Photoacoustic hygrometer for icing wind tunnel water content measurement: design, analysis, and intercomparison
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Atmos. Meas. Tech., 14, 2477–2500, 2021
https://doi.org/10.5194/amt-14-2477-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
Photoacoustic hygrometer for icing wind tunnel water content
measurement: design, analysis, and intercomparison
Benjamin Lang1,2,3 , Wolfgang Breitfuss4 , Simon Schweighart2 , Philipp Breitegger1 , Hugo Pervier5 ,
Andreas Tramposch2 , Andreas Klug3 , Wolfgang Hassler2 , and Alexander Bergmann1
1 Graz University of Technology, Institute of Electrical Measurement and Sensor Systems, Graz, Austria
2 FH JOANNEUM GmbH, Institute of Aviation, Graz, Austria
3 AVL List GmbH, Nanophysics & Sensor Technologies, Graz, Austria
4 RTA Rail Tec Arsenal Fahrzeugversuchsanlage GmbH, Vienna, Austria
5 Cranfield University, School of Aerospace, Transport and Manufacturing, Cranfield, United Kingdom
Correspondence: B. Lang (benjamin.lang@tugraz.at)
Received: 21 July 2020 – Discussion started: 8 September 2020
Revised: 15 January 2021 – Accepted: 26 January 2021 – Published: 31 March 2021
Abstract. This work describes the latest design, calibration 1 Introduction
and application of a near-infrared laser diode-based photoa-
coustic (PA) hygrometer developed for total water content
measurement in simulated atmospheric freezing precipita-
tion and high ice water content conditions with relevance Atmospheric water in the form of clouds and precipitation is
in fundamental icing research, aviation testing, and certifi- of particular concern to aviation at temperatures below freez-
cation. The single-wavelength and single-pass PA absorp- ing, as supercooled liquid water and ice crystal environments
tion cell is calibrated for molar water vapor fractions with present potentially hazardous conditions to aircraft, leading
a two-pressure humidity generator integrated into the instru- to airframe and air data probe icing (Vukits, 2002; Gent et al.,
ment. Laboratory calibration showed an estimated measure- 2000) or in-flight engine power loss (Mason et al., 2006).
ment accuracy better than 3.3 % in the water vapor mole frac- Freezing precipitation containing supercooled large drops
tion range of 510–12 360 ppm (5 % from 250–21 200 ppm) (SLDs) with drop diameters in excess of 50 µm and convec-
with a theoretical limit of detection (3σ ) of 3.2 ppm. The hy- tive mixed-phase and glaciated clouds with high mass con-
grometer is examined in combination with a basic isokinetic centrations of ice crystals, i.e., ice water content (IWC) up to
evaporator probe (IKP) and sampling system designed for ic- several grams per cubic meter, constitute two particular mete-
ing wind tunnel applications, for which a general description orological environments associated with severe icing events
of total condensed water content (CWC) measurements and (Politovich, 1989; Bernstein et al., 2000; Cober et al., 2001b;
uncertainties are presented. Despite the current limitation of Riley, 1998).
the IKP to a hydrometeor mass flux below 90 g m−2 s−1 , a SLD icing environments of freezing drizzle (maximum
CWC measurement accuracy better than 20 % is achieved drop diameters from 100 to 500 µm) or freezing rain (max.
by the instrument above a CWC of 0.14 g m−3 in cold air diameters greater than 500 µm), as classified for the certifi-
(−30 ◦ C) with suitable background humidity measurement. cation of large transport aircraft, are comprehensively char-
Results of a comparison to the Cranfield University IKP in- acterized by envelopes of liquid water content (LWC), tem-
strument in freezing drizzle and rain show a CWC agreement perature, pressure altitude, drop size distributions, and hori-
of the two instruments within 20 %, which demonstrates the zontal extent in Appendix O of the European Aviation Safety
potential of PA hygrometers for water content measurement Agency Certification Specifications 25 (EASA CS-25, 2020)
in atmospheric icing conditions. and the Code of Federal Regulations Title 14 Part 25 (FAA
CFR-25, 2019). Mixed-phase and ice crystal environments
are likewise covered with a total condensed water content
Published by Copernicus Publications on behalf of the European Geosciences Union.
2478 B. Lang et al.: Photoacoustic hygrometer for icing wind tunnel water content measurement
envelope by Appendix P and D of the two documents, re- tation has motivated the development of the hygrometer and
spectively. sampling system described in this work.
Replication of the full SLD, mixed-phase, or high IWC Hygrometers in devices specifically designed for IWT
condition envelopes in icing wind tunnels (IWTs) has been operation typically apply commercially available non-
largely accomplished by organizations devoted to the exper- dispersive infrared (NDIR) gas analyzers based on optical
imental simulation of icing environments for the purpose of absorption spectroscopy (e.g., Strapp et al., 2016; Bansmer
fundamental icing research and certification of aeronautical et al., 2018, Sect. 4.3). The upper end of water content that
components but is associated with a lack of appropriate in- has to be within the range of suitable hygrometers is given
strumentation and is still a work in progress for some condi- by the combined background and condensed water content
tions (Orchard et al., 2018; Van Zante et al., 2018; Bansmer in the measurement environment. The former is approxi-
et al., 2018; Breitfuss et al., 2019; Chalmers et al., 2019). mately limited to fully saturated air at a static air tempera-
The accuracy and reliability of conventional water con- ture (SAT) of 0 ◦ C, and the latter may be taken as an upper
tent instrumentation in the conditions encompassed by Ap- bound of 10 g m−3 to the peak CWC of 9 g m−3 in high IWC
pendix O and P/D is an issue frequently addressed for in- conditions (EASA CS-25, 2020). This may add up to mo-
flight and IWT characterization (Strapp et al., 2003; Korolev lar water vapor fractions of 18 500 ppm at standard pressure
et al., 2013; Orchard et al., 2019). Conventional instrumenta- (1000 hPa). Accuracy requirements are primarily determined
tion in this context refers to ice accretion blades or cylinders by high BWV concentrations that have to be subtracted from
for LWC measurement and evaporating (multi-element) hot- high total water concentrations at low CWC and high ambi-
wire sensors used for simultaneous LWC and total condensed ent temperatures (Davison et al., 2016). The necessary hy-
water content (CWC;1 combined LWC and IWC) measure- grometer limit of detection highly depends on the specific
ments. Both methods are either known or suspected to suffer measurement conditions but may be estimated from the fact
from size- and water-content-dependent inaccuracies in large that detection of a CWC of 0.05 g m−3 in dry air at standard
drop or ice crystal icing environments due to uncertainties pressure requires an accuracy and limit of detection better
in collection efficiency and mass losses before accretion or than 48 ppm.
evaporation (Cober et al., 2001a; Strapp et al., 2003; Emery With the measurement system described in detail by Sza-
et al., 2004; Isaac et al., 2006; Korolev et al., 2013; Steen káll et al. (2001), Tátrai et al. (2015) have first demon-
et al., 2016). strated the suitable accuracy of photoacoustic (PA) hygrome-
This situation has led to the development of new bench- ters in and beyond the above measurement range. Compared
mark isokinetic evaporator probe (IKP) instruments for CWC to NDIR sensors, photoacoustic spectroscopy offers the po-
measurement (Davison et al., 2008; Strapp et al., 2016), re- tential of achieving higher signal-to-noise ratios (SNRs) with
garded as closest to a first principles measurement and pri- equal response time, while providing high selectivity and
marily designed for and deployed in the characterization of high robustness due to the possibility of optical single-pass
high IWC mixed-phase and glaciated conditions (e.g., Rat- arrangements and an instrument response that is invariant
vasky et al., 2019). IKPs are used to extractively sample to the total absorption pathlength (Hodgkinson and Tatam,
droplets and ice crystals in the icing environment with a 2013).
forward-facing, isokinetically operated inlet. After sampling, In this work we describe the latest design, preliminary cal-
hydrometeors are evaporated to measure the combined con- ibration, and basic properties of a new PA hygrometer and
densed and ambient air water content with a suitable hygrom- two-pressure humidity generator, developed with the goal of
eter. Ambient air background water vapor (BWV) is mea- providing the total water measurement and calibration ranges
sured separately and subtracted from the total water content typical for simulated atmospheric icing conditions applied in
(TWC) to derive the condensed water content. Measurement aviation testing and certification. The hygrometer is exam-
of the BWV concentration is usually accomplished via a sec- ined in combination with a basic IKP and sampling system,
ond, backward-facing inlet connected to another hygrometer. designed for IWT application in Appendix O conditions, for
Due to the isokinetic sampling, losses of droplets or particles which a description of CWC measurement and its associated
by re-entrainment into the flow after entering a sufficiently uncertainties are presented. Finally, results of water content
long inlet are improbable. Hence, IKP particle size distribu- measurements in freezing drizzle and rain conditions in a
tion dependence is in theory only governed by the aspiration closed-circuit IWT, calibrated according to SAE Aerospace
efficiency of the inlet. Recommended Practices (SAE ARP-5905, 2015), are pre-
Collectively, only few such reference instruments for sented and compared to measurements with a reference IKP
CWC measurement in icing conditions similar to Ap- and a hot-wire instrument.
pendix O and P/D currently exist. This lack of instrumen-
1 Often abbreviated as TWC. To provide a clear distinction to
total water content, we adhere to the nomenclature and reasoning
given by Dorsi et al. (2014).
Atmos. Meas. Tech., 14, 2477–2500, 2021 https://doi.org/10.5194/amt-14-2477-2021
B. Lang et al.: Photoacoustic hygrometer for icing wind tunnel water content measurement 2479
2 Instrument design In the following subsections, the major components of the
instrument are described in further detail.
A schematic overview of the entire instrument is shown in
Fig. 1a. The system consists of a sampling probe positioned 2.1 Photoacoustic hygrometer
inside the icing wind tunnel and a measurement and sam-
pling unit integrated into a 19 inch rack, positioned outside The hygrometer is a custom-built single-cell photoacoustic
the tunnel and connected by 7 m long heated and thermally absorption spectrometer, providing a signal proportional to
insulated PTFE tubing, temperature-controlled to the mea- the water vapor number concentration in the total water or
surement temperature of 35 ◦ C to prohibit condensation. The background water air stream. Figure 1b presents a schematic
probe is a total water (TW) sampling probe operated isoax- of the PA cell together with the optic configuration and elec-
ially and near isokinetic conditions, which also features a tronic setup.
second inlet port intended for BWV measurement. Hydrom- A fiber-coupled distributed feedback laser diode (NEL,
eteors entering the forward-facing TW inlet are evaporated NLK1E5GAAA) is intensity modulated at approximately
inside the probe, enriching simultaneously sampled ambient 4584 Hz (at 35 ◦ C) to excite the fundamental acoustic
air with the evaporated condensed water. resonance mode of the PA cell when water vapor is
The sampling system is designed to provide five main op- present. The diode is temperature-controlled to the peak
erating modes: of a ro-vibrational water vapor transition at 1364.68 nm
1. TW measurement (path 1 in Fig. 1a) (7327.68 cm−1 ; 296 K), which was chosen based on HI-
TRAN simulations (Gordon et al., 2017) as it exhibits the
2. BWV measurement (path 2) highest spectral line intensity in the 1.38 µm absorption band
3. zeroing (PA background signal measurement; path 3) (1.86 × 10−20 cm molec−1 ) and low interference from other
anticipated atmospheric constituents. At the PA cell operat-
4. calibration (path 4) ing conditions (308 K, 800 hPa) and low water vapor concen-
trations, the selected line has a maximum absorption cross
5. inlet purging (path 3 combined with path 1 or 2).
section of 8.01 × 10−20 cm2 molec−1 . This is similar to and
For TW and BWV measurement, air sampled through the higher than the cross sections around 1368.6 and 1392.5 nm,
respective inlet is continuously pumped to the measurement respectively (8.09 × 10−20 and 5.99 × 10−20 cm2 molec−1 ),
unit, where the PA hygrometer (PA cell) is used to measure two regions that have been targeted in previous photoacous-
the water vapor mole fraction in parts of the TW or the full tic water vapor sensing applications (e.g., Besson et al., 2006;
BWV inlet air flow. Currently, only a single hygrometer has Kosterev et al., 2006; Tátrai et al., 2015). Intensity modu-
been implemented and humidity measurement may only be lation is performed by square wave modulating the applied
alternated between TW and BWV measurement. laser current at the resonance frequency from the maximum
During isokinetic TW sampling, the majority of the flow permissible laser diode current down to just below the lasing
bypasses the hygrometer (path 5 in Fig. 1a) to the scroll threshold with a benchtop laser driver (Thorlabs, ITC4001),
pump (Edwards, nXDS10iC). The hygrometer is supplied maintaining an average optical power of 9.9(1) mW. Square
by a constant standard volumetric flow rate of 0.75(4) stan- wave rather than sinusoidal modulation was applied, as a
dard L min−1 (slpm; reference conditions: 273.15 K and higher signal amplitude is theoretically expected for the for-
1013.25 hPa), set by a pressure controller (Vögtlin Instru- mer (e.g., Szakáll et al., 2009). Modulation of the laser cur-
ments, GSP-B9SA-BF26) upstream the cell and a critical rent to just below the threshold current resulted in maximized
orifice of 350 µm nominal diameter downstream the cell. A photoacoustic signal amplitudes. It should be noted that mod-
calibrated mass flow controller (MFC; Vögtlin Instruments, ulation to slightly above the threshold current may be ad-
GSC-C9SA-FF12) is used to control the bypass flow rate vantageous for practical reasons (Bozóki et al., 2011). The
and a calibrated flowmeter included in the pressure controller laser beam is collimated to a diameter of 2 mm and directed
measures the actual hygrometer flow rate. Isokinetic sam- through the resonator via two N-BK7 Brewster windows an-
pling at the TW inlet is set by adjusting the MFC flow rate gled at 56.4◦ . A thermal power meter (Thorlabs, PM16-401)
to a combined flow rate matching the isokinetic conditions, is used to measure average optical power when the cell is
which are calculated using the IWT test section operating pa- flushed with zero air during PA background signal measure-
rameters and TW inlet geometry parameters (cf. Sect. 4). ments. Monitoring of the laser power during measurements is
The instrument features a two-pressure humidity genera- accomplished by a fiber splitter with a 99 : 1 split ratio (Thor-
tor also integrated into the rack, which in combination with labs, TW1300R1A1) in combination with a temperature-
zero air is used for calibration and zeroing of the hygrometer. controlled InAsSb photodetector (Thorlabs, PDA10PT-EC).
Control of flow, temperature, and pressure, together with sig- However, the high wavelength and output power stability of
nal processing and data logging for the sampling system and the laser diode allows stable operation over the duration of
humidity generator, is performed with a dedicated embedded typical measurement series, thus no wavelength locking on
system (National Instruments, NI cRIO 9063). the absorption line or power correction is applied on mea-
https://doi.org/10.5194/amt-14-2477-2021 Atmos. Meas. Tech., 14, 2477–2500, 2021
2480 B. Lang et al.: Photoacoustic hygrometer for icing wind tunnel water content measurement
Figure 1. (a) Schematic of the instrument showing the isokinetic evaporator probe (IKP) and the measurement (PA cell), sampling, and
calibration system (two-pressure humidity generator and zero air). Locations of temperature and pressure control are indicated by (T ) and
(p), respectively. Indicated numbers enumerate the individual flow paths. The rearward-facing BWV probe indicates the extension of the
BWV inlet port not applied in this work. (b) Schematic of the photoacoustic cell together with the optical and the electronic setup, showing
the control, data acquisition, and signal processing performed on the real-time embedded system.
sured signals in between calibration cycles. The two outer- installed in the sampling gas stream approximately 100 mm
most volumes of the PA cell, on the left-hand side enclosed upstream of the cell, is used to control the gas temperature
by the optical collimation unit and the Brewster window, are to 35.0(3) ◦ C inside the PA cell by controlling the heating of
filled with ambient air and are sealed by gaskets and PTFE the upstream tubing in the measurement unit. This tempera-
thread seal tape. Attenuation of the laser optical power due ture also sets the theoretical upper water vapor mole fraction
to absorption from water vapor in these volumes remained measurement limit of 58 600 ppm before condensation of wa-
constant within the above stated bounds of the optical power ter vapor in the sampling lines and the PA cell occurs.
in between calibrations. Although the sampling system and the IKP are designed to
Measurement air is pumped through the stainless steel PA operate around standard pressure, the PA cell pressure may
cell via milled 6 mm inner diameter (ID) cylindrical ducts. be set with the pressure controller upstream of the hygrom-
At the center of the modularly designed cell a 34 mm long eter within the limits given by the pressure loss of the up-
cylindrical resonator is formed by a termination on either stream flow elements down to 100 hPa. The sensitivity of
side with two acoustically short concentric resonators (Se- the PA hygrometer, however, is maximized towards higher
lamet and Radavich, 1997). Short concentric resonators are cell pressures (cf. Appendix A). For IWT measurement, the
used instead of larger expansion chambers (buffer volumes) cell pressure is set to 800(8) hPa, close to the pressure of op-
to decrease gas exchange and measurement response time timal signal-to-noise ratio (SNR) at approximately 850 hPa
(cf. Sect. 3.1). The diameters and distances in between the (cf. Fig. A1). A lower than optimum cell pressure was used
small volume acoustic band-stop filters are tuned to maxi- during measurements to allow for the occurring head loss at
mize the resonator quality factor (Q = 17), while minimiz- high IWT airspeeds and TW sampling flow rates. To further
ing transmission of external noise into the cell. At the cen- decrease signal noise, the PA cell is vibrationally decoupled
ter of the resonator and the location of the antinode of the from the scroll pump mounted in the rack by a vibration-
fundamental longitudinal resonance mode, an electret con- absorbing mount and short sections of PTFE tubing at the
denser microphone (Knowles, EK-23028) is connected in a gas in- and outlet of the cell.
small volume gas- and noise-tight enclosure to measure the Laser current control, signal processing, and data logging
PA pressure signal. of microphone and power monitoring signals is carried out
The PA cell is operated at constant temperature, pressure, with a second dedicated embedded system (National Instru-
and flow to maintain a microphone sensitivity and resonance ments, NI cRIO 9031), a real-time processor combined with
frequency independent of ambient and IWT conditions. a reconfigurable field programmable gate array (FPGA). The
The temperature of the thermally insulated PA cell is con- laser current modulation signal is generated by a function
trolled to 35.0(3) ◦ C by two integrated heating cartridges generator implemented on the FPGA. Data acquisition of
to stabilize resonance frequency and microphone sensitiv- the microphone signal after analog amplification with a tran-
ity.2 An additional resistance temperature detector (RTD), simpedance amplifier (10-fold gain), together with the pho-
todetector signal, is carried out with a 24 bit ADC (National
2 The number in parenthesis gives the half-width of the rectan- Instruments, NI 9234) at a sampling rate of 52.1 kHz. A digi-
gular confidence interval in terms of the last digit. tal dual-phase lock-in amplifier implemented on the FPGA is
Atmos. Meas. Tech., 14, 2477–2500, 2021 https://doi.org/10.5194/amt-14-2477-2021
B. Lang et al.: Photoacoustic hygrometer for icing wind tunnel water content measurement 2481
used to determine in-phase and quadrature components of the tegrated into the instrument. Two-pressure humidity genera-
microphone signal at the frequency of modulation. The lock- tion offers the benefit of enabling rapid and accurate setting
in signal amplitude (referred to as PA signal) used to derive of a wide range of humidity levels in a saturation chamber at
the water vapor mole fraction is calculated and logged on a convenient and constant temperature by varying the pres-
the real-time operating system with a 10 Hz rate after phase- sure and thus the molar water vapor fraction (Wernecke and
correct background signal correction (cf. Appendix B). Wernecke, 2013).
Despite operation at controlled measurement conditions, Zeroing of the instrument is performed by acquiring a PA
the hygrometer sensitivity is a function of the measured background signal after continuously flushing the PA cell
water content for several reasons. Increasing water con- with zero air from an external gas cylinder (Messer, scien-
tent causes decreasing irradiance along the absorption path tific grade synthetic air; residual water volume fraction below
(Beer–Lambert law) and therefore reduce sensitivity. In ad- 2 ppmv) until a stable reading is attained (approx. 20 min).
dition, the electret microphone sensitivity is a function of hu- For calibration, zero air is initially humidified in a pre-
midity (specified 0.02 dB % RH−1 ; Langridge et al., 2013). saturation stage, i.e., a porous ceramic with honeycomb
Furthermore, speed of sound and therefore resonator res- structure (IBIDEN Ceram) in a room temperature water bath,
onance frequency is a function of humidity (Zuckerwar, to a dew point well above the main saturation chamber dew
2002). Shifts in resonance frequency may reduce effective point. The humidified air is subsequently passed through a
resonator amplification and sensitivity according to the ap- lower temperature and pressure-controlled 1 m long coiled
proximately Lorentzian resonator frequency response, if the tube heat exchanger and the main saturator, where the air is
frequency of modulation is not shifted accordingly (Szakáll saturated with respect to the local temperature and pressure.
et al., 2009). Finally, photoacoustic conversion efficiency The saturator is a (6 × 25 × 600) mm
(i.e., conversion of absorbed laser radiation to a detectable (width × height × length) channel milled into a stain-
pressure signal) for water vapor in air is concentration de- less steel block, hermetically sealed and partially filled
pendent and over the range of typical atmospheric concen- with distilled water. Both the heat exchanger and saturator
trations and pressures varies by a factor of five (Lang et al., are placed in a stirred and thermally insulated water bath,
2020). temperature-controlled by thermoelectric coolers within the
All of the above effects are to a great extent accounted range of 1 ◦ C to ambient temperature. Saturator air pressure
for by calibrating the hygrometer over the range of expected is controlled within the range of 1000 to 8000 hPa with an
water vapor concentrations and by applying a suitable non- MFC (Vögtlin Instruments, GSC-C9SA-FF12) upstream of
linear calibration function, which is described in greater de- the HG. By increasing the saturator pressure to its maximum
tail in Lang et al. (2020). The PA signal reduction associated value, the 1000 hPa water vapor saturation fraction may be
with resonance frequency humidity dependence (0.5 % for reduced by a ratio of 1 : 7.8.
the 14 Hz shift from 0 to 20 000 ppm) is taken into account Bath temperature and saturator air pressure are measured
by maintaining the laser modulation frequency at the dry air with a high-precision four-wire Pt100 (Omega Engineering,
resonance frequency (4584 Hz at 35 ◦ C) for calibration and P-M-1/10-1/8-6-0-PS-3) combined with a calibrated 24-Bit
measurements. This method results in maximum amplifica- ADC (National Instruments, NI 9217) and a calibrated pres-
tion and PA signal at low concentrations. The approximately sure transducer (KELLER AG, PAA 33X), traceable to NIST
quadratic sensitivity loss for higher concentrations is consid- and Swiss national standards, respectively. Associated mea-
ered in the second-order term of the calibration function. surement uncertainties are given in Table E1. The molar wa-
ter vapor saturation fraction, which remains constant dur-
2.2 Calibration unit ing expansion to the lower pressure level of the hygrom-
eter, is calculated from the measured saturation tempera-
Determination of the water vapor concentration from the hy- ture and pressure according to Wagner and Pruss (1993) and
grometer signal requires background signal correction (ze- Greenspan (1976).
roing) and calibration with known concentrations of water In the described configuration, the operational range of
vapor. The system is calibrated by generating and providing the HG extends from 845 ppm to approximately 22 000 ppm
a stable flow of humidified air with known molar fractions (maximum saturator temperature of 19 ◦ C). Two saturator
of water vapor to the inlet of the hygrometer (e.g., Dorsi temperature set points are used for calibration, covering the
et al., 2014; Tátrai et al., 2015). This approach is preferred full humidity range by varying the saturator pressure. The
to the method of introducing a continuous stream of liquid settling time to a stationary hygrometer signal after changes
water or ice into the TW inlet and calibrating for CWC (e.g., in the HG settings is below 7 min. This figure is mainly deter-
Strapp et al., 2016), as calibration may be performed during mined by the relatively low signal noise of the PA hygrome-
IWT operation without removing the sampling probe. With ter compared to the slow water vapor adsorption–desorption
the goal of performing calibration over a major part of the processes at the piping and cell walls.
necessary water content range within a short time, a compact An independent calibration of the humidity generator is
custom-made two-pressure humidity generator (HG) was in- still pending, which in particular is necessary to verify full
https://doi.org/10.5194/amt-14-2477-2021 Atmos. Meas. Tech., 14, 2477–2500, 2021
2482 B. Lang et al.: Photoacoustic hygrometer for icing wind tunnel water content measurement
2.3.1 Total water inlet
TW is sampled through a screw-on aluminum nozzle with a
sharp leading edge and a tapering half angle of 20 ◦ . For the
measurements presented, a nozzle with an inlet inner diam-
eter of 3.30(15) mm, measured with a standard caliper, was
used. The particular choice of the comparatively small in-
let diameter is based on the maximum continuous flow rate
attainable with the low-noise vacuum pump in use, which in
combination with the TW inlet area determines the maximum
wind tunnel airspeed for which isokinetic sampling may be
maintained. The ID of 3.3 mm corresponds to a maximum
airspeed slightly above the main targeted wind tunnel air-
speed of 60 m s−1 . The stated nozzle inner diameter uncer-
tainty is attributed to the measurement method and measur-
able inlet deformations caused by the machining process.
As the TW inlet is considered a thick-walled inlet with
an aspiration efficiency expected to deviate from an ideal
sampling behavior (Belyaev and Levin, 1974), the collec-
tion efficiency of the inlet was determined from combined
Figure 2. Schematic of the isokinetic evaporator probe assembly computational fluid dynamics (CFD) and Lagrangian parti-
showing a partial cut through the main components: TW and BWV cle tracking simulations. Definitions of aspiration and col-
inlet lines with TW inlet nozzle, the carbon fiber reinforced polymer lection efficiency, as well as the particle Stokes number Stp
(CFRP) pylon, aluminum fairing, and evaporator. Fairing cartridge used in the evaluation, are given in Appendix C. Simulations
heaters extending alongside the TW inlet sheath are not indicated. were carried out in COMSOL Multiphysics software with a
workflow similar to the one described by Krämer and Af-
chine (2004) and showed good agreement with simulations
saturation at high loads (high saturator temperature). To as- carried out in ANSYS CFX for the same probe with an in-
sess the HG and thus hygrometer accuracy, the uncertainty let diameter of 4.6 mm. However, instead of determining the
in the generated humidity is calculated from first principles, limiting freestream area Alim comprising all particle trajecto-
i.e., the measured saturator temperature and pressure and the ries entering the inlet, collection efficiencies E(dp ) for each
associated uncertainties, according to Meyer et al. (2008). droplet diameter dp considered were calculated from the ratio
The resulting uncertainty (95 %) is below ±2.1 % over the of the number Ns of droplets sampled to the number Ninlet of
entire range of humidities provided by the HG and is domi- droplets passing through the probe TW inlet equivalent area
nated by the saturator temperature measurement uncertainty Ainlet in freestream (cf. Appendix C):
(cf. Table E1).
Alim Ns
E(dp ) = ≈ . (1)
2.3 Isokinetic evaporator probe Ainlet Ninlet
The inlet system was designed around the three requirements Figure 3 shows the determined collection efficiencies for
of enabling reasonably representative isokinetic TW sam- two IWT freestream airspeeds Ua and different isokinetic
pling while providing the necessary heating power for hy- factors IKF = U s /Ua , i.e., velocity ratios of mean inlet sam-
drometeor evaporation and maintaining the probe free from pling velocity U s to freestream airspeed. Low collection
ice accretion at high water content. The probe inlets are efficiencies at Stokes numbers around 1 are the result of
housed in an airfoil-shaped (32 × 132) mm (width × length) the thick-walled inlet design (Rader and Marple, 1988). At
carbon fiber reinforced polymer (CFRP) pylon capped by an the conditions of the measurements presented herein (Ua =
additively manufactured aluminum fairing with the TW cen- 60 m s−1 and IKF ≈ 1), the simulated collection efficiency
terline extending 220 mm perpendicular to the free-stream reaches a minimum of 88 % for particles of 3 µm diameter
flow from a (100 × 195) mm base flange. A CAD drawing and is practically independent of the IKF in the range of 0.95
of the IKP is shown in Fig. 2. to 1.05 for diameters above 10 µm (Stp ≈ 7). For Stp ≪ 1,
The fairing is controlled to a TW inlet nozzle temperature the collection efficiency tends towards the value of the isoki-
of approximately 50 ◦ C by maintaining a constant 80 ◦ C at netic factor. Consequences of the non-representative sam-
the RTD (Pt100) inside the fairing front tip. To this end, in- pling on cloud CWC measurement depend on the individual
tegrated cartridge heaters in the aluminum enclosure provide particle size distribution and are discussed in further detail in
a maximum combined heating power of 390 W. Sect. 4.3.
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B. Lang et al.: Photoacoustic hygrometer for icing wind tunnel water content measurement 2483
Figure 4. Calculated droplet mass remaining after traversing the
probe TW pipe following the evaporator bend and stopping dis-
Figure 3. Isoaxial TW inlet collection efficiency as a function of tance as a function of the initial droplet diameter, assuming an am-
particle diameter determined from combined CFD and Lagrangian bient air temperature, pressure, and freestream airspeed of −5 ◦ C,
particle tracking simulations at different freestream airspeeds Ua 1013.25 hPa, and 60 m s−1 , respectively. The indicated evaporator
and isokinetic factors (IKFs), assuming an ambient air tempera- diameter marks the stopping distance equal to the inlet pipe diame-
ture and pressure of −5 ◦ C and 1013.25 hPa, respectively. Particle ter of 6 mm.
Stokes numbers given in the upper x axis are only valid for 60 m s−1
data. The lines between the evaluation points are used to guide the
eye.
ture of 50 ◦ C was assumed, which was determined from the
CFD and heat transfer analysis. Inlet ambient air was as-
sumed to be fully saturated at −5 ◦ C, with an additional worst
Hydrometeors aspirated through the TW inlet are trans- case evaporated cloud CWC of 10 g m−3 .
ported down 6 mm inner diameter stainless steel tubing to the Droplets with diameters above 15 µm impact the 180 ◦ C
evaporator, a (125×44×16) mm aluminum block controlled evaporator walls and are assumed to evaporate due to the in-
to 180 ◦ C by a 400 W cartridge heater. An aluminum sheath creased heat transfer or break up into smaller, more easily
connects the evaporator and the nozzle and ensures addi- evaporated droplets. Minimum residence times of 1 s in the
tional heat transfer from the evaporator to the inlet. A sharp attached 7 m long tubes heated to 35 ◦ C are considered suf-
90 ◦ bend of the tubing approximately 100 mm downstream ficient to achieve full evaporation of smaller droplets. How-
from the inlet forms an impactor, where larger droplets and ever, observable TW signal oscillations for inlet condensed
particles are impacted on the heated wall to increase heat water mass flow rates above 0.8 mg s−1 (hydrometeor mass
transfer and promote droplet or particle break-up. At the flux of approx. 90 g m−2 s−1 ) suggest temporary accumula-
bend, the piping is enclosed and in good thermal contact with tion of water or ice in the small diameter nozzle or at the
the evaporator. evaporator and are the reason for further investigation into
For the airspeed of 60 m s−1 and the conditions of the mea- the process of droplet and particle evaporation for the chosen
surements presented, calculated particle stopping distances inlet diameter and evaporator geometry.
Sp (cf. Appendix C) predict impaction at the bend for par-
ticles with diameters larger than approximately 15 µm. This
is in close agreement with the CFD and Lagrangian particle 2.3.2 Background water vapor inlet
tracking calculations. The calculated stopping distance in de-
pendence of the particle diameter is shown in Fig. 4 together The BWV inlet port is used for sampling ambient air with
with the stopping distance equal to the evaporator pipe diam- the PA cell mass flow rate of 0.75 slpm and may be extended
eter (dotted line). by a rearward-facing probe with a 16 mm ID connected
Also shown is a theoretical calculation of the evaporative to 4 mm ID tubing. The connection between the rearward-
mass loss of supercooled spherical droplets when passing the facing probe and the port was thermally insulated to reduce
heated probe pipe section following the 90 ◦ bend. Droplet heating of the inlet, as the port pipe is in direct contact with
evaporation was calculated with the two-parameter model the evaporator. For the measurements presented, only a sin-
(droplet mass and temperature) summarized by Davis et al. gle hygrometer used for TW measurement was available,
(2007), which includes diffusion of water vapor from the thus the IKP was used without the rearward-facing probe
droplet to the humid inlet air, associated latent heat losses, and BWV was estimated from IWT humidity sensors. The
and conductive heating of the droplet by the heated inlet air. method of BWV estimation is described in further detail in
For the computations, a minimum (centerline) air tempera- Sect. 5.
https://doi.org/10.5194/amt-14-2477-2021 Atmos. Meas. Tech., 14, 2477–2500, 2021
2484 B. Lang et al.: Photoacoustic hygrometer for icing wind tunnel water content measurement
nal change) of τ63 = 1.7(2) s and τ63 = 2.2(2) s, respectively,
have been determined by alternately sampling humidified
zero air and ambient air. Response and recovery times for
90 % signal change are about four times the stated values
of τ63 . An example response time measurement is shown
in Fig. D1 in Appendix D. It is noted that response and
recovery times of the described setup are assumed to be
longer for measurements of background or total water con-
centrations below 500 ppm (dew points below −30 ◦ C) due
to adsorption–desorption effects associated with the polar na-
ture of water and the long PTFE tubing connecting the probe
and the measurement unit (Wiederhold, 1997).
Figure 5. Allan deviation σA calculated from the measured signal 3.2 Hygrometer calibration
amplitude of a 1 h background measurement with zero air as a func-
tion of the lock-in integration time τ . The dotted line indicates a The hygrometer is calibrated at constant PA cell temperature
√
1/ τ decrease in noise, typical for white noise averaging. and pressure (800 hPa, 35 ◦ C) with the built-in two-pressure
HG. To quantify measurement uncertainties at dew points
lower than provided by the HG, a gas diluter (Breitegger and
3 Hygrometer characterization and calibration Bergmann, 2018) was used for an initial laboratory calibra-
tion. Using the gas diluter, humidified air provided by the
3.1 Noise, limit of detection, and response time humidity generator was further diluted with zero air, down
to a minimum water vapor mole fraction of 124 ppm. Back-
To quantify measurement noise, expectable system drift, and ground corrected calibration data recorded at concentrations
the limit of detection (LOD) of the hygrometer, an Allan in the range of 124 to 22 150 ppm and the inverse calibration
deviation analysis (Werle et al., 1993) was performed on a curve used to determine the water vapor mole fraction during
background measurement with zero air acquired at 10 Hz water content measurement are shown in Fig. 6. Signal am-
with an integration time of 0.1 s. Figure 5 shows the Allan plitude noise of the hygrometer during calibration is typically
deviation σA , i.e., an estimate for the standard deviation of below water vapor mole fractions of 10 ppm or 0.7 % (the
the mean of the background signal, as it depends on the av- higher value in absolute terms applies). The former value,
eraging or integration time τ√. applicable at low concentrations, is on the order of the back-
The system exhibits a 1/ τ decrease in noise, typical for ground signal noise (1σ ) determined by the Allan deviation
white noise averaging, up to a maximum useful averaging analysis for the integration time of 1 s.
time of 150 s, where drift starts to deteriorate system per- For the determination of the water vapor mole fraction
formance. The effectiveness of increasing integration time during water content measurement, the calibration data are
is limited by a slow drift of the measurement gas tempera- approximated by the inverse of the theoretically motivated
ture. For half the maximum useful averaging time, an LOD nonlinear five-parameter calibration function given by Lang
(3σA ) calculated from the calibration curve (see Sect. 3.2) of et al. (2020), which accounts for the humidity-dependent hy-
3.2 ppm water vapor mole fraction or 2.0 mg kg−1 in terms grometer sensitivity. As opposed to higher-order polynomi-
of humid air mass mixing ratio at standard temperature and als, which are necessary to reproduce the nonlinear func-
pressure (STP; 273.15 K and 1000 hPa) can be achieved. tional relationship, this calibration function adds the benefit
More practical averaging times of 1 and 10 s result in 3 σA of a well-defined behavior for inter- and extrapolation when
noise equivalent concentrations of 23 and 7 ppm, respec- faced with a reduced number of calibration points. The pa-
tively. A comparison to literature-reported detection limits rameters b of the calibration curve are determined with the
of photoacoustic hygrometers is given in the Supplement to weighted nonlinear least-squares method, minimizing
this work. The implementation of a wavelength modulation N i2
scheme of the laser diode is expected to result in a reduction
h
χ2 =
X
wx,i xw,i − f −1 (Si , b) (2)
of the background signal noise and a significant improvement i=1
of the achievable LOD.
As the 1 s averaging time precision – equivalent to over the N calibration measurements, where f −1 (Si , b) is
14 mg kg−1 mass mixing ratio at STP – is sufficient for IWT the inverse calibration function evaluated at the measured
water content measurement and results in a favorable re- PA signal amplitude Si and for the parameter set b. The in-
sponse time, this lock-in integration time is applied in cal- verse of the calibration function was used in order to include
ibration and water content measurements. With a 1 s aver- the uncertainty of the calibration water vapor mole fraction
aging time, response and recovery times (63.2 % PA sig- u(xw,i ) in the determination of the parameters and parame-
Atmos. Meas. Tech., 14, 2477–2500, 2021 https://doi.org/10.5194/amt-14-2477-2021
B. Lang et al.: Photoacoustic hygrometer for icing wind tunnel water content measurement 2485
tions. Nevertheless, in the range of expected condensed wa-
ter content and background humidities encountered during
typical IWT evaluation, the hygrometer exhibits an accuracy
better than 2.5 % to 3.3 %. This target water content range is
defined by the lower limit of cloud-free, but fully saturated,
air (with respect to supercooled liquid) at −30 ◦ C and the up-
per limit of 5 g m−3 in fully saturated air at 0 ◦ C. These lim-
its correspond to 512 and 12 361 ppm at standard pressure,
respectively. Fully saturated air is assumed, as high relative
humidity is typical during measurement in closed-circuit ic-
ing wind tunnels. Increasing lock-in integration time can be
seen to not yield notable performance improvement, as accu-
racy in the range of interest is dominated by the uncertainty
Figure 6. Laboratory calibration data of the PA hygrometer oper- in the calibration humidity.
ated at 35 ◦ C, 800 hPa, and an integration time of 1 s. Calibration The determined PA hygrometer accuracy is lower than
humidities were set with the internal humidity generator and in the accuracy specified for NDIR systems providing a similar
combination with the gas diluter. The fit indicates the best-fit cal- measurement range (e.g., 1.5 %; LI-COR Inc., 2020). How-
ibration curve with the parameters obtained by the weighted non- ever, because the accuracy of the hygrometer is currently
linear least-squares method. Error bars of the measurements indi- dominated by the accuracy of the humidity generator, it is
cate the 95 % uncertainty of the humidity generation and standard
expected that improvement of saturator temperature stability
deviation of the lock-in signal for the y and x axes, respectively.
and temperature measurement, combined with the indepen-
dent calibration of the HG, will further improve the accuracy
ter confidence intervals. To this end, each calibration point i of the hygrometer to similar levels.
is weighted by wx,i = 1/σx,i2 = 1/u2 (x ), i.e., according to
w,i
the combined uncertainty in the humidity provided by the hu- 3.4 Measurement stability and repeatability
midity generator and gas diluter. The uncertainty in the mean
of the measured PA signal amplitude is negligible in com-
parison to the uncertainty in the mole fraction and therefore The short-term stability of the hygrometer during measure-
is disregarded in the least-squares fit. Residuals, i.e., the dif- ment, which is essential to the instrument accuracy in be-
ferences between calibration data and calibration curve, are tween calibrations, was evaluated by supplying a steady flow
typically below 3 %. This remaining variability is largely ex- of humidified air to the PA cell using the instrument calibra-
plained by the error in the generated humidity and changes in tion unit. The stability measured over a period of three hours
microphone sensitivity from temperature oscillations of the is shown in Fig. 8a, which shows the relative deviation of
PA cell. the estimated water vapor mole fraction from a 1 s running
average of the mole fraction supplied by the instrument’s
3.3 Estimation of hygrometer measurement humidity generator over time. Estimated concentrations re-
uncertainty mained within ±1.8 % of the reference concentration and are
well within the ±2.4 % relative uncertainty of the humidity
The measurement uncertainty of the PA hygrometer is the re- generator (95 % coverage). The determined stability is also
sult of uncertainties originating from the calibration and from within the 3.3 % accuracy of the hygrometer. Negative peaks
noise during measurement. Calibration uncertainty itself in- in Fig. 8a at 0.4, 0.8, and 1.2 h are the result of decreased
cludes uncertainties from humidity generation and from the microphone sensitivity due to minor temperature rises of the
approximation by the calibration function. These uncertain- PA cell, and the observable oscillation with a period of ap-
ties have been jointly estimated from the parameter uncer- proximately 3 h correlates strongly with the drift-corrected
tainties obtained with the nonlinear least-squares method. In- temperature inside the instrument rack. Stabilizing the rack
strument signal noise (1σ ) is taken to be equivalent to the cal- temperature is, thus, expected to further improve the instru-
ibration noise (10 ppm or 0.7 %, whichever is higher). Details ment stability and accuracy.
of the determination of the combined hygrometer uncertainty The hygrometer is calibrated on a daily basis because for
are given in Appendix F of this work. longer intervals drift in the lower percentage range has been
The calculated relative measurement uncertainty of the hy- observed in between calibrations. This drift is mainly associ-
grometer (95 % coverage) as a function of the measured wa- ated with a drift in the laser power and the non-existent laser
ter vapor mole fraction is shown in Fig. 7. Measurement un- power correction of the PA signal (cf. Sect. 2.1). Therefore,
certainty can be seen to increase rapidly for mole fractions measurement repeatability was assessed only by an analysis
below 200 ppm and above 23 000 ppm, due to the lack of cal- of the stability over intervals of 2 consecutive days, where no
ibration points at lower and higher water vapor concentra- drift greater than 2 % was observed (cf. Fig. 8b).
https://doi.org/10.5194/amt-14-2477-2021 Atmos. Meas. Tech., 14, 2477–2500, 20212486 B. Lang et al.: Photoacoustic hygrometer for icing wind tunnel water content measurement
Figure 7. Relative measurement uncertainty (95 % coverage) of the photoacoustic hygrometer operated at 35 ◦ C, 800 hPa, and with integra-
tion times τ of 1 and 10 s. The gray area bounded by dotted vertical lines marks the target range of background and total water content,
defined by the lower limit CWC of 0 g m−3 at −30 ◦ C (512 ppm) and the upper limit of 5 g m−3 at 0 ◦ C (12 361 ppm). The air is assumed to
be fully saturated with respect to supercooled liquid.
Figure 8. Hygrometer measurement stability. (a) Relative deviation of the measured water vapor mole fraction from the reference concentra-
tion of 9620(80) ppm supplied by the calibration unit over time. (b) Relative deviation on two consecutive days, measured at a mole fraction
of 18 800(160) ppm and calculated using the calibration of day 1 in both measurements. The gray bands mark the relative uncertainty of the
water vapor mole fraction provided by the humidity generator (a ±2.4 %, b ±2.2 %, both 95 % coverage). The lock-in integration time used
for all measurements was 1 s.
4 CWC measurement and uncertainty ficiency of the probe for the given particle size distribution
ηasp (cf. Appendix C; Belyaev and Levin, 1974):
Derivation of the cloud condensed water content from the
E
measured TW mole fraction xw,tot and the ambient air BWV CWCi = ηasp CWC = CWC . (3)
mole fraction xw,a requires additional input from the instru- IKF
ment’s flow measurement, together with input about the icing Here, CWCi is the indicated or measured condensed water
wind tunnel operating conditions. Equations used to derive content and E is the mass averaged hydrometeor collection
the actual condensed water content and the corresponding efficiency of the probe.
measurement uncertainty from the measured quantities are Under ideal and isokinetic sampling conditions, the CWC
briefly described in the following subsections. is equal to the ratio of the mass flow rate of hydrometeors to
Measurement of the CWC, defined as the mass of con- the volumetric flow rate of air entering the probe TW inlet.
densed water in the form of hydrometeors per volume of At the inlet, the volume of air occupied and displaced by the
air, is accompanied by hydrometeor and air sampling errors liquid or solid hydrometeors can be assumed to be negligi-
introduced by deviations from the ideal and isokinetic sam- ble for the water content of interest (Davison et al., 2016).
pling at the TW inlet. These errors are corrected by account- Indicated condensed water content CWCi is the ratio of the
ing for the actual mass averaged hydrometeor aspiration ef- actually sampled hydrometeor mass flow rate ṁh to the sam-
Atmos. Meas. Tech., 14, 2477–2500, 2021 https://doi.org/10.5194/amt-14-2477-2021B. Lang et al.: Photoacoustic hygrometer for icing wind tunnel water content measurement 2487
pled volumetric flow rate of air qa . Thus, using Eq. (3), CWC isokinetic sampling and is determined during measurement
may be calculated from the expression from
IKF ṁh IKF Us ṁa 4 ṁa
CWC = CWCi = · . (4) IKF = = = , (12)
E qa E Ua Ua ρa Ainlet 2 π
Ua ρa dinlet
4.1 Indicated CWC
where dinlet is the diameter of the circular probe TW inlet.
The flow rates ṁh and qa may be expressed in terms of the Since, with a decrease of the IKF, the collection efficiency
total mass flow sampled through the TW inlet ṁtot (IWT air, at high particle Stokes numbers decreases sub-proportionally
including hydrometeors), the mass flow of humid ambient air to the efficiency at lower Stokes numbers (cf. Fig. 3), con-
ṁa (IWT air, excluding hydrometeors), and the ambient air densed water content is overestimated for typical particle size
density ρa . The indicated CWC is then calculated from distributions. For each specific particle size distribution en-
countered during measurement, the mass averaged collection
ṁh ṁtot − ṁa efficiency E in Eq. (4) may be used to correct for the size and
CWCi = = (5)
qa ṁa /ρa IKF-dependent sampling efficiency.
ωda,a
= ρa −1 (6) 4.2.1 Mass flow measurement
ωda,tot
pa Mw xw,tot − xw,a The ambient air mass flow rate ṁa required for the calcula-
= · , (7)
R Ta 1 − xw,tot tion of the IKF is determined from the total mass flow sam-
where the density of the air was calculated assuming an ideal pled through the TW inlet, i.e., the combined mass flow rates
gas mixture of dry air (subscript da) and water vapor: through the PA cell ṁcell and the bypass path ṁbp . Together
with Eqs. (10)–(11), the ambient air mass flow rate (exclud-
ρa = ρda + ρw,a (8) ing hydrometeors) through the TW inlet is given by
pa ωda,tot ωda,tot
(9)
= Mda (1 − xw,a ) + Mw xw,a . ṁa = ṁtot =
ṁcell + ṁbp . (13)
R Ta ωda,a ωda,a
ωda,tot and ωda,a are the dry air mass fractions of the sampled
TW air, which includes evaporated hydrometeors, and of the The thermal mass flowmeters are calibrated for dry air as-
ambient air, respectively: suming dry air specific heat capacity for the gas to be mea-
sured. As humid air isobaric heat capacity increases by 1 %
ṁda Mda (1 − xw,tot ) at the maximum expected TWC (10 g m−3 CWC, fully satu-
ωda,tot = = , (10)
ṁtot Mda (1 − xw,tot ) + Mw xw,tot rated air at STP), the indicated volumetric standard flow rates
ṁda Mda (1 − xw,a ) of the flowmeters, qcell,0 and qbp,0 , are converted to humid air
ωda,a = = . (11) mass flow rates (Hardy et al., 1999):
ṁa Mda (1 − xw,a ) + Mw xw,a
cp,da
Ta and pa are the icing wind tunnel static air temperature and ṁj = ρda,0 qj,0
pressure. Mda and Mw are the molar masses of dry air and cp,tot
water and R is the universal gas constant. Real gas effects at cp,da
= ρda,0 qj,0 , (14)
the measurement temperatures, pressures, and humidities of cp,da ωda,tot + cp,w (1 − ωda,tot )
interest are minor.
where j = {cell, bp} refers to the cell or bypass measure-
4.2 Isokinetic factor and collection efficiency ment, ρda,0 is the dry air density at standard temperature and
1013.25 hPa, cp,da is the isobaric specific heat capacity of dry
The TW inlet flow rate is only set to isokinetic sampling once air, and the specific heat capacity of humid air cp,tot is calcu-
before activation of the IWT spray system. As the inlet to- lated assuming an ideal mixture model. The remaining mass
tal mass flow rate is held constant and is measured down- flow error after applying the above heat capacity correction
stream the evaporator, water vapor originating from hydrom- has not yet been determined. However, the error is assumed
eteor evaporation reduces the inlet air flow rate during TW to be below 1 %, as the change in air specific heat capacity
measurement, altering the flow field at the probe inlet and itself is below 1 % at the maximum expected total water con-
reducing the IKF. In addition to this reduction of the IKF, tent.
minor changes in the IWT air density ρa or airspeed Ua dur-
ing measurement also lead to deviations from the initially set 4.2.2 CWC estimation
isokineticity.
The isokinetic factor in Eq. (4) corrects for these sources The final expression used for icing wind tunnel CWC estima-
of disproportional sampling of ambient air in comparison to tion is obtained by combining Eq. (4) with Eqs. (7) and (10)–
https://doi.org/10.5194/amt-14-2477-2021 Atmos. Meas. Tech., 14, 2477–2500, 20212488 B. Lang et al.: Photoacoustic hygrometer for icing wind tunnel water content measurement
(14):
4 Mw
CWC = 2 U E
π dinlet a
ρda,0 cp,da (qbp,0 + qcell,0 )
·
cp,da Mda (1 − xw,tot ) + cp,w Mw xw,tot
xw,tot − xw,a
· . (15)
1 − xw,a
Although IWT static air temperature and pressure are re-
quired to set the total sampling mass flow to isokinetic TW
sampling, this result shows that if the isokinetic factor is not
calculated explicitly, air temperature and pressure only ap-
pear in the hydrometeor collection efficiency (through air Figure 9. Hygrometer measurement uncertainty contributions to
the 95 % CWC measurement uncertainty at three static air tem-
viscosity and slip correction) and otherwise are not required
peratures, an airspeed of 60 m s−1 , and a static air pressure of
to calculate the condensed water content. For minor tempera-
1013.25 hPa. Condensed water content uncertainty contributions
ture and pressure fluctuations during IWT water content mea- are given relative to the actual CWC and for isokinetic sampling.
surement, only marginal impact on CWC measurement and The ambient air is assumed to be fully saturated with respect to su-
uncertainty is anticipated by disregarding changes in IWT air percooled liquid.
temperature and pressure.
4.3 CWC measurement uncertainty
Corrections and errors introduced by the collection efficiency ter activation of the spray and before reaching a stable read-
are specific to the respective wind tunnel icing conditions ing. As a consequence of alternating TW and BWV mea-
and hence are not considered in the following general analy- surement, errors highly depend on subjective assessment dur-
sis. Instead, a mean mass averaged collection efficiency of ing evaluation and are specific to the IWT operating condi-
1 is assumed. With the numerically determined collection tions. With the goal of assessing instrument accuracy with a
efficiency given in Fig. 3, maintaining this assumption for planned second dedicated PA cell for background humidity
the evaluation of the presented measurements in icing condi- measurement, the uncertainties of the TW and BWV content
tions of freezing drizzle or rain, with median volume diame- measurement are both taken to be equal to the hygrometer
ters (MVDs) in the range of 100 µm to 650 µm, the potential measurement uncertainty given in Sect. 3.3. The presented
CWC underestimation is below 1 % (size distribution data uncertainties may, however, be taken as upper limits for a
taken from Cober et al., 2009). different hygrometer used for background humidity measure-
The uncertainty of the condensed water content measure- ment with similar or better accuracy.
ment is derived from a first-order propagation of the uncer- Figure 9 shows the calculated hygrometer contribution
tainties of the quantities appearing in Eq. (15) according to to the condensed water content measurement uncertainty at
the Guide to the Expression of Uncertainty in Measurement three IWT static air temperatures. Temperatures of −30,
(GUM; Joint Committee for Guides in Metrology, 2008a). −18, and −5 ◦ C were examined, again assuming fully sat-
Uncertainties not distributed normally have been converted urated air with respect to supercooled liquid water, as this
to standard uncertainties for the analytical calculations. Un- is expected for the closed-circuit icing wind tunnel. The
less otherwise stated, all uncertainties are given in terms of measurement uncertainty contributions are given relative to
the 95 % coverage interval. A summary of the individual un- the actual CWC. The contributions to the measurement of
certainties of the input quantities is given in Table E1 in Ap- the background water vapor concentration (Uxw,a ; dashed
pendix E of this work. lines) indicate constant background humidities with associ-
The current single-hygrometer instrument only allows ei- ated constant absolute measurement uncertainties.
ther TW or BWV content measurement. Alternating between The hygrometer’s contribution to the CWC measurement
both measurements to determine the CWC inevitably results uncertainty increases rapidly with lower water content and
in a measurement error due to the dynamic behavior of the increasing temperature. The latter circumstance is a result
background water content, which is mainly defined by the of the rising absolute BWV concentration uncertainty with
initial IWT air saturation level and stability of the tempera- increasing background humidity, which dominates the dif-
ture conditioning during the measurement. Depending on the ference of measured total and background water vapor con-
saturation level preceding activation of the spray, the back- centrations at low CWC (last term in Eq. 15). For a con-
ground water content during the probe intercomparison in- densed water content of 0.5 g m−3 and an IWT temperature
creased by up to 0.5 g m−3 for as long as five minutes af- of −5 ◦ C, the combined hygrometer uncertainty contribution
Atmos. Meas. Tech., 14, 2477–2500, 2021 https://doi.org/10.5194/amt-14-2477-2021You can also read
