Coupling Numerical Methods and Analytical Models for Ducted Turbines to Evaluate Designs

Abstract

Hydrokinetic turbines extract energy from currents in oceans, rivers, and streams. Ducts can be used to accelerate the flow across the turbine to improve performance. The objective of this work is to couple an analytical model with a Reynolds averaged Navier-Stokes (RANS) computational fluid dynamics (CFD) solver to evaluate designs. An analytical model is derived for ducted turbines. A steady-state moving reference frame solver is used to analyze both the freestream and ducted turbine. A sliding mesh solver is examined for the freestream turbine. An efficient duct is introduced to accelerate the flow at the turbine. Since the turbine is optimized for operation in the freestream and not within the duct, there is a decrease in efficiency due to duct-turbine interaction. Despite the decrease in efficiency, the power extracted by the turbine is increased. The analytical model under-predicts the flow rejection from the duct that is predicted by CFD since the CFD predicts separation but the analytical model does not. Once the mass flow rate is corrected, the model can be used as a design tool to evaluate how the turbine-duct pair reduces mass flow efficiency. To better understand this phenomenon, the turbine is also analyzed within a tube with the analytical model and CFD. The analytical model shows that the duct's mass flow efficiency reduces as a function of loading, showing that the system will be more efficient when lightly loaded. Using the conclusions of the analytical model, a more efficient ducted turbine system is designed. The turbine is pitched more heavily and the twist profile is adapted to the radial throat velocity profile.

A Theory for Power Extraction from Passive Accelerators and Confined Flows

“…Qualification of a specific accelerator's performance is necessary to model non-ideal states and to benchmark a particular geometry. The Thrust Model [15] satisfies these requirements.…”

“…We show that the Thrust Model is related to Rankine-Froude's Momentum and Actuator Disk Theory [15] and thereby Betz's Law [9] with additional constraints. When related to the Coefficient of Thrust (CT) and the area ratio between the throat and maximum area is set to one, Rankine-Froude momentum theory's wake velocity equation is the same as the Thrust Model's disk velocity equation.…”

“…This illustrates the relationship between the Thrust and Rankine-Froude Momentum theory and the additional continuity constraints in the Thrust Model. The Thrust Model and AMs' predictions are A hypothesis, referred to as the Thrust Model, was derived by Knight et al [15]. This paper provides a detailed mathematical analysis of the preceding AMs and the Thrust model, which was specifically developed for the analysis of power extraction from confined flows, uses accelerator performance and actuator disk body forces to predict C P performance.…”

“…AM Method 2: Jamieson Jamieson [11] states that the maximum coefficient of power for a shrouded rotor is the product of the Betz Limit times (1 -a 0 ). His variable a 0 , in his Equation (15) or Equation (A8), is the axial induction at the extraction plane under no extraction. For an ideal accelerator, Jamieson states, β = 1 − a 0 .…”

Noise Characteristics Analysis of the Horizontal Axis Hydrokinetic Turbine Designed for Unmanned Underwater Mooring Platforms

“…Subsequently, they investigated several types of HAHT [5,7,8], and the results showed that the maximum power coefficient has significantly improved. The investigation of HAHT is still a hot topic all over the world [9,10].…”