Test equipment (part 1)

One of the key areas for ensuring good CFD correlation for floor/diffuser design is the front wheel wake and tyre squirt. Measuring surface flow/shear direction is relatively simple, using uses wool tufts and flow-vis paint, both of which are cheap to obtain and easy to apply. When it comes to measuring pressures (and thus being able to get an accurate estimate of actual aerodynamic performance), the required sensors add a whole different level of complexity and cost. For measuring off-body flow such as wheel wake, the complexity is even greater and requires consideration of both local airflow direction and static pressure, in an area where there is no car to mount to. The answer is an aero rake, modern versions of which are usually made using metal printing/sintering. 

The most important items to obtain were the pressure sensors, as these are applicable to many different test cases and equipment: static taps, rakes (Kiel probes), pitot-static probes, and yaw probes. The cheapest differential pressure sensors we could find were around $30 each, so the question was then how many do we want, and how many can we justify buying?

We knew we needed one for a pitot-static tube, one for a yaw probe, and a decent number to get sufficient resolution for rakes and static tap setups to get enough coverage and detail with a single setup. 20 sensors seemed like a good number and was enough to push the price down to $28 each with a bulk discount, so they cost us around $560 shelf price, with a bit of sponsorship getting this down closer to $300. Getting only 10 was an option if the budget was too tight, but it would have meant running a repeat of each track test with the sensors connected in different places.

To maximise the precision of the data, we needed sensors that were tuned to the pressure range we were expecting. We considered the maximum pressure magnitude we would ever want to measure would be for the pitot-static probe at Vmax. Total pressure at this speed on a day with dense air is 625 Pa. Unfortunately this was too high for a 500Pa or 2.5-inch-H2O sensor, and 1000Pa sensors were rare, so we settled for 5-inch-H2O sensors with about twice the range we need, but this was acceptable considering the datasheet states the expected maximum error is 20 Pa.   

Upon receiving the sensors, we handed them and a list of our expected operating conditions to the low voltage team to do up some shiny new PCBs that would spit out CAN values. The initial design had just 10 sensors and was very spacious to allow easy component replacement and attachment/detachment of pneumatic tubes while we were still figuring things out and calibrating resistor values. After we were happy with their performance, a smaller and denser board with all 20 sensors was made.

The next items to acquire were the various probes. Off-the-shelf pitot-statics started at around the $50 for a small and cheap option, so not cheap but still somewhat reasonable. Kiel probes on the other hand were a couple hundred dollars each for low order quantities, and much the same for yaw probes. We wanted 18-20 Kiel probes, so we had no choice but to make them ourselves.

Pitot-static probe

Luckily we already had a single pitot-static tube from a few years ago that had never been used. For the Kiel probes, we ordered a couple metres of stainless steel tubing, and 20 metres of flexible pneumatic tubing. We used a resin printer to make the inlet shapes for both probe types, starting with a pitot inlet shape to see if it would return values acceptably close to the off-the-shelf model. Both probes are shown in Figure 2, and from looking at them you'd never know that one cost about $50 and one cost $8. 

We took both probes to the wind tunnel for testing, with two goals:

1. Make sure the custom probe gave identical readings to the purchased probe to confirm that the methods used to seal the internal connections was suitable, and that the inlet shape and size was not affecting readings

2. Use the known airspeeds in the wind tunnel to create a voltage-pressure calibration function for each of the 20 sensors.

In tests conducted between 5 ms-1 and 20 ms-1, the custom pitot-static tube matched the OEM probe results. The differential pressure sensors demonstrated only minor small fluctuations around a stable value, with no hysteresis or repeatability errors within the precision of the measurements taken. Voltage offsets between the sensors were significant, so we installed different resistors depending on the offset to avoid clipping at either end of the pressure range. The remaining smaller offsets can be dealt with by simply measuring and applying the offset to the recorded data. Each sensor had a slightly different voltage-pressure slope that wouldn't have caused any issues if we assumed they were identical, but since we had the means of easily calibrating them all, we did. 

Yaw angle sensitivity tests were conducted by adjusting the motorised load cell angle to which the probe was mounted, allowing precise angular measurements. As expected, the pitot-static tubes were highly yaw-sensitive, with readings changing by 8% with only 5 degrees of yaw in either direction. 

Kiel probe

We've shown the custom pitot-static tube is perfectly adequate for its job, but we'll still use the single OEM probe for its more durable plastic. Next up were the Kiel probes.

A Kiel probe works by forcing freestream flow to be aligned with the dynamic port before being expelled downstream of the inlet. This was my first experience with Kiel probes, so I wasn't sure what the critical design criteria were, or how they would affect the readings it gave. Some research and comparison of different available models suggested most of the design intricacies were focussed on maximising the stability of the reading, and that just achieving a moderate level of yaw insensitivity would not be too difficult. I drew up an inlet design that would hopefully be strong enough to survive normal handlign and use when printed in resin. The inlet ended up larger in diamter than the 4mm tubing after smaller versions failed to print properly. This meant there would be some flow curvature over the outlet/bleed holes that could alter the pressure and affect the readings, but this wouldn't matter if they had their own calibration function. 

I designed the Kiel probes to have a two-part assembly for easy installation; the whole probe is held together with just the friction of the pneumatic tubing in an interference fit between the inner and outer tubes. This saves lots of time setting up at the track when there's up to 20 probes to install.

Another wind tunnel test session was conducted for the new custom Kiel probes to determine their pressure map, and yaw sensitivity. The tests we conducted are summarised below.

Voltage-pressure mapping and linearity (conducted with pitot-static probes)

A test of all 20 sensors to ensure there were no issues with them, to calibrate the probes, and to measure linearity of the voltage/pressure relationship. The largest measured deviation from linearity for any sensor was 0.040 V. 

Repeatability

Random airspeeds were chosen to jump between to ensure the reading was the same for a given airspeed and not dependent on the prior airspeed or rate of change. Results showed no bias or repeatability issues, and no hysteresis error. 

Kiel probe manufacture tolerance

Testing all 20 Kiel probes on a single sensor to ensure slight differences in manufacture tolerance such as the airtight seals, and the length of the probe or inlet, were not affecting the measurements obtained. The largest deviation for any speed between any two probes was 0.005 V, or 0.1% of the voltage range. This was considered low enough to be negligible and thus all probes were treated as equivalent.

Yaw sensitivity

Using a Kiel probe, the angle of incidence was adjusted from 0 (fully aligned) until a significant change in reading was observed. Readings remained stable up to 35 degrees for two tested airspeeds. There was some slight fluctuation from a constant value as angle changed while still below 35 degrees, with a maximum deviation of 0.025 V. 

Professional Kiel probes are typically accepted as having somewhere in the range of 45 degrees of yaw insensitivity, so achieving 35 degrees was a pretty good result. 

Total uncertainty calculation

Uncertainty estimates for a measurement taken using an arbitrary sensor with an arbitrary Kiel probe were calculated based on these results using a simple sum of squares, or 2-Norm approach, with an additional 1.25 factor of safety. 

U_Total = sqrt((U_Linearity)^2+(U_Manufacture)^2+(U_Yaw)^2+(U_Noise)^2)

U_Total = sqrt((0.04)^2+(0.005)^2+(0.025)^2+(0.02)^2)

U_Total = 0.048 Volts x 1.25 = 16 Pascals

This was a pleasing result given the sensor datasheet estimated the maximum error to be 18 Pa for just the sensor alone, before considering any other sources such as those tested above. 

Temperature sensitivity

The sensors were placed on a heated 3D printer bed raised from ambient (15 degrees) up to 40 degrees. An average change of around 0.1 V was noted for every 10 degree change in temperature. This is a significant sensitivity, but should be reduced to negligible levels by applying a zero offset at the start of each test run. During longer test runs or where temperature is expected to change noticeably, sacrificing one sensor to be left open to ambient pressure inside the cockpit would allow its reading to be used as a temperature offset for the remaining sensors.