Flow Simulation Around a Rim-Driven Wind Turbine ...

Proceedings of ASME Turbo Expo 2013: Turbine Technical Conference and Exposition GT2013 June 3-7, 2013, San Antonio, Texas, USA

GT2013-94054

FLOW SIMULATION AROUND A RIM-DRIVEN WIND TURBINE AND IN ITS WAKE Bryan E. Kaiser University of New Mexico Albuquerque, New Mexico, U.S.A.

Michael A. Snider University of New Mexico Albuquerque, New Mexico, U.S.A

Svetlana V. Poroseva University of New Mexico Albuquerque, New Mexico, U.S.A.

Rob O. Hovsapian Idaho National Laboratory Idaho Falls, Idaho, U.S.A.

ABSTRACT A relatively high free stream wind velocity is required for conventional horizontal axis wind turbines (HAWTs) to generate power. This requirement significantly limits the area of land for viable onshore wind farm locations. To expand a potential for wind power generation and an area suitable for onshore wind farms, new wind turbine designs capable of wind energy harvesting at low wind speeds are currently in development. The aerodynamic characteristics of such wind turbines are notably different from industrial standards. The optimal wind farm layout for such turbines is also unknown. Accurate and reliable simulations of a flow around and behind a new wind turbine design should be conducted prior constructing a wind farm to determine optimal spacing of turbines on the farm. However, computations are expensive even for a flow around a single turbine. The goal of the current study is to determine a set of simulation parameters that allows one to conduct accurate and reliable simulations at a reasonable cost of computations. For this purpose, a sensitivity study on how the parameters variation influences the results of simulations is conducted. Specifically, the impact of a grid refinement, grid stretching, grid cell shape, and a choice of a turbulent model on the results of simulation of a flow around a mid-sized Rim Driven Wind Turbine (U.S. Patent 7399162) and in its near wake is analyzed. This wind turbine design was developed by Keuka Energy LLC. Since industry relies on commercial software for conducting flow simulations, STAR-CCM+ software [1] was used in our study. A choice of a turbulence model was made based on the results from our previous sensitivity study of flow simulations over a rotating disk [2].

Erick Johnson Montana State University Bozeman, Montana, U.S.A.

INTRODUCTION Improvements in conventional HAWT design have raised the range of typical power coefficients to between 0.4 and 0.5 [3], but negative wake/turbine interactions between HAWTs in wind farms cause annual power losses of 12% and 8% in onshore and offshore wind farms, respectively [4]. Additionally, viable geography for conventional HAWTs is significantly restricted by high cut-in wind speed requirements. The Keuka Rim-Driven Wind Turbine (RDWT) is a midsized, drag-driven wind turbine designed for onshore wind energy extraction. The design is passive stall-controlled for simplicity and lower capital expense. It features high solidity (16 blades) (Fig. 1) and is power-rated at 15kW. The diameter of the turbine analyzed in the current study is 7.5 m. Larger turbines are also under investigation.

Figure 1: The Keuka Wind Turbine, front view.

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Copyright © 2013 by ASME

𝐶𝑝 = 4𝑎(1 − 𝑎)2 .

Although experimental testing of the Keuka RDWT [5] determined a lower power coefficient than that of the newest conventional HAWTs [3], RDWT is designed to be operated at wind class three or below, that is, in locations where conventional HAWTs are not suitable. Thus, at such conditions, RDWT should have higher power output than conventional HAWTs. Furthermore, if its wake characteristics prove to be less taxing on downstream turbines, RDWT can be used to enhance the efficiency of the HAWT wind farms. Since RDWT is a new design, simulations of a flow around and behind RDWT are required for evaluating a full potential of the design. The current study is the first computational study of RDWT in this regard. Simulations are expensive. Therefore, the immediate goal of the current study is to determine a set of computational parameters that allows one to conduct accurate and reliable flow simulations at a reasonable cost. This set of parameters will be used in our future studies to analyze the RDWT performance. Flow simulations were conducted around a single turbine blade and around a quarter of the turbine. Computational results were obtained with STAR CCM+ computational fluid dynamic (CFD) software [1]. In addition, fluid forces on and around the RDWT blades were examined analytically. The analytical model provides information regarding the maximum possible power output for the turbine and for verification of computational results. Analytical and computational results are compared with experimental data collected from the turbine prototype installation test site in Lubbock, TX [5].

A value of the axial induction factor, a, varies depending on a flow state. Three different flow states are recognized: windmill flow state, turbulent wake flow state, and reversed thrust flow state. Wind turbines primarily operate in the windmill flow state. An exception occurs during starts up and shuts down, when the turbulent wake flow state is induced. One can analytically estimate a value of the axial induction factor from a value of the thrust coefficient [7]. The analytical thrust coefficient, Ct, of the RDWT in the windmill flow state is calculated as follows: � 𝑈∞ 𝜌𝑈 ∙ 𝑛� 𝑑𝑆 = � 𝐹𝑡 𝐶𝑆

𝐶𝑡 =

In evaluating the thrust coefficient, an incompressible flow was assumed to pass over a single twisted plate-like blade at Re ≥ 1.4 ∙ 106 (U∞ = 1 m/s). A simple thrust force calculation was performed by assigning a fixed control volume to a flow around the geometry, shown in Fig. 2. For a steady flow, the net rate of linear momentum through the control surface is equal to the time rate of change of the linear momentum of the system and the net force on the contents of the control volume (the blade).

NOMENCLATURE ρ = air density a = axial induction factor A = rotor swept area Ct = thrust coefficient, Keuka turbine CT = thrust coefficient (simulation result) Cp = power coefficient, Keuka turbine Ft = thrust force f = aerodynamic loss factor h = mesh cell characteristic length NB = total number of turbine blades 𝑛� = normal vector to control volume surface p = mesh pointwise error exponent R = blade length Re = Reynolds number r = mesh refinement factor U∞ = free stream wind velocity in the axial direction U = fluid velocity through control volume I.

𝑁𝐵 𝐹𝑡 1 2 𝜌𝐴𝑈∞ 2

Figure 2: Control volume of a flow over a single blade for the analytical calculation. Gravitational and viscous effects were neglected. Adverse pressure gradients acting on the back of the blade was also neglected. II.

The Analytical Model

The Computational Model

A complex structure of a flow around RDWT presents many challenges for conducting accurate and reliable numerical simulations. The presence of dynamic stall, turbine operation over a broad range of Reynolds numbers, and interaction with atmospheric turbulence are just a few of them. Requirements

Following the classical momentum theory [6], the wind turbine power coefficient can be calculated analytically in terms of the axial induction factor as follows:

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for the appropriate computational grid resolution render the Direct Numerical Simulations (DNS) and the Large Eddy Simulations (LES) to be computationally unfeasible for such computations. Computations with the Reynolds-Averaged Navier-Stokes (RANS) turbulence models are the only alternative that can provide accurate and reliable results without computational cost of DNS and LES. RANS models are also readily available in many CFD software packages. Therefore, this approach is used in the current study to simulate a flow around RDWT. A choice of the specific RANS model in the current study was made based on the results from our previous sensitivity study of flow simulations over a rotating disk [2]. It was found in [2] that the standard k-ε turbulence model [8] provides an accurate description of the flow physics over the rotating disk surface if paired with a suitable grid. In particular, it was demonstrated that combining this model with the “high y+ wall treatment” in STAR-CCM+ allows for accurate solutions over a range of grid stretching, including relatively coarse grids at the wall surface. Computations were also conducted with the shear stress transport (SST) turbulence model [9] because of the model’s ability to accurately represent the structure of adverse pressure gradient flows including flows with separation. To ensure that possible over-refinement of portions of the surface mesh on the turbine would not result in inaccuracies of simulation results, the “all y+ wall treatment” was selected for the SST model in STAR-CCM+. All computations were conducted using the second-order upwind numerical scheme within STAR-CCM+ [1] for enhanced accuracy. Although this choice increases computational cost of simulations, it improves the solution convergence [2]. Hybrid computational grids (meshes) offer a suitable compromise between the solution accuracy and the ease of use [10]. Such meshes as well as polyhedral-only meshes were used in the current study. Both types of meshes were generated in STAR-CCM+. A computational domain for simulations of a flow around a single blade was chosen to be 10Rx20Rx20R, composed of 80,600 cells (Fig. 3). Discussion of the choice of the computational domain dimensions is provided in the Results section. A computational domain for a flow simulation around a quarter of RDWT is shown in Fig. 4. The final domain for these simulations was chosen to be 4Rx4Rx10R, composed of 750,400 cells. This domain is smaller than the domain for the single blade flow simulations due to the overwhelming grid complexity around the quarter of the turbine. The smaller size was chosen in order to limit computational time to less than one hour. Boundary conditions chosen for the two domains were as follows. In both domains, the blade/turbine boundary was represented as a wall with the no-slip condition. The flow enters both domains through a velocity inlet, shown as the plane facing out of the page (normal to the -x direction) (see

Figs. 3, 4). For the single blade simulations, the inlet velocity was prescribed as a uniform inlet velocity of 1m/s in the +x direction.

Figure 3: Selected computational domain for single blade simulations

Figure 4: Quarter turbine computational domain The plane touching the single blade was assigned the symmetry plane boundary condition to artificially force the normal velocity and normal gradients of all variables to be zero at the surface of the plane. The two planes touching the quarter turbine were set to be periodic planes rotating about the x axis, ensuring that the pointwise pressure difference across the planes is zero [1]. The remaining boundaries of both simulations were assigned the pressure outlet boundary condition with a prescribed gage pressure of zero. The pressure outlet boundary condition in STAR-CCM+ allows fluid to leave

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because the windmill flow state axial induction factor (a ≅ 0.20) calculated from this value of the thrust coefficient is the closest to the analytical solution (a ≅ 0.07). The considerable gap between the analytical and computed axial induction factors is expected because the analytical method neglects viscous forces on the blade, adverse pressure gradients on the back of the blade, and vortex shedding. In the second set of simulations, a sensitivity of the thrust coefficient to variations of the polyhedral filled volume beyond the prism layers at the blade surface was examined for both turbulence models. Preliminary simulations revealed that a minimum total prism layer thickness of at least 0.1m ensured residual convergence below four orders of magnitude, as suggested by Baker for accurate drag predictions [10]. A single prism layer was constructed of cells with the target aspect ratio of 2.5. The polyhedral cell growth rates were selected to be 1.05, 1.07, and 1.1 in the three meshes. The resulting estimated axial induction factors were a ≅ 0.21 and a ≅ 0.22 for the SST and k-ε models, respectively. In the third set of simulations conducted with the SST turbulence model, the growth rate for a polyhedral-only mesh was varied. The SST model combined with the “all y+ wall treatment” in STAR-CCM+ was selected because of the increased variation in the cell centroid locations on the blade surface in relation to a mesh with prism layers. The polyhedral cell growth rates were chosen to be 1.05, 1.1, and 1.3 for the three meshes. The resulting axial induction factor was estimated as a ≅ 0.19. In the second and third sets of simulations, the generalized Richardson extrapolation demonstrated by Baker [10] as applicable to the mesh generation was used to estimate the thrust coefficient (and the axial induction factor). The advantage of applying the Richardson extrapolation [11] to meshes in CFD simulations is that it allows for an estimation of a value of thrust for a specified value of error (0.0001 in this study). Provided a constant refinement factor r between separate mesh characteristic lengths (h1,h2,h3) and the resulting thrust coefficients (CT1, CT2, CT3), the order of the pointwise error p and subsequently, the thrust coefficient Ct, may be calculated for the set of three meshes as follows [10]:

the computational domain through such boundaries without returning back into the domain [1]. METHODOLOGY I. The Analytical Model The windmill flow state axial induction factor was found to be a = 0.0685. The thrust and power coefficients corresponding to the windmill flow state axial induction factor were calculated using classical momentum theory and found to be Ct = 0.2552 and Cp = 0.2377. II. The Computational Model Initially, simulations of a flow around the single RDWT blade were conducted with the SST model varying the computational domain width and height to determine appropriate domain dimensions for a hybrid mesh. The initial set of simulations was used to examine the sensitivity of the thrust coefficient solutions to the ratio of domain height and width. The SST turbulence model was chosen because previous study found that simulations with this model are more sensitive to mesh variation. [2] A cell growth ratio of 1.07 in the direction normal to the blade surface was prescribed for the first 10 prism layers next to the blade surface. The total thickness of the prism layers was set to be 5% of the blade length, or 0.05R ≈ 0.17m. The remaining volume was meshed with polyhedral elements with the growth ratio of 1.3 in the direction normal to the blade surface. Figure 5 shows the trend of the thrust coefficient solutions as the domain width to height ratio grows. The domain height of 10R ≈ 34.74 m was kept constant.

𝑝=

log �

𝐶𝑇3 − 𝐶𝑇2 � 𝐶𝑇2 − 𝐶𝑇1 , log(𝑟)

𝐶𝑡 = 𝐶𝑇3 +

Figure 5: Thrust coefficient variation in flow simulations around a single RDWT blade conducted with the SST model.

𝐶𝑇3 − 𝐶𝑇2 . ℎ �( 2 )𝑝 − 1� ℎ3

Here, CT3 is the finest mesh of each set of the three meshes. The fourth (and final) set of simulations was performed with both turbulence models to qualitatively examine the wake flow behind the quarter of RDWT. To simulate dynamic interactions between the turbine and a uniform free stream wind velocity, the quarter of the turbine was prescribed an angular velocity corresponding to the mean rotational speed of the

The final domain chosen for all other single blade simulations was 10Rx20Rx20R and composed of 80,600 cells (Fig. 3). The value of the thrust coefficient corresponding to this domain is shown in Fig. 5 as the furthest data point to the right. The largest domain width to height ratio was chosen

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RDWT prototype at the specified free stream wind velocities collected over 8 days in February and March of 2011 [5]. The computational domain size of the hybrid mesh in flow simulations for the quarter of the turbine was selected to ensure fast computations (less than one hour, as with the single blade simulations). The thickness of the prism layers was set as 0.15R ≈ 0.5 m, the prism layer growth ratio as 1.07, the target prism layer aspect ratio as 2.5, and the polyhedral growth rate as 1.3. The resulting mean thrust coefficient was found to be greater than 1, indicating that simulations correspond to the turbulent wake flow state in which the slipstream has effectively disappeared and the classical momentum theory no longer applies. Buhl [12] derived an equation relating the turbulent wake state thrust coefficient (Ct > 1) to an axial induction factor that best fits empirical data and potentially accounts for the tip and hub losses as well: 𝐶𝑡 =

polyhedral-only meshes [10] seems to be valid for the flow geometry investigated in the current study.

8 40 50 + �4𝑓 − � 𝑎 + � − 4𝑓� 𝑎2 . 9 9 9

Figure 6: Power curves

In our study, for the sake of simplicity, the hub and tip losses were assumed to be negligible (f = 1).

The quarter turbine simulations conducted with the two turbulence models produced power coefficients about 50% smaller than the results of the single blade simulations (see Table 1 and Fig. 6). The decrease in the power extraction occurs because the quarter of the turbine was rotated at the mean angular velocities extracted from the experimental data [5]. Rotation causes the quarter turbine to exert less force in the axial direction on the incoming flow than in a case of the static quarter turbine, as was in flow simulations around the single blade. The axial induction factors shown in Tab. 1 for the quarter turbine simulations indicate that the slipstream dissolved and the turbulent wake flow state was produced [6]. These results need to be further analyzed though. For example, the thrust coefficient computed with the two models for the quarter of turbine is much larger than the one found in experiments. We believe that this is because the current simulations do not include the hub and the turbine rim that do not contribute to power generation and are not accounted for by momentum theory. Nevertheless, these simulations predict the power coefficient in a reasonable agreement with the experimental data. Also the power output profiles obtained with different turbulence models are relatively close to each other for a given flow geometry (Fig. 6). Finally, analytical predictions are in a very good agreement with the experimental data regardless simplifications used in such calculations. The quarter turbine wake was also investigated qualitatively. Predicted vorticity level is shown in Figs.7 and 8 for the two turbulence models, respectively. Although plots are qualitatively similar, simulations with the SST model predict higher vorticity in the wake. All simulations were performed in less than one hour on a desktop computer (Windows 7, 64-bit, Intel Core i7-2600,

RESULTS Mean thrust coefficients, axial induction factors, and power coefficients were calculated over the range of wind speeds. Their values are compared with analytical and experimental results in Table 1. Table 1: Parameters evaluation for the Keuka RDWT

Analytical k-ε, hybrid SST, hybrid SST, polyhedral k-ε, ¼ turbine, hybrid SST, ¼ turbine, hybrid Experimental

a 0.0685 0.2181 0.2050 0.1878 0.6880 0.7040 0.0515

Ct 0.2552 0.6821 0.6518 0.6101 1.3203 1.3483 0.1954

Cp 0.2377 0.5333 0.5183 0.4955 0.2679 0.2467 0.1852

Figure 6 shows computed and analytical power output predictions for the Keuka RDWT along with the normalized power curve obtained from the experimental data [5]. Solid lines correspond to a flow around a single blade. Dash lines correspond to flow simulations over the quarter of the turbine and experimental data for the full turbine (black dash line). Solid black line corresponds to the theoretical maximum [6]. The hybrid mesh simulations of a flow around the single RDWT blade (including one prism layer) conducted with both turbulence models produced the power output close to the theoretical maximum. These simulations did not account for blade rotation. Thus, large thrust and power values (Table 1) are reasonable, but unusable for the power output predictions. The simpler, polyhedral-only mesh simulations produced a power coefficient within 7% of the solutions obtained with the hybrid meshes. The closeness of the results suggests that the Baker’s claim that prism layers offer no obvious advantage over

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3.40GHz, 8BG RAM). To keep computational cost low was a requirement from industry.

The paper presents results of the initial investigation of the RDWT performance with the focus on suitable meshes, computational domain size, and turbulence models. These results will be used in the future studies to conduct flow simulations around the full rotating RDWT. ACKNOWLEDGMENTS The authors would like to acknowledge the support from the Center for Advanced Power Systems (CAPS) at the Florida State University, also from the Center of Advanced Research Computing at the University of New Mexico for providing access to high-performance computing facilities and consulting support for this research, and from CD-Adapco for providing STAR CCM+ to the University of New Mexico for academic purposes. REFERENCES [1] STAR-CCM+. Ver. 6.02.007, CD-Adapco. [2] Snider, M. A. and Poroseva, S. V., 2012, “Sensitivity Study of Turbulent Flow Simulations Over a Rotating Disk,” 42nd AIAA Fluid Dynamics Conference and Exhibit Proceedings. [3] Vermeer, L. J., Sørensen, J. N., Crespo, A., 2003, “Wind Turbine Wake Aerodynamics,” Progress in Aerospace Sciences, 39, pp. 467-510. [4] Sanderse, B., Van der Pijl, S. P., Koren, B., 2011, “Review of Computational Fluid Dynamics for Wind Turbine Wake Aerodynamics,” Wind Energy, 14, pp. 799-819. [5] Rankin, A. J., Poroseva, S. V., Hovsapian, R. O., 2011, “Power Curve Data Analysis for Rim Driven Wind Turbine,” ASME Early Career Technical Journal, 10, pp. 27-32. [6] Lanchester, F. W. 1915, “A Contribution to the Theory of Propulsion and the Screw Propeller,” Trans. Inst. Naval Archi. pp. 57-98. [7] Spera, D. A., 2009, Wind Turbine Technology: Fundamental Concepts in Wind Turbine Engineeering, 2nd Edition, ASME Press. [8] Jones, W. P., Launder, B. E., 1973, “The Calculation of Low-Reynolds Number Phenomena with a Two-Equation Model of Turbulence,” Int. J. of Heat and Mass Transfer, 16, pp. 1119-1130. [9] Menter, F. R., Rumsey, C. L., 1994, “Assesment of TwoEquation Turbulence Models for Transonic Flows,” AIAA-942343. [10] Baker, T. J., 2005, “Mesh generation: Art or Science?” Progress in Aerospace Sciences, 41, pp. 29-36. [11] Richardson, L.F., 1910, “The Approximate Arithmetical Solution by Finite Differences of Physical Problems Involving Differential Equations, with an Application to the Stresses in a Masonary Dam.” Trans. Royal Soc. of London. Series A, 210, pp. 307-357. [12] Buhl, M. L. Jr., 2005, “A New Empirical Relationship between Thrust Coefficient and Induction Factor for the Turbulent Windmill State,” Technical Report, National Renewable Energy Laboratory, Golden, CO.

Figure 7: Vorticity level behind the blade segment (1/4 turbine simulations with the k-ε model at U∞ = 7 m/s).

Figure 8: Vorticity level behind the blade segment (1/4 turbine simulations with the SST model at U∞ = 7 m/s). CONCLUSION The current paper presents the results of a sensitivity analysis of flow simulations around the single blade and the quarter of the new drag-driven design of a wind turbine, the Keuka RDWT. Simulations were conducted with two turbulence models – SST and 𝑘-𝜀 – on hybrid and polyhedral meshes. Results were compared with experimental data [5] and the analytical solution. Computational results obtained with different models on different meshes were found to be close for a given flow geometry. Fast reliable simulations were possible with both turbulence models. Simpler polyhedral meshes produced results comparable with those obtained on more complex hybrid meshes. As expected, the quarter turbine simulations predict more realistic power output. Analytical estimates are in a very good agreement with the experimental data.

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