Turbulence Sphere Method: Evaluating Wind Tunnel Flow Quality

To maintain dynamic similarity in low-speed flows, the Reynolds number of an experiment must be the same as the Reynolds number of the flow phenomenon being studied. However, experiments performed in different wind tunnels and in free air, even at the same Reynolds number, could provide different results. These differences may be attributed to the effect of the free-stream turbulence inside the wind tunnel test section, which could be perceived as a higher "effective Reynolds number" for the wind tunnel test [1].

A simple method that is used to obtain the effective Reynolds number for a wind tunnel and estimate its turbulence intensity is the use of the turbulence sphere. This method obtains an indirect measurement of the turbulence intensity by determining the turbulence factor of the wind tunnel. The turbulence factor, TF, correlates the effective Reynolds number, R_eff, with the tunnel Reynolds number, Re_test, as

The turbulence intensity can be measured directly by a hotwire anemometry, Laser Doppler Velocimetry, or Particle Image Velocimetry flow field survey. Before the introduction of these direct measurement methods, a turbulence sphere was the primary way to measure the relative turbulence of a wind tunnel. Since the direct methods are usually time consuming and expensive, the conventional turbulence sphere method still remains a fast and inexpensive alternative for gauging air flow quality.

The turbulence sphere method relies on two empirical results: the sphere drag crisis and the strong correlation between the critical Reynolds number, Re_c, and the flow turbulence intensity. The drag crisis refers to the phenomenon that the sphere drag coefficient, C_d, suddenly drops off due to the backward shift of the flow separation point. When the flow reaches the critical Reynolds number, the boundary layer transition from laminar flow to turbulent flow occurs very close to the leading edge of the sphere. This early transition causes a delayed flow separation because the turbulent boundary layer is better able to negotiate an adverse pressure gradient for a longer distance and is therefore less prone to separation than the laminar boundary layer. The delayed separation promotes better pressure recovery, which reduces the size of the wake and the pressure drag and significantly decreases the overall drag.

The turbulence spheres used in this demonstration have one pressure tap at the leading edge and four pressure taps at points located 22.5° from the trailing edge. Three spheres with diameters of 4.0, 4.987 and 6.0 in, respectively, will be investigated. For a smooth sphere, the critical Reynolds number is well defined and occurs when C_D = 0.3. This corresponds to a value of ΔP/q = 1.220, where ΔP is the difference between the average pressure measured at the four rear pressure ports and the stagnation pressure at the sphere leading edge, and q is the flow dynamic pressure.

While Re_c is well defined by C_D and ΔP/q, it strongly depends on flow turbulence. This demonstration using spheres can be used to define the turbulence factor. Early flight measurements found that in the free atmosphere, Re_c = 3.85 x 10⁵ for a smooth sphere. The free air critical Reynolds is correlated to the wind tunnel turbulence by the following equation:

For each sphere, the stagnation pressure and the pressure at the aft ports were measured. The difference between these two values gives the pressure difference, ΔP. The total pressure, P_t, and static pressure, P_s, of the test section were also measured, which are used to determine the test dynamic pressure, q = P_t - P_s, and the normalized pressure . The ambient air pressure, P_amb, and the airflow temperature was also recorded to calculate the air flow properties, including the air density, ρ_test, and viscosity, μ_test. The density is obtained using the ideal gas law, and the viscosity is obtained using Sutherland's formula. Once the air density and viscosity are determined, the test Reynolds number can be computed.

By plotting the test Reynolds number with respect to the normalized pressure difference, the critical Reynolds number for each sphere was determined (Figure 1). The critical Reynolds number corresponds to a normalized pressure value of = 1.220. The three curves for the three spheres provide a more accurate estimate of the critical Reynolds number, Re_Ctunnel, because an averaged value is used. With the Re_Ctunnel estimate, the turbulence factor, TF, and the effective Reynolds number can be determined according to the following equations:

and

Figure 1. Critical Reynolds number for each sphere.

Turbulence spheres are used to determine wind tunnel turbulence factor and estimate the turbulence intensity. This is a very useful method to evaluate a wind tunnel flow quality because it is simple and efficient. This method does not directly measure the air velocity and velocity fluctuations, such as hotwire anemometry or particle image velocimetry, and it cannot provide a complete survey of the flow quality of the wind tunnel. However, a complete survey is extremely cumbersome and expensive, so it is not suitable for periodic checks of the wind tunnel turbulence intensity.

The turbulence factor can be checked periodically, such as after making minor modifications to the wind tunnel, to gauge the flow quality. These quick checks can indicate the necessity of a complete flow turbulence survey. Other important information obtained from the turbulence factor is the effective Reynolds number of the wind tunnel. This correction on the Reynolds number is important to ensure the dynamic similarity and the usefulness of data obtained from scaled models and their application to full-scale objects.

The turbulence sphere principle can be also used to estimate the turbulence level in other environments besides the wind tunnel test section. For example, this method can be used to measure inflight turbulence. A turbulence probe can be developed based on the principles of the turbulence sphere and installed in airplanes to measure turbulence levels in the atmosphere in real-time [2].

Another application is the study of flow structures during a hurricane. In situ measurements of the flow inside a hurricane can be extremely dangerous and complicated to obtain. Methods like hotwire anemometry and particle image velocimetry are unattainable in these conditions. The turbulence sphere principle can be used to make an expendable measurement system which can be placed in a region prone to hurricanes to measure the flow turbulence inside a hurricane safely and at a low cost [3].