A river bed hydrokinetic turbine. A laminated composite material rotor design

This chapter presents the composite materials applied to Water Current Turbine (WCT) hydrokinetic turbines. Here will be briefly described the features of these turbines, the fluiddynamic behavior of the rotor, and its structure formed into a composite material. From the structural viewpoint an advanced composite material formulation that allows an appropriate structural design is introduced. The generalized composite formulations here introduced take into account the nonlinear mechanical behavior of the component materials (matrix and fiber), as the local behavior of plasticity and damage, its anisotropy, the fiber matrix debonding, its material composition via a general mixing theory, and also the homogenized structural damage index definition. Hydrokinetic turbines bring newer advantages and greater possibilities for green hydroelectric power generation. For this reason, achieving a very high lift blade rotor to take the maximum kinetic energy advantage for rivers with a slow velocity flow is very important. A very low inertia rotor permits a self-starting effect for the axial water flow turbine to take the maximum advantage of the river kinetic energy which is very important in this kind of devices. A turbine rotor hydrofoil made in composite material can be designed for this purpose. One of the most commonly used composite material analysis formulation is herein introduced. Specifically, a particular Serial/Parallel (S/P) Mixing Theory with a better relation between model accuracy vs. computational cost is provided. In front to other formulation, the S/P Mixing Theory not increasing the degrees of freedom of the problem because is a constitutive formulation. A brief introduction to fluid-dynamic concept involving in the analysis of a rotor of this type of turbines is presented. This allows seeing the origin of the actions applied to the rotor of this type of turbines. In addition, two simple examples that show the potentiality of the model are presented in this chapter. Then, an application to the design of a rotor blade of a passing turbine, made of carbon fiber-reinforced matrix composite material, is shown. 1 General Introduction According to United Nations, 20% of the global population does not have access to electricity, and a further 14% lack reliable access [54]. The use of an axial flow rotor turbine in remote area was claimed to have for pumping irrigation and electrical power generation. Hydrokinetic turbines bring newer, greater possibilities and advantages for hydroelectric power generation. There are applications in water currents of 0.5 m/s in more [53]. Development of renewal energy production in rivers and channels still preserve a very interesting power production potential, being not subjected to the classical hydraulic power exploitation. This solution avoids the construction of expensive dams and reduces considerably the environmental impact produced by classical hydropower generation [52]. Low speed flux and lack of depth are the main obstacles in hydrokinetic operation. For this reason, achieving a very high lift rotor to take the maximum advantage of the kinetic energy of a slow velocity water flow, which belongs to a lowland river type, is a very important topic. The use of a high lift aerodynamic/hydrodynamic profile and composite material for the blades serve to accomplish the task. The main purpose of this chapter is to describe a general procedure to achieve a very low inertia rotor minimizing the start-stop effect for the axial water flow turbine, in which is important to take the maximum advantage of the kinetic energy. The composite hydrofoil of the turbine rotor can be designed using reinforced laminate composites, to obtain the maximum strength and lower rotational-inertia. The mechanical and geometrical parameters involved in the design of this fiber-reinforced composite material are the fiber orientation, number of layers, stacking sequence and laminate thickness. For this reason, it will be briefly described the features of hydrokinetic turbines (WCT Water Current Turbine) for river use, their basic design requirements and the response by using matrix-reinforced composite structures. Design requirements for these turbines need a numerical process simulation of the fluid dynamic problem coupled with the behavior of the structure made of composite materials. From the structural viewpoint it is necessary the use of an advanced composite material formulation that allows an appropriate structural design. For this purpose, a "mixing theory" [1,2,7,8,27,29,30,31,32,38,39,42,50] and / or "homogenization theory" [3,4,5,9,43,47,48,49,51] of simple substances are used, with a mapping spaces formulation [6] that allow considering the anisotropy of the constituent and composite materials in the most general possible way, and a fiber matrix debonding formulation [2,29,31,39]. Moreover, within these general formulations, it is also taken into account the nonlinear mechanical behavior of the component materials (matrix and fiber), which allows to know precisely the limits of participation of each one of them into the composite. The study of composite materials has been one of the major objectives of computational mechanics in the last decade. The numerical simulation of orthotropic composite materials has been done by means the average properties of their constituents, but this approximation, no model has been found able to work beyond the constituents elastic limit state. Thus, these procedures are limited to the numerical computation to elastic cases. Different theories have been proposed to solve this problem, taking into account the internal configuration of the composite to predict its behavior. The two most commonly used are herein remarked. Homogenization theory: This method deals with the global problem of composite material in a two-scale context. The macroscopic scale uses the composite materials to obtain the global response of the structure; composites are considered as homogeneous materials in this scale. The microscopic scale corresponds to an elemental characteristic volume in which the microscopic fields inside the composite are obtained; this scale deals with the component materials. Homogenization theory assumes a periodical configuration of the composite material to relate these two scales [3,4,5,9,43,47,48,49,51]. Mixing theory: The first formulation of the mixing theory corresponds to Trusdell and Toupin [7] and it is based in two main hypothesis: 1. All composite constituents have the same strains. 2. Each constituent collaborates to the composite behavior according to its volumetric participation. The main problem of the mixing theory is the iso-strain condition, which forces a parallel distribution of the constituents in the composite. Some improvements to the original formulation can be found in [1,2,7,27,29,30,31,32,38,39,42,50]. In this chapter a brief introduction to the “Serial / Parallel theory of mixtures”, a more advanced formulation than the classic one, is presented. The election of the mixing theory instead of a homogenization theory is based in the better relation between model accuracy vs. computational cost provided by the former one [5]. A homogenization theory requires a micro-model for each point of the structure that becomes non-linear. Despite the advances made in strategies to reduce the amount of micro-models solved [9,44,46,48,51], the resolution of a real structure with this procedure generates such a big amount of degrees of freedom that the calculation is beyond the computation capabilities of nowadays personal computers. On the other hand, the mixing theory does not increase the degrees of freedom of the problem, as it is only present in the constitutive section of the finite element code. 2 Hydrokinetic Turbines Introduction This section provides an overview of a "Water Current Turbine" (WCT) allowing understand the hydrodynamic basis for their design and its requirements for the structural function [10,11,12,13,14,15,16,15]. Then, Section 5 presents the basis for the analysis of its structure made up in a reinforced composite material, and a simple application in the examples section are shown too. Rivers kinetic energy for electric power generation is a very valuable alternative source. This emerging class of renewable energy technology, the hydrokinetic conversion device (HCD), offers ways to capture the energy of flowing water without the impoundment or diversion of the conventional hydroelectric facilities based on dams and penstocks. Hydrokinetic technologies are designed for deployment in natural streams, like rivers, tidal estuaries, ocean currents, and in some constructed waterways [10,11,12,13,14,15,16,15]. As opposed to the rigid, expensive, and environmentally aggressive construction of tidal barrages, the modularity and scalability of hydrokinetic devices are attractive features [11]. River streams and other artificial channels have potential for generating electric power through several hydrokinetic energy technologies. This nascent class of renewable energy technology is being strongly considered as an exclusive and unconventional solution falling within the area of both in-land water resource and marine energy [12]. Conventional large or small hydroelectric systems use reservoirs and penstocks to create an artificial water head and extract the potential energy of downwardly falling water through suitable turbo-machinery. In contrast, a river turbine, which could be built as a free-rotor or part of a channel augmented system, may provide an effective alternative mean for generating power. Such systems would potentially require little or no civil work, causing less environmental impact [13,14]. Khan, Iqbal and Quaicoe [13] showed values that indicate the possibility of higher energy capacity through a river turbine when compared to an equally sized wind energy converter. Wind turbines are usually designed to operate with rated wind speed of 11–13 m/s while, in contrast, river turbines with augmentation channels could be designed for low effective water velocities of 1.75–2.25 m/s or even higher, depending on site resources. Unlike wind energy, the size of these engines is a limitation for this type of energy generation and must be reduced according to the river depth. Another drawback is the low flow velocity, and it requires a set of blades and rotor with a specific design to generate the greater amount of kinetic energy as possible from the water flow [15]. This chapter describes a general procedure for an efficient fluid-mechanical design of the rotor ́s blades. The use of high lift airfoils, and composite materials structural design for low rotational inertia, guarantees the hydrodynamics efficiency. Thus, the chapter is structured taking into account the analysis of this axial hydrokinetic river turbine as the fluid dynamic design of the rotor turbine; and the structural design of the rotor by composite materials. These areas converge in a multidisciplinary methodology depicted in Figures 5. 3 Rotor hydrokinetic turbine design. Fluid-Solid interaction Hydrokinetic turbines, unlike conventional hydraulic turbines utilize the kinetic energy of river/channels water for power generation. The performance of these turbines depends of the number of blades, tip speed ratio, type of airfoil, blade pitch, chord length and twist and its distribution along the blade span [55]. Knowing the inlet and outlet pressure in the micro-scale volume control (VC1), a procedure for the rotor design of a hydrokinetic turbine for riverbed operation is described in this section. The study is focused on the conditions of a standard large-medium sized lowland river. The structural analysis of this rotor engineered in composite materials with reduced inertia and better functionality for low speed currents fluvial beds, is described in Sections 4 and 5. The results of the numerical simulation of the composite rotor structure can also be found in the Section of examples. 3.1 Hydrofoil profile and rotor Inside of the micro-scale control volume (VC2) a composite material rotor turbine is placed. A brief hydrofoil design of its profile is here presented. The supplied turbine power W is directly proportional to the machine’s operating angular speed  and its torque T produced at that specific speed, W T.   (1) Figure 1: Hydrofoil S1223 profile If more lift is obtained by one blade, more torque and angular velocity will be obtained by the turbine. This commitment is achieved by selecting the S1223 foil [16], which belongs to the high lift low Reynolds profiles class (see Figure 1). Initially designed as an airfoil for air working conditions, the S1223 profile has also been tested as a hydrofoil under water conditions operation, showing very good operational qualities [17]. A rotor with S1223 hydrofoil profile keeps the proper balance between lift and drag and maintains an attached flow in the hydrofoil neighborhood. In consequence, this rotor has a better pressure distribution and presents hydrodynamic stability, preventing interference with the rest of the hydrofoils forming the rotor. 3.2 Simplified hydrofoil analytical pre-design For turbine application, hydrofoil must be designed starting from the premise that it has to maintain fluid mechanics parameters (such as angle of attack, homogeneous pressure distribution, etc.) along the whole wingspan, despite the fact that rotary operating conditions produce different linear velocity of rotation ( u ) along the blade axis (which gets higher the nearer the point is from the wingtip). Working with this condition involves the variation of the blade geometry parameters (like camber angle, airfoil chord, etc.) in relation with the wingspan axis. Figure 2 shows the notation for angles and velocities on the blade profile, where v is the absolute flow velocity in the micro-scale VC2 volume control, u represents the blade’s linear rotational speed and c is the relative flow velocity. The angle of attack  is an aero-hydrodynamic angle defined between c and the airfoil chord, and depends on the airfoil profile and its camber angle . Instead, camber angle  represents a mechanical angle, defined between the hydrofoil chord and its plane of rotation. By Figure 2: Notation for angles and velocities on the blade profile u combining hydrodynamics and mechanical angles, the sustentation angle (θ) appears which is very useful to obtain the variation camber angle in a rotating blade. Parameters involving the use of a S1223 profile working as a non-twisted, non-rotatory and unturbined designed hydrofoil are explained below [17]. The suitable angle of attack occurs at the optimum angle of attack α0 = 10 , which is considered as a starting parameter of the design sequence; it involves lift coefficient cy = 2.2 and drag coefficient cx = 0.046. Lift coefficient can raise until it reaches its maximum at αmax = 15 , but beyond that angle, detachment of the boundary layer will happen, dropping lift coefficient and increasing drag coefficient enormously [18]. The Tip Speed Ratio (TSR or λ) is a non-dimensional parameter that is defined by taking the relationship between the absolute river flow axial flow velocity c and the blade speed turbine rotor u , and it is given by λ = (ω ∙ R v ⁄ ) (2) where R is the rotor radius. According to Betz ́s law [19], turbine mechanical power W specified for axial turbines depends on the flux density  and flow speed v in VC2 volume control; both values are fixed by the river flow, and so these parameters are fixed as initial conditions and will not be modified during the process of the rotor design. According to this, rotor nominal power can be established, and is computed from W = (8 ∙ ρ ∙ A ∙ v) 27 ⁄ (3) The swept area (A) is the unique variable in Equation (3), and it depends R (radius of the rotor). Despite the rotating condition, it is necessary to maintain the angle of attack along the wingspan; this scenario permits to keep the rotor’s fluid dynamic stability. These commitments are accomplished by varying the geometry parameters of the hydrofoil chord size L and camber angle  , along the wingspan. To achieve this goal the Blade Element Theory can be used; according to Froude [20,21], the airfoil ́s total length (X) is split in several segments, and each one is designed individually as x (Figure 3). Sustentation angle  (Figure 2) is obtained by means of Equation (4), as follows: θ = arccot((ω ∙ x) v ⁄ ) (4) The chord size of the airfoil is therefore computed for each segment x L by wing x x y SP x L c n  (5) where wing n is the actual number of airfoils in the rotor, y c is the lift coefficient corresponding to a defined profile section at a certain radius x, and the airfoil shape factor SPx can be computed by a curve approximation given by SPx = 2.2762 ⋅ (SRx ) (6) In Equation (6) the non-dimensional parameter SRx is given by SRx = (TSR ∙ x) X ⁄ (7) As a result of the chord modification during the process by Equation (5), the initial attack angle α0 has to be recalculated too through Equation (9), obtaining a new angle of attack αn for each chord Lx in each segment x. For this recalculation, the KL parameter, which represents a relationship between the wingspan and the average of the chord, Lavg is necessary,