Scaling Small-Scale Wind Turbines for Wind Tunnel Testing

Abstract

Wind tunnel testing of wind turbines can provide valuable insights into wind turbine performance and provides a simple process to test and improve existing designs. However, the scale of most wind turbines is significantly larger than most existing wind tunnels, thus, the scaling required for testing in a typical wind tunnel presents multiple challenges. When wind turbines are scaled, often only geometric similarity and tip speed ratio matching are employed. Scaling in this manner can result in impractical rotational velocities. For wind tunnel tests that involve Reynolds numbers less than approximately 500,000, Reynolds number matching is necessary. When including Reynolds number matching in the scaling process, keeping rotational velocities realistic becomes even more challenging and preventing impractical freestream velocities becomes difficult. Turbine models of 0.5, 0.4, and 0.3 m diameter, resulting in wind tunnel blockages up to 52.8%, were tested in order to demonstrate scaling using Reynolds number matching and to validate blockage corrections found in the literature. Reynolds numbers over the blades ranged from 20,000 to 150,000 and the tip speed ratio ranged from 3 to 4 at the maximum power point for each wind speed tested.

An experimental and computational assessment of blockage effects on wind turbine wake development

“…If both closed and open test sections are considered, the blockage ratio within this sample of approximately two dozen experiments ranges from 1% to 53%. 7,8,[11][12][13]15 Figure 1 also demonstrates that the majority of existing experiments have been conducted with blockage ratios that are greater than 10%. Given the wide range of blockage ratios observed in literature, an understanding of blockage effects on the initial wake expansion is desirable in order to more carefully consider wake interference studies.…”

Small-Scale Wind Turbine Testing in Wind Tunnels Under Low Reynolds Number Conditions

“…Chen and Liou [18] have documented the correction factor necessary to account for tunnel blockage due to the rotating blades, as seen in Equation 15. …”

“…BEMT design methods as well as demonstrate geometric and Reynolds number scaling 12 JERT-14-1403, Van Treuren [18,19]. Other tests can be conducted on tip speed ratio (TSR), number of blades, optimization of twist, effects of roughness, etc., such as was studied by Gregg and Van Treuren [54,55].…”

“…This blockage factor, , is applied to the coefficient of power based on the U M (C P,M , Equation 18) and used to calculate the corrected power coefficient, C P , as seen in Equation 19. For all the power coefficients, P is the rotor power from the wind turbine (a JERT-14-1403, Van Treuren function of the angular velocity Ω), ρ is the air density, and A = πR 2 is the area swept by the rotating wind turbine blades.…”

“…At Reynolds numbers below 500,000, however, "extreme and unusual behavior is caused by anomalous transition, separation, and bubble formation phenomena" [5]. Burdett and Van Treuren have investigated the case for scaling when Reynolds number matching is included [18]. Table 2 shows that values, such as the rotational velocity, scale as one over the radius squared instead of one over the radius, as seen in Table 1 for rotational speed.…”