# Task Overview

__Contacts__:

__Industry Challenge__: Due to the highly localized nature of the in-stream resource, the space
available for array development is limited. Therefore, it will be important to optimize array deployment within tidal
channels. This will require an understanding of the potential for arrays to substantially divert high velocity flows and
an understanding of the maximum packing density for individual devices.

__Approach__: Numerical modeling, measurements from field testing, and large-scale experiments will
be used to investigate these issues. Flow redirection, which may occur when an array only occupies a portion of the
channel cross-section, will be investigated using the SUNTANS oceanographic code from Stanford University. Maximum
packing density will be investigated primarily by numerical modeling of turbine-turbine interaction. These models will
include the physics of the wake and interaction with the free surface. Models will be calibrated against data collected
during pilot testing and flume experiments. In addition to investigating wake dynamics, modeling results will improve
the parameterization of turbines in estuary-scale modeling. The long-term objective of this work is engineering rules
for maximum device packing density, which will be prototyped numerically and validated in a large flume or tow tank.
The UW is weighing the construction of an on-campus flume for experimental work. If this facility is constructed,
additional experiments to characterize the nature of device wakes would be possible.

__Outcomes and Impacts__:

*Research*: Improved understanding of in-stream turbine wakes in cases where free surface and boundary layer effects are important to the flow.*Industry*: Engineering rules for minimizing flow redirection and maximizing turbine packing density.*Regulatory*: Guidance on environmental implications for possible array configurations.

# Wake Modeling

**Introduction**

The use of submerged turbines to generate electricity from the motion of water in streams, tidal and ocean currents is an area of active research due to
the potential to provide highly predictable, non-polluting energy from a renewable source. The study of turbine wakes is a key element in understanding the
effectiveness and environmental impact of in-stream turbines. High energy density is typically found in narrow channels that connect sensitive estuarine
environments with the open ocean. Because of the concentrated nature of this resource, the optimum packing of turbines within the confinement of a tidal
channel is key to the efficiency and economic feasibility of energy extraction. Moreover, given the high environmental sensitivity of these areas, it is
imperative to understand the effect of turbine installations on the local ecosystem to avoid any undesired impacts.

In order to understand and study the detailed dynamics of the turbine turbulent wake and its potential effect on energy extraction and environmental
impact, we have developed a hierarchy of numerical models to simulate the mechanics of flow around and behind single turbines and full arrays. These
models are: Sliding Mesh, Single Rotating Reference Frame, Virtual Blade Model and Actuator Disk, in decreasing order of computational cost and fidelity
to the underlying physics. The methodology that has been developed in this research will provide the option to study different configurations of
horizontal axis turbines with a numerical model that captures the key physics of the problem and balances this with the right computational cost to
provide insight in an adequate timeframe for the problem.
**Single Reference Frame (SRF)**

SRF is a numerical model for FLUENT solver, which provides the option of solving the equations of motion in a reference frame rotating at constant speed (equal to the rotational speed of the turbine) by adding two forcing terms, i.e. Coriolis and centripetal forces to the momentum equation. This model provides sufficient detail and a greatly reduced computational cost compared to Sliding Mesh Model, but requires periodic boundary conditions to conform to axial symmetry. Below, we can see the domain for SRF model, its boundary conditions and a zoom-in to the complex structure around the blade section for creating a high quality structured mesh.

*Figure 1: SRF full domain (left) and complex structure around the blade (right)*

The SRF simulation gives us detailed information about the flow around the turbine blades and the development of the wake. The velocity at different planes perpendicular to the free stream is shown in the contour plots below. From left to right, top to bottom, we see the velocity from the inlet plane (Y/R = -0.25), around the turbine blades (Y/R = 0) and downstream in the near wake as it develops (Y/R = 2.5). We can see the flow on the blade suction and pressure surfaces and the development of the wake, with the asymmetric flow slowly losing memory of the blade passage and becoming an axisymmetric momentum deficit at approximately Y/R = 2.

*Figure 2: Characteristic result from SRF*
**Virtual Blade Model (VBM)**

While SRF calculates the detailed flow field around the blades and in the near wake, it involves time consuming meshing of a very complex geometry and computationally expensive calculations, with a very long (~ 1 week) turn around. If we are interested in the dynamics of the wake at a certain distance from the turbine, typically a few diameters, the flow field is axisymmetric and we can use a different model that captures the momentum deficit and rotation introduced by the turbine without the details of the blade passage. One such model is the Virtual Blade Model. Unlike more complicated models like Sliding Mesh and SRF, this model uses body forces to represent the lift and drag exerted on the fluid by the blade sections. It uses a look up table for the lift and drag coefficients as functions of the angle of attack and Reynolds number at each blade section, but does not need a detailed representation of the blade geometry.

*Figure 3: VBM full domain*

VBM is a more versatile simulation tool than other more detailed models. Realistic domains, including the effect of bottom and free surface boundaries and non-uniform velocity at the inlet can be studied without an unreasonable computational cost and extended time frame.
**Actuator Disk Model (ADM)**

Actuator Disk Model simulates the presence of a turbine by introducing a porous disk that produces the same drag and energy dissipation as the operating turbine. The characteristics of this porous disk are defined by the Actuator Disk Theory, assigning two porous coefficients based on the efficiency of the turbine, pressure difference across the disk. This is the simplest model used in process of development of this methodology, and correspondingly the one with the lowest computational requirements. It enables us to study large arrays of turbines in an extended domain with complex topography.
**Results**

Figure 4 shows the axial velocity contours on a plane cut along the domain of different models starting from inlet to the outlet with the velocity profiles at planar sections perpendicular to the domain and flow. The colder colors indicate lower velocity, whereas the warmer ones show the higher axial velocity. As it can be seen, SRF models the flow around the blade and in near wake precisely and the details of vortex shedding are observed at the tip of the blade.

*Figure 4: Results from three models*

As expected, VBM misses some of the details of the flow field around the blades and in the near wake. For example, vortex shedding observed in SRF appears in VBM as a crown shape acceleration. The far wake is in a very good agreement in SRF and VBM simulations. Figure 5 shows a detailed comparison between SRF and VBM velocity profiles at three positions along the wake. There are significant differences at the first station, very close to the turbine, but those differences become negligible at the other locations further downstream.

*Figure 5: SRF versus VBM results*

The results from figure 4 show the limitations of the ADM model in quantifying the flow field in the far wake. That first set of data corresponds to the validation of the simulation against experimental results. The wind tunnel conditions for the experiments, that were matched in the simulations, include a background turbulent intensity equal to 1% of the mean inlet velocity. When more realistic conditions, adequate for marine flows, are simulated, the results of the ADM match the velocity profiles from both SRF and VBM in the far field (Y/R>10), as shown in figure 6. The background turbulent intensity is 10%, and the enhanced mixing associated with this higher turbulence values, tends to homogenize the velocity profile in a way consistent with the approximations in the ADM model.

*Figure 6: Results from all three models with 10% Turbulent Intensity*
**Current Work**

With the methodology described above implemented and validated against experiments, we are studying different aspects of tidal turbine efficiency and environmental impact. One important question in the installation of in-stream turbines is the potential effect on sediment transport and its impact on benthic communities. Although tidal channels are, by its very nature, typically barren of natural sediment, the momentum deficit introduced by the turbines can potentially lead to sediment deposition downstream. At the same time, local acceleration induced by the blade passage and the foundation, can lead to scouring in the near field. We are tracing sediment in the simulated velocity field around turbines to investigate these effects.

Another poorly understood phenomenon is the presence of low pressure regions in the flow around and immediately downstream of turbine blades. Possible cavitation is an important concern, but impact on fish swimming bladder is a significant source of uncertainty in understanding the interaction of turbines with the marine environment. Detailed characterization of the pressure field and other physical variables associated with impact on marine life is underway with the ultimate goal of better understanding, quantifying and minimizing environmental impact.