### Overview

Source: Jose Roberto Moreto and Xiaofeng Liu, Department of Aerospace Engineering, San Diego State University, San Diego, CA

Wind tunnel tests are useful in the design of vehicles and structures that are subjected to airflow during their use. Wind tunnel data are generated by applying a controlled air flow to a model of the object being studied. The test model usually has a similar geometry but is a smaller scale compared to the full-sized object. To ensure accurate and useful data is collected during low speed wind tunnel tests, there must be a dynamic similarity of the Reynolds number between the tunnel flow field over the testing model and the actual flow field over the full-sized object.

In this demonstration, wind tunnel flow over a smooth sphere with well-defined flow characteristics will be analyzed. Because the sphere has well-defined flow characteristics, the turbulence factor for the wind tunnel, which correlates the effective Reynolds number to the test Reynolds number, can be determined, as well as the free-stream turbulence intensity of the wind tunnel.

### Principles

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 Δ

*P*/

*q*= 1.220, where Δ

*P*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 Δ

*P*/

*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 10

^{5}for a smooth sphere. The free air critical Reynolds is correlated to the wind tunnel turbulence by the following equation:

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### Procedure

**1. Preparation of turbulence sphere in the wind tunnel**

- Connect the wind tunnel pitot tube to port #1 on the pressure scanner, and connect the static pressure port to port #2 on the pressure scanner.
- Lock external balance.
- Fix the sphere strut to the balance support inside the wind tunnel.
- Install the sphere with 6 in diameter.
- Connect the leading-edge pressure tap to port #3 on the pressure scanner, and connect the four aft pressure taps to port #4 on the pressure scanner.
- Attach the air supply line to the pressure regulator, and set the pressure to 65 psi.
- Connect the manifold of the pressure scanner to the pressure line.
- Start up the data acquisition system and pressure scanner. Make sure to turn them on at least 20 minutes prior to the test.
- Estimate the maximum dynamic pressure based on the free-air critical Reynolds number for a smooth sphere: . See Tables 1 and 2 for recommended test parameters.
- Define the dynamic pressure test range from 0 to
*q*and define the test points by dividing the range in 15 intervals._{max}

Table 1. Parameters for the first test.

Sphere diameter (in) |
q_{Min} [in H2O] |
q_{Max} [in H2O] |

4 | 4 | 6 |

4.987 | 2 | 3.4 |

6 | 1 | 2.4 |

Table 2. Parameters for the second test.

Sphere diameter (in) |
q_{Min} [in H2O] |
q_{Max} [in H2O] |

4 | 3.4 | 7.2 |

4.987 | 1.3 | 5.1 |

6 | -- | -- |

**2. Conducting stabilization and pressure scan measurement**

- Read the barometric pressure and room temperature and record the values.
- Apply the corrections to the barometric pressure using equations provided by the manometer manufacturer.
- Setup the data acquisition software and connect it to the pressure scanner, setting the proper IP address.
- Insert the following commands pressing enter after each command.

>calz

>set chan1 0

>set chan 1-1..1-4

>set fps 10 - Check that the test section and wind tunnel are free from debris.
- Close the test section doors.
- Set the wind tunnel speed dial to zero.
- Turn on the wind tunnel and wind tunnel cooling system.
- With the wind speed at 0 mph, start recording data, then insert the following command to scan the pressure:

>scan - Record the wind tunnel air temperature.
- Increase the wind speed up to the next test point dynamic pressure as defined in step 1.10.
- Wait until the airspeed stabilizes, then repeat steps 2.9 - 2.11 until the last test point is executed.
- Slowly reduce the airspeed to zero.
- When all the points have been measured, replace the 6 in sphere with the next sphere following steps 1.2 - 1.5.
- Repeat steps from 2.3 - 2.14 to repeat the stabilization and pressure scan experiments.
- Wait the wind tunnel to cool down after the test is executed for all three spheres.
- Turn off the wind tunnel and data acquisition software.

In aerodynamics testing, wind tunnels are invaluable to determining the aerodynamic properties of various objects and scaled aircraft. Wind tunnel data is generated by applying a controlled flow of air to a testing model, which is mounted inside the test section. The testing model typically has similar geometry, but at a smaller scale, as compared to the real object.

In order to ensure usefulness of the data generated in wind tunnel tests, we must ensure dynamic similarity between the wind tunnel flow field and the actual flow field over the real object. To maintain dynamic similarity, the Reynolds number of the wind tunnel experiment must be the same as the Reynolds number of the flow phenomenon being tested.

However, experiments performed in wind tunnels or in free-air even with the same test Reynolds number can provide different results due to the effects of free-stream turbulence inside the wind tunnel test section. These differences may be perceived as a higher effective Reynolds number for the wind tunnel. So how do we correlate testing in the wind tunnel to free-air experiments?

We can estimate the intensity of the free-stream turbulence in the wind tunnel using a well-defined object with known flow behavior, like a sphere. This method is called the turbulence sphere method. The turbulence sphere method relies on the well-studied condition called the sphere drag crisis.

The sphere drag crisis describes the phenomenon where the drag coefficient of a sphere suddenly drops as the Reynolds number reaches a critical value. When the flow reaches the critical Reynolds number, the boundary layer transitions from laminar to turbulent very close to the leading edge of the sphere. This transition, as compared to flow at a low Reynolds number, causes delayed flow separation and a thinner turbulent wake and thus decreased drag.

Therefore, we can measure the drag coefficient of a sphere at a range of test Reynolds numbers to determine the critical Reynolds number. This enables us to determine the turbulence factor, which correlates the test Reynolds number to the effective of Reynolds number.

In this experiment, we will demonstrate the turbulence sphere method using a wind tunnel and several different turbulence spheres with built-in pressure taps.

This experiment utilizes an aerodynamic wind tunnel as well as several turbulence spheres with varying diameter to determine the turbulence level of the free-stream flow in the tunnel test section. The turbulence spheres, each with a pressure tap at the leading edge as well as 4 pressure taps located 22.5° from the trailing edge, have well-defined flow characteristics, which help us analyze turbulence in the wind tunnel.

To set up the experiment, first connect the wind tunnel pitot tube to pressure scanner port number 1. Then, connect the wind tunnel static pressure port to port number 2. Now, lock the external balance. Fix the sphere strut in the balance support inside the wind tunnel.

Then, install the 6 in sphere. Connect the leading edge pressure tap to the pressure scanner port number 3 and connect the four aft pressure taps to port 4. Connect the air supply line to the pressure regulator, and set the pressure to 65 psi. Then, connect the manifold of the pressure scanner to the pressure line regulated at 65 psi.

Start up the data acquisition system and pressure scanner. While the system equilibrates, estimate the maximum dynamic pressure, q max, necessary for the test based on the free-air critical Reynolds number for a smooth sphere.

Here, we list the recommended test parameters for the first and second test of each sphere. Now, using these parameters, define the dynamic pressure test range from zero to q max, and then define the test points by dividing the range into 15 intervals.

Before running the experiment, read the barometric pressure in the room and record the value. Also, read the room temperature and record its value. Apply the corrections to the barometric pressure using the room temperature and the geolocation using equations supplied by the manometer manufacturer.

Now, set up the data acquisition software by first opening the scanning program. Then, connect the software DSM 4000, which reads and calibrates the signal from the pressure sensor, by setting the proper IP address and pressing connect. Insert the commands as shown, which are defined by the manufacturer, remembering to press enter after each command.

Now that the software is ready, check to make sure that the test section and wind tunnel are free from debris and loose parts. Then, close the test section doors and check to see that the wind tunnel speed is set to zero. Turn on the wind tunnel, and then turn on the wind tunnel cooling system.

With the wind speed equal to zero, start recording data on the data acquisition system, then type the command scan to start pressure measurement. Then, record the wind tunnel temperature. Since wind speed is directly related to the dynamic pressure, increase the wind speed until you reach the next dynamic pressure test point. Then, wait until the air speed stabilizes and commence the pressure scan again. Be sure to record the wind tunnel temperature. Continue the experiment by conducting a pressure scan at each of the dynamic pressure points, recording the wind tunnel temperature each time. When all points have been measured for the 6-inch sphere, repeat the stabilization and pressure scan experiment for the 4.987 inch and 4-inch turbulence spheres.

For each sphere, we measured the stagnation pressure at pressure port 3 and the pressure at the aft ports via pressure port 4, which are subtracted to give the pressure difference, delta P. We also measured the test section total pressure, Pt, from pressure port one and the static pressure, Ps, from pressure port two, which are used to determine the test dynamic pressure, q.

Then we can calculate the normalized pressure, which is equal to the pressure difference divided by the dynamic pressure. The air pressure and the airflow temperature were also recorded, enabling the calculation of airflow properties. Recall that there is a slot in the test section, meaning that it is open to ambient air. Therefore, assuming that there is no streamwise pressure gradient in the test section, the absolute value of the local static pressure of the free-stream flow can be used as the ambient air pressure.

The density is obtained using the ideal gas law and the viscosity obtained using Sutherland's formula. Once the air density and viscosity have been determined, we can calculate the Reynolds number. Here we show a plot of the Reynolds number versus the normalized pressure difference, delta P over q.

Using this plot, we can determine the critical Reynolds number for each sphere, since the critical Reynolds number corresponds to a normalized pressure value 1.22. With each critical Reynolds number, we can evaluate the turbulence factor and the effective Reynolds number. The turbulence factor is correlated to the intensity of the turbulence in the wind tunnel.

In summary, we learned how the free-stream turbulence affects testing in a wind tunnel. We then used several smooth spheres to determine the turbulence factor and intensity of the wind tunnel flow and evaluate its quality.

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### Results

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, Δ*P*. The total pressure, *P _{t}*, and static pressure,

*P*, of the test section were also measured, which are used to determine the test dynamic pressure,

_{s}*q*=

*P*-

_{t}*P*, and the normalized pressure . The ambient air pressure,

_{s}*P*, and the airflow temperature was also recorded to calculate the air flow properties, including the air density,

_{amb}*ρ*, and viscosity,

_{test}*μ*. 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.

_{test}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.

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### Applications and Summary

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].

Name |
Company |
Catalog Number |
Comments |

Equipment |
|||

Low-speed wind tunnel | SDSU | Closed return type with speeds in the range 0-180 mph | |

Test section size 45W-32H-67L inches | |||

Smooth spheres | SDSU | Three spheres, diameters 4", 4.987", 6" | |

Miniature pressure scanner | Scanivalve | ZOC33 | |

Digital Service Module | Scanivalve | DSM4000 | |

Barometer | |||

Manometer | Meriam Instrument Co. | 34FB8 | Water manometer with 10" range. |

Thermometer |

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### References

- Barlow, Rae and Pope. Low speed wind tunnel testing, John Wiley & Sons, 1999.
- Crawford T.L. and Dobosy R.J. Boundary-Layer Meteorol. 1992. 59; 257-78.
- Eckman R.M., Dobosy R.J., Auble D.L., Strong T.W., and Crawford T.L. J. Atmos. Ocean. Technol. 2007; 24; 994-1007.