Georgia Institute of Technology School of Earth and Atmospheric Sciences EAS 4641, Spring 2007 Lab 3 Introduction to Quantitative Analysis: Pumps and Measurements of Flow Purpose of Lab 3: 1) To gain a basic understanding of air pumping and air flow measurements 2) More insight into measurement errors, error propagation, and instrument calibrations In practically all situations in atmospheric air quality monitoring, a known quantity of air is extracted from the atmosphere through an inlet, conducted to the detector through a sampling line, and then analyzed for constituents of interest. Among other things, this requires 1) a pump to move the air and 2) a way to monitor or determine the amount of air sampled (e.g., a flow meter). The schematic below shows a typical arrangement of components. In this laboratory we will focus mainly on the measurement of flow. In Lab 4 we will look at sample inlet and transmission issues, and the subsequent labs will deal with detection and ambient measurements. Inlet Sample Transmission line Detector Flow Meter or Flow Control Vacuum Pump Air Movers can be classified into three basic groups: volumetric displacement, centrifugal acceleration, and momentum transfer. Volumetric displacement usually involves an air-tight chamber in which the internal volume is changed by mechanical means. These are generally referred to as pumps. In a diaphragm pump a flexible wall in a chamber is oscillated, and through a series of valves air is drawn into the chamber when the chamber is expanded and forced out when the chamber is compressed. A piston pump is similar to diaphragm except that a piston sliding in a cylinder is used instead of the diaphragm. Bellows can also be used instead of a diaphragm or piston. Piston and bellows pumps are capable of developing higher vacuum and positive pressures than diaphragm pumps. For these pumps, the low frequency of the chamber volume oscillation often makes a pulse dampening system necessary to smooth out pressure variability. Rotary vane pumps are used extensively and are composed of a rotor with vanes mounted off-center in a cylindrical chamber. Rapid rotation of the rotor and the lack of valves 1
produce a smooth vacuum or pressure. A commonly employed rotary vane pump uses non-lubricated carbon vanes held against the cylinder walls by centrifugal force. The pressure side of these pumps must be filtered since vane wear produces larger concentrations of aerosol particles that should not be inhaled and must be isolated from sample air. Similar concerns pertain to oil mist from lubricated pumps. A schematic of an oil lubricated rotary vane pump is given below. The second basic method is centrifugal acceleration. These are often referred to as blowers when the airflow is radial, and called fans when the flow is axial (fans are not used in air quality work). Blowers are typically used in applications where high flow rates and low differential pressures are required, whereas pumps are used in situations of low flow rates and high differential pressures. The type of air mover used for a specific application will depend on the pressure differential the pump must maintain at a specified flow rate. Pump performance curves showing differential pressure versus flow rate is typically reported for specific pumps. 1. Oil Mist Eliminator,2. Exhaust, 3. Gas Ballast (RA),4. Inlet, 5. Inlet Screen, 6. Anti-Suckback Valve, 7. Vane, 8. Rotor, 9. Main Oil Feed Line, 10. Spin-On Oil Filter, 11. Oil Sight Glass, 12. Exhaust Valve (RA), 13. Oil Return Valve (RA), 14. Oil Return Line (RC) Flow Meters To determine concentrations of atmospheric constituents, a known quantity of air must be analyzed. Typically, this requires a measurement of a flow rate (i.e., how much air was sampled over a period of time). Flow meters can be divided into two types, mass and volumetric, and the corresponding flow rates given on a mass or volumetric basis. Measurements of trace gases typically involve mass flow rates, whereas aerosol measurements are most often done on a volumetric basis. Volumetric flow rate (e.g. unit, cm 3 /s) depends on the gas T and P. However, concentrations are often reported at some reference condition, i.e., standard T and P (20 C, 1 atm). One can convert between different states by the ideal gas law. That is Q s = Q a P a /P s T s /T a where s = standard conditions; a = ambient conditions The concentration will then be: C s = C a (Q a /Q s ) 2
Mass flow meters (e.g. unit, g/cm 3 ) and mass flow controllers are ubiquitous and more readily available then volumetric meters and flow controllers. Using mass flow rates trace gas concentrations are reported as mixing ratios (e.g., ppbv, pptv, etc see any chemistry or atm. chemistry text for more info on mixing ratios). Flow rate Measurement Methods. (Reference: Aerosol Measurement; Principles Techniques and Applications, Editor Willeke and Baron, Chapter 22) Also see Appendix Methods to measure flow rates include: Pitot tube (measures velocity that can be converted to a flow rate) Hot wire or film anemometer (velocity measurement) Obstruction Meters o Venturi or orifice meter (measure DP across calibrated resistance) o Critical orifice (used to maintain constant volumetric flow) o Rotameter (variable area) Laminar flow meter (useful since can transmit particles/gases efficiently) Positive displacement meters o soap bubble o piston, which includes gas meters Mass flow meter A note of caution when measuring volumetric flow rates; care must be taken as to where the flow meter is placed since volumetric flow depends on P. Typically a volumetric flow meter is situated so that one side of the flow meter is at ambient P. In this way the measurement is of the flow rate at ambient conditions. Details on Some Specific Flow Meters (See web page file: Appendix 1 Meas of Flows.pdf for more details) Positive displacement meters are primary standards because their calibrations can be determined by direct physical measurement. The simplest and most accurate of these meters use a water surface (spirometer), or a soap bubble film (bubble flow meter) to produce a sealed chamber with variable volume. In these instruments water vapor is typically added to the gas since after exiting the meter the sample air has increased in RH, reaching roughly 100%. Often a saturator is placed in front of the wet meter to produce a 100% RH air stream entering the meter. This eliminates uncertainties due to continued addition of water vapor within the meter. Assuming the meter is measuring a flow of saturated air, the ideal gas law can be employed to calculate the actual dry-air flow rate. Laminar Flow meters are commonly employed in aerosol science since the flow meter is simply a straight narrow-bore tube that will efficiently transports particles (minimal wall losses). Thus a laminar flow meter can be used to monitor a sample flow upstream of the detector and the air to be sampled can be passed through the meter. The device is based on measuring the pressure drop through a known length of tube under fully developed laminar flow conditions. Under so-called Hagen Poiseuille flow pressure drop is directly proportional to volumetric flow rate. For circular tubes, laminar flow requires a 3
Reynolds Number less than ~ 2000. Laminar flow meters can typically only measure flow rates up to approximately 2 L/min A critical orifice is a small circular restriction placed in a tube to maintain a constant flow when upstream conditions are constant. If the absolute pressure downstream of an orifice is less than 0.53 times the upstream pressure the flow in the orifice throat will be sonic and further reduction in pressure does not change the flow rate. These devices are useful for taking constant flow rate samples with a vacuum pump. (E.g., often used in integrated filter measurements). Flow Controllers: A flow controller combines a flow measurement with a metering valve. A feed back loop is used to maintain a constant user preset flow rate by automatic adjustment of the valve. Mass flow controllers are common and used extensively in trace gas measurement systems. 4
MORE DETAILS ON UNCERTAINTIES ANALYSIS Propagation of Errors. In general, determining a physical quantity requires making measurements, and determining the value of that quantity by using some expression that includes a variety of measured variables. To obtain an estimate of the uncertainty in the final quantity, the uncertainties associated with all the measurements must be combined. Example, consider a condensation particle counter (also referred to as a condensation nucleus (CN) counter). If the CN counter measures 9833 particles per 1 sec sampling air at 1 l/min. Say the instruments timer is accurate to ±0.001 sec and flow rate accurate to within 2% (DQ /Q=0.02, or DQ= 0.02 L/min). What accuracy should be report with the measured concentration? Method 1: Exact Solution; it can be shown that the final error due to the combined independent and random errors of individual measurements is (with negligible approximation, a 1 st order Taylor series expanded about 0: Dy = Dx 1 df/dx 1 + Dx 2 df/dx 2 + Dx 3 df/dx 3 + Dx 4 df/dx 4 + (partial derivatives), If the errors are independent, then one can expect some cancellation between errors, and the total error will be less. Thus, it is likely better to use a quadrature sum in the above equation. For our example, first without quadrature sum; CN = C/(Q t), and DCN = DC 1/(Qt) + DQ Ct/(Qt) 2 + Dt CQ/(Qt) 2 Where, CN is the particle concentration, C the counts, Q the volumetric flow rate, t the sample time. Then, DCN = sqrt(9833)/(16.67 cm 3 /s * 1 s) + (0.33cm 3 /s)(9833)(1s)/(16.67 cm 3 /s * 1 s) 2 + (0.001s)(9833)(16.67 cm 3 /s)/ (16.67 cm 3 /s * 1 s) 2 DCN = 5.95 + 11.68 + 0.59 [1/cm 3 ] = 18.22 1/cm 3 and the concentration is 590±18 Using quadrature sum: DCN = sqrt[5.95 2 + 11.68 2 + 0.59 2 ] = 13.12 (less than above). Method 2. A simpler approach is to use propagation of relative errors, In this case, when adding or subtracting; add the errors Multiplying and dividing add relative errors. This is the most common situation (often the fractional errors are squared then summed, i.e., quadrature sum) Our example; (DCN/CN) 2 = (DC/C) 2 + (DQ/Q) 2 + (Dt/t) 2 (DCN/CN) 2 = (0.01) 2 + (0.02) 2 + (0.001) 2 = 5.03 E- 4 or DCN/CN = 0.022 and the answer is 590 ± 13. 5
Method 3. Use the range in the final answer as the uncertainty. Calculate the range by substituting in values that have the uncertainty added or subtracted to each measurement in a manner to give the max or min value. The resulting uncertainty (i.e., ±CN) is the difference in the max and min values (i.e., the range) divided by two. How To Evaluate Uncertainties associated with a measurement Reading scales (ruler, graduated cylinder etc) ~ 1/2 smallest graduation Use manufacturers stated precision Use ± smallest digit on digital readout (i.e., stop watch) {this is really not good because reaction time is greatest cause of uncertainty}. In situations of counting, relative uncertainty is 1/sqrt(counts) Repeat the measurement and use the range, or better, the standard deviation really we need a statistical analysis; (typically, the better the analysis the lower the uncertainty) No matter the method used, state your approach, i.e., how you estimated the uncertainty. In some cases there is no way to compare the measurement to a correct value, (i.e., measurements of particle chemical composition). Normally; one compares their measurement to a more accurate standard. If you have no accurate standard, you may have a very precise measurement but it could be far off from the correct answer. One needs a gold standard to test the accuracy of measurement Comparing Measurements or Measurements to Models Compare error bars, if overlap than Comparing numbers: Is there a difference? 7.5 there is no difference between measurements, or no discrepancy. Discrepancy is the difference in the 7 ± 0.5 5 estimated quantity. If the 6.5 4 discrepancy is larger than the 3.5 3 combined margin of error than the 4 2 numbers do not agree. The 3 ± 1 2 0.5 combined margin of error is the sum of the absolute uncertainties (recall that uncertainties are added for + or Difference: (7-3) ± (0.5 + 1) 4 ± 1.5 Difference: (4-2) ± (1 + 1.5) 2 ± 2.5 operations). A situation in which numbers are compared includes Yes, there is a difference No, there is not a difference comparing the mean ± std error (or can't tell from these data) from two different measurements. Alternatively, the two measurements could be plotted and a hypothesis test performed to see if the slope is different from zero. 6
Experiment No 3: Measurement of Flow In the following experiment you will calibrate methods used to measure volumetric and mass flow rates. An uncertainty analysis should be applied to all calibrations. Part 1. Calibration of a laminar flow meter with a bubble meter. Procedure: Set up the system as shown in Lab Figure 1. Adjust the valve to change the flow rate. You should do a total of about 5 different flows spanning the full range of the laminar flow meter s DP range. For each valve (flow setting) make approximately 5 or so repeated measurements with the bubble flow meter. For each, record the stop-watch elapsed time, bubble flow meter volume, and laminar flow meter DP. (Note, when using the bubble flow meter do not start timing at the 0 mark, but instead use the 0.1 L mark or higher). Also record the ambient T, RH (use stop watch), P (estimate), and any other parameters of interest. 3:34.00 Ambient T and P. Stop Watch Pressure Gauge DP Temperature Lab Figure 1. Bubble Flow Meter Laminar flow meter Note the direction. Install as shown, noting position of pressure taps valve Vacuum Pump (small GAST diaphragm pump) Part 2. Calibration of a Critical Orifice with a gas meter Set up the experiment shown in Lab Figure 2. Note this is a different vacuum pump than used in Part 1. Start with the valve totally closed and make a series (say 5 or so) repeated measurements with the gas meter and stop-watch at each valve setting. Record all pertinent data for each valve setting (e.g, volume, elapsed time, ambient pressure P 1 and pressure P 2. Make measurements for a total of 5 or so different valve settings. As you perform this experiment construct a graph of the absolute pressure ratio P 2 /P 1 vs Q. (Note, P 1 is the ambient pressure, use 1 atm). For the last data point, remove the valve and determine the flow rate 7
Pressure Gauge Flow Meter P 2 P 1 Temperature Valve Lab Figure 2. 16.7 L/m Critical Orifice Vacuum Pump (larger vane pump) Part 3. Calibration of a mass flow controller (MFC) Set up the experiment shown in Lab Figure 3. Cap both ends of the MFC and take a zero-flow voltage reading. Set MFC set point to 1/5 of full-scale (FS) range. (The full scale range is 5 V, and the flow controller s range is 0-2 L/min). Take 10 readings of measured volumetric flow rate Q a, ambient barometric pressure (assume 1 atm) and air temperature (P b, T a ) and water temperature (T w ) at saturator. Note arithmetic mean and standard deviation of Q a and corresponding average of P b, T a and T w and any small variations in analog Vdc setting. Set MFC set point to roughly 2/5, 3/5, 4/5, 5/5 of FS range, and repeat the above two steps for each setting. Control unit set point Analog signal Vdc P b, T a Ambient pressure and temperature Compressed N 2 tank Pressure regulator Shut-off valve MFC Volumetric flow measurement, e.g. soap-bubble-meter T w H 2 O temperature Saturator Lab Figure 3 8
Questions Part 1. 1. For the laminar flow meter calibration, make a calibration graph of Q versus DP, include error bars on data points and a linear regression fit with equal weights and show the fit parameters (intercept, slope, r, uncertainties in slope and intercept). Explain how the uncertainties were calculated. 2. Describe the curve. Is the shape as expected? Do your results agree with theory (see Appendix 1: Measurement of Flows) if the laminar flow meter inside diameter is 0.071 inch and length 5.000 inches. For example, is the flow laminar? What is the predicted ratio of flow rate to pressure drop? Part 2. 1. Make a graph of Q versus the pressure ratio (P 2 /P 1 ), include error bars and state how they were determined. 2. Is the orifice s behavior as expected, explain? If the orifice is used in an experiment to maintain a constant flow, how would you know if it is working properly (what would you monitor). Can you think of problems when using a critical orifice when measuring aerosols. 3. Assume a critical orifice with 0.4 mm diameter is fabricated for air sampling purposes and used downstream of a filter. The flow rate is measured to be 1L/min when the upstream pressure is close to the ambient pressure (760 mm Hg, 20 C). (See Appendix 1: Measurement of Flows for equations). a) What size of orifice must be fabricated if the sampling flow rate is 2 L/min and assuming the downstream pressure is still less than 0.53 the upstream pressure. b) What is the sampling flow rate when this orifice is used in Albuquerque, NM (ambient pressure is 625 mmhg)? c) When the filter is loaded and the pressure gauge upstream of the orifice is 10 cmh 2 O, what is the sample flow rate? Part 3. 1. Calculate the standard mass flow rate M s for dry air. You will have to first convert the volumetric measurements of N 2 (assume molecular weight of N 2 [28 g/mole] is same as dry air [28.9 g/mole]) to mass using the density of dry air calculated from the ideal gas law, with T a and P a. Then convert from ambient to standard conditions. M s = M a x (P a /P s ) x (T s /T a ) with P a = P a - P w P w = water sat. vapor pressure @ T w (from tables) P s = 1013.25 mbar=760 Torr T s = 273.15 K 9
2. Plot M s versus Vdc and do a linear regression with equal weights on all 6 data points (i.e. no-flow, 1, 2, 3, 4 and 5 Vdc). Estimate uncertainties of P and T measurements and incorporate into overall uncertainty estimate for M s. 3. Using the data collected above, recalculate the calibration curve if the gas to be controlled is Ar instead of dry air. 10