Ali Alhamaly

Report 1

Propeller and Wind Turbine Wakes

Introduction

The understanding of wake dynamics of rotating bodies is of fundamental importance to engineers. Flow over rotating bodies occurs in many important engineering devices. Turbomachines is a great example in which the fluid flow happens over rotating bodies (rotor blades). The wake dynamics behind rotor blades are important field that need to be understood to great details. This is so because the wakes of the rotor blades affect the performance of whole turbomachine. Wake dynamics are also important for wind turbines, especially for the case when the turbines are installed in a farm. The inherent complexities in geometry and flow field for rotor system make the understanding of the wake dynamics rather a hard goal to achieve. Hence, the study of the wake for a simple geometry body is important because it allows us to understand the basic fundamental physics behind the wake dynamics, without including complex geometry and secondary effects. For this reason, the study of rotating cylinder is a good start to understand the effect of body rotation on the wake evolution. A brief look through the recent literature reveals the fact that a lot of application of wake dynamics and evolution is with regard to turbomachinery, propellers, and wind turbines. Based on this fact, I choose to investigate wake dynamics behind rotating bodies with application to wind turbines and propellers as my term project for ME 532.

Relevance to Engineering and Industry

There are a lot of engineering application to the study of propeller and wind turbine wakes. For instance, when wind turbines are placed in large farms, the downstream turbine rotors are influenced by the wakes of the upstream turbines. The flow field associated with the wake corresponds to unsteady loadings to the downstream turbine blades. Excessive unsteady loading might cause fatigue problems to the blade structure and also cause performance reductions. Hence understanding the wake dynamics can help in design the proper location of downstream turbines. In addition, understanding the loss mechanism in the wake might lead to a better aerodynamic design of the turbine blades. In general, wake dynamics and evolution plays essential role in performance, vibrations, noise and structural problems of rotor blades [1].

Literature Review

Several researchers in the literature want to understand the wake behind of rotating turbomachinery blades, propellers, and wind turbines. [2] Reported that in rotating turbomachinery wakes, the dominant cross-stream turbulent shear stress may remain of one sign only, hence losing its antisymmetric nature. This antisymmetric nature exists for non-rotating blade. Given this simple fact, we can see that the complexity associated with rotating blades calls for the need to measure the wake of simpler rotating body. The choice of [2] was to study the wake of circular cylinder rotating with its axis normal to the free-stream velocity i.e. rotating vertical cylinder like a propeller. The flow around a cylinder along with its wake is well understood and documented in the fluid dynamics research community. In addition, the cylinder has relatively large drag coefficient. This leads to a clear wake that can be distinguished based on its width and depth easily. These reasons were among others that led [2] to study the rotating cylinder wakes as a mean to understand the wakes of a more complex geometry like turbomachinery blades. Based on the main experimental results reported by [2], it was shown that the rotation of the cylinder altered the wake significantly. The exact effect of rotation on the wake varies with the dimensionless rotation rate, which was defined in [2] as the inverse of the Rossby number. Furthermore, the main changes to the Reynolds normal stresses come from rotationally-induced terms in the dynamical equation for the Reynolds normal stresses. This means that although the Reynolds normal stresses do not depend explicitly on the rotation, they are affected strongly by rotation due to terms in the Reynolds stress equations that are common to both rotating and non-rotating cylinders. Recently in the literature, a lot of work has been done on the wake of rotor system (such as: propellers and wind turbines). Brief look into recent work on rotor system wakes shows the complexity of such wakes compared with the rotating cylinder wake. For instance, the short article by [3] associates the near wake behind the rotor system with strong tip and hub vortices (the tip vortex called helical vortex as well). These vortices are formed because the flow behind the rotor consists of vortex sheets. These sheets arise due to the aerodynamic load distribution along the span of the rotor [3]. The rotor system has also far wake that is not in the neat vicinity of the blade. Unlike the near wake, the far wake does not depend on the rotor characteristics as much. It is governed mainly by small scale turbulence. It is worth to notice here, that the far wake of the rotor occurs because of breakdown or instability of the near wake vortical structure [3]. Hence, full understanding of the wake behind the rotor requires the understanding of the near wake behavior, its stability, and the growth of far wake turbulence.An extensive and elaborative experimental work on near and far wake of marine propeller has been done in [1]. Wake of marine propeller with different blade numbers and advance ratios were studied systematically and rigorously. In this paper, the authors explain that multiple factors affect the wake evolution in the near and far wake. These factors are: the radial and axial varation of the helical geometry of the tip vortex, interactions between nearby vortices, the deformation of the tip and hub vortices, and the effect of turbulence and viscosity. The article explains more in depth about the mechanism of transition from near wake to far wake structure. The authors shows experimentally that the number of blades affect the location of instability and transition of the helical tip vortex. More specifically, the number of the blades affects the distance between the adjacent helical vortices which in turns affect the interaction between nearby tip vortices. In regards to the distinction between the instability location of the hub and tip vortices, it was shown for different rotor configurations (such as: advance ratio and number of blade) that the location of instability of the hub vortex is always downstream of the tip vortex. It is conjectured that this is probably because the instability of the tip vortex create perturbation that destabilized the hub vortex. The far wake is characterized by distortion of the tip and hub vortical structures. In addition, as the distance from the propeller increases beyond the instability inception location, the vortices become weaker and weaker. This is due to vorticity diffusion which is a viscous mechanism. Vorticity diffusion acts to smooth the high pressure gradient within vortex core until flat profile of pressure is reached in the vortex core. The paper [1] includes more results and conclusions that are not included in this brief review. For instance, the paper discusses the chaotic behavior of the vortex system and also discussed the power spectral density for instantaneous velocity measurements.Much work in the literature has been devoted to model the flow field analytically for propellers and wind turbines. These models vary in their simplicity, assumptions, and applicability. Some of the models are intended to give the overall integrated performance of the rotor without obtaining details about the flow field itself. Example of these models is the famous actuator disk theory. This theory approximates the performance of the rotor by infinite number of blades. These infinite blades represent the disk. This disk acts as a discontinuity surface in which the flow passing through it will be exposed to concentrated force (called thrust) [4]. Based on the thrust value, performance parameters of the rotor can be obtained. There are several refinements of this basic model which relaxes the axisymmetric assumption of the actuator disk theory. In addition, some models allows for varation of loading along the span of the blade [4]. Another type of analytical models is the vortex based formulation models. The main assumption of these types of models is that for uniform free stream velocity, the fluid can acquire vorticity through the interaction with the rotor only. Hence, the vorticity is confined within the rotor wake and is bounded by the tip vortex [4]. The paper [4], describes new vortex based formulation that solves for the near wake vortical structure for propeller or wind turbine. Detailed description of the model with numerical implementation is included in [4]. Here, I provide only very brief description of the overall model. The model is based on finite core size vortex filaments. The model uses asymptotic expansion of the Biot-Savart law. This is done to account for the finite core size filament. The filament core is assumed to be of one size and has circular top-hat vorticity distribution inside the core filament. The model determines the steady state wake vortices path along with the induced velocity field due to the presence of the rotor. The analysis is done in rotating frame of reference.

Proposed Improvements of the Selected Work

A lot of work and improvement can be done with regards to understanding the wake of rotor systems. However, constrains related time and recourses dictate the type of improvements that can be done. With this in mind, I would like to propose small improvement on the analysis done in [4]. I would like to extend what has been done in [4] to include description of the far wake of a wind turbine (or propeller). I would like to study the effect of viscosity and turbulence on the evolution of the near wake to a fully distorted and mixed far wake. This small improvement allows a better description of the performance of the rotor system. In addition, this improvement (if successful) can be used to study the effect of the far wake interaction with a downstream rotor.

Method for implementing the Proposed Solution

The proposed solution will be implemented in two main steps. The first step is to adapt the model proposed by [4] and program it in Matlab. The programmed version of the model shall have same capabilities as described in [4]. Verification of the published results in [4] should be the benchmark to see whether the self-programmed version of the model is accurate or not. Upon completing and verifying the first step, second step shall be started. In the second step, I will be using commercial CFD software to solve for the viscous evolution of the near wake solution. The CFD software will take as an input the solution obtained from the first step. The input will be given in terms of the velocity distributions at the inflow boundary. From the inflow boundary condition, the CFD software will solve Navier-Stokes equation to determine at the outflow the velocity distributions. From the velocity distributions, information about the fat wake will be deduced. It is worth noticing that I am not trying to capture the instability mechanisms that lead to the breakdown of the vortex system. Rather, I am interested in the end results of the flow field at far away distance downstream from the inflow boundary.

Schematic View of the Problem

The basic view of the problem is a shown below in the figure. The figure is taken from [5]. The figure shows a three bladed wind turbine with the paths of the helical tip vortices and the hub vortices.

Bibliography

[1] M. Felli, R. Camussi and F. Di Felice, "Mechanisms of Evolution of The Propeller Wake in The Transition and Far Fields," J. Fluid Mech., vol. 682, pp. 5-53, 2011. [2] D. Wood, P. Peterson and P. Clausen, "The turbulent wake of a circular cylinder rotating about the streamwise axis," Experiments in Fluids, pp. 375-384, 1994. [3] J. N. Sorensen, "Instability of Helical Tip Vortices in Rotor Wakes," J. Fluid Mech., vol. 682, pp. 1-4, 2011. [4] A. Segalini and P. H. Alfredsson, "A Simplified Vortex Model of Propeller and Wind-Turbine Wakes," J. Fluid Mech., vol. 725, pp. 91-116, 2013. [5] S. Ivanell, R. Mikkelsen, J. N. Sorensen and D. Henningson, "Stability Analysis of The Tip Vortices of a Wind Turbine," Wind Energy, vol. 13, pp. 705-715, 2010.

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