Peter Bachant, Andrew Wilson, Phillip Chiu, Martin Wosnik, Vincent Neary
TODO: Write abstract.
To accelerate the development of marine hydrokinetic turbine technology, Sandia National Laboratories (SNL) developed the Code for Axial and Cross-flow TUrbine Simulation (CACTUS), based on Strickland's VDART model [@Strickland1981], originally developed for SNL in the 1980s to aid in the design of Darrieus vertical-axis wind turbines (VAWTs). Upgrades to CACTUS beyond VDART include ground plane and free surface modeling, a new added mass correction, and a Leishman--Beddoes (LB) dynamic stall (DS) model, in addition to that from Boeing--Vertol (BV) [@Murray2011].
CACTUS was previously validated using experimental data from relatively low
solidity
The RM2 was the subject of an experimental investigation in the University of
New Hampshire (UNH) tow tank, where mechanical power output, overall streamwise
drag or thrust, and near-wake velocity were measured with a 1:6 scale physical
model. A Reynolds number dependence study was performed, which showed strong
In this study we sought to evaluate the effectiveness of the CACTUS vortex line model for predicting the experimental performance results acquired for the 1:6 scale RM2 physical model experiments at UNH. Furthermore, we hoped to establish some best practice guidelines for its application. In case performance predictions were not adequate, a survey of static foil coefficient input data was also performed.
CACTUS assumes an incompressible potential flow field and uses a system of constant-strength vortex filaments to model the unsteady rotor wake. Each blade is modeled as a series of bound vortex filaments which span the blade's quarter-chord line. The strength of each bound vortex is computed based on the local velocity, and on the lift coefficient which is found from the local angle of attack and a specified airfoil table. At each timestep, spanwise and trailing vortices are shed from these bound vortices; their strengths are computed in accordance with Helmholtz's circulation theorems. Each vortex filament induces a velocity field, and each filament of the wake advects under the total velocity influence of the wake system. Airfoil drag forces contribute to the blade and rotor loads.
The influence of walls on the flow field is modeled using a system of first-order constant strength quadrilateral source panels. The strengths of these source panels are updated at each timestep to satisfy the no flow-through condition at each panel's center. As with the vortex filaments representing the wake, each source panel contributes to the velocity field, and thus the velocity influence of the wall system influences both the local velocities along the blade elements and the advection of the wake.
The 1:6 scale RM2 experiment performed in the UNH tow tank, for which the data
is available from [@Bachant2016-RM2-data], was replicated for a tow speed of 1
m/s, which corresponds to a turbine diameter Reynolds number
Static foil coefficient data for the NACA 0021 profiles was taken from Sheldahl and Klimas [@Sheldahl1981], as it is the only dataset for the moderate Reynolds numbers simulated here. However, it is important to note that this dataset is "semi-empirical" in that extrapolations were made for various profiles and Reynolds numbers. Recently, Bedon et al. [@Bedon2014] showed with a double multiple streamtube (DMST) momentum model that this dataset may be unreliable at lower Reynolds numbers.
The model was run for eight revolutions, over the latter half of which performance quantities were averaged.
Sensitivity of the model results to the time step (or number of time steps per
revolution
The performance curve of the RM2 was simulated using both the Boeing--Vertol and
Leishman--Beddoes dynamic stall models, as well as with dynamic stall modeling
deactivated, and is shown in Figure 3. Dynamic stall has a very significant
deleterious effect on
To predict the interactions of turbines within arrays and with the environment...
Potential flow methods such as that used here may not be as useful when predicting the evolution of the wake since they do not model nonlinear advection or turbulent transport---as higher fidelity Navier--Stokes models would---but adequate resolution of the near-wake mean velocity field may help determine optimal layouts for tightly spaced cross-flow turbine arrays.
TODO: Write section on wake results.
Since there were significant discrepancies between the CACTUS results and
experiments---and also for the ALM using the same static foil data---a
comparison of the lift and drag coefficients was made at
In the unstalled regime, all datasets have similar lift slopes (
The post-stall drag coefficients in the Sheldahl and Klimas dataset are
significantly higher than those measured by Gregorek and simulated with XFOIL.
However, this may not affect the results when using the LB DS model, since the
force coefficients are parameterized based on the trailing edge separation
point. For
The Reynolds number dependence of the CACTUS performance predictions was
assessed in a similar fashion as it was in the RM2 tow tank experiment---by
keeping the tip speed ratio constant at 3.1 and varying the free stream
velocity. In this case CACTUS was run using the Sheldahl and Klimas foil data at
higher Reynolds numbers than measured in experiment, the results from which are
shown in Figure 5. In accordance with the Bedon et al. [@Bedon2014] results
(obtained without dynamic stall modeling), the Sheldahl and Klimas data appears
to exaggerate the decrease in performance at low
The validity of the Sheldahl and Klimas dataset was assessed for a NACA 0021 airfoil at low Reynolds number---$Re_c=1.6 \times 10^5$ by comparing with the wind tunnel data from Jacobs and Sherman [@Jacobs1937]. The results plotted in Figure 6 show how in the attached regime both datasets agree well, but the stall characteristic in the Sheldahl data appears to overestimate the detrimental effects of separation on the lift coefficient. This comparison implies that the use of the Sheldahl and Klimas static 0021 foil data could be the cause of the discrepancies in predicted turbine performance, which is reinforced by the aforementioned potential extrapolation of the Reynolds number dependence plotted in Figure 5. Note that the Jacobs 0021 database does not include drag coefficient data at the Reynolds numbers of interest.
TODO: Finish conclusions.
CACTUS results with the LB DS model were similar to those from an actuator line model, which implies the flow modeling is comparable to RANS, but the dynamic stall modeling is likely in need of revision.