Computational Fluid Dynamics 46

Computational fluid dynamics (CFD) is one of the branches of fluid mechanics that uses numerical methods and algorithms to solve and analyse problems involving fluid flows. CFD is a powerful tool which, when used either singly or in conjunction with other tools, can provide vital information as to the performance of a tidal turbine in varying flow conditions. Turbine performance data can be obtained; lift and drag readings can be converted into thrust, torque and power estimates, and also pressure distribution on the device enabling computation of likely cavitation. CFD can also give a detailed picture of the flow around the turbine enabling a more advanced outlook on possible environmental problems, such as scour,

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erosion and the change in tidal magnitude, to be understood and in addition provides vital data regarding the positioning of tidal device arrays.

The fundamental basis of any CFD code are the Navier-Stokes momentum equations, which define single-phase fluid flow. Simplification of these equations by removing terms describing viscosity, yields the Euler equations. If the terms describing vorticity are also discarded the full potential equations are produced; these equations can then be linearised to yield the linearised potential equations.

3.1.3.1 Two Dimensional Analysis

In the two-dimensional realm, panel codes have been developed for airfoil analysis and design. These codes typically have a boundary layer model included, so that viscous effects can be modelled. Some incorporate coupled boundary layer codes for airfoil analysis work. Codes such as XFOIL use a conformal transformation and an inverse panel method for airfoil design. XFOIL is a linear vorticity stream function panel method, with a viscous boundary layer and wake model; and has been found to be suitable for producing section performance data and cavitation criteria for a tidal turbine at the preliminary design stage [75], although care should be taken to consider the apparent underestimation of drag and the overestimation of leading edge pressure coefficient [69]. Two dimensional analyses can be achieved using most CFD programs, although some are more suited to the technique. Section performance data at this stage includes the lift and drag coefficients of differing sections from which estimates of the power, thrust and torque on the turbine rotor and structure can be attained.

Figure 3-6 illustrates a typical plot of data acquired from XFOIL. The foil under examination is a NACA 63815 at an angle of attack of 6o and a Reynolds number of 2.101x106. The blue line represents the CP distribution over the upper surface of the foil, and the red line that over the lower surface. Evaluation of ventilation and cavitation of tidal turbine blades is required in the design process, this is discussed in further detail in Section 3.2, with specific reference to CP plots of the form illustrated in Figure 3-6.

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Figure 3-6: Pressure distribution over the NACA 63-815 section

Some two-dimensional analysis codes also provide fundamental section structural characteristics, such as second moment of area, for minor modifications to the base section made within the program. This data can be used for basic structural analysis of the turbine blade, which is important at this stage in the design process. Computational times are very short – in the order of seconds.

The process is very easy to parameterise and optimise due to its simplicity. Two dimensional analyses prove a powerful tool at the preliminary design stage for a tidal turbine and should not be underestimated; it is apparent, however, that for more detailed design information a more complex code able to model the more complex three-dimensional situations is required.

3.1.3.2 Three Dimensional Analysis

Surface panel codes allow a more thorough analysis of the performance of the turbine to be attained. Such codes calculate the characteristics of each panel over the surface of the body under analysis to produce lift and drag data for the panel and a pressure distribution, and ultimately the body as a whole. The calculated local pressure distribution can be used as a more detailed prediction of cavitation inception on the turbine blades and also as a source of detailed blade loading data for further structural calculations. Since the panels are geometric shapes and are flat, increasing the panel density models a three-dimensional, complex curved

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shape such as a tidal turbine more effectively. Surface panel codes are more computationally intensive than two dimensional analysis methods; overall a reasonable compromise between computational effort and physical accuracy in modelling the flow interaction may be achieved [81, 82].

The surface panel code used in this work is PALISUPAN (PArallel LIfting SUrface PANel) [83] and was initially developed to investigate ship rudder-propeller interaction. By describing a set of quadrilateral panels on the surface of a body, and distributing a set of surface sources and dipoles on the surface of the model, the code generates a numerical solution of the flow over the individual components. For a lifting body, a wake is described downstream of the body to solve for the Kutta Condition. This condition is imposed by iteration until the solution has converged to a defined maximum value.

The basic potential flow mathematical model was refined by the addition of an empirical skin friction calculation which enabled viscosity effects to be considered. It does not, however, model the boundary layer, separation or stall in any form. An additional module allows boundary layer interaction to be studied. For rotating devices, such as propellers or turbines, operating at high Reynolds numbers the boundary layer is thin in comparison to the geometry of the body and therefore this viscous component forms only a small part of the total resistive torque; the majority of load arising from lift based processes. This code has been used to model the behaviour of a representative tidal turbine and good comparisons were obtained with published data, although significant problems were experienced in getting low twist sections to work [69].

The panel distribution over the turbine model becomes very important with relation to the accuracy of the results and the time taken for each calculation. During previous studies [69] it has been found that an optimum panel distribution can be achieved that maintains the accuracy of the result obtained with a finer distribution, but reduces the calculation time to around twenty minutes. Parameterisation and optimisation of surface panel codes is relatively simple, due to the low process times when implementing multiple runs – over 30 at a time – being highly feasible. Using a frozen wake model it is possible to reproduce the helical wake characteristic of tidal turbines. The number and distribution of panels in the wake is also very important for accurate modelling of device performance. Codes have been

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developed that generate optimal panel distributions over complex shapes, such as a propeller or tidal turbine, and the associated wake panel arrangement [84].

These simple three-dimensional analyses provide a much more detailed picture of the pressure distribution over the turbine blades and body, therefore giving a more comprehensive picture of areas of the blade at which cavitation will occur. Figure 3-7 illustrates the pressure distribution of a three bladed tidal turbine obtained from a surface panel code.

Figure 3-7: Representation of the pressure distribution over a three bladed turbine obtained using a surface panel code

The areas of red illustrate those parts of the blade where low pressure occurs, i.e. where the pressure coefficient is a minimum, and onset of cavitation is most likely. Areas of green are those with a more even pressure, and those nearing blue are areas tending towards stagnation.

Due to their simplicity, surface panel codes cannot capture severe changes in the flow regime, i.e. separation and stall. For a full design scenario, more advanced numerical simulation of the area around the turbine may be necessary in order to incorporate these effects.

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3.1.3.3 Reynolds Averaged Navier Stokes Models

The Reynolds-averaged Navier-Stokes (RANS) equations result from time-averaging the Navier Stokes equations, and represent the mean flow. They are primarily used while dealing with turbulent flows. These equations can be used, with approximations based on knowledge of the properties of flow turbulence, to give approximate averaged solutions to the Navier-Stokes equations. The nature of RANS equations brings about the need for complex domain discretisation schemes as well as complex modelling with large numbers of elements. This leads to complex mesh structures on which the equations must be solved, and building such meshes is time consuming.

Turbulent flows contain many unsteady eddies covering a range of sizes and time scales. The RANS equations are averaged in such a manner that turbulent fluctuations in space and time are eliminated, and become expressed by their mean effects on the flow through the Reynolds, or turbulent, stresses. These stresses need to be interpreted in terms of calculated mean flow variables in order to close the system of equations, thereby rendering them solvable. This requires the construction of a mathematical model known as a turbulence model, involving additional correlations for the unknown quantities [85].

The RANS solver ANSYS CFX 11.0 was used to model a 20m diameter, three bladed, free stream, tidal turbine. The analysis did manage to converge, Figure 3-8, however the numerical results were poor when compared to validated BEMT data. Subsequent research into the field of RANS solvers for large scale tidal turbines has shown that commercial packages are too generic in their approach. While acceptable results can be achieved for small scale turbine modelling [86], the mesh complexity, coupled with cavitation analysis and streamline contraction, proves too complex and many groups are in the process of developing multifaceted in-house software aimed specifically at solving the tidal turbine problem accurately [87].

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Figure 3-8: Velocity streamlines around a 20m, three bladed, free stream tidal turbine in CFX