Several simulations were also done to study the effect of a nozzle and diffuser on the performance of the cross-flow wind turbine. The final objective is to compare the performance characteristics of the 10kW horizontal type wind turbine with the 10kW cross flow type turbine with a nozzle and diffuser.
Introduction
Background
- Classifications of wind turbines
The final method described here classifies wind turbines based on the size of the rotor diameter. Both the output power and the size of the wind turbines can vary from machine to machine.
Motivation for study
Basic theory of wind turbines
- Betz theory
- Blade element momentum theory
- The momentum theory
- Rotating wake/ Rotating annular stream tube
- Blade element theory
- Prandtl’s tip loss factor
- Design of a horizontal axis wind turbine blade
- Cross flow type wind turbine
Thicker airfoils increase blade thickness and provide greater strength, but have lower aerodynamic properties [13]. The performance characteristics of a cross-flow wind turbine will be compared with a HAWT wind turbine.
Methodology
Numerical modeling
Obtaining closure implies that there are a sufficient number of equations to be solved for all unknowns including Reynolds stresses and Reynolds fluxes. The advantage of using this model is that it combines the advantages of other turbulence models (k-ε, Wilcox k-ω and BSL k-ω). To understand the advantage that the SST model provides, the other 3 turbulence models will be briefly discussed.
Turbulence models
- Two equation turbulence models
The values for k and ε come from the differential transport equations for the kinetic energy of turbulence and the dissipation rate of turbulence. A buoyancy term can be added to the previous equation if the full buoyancy model is used. Therefore, a mixture of the k-ω model near the surface and the k-ε in the outer region was made by Menter [23], resulting in the formulation of the BSL k-ω turbulence model.
It consists of the transformation of the k-ε model into the k-ω formulation and the subsequent addition of the resulting equations. Outside the boundary and at the edge of the boundary layer, the standard k-ε model [22] is used. Although the BSL k-ω model combines the advantages of the k-ε and Wilcox k-ω turbulence models, it fails to correctly predict the onset and amount of flow separation from smooth surfaces.
The k-ε and Wilcox k-ω turbulence models do not consider the transport of the turbulent shear stress, resulting in an overprediction of the eddy viscosity. F2 is a mixing function that constrains the limiter to the wall boundary and S is the invariant measure of the strain rate. y is the distance to the nearest wall and v is the kinematic viscosity. Generating the mesh of the geometry c) Defining the physics of the model d) Solving the model.
Creating the geometry
- Model of horizontal axis wind turbine (HAWT)
- Model of the cross flow turbine
For comparison purposes, the swept area of the HAWT is made equal to the inlet area of the nozzle for the cross-flow type turbine to ensure that the ratio of power to area was the same for both turbines. To analyze the effect of the nozzle on the performance of the crossflow turbine, two geometric factors were considered. These two factors were the entrance arc angle and the shape of the nozzle walls.
The inlet arc is the arc angle made by the intersection of the top and bottom walls of the nozzle with the outside diameter of the turbine, as shown by the angle δ in Figure 345 below. After analyzing the angle of the inlet arc, we also investigated the shape of the nozzle wall. For this analysis, the nozzle walls were modified as shown in Fig. 3.9 to fig. 3.14.
Similar to the turbine inlet arc angle, the diffuser arc angle is the angle of the arc formed by the intersection of the top and bottom walls of the diffuser with the outer diameter of the turbine shown in Fig. 3.15 as δ2. When this study was completed, the effect of the geometry of the shape of. After all the geometries were created, the mesh of the geometries for numerical modeling was generated.
Mesh generation
- Horizontal axis wind turbine mesh
- Cross flow turbine mesh
Therefore the distance of the first node from the blade surface (or Y-Plus) must be taken into account. Unlike the HAWT blade, the crossflow turbine simulation requires several meshes which are generated independently before combining several meshes together. The parts were named as Main Domain, Nozzle Domain, Turbine Domain, Internal Fluid Domain, High Strip/Low Belt Domain and Diffuser domain.
For all analysis involving the cross-flow turbine, approximately the same number of nodes was used for the different domains. This is done to create a higher quality mesh around the regions and simplify the mesh generation. The top and bottom strip meshes were identical except for their location in the geometry.
The bottom bar grid was only used in case 6 of the orifice shape analysis and 90°. Only one blade was meshed and the remaining 29 blades were added to CFX-Pre by mesh transformation. The next step after generating the mesh is to determine the necessary boundary conditions, fluid velocities and rotational velocities for the analysis.
Simulation setup
- HAWT setup in CFX Pre
- Cross flow turbine setup in CFX Pre
Fig.3.31 shows the interface boundary where the rotation periodicity is chosen as the interface model. Fig.3.32 below shows the configuration for the cross-flow turbine of the analysis in CFX-Pre. Where ω is the angular velocity (rads/sec), r is the turbine radius (m) and Vinlet is the inlet velocity (m/s) which is set to 10m/s for all simulations.
Solving the simulation
Post processing
The results obtained from the simulations of the two turbines were analyzed in CFX-Post and the results will be discussed in the next chapter.
Results and Discussion
Horizontal axis wind turbine analysis
- Power output
- Streamlines
The power factor is the ratio of the output power of a wind turbine to the available kinetic power of the wind, essentially the efficiency of the turbine at a given wind speed. The design CP of the blade was 0.43 at 10 m/s was exceeded and the blade achieved a higher CP value. To further investigate the flow field above the wind turbine, the streamlines of the flow across the blade were analyzed.
This stall is mainly due to the high angle of attack on the blade in this section. As the wind speed increases to 10 m/s, more stagnation occurs near the root of the blade, but most of the flow remains trapped elsewhere on the blade. It can also be seen that the separated current moves at the root towards the tip of the blade.
This movement towards the tip can be seen more clearly at 15m/s where most of the blade, especially near the trailing edge, is under stall. The increase in the amount of stall at this wind speed is also consistent with the decrease in CP value shown in the previous graph of the coefficient versus wind speed. Eventually at 20m/s, most of the blade is under stall, although the flow remains attached from the leading edge of the blade to about midpoint on the suction side of the blade.
Cross flow wind turbine analysis
- Turbine entry arc analysis results
- Nozzle shape analysis
- Diffuser entry arc analysis
- Diffuser shape analysis
The flow accelerates and increases on the wall of the nozzle, while the flow within the center of the nozzle remains low. This greater volume flow rate can be plotted and seen in the volume flow rate of the air just before it enters the turbine at the various tip speeds indicated in Fig.4.16. The figure shows that at 135° entrance arc angle, the flow rate remains the highest of all the cases.
As the arc angle increases, the velocity profile improves and the magnitude of the flow into the turbine also increases. The flow velocity at the entrance arc to the turbine for the different cases was investigated, and this is shown in Fig.4.19, where the air flow velocity at the different peak velocity conditions is compared. The lower performance despite the higher flow rate can be attributed to the geometry of the lower nozzle wall near the turbine inlet.
Similar to what was discussed in the previous section, the figures show how the fluid velocity decreases at the nozzle inlet. The velocity vectors also show how the approaching flow near the top and bottom of the nozzle tends to flow around the nozzle rather than into the nozzle. This figure shows that the arc housing with a 135° diffuser has a higher flow rate in and out of the turbine than the 90° housing.
This significant difference between flow rates for these 2 cases can affect the efficiency of the turbine. Therefore, it can be interpreted that the effect of the diffuser is minimal compared to the effect that the diffuser entrance arc angle and nozzle.
Comparison of the HAWT and cross flow turbine
The minimal effect that the diffuser shapes had can be attributed to the two figures, Fig.4.36 and Fig.4.37, which show that cases did not affect the flow velocities in the turbine as significantly as the nozzle shapes. It was also seen that as the nozzle shapes improved the flow rate in the turbine, the efficiency of the cross-flow turbine improved.
Conclusion
In the case of the diffuser shape analysis, the most efficient diffuser shape had a CP of 0.11 compared to the other shapes. However, the graph showed that the diffuser shape was not as effective in increasing the power output compared to the nozzle. The Meteorological Aspects of Siting Large Wind Turbines. United States of America: United States Department of Energy; 1981 [4] Manwell.J.F, McGowan.J.G, Rogers.A.L., Wind Energy Explained.
12] Hau.E, Wind Turbines: Fundamentals, Technologies, Application, Economics. 2nd ed. Springer-Verlag, New York; 2006 Chapter 5, Rotor Aerodynamics; page 102. 13] Hau.E, Wind Turbines: Fundamentals, Technologies, Application, Economics. 2nd ed. Springer-Verlag, New York; 2006 Chapter 5, Rotor Aerodynamics; p. 139. A study on optimal design of horizontal axis wind turbine and analysis of its aerodynamic performance.
17] Ingram.G, Wind Turbine Blade Analysis using the Blade Element Momentum Method .Durham University Retrieved, 04 February 2012, http://www.dur.ac.uk/g.l.ingram/download/wind_turbine_design.pdf. 18] Holgate.M.J., A Cross Flow Wind Turbine.Proceedings of the International Simposium on Wind Energy Systems; September 7-9, 1976; Cambridge, England. 19] Shigetmitsu.T, Fukutomi.J, Takeyama.Y., Study on performance improvement of cross flow wind turbine with simmetric casing.
![Figure 2.2: The relationship between the power coefficient and the velocity ratio When v 2 /v 1 = 1/3, the maximum power coefficient becomes C P = 16/27= 0.593 [10]](https://thumb-ap.123doks.com/thumbv2/123dokinfo/10546512.0/22.892.185.648.207.526/figure-relationship-power-coefficient-velocity-ratio-maximum-coefficient.webp)
