A CFD analysis of the performance characteristics of different Darrieus turbine runners *

. This paper presents the capabilities of analyzing different Darrieus wind turbine runners with the computer program Ansys Fluent. A K-omega turbulence model was used in the case of a two-dimensional flow with a suitable computational grid around the profile of the blades. The obtained theoretical performance characteristics were validated on test rig №7 (Wind Turbines) in the Laboratory of Hydropower and Hydraulic Turbomachinery (HEHT Lab) the Technical The data analysis shows that it’s possible to predict the performance characteristic and the optimum operating regime of the Darrieus wind turbine. analyse the flow through a synthesized blade system of a wind turbine runner.


Introduction
The most commonly used mathematical models for calculation of tangential forces acting on wind turbine blades consider the runner as an 'active disk' [1,2]. It is assumed to be an imaginary rotating body covered by one or more stream tubes. The induced velocities through the 'disk' are considered to be constant. The calculations of the acting forces are performed for a rotating blade that crosses the stream tubes at a given moment. The chord of this blade has a length equal to the sum of the chord lengths of all the blades in the real runner. This simplified scheme is insufficient for a more in-depth study of the workflow. It gives satisfactory results in some cases with two and three-bladed runners (depends on solidity).
The complex unsteady flow in most cases is impossible to be studied with classical stream tube models. Therefore, we go to the so-called numerical modelling of flows -Computational Fluid Dynamics (CFD). CFD modelling gives us detailed information about the flow (temperature, pressure, velocity field, etc.) at each point of the computational space. It calculates the stresses on streamlined surfaces and gives us the opportunity to visualize these results in the form of colour contours, isolines, graphs and stream line pictures. The results obtained by the CFD modelling can be compared with the results obtained by experimental research, which significantly reduces the time for conducting physical experiments. A sequential application of a numerical and physical experiment gives us the opportunity to analyse the flow through a synthesized blade system of a wind turbine runner.

Geometr
The studied wi to switch fro significantly r eliminates the Fig. 1

A CFD gr
Apart from the modelling of t coefficient y + blade wall.
In the equation the streamline contour (measu A lot of ca by setting the viscosity of th chord of the ai by running a t below the need Fig.3 show the Ansys-reco domains. The he side walls is ons and boundar

The turbulence model
The turbulence model k-ω SST (Shear Stress Transport) is a hybrid. It combining the Wilcox k-omega and the k-epsilon models. A blending function activates the Wilcox model near the walls and the k-epsilon model in the free stream. This ensures that the appropriate model is utilized throughout the flow field. The transport equations of the k-ω model are described below. Specific dissipation is defined as: In equation (2) k is the turbulence kinetic energy and ε is the rate of dissipation of turbulence kinetic energy. The equation for the balance of turbulence kinetic energy k [8] is: where β and σ k are constants, ω is the specific dissipation, μ 1 is the molecular viscosity and μ t is the turbulence viscosity. The first term on the left side of the equation is local, transient, taking into account the degree of change of the turbulence kinetic energy k; the second is convective, taking into account the transfer of k by convection. The first member on the right of the equation is a source taking into account the degree of generation of k; the second is dissipative, taking into account the degree of dissipation of k, the third is diffuse, taking into account the transfer of k by diffusion.
The equation of the specific dissipation ω [8] is: The first term on the left side of the equation is local, transient, taking into account the degree of change of ω; the second is convective, taking into account the transfer of ω by convection. The first term on the right-hand side of the equation is the source, taking into account the degree of generation of ω; the second is dissipative, taking into account the degree of dissipation of ω, the third is diffuse, taking into account the transfer of ω by diffusion; the fourth is 'mixed-diffuse', which is an additional source member, responsible for modelling the transition from ε to ω.

Compared quantities
The power factor values are determined by the dependence [3,8]: In equation (5) P is the effective power (on the shaft) of the turbine and P w is the power of the airflow. In equations (6) and (7) M b is the torque; n -angular velocity, c w,s -average wind speed, S = H.D 1 -cross-section of the runner, perpendicular to the vector of the wind velocity. It should be noted that in the two-dimensional CFD model the dimension D 1 is used in equation (7) instead of S. The calculations and experiments were conducted for the same average wind velocity: c w,s = 8.1 m/s. For each experiment the so-called speed ratio TSR [3,8] was used. This is the ratio between the tangential speed of the tip of the blades -u and actual speed of the wind -c w,s .

TSR =
The experiments were performed on test rig №7С in the laboratory of Hydropower and Hydraulic Turbomachinery at the Technical University of Sofia -HEHT [3,4,5,9].

Solver settings
Since the Mach number in the current conditions is below 0.3 we consider the flow to be incompressible. That's why we switch to a pressure-based solver. This solver allows us to resolve a flow problem in either a segregated or a coupled manner. Ansys Fluent provides the option to choose among five pressure-velocity coupling algorithms: SIMPLE, SIMPLEC, PISO, Coupled, and Fractional Step (FSM) (for unsteady

Results
Two runners w give us an opp the calculation both in a dimen

Analysis
The analysis o conclusions: • The law of ch he non-iterative pt for the 'coup calculation sch   • Numerical results predict the location of the maximum value of the power coefficient with an error up to 0.3 %. • The differences in the maximum value of the power coefficient between the numerical and experiment data is 7 % (Fig. 4a) and 4 % (Fig. 4b).
• Numerical and experimental data give similar results at values of tip speed ratio lower than 0.27 (Fig. 4a) and 0.285 (Fig. 4b).
The numerical and the experimental data from other similar studies [6,7] shows up to 57 % difference of power coefficient with k-omega SST turbulence model and 20 % with RNG k -ε turbulence model.