The RTD(Resistance Temperature Device) flowmeter LWDAQ(Long-Wire Data Acquistion) instrument measures the mass flow rate of gas through a pipe. The flowmeter uses a single RTD sensor operating under the theory that the rate of mass flow is proportional to the rate at which a gas is able to cool a heated RTD sensor. More accurately, dimensional analysis shows that mass flow is proportional to [(pipe_area × sensor_thickness × sensor_density × sensor_heat_capacity) ÷ (cooling_inverse_time_constant × gas_heat_capacity) ]. In theory, for a given sensor and calibrated pipe, mass flow will be proportional to the cooling inverse time constant (ITC). Provided the flowmeter is calibrated for the operating temperature, pressure, and gas we predict that a standard deviation of measurements better than 1% can be achieved.
The Flowmeter Head(A2053F) provides a constant, precise amount of current to up to 11 RTD sensor elements. We apply constant current to the sensor element for a given amount of time which causes the element to increase in temperature. We measure this temperature as described in the Thermometer Instrument. The current is then removed from the element,the temperature of the sensor begins to decrease be it from the surrounding air or gas flow, and will continue to decrease until it reaches the ambient temperature. We measure the temperature not when it reaches ambient temperature, but at some fraction of the time before it reaches ambient temperature. We calculate the inverse time constant as follows: ITC = [ln(end_temp_above_ambient_C) - ln(start_temp_above_ambient_C)] ÷ time_from_start_to_end. The next measurement is taken no sooner than 5 time constants (about 30 seconds) after the previous measurement to ensure the sensor element has had sufficient time to reach ambient temperature. Below is an example output from the LWDAQ Flowmeter instrument.
To prove our instrument's effectiveness and to relate it's measurements to actual mass flow, we used two mass flow meters independent of our LWDAQ system. From these mass flowmeters we are able to obtain through calculation the actual mass flow as well as data to which we compared our measurements. These two instruments provide a voltage output which is proportional to the mass flow.
We obtained large canisters of argon and nitrogen. Most commercial flowmeters are calibrated for nitrogen, and the ATLAS experiment for which this flowmeter is destined uses argon. We have both gases available for testing. The gas canister, be it argon or nitrogen, connects to a gauge pressure manometer. The ATLAS experiment will be operating at 30 psi above atmospheric pressure which corresponds to 44 psi absolute pressure. The manometer allows us to measure the pressure accurately during many experimental cycles and affords us a degree of consistency. The gas flows through the manometer and proceeds into one of the two test apparatus' available. The test apparatus' will be explained later. Next in the chain comes the commercially available Omega Mass Flow meter FMA-A2108. Following this is a Bronkhorst flowmeter/control valve model F-201C-RA-33-V. The gas exits the Bronkhorst control valve into free air. See Figure 2.
The Omega and Bronkhorst flowmeters provide a voltage output which corresponds to the mass flow. We read this voltage using the Input/Output Head (A2057) which connects to the LWDAQ driver with Ethernet Interface (A2037E). The Bronkhorst control valve is adjusted using the same Input/Output Head that acquires the voltage outputs.
The A2053 RTD Head heats and acquires temperature measurements from the RTD elements inserted in either of the two test apparatuses. The RTD Head, like the Input/Output Head, connects to the ethernet driver.
We wrote a TCL/Tk script to allow us to collect data from all parts of the experiment remotely and automatically. The gas flow can be altered as needed and any changes to the gas flow can be recorded as changes are made. The only hand operation needed is to turn on the gas at the canister.
As stated above, we have two sensor blocks. The first is named A-1 and can be seen in Figure 3. The elements are inserted into machined aluminum blocks which have different pipe diameters. Sensor Block A-2 has the elements inserted into an aluminum block which assures us exactly the same pipe diameters for each element. Also, as noted in Figure 4, the gas flows across the elements in the same direction. This was achieved by connecting the gas to the inlet of the first element, then chaining the rest of the elements in series. The looping plastic tubes provide the series connections. The plastic tubes are of equal length.
In both sensor blocks, the sensor elements are placed in the gas flow in the same fashion. The shape of the RTD elements is that of a rectangle with a bit of thickness. The elements are inserted so that the thin side faces the oncoming gas flow and provides the least amount of disturbance to the gas flow. See Figure 5.
The ability of the commercially available flowmeters to provide precise and accurate measurements is one of the factors in our proof of how well our RTD flowmeter performs. The best precision we achieve with the commercial flowmeters is the best precision we can prove for our own flowmeter.
The Omega flowmeter model FMA-2108's data sheet can be found here. The gas flow range for this particular model is 0-5 SLM, it's claimed accuracy is ±1% full scale, and it's output is linear. Also of interest is it's full scale repeatability of ±0.15%.
The Bronkhorst Flowmeter model F-201C-RA-33-V's specification sheet can be found here. The gas flow range is up to 1 ln/min, it's claimed accuracy is ±0.5% of reading plus ±0.1% of full scale. The controller's stability is less than ±0.1% full scale and repeatability is ±0.2%.
Our first experiment tested the precision of the two meters at the maximum flow rate permitted by the Bronkhorst flow controller. The valve was set to fully open, and 50 samples were taken with no delay between readings. Our test was run using nitrogen at 44psi absolute pressure. We found the Omega's error to be ±0.5%, and the Bronkhorst's error to be ±0.1%. See Table 1 and Figure 6.
Our second experiment tested the meters over the full range of flow 0-100% valve opening. We tested the output linearity of the meters, and how well the meters track each other. The experiment was performed using nitrogen at 44psi. The Bronkhorst valve was used to open the valve in steps. Our TCL/Tk script performed the following steps: 1. Set Valve, 2. Wait 25 seconds for valve to settle, 3. Take both meter readings, 4. Increment valve opening by 2%, 5. Repeat all steps for 0-100%.
The graph in Figure 7 show the linear output for both meters as the valve is opened. The Omega meter has 5 times the range of the Bronkhorst meter. The Bronkhorst's maximum analog voltage output(i.e. it's flow measurement output) is 5V. After it reaches approximately 5V, the flow measurements flatten out as in Figure 7. This flattening out occurs when the valve has surpassed a setpoint of 90%. From here on, we will consider all readings above 90% as invalid.
The graph in Figure 8 shows the precision of both meters over the valve's range of flow. We fit a straight line to the data to find the residuals. The Omega is within it's stated bounds with a full scale precision of ±0.5%. The Bronkhorst meter is far within it's bounds with a full scale precision of ±0.2%. It is interesting to notice the cyclical nature of the Bronkhorst residual values. The four sharp edges seen in the graph all the same height(in V) which seems to indicate the cyclic changes are either a function of the Bronkhorst reading or a mechanical function of the Bronkhorst valve such as screw lash. We therefore assume the cyclic behavior is not a function of actual gas flow.
Finally, the meters were plotted against one another to verify that they track linearly. As you can see in Figure 9, they do in fact track approximately linearly.
We will first show how our RTD flowmeter elements are able to track mass flow. We show that the elements are sensitive to mass flow nuances, and how mass flow can differ in different pipe diameters. We will then go on to show the precision and repeatability of our RTD elements.
In the first experiment with our RTD flowmeter, we used sensor block A-1 which has two different pipe diameters and has a known irregularity. There are 4 elements in A-1 wherein elements 1 and 2 are in a 6mm diameter pipe and elements 3 and 4 are in a 10mm diameter pipe. The irregularity in sensor block A-1 lies in it's design. Looking back at Figure 3, you will see that there is an extra piece of pipe connected in front of element 1(red/black wire). In earlier experiments, we found that the absence of this extra pipe creates a disturbance in the flow which causes irregular measurements between the two elements in that particular pipe. So, in this experiment we show the ability of our flowmeter to track this irregular flow.
Let's say that when we look at the sensor block(regardless of orientation), the gas flows into the sensor block from the left, and exits from the right. Now, looking at Figure 3, the extra pipe is on the left and element 1(red/black wire) is the first in line to see the gas flow. We call this the forward direction. The forward direction has stable flow across all four sensors, the reverse flow direction has the irregular flow across two of the sensors(elements 3,4). We took measurements for both the forward and reverse direction. Figure 10 shows these results.
In comparing the inverse time constant residual curves in the forward and reverse directions, we notice that in the forward direction both element pairs in similar pipe diameters are consistent with each other, while in the reverse direction one pair of elements' residual curves are very inconsistent. The inconsistency in the flow measurements for this pair of elements is the result of gas flow changing pipe diameters very close to the elements causing turbulence and eddies. The turbulence and eddies in close proximity to these elements cause temperature fluctuations and therefore irregular flow measurements.
In the second experiment, we used sensor block A-2 which has all four elements in exactly the same pipe diameters. Also, the lengths of tubing between each pipe are similar and there is enough distance before and after the sensor in the pipe to prevent unwanted turbulence as seen in sensor block A-1. The first set of measurements show how similar the flow curves are for four elements. In figure 10, we see that all four elements seem to track with similar curves, except for simple offsets.
Provided pipe diameters are similar and that gas flow has had a chance to stabilize itself before reaching the elements, the elements track similarly. Now that we know 4 elements track gas flow similarly, we explore the repeatability of these measurements. To do this, we took measurements from elements 1 and 2 over the full flow range for 5 cycles on different days. One cycle was taken after having removed and reinstalled element 1 to see if reinstallation had any effect on measurements. See figure 11.
Looking at the graphs in Figure 11, we see that one element can precisely measure mass flow rates. It is interesting to note how the inverse time constant is not quite a straight line over the flow range, and because of this the residual values over the flow range are second-order in nature. If the residual values were not repeatable, we would have a problem in calibrating the sensor elements to produce precise results. We would then be left with a precision of no better than 10%. As it turns out, the standard deviation for a single element over the full flow range is 0.1%. See Figure 12.
Side bar: At first glance, we thought the reason behind the curvature in the inverse time constant readings was because the gas was at first laminar, then went into a transition period, and finally became turbulent. To determine whether the gas flow in our instrument was in fact changing from laminar to turbulent, we calculated the Reynold's number. A lower critical Reynold's number value of around 2000 would be a good indicator of a transition from laminar to turbulent. We calculated a Reynold's number at the maximum flow rate and found the number to be well below 1000. We can now assume our flow is strictly laminar.
Using sensor block A-2, we performed an experiment to find the resolution of an element's readings over numerous samples. The Bronkhorst valve was set to a 50% setpoint. Keeping the valve set at one opening took any error the valve might introduce out of play. We then took 56 readings from elements 1,8,9,and 10 with a 30 second delay between each reading. All the samples for each element were averaged together, and the deviation from the mean for each sample was plotted. See Figure 13.
We see that the standard deviation over 56 samples is approximately 0.0003(1/s). Now we look at Figure 11 and see that the slope of the straight line fit for element 1 is approximately 0.1(1/s*valve(%)). This gives us a resolution at 50% valve opening of 0.3%.
Our commercially available mass flowmeters will not always be available to us for use as a reference. As such, we must use one of our RTD elements as a reference. We have shown above that our elements have a standard deviation of 0.1% and a resolution at 50% valve opening of 0.3%. Now, we can assume that our own elements can be used as references. As of this writing, we will be using element 1 in sensor block A-2, position 1 as a reference element for which to base our future measurements from other elements.
Having chosen our reference element, we took several sets of data which relate element 1's measurements to the Bronkhorst's measurements. Each set of data includes measurements over the full range of valve opening in 2% increments. This set of data is what we use to determine actual mass flow rates for a given inverse time constant measurement. It is also used as calibration data for all other elements, and future reference elements.
Using a linear interpolation function, we sought to find the minimum amount of data points necessary to effectively calibrate sets of data. The linear interpolater takes as input an 'x' coordinate, and a set of data in the form xi,yi...xn,yn. The interpolater takes the input x, finds the nearest two xi points in the data set and fits a straight line between these two points. Then using the equation which relates the two xi points, the y value for the x input is found. The interpolater has the possibility of introducing error when the data points are spread too far apart and the line formed from the data set has a large curve between the two points. In this case, the output y value maybe a bit above or below the actual y value.
We took the 50 data points relating element 1's inverse time constant to the Bronkhorst measurements, and we extracted three differently sized calibration data sets...10,25, and 50 points. Each calibration data set was used as the xi,yi data set input for the linear interpolater. The x input to the linear interpolater was each of the 50 inverse time constant values for element 1. When the linear interpolater was run for each calibration set, the value returned was the interpolated Bronkhorst voltage reading. The results can be seen in Figure 14.
When the 50 point calibration data was used to interpolate the Bronkhorst reading from the 50 point data set, the input inverse time constants land exactly on points in the calibration data, producing zero error as expected. When the 25 point calibration data was used, half of the data point produce zero error, while the rest produce some error. Then when the 10 point calibration data was used, 10 points produce zero error and the rest show even more error then the last.
Taking 50 data points for calibration data and be quite lengthy and doesn't provide significantly better linear interpolation performance, so to strike a middle ground we chose to use 20 point calibration data sets.
In acquiring calibration data, first we take data from our reference element(element 1) and the Bronkhorst meter at valve openings from 0-100% in 5% increments. This gives us a relationship between inverse time constants and mass flow. Next, we take data using the same valve range and increments from our reference element and the element which needs to be calibrated. We create text files which contain data in the format seen below in Figure 15.
Once the calibration data is saved to a text file, the "to-be calibrated" element is now calibrated. We acquire calibration data for every element. Here is an example of how the calibration data is used: 1. A new itc measurement is taken from a calibrated element, 2. Our TCL/Tk script takes the itc value, opens up the text file which relates the reference element to the calibrated element, 3. We linear interpolate to find the reference itc value associated with the calibrated element's itc value, 4. We take the linear interpolated itc value and interpolate again using the data which relates the reference element's itc to the Bronkhorst's data, 5. This linear interpolated Bronkhorst voltage is used to calculate the actual mass flow rate.
Our first step in showing calibration performance was taking raw inverse time constant measurements from 10 elements at different times and days. We took measurements across the valve range in 5% increments. The itc values for each element at a given valve opening were averaged together. The average itc value was then subtracted from each element's raw itc value at each valve opening. We plotted these deviations in the graph below. We see that the maximum deviation is 0.015(1/s) and the minimum deviation is -0.015(1/s). We find the difference of these two values and divide by the maximum achievable itc value for the flow range. This calculation shows the precision amongst 10 uncalibrated elements is 12% over the full range
Our single point calibration means we take a single point(i.e. at 50% valve opening) from a set of data which relates reference element 1 to a given element and find the difference between the two values. Then the difference is added to the newly acquired itc measurement for the given element across the entire range of measurements. We then find the difference between each single-point calibrated elements' itc value and the respective reference element 1's itc value to find the deviations. We the find the maximum standard deviation of these differences and divide by the maximum achievable itc value for the flow range. From this we see the precision amongst single point calibrated elements is 1.6% over the full range. Below is a graph which shows the performance of our single point calibrations for 9 elements with respect to the reference element 1.
We ran several experiments to show the performance of our 20 point calibrated elements. We took two sets of data under several conditions for 3 elements. The first data set is 10 cycles at 50% valve opening and the second data set is one cycle over the full range of valve opening 0-100% in 4% increments. These two data sets were taken on different days(possible temperature/humidity change) and on these days the gas pressure was changed. It can be seen from the data below, that the ambient temperature and varied pressure has little or no effect on our measurements. Our 20 point calibration improves the precision of our elements as calculated in the single point calibrations to better than 0.8%. See Figures 18 and 19.
The Bronkhorst flowmeter provides an analog voltage proportional to the actual mass flow. We need to convert this analog signal into a meaningful representation of flow. The Bronkhorst meter is calibrated for nitrogen at 20C, 1atm. It's maximum flow is represented by a 5.365V voltage, which is 1ln/min of nitrogen. The manual for the flowmeter provides us with a conversion equation and a table of conversion factors so we may adjust for different types of gas. Here is the equation: Mass Flow = (Vmeas/Vmax)*(Cf)*(MFmax)*(60min/hr), where Vmeas=Measured Analog Voltage, Vmax=5.365V, Cf(conversion factor)= 1.4(Argon) , and MFmax= 1 ln/min(Max nitrogen calibrated flow).
Our standard RTD head uses several EL2244CS operational amplifiers. When we began our calibration testing we noticed that we were not able to obtain our expected calibration precision. The EL2244CS op-amps get hot when taking consecutive measurements, and cool down only when the RTD Head is put to sleep. The heating of the op-amps was causing an offset voltage. We replaced all of the op-amps with JFET input TL082 op-amps which have lower offset voltage temperature coefficients and noticed increased calibration precision. Finally, we replaced all the op-amps with precision OPA2277 op-amps and cured the offset voltage problem all together.
The Bronkhorst valve/mass flowmeter was borrowed from Freiburg. We have since returned the instrument to the Freiburg team. The Brandeis HEP lab has an electronic proportional valve made by Hass Manufacturing in house. This valve can allow a much larger flow than the Bronkhorst. We can restrict the maximum flow through the valve by switching some jumpers on the valve's controller pcb. Inspection of Hass Mfg. manual for their EPV-SS-4MG valve suggests placing jumpers on connectors J5 and J6 so that the valve is allowed to make at most 1 turn from closed to open, or vice versa. We have found that by setting the valve to 80% of 1 turn achieves a maximum flow comparable to the Bronkhorst valve.
Our RTD mass flowmeter meets the ATLAS requirements of 1% precision and 2% accuracy at a pressure of 3bar over a flow range of 2-100 vol-ltr/hr. Each RTD element's individual measurements are precise to 0.1% of full scale and their resolution at 50% of the flow range is 0.3%. Agreement of 10 elements before calibration is better than 15%. Our single point calibration improves the standard deviation of measurements from calibrated elements to 1.6% over the full range. Using 20-point calibration curves, the standard deviation of the measurements across all calibrated elements improves to better than 0.8% over the full range.