%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% %% %% Please do not use \input{...} to include other tex files. %% %% Submit your LaTeX manuscript as one .tex document. %% %% %% %% All additional figures and files should be attached %% %% separately and not embedded in the \TeX\ document itself. %% %% %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%\documentclass[referee,sn-basic]{sn-jnl}% referee option is meant for double line spacing %%=======================================================%% %% to print line numbers in the margin use lineno option %% %%=======================================================%% %%\documentclass[lineno,sn-basic]{sn-jnl}% Basic Springer Nature Reference Style/Chemistry Reference Style %%======================================================%% %% to compile with pdflatex/xelatex use pdflatex option %% %%======================================================%% %%\documentclass[pdflatex,sn-basic]{sn-jnl}% Basic Springer Nature Reference Style/Chemistry Reference Style %%\documentclass[sn-basic]{sn-jnl}% Basic Springer Nature Reference Style/Chemistry Reference Style \documentclass[sn-mathphys]{sn-jnl}% Math and Physical Sciences Reference Style %%\documentclass[sn-aps]{sn-jnl}% American Physical Society (APS) Reference Style %%\documentclass[sn-vancouver]{sn-jnl}% Vancouver Reference Style %%\documentclass[sn-apa]{sn-jnl}% APA Reference Style %%\documentclass[sn-chicago]{sn-jnl}% Chicago-based Humanities Reference Style %%\documentclass[sn-standardnature]{sn-jnl}% Standard Nature Portfolio Reference Style %%\documentclass[default]{sn-jnl}% Default %%\documentclass[default,iicol]{sn-jnl}% Default with double column layout %%%% Standard Packages %% %%%% %%%%%=============================================================================%%%% %%%% Remarks: This template is provided to aid authors with the preparation %%%% of original research articles intended for submission to journals published %%%% by Springer Nature. 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A detailed User Manual is available in the %%%% template package for technical guidance. %%%%%=============================================================================%%%% \usepackage{graphicx} \usepackage{array} \newcolumntype{M}[1]{>{\centering\arraybackslash}m{#1}} \newcolumntype{N}{@{}m{0pt}@{}} \jyear{2021}% %% as per the requirement new theorem styles can be included as shown below \theoremstyle{thmstyleone}% \newtheorem{theorem}{Theorem}% meant for continuous numbers %%\newtheorem{theorem}{Theorem}[section]% meant for sectionwise numbers %% optional argument [theorem] produces theorem numbering sequence instead of independent numbers for Proposition \newtheorem{proposition}[theorem]{Proposition}% %%\newtheorem{proposition}{Proposition}% to get separate numbers for theorem and proposition etc. \theoremstyle{thmstyletwo}% \newtheorem{example}{Example}% \newtheorem{remark}{Remark}% \theoremstyle{thmstylethree}% \newtheorem{definition}{Definition}% \raggedbottom %%\unnumbered% uncomment this for unnumbered level heads \begin{document} \title[Article Title]{Novel custom-made design, analysis and simulation of hydrogen PEM fuel cell for high endurance small UAV applications} %%=============================================================%% %% Prefix -> \pfx{Dr} %% GivenName -> \fnm{Joergen W.} %% Particle -> \spfx{van der} -> surname prefix %% FamilyName -> \sur{Ploeg} %% Suffix -> \sfx{IV} %% NatureName -> \tanm{Poet Laureate} -> Title after name %% Degrees -> \dgr{MSc, PhD} %% \author*[1,2]{\pfx{Dr} \fnm{Joergen W.} \spfx{van der} \sur{Ploeg} \sfx{IV} \tanm{Poet Laureate} %% \dgr{MSc, PhD}}\email{iauthor@gmail.com} %%=============================================================%% \author[1]{\fnm{Soham} \sur{Prajapati}}\email{sohamprajapati0511@gmail.com} \author[2]{\fnm{Parth S.} \sur{Thakar}}\email{parth.thakar@sot.pdpu.ac.in} \author*[3]{\fnm{Anilkumar} \sur{Markana}}\email{anil.markana@spt.pdpu.ac.in} \affil[1]{\orgname{Pandit Deendayal Energy University}, \orgaddress{\city{Gandhinagar}, \postcode{382007}, \state{Gujarat}, \country{India}}} \affil[2]{\orgdiv{Dept. of Electronics and Communication}, \orgname{Pandit Deendayal Energy University}, \orgaddress{\city{Gandhinagar}, \postcode{382007}, \state{Gujarat}, \country{India}}} \affil[3]{\orgdiv{Dept. of Electrical Engineering}, \orgname{Pandit Deendayal Energy University}, \orgaddress{\city{Gandhinagar}, \postcode{382007}, \state{Gujarat}, \country{India}}} %%==================================%% %% sample for unstructured abstract %% %%==================================%% \abstract{The purpose of this paper is to propose a new methodology to devise a custom-made hydrogen-based proton exchange membrane fuel cell (HPEMFC) system for an experimental fixed-wing small unmanned aerial vehicles (SUAVs) discussed in \cite{sharma}. The proposed fuel cell is designed for three times higher flight endurance than the conventional battery-based powertrain. The chosen SUAV representing a class of high-altitude UAVs, has an operational altitude of 4500 m, cruising speed of 12-20 m/s, take-off weight of 4 kg, wing-span of 1.61 m and battery-powered flight endurance of one hour. The characteristic parameters and design configurations of the fuel cell are determined by employing first principles of electrochemistry and thermodynamics. Corresponding simulations are performed using the popular development tools like MATLAB/Simulink. The vital results in the form of – polarization and power curves for fuel cell, against the current density are obtained, which are further narrowed down to meet the target power requirements in determining the size of the hydrogen storage tank. The paper also comments on the auxiliary systems and fuel cell powertrain for SUAVs. Finally, the design efficiency of 54\% for the fuel cell is achieved with respect to open circuit voltage. } %%================================%% %% Sample for structured abstract %% %%================================%% % \abstract{\textbf{Purpose:} The abstract serves both as a general introduction to the topic and as a brief, non-technical summary of the main results and their implications. The abstract must not include subheadings (unless expressly permitted in the journal's Instructions to Authors), equations or citations. As a guide the abstract should not exceed 200 words. Most journals do not set a hard limit however authors are advised to check the author instructions for the journal they are submitting to. % % \textbf{Methods:} The abstract serves both as a general introduction to the topic and as a brief, non-technical summary of the main results and their implications. The abstract must not include subheadings (unless expressly permitted in the journal's Instructions to Authors), equations or citations. As a guide the abstract should not exceed 200 words. Most journals do not set a hard limit however authors are advised to check the author instructions for the journal they are submitting to. % % \textbf{Results:} The abstract serves both as a general introduction to the topic and as a brief, non-technical summary of the main results and their implications. The abstract must not include subheadings (unless expressly permitted in the journal's Instructions to Authors), equations or citations. As a guide the abstract should not exceed 200 words. Most journals do not set a hard limit however authors are advised to check the author instructions for the journal they are submitting to. % % \textbf{Conclusion:} The abstract serves both as a general introduction to the topic and as a brief, non-technical summary of the main results and their implications. The abstract must not include subheadings (unless expressly permitted in the journal's Instructions to Authors), equations or citations. As a guide the abstract should not exceed 200 words. Most journals do not set a hard limit however authors are advised to check the author instructions for the journal they are submitting to.} \keywords{PEM fuel cell, Hydrogen storage tank, UAVs, High endurance flight, Clean technology} %%\pacs[JEL Classification]{D8, H51} %%\pacs[MSC Classification]{35A01, 65L10, 65L12, 65L20, 65L70} \maketitle \section{Introduction}\label{sec1} In recent times, with the advent of UAV industries, the demand of high endurance flight is ever increasing. Such flights have a number of applications in agriculture, medical, military and surveillance sectors. The fixed-wing aircrafts are well-suited for such applications, since their geometric design favor a high lift to drag ratio. Besides geometry, flight endurance is also dependent on the energy content of the power system. Some industries utilize micro internal combustion engines (ICEs) for power generation using aviation fuels. However, the aviation fuels produce toxic and greenhouse gases like the oxides of nitrogen, sulphur and carbon among which, carbon alone by aviation industry contributes to 2.1\% of the global carbon emission. In order to reduce such emissions, research is gaining momentum towards providing sustainable technologies. The battery powertrain technology is popularly conceptualized as a sustainable solution. In fact, the most popular power system in present day UAV industry uses batteries. Although, this battery technologies are working towards offering rather efficient solutions, they still fail being sustainable. Many literary scholars \cite{hammack} argue in terms of the life cycle assessment of batteries that even before the battery powered vehicle arrives the dealership, many fossil fuels are burnt for their production, transportation and recharging purposes. Therefore, recently there has been an increasing interest in rather more sustainable alternatives to empower UAVs. Among which, hydrogen-based proton exchange membrane fuel cells (HPEMFCs) have shown some promising evidences by offering more efficient and robust power system solution in the market. The above statement can be supported by data sheets of fuel cells manufactured by a UK based fuel cell company: Intelligent energy systems. Whereas the conventional batteries mainly use rare earth elements like Lithium, HPEMFC utilizes the quite abundantly available gases, hydrogen and oxygen which can be readily extracted from either water or air directly through the use of water electrolysis. The injection of these gases at sufficient partial pressures will yield the required power and in turn exhausts pure water vapor as the output. Besides, PEMFCs, also features relatively higher power density, light weight and higher discharge rating. Therefore, in terms of its suitability and implementation, they show a great potential as power systems especially for UAVs and automobiles alike. For instance, the gravimetric power density of HPEMFC system along with its storage tank and auxiliary equipment, is three times higher than the commercially available batteries. For these reasons we propose here a hydrogen fuel cell-based power system design and custom-made solution for a specific fixed-wing UAV. The fixed-wing SUAVs that are less than 20 kg, are small enough to be man-portable and having practically no take-off runways. Thus, they even can be launched directly by high-altitude throw. Therefore, in this work, a particular SUAV of such kind, which is an experimental high altitude fixed-wing aircraft as given in \cite{sharma} is considered. The chosen SUAV in this work, has an operational altitude of 4500 m, cruising speed of 12-20 m/s, take-off weight of 4 kg and a wing-span of 1.61 m. The flight endurance of battery powered SUAV here, is one hour. This endurance is subject to a nominal flight profile which involves short duration 150 W take-off and landing phases and long duration 40 W cruising phase. In this work, we develop a fuel cell system with higher endurance and discuss the important auxiliary systems required for a desirable response for similar power requirements. \subsection{Literature Review}\label{litreview} In the context of UAV based fuel cells, \cite{apeland} has implemented and analyzed suitability of fuel cells in quadcopter. Many authors like \cite{rakhtala}, \cite{yigit} have done experimental analysis to check fuel cell compatibility with current power electronics. Yegit et. al., from \cite{yigit16} discusses a mathematical model of an electrolyzer to generate hydrogen gas from water. The thermodynamics and electrochemistry of the HPEMFCs according to the current trend and thumb rules is mentioned in works like \cite{chen}, \cite{hoogers}, \cite{pukrushpan} and \cite{spiegel}. In \cite{spiegel}, Spiegel discusses in-depth mathematical models of HPEMFCs. Westenberger et. al., in \cite{westenberger} has shown that the fuel cell energy content drastically increases by storing the hydrogen at cryogenic temperatures as an increase in density. Furthermore, Gomez et. al., from \cite{gomez} has shown the storage configuration of such liquid hydrogen tanks in commercial aviation. Many academic and industrial organizations of various governments of the world have captured interest in this technology. Authors like \cite{delorme}, \cite{hosseini}, \cite{rousseau}, \cite{singla} and \cite{zheng} have presented the prospective future of hydrogen using current statistics and demands in economy. \subsection{Main Contribution}\label{maincontri} There is a strong demand in UAV industries for high endurance and fast recharging power systems. The popular engineering alternative-batteries fail in meeting this demand. The work demonstrated in this paper proposes a HPEMFC mathematical model for powering an existing UAV and discusses the industrial, chemical and engineering advantages of its utilization. Following the method proposed, one may iterate the inputs to emulate the desired power requirements. The paper also focuses on the storage tank and auxiliary systems that make the fuel cell response adaptive and robust. This work also discusses the risks of hydrogen that is restraining its adoptability in the market. These critical properties are justified using academic evidences. Finally, after deriving the necessary mathematical models of various subsystems, the work illustrates the hydrogen powertrain technology for the SUAV. \subsection{Paper Organization}\label{paperorg} Section 2 identifies the power requirements of the SUAV discussed. Section 3 discusses the engineering perspective of fuel cells for sustainability. It also highlights some crucial risks associated with the properties of hydrogen. Section 4 delineates the overall architecture of the HPEMFC. Section 5 derives the methodology to derive the target power requirements of the SUAV. From the results obtained from Section 5, the storage tank design is computed in Section 6. Section 7 discusses the auxiliary systems required for an improved fuel cell performance. Section 8 summarizes the results. Finally, Section 9 concludes the research findings. \section{Identifications of Power Requirements}\label{sec2} For the SUAV considered here, the maximum power requirement for take-off and landing phase is about 150W and for cruising phase is about 40W. Therefore, a maximum energy content of the flight for an endurance of 60 minutes, will be about 150 Wh when used batteries for powering \cite{sharma}. The battery specifications are not revealed in \cite{sharma}, thus we will tailor some assumptions about the power and propeller specifications. The wingspan of the SUAV is 1.61m. Generally, a propeller having a diameter $\frac{1}{4}$th span of the wingspan is favorable, obviating the torque and gyroscopic effects. The pitch of the propeller is motor specific, and we can arbitrarily select here. Therefore, we choose propeller diameter of 16 inch and pitch of 10 inch (commercially available dimensions). Using these dimensions of the propeller, from APC propeller performance data, we can develop the curve illustrated in Figure \ref{figrpm}, the power (W) utilized by propeller of said dimension vs propeller rpm. From Figure 1, we can say that for 150W of power demand, we can assume the rpm of about 4600 rpm for the selected propeller dimensions. \begin{figure}[H]\label{figrpm} \centering \includegraphics[scale=0.3]{"rpm.png"} \caption{Propeller power requirement (W) vs Propeller rpm} \end{figure} Furthermore, we supplant the battery specification by assumed HPEMFC power requirements for 150W power demand as, \begin{table}[h] \begin{center} \begin{minipage}{174pt} \caption{HPEMFC power performance requirement}\label{tabreq}% \begin{tabular}{@{}llll@{}} \toprule Performance & Required Values\\ \midrule Maximum power & 150W \\ Flight endurance & 3 hrs. \\ Total energy content & 450 Wh \\ \botrule \end{tabular} \end{minipage} \end{center} \end{table} Most of the commercially available lithium batteries have 3 cell configurations with 3.7V each. Thus, selecting a value of 11.1V for fuel cell system will bring clarity in comparing the battery performance. \section{Fuel Cells - Engineering Perspective}\label{sec3} In \cite{hammack}, Hammack et. al., gives fact-based case studies for clarifying the popular misconception that batteries are free from producing carbon emissions. The pre-processing tasks consume an incredible amount of fossil fuel energy before the product arrives at the dealership. There has been some great progress in the development of hydrogen fuel cell systems for UAVs. Many commercially built versions have commenced to become ecumenical for business fleets, like \textit{Intelligent Energy Systems} has a range of products that are powered by hydrogen fuel cell systems. The empirical data shown in their product datasheets shows that specific energy content of HPEMFCs (including the storage tank) is three times that of the battery. Lithium batteries are compared with HPEMFCs in Table \ref{tabcompare}. \begin{table}[h] \caption{HPEMFCs vs Lithium batteries techno-political comparison} \begin{tabular}{M{3.7cm} M{3.7cm} M{3.7cm}} \toprule Aspect of the system & Lithium Batteries & HPEMFC + storage tank\\ \midrule Specific energy content & 150-200 Wh/kg & 400-450 Wh/kg\\ Closed loop zero carbon emission economy & Unsustainable & Sustainable\\ Self-dependency of every country & Lithium mines are only available in countries like Chile, Argentina, Australia and China. Thus, makes the world dependent on these countries. & Water is available throughout the world now, and power can be obtained green hydrogen from renewable energy sources. \\ Processing and post processing tasks & Consume a lot of fossil fuels & Very expensive due to fewer demand so far\\ High endurance applications with extreme flight maneuvers & Unsuitable & Suitable \\ \botrule \end{tabular} \label{tabcompare} \end{table} Besides endurance or battery life, the discharge capacity is also a critical aspect to consider for designing the power system. The discharge rating improves the maneuverability of the vehicle. Discharge capacity (C) of the battery is the maximum current transient it can deliver to the actuators. Among all the commercially available lithium batteries, Li-Po batteries are popular for high discharge ratings (at least 20C) but drastically low battery life for full power conditions (up to 4 minutes). On the other hand, Li-ion batteries are commercially engineered for high battery life (up to 30 minutes) but a scanty discharge rating (up to 5C). This is one of the most critical aspects of batteries, that, both the powering capability and energy content are constrained to one hardware configuration and lack the ease of determining both the aspects individually. The battery starts degrading in both, the power capacity and the energy content with time. Thus, unlike for batteries, in HPEMFCs, the energy content and power requirement can be independently determined. The storage tank and fuel cells are embroidered for independent energy content and power capacity respectively. Automobile industries have commenced in implementing HPEMFC technology in high range vehicles \cite{hosseini}, \cite{zheng}. There are some prominent scholars like \cite{delorme}, \cite{rousseau} who discuss the evolution and prospects of hydrogen vehicles on fuel economy. Even further, aviation industries like Airbus and ZeroAvia have definite plans for zero-emission power systems. There are rigorous concepts being built at Airbus to deploy turboprop, blended-wing and turbo-fan hydrogen hybrid engines for high endurance flights ranging from 1000 to 2000 nautical miles carrying up to 200 passengers. These industries target green hydrogen production \cite{yigit16} using large-scale electrolyzer. \subsection{Risks association with hydrogen storage}\label{subsec3.1} It is a popular misconception that hydrogen storage devices are considered as detonation devices due to spontaneous flammability of hydrogen gas \cite{liu}. However, there are experimented evidences showing the flame diffusion from hydrogen tanks due to leakage as shown in the below picture which illustrates the hydrogen gas leak from an orifice in the storage tank. \begin{figure}[H]\label{figrpm} \centering \includegraphics[scale=0.6]{"flame.png"} \caption{Hydrogen flame from ruptured tank} \end{figure} Hydrogen has higher buoyance and diffusivity; thus, their fires rise quickly. Their flame length is less than 500 diameters \cite{lanz} from the hole – for 1mm diameter leak, the flame length will have 0.5m. Additionally, hydrogen has an unavoidable electroconductivity \cite{lanz}; this may generate electrostatic charges that could result in spark. Therefore, all hydrogen storage equipment must be thoroughly grounded to the parent system. \section{HPEMFC architecture}\label{sec4} A typical hydrogen fuel cell consists of two electrodes, gas inlet/outlet passages and an electrolyte for proton transfer. Many a times, the process is speeded up using a catalytic layer at the electrodes. The chemical reaction in a hydrogen fuel cell is given as, \begin{tabular}{rcc} Anode: & $H_2 \longrightarrow H^+ + 2e^-$ \\ Cathode: & $\frac{1}{2} O_2 + 2H^+ + 2e^- \longrightarrow H_2O$ \\ Overall: & $H_2 + \frac{1}{2}O_2 \longrightarrow H_2O$ \\ \end{tabular} The electrolyte transfers the $H^+$ to the cathodic side which produces electron affinity at the cathode layer to produce stable $H_2O$. Due to this electron affinity, the cathodic layer attracts the electron, however, the electrolytic membrane restrains the electron transfer due to its intrinsic properties and thus the electron passes through the load to create current. Due to this property of the electrolyte, it is also termed as proton-exchange membrane which only allow proton conduction. Such membranes are semipermeable fluoropolymers. The chemical structure is similar to Teflon. The overall picture of a proton-exchange membrane fuel cell is well-defined in \cite{spiegel} as shown below, \begin{figure}[H]\label{figfc} \centering \includegraphics[scale=0.6]{"diagfc.png"} \caption{Detailed schematic of HPEMFC \cite{spiegel}} \end{figure} The hydrogen gas is supplied from the flow-field or bipolar plates. The gas diffusion layers utilize their conductive permeability in distributing the gas from bipolar plate to the catalytic layer. Later, the multi-phase electrochemical reactions take place at the catalyst and electrolyte layers to transfer hydrogen proton to the cathode. At the cathode, the oxygen from air reacts with the proton and electron to form water and exits from the bipolar plate at the cathode. A more realistic picture of the fuel cell is shown below, \begin{figure}[H]\label{figfc} \centering \includegraphics[scale=0.5]{"exploded.png"} \caption{Exploded-view of the fuel cell stack \cite{spiegel}} \end{figure} From the above figure it is clear that the HPEMFCs contain solid electrochemical layers, which offer low corrosion, high power density and a long cell and stack life \cite{pukrushpan}. Moreover, the HPEMFCs have a lower operating temperature which eliminates the need of thermal insulation. \section{Mathematical Modelling of the HPEMFC}\label{sec3} In this work we develop a fuel cell system with the endurance, which is three times that of the endurance proposed in \cite{sharma}, but with the same power requirements of 150 W. The below Figure \ref{fig5} shows the model of the fuel cell used to obtain the polarization curve. It utilizes the general parameters \cite{hoogers} for modelling. \begin{figure}[H]\label{fig5} \centering \includegraphics[scale=0.4]{"fig5.png"} \caption{Exploded-view of the fuel cell stack \cite{spiegel}} \end{figure} The fuel cell utilizes four input conditions, which were iterated numerically until the target power requirements were obtained. \begin{itemize} \item Current density ($i$) is a ramp signal with limiting value $i_L=1.4 A/cm^2$ \item Active area of fuel cell: $A_{cell} = 13 cm^2$ \item Number of cells in the stack $N_{cell} = 18$ \item Hydrogen and oxygen injection fed pressure $p_{in} = 3 atm$ \end{itemize} Target power requirements, \begin{itemize} \item $V_{out} =$ Output voltage as a function of current density \item $P_{out} =$ Output power ($W$) as a function of current density \end{itemize} Modelling parameters inside the fuel cell “black box”, \begin{itemize} \item Operating temperature: $T_{op}=80^\circ C$ \item Transfer coefficient (is a measure of symmetry of energy barrier): $\alpha_{transfer}=0.5$ \item Exchange current density (is a measure of spontaneity of the electrode to proceed with the chemical reaction): $i_o=10^{-6.912}$ \item Amplification constant of fuel cell: $\alpha_1=0.085$ \item Gibbs function in liquid form: $G_{(f,liq)}= -228170 J/molK$ \item Mass transport coefficient: $k=1.1$ \item Internal resistance: $R=0.19 \Omega$ \end{itemize} Using the above conditions and parameters, we can develop the underlying thermodynamics of the fuel cell design. The saturation water pressure ($p_{H_2O}$) can be calculated using the assumed operating temperature $T_{op}$ \cite{spiegel} as, \begin{equation}\label{eqn1} P_{H_2O}=10^{-2.18 + 0.03(T_{op})-9.19×10^{-5} (T_{op})^2+1.45(T_{op})^3 } \end{equation} The partial pressures of hydrogen ($p_{H_2}$) and oxygen ($p_{O_2}$) can be obtained as, \begin{equation}\label{eqn2} p_{H_2} = 0.5\frac{p_{in}}{exp\left(\frac{1.653i}{T_{op}^{1.334}}\right)}-P_{H_2O} \end{equation} \begin{equation}\label{eqn3} p_{O_2} = \frac{p_{in}}{exp\left(\frac{4.192i}{T_{op}^{1.334}}\right)}-P_{H_2O} \end{equation} The partial pressures are a function of the current density input ramp signal. The fuel cell operation at high pressures is drastically improves the efficiency and power density. These partial pressure distributions can be utilized in obtaining the Nernst voltage ($E_{nernst}$) for a range of current density, given as, \begin{equation}\label{eqn4} E_{nernst} = \frac{-G_{f,liq}}{2F}-\frac{RT_{op}}{2F}\log\frac{P_{H_2O}}{p_{H_2}p_{O_2}^{0.5}} \end{equation} The Nernst voltage does not speculate the losses occurring in the fuel cell. The HPEMFCs possess three types of inevitable losses: activation, ohmic and mass transport losses. The activation losses will be larger if the exchange current density is low, which also makes other kinetics slow. The activation losses occur at low current densities. These losses also get affected due to change in polarization that leads to a change in the reaction rate. This effect can be measured by transfer coefficient ($\alpha$) which is typically taken as 0.5 \cite{spiegel}. Once the fuel cell has crossed the energy barrier after low current densities, the activation losses become diminutive. From Figure 4, the initial fall in cell voltage illustrates the effects of activation losses. The activation losses can be quantified using the Tafel equation, \begin{equation}\label{eqn5} V_{act}= \frac{RT_{op}}{2\alpha_{transfer}F}\log\left(\frac{i}{i_o}\right) \end{equation} When the current densities build up to a sufficient amount (typically $> 0.1 A/cm^2$), the ohmic losses dominate due to the hardware used. The HPEMFCs consist of metallic elements in a compact contact like flow field, contact, cooling and bipolar plates. These elements possess their innate electron conductivity. Furthermore, as the proton exchange membrane, popularly Nafion material is used, which is has ionic conductivity. Therefore, it is generally better to identify the resistance empirically. Here we will consider the internal resistance to be $0.19\Omega$. The ohmic losses due for single cell can be given as, \begin{equation}\label{eqn6} V_{ohmic} = -iR \end{equation} The mass transport or concentration losses in the fuel cell occurs due to convection and fluid density gradients involved among the various elements of the fuel cell, like, flow field plates, gas diffusion layers and catalyst layers. This phenomenon occurs at high current densities, where the charges start to stagnate. The mass transport effects can be modelled using, \begin{equation}\label{eqn7} V_{conc} = \begin{cases} \alpha_1 i^k \log\left( 1 - \frac{i}{i_L}\right) & 1 - \frac{i}{i_L} > 0\\ 0 & 1 - \frac{i}{i_L} \leq 0 \end{cases} \end{equation} Using all the above losses, when added to the Nernst voltage results in the polarization curve or voltage distribution for a single cell with respect to the current density variation as, \begin{equation}\label{eqn8} V=E_{nernst}+V_{act}+V_{ohmic}+V_{conc} \end{equation} The power distribution of the system can be obtained in \eqref{eqn9} using the total active area of the fuel cell system $A_{cell}$ and is calculated to be about $150 W$, as, \begin{equation}\label{eqn9} P=N_{cell} V i A_{cell} \end{equation} The obtained polarization and power curves are shown in Figure \ref{fig6}. \begin{figure}[H]\label{fig6} \centering \includegraphics[scale=0.7]{"result_1.png"} \caption{Voltage and Power vs Current Density plots to determine the design parameters for the target power requirements} \end{figure} From the above figure, we interpolate the voltage and current density operating conditions for 150W of power requirement for the entire fuel cell system. Thus, the voltage operating point for a single cell will be $V_{op}=0.8V$ and current density operating point as $i_{op} = 0.81 A/cm^2$. For HPEMFCs, the open circuit voltage, $E^\circ$ is $1.48 V$. Thus, the efficiency of our fuel cell can be calculated as, \begin{equation}\label{eqn10} \eta_{eff}=\frac{V_{op}}{E^\circ} = 0.54 \end{equation} A 54\% of efficiency is obtained in our current design of fuel cell. The operating voltage and current are further manipulated using power electronics to boost or buck the voltage and generate favorable voltage for the power distribution board of the SUAV. \section{Storage Tank Design} The obtained power system design features are essential to identify the volume the storage tank. From the current density $i=0.81 A/cm^2$, we can obtain the molar flow rate of hydrogen gas needed, \begin{equation}\label{eqn10} \frac{dN}{dt} = \frac{iA_{cell}}{n_e F} \end{equation} \begin{equation*} \frac{dN}{dt} = 3.274×10^{-3} mol \frac{H_2}{min} \end{equation*} where, $n_e$ = number of electrons transferred per mole$ = 2$ $F$ = Faraday`s constant$ = 96,485 C/mol$ For a flight endurance of minimum 3 hrs., the total amount of charge to be consumed will be, \begin{equation} Q=iA_{cell}t = 113,724 C \end{equation} Total moles $H_2$ consumed per second will be $Q/(n_e F)= 0.589 moles$. Using the ideal gas equation, total volumetric flow rate can be calculated as, \begin{equation} \frac{dV}{dt} = \frac{dN}{dT} \frac{RT}{p_{in}} = 0.0136 litre/min \end{equation} Thus, for 3hrs., or 180 minutes, the total mass of hydrogen gas compressed at 30 MPa will be, $\rho$ at 30 MPa \& $20^oC$ $= 20 kg/m^3$: $m = 0.114kg and V = 5.688 litres$ The storage tank geometry can be identified based on total volume required for the flight. The density of $23 kg/m^3$ is decided as per the standard storage conditions for composite hydrogen fuel tanks. The storage pressure can be further increased up to 70 MPa as per the industrial standards of hydrogen systems. Commercially, cylindrical hydrogen tanks are available with spherical ends for SUAV purposes. A variety of literature \cite{westenberger}, \cite{gomez}, \cite{brewer} have shown that hydrogen storage tank is to be distributed along the longitudinal axis of the vehicle. As the fuel is being consumed, the center of gravity location would be changed. Thus, the hydrogen storage tank position is very critical to the longitudinal stability of the aircraft. \begin{table}[h] \begin{center} \begin{minipage}{174pt} \caption{Design features obtained}\label{tabdesign}% \begin{tabular}{cc} \toprule Design Features & Values\\ \midrule Cell Voltage & 0.8 V\\ Cell current density & 0.81 $A/cm^2$\\ Stack Voltage & 14.4 V\\ Stack Power & 151.6 W\\ Cell efficiency & 54\% \\ Storage tank volume & 5.688 litre\\ $H_2$ mass consumed & 0.114 kg\\ \botrule \end{tabular} \end{minipage} \end{center} \end{table} \section{Auxiliary subsystems}\label{sec7} The design features obtained for the fuel cell and storage tank systems sufficiently justifies the system for steady-state applications. However, in order to ensure a technological standards like good continuity, robustness, adaptiveness for a range of power and response, more parameters are to be taken for consideration. There are five main parameters that need continuous tuning and regulation \cite{pukrushpan}. They are: \begin{enumerate} \item Reactant flow rate \item Total pressure \item Reactant partial pressure \& temperature \item Humidity of the membrane \item Output power at the actuator \end{enumerate} In order to regulate this parameters, auxiliary systems are required for fast adjustments and smooth process. These systems not only extend the life-cycle of the fuel cell system, but also improve the range of operating conditions. A precise control \cite{heddad} of these parameters will promise versatility, efficiency and ruggedness of the entire system. All the auxiliary systems can be segregated into five main systems \cite{pukrushpan}. These systems are intricately coupled with each other and the fuel cell. \subsection{Reactant flow system} The objective of this system is to ensure sufficient reactant mass flow rate and partial pressure at the fuel cell inlet as per the actuator power requirements, so that the auxiliary power consumption is minimized \cite{yigit}, \cite{rakhtala}. For airflow supply at the cathode, compressor and supply manifold play essential roles. Whereas, at the anode, pressure regulator is the only component required to supply a sufficient amount of hydrogen gas. \begin{figure}[H]\label{fig7} \centering \includegraphics[scale=0.4]{"fig7.png"} \caption{Reactant flow system} \end{figure} As shown in Figure 7, the air from atmosphere is compressed to fed into the fuel cell. The supply manifold is the control volume associated with the pipes and connections between the compressor and fuel cell bipolar plates. Like supply manifold there will be a return manifold at the exhaust. The supply manifold also comprises of humidifier discussed in water management section. The storage tank contains high pressure hydrogen gas. The fuel cell cannot be fed with such high-pressure hydrogen; thus, a pressure regulator is utilized to maintain the inlet fed pressure. Additionally, it is essential to minimize the pressure differences between the cathode and anode to avoid diffusion due to pressure gradient. From \cite{pukrushpan} a proportional controller model in the form of pressure regulator valve is given below, \begin{equation}\label{eqn13} \dot{m}_{an,inlet} = K_1 (K_2 p_{sm}-p_{an}) \end{equation} where, $\dot{m}_{an,inlet}$ = mass flow rate at the anode inlet, $p_{sm}$ = pressure at supply manifold, $p_{an}$ = pressure at anode and $K_1$ \& $K_2$ are proportionality constants. \subsection{Heat and temperature system} The heat and temperature systems are used in fuel cells to regulate the stack and reactant temperature. These subsystems are generally required for fuel cells with large stack size, for instance in stationary power generation and automobile sectors. For the SUAV discussed here, we assume that the heat generated can be passively dissipated by convective airflow using micro-exhaust fans and so we can neglect this system. \subsection{Water management system} The goal of water management system is to maintain the moisture content of the electrolytic membrane by regulating the humidity of inlet airflow. This goal is achieved by a humidifier located at the supply manifold. The absence of a humidifier can result into high ohmic and concentration losses due to dry/flooded fuel cell membranes. These losses can adversely accrue and led to a 20-40\% voltage drop. The content of moisture in cathode and anode should not exceed a concentration gradient to avoid undesired water diffusion. Therefore, a proper humidity ratio should be attained by tuning water vapor injection rate from below equations. The humidity ratio can be calculated as, \begin{equation}\label{eqn15} \phi = \frac{M_v p_v}{M_a p_a} \end{equation} where, $\phi$ = humidity ratio, $M_v,M_a =$ molar masses of vapor and dry air (kg/mol) and $p_v,p_a =$ partial pressure of vapor and air at fuel cell inlet. Further, from \eqref{eqn15}, water injection rate ($\dot{m}_v$ in kg/s) can be given as, \begin{equation} \dot{m}_v = \dot{m}_{h,in}\left(1-\frac{1}{1+\phi}\right) \end{equation} where, $\dot{m}_{h,in}$ = humidifier inlet airflow rate. The above equations represent a static model of the humidifier, taking into account the continuity equation \cite{pukrushpan} and laws of thermodynamic gas mixture \cite{lide}. \subsection{Power conditioning system} The goal of power management system is to control the fuel cell system for fulfilling the actuator power requirements. The fuel cell power output possesses a lot of disturbances. Thus, conditioning of such signals is often mandatory before it reaches the actuator electronics. Sometimes a battery is used here compensate for significant losses and hikes in power output. \section{Fuel cell powertrain} A powertrain consists of the engine and drivetrain. For our SUAV, the engine is the fuel cell and the drive train includes the model (controller and state estimator), actuators and power electronics \cite{apeland}. All the components discussed can be illustrated in the fuel cell powertrain in Figure \ref{fig8}. \begin{figure}[H]\label{fig8} \centering \includegraphics[scale=0.3]{"flowchart.png"} \caption{Fuel cell powertrain for UAV} \end{figure} \begin{itemize} \item UAV Actuators: The SUAV considered here consists of brushless dc motors for thrust and servo motors at control surfaces. \item State estimator: This block estimates the states of the SUAV like position, velocity, acceleration, angular rates, angular positions etc. Generally, we use gyroscopes, accelerometers, magnetometers, optical flow sensors and ultrasonic sensors to determine these states. \item Controller: The controller takes in the state estimations, compares to the required set points of the flight and generates a control signal. This control signal is normalized and passed to the ESC’s input range. The state estimation input signal frequency is higher than the control signal to ESC, so that the estimator error converges to zero quickly. \item Electronic Speed Controller (ESC): The ESC is an electronic circuit that takes in the input from the controller and generates the mapped output signal to the actuator. It outputs this signal in the form of a pulse-width modulated signal for brushless dc motors and servo motors. \item Power Distribution Board (PDB): As the name suggests, this board distributes the power to the ESCs connected. The power supplied to individual ESC is determined by the controller. \end{itemize} The fuel cell and its subsystems including the power conditioning system receive input signals from the controller demanding the necessary power requirements. This input signals can be given as, \begin{itemize} \item $u_1$: $H_2$ gas supply to anode \item $u_2$: de-ionized coolant water \item $u_3$: $O_2$/air supply to cathode \item $u_4$: de-ionized water supply at the humidifier \item $u_5$: conditioned power \end{itemize} The output is the quick and smooth transient and robust system response for a variable power. All these inputs are a function of the controller setpoints. The system interactions between these inputs and the controller are crucial to the viability, efficiency and robustness of the fuel cell. \section{Discussion}\label{sec12} Two important results obtained in this work are the plots of voltage and power curves against the current density and storage tank size computation. These curves are then further narrowed down to the desired power requirements i.e., $P=150W$,$V/cell=0.8V$ at $i=0.81A/cm^2$ for the design criteria and necessary constraints. The determined volumetric flow rate is $3.16\times10^{-2} L/min$. Thus, for an endurance of minimum three hours, total volume of the tank size required will be $5.688\times10^{-3} m^3$. Noting the above features, appropriate auxiliary systems can be designed. \section{Conclusion}\label{sec13} A unique deployable fuel cell model with sufficient design parameters is built for a fixed-wing SUAV. The methodology used here is generic and can be used for any such fuel cell system employed in UAVs. A design efficiency of 54\% is achieved. It should be noted that such fuel cell systems operate with high pressure storage processes of highly flammable hydrogen gas, and hence we recommend its implementation with proper safety and expert guidance. Further work involves optimal design considerations and the system interaction between the fuel cell auxiliary systems and the controller demands. \section*{Declarations} \textbf{Funding} The authors did not receive support from any organization for the submitted work. \noindent \textbf{Conflict of interest} The authors have no conflicts of interest to declare that are relevant to the content of this article. \begin{thebibliography}{99} \bibitem[Apeland(2020)]{apeland} Apeland, J., Pavlou, D. and Hemmingsen, T., 2020. Suitability analysis of implementing a fuel cell on a multirotor drone. Journal of Aerospace Technology and Management, 12. \bibitem[Brewer(2017)]{brewer} Brewer, G.D., 2017. Hydrogen aircraft technology. Routledge. \bibitem[Chen(2001)]{chen} Chen, E.L. and Chen, P.I., 2001, November. Integration of fuel cell technology into engineering thermodynamic textbooks. In ASME International Mechanical Engineering Congress and Exposition (Vol. 35524, pp. 389-394). 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