible for not capturing the tip vortices in the BEM simulations.

The far wake description of both computational models is consistent, with very close results in both the shape of the profiles and the absolute values of the velocity contours, as shown in both Figs. 8 and 9. The evolution of the wake can be quantitatively compared by superimposing the velocity deficit profiles averaged from the PIV velocity measurements, or computed from simulations, at different stations downstream of the rotor, as shown in Fig. 9. The velocity profiles at 2D downstream show much better agreement between the RRF predictions and the experiments than for the BEM simulations. It should be noted that this station is located exactly downstream of the tapered end of the nacelle, where the limitation of both numerical models to accurately capture flow details in this region significantly affects the shape of the velocity deficit profiles near it. This agreement confirms the capability of the RRF model to capture the details of the flow field in the turbine near wake region. The velocity deficit predicted by BEM (red) shows good agreement with the experimental data close to the blade tip (⁠$0.6<zr<1$⁠). However, in the region close to the axis of rotation (where the wake originates from the blade root and the nacelle), this agreement becomes poor and BEM overpredicts the deficit in the velocity.

At Y = 3D downstream, both the RRF and BEM simulations miss the fast recovery of the velocity in the outer half of the wake (⁠$0.6<zr<1$⁠), giving a very similar prediction of the mixing in this region that dominates the velocity recovery (or lack of it, in this case). In the inner wake region (⁠$0<zr<0.5$⁠), the RRF model still predicts the experimental velocity profile well, while the BEM still underpredicts it. The turbulence intensity in the experimental flume is very high (≈7%–10%) and the effect of the nacelle, bottom, and wall boundary layers is high due to the high blockage ratio (the rotor swept disk is over 20% of the cross-sectional area of the flume, and so, the blade tips are never very far from the edges of the flume). These two combined effects can explain the discrepancy between the rate of entrainment of high momentum fluid that controls the wake recovery in the experiments and the simulations.

Stations Y = 5D and 7D downstream show that the agreement between simulated velocity profiles and the experimental data improves, specifically in the outer wake region. As the wake becomes more axisymmetric, the BEM starts to better match the more accurate RRF results, and both models start to capture the experimentally observed entrainment of high momentum fluid from outside the wake and its mixing with the wake flow in the $0.6<zr<1$ range. The velocity deficit in the inner region (⁠$0<zr<0.5$⁠) is, however, still not well predicted, even at the farthest location downstream, Y = 7D.

We hypothesize that the enhanced mixing process due to the effect of the nacelle's wake and the high turbulence level in the experimental flow field, either idealized or not modeled in the simulations, results in a faster wake recovery and lower momentum deficit in the experiments. Due to the idealizations incurred in the numerical domain imposed by the models and limitations of the rotor representation in the RANS-equation simulations, the effects of the enhanced mixing process caused by the high turbulence level in the experimental flume (associated with surface waves and bottom, side walls, and nacelle) are absent in the numerical results.

The velocity deficit profiles exaggerate the importance of the inner part of the wake, as it is presented as equal to the outer wake in this cross-sectional view, but really occupies only about 25% of the volume of the wake, compared to 75% occupied by the outer wake. Additionally, the momentum flux is quadratic on the velocity, and so, the regions with higher velocity (again the outer wake) play a dominant role. The momentum deficit profiles are used as a more dynamically meaningful metric to compare the numerical and experimental results in the wake recovery, both for purposes of assessing environmental effects and for the predictive capabilities of energy production in arrays of HAHTs.

Figure 10 shows the momentum deficit profiles at the four downstream stations studied. The local streamwise momentum flux is integrated over the ring swept by each blade section. This area-weighted momentum deficit profiles show much closer approximation to the experimental data by both the RRF and BEM models. Although there are also significant differences in this metric between the simulations and the experiment, as well as between the two simulation models; the relevance of the differences is better put in context by this way of evaluating the data: the difference in momentum flux is never above 10% of the free stream baseline due to the mixing in the experiments, not fully captured by the simulations, leading to fast recovery of the wake starting in the outer edge near the blade tip vortices and moving quickly inwards towards the nacelle wake as the downstream distance increases.

Experimental analysis of a scale-model HAHT, matched to the DOE RM 1 Cp–TSR performance curve, sheds light on the performance and wake development of this type of turbine. The experimental database is publicly available and can be used as a source for validation of numerical models of HAHTs.

Numerical simulations using two highly idealized rotor implementations in a RANS-equation fluid solver were performed at the same conditions studied in the experiment. The agreement between RRF and experimental results, both for the coefficient of performance and the velocity deficit profiles in the near wake (2D downstream), showed encouraging, albeit incomplete, ability to predict the flow field of the HAHT. The RRF model showed limitations to model the effect of the dynamic stall on the performance coefficient at low TSRs and of solid walls (bottom, side walls, and nacelle) in wake recovery. The BEM predicted well the coefficient of performance of the modeled turbine operating in the near-optimal TSR range. BEM showed limitations to model the turbine performance accurately at very low and high TSRs, underpredicting the performance of the device due to lacking dynamics stall and 3D centrifugal flow, respectively. The BEM showed a good balance of accuracy and cost in the simulation of the far wake region of the turbine, making it a candidate for the investigation of optimization of HAHT spacing in large arrays or of potential environmental effects that depend strongly on the turbine's far wake (i.e., effect of the turbine on the sedimentation of suspended particles or on water quality through mixing in a tidal channel).

The flow field and velocity deficit comparison between RRF and BEM in the far wake region of the turbine (⁠$yr>3D$⁠) shown in Figs. 8 and 9 confirms that although BEM is limited in capturing the details of the flow field in the near wake region, it is capable of simulating the far wake region as accurately as RRF, with an order of magnitude lower numerical cost (in CPU time, memory needs, and human operator time in creating the mesh of the domain).

Despite the differences in the level of complexity of these two numerical models, they simulate the resultant momentum deficit created by the turbine to a very similar extent, as long as the area of interest is outside the very near wake (Y > 3D). On the other hand, both numerical models overpredict the momentum deficit at all stations downstream of the turbine compared to the experiments. The relative error in the simulations, defined with the discrepancy between experiments and simulations in the momentum deficit profiles as a metric, is of the order of 10% of the incoming momentum flux, compared to 20%–30% error when based on the velocity deficit.

The authors would like to thank the National Northwest Marine Renewable Energy Center (NNMREC) in the University of Washington for support of this work through the Department of Energy (DOE) under Award No. DE-FG36-08GO18179.

This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, expressed or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. References herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise do not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of the authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.