Developing a Fast-Running Turbine Wake Model

As part of the international collaboration for DTOcean, a project aimed at accelerating the industrial development of ocean-energy power-generation knowledge and providing design tools for deploying the first generation of wave and tidal energy converter arrays, Sandia is developing a fast-running current energy converter (CEC) wake-interaction model. Toward this end, Sandia has begun implementing parametric models that use basic information about CEC devices and inflow conditions to produce a numerical representation of the resulting wake. Currently, two types of models are being investigated.

The first model is based on the analytic solution to the conservation of mass and momentum equations, as derived by Larsen [1] (shown in Figure 1). The model takes into account parameters such as turbulent intensity, coefficient of thrust, and turbine diameter. The model has the ability to calculate multiple turbine wakes simultaneously with little extra effort. However, initial model to data comparisons indicate that the model accuracy may be a concern for CEC application.

The second modeling method, currently under development, involves creating a numerical database of CEC wake properties. This involves running computational fluid dynamic (CFD) simulations of various CEC devices using a simplified means to represent the turbine within the model (i.e., actuator disk, porous disk, blade element methods). CFD modeling provides the capability to capture features such as near-turbine wake effects and even upstream pressure effects, all of which are ignored when using Larsen’s parametric wake model, resulting in more accurately represented wake fields.

Once the modeling technique is validated by comparison to physical measurements and the numerical database is populated, the database will then be reduced to empirical relations between CEC properties, inflow conditions, and wake structures and features. The image in Figure 2 shows preliminary results of a CFD simulation using an actuator disk representation of a CEC turbine.

When varying α_md, Figure 3 shows that the wake recovers more quickly downstream, resulting in a decreased velocity deficit (1 – U_wake/U_upstream) as α_md increases. Note that velocity data were not collected further downstream of the turbine into the Canal expansion because increasing the Canal width significantly decreases flow speed, rendering the velocity deficit calculation inapplicable.

1. G. C. Larsen, “A Simple Wake Calculation Procedure,” Riso National Laboratory, DK-4000 Roskilde, Denmark, December 1988.
2. Renkema D.J., “Validation of Wind Turbine Wake Models Using Wind Farm Data and Wind Tunnel Measurements,” Master Thesis, Delft University of Technology, 2007.