Solution of the flow over a non-uniform heavily loaded ducted actuator disk

2017

IJTPP

This paper investigates the impact of the standard approximations embodied in the well-known Momentum Theory on its performance prediction capabilities. To this aim, the results of the momentum theory, which is still widely used in all Blade Element/Momentum codes for the analysis and/or design of wind turbines, are compared with those obtained with an actuator disk model based on Computational Fluid Dynamics techniques. In this method, the axisymmetric and steady Euler equations are solved with a classical finite volume approach, while the turbine effects are modelled through a set of axial and tangential body forces distributed over a disk shaped region representing the rotor swept surface. Since this method does not rely on the momentum theory simplifying assumptions, it can be suitably employed to verify the momentum theory validity. The analysis is carried out using the well documented experimental data of the National Renewable Energy Laboratory Phase VI wind turbine.

Section: The Cfd Actuator Disk Methodsmentioning

confidence: 99%

“…This method has been mainly developed by Conway [13] and extended to rotors with a finite hub or a duct in [14][15][16][17][18][19]. The SA-AD is also based on the exact flow equations and it only introduces a few numerical errors embodied in the semi-analytical solution procedure.…”

Section: Introductionmentioning

confidence: 99%

Effects of the Approximations Embodied in the Momentum Theory as Applied to the NREL PHASE VI Wind Turbine

2017

IJTPP

“…Part 1 913 body with axis coincident with the ζ axis. Following the classical approach of Wu (1962), Bontempo & Manna (2013) proved that the governing equation of the steady, axysimmetric, incompressible and inviscid flow around the actuator disk and the axysimmetric body reads…”

Section: Theoretical Aspectsmentioning

confidence: 99%

“…In more detail, they coupled in an interactive and iterative manner the partially parabolic method of Chen & Patel (1985) with the vortex-lattice lifting-surface model In the following section, a brief description of the theoretical and numerical aspects characterising the flow problem is presented. In particular, in the first subsection, the mathematical treatment developed in Bontempo & Manna (2013, 2014, 2016a and Bontempo et al ( , 2015a, Bontempo, Cardone & Manna (2015b) for the flow around an actuator disk coupled with an axisymmetric duct is summarised and generalised to allow the treatment of an open actuator disk with an axisymmetric hub. A detailed and thorough analysis of the mathematical aspects related to this issue can be found in Bontempo & Manna (2013) and references therein.…”

mentioning

confidence: 99%

“…In particular, in the first subsection, the mathematical treatment developed in Bontempo & Manna (2013, 2014, 2016a and Bontempo et al ( , 2015a, Bontempo, Cardone & Manna (2015b) for the flow around an actuator disk coupled with an axisymmetric duct is summarised and generalised to allow the treatment of an open actuator disk with an axisymmetric hub. A detailed and thorough analysis of the mathematical aspects related to this issue can be found in Bontempo & Manna (2013) and references therein. At the end of the first subsection, the exact solution of the through-flow problem, although in an implicit formulation, is provided.…”

mentioning

confidence: 99%

See 1 more Smart Citation

A nonlinear and semi-analytical actuator disk method accounting for general hub shapes. Part 1. Open rotor

2016

J. Fluid Mech.

Self Cite

The paper presents a newly developed method for the analysis of the flow around open rotors characterised by hubs of general shape. The exact and implicit solution of the axysimmetric, inviscid and incompressible flow is represented as the superposition of infinite ring vortices properly arranged along the hub surface and the rotor wake. The solution is made explicit through a semi-analytical and iterative procedure. The proposed semi-analytical approach can deal with hubs of arbitrary shape and with quite general rotor load distributions. The method strongly couples the flow induced by the rotor and the hub. Moreover, the contraction/divergence and the rotation of the wake can be fully taken into account. The results of the semi-analytical method are also compared with those obtained with a widely diffused actuator disk model based on computational fluid dynamics (CFD) techniques. Finally, in comparison with more advanced methods, such as those relying on a CFD approach, this method is characterised by an extremely reduced computational cost. The computer code is freely available on contacting the authors.

Highly accurate error estimate of the momentum theory as applied to wind turbines

2017

Wind Energy

Self Cite

The paper provides a verification of the well-known momentum theories by comparing their results with those of a semi-analytical method based on the exact solution of the flow through an actuator disk. In fact, many error sources are disseminated in these theories. Specifically, the axial momentum balance is diffusely applied in an approximate differential form, and several linearization are customarily introduced in the equations of the motion. In the present study, an analytical formulation of these two kinds of errors is provided and a set of data generated with controlled accuracy is used to quantify them both in terms of global (power coefficient) and local (axial velocity at the disk plane) quantities. The overall errors increase by increasing the thrust coefficient and decreasing the tip speed ratio. Although the errors can be generally considered small in terms of global performance coefficients, the differences between the two methods are significant when looking at local quantities. In particular, for the cases presented herein, the momentum theory is shown to overestimate the axial velocity at the tip and at the disk centre regions and to underestimate this velocity elsewhere. For low values of the tip speed ratio, an underestimation also occurs in the zone near to the disk centre