Insights into Humidification Measurement Methods: Resolving High Water Contents with an Optical Gas Diagnostics Tool

EFCF 2025: Low-Temp. Fuel Cells, Electrolysers & H2 Processing 1 – 4 July 2025, Lucerne Switzerland https://doi.org/10.5281/zenodo.17476269 B0709 Page 1/10 B0709 Insights into Humidification Measurement Methods: Resolving High Water Contents with an Optical Gas Diagnostics Tool Katharina Braun*, Bastian Rüppel, Lukas Weiß, Michael Wensing Friedrich-Alexander-Universität Erlangen-Nürnberg, Professorship for Fluid Systems Technology, Cauerstraße 4, 91058 Erlangen/Germany; *Contact corresponding authors: www.EFCF.com/ContactRequest Abstract The humidification of feed gases, and water management in general, is crucial for the performance and durability of proton exchange membrane fuel cells (PEMFC). Research and development require precise and, for dynamic operation, time-resolved determination of the water content of the gas flows on the cathode and anode side. Available sensors show measured value deviations especially in the operating range of PEM fuel cells (temperatures around 80°C at high relative humidities close to saturation). Occurring condensations of liquid water lead to a flooding of the sensor with long recovery times. Via this study we sought to better understand the measurement of relative humidity. We investigate the influencing factors and accuracy of sensors based on electrical capacitance. Furthermore, we analyze the dynamics of the sensor to evaluate the temporal resolution of the operating conditions. As a reference measurement and alternative option for research and development, we use an optical measurement of gas humidity based on Raman scattering [1]; after directing a laser beam into the gas flow, this method analyzes backscattered light using a spectrometer and advanced processing techniques. The results show the molar composition of the gas mixture. For this study, we tailored the analysis and calibration procedures specifically to the assessment of water content. The incorporation of data on temperature and pressure enables us to determine relative humidity accurately and with temporal resolution. This method is a valuable addition to conventional humidity sensors, especially in measurement environments where gas flows with variable composition, state conditions and high water contents are present, such as in fuel cell research. EFCF 2025: Low-Temp. Fuel Cells, Electrolysers & H2 Processing 1 – 4 July 2025, Lucerne Switzerland https://doi.org/10.5281/zenodo.17476269 B0709 Page 2/10 Introduction Polymer electrolyte fuel cells (PEFCs) consist of ion conducting membranes. These have higher conductivities with a higher water content and therefore lead to a higher performance. Besides the water produced during the operation, water is also supplied by humidifying the inlet gases to keep the membrane hydrated. However, too much water leads to flooding and mass transport limitations inside the cell followed by degradation. Therefore, water management is a key element of fuel cell operation. So far, PFSA based membranes such as Nafion have been used in PEFCs, but due to the impending ban on perand polyfluoroalkyl substances (PFAS), researchers are focusing on hydrocarbon-based materials for proton exchange membranes (PEM). These different types of membranes exhibit different swelling behavior and ion conductivity at different relative humidities (RH). In order to identify these different membrane properties, we first must be able to precisely set these operating conditions during fuel cell testing. This requires appropriate humidification methods, which we discussed in a previous publication [2], and humidity sensors, which we focus on in this work. We want to give a deeper insight in measuring relative humidity by showing the underlying physical relations and currently available measuring methods. Measuring relative humidity in fuel cell environment, requires measurement at high humidities of 70 to 100%, and temperatures of 65-90°C. To avoid condensation usually sensors with heated sensor heads are used. We analyze inaccuracies and practical issues, which make precise RHmeasurements quite complex. 1. Scientific Approach When reporting the results of fuel cell tests, the relative humidity is usually specified as the operating condition. The relative humidity 𝜑 is the degree of saturation of a humid gas. It describes how much water is contained in relation to how much water can be contained without condensation at a certain temperature. It is defined as the ratio of vapor partial pressure 𝑝𝑤 to saturation vapor pressure 𝑝𝑠. 𝜑 = 𝑝𝑤 𝑝𝑠 (1) The saturation vapor pressure defines the saturated state of the gas-water mixture. In this state, the water vapor content becomes maximum and additional water supplied to the system occurs in liquid state. It cannot be carried as vapor. The saturation vapor pressure is only dependent on the temperature. The relationship is given by the vapor pressure curve, which marks the boundary line between vapor and liquid. The saturation pressure can be calculated by simplified equation, e.g. equation according to Antoine [3] or looked up in socalled steam tables [4]. How to physically adjust the operating condition “relative humidity” in a test bench depends on the type of humidification system. Usually, the dew point temperature is set, for example in a commonly used bubble humidification system. It corresponds to the water temperature inside the bubble humidifier, from which 100% humidified gas emerges. It is then heated to the temperature of the fuel cell, thereby setting the desired relative humidity in relation to the operating temperature of the fuel cell. For a desired fuel cell temperature 𝑇𝐹𝐶, and a desired relative humidity 𝜑𝐹𝐶 of the gas in the fuel cell, the water content 𝑥 can be calculated with the molar mass of water 𝑀𝑊, the molar EFCF 2025: Low-Temp. Fuel Cells, Electrolysers & H2 Processing 1 – 4 July 2025, Lucerne Switzerland https://doi.org/10.5281/zenodo.17476269 B0709 Page 3/10 mass of dry gas 𝑀𝐺,𝑑𝑟𝑦 , the overall pressure 𝑝 and the saturation vapor pressure 𝑝𝑠 corresponding to the fuel cell temperature 𝑇𝐹𝐶 (see equation 2). [5] 𝑥𝐹𝐶 =𝑀𝑊 𝑀𝐺,𝑑𝑟𝑦 ∙𝑝𝑤 𝑝 − 𝑝𝑤 =𝑀𝑊 𝑀𝐺,𝑑𝑟𝑦 ∙𝑝𝑠(𝑇𝐹𝐶)∙ 𝜑𝐹𝐶 𝑝 − 𝑝𝑠(𝑇𝐹𝐶)∙ 𝜑𝐹𝐶 (2) The water content 𝑥 is a parameter which remains constant when a humidified gas is heated or cooled. It only changes when water is added or removed, e.g. in a water separator. Thus, the water content is only dependent on the mass of water and gas and can also be described as the ratio of mass of water 𝑚𝑤, and mass of dry gas 𝑚𝐺,𝑑𝑟𝑦: 𝑥 = 𝑚𝑊 𝑚𝐺,𝑑𝑟𝑦 (3) To stay with the example of the bubble humidification: The water content in the bubbler, where the temperature of the saturated gas is the dew point temperature, is the same as in the gas inlet of the fuel cell, where temperatures are higher than the dew point temperature. So, to calculate the dew point temperature out of a given relative humidity, we equate the water content 𝑥𝐹𝐶 with the water content 𝑥𝑑 at the dew point temperature. Thus, using eq. 2 and setting the relative humidity to 100 % leads to the saturation vapor pressure 𝑝𝑠. From this pressure, the dew point temperature 𝑇𝑑 can be extracted out of the steam table. Here, the overall pressure 𝑝 must be known. 𝑥𝐹𝐶 =𝑀𝑊 𝑀𝐺,𝑑𝑟𝑦 ∙𝑝𝑠(𝑇𝐹𝐶)∙ 𝜑𝐹𝐶 𝑝 − 𝑝𝑠(𝑇𝐹𝐶)∙ 𝜑𝐹𝐶 = 𝑥𝑑=𝑀𝑊 𝑀𝐺,𝑑𝑟𝑦 ∙𝑝𝑠(𝑇𝑑)∙ 1 𝑝 − 𝑝𝑠(𝑇𝑑)∙ 1 (4) 𝑝𝑠(𝑇𝑑)=𝑥𝑑∙ 𝑝 𝑀𝑊 𝑀𝐺,𝑑𝑟𝑦 + 𝑥𝑑 (5) Comparing the two thermodynamic parameters dew point temperature and relative humidity, the dew point temperature is an absolute parameter, which defines the amount of water in a saturated gas flow. The relative humidity expresses a comparison of the amount of water (via the partial pressure) to a reference value, here saturation pressure, which is temperature dependent, at a given water content and temperature. This applies in the equation context shown and the system described. Generally, knowing the water content of a gas mixture gives you an information about the mass fractions. From this point, relative humidity can be calculated taking temperatures and pressures into account. In addition to the water content, the partial pressure of water is also a fundamental parameter for comparing humidified gases, which we use in our optical gas diagnostic tool. Based on these explanations, the question arises how relative humidity sensors measure. Measuring in fuel cell systems and test stands requires precise measurement technology. They have to be able to measure reproducibly at high relative humidities. We also need a short response time for dynamic test procedure. There are different kind of humidity sensors based on their working principle. Mostly, capacitive sensors are used. They are mounted in gas channels and usually need heating to be able to measure at the high humidities, which are required for ideal fuel cell operation. The heated sensor head should avoid flooding of EFCF 2025: Low-Temp. Fuel Cells, Electrolysers & H2 Processing 1 – 4 July 2025, Lucerne Switzerland https://doi.org/10.5281/zenodo.17476269 B0709 Page 4/10 the sensor, which would otherwise require long flushing periods with dry gas to recover the sensor. To avoid flooding of the sensor, also the right mounting position is beneficial. Capacitive sensors have a polymer layer between capacitor electrodes and measure the change of the dielectric constant. The polymer is hygroscopic and therefore the dielectric constant increases as the polymer absorbs water [6]. In the following, we describe the detailed calculation path in a heated humidity sensor. As the directly measured relative humidity belongs to the temperature of the heated sensor head rather than the gas temperature, calculations are necessary to receive the relative humidity at the measured point. Figure 1 shows the calculation scheme. Figure 1: Calculation scheme of a capacitive humidity sensor measuring the electric capacity Each sensor has a calibration curve, which relates the measured electric capacity 𝐶 to a resulting relative humidity. With the temperature of the heated sensor head 𝑇𝑠𝑒𝑛𝑠𝑜𝑟 ℎ𝑒𝑎𝑑 the vapor saturation pressure can be determined. Using that with the relative humidity the partial pressure of water 𝑝𝑤 results. This pressure is equal to the saturation pressure at the dew point temperature we are looking for. To evaluate the relative humidity of our measurement point as well, we require two more properties, temperature and pressure, at this specific measurement point. Figure 2 shows the calculation scheme for the relative humidity out of the measured dew point temperature. Figure 2: Calculation scheme for determination of the relative humidity out of three measured parameters – dew point temperature Td, pressure p and temperature T With the vapor saturation pressure 𝑝𝑠(𝑇𝑑), the water content 𝑥𝑑 can be calculated (Eq.6). Using the measured system pressure, the partial pressure of water can be determined (Eq 7). Taking the ratio of this pressure and the vapor saturation pressure 𝑝𝑠(𝑇), which belongs RHC EFCF 2025: Low-Temp. Fuel Cells, Electrolysers & H2 Processing 1 – 4 July 2025, Lucerne Switzerland https://doi.org/10.5281/zenodo.17476269 B0709 Page 5/10 to the measured temperature, results in the relative humidity 𝜑 at our specific measurement point (Eq. 8) 𝑥𝑑=𝑀𝑊 𝑀𝐺,𝑑𝑟𝑦 ∙𝑝𝑠(𝑇𝑑)∙ 1 𝑝 − 𝑝𝑠(𝑇𝑑)∙ 1 (6) 𝑝𝑤=𝑥𝑑∙ 𝑝 𝑀𝑊 𝑀𝐺,𝑑𝑟𝑦 + 𝑥𝑑 (7) 𝜑 = 𝑝𝑤 𝑝𝑠(𝑇) (8) As we see, the relative humidity given by the humidity sensor depends on two further parameters, namely temperature and pressure. In practice, this means sensors, which tell us a “relative humidity” value and have a heated sensor head, must measure those two parameters additionally. The capacity measured belongs to a local humidity condition influenced by the sensor heating. To determine the relative humidity in the measuring point, the temperature of that specific point must be included. The more parameters are measured, the higher the inaccuracy of the measurement due to systematical and statistical errors. Figure 3 shows an error dependency of the relative humidity. Figure 3: Deviation of relative humidity in dependence of deviation from measured values (dew point temperature and temperature) to their respective true values Assuming no difference between the measured dew point temperature 𝑇𝑑,𝑚 and the true value 𝑇𝑑,𝑡 , and no deviation of the measured temperature 𝑇𝑚 from the true temperature 𝑇𝑡 , the result is the true relative humidity 𝑅𝐻𝑡. However, the reality shows, we usually have deviations in all parameters we measure. Figure 3 shows the deviation of the calculated value relative humidity as a function of the deviation of the dew point temperature measured EFCF 2025: Low-Temp. Fuel Cells, Electrolysers & H2 Processing 1 – 4 July 2025, Lucerne Switzerland https://doi.org/10.5281/zenodo.17476269 B0709 Page 6/10 with the humidity sensor and the temperature measured for example with an Pt100 element from their respective true values. The pressure is assumed constant. We want to make a short example: At a fuel cell temperature of 80°C and a desired relative humidity of 80 %, the dew point temperature must be 74.58°C. Overestimating the dew point temperature with 1 % und underestimating the temperature with 1.5 %, concludes in a relative humidity 8.3 % higher than the true value. This would result in a relative humidity of 86.6 %. Thinking of this deviation in the context of fuel cell operation, we would expect a considerable deviation in performance from what we have according to our actual operating conditions. In a capacitive sensor, there are internal calculations to get the dew point temperature, as shown in figure 1. We want to present a sensor, an optical gas diagnostics tool, which directly measures the partial pressure. Further advantages are shown in the experimental part. The optical gas diagnostic tool treats water the same way as the other species of a gas mixture. Most molecules show the phenomenon of inelastic light scattering. In a comparatively rare process named Raman scattering, incident light excites an electron of the molecule. The relaxation happens along with the emission of light whereby a small portion undergoes a frequency shift that is characteristic per species, the so-called Raman shift. This species dependency allows for spectroscopic measurements. A laser provides high intensity excitation and the scattered response contains information on the composition of the sample. [7] In our case, these samples are the gas flows inside the fuel cell system. The major species are hydrogen, oxygen, nitrogen and water. The Raman signals of some of them are shown in figure 4. Figure 4: Example of the Raman spectrum of humidified air with detected signals Their vibrational Stokes-Raman lines are well separated and the basis for our evaluation. The intensity of each of them linearly scales with the number density of the respective molecule. However, for quantitative results the method needs calibration. On one hand, the species are unequally likely to undergo Raman scattering after incident of a photon. The scattering cross section is quantizing this and often given relative to that of nitrogen. On the other hand, there are factors in detection efficiency that are wavelength dependent, for example the quantum efficiency of the detector. These are specific for the individually used hardware. Together with the cross sections, we experimentally determine these influences in known model gas mixtures, resulting in calibration constants 𝑐𝑖. We apply them to the intensities 𝐼𝑖 when evaluating the mole fraction 𝑦𝑖 of component 𝑖 in a mixture with 𝑘 species through equation 9. 𝑦𝑖= 𝐼𝑖 𝑐𝑖 ∑𝐼𝑘 𝑐𝑘 𝑘 (9) EFCF 2025: Low-Temp. Fuel Cells, Electrolysers & H2 Processing 1 – 4 July 2025, Lucerne Switzerland https://doi.org/10.5281/zenodo.17476269 B0709 Page 7/10 When it comes to humidity measurement, with Raman scattering the mole fraction is the primary measured quantity. It links to the water content 𝑥 via the molar masses and to the partial pressure via Dalton’s law and the equation of state. The relative humidity calculation can follow from either. 2. Experiments Beside the difference in the principle of measurement, we want to evaluate the dynamic behavior of the two measurement methods experimentally. We built a setup (see Figure 5) with a measuring cell (1) to which we supply humidified gas. With three different mass flow controllers (7), we are able to define a gas mixture of nitrogen, oxygen and/or hydrogen. A controlled evaporator and mixer (CEM) (8) evaporates the water supplied via a mass flow controller (9) from a water reservoir (10) and mixes it with the dry gas mixture. We can define the relative humidity by setting the flows and temperature in the CEM. This setup provides controlled humidified gas flows, which we used to validate our humidity sensors. We implemented a capacitive sensor from Vaisala (5) with integrated sensor heating and compared it with the gas diagnostic tool presented in this work. The gas diagnostics tool utilizes a frequency-doubled Nd:YAG laser (4). It emits 500 mW of green light at 532 nm in continuous wave operation. An optical fiber guides the laser beam to a set of optics contained in a rigid setup, which we call Raman Gun (2). On the outlet, a lens focuses the excitation light into a point in the gas flow and collects a fraction of the scattered light simultaneously. Another optical fiber bundle connects the optics to a spectrometer (3). There, an optical grating disperses the light due to the different wavelengths and a line-shaped charge-coupled device (CCD) sensor detects the intensities as a function of the Raman shift. Its readings are post-processed and evaluated in a Python software that eventually provides the results to the data acquisition system. [8] The intensity of the scattered light however is small. Experimentally, we address this with an appropriate integration time of the CCD among other actions. A typical value would be one second within which the sensor accumulates the signals. This limits the sample rate of the optical tool in a way that is unknown with electrical sensors. As the intensity scales linear with increasing mole fraction and pressure, this technique performs best in high humidity environments. For the required optical access, we implement a window insert where the correct thread is available by design or a measuring cell that blends in any piping with arbitrary adapters. The latter comes with temperature control, because we need to avoid condensation on the window. As explained in section 1, we also add a temperature sensor to be able to determine not only the dew point temperature but also the relative humidity at the measuring point. EFCF 2025: Low-Temp. Fuel Cells, Electrolysers & H2 Processing 1 – 4 July 2025, Lucerne Switzerland https://doi.org/10.5281/zenodo.17476269 B0709 Page 8/10 Figure 5: Setup with measuring cell (1), Raman Gun (2), spectrometer (3), laser (4), capacitive humidity sensore (5), temperature sensor (6), mass flow controller (7), Controlled evaporator and mixer (CEM) (8), Coriolis-mass flow meter (9), pressurized water reservoir (10) 3. Results There are many interesting characteristics in measurement of humidity, such as the evaluation of reproducibility of the measurement, the determination of statistical and systematical errors of the measurement, the installation and durability of the sensor or the dynamic behavior of the sensor. Since we see a high potential for improvement in fuel cell testing by accelerating test procedures and using data between steady-state operating conditions, we want to compare the dynamic behavior of our two measurement principles. Figure 6: Temporal resolution of the water content derived from Raman spectrum and capacitive humidity sensor measurement CEM 2 3 4 5 67 7 7 8 9 10 1 EFCF 2025: Low-Temp. Fuel Cells, Electrolysers & H2 Processing 1 – 4 July 2025, Lucerne Switzerland https://doi.org/10.5281/zenodo.17476269 B0709 Page 9/10 We applied a change of water content in a constant gas flow and displayed the temporal evolvement in figure 6. We see a direct response from the Raman sensor and a 50 s belayed increase of water content in the conventional sensor. This shows one of the main characteristics of the optical gas diagnostic tool. 4. Conclusion To summarize, we showed the challenges of measuring relative humidity. First, we emphasized the difference of the parameters “relative humidity” and “dew point temperature”: The first one expresses a comparison of the amount of water in a humidified gas to a reference value, here saturation pressure, and the second defines the amount of water in a saturated gas flow. We described the measurement principle of conventional capacitive humidity sensors, which measure a local relative humidity and return the dew point of the measuring point. From there, we can determine the relative humidity of the measuring point by considering the measured temperature and pressure. With a sample calculation, we showed that small deviations in measurement of dew point temperature and/or temperature result in relevant deviations of relative humidity, which lead to a considerable deviation in fuel cell performance. We introduced an optical gas diagnostic tool which is based on Raman scattering and measures the molar fraction. First results show a short response time in comparison to the conventional sensors. We see further benefits in directly calculating the partial pressure of water from the molar fraction and with that less influence of further measured values. The optical diagnostic tool will be evaluated in further research. Acknowledgements This work was carried out as part of the MABAS project, which is funded by the German Federal Ministry of Economy and Climate Protection. The funding directive is coordinated and implemented by Projektträger Jlich Forschungszentrum Jlich GmbH. References [1] C.-Y. Lee et al., "Embedded flexible micro-sensors in MEA for measuring temperature and humidity in a micro-fuel cell," Journal of Power Sources, vol. 181, no. 2, pp. 237– 243, 2008, doi: 10.1016/j.jpowsour.2008.01.020. [2] K. Braun et al., "Advancing Fuel Cell Testing Environments: Overcoming Limitations in Conventional Humidification Methods," in SAE Technical Paper Series, Columbus, Ohio, United States, K. Braun, J. Luetzenkirchen, L. Weiss, and M. Wensing, Eds., 2024, doi: 10.4271/2024-01-4321. [3] H. Korsten, "Vorausberechnung von Dampfdruckkurven mit Hilfe eines einzigen Parameters," Chem.-Ing.-Tech., vol. 72, 1-2, pp. 78–81, 2000, doi: 10.1002/15222640(200001)72:1/2<78::AID-CITE78>3.0.CO;2-B. 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