Development of an airfoil-based passive volumetric air sampling and flow control system for fixed-wing UAS

Abstract

This study aims to develop a concept of a passive volumetric flow control system for gas sampling applications onboard fixed-wing UAS based on the pressure field around airfoils. The passive flow control system utilizes the aerodynamics of a UAS to create a vacuum pump effect that ensures constant gas sampling, which can be used to facilitate airborne aerosol and gas measurements. The pump effect is achieved by short-circuiting the pressure field’s minima and maxima points around an airfoil through pipes and 3D printed structures that could function both as a pump system and a gas measurement chamber. The design of this structurally integrated functionality brings many advantages for scientific applications, especially onboard small research UAS, which would dispense entirely with complex active pump systems, thus reducing weight and ensuring gas sampling at a constant volumetric flow rate independent of altitude and atmospheric variance. In favor of developing further applications, this paper outlines the development steps of the passive pump concept starting from the theory and numerical modeling of the effect to the implementation on board a fixed-wing UAS. Finally, possible improvements based on numerical models and flight measurements are discussed.

1 Introduction

The main scope of this study is to motivate air sampling applications onboard fixed-wing UAS by presenting a detailed overview of the development of a novel passive sampling method, which can be adapted to future applications, e.g., aerosol and gas measurements. The demand for gas sampling systems onboard unmanned airborne systems (UAS) is founded on the need for airborne gas and particulate matter sensors to study the atmosphere’s chemical composition for environmental and meteorological applications. Advancements in unmanned airborne vehicle (UAV) technologies and their manufacturing in the last decade have helped push down the costs and increase the flexibility of UAS operations, thus democratizing UAS technologies and making them accessible for a broad scope of scientific applications (Nex and Remondino 2019). UAS are becoming ever more adherent to mesonet concepts applied in atmospheric boundary layer research as well as meteorological measurement campaigns (Jacob et al. 2018; Kral et al. 2018; VALUAS 2020). The validity of UAS measurements for meteorological, environmental, and climate research applications is further motivated by studies on the placement of the sensor onboard small UAS (Greene et al. 2018), sensor design and evaluation schemes (Hall and Povey 2017), and sensor deployment strategies (Yang et al. 2018).

While much research conducted with UAS has focused on the wind and the physical phenomena in the atmospheric boundary layer (ABL) (Van den Kroonenberg et al. 2008; zum Berge et al. 2021), the interest in resolving particulate and chemical composition of the ABL is growing as UAS could play an important role conducting air quality and gas measurements in inaccessible terrains, urban, and hazardous environments; (Brady et al. 2016; Guzman 2020; Kunz et al. 2018). The resulting data would benefit strategies for fine-grained air quality monitoring (Hu et al. 2019), gas leak detection operations (Kersnovski et al. 2017; Yuan et al. 2019), and monitoring wildfires (Nelson et al. 2019). To achieve these measurements, UAS require more demanding mission profiles with longer flight distances/duration, higher altitudes, and challenging flight maneuvers that bring the UAS closer to pollutant sources at higher deployment frequency. Furthermore, because gas sensors are relatively heavier, more expansive, and require a complex sensor periphery, the airborne gas sensor system’s operation is highly complicated.

An overview of the approaches developed for air quality measurements with UAS can be found in (Lambey and Prasad 2021). Novel approaches that integrated open-path sensors for detecting natural gas leaks have been developed (Barchyn et al. 2018), and other low-cost strategies can also be found in the literature (Razali and Yusof 2021). Yet lightweight and passive techniques for closed-path gas sensors onboard fixed-wing UAS can still be considered a niche field with much development potential. Gas measurements using fixed-wing UAS can play an essential role because of the their capacity for longer flight endurance on a single battery cycle due to their efficient aerodynamic design. Furthermore, fixed-wing aircraft offer higher safety in the case of motor power loss and stability in high wind conditions compared to multi-copters, thus facilitating flight operations. Furthermore, fixed-wing UAS would only cause a minor disturbance to the measured field, making them inherently ideal for accurate turbulence and flux measurements (Bange et al. 2021).

For fixed-wing UAS, even with high aerodynamic efficiency, the problem of ensuring adequate air sampling for gas or aerosol measurement systems arises from the stagnation pressure at the sensor’s inlet, which results from the sensor’s internal flow resistance. The stagnation pressure gradient could contribute to under or over-sampling of the measured volume, especially under turbulent conditions. For aerosol measurements which require isokinetic sampling, the higher pressure at the inlet would divert particulate matter from the sensor, thus resulting in statistical deviation of the measured quantities depending on the inertia of the particulates (McNaughton et al. 2007). Under consideration of the complexity of the system and the need for a pump pressure to achieve the required volumetric flow for the sensor system, a closed path sensor system would suffer because the pump must constantly account for constant small-scale as well as abrupt fluctuations in the pressure and wind fields around the UAS. These fluctuations could range from gradual variation of the measurement altitude to strong turbulent conditions in ABL. As a result, the sensors system’s faculty of adequate or isokinetic sampling would also set an upper limit to the system’s fidelity to measure fluxes and small-scale phenomena, as numerical corrections schemes would be required in case of over or under-sampling to achieve a representative volume of air. An in-depth understanding of air pollutant sampling techniques and gas measurement fundamentals can be found in Wight (2018).

This study aims to develop a concept for a passive gas sampling system onboard fixed-wing UAS that utilizes the aerodynamically induced pressure field around an airfoil to generate the required pump pressure for the sensor system. Passive sampling is very advantageous as it reduces the complexity of the measurement system by dispensing with pumps and active flow control elements, thus reducing weight and power consumption and ultimately contributing to the flexibility and operationality of UAS. A passive system autonomously corrects the sampling flow to perturbations, thereby contributing to measurement fidelity. Figure 1 shows the proposed pump system, which is created by placing the inlet and outlet for the sensor system at the minima and maxima of the pressure field around an airfoil. The study presents one iteration of the design process, starting from a theoretical study to a computational fluid dynamics (CFD) simulation and ending with flight measurements onboard a UAS.

Fig. 1

The simulated (OpenFOAM) dynamic pressure field around the proposed wing pod (Fig. 4) for a wind speed $|\textbf{U} |=19.5$ ms$^{-1}$ and an air density of $\rho =1.2$ kgm$^{-3}$, and a stagnation pressure of $P_{\text {stagnation}} = \frac{\rho }{2} \textbf{U}^2 \approx 230$ Pa. The suggested points for an inlet and outlet of pump system coincide around the maxima and minima of the pressure field

The concept developed in this study falls alongside other concepts that underline the axiom of abstracting the aerodynamics and flight mechanics of a UAS to conduct high-fidelity measurements in the ABL. By coupling the constitutive relationships of both the sensor system and the flight mechanics, it would be possible to expand the measurements’ fidelity and lessen the effect of perturbations caused by the UAS’s flight mechanics. The study builds on instruments, methods, and results using the same multi-purpose airborne sensor carrier (MASC)-UAS series (Van den Kroonenberg et al. 2008; Rautenberg et al. 2019; Wildmann et al. 2013, 2014a, b; zum Berge et al. 2021, 2022) to conduct measurements using a UAS in ABL that account for the flight mechanics of a UAS in favor of higher resolution measurement. The proposed approach is similarly motivated by the idea of minimizing any perturbation resulting from the measurement system to the measured environment by utilizing UAS aerodynamics and flight altitude to achieve the required measurement. The scope of this study will only focus on the stationary aspects and the 1D and 2D analysis of the studied pump effect. Effects due to perturbation of UAS during the flight operation and measurements such as dynamic variation of the angle of attack (AoA, $\alpha$) and airspeed or 3D aerodynamic effects will be discussed comprehensively in future studies. This study focuses on developing a fundamental understanding of the pump effect and the development of application in gas and aerosol measurement system, thus establishing a proof of concept and preliminary relationship to UAS’s flight mechanics that can be further expanded to account for perturbations in future studies.

2 Methods

Three methods were used to develop the airfoil-based passive volumetric air sampling concept and the underlying pump effect proposed in this study. These methods help model and study pressure fields around airfoils and other derived aerodynamic geometries. They are chosen to illustrate the potential of the proposed passive flow control system to create the required pump effect for gas sampling applications onboard fixed-wing UAS. This study applies the methods to a subset of airfoils and airfoil-derived geometry to characterize the induced pump effect and resulting air sampling. Both the chosen geometries and methods are intended to give both an abstract and practical overview of the pump effect and its applications that could be used to further develop the concept for other geometries and sensor systems. The three methods used are as follows:

• 1. 1D-Analysis for modeling the pressure field using XFOIL (Drela 1989) to give a theoretical characterization of the pump effect.

• 2. 2D simulation using an OpenFOAM (OpenCFD Ltd 2021) CFD model to study the effect of the internal flow and viscosity on the resulting pump effect for complex and practical geometries.

• 3. Flight experiment to quantify and validate the pump effect under actual flight conditions using MASC as an UAS platform (Fig. 3).

2.1 Geometry

To develop an understanding of the underlying pump effect, an initial set of geometries based on practical and theoretical considerations were studied. The choice of geometries comprises both a set of airfoils representing those of the standard national advisory committee for aeronautics (NACA) (Abbott et al. 1945) and derivatives of these geometries that are viable for practical applications, such as sensor integration and integration onboard an UAS as a nacelle-shaped wing pod. While the NACA profiles are essential to developing a fundamental and theoretical understanding of the pump effect, the derived geometries build upon this towards a practical implementation that can be studied onboard an UAS-based flight experiment to validate the effect under actual ABL conditions. Through the ability to 3D print any geometry, it was possible to consider a broad scope of geometries, integrate sensors, and include modifications such as inlet nozzles into the scope of this study. This section discusses the choice of geometries for each method and gives an outline of the design process.

As the inner tube’s length and the shape of the internal flow path depend on the used sensors and their internal geometry, these parameters are therefore given by the sensor’s manufacturer. They are not the design parameters of the wing pod itself. Intuitively, a longer inner tube and a sensor with a more complex flow path would result in higher pressure losses, negatively affecting the wing pod’s performance. Thus, for practical applications, considerations should be made to keep the length as short as possible and avoid obstruction of flow through tubes with rough surfaces or sharp corners. If possible, similar considerations can be made for the choice of sensors, as a sensor with a streamlined flow path would be favorable for the concept of this study. A detailed overview of the integration of gas sensors can be found in Munger et al. (2012), and overview of aerosol measurements can be found in Kulkarni et al. (2011).

Fig. 2

Airfoils NACA0012, NACA0024, and NACA4525 are studied using XFOIL alongside the scaled cross-section of the final wing pod design. All profiles in this plot have a chord length $c_{\text {NACA}}=c_{\text {Wingpod}}=0.4$ m, and dimensions are normalized by the chord length

For the 1D-Analysis of the study, a set of NACA profiles were chosen, as they are well-established in the literature. The pressure field around them can be estimated using software packages such as XFOIL. The choice of the airfoil shape and chord size was based on the design consideration for application on the wing of the MASC sensor system of type Xplorer (NANModels 2022), which itself has a chord length of $c_{\text {MASC}}=0.246$ m. Figure 2 shows three exemplary chosen NACA airfoils. For reference, the airfoil geometry of the wing pod, which was developed for the flight experiment, is also shown. All NACA airfoils are modeled to have the same chord length of $c_{\text {NACA}}=0.4$ m. The added chord length compared to $c_{\text {MASC}}$ was intended as extra space to accommodate sensors. Since both the NACA0012 and NACA0024 are symmetrical airfoils, the NACA4525 is chosen as an example of a chambered airfoil with a maximum thickness similar to the later used wing pod and an asymmetry due to the mounting on the wing of the MASC, as seen in Fig. 2.

For the experiment and simulation, the baseline geometry used for the wing pod is based on an arbitrary symmetrical airfoil and considerations derived from the studied methods. Being the first iteration of the development, the main intention for the shape was to be simple enough to give a fundamental understanding of the pump effect and large enough to accommodate several gas sensors for testing, e.g., the Alphasense - OPC-N-Series (Alphasense 2022), Vaisala-CO$_2$-GMP343 (Vaisala 2022), and Alphasense - Electro-Chemical-Cell sensors (Alphasense 2022). The cross-section of the wing pod can be described as an ovoid that is streamlined towards the back and that has a length of $c_{\text {simulation}} = 0.45$ m on the major axis and a thickness of $b = 0.11$ m on the minor axis. The final shape is created by revolving the shape around its major axis and subtracting the MASC airfoil profile to create an airfoil-shaped gap for mounting on a UAS’s wing. The choice of a rotationally symmetrical shape for the flight experiment is strongly motivated by safety considerations. While a rational symmetry will result in an induced drag due to the vortex rolling up the sides of the 3D pod, the final shape and placement on the top side of the wing (Fig. 3) were chosen based on practical safety considerations and to avoid negatively affecting the UAS flight mechanics, especially during take-off and landing. Through the intersection with the wing and placement in the mid-wing section, 3D vortexes are expected to be suppressed and the pump efficiency to be improved. Further 3D-Aerodynamic considerations regarding the pod’s geometries, e.g., a longer span or other flow control features, are expected to affect the pump’s efficiency positively and should be considered in future studies.

Fig. 3

Left: two wing pods mounted on the MASC-3 while airborne during a measurement flight at the VALUAS field campaign in July 2020; picture by Ines Weber (Environmental Physics Work Group - University of Tübingen [Link]). Right: annotated close-up of the wing pod during the pre-flight setup

To further elaborate on the underlying pump effect, Fig. 4 shows a 2D cross-section of the wing pod which was created to represent the final model used in the flight experiment. The 2D model is intended to study the generated pump effect and compare it to the XFOIL results with a yet better-resolved flow and pressure fields using a 2D CFD simulation. The model approximates the pump effect and provides a more realistic representation of the aerodynamics of the complex geometries that better represent the actual gas measurement system and accounts for mixing turbulence and other viscous effects.

For the simulation, the simplified 2D cross-section of three variants of the pod’s geometries considered for flight testing was modeled and studied in the next section. Since this study focuses on the outer aerodynamics effect, the shape and length are chosen arbitrarily but with considerations to minimize flow resistance and losses. The inner tubes were chosen as a simple geometry with a constant diameter. The length of tubes resulted from streamlining the tube between the inlet and outlet to avoid sharp angles that would result in internal pressure losses. The first variant represents the pod mounted on the UAS’s airfoil and has no inner tubing. The other two variants of wing pod Fig. 4 included inner tubes and profile of the airfoil of the UAS used for mounting. One variant adds an isokinetic diffuser nozzle in the front of the wing pod, which results in extending the “per se” chord length. The sensor payload requires the added diffusor nozzle for aerosol measurement applications and acts as a funnel to facilitate isokenict sampling, especially for larger-sized particles. It is designed loosely based on the University of New Hampshire diffuser inlet (McNaughton et al. 2007), but excludes the external covering shroud. The diffuser’s tip has an inlet diameter of $D_{\text {Diffuser}}= 2.75$ mm. The diffuser has a conical shape that encompasses the inlet of the pod $D_{\text {Inlet}}= 8$ mm and thus creates a bypass duct around it with a diameter of $D_{\text {Bypass}}= 20.5$ mm. The cross-section of the diffuser can be seen in Fig. 5 in the representation of the computational mesh of the 2D simulation. The added diffuser results in higher internal pressure resistance and a lower flow rate due to the smaller inlet diameter. A description of the diffuser and examples of measurements can be found in (Shingler et al. 2012). A detailed discussion of the used diffuser inlet is out of the scope of this study. It would be left for studies that discuss the functionality of optical particle sensor systems (McNaughton et al. 2007; Shingler et al. 2012; Gonzalez Vera et al. 2021).

For the sake of the simulation, the inner geometry of both pod variants is kept as simple as possible to achieve a qualitative comparison between the 1D-XFOIL results and experimental flight measurements. As will be discussed in the following chapters, the wing pod’s profile builds on the results of the 1D-XFOIL study Section 3.1 and 2D simulation Section 3.2. It is thus pitched at an angle of incidence of $5^{\circ }$ to the horizon to amplify the pump effect and avoid negative AoA resulting from in-flight motion that would negatively influence the pump effect. On the other hand, the nozzle major axis is pitched parallel to the horizon against the angle of incidence of the wing pod for coaxiality. The profile of the wing pod considers the UAS flight mechanics as it extends over the wing flaps (seen in white in Fig. 4) to allow for their motion, which is required for UAS flight.

Finally, for the flight measurements, as will be discussed in the following chapters, a wing pod geometry was chosen for flight testing and measurement that is based on the XFOIL study and the simulation. The geometry was 3D printed and fitted as nacelle onboard the MASC (Fig. 3). The rotational symmetry of the final wing pod minimizes the influence of the overall flight aerodynamics of the UAS and also reduces the stagnation effects that could occur when using spanned 2D geometries (see Section 3.2). The wing pods were 3D printed using acrylonitrile butadiene styrene (ABS)-Martial on Stratasys F170 fused deposition modeling printer (Stratasys 2022). After the printing, the surface material was treated with acetone. Because acetone acts as a dissolvent for ABS, the porous surface of the 3D printed layers can be smoothed and mended to a dense and impregnable cover, which has more favorable properties for the application as an aerodynamic surface.

Fig. 4

Profile of the two simulated models with the diffuser inlet (right) and without (left). The wing pod geometry is colored white, the inner tubes red, and the diffuser inlet and MASC’s/UAS’s airfoil are colored green and colored purple

2.2 1D-Analysis

The first method is used to establish a theoretical understanding of the under-laying pressure field around different airfoils and to give theoretical estimations of the studied pump effect. This is done using XFOIL, which relies on an analysis technique based on the Blade Element Momentum (BEM) theory (Drela 1989). The study used the pyfoil python library (De Vries 2019) to interface with Fortran functions of the XFOIL code. The advantage of using XFOIL and especially in conjunction with the python library for establishing a simple theoretical formulation of the pump effect that allows for a quick and accurate representation of the aerodynamic performance at low Reynolds numbers (Morgado et al. 2016) for a variety of angles and airspeeds. Furthermore, the results of XFOIL are well established and can be cross-referenced with general theories regarding lift and drag generation and fundamental airfoil design concepts (Gudmundsson 2014).

Using the XFOIL calculated pressure coefficients, a theoretical pump effect is studied by calculating the pressure field around the airfoil. The pump effect around the airfoil can then be calculated from the pressure field around the airfoils by assuming two points around the airfoil to be the inlet and outlet of the sampling flow channel. The resulting pump pressure $P_{\text {pump}}$ by interconnecting these two points is thus equal to the difference of their pressures. In theory, the maximum pump pressure can be generated for the condition that the stagnation point would be connected to the minima pressure points ($P_{ \,\text {Stagnation-Point}}$ and $P_{ \, C_{P_{\text {min}}}}$) on the airfoil. For a 1D flow where the flow speed $\textbf{U} = (u,v, w)$ and $v=0, w=0$, the pressure values at the stagnation and the minima can be derived from pressure coefficients calculated using XFOIL and Eqs. 1 and 2, where $C_{p}$ is the pressure coefficient, and $P_{\infty },\; q_{\infty },\; \rho _{\infty } \text { and } u_{\infty }$ are the static pressure, dynamic pressure, density, and velocity at an infinitely far away point from the airfoil in the freestream:

$$\begin{aligned} C_{p} = \frac{P-P_{\infty }}{q_{\infty }} \text { and } q_{\infty }= & {} \, 0.5 \, \rho _{\infty } u_{\infty }^2 \nonumber \\ \Rightarrow P= & {} C_{p} \; q_{\infty } + P_{\infty } \end{aligned}$$

(1)

$$\begin{aligned} \text { for } \Delta P_{\text {pump}_{\text {max}}}= & {} P_{ \,\text {Stagnation-Point}} - P_{ \, C_{P_{\text {min}}}} \nonumber \\ \text { with } C_{p \, \text {Stagnation-Point}}= & {} 1 \nonumber \\ \Rightarrow \Delta P_{\text {pump}_{\text {max}}}= & {} (1 - C_{P{\text {min}}}) \, q_{\infty } \end{aligned}$$

(2)

Considering the Eq. 1 and the goal of the pump effect to facilitate isokinetic sampling, a net pump pressure greater than the stagnation pressure is required; this demands that $Cp_{\text {min}} < -1$ at the outlet. For values of $Cp_{\text {min}} > -1$, a pump effect would be present that would minimize the stagnation pressure, but the resulting flow would not facilitate isokinetic sampling. $Cp_{\text {min}} < -1$ values are also needed in the case of a practical application since the pump pressure also has to compensate for losses due to the flow friction and internal resistance within the pipes and sensor system.

It should be noted that the results of this method are very theoretical, and their validity is strongly dependent on the magnitude of the resulting flow because the induced flow by the pump effect would result in changing the kinetic impulse around the geometry, which is not taken into account here. Nevertheless, the premise of this theoretical method is that the actual pressure field would converge towards the XFOIL model value as the mass flow goes to zero, thus giving maxima of the possible pump pressure gradient.

Using the XFOIL-based formulation of the pump effect under the simplification that a break of the momentum conservation through the mixing of internal and external flows does not influence the pressure field, an isokinetic flow can be achieved by choosing the inlet and outlet so that the total pressures at the freestream, inlet, and outlet are equivalent and any inner pressure losses due to friction are compensated through the generated pump pressure. This relationship and the condition for an isokinetic air sampling can be expressed by considering pressure losses due to friction $P_{\text {Loss}}$ and rearranging the Bernoulli equation to Eq. 3, where $\text {A}_{\infty }$ is a fictive cross-section area in the freestream that would result in a volumetric flow $Q_{\infty }$. In the case of isokinetic sampling, the volumetric flow $Q_{\text {Inlet}}$ at the inlet of the sensor becomes a function of only the inlet’s area $\text {A}_{\text {Inlet}}$.

$$\begin{aligned} P_{\infty } + \frac{\rho {u^2_{\infty }}}{2}= & {} P_{\text {Inlet}} + \frac{\rho {u^2_{\text {Inlet}}}}{2} = P_{\text {Outlet}} + \frac{\rho {u^2_{\text {Outlet}}}}{2} + \Delta P_{\text {Sum}} \nonumber \\ u_{\text {Outlet}}= & {} \sqrt{u_{\text {Inlet}}^2 - \frac{2\,\Delta P_{\text {Sum}}}{\rho }} \text { with } \Delta P_{\text {Sum}} = P_{\text {Loss}} + P_{\text {Pump}} \nonumber \\ \text {isokinetic}&\implies&\left\{ \begin{array}{ll} P_{\text {Pump}} &{}= P_{\text {Loss}} \\ \ u_{\infty } &{}= u_{\text {Inlet}} = u_{\text {Outlet}} \\ Q_{\text {Inlet}} &{}= u_{\text {Inlet}} \cdot \text {A}_{\text {Inlet}} = u_{\infty } \cdot \text {A}_{\infty } = Q_{\infty } \ \text {(continuity)} \\ \text {A}_{\text {Inlet}} &{}= \text {A}_{\infty } \end{array}\right. \end{aligned}$$

(3)

By placing the inlet at the stagnation point of the airfoil and the outlet at the minimal pressure point on the suction side, a pressure gradient that is multiple of the dynamic pressure in the freestream can be generated, which would consequently drive the sampling flow. Using XFOIL, it is possible to study the pressure field for different AoA and placements of the inlet and outlet. The results would help quantify the pump potential and give a fundamental understanding of the germane effects. For XFOIL model, a Reynolds number of $\text {Re} = 5.1\cdot 10^5$ and a constant airspeed of $|\textbf{U}_{\infty }|= 19.5$ m/s were used. Furthermore, to account for the roughness of the airfoil and turbulence of the fluid around the airframes, a value of $N_{\text {crit}} = 9$ was used as a measure of freestream turbulence in the XFOIL model to focus on laminar effects. On the other hand, a $N_{\text {crit}} \approx 0$ was used for the evaluation of the 2D simulation model in Section 1. The $N_{\text {crit}}$ value sets the boundary layer laminar/turbulent transition point on the airfoil and is determined by the $e^{\text {N}}$ method for flow transition prediction. $N_{\text {crit}}$ correlates to the turbulence intensity I, where small values for $N_{\text {crit}} \gtrsim 0$ constitute very turbulent flows with $I \rightarrow 10 \%$, while $N_{\text {crit}} > 10$ constitute laminar flows with $I \rightarrow 0.1 \%$ (van Ingen 2012).

2.3 2D simulation

The second method uses a stationary 2D CFD-Simulation model to expand upon the theoretical results of the 1D-Analysis and to study the pump effect of an aerodynamical shape that better represents the complexities of gas measurement systems. A 3D simulation of the geometry was out of this study’s scope to limit the discussion to only the 2D aerodynamic effects in favor of developing a fundamental understanding of the pump effect and establishing the simulation model. 3D-flow effects such as induced drag, 3D vortices, or wingtip-induced drag similar effects are expected to have a negative effect on the pump’s efficiency due to the rotational symmetry of the final geometry used in the flight experiment (Fig. 3). Still, given enough computational resources, the 2D simulation model can be expanded to a 3D model and will be a key topic of interest for future studies to validate the pump effect.

To allow for computational scalability, all the meshing, simulations, and pre-and post-processing were conducted using standard open source software packages included in ESI-OpenCFD OpenFOAM v2106 (OpenCFD Ltd 2021) distribution. OpenFOAM was chosen due to its ability to simulate airfoil aerodynamics (Rahimi et al. 2014; Fernando and Narayana 2016) and sensors onboard UAS (Wildmann et al. 2014a). Especially for application within this study, OpenFOAM multi-element airfoils simulations have shown a good comparison to wind tunnel results (Eisele and Pechlivanoglou 2014).

The OpenFOAM model of the wing pod was created using an unstructured Mesh, where the geometry was rotated for each AoA to achieve higher mesh aliment to the flow direction. A C-shaped computational space is used to reduce the mesh size (Fig. 5). The choice of the cell refinement spaces also considers the overall mesh size, as the focus is not to create a high-resolution approximation of the pressure field around the profile but rather an estimate that resolves the pump effect. The used domain is limited to $\pm 3$ m in x-axes and $\pm 1.5$ m y-axes in favor of higher cell count in and around the profile. The mesh was created with cfMesh (Juretic 2020) using the 2D-Cartesian method, with an average of $1.5 \cdot 10^6$ cells and a cell size small enough to resolve the viscous sub-layer around the pod. The size of the prism layer cells on the pod’s surfaces was chosen so that the dimensionless wall distance is $y^+=\frac{u_* \, y}{\nu }<1$, where $u_*$ is the friction velocity at the nearest wall, y is the distance to the nearest wall, and $\nu$ is the local kinematic viscosity. An example of the mesh grid around the wing pod and the inlet diffuser is shown in Fig. 5.

Fig. 5

The mesh of the computational space of the 2D simulation of the wing pod without the diffusor, flow direction, and boundary names around the wing pod (left) and a close-up of mesh around the inlet diffusor (right). The mesh was created using the OpenFOAM (OpenCFD Ltd 2021) and the cfMesh library (Juretic 2020)

The simulation was intended to model the realistic flight condition of the ABL. All assumptions about the gas constants and the airflow can be found in Table 1. The corresponding boundary conditions used in the model are listed in Table 3. The OpenFOAM:free-stream boundary condition for the edges of the computational domain plays a central role in the model because it provides an inlet–outlet/outlet-inlet condition depending on the velocity vector’s orientation, thus giving a suitable representation of the freestream flow independent of the flow field around the wing pod, thus avoiding back-flow and other circulation effects in and out of the computational domain.

Table 1 The OpenFOAM solver and fluid-models used in the simulation model

Since the static pressure would not affect the simulation results, this was set to $P_{\infty }=0$ Pa. A high turbulence intensity of $I = 10 \ \%$, which is defined as the ratio of the standard deviation of fluctuating wind velocity to the mean wind speed (Kimura 2022), is assumed to give a realistic representation of extreme conditions in ABL, corresponding to the upper limit of values found in the literature (Versteeg and Malalasekera 2007; Li et al. 2011). As the turbulent length scale L corresponds to the size of the high-energy eddies, the assumption was made to only consider eddies in the freestream which are 10 % of the profile’s chord length $c_{\text {wingpod}}$. This assumption is valid for a steady-state simulation since only eddies proportional to the characteristic length of the wing pod would have the most impact in terms of the size of the wing pod. Larger eddies are not considered in this simulation as they are perceived by the wing pod as winds. Any smaller eddies generated in the freestream by the dissipation of larger eddies are still accounted for as the energy dissipation rate $\epsilon$ across the energy spectrum is constant. This same consideration was taken into account for the dimensions of the computational space.

The OpenFOAM implementation of the kOmegaSST turbulence model (Menter and Center 1992; Rumsey 2021) was chosen to solve Reynolds-averaged Navier–Stokes (RANS) equations, as it has been found to give good results for aerospace and industrial applications (Ashton and Skaperdas 2019; Villalpando et al. 2011; Suvanjumrat 2017). The model was especially considered to simulate the turbulent and viscous effects around the wing pod because it can model flow separation that would result from high AoA and the mixing of internal and external flows at the outlet of the wing pod. Furthermore, as a RANS-Model, the simulation model would offer a simple and computationally efficient method for studying more variants of the wing pod and AoA. A higher-order and more complex turbulence modeling is out of this study’s scope, especially as experimental results of the wing pod’s aerodynamics are not available for comparison.

The freestream flow’s values (subscript $X_\infty$) for turbulent kinetic energy k and the specific dissipation rate $\omega = \frac{\epsilon }{k}$ are set under considerations found in the literature (Menter 1993; Wilcox 2008; Matyushenko and Garbaruk 2016), that use a specific dissipation rate in the range $\omega = (1 \rightarrow 10) \cdot |\textbf{U}_{\infty } |/L_D$, where $L_D\approx 3$ m is the approximate length of the computational domain used in this study and $\textbf{U}_{\infty }$ is the freestream’s velocity. Using the definitions for the turbulence variables from Versteeg and Malalasekera (2007), the values at the boundary conditions are calculated using Eqs. 4 to 6.

$$\begin{aligned} \text {turbulent kinetic energy:} \ k= & {} \frac{1}{2} \left( \, \overline{(u')^2} + \overline{(v')^2} + \overline{(w')^2} \,\right) \nonumber \\= & {} \frac{3}{2} \; (|\overline{\textbf{U}}|\, I)^2 \end{aligned}$$

(4)

$$\begin{aligned} \text {specific turbulence dissipation rate:} \ \omega= & {} \sqrt{k}/L = \epsilon /k \end{aligned}$$

(5)

$$\begin{aligned} \text {turbulent kinematic viscosity:} \ {\nu _t}= & {} \frac{k}{\omega } \end{aligned}$$

(6)

For the boundary conditions at the wing pod wall, a small number was used for turbulent kinetic energy instead of zero to ensure numerical stability and limit the mesh cell size. Furthermore, the kLowReWallFunction boundary condition was used for turbulent kinetic energy k and the nutLowReWallFunction boundary condition for the turbulent viscosity term to ensure numerical stability while resolving the viscous sub-layer. The advantage of LowReWallFunction boundary condition-type is that they operate in both low- and high-Reynolds number turbulent flow cases. The boundary condition calculates the value at the boundary for each quantity based on the computed laminar-to-turbulent switch-over $y^+$ value. It can provide a turbulent kinetic energy wall function condition for both the log-law and viscous region of the flow (Liu et al. 2017). Furthermore, the nutLowReWallFunction boundary condition can set $\nu _t$ to zero to account for relatively larger mesh cells compared to the velocities around the wing pod. It also provides an access function to calculate $\nu _t$ depending on the dimensionless wall distance $y^+$ value within the viscous sub-layer in case needed. While these switching boundary conditions can be considered over-engineered for cases where all cells in the mesh have a value of $y^+ < 1$, they were used throughout the development process to facilitate experimentation. They were kept for consistency and to establish the simulation model, so it can be used in future studies on different, more complex geometries where the condition $y^+ < 1$ is not guaranteed by the mesh.

For $\omega$ at the wall of the wing pod, the value was arbitrarily set to the same value as in a freestream, as practical experience with the model has shown that the results do not depend too much on the precise details of the treatment of this boundary condition (Versteeg and Malalasekera 2007). The used wall boundary condition omegaWallFunction is also valid for both low- and high-Reynolds number turbulence models. It is a special wall function that can switch between viscous and logarithmic regions according to the value of $y^+$ (Liu 2016). Thus, also ensuring numerical stability.

2.4 Flight experiment

Within the scope of the development process of the sampling system, it is essential to differentiate the numerical models from the flight measurements because they assume a simplified internal flow resistance and stationary turbulent statistics. Furthermore, the flight measurements are also subject to many factors, including changing turbulent conditions in the ABL, the flight dynamics of UAS, and the active control of the autopilot. As outlined in the introduction, this study’s focus will be on the stationary effects and averaged statistics; other effects, such as the dynamics of airspeed and AoA during flight measurements, will be discussed in future studies.

The flights were conducted during the VALUAS (VALUAS 2020) measurement campaign in July 2020 on the German Weather Service’s (DWD) boundary-layer field-site (in German: Grenzschichtmessfeld, GM) at Falkenberg (52$^{\circ }$10’N, 14$^{\circ }$07’E, 73 m above main sea level) near the Lindenberg meteorological observatory, about 60 km south-west of Berlin Germany. The site is characterized by its almost flat and homogeneous topography formed by inland glaciers during the last ice age (Beyrich and Engelbart 2008; Neisser et al. 2002), which makes it ideal for the conducted experiment due to the absence of complex terrain and wind fields.

The flight measurements were conducted onboard the airborne measurement platform MASC (Rautenberg et al. 2019; Schön et al. 2022; Mauz et al. 2020; Platis et al. 2016), which is a specialized UAS for meteorological measurements in the atmospheric boundary layer. The MASC is an autonomously flying UAS that has a 4 m wingspan and a weight of about 6–8 kg, which includes a scientific payload of about 1 kg to 1.5 kg. Depending on payload and battery configuration, a total flight time of up to 2.5 h can be achieved. The system’s autopilot (Pixhawk “Cube”-Series (Pixhawk 2022)) can hold both position and altitude within a few meters of a programmed flight path for a variety of conditions. More importantly, for the functionality of the wind pods, the autopilot can be programmed to hold the UAS at a constant airspeed by balancing the engine throttle and flight control surfaces. In this study, the target airspeed of the MASC was fixed to 19.5 m/s. The autopilot parameters were tuned to strive for stable flight conditions that consider the validity of the sensor, the conducted measurements, and the flight mission profile.

In the used configuration, the MASC included a sensor payload to measure the atmospheric values and the UAS’s attitude, which also would validate wind pod measurements. The MASC sensor payload included the following:

• 1. A high-frequency sensor suite consisting of a five-hole probe and fine-wire resistance thermometer for wind vector and temperature measurements at frequencies up to 30 Hz (Rautenberg et al. 2019; Wildmann et al. 2013)

• 2. A SHT31: (Sensirion 2018) placed within an open-ended tube for low-frequency water vapor and temperature measurements at about 1 Hz

• 3. A SBG-Systems: Ellipse 2N INS: (SBG-Systems 2022) for IMU, magnetometer, and GPS data logged at frequencies up to 100 Hz

The MASC, as a UAS, is considered an ideal flight platform to test the functionality of the pods as it offers a glider profile with a pusher engine placed at the tail of the airframe, which results in a minimum amount of disturbance to the sensor and incoming air volumes. The system has proven its ability to resolve turbulent exchange and transport processes in the atmospheric boundary layer (ABL), including momentum and turbulent fluxes (zum Berge et al. 2021; Rautenberg et al. 2019; Wildmann et al. 2014b).

For the flight measurements, a pod geometry based on practical considerations and conclusions derived from the numerical methods was 3D printed and mounted as a nacelle on the wing of the MASC, as shown in Fig. 3. Onboard several measurement flights, geometrically identical wing pods with different aerosol and gas sensor configurations were tested. The aerosol and gas measurements are beyond the scope of this study, as the focus will be on characterizing the pump effect of the wing pod and the resulting volumetric flow in conjunction with UAS flight mechanics. All flow pods were equipped with a flow sensor Sensirion:SFM3400-33-AW (Sensirion 2020) to study the flow through the wind pods. This study will present data from a vertical profile flight of the VALUAS campaign, which carried a wing pod, that houses an optical particle counter which required a volumetric flow of around 5.5 L/min.

3 Results

3.1 XFOIL analysis

The pressure coefficients around the profiles NACA0012, NACA0024, and NACA4525 are plotted using XFOIL in Fig. 6 to study their distribution for positive AoA and to show the potion of the pressure field’s minima and maxima, which would constitute the inlet and outlet for the studied pump effect. While the pressure minima point could be on the bottom side of the profile for negative AoA, especially for symmetrical airfoils, it is considered a trivial case, which can be avoided for a practical application by using a small angle of incidence. Fig. 6 shows that the pressure minima would fall in the front of the profile at a chord length of $x<0.15$ and move to the back by a small margin for higher AoA. Compared to NACA0012, thicker (NACA0024) and non-symmetrical airfoils (NACA4525) have their minima further back in the profile. The maxima of pressure coefficients for each airfoil, which are also the stagnation points, have a value of 1.0 and are always at the tip of airfoil’s chord length $x_s=0.0$ for the corresponding AoA.

Fig. 6

Pressure coefficients $C_p$ distribution around the NACA0012, NACA0024, and NACA4525 profiles for AoA $\alpha = 0, \; 3$ and $5 ^{\circ }$. The top side of each pressure coefficient curve (solid line) corresponds to the top side of the airfoil and vice versa for the bottom side (dash line). Note that the pressure coefficient values for the symmetrical profiles at zero angles of attack fall together on one line

Fig. 7

Resulting pump pressure divided by the freestream dynamic pressure ($q=0.5 \; \rho {\textbf{U}_\infty }^2 \approx 230$ Pa) over AoA in degrees for outlets at chord lengths $x \in [0.05,0.1,0.2,0.3]$ at the top side of the profiles for each of the profiles NACA0012, NACA0024, and NACA4525, and an inlet either at profile’s tip (case T) or at the stagnation point where $C_p=1$ (case S)

The pressure coefficients of the profiles in Fig. 6 also show the correlation of the pump effect to the total lift of each profile, which is a positively correlated function of the area enclosed by $C_p$. This area increases for higher AoA as the difference between the minima and maxima (stagnation point) of the pressure field also increases, resulting in higher pump pressure and higher lift. For $\alpha = 0$, the symmetrical airfoils show minimal pump pressure as the area enclosed by the profile reaches zero, as seen in Fig. 6 for the NACA0012 and NACA0024 profiles, which also correlated to zero lift. The minimal pump pressure at zero AoA can be explained by the drop of the dynamic pressure by the accelerated airflow due to the deflection around the airfoil.

To further illustrate and compare the pump effect and the relation to the AoA, the generated pump pressure was plotted in Fig. 7 for the different profiles using an outlet at chord lengths $x_{\text {Outlet}} \in [0.05,0.1,0.2,0.3]$; the results were then sorted accordingly for chord length. The figure compares the resulting pump pressure for two cases:

• Case S: plotted as solid lines, where $x_{\text {Inlet}}$ is chosen at the corresponding stagnation point for the current AoA. In this case, the stagnation $x_{\text {Inlet}}$ would change for each AoA. Thus, the positive pump pressure can be achieved even for high negative angles of attack. Therefore, this case represents the maximal possible pump pressure for a given $x_{\text {Outlet}}$.

• Case T: plotted as scatter points, where $x_{\text {Inlet}}$ is chosen at the tip (leading edge) of the profile at the AoA $0 ^{\circ }$. This case represents a more practical case as it describes the resulting pump pressure for a fixed set of $x_{\text {Inlet}}$ and $x_{\text {Outlet}}$. For an AoA of $\alpha = 0 ^{\circ }$, both cases coincide because the stagnation point coincides with the tip of the airfoil’s geometry.

It can be seen in Fig. 7 that the profile NACA4525, which also by definition generates the highest lift, yields the highest pump pressure. The figure also shows that choosing an inlet, not at the stagnation point, would lower the pump pressure. Figure 7 shows that for the case where the outlet is on the top side of the profile (case T), negative AoA result in a faster decay of pump pressure and would even result in a negative pump pressure that would invert the induced flow. This correlates with the profile’s net lift, as profiles would also exert a negative lift for negative AoA. This is especially the case for symmetrical profiles, as seen in Fig. 7 for the NACA0012 profile, which generates the least lift and pump pressure.

Figure 7 shows that the $x_{\text {Inlet}} \approx 0.1$ has the highest generated pump effect. It can also be noted that for $x_{\text {Inlet}}>0.1$ at larger chord lengths, the resulting pump effect would be in a regime that would not be very sensitive to perturbations in the AoA. The sensitivity is especially evident for $x_{\text {Inlet}}<0.1$ and thinner profiles like NACA0012. Considering the aircraft would, under actual flight conditions, oscillate around an AoA, the choice of an $x_{\text {Outlet}}$ point that would marginally trade pump pressure for stability is important for a practical application. This effect can also be seen in Fig. 6 as the position of the minima with $x_{\text {Inlet}}<0.1$ would rapidly change for small changes in the AoA.

3.2 2D simulation

An evaluation of the simulation model can be found in Section 1 in the appendix. The simulation model ran for the pitched wing pods for a range of AoA $\alpha \in [-7, -5, -3, -1, 0, 1, 3, 5, 7] ^{\circ }$. A comparison of the resulting pressure field $\Delta p$ of all three studied geometries at an AoA of $0 ^{\circ }$ can be found in Fig. 8. The figure shows how the pressure field changes due to internal flow resulting from the pump effect. Especially on the top side, the internal flow shrinks and moves the negative dynamic pressure field further to the back of the profile. At the same time, the shrunken pressure field with the inner flow on the top side has a lower pressure value, which can be interpreted as the contribution of the internal to the external flow around the airfoil. In the front of the outlet, the pressure is higher due to the mixing of the two fields. The stagnation point at the inlet of the pod without the diffuser is split between the corners of the inlet as a result of the internal flow. Due to 2D symmetry, these corners have a more abrupt effect on the flow, and the final 3D geometry would need to be smoothed to avoid the impact of a blunt surface on the flow.

The 2D simulation results of the wing pod using an inlet diffuser nozzle were found not to give comparative results to the final rotationally symmetrical 3D model, which would be later used for flight measurement. The reason is that for the used 2D symmetry approximation, a second stagnation point occurs on the downside of the profile between the nozzle and the wing pod, which results from the wing pod geometry acting as a long stretched wall due to the used 2D symmetry condition. This, in conjunction with the existing pump effect, results in backward flow through the nozzle’s bypass, as can be seen in the path of the streamlines passing through the cross-section of the tubes in the bottom picture of Fig. 8 in the appendix.

Fig. 8

The simulated dynamic pressure field in Pa at an AoA $\alpha = 0 ^{\circ }$. The velocity vector field (arrows) and streamlines passing through the inner tubes are colored by velocity magnitude m/s; for the wing pod without inner tubes (top), wing pod without a diffuser (middle), and with the diffuser inlet (bottom). The inner tubes are also shown in the top figure as a reference

The ratio of the back-flow in the inlet diffuser would increase for higher AoA (Fig. 18 in the appendix) which advocates the effectiveness of the pump effect but still underlines the limitations of the 2D simulation. For this reason, the results are still shown here for a qualitative comparison of the pump effect for complex geometries. This result also motivates the use of a rotationally symmetrical wing pod shape for complex geometries, such as an inlet diffuser nozzle, to avoid this flow stagnation effect. Due to the wing pod’s 3D ovoid streamlined shape, the second stagnation point and the adherent backward flow are unlikely to occur for small AoA. As the goal of this study is to develop a fundamental understanding of the pump effect, such 3D flow effects will be investigated in future studies and pod designs.

A complete comparison of the effect of the AoA on the pressure field of a wing pod with inner tubing can be seen in Fig. 19 in the appendix. The contour lines of the stagnation point and minima pressure fields are interrupted around both the inlet and the outlet of the wing pod with the inner tubing compared to the pod without the tubing, which indicates the contribution of the momentum of the internal flow to the total pressure field. The resulting pressure field has a stagnation point around the inlet yet with a small eccentricity counter proportional to the AoA. On the top side of the pod, the pressure field has a minimum right behind the outlet, which could also be explained by the velocity contribution of the inner flow. The region right above the outlet has a lower pressure due to the mixing of the inner and outer flows. On average, the streamlines running through the pod show little deviation at the inlet, with a minimum deviation around AoA in the range of $\alpha \in [0,-2]^{\circ }$. Flow separation due to the mixing with the internal flow can be seen the velocity vector field in Fig. 8, where the region on the top side of the tubed wing pod without a diffuser indicates a reversed flow. Similarly, a minute reversed flow region of attack can be seen for the pod with the diffuser inlet, which is proportional to the smaller volumetric flow due to the diffuser. This minute region has the potential to grow for larger AoA (Fig. 18).

Fig. 9

Averaged vertical profiles of each flight leg for the true air speed and AoA ($\alpha$) and volumetric flow for both ascent and descent; airborne: 18:20 to 19:10 (LC) on 16 July 2020

3.3 Measurement flights

The study uses data from vertical profile flight (flight IDs 27 of the VALUAS (VALUAS 2020) measurement campaign), to illustrate the functionality of the wing pods and the pump effect. The pod payload consisted of an optical particle counter which required a volumetric flow of around 5.5 L/min. The flight path is plotted in Fig. 16 in the appendix. The flight was conducted on 16 July 2020, airborne: from 18:20 to 19:10 (local time), and consisted of a “zigzag” vertical profiling mission up to an altitude of 2700 m. In this flight, the route of the UAS was devised to study the influence of altitude and the corresponding atmospheric pressure on the pods. Over the length of each measurement leg, the path of the UAS was pitched to achieve the rally points at the next altitude. The flight’s profile also allows for studying the effect of the angle of attack on the volumetric flow of the wind pods. The mean profiles of the UAS attitude (True Air Speed and AOA) and the corresponding measured volumetric flow are plotted in Fig. 9. The flight was conducted under stable boundary layer conditions during the late afternoon-early evening transition. The vertical profiles of the potential temperature, as well as wind speed and direction measured and calculated using the MASC sensor hood according to (Rautenberg et al. 2019), are plotted in Fig. 10.

Fig. 10

Averaged vertical profiles of each flight leg for the potential temperature and the wind speed and direction for both ascent and descent; airborne: from 18:20 to 19:10 (LT) on 16 July 2020

The measured volumetric flow, altitude, angle of attack, and true airspeed are plotted over of the measurement time in Fig. 11. An enlargement of the first five measurement legs is plotted in Fig. 12. Both figures show that the pod was, on average, able to hold the required constant volumetric flow during the measurement legs. Figure 12 shows that the variance is higher at altitudes below 1000 m, which is attributed to turbulence in the convective mixing layer in the lower neutral part of ABL. During the whole flight, the measured volumetric flow exhibited only a marginal correlation to altitude.

The flight sections between each measurement leg, which are not marked in a greyscale in Figs. 11 and 12, consist of abrupt turns with sudden changes in the airspeed and AoA (seen Fig. 16). These sudden changes in the flight attitude are also reflected in spikes in the volumetric flow. The dynamics of the spikes exhibit the auto pilot’s action to hold the UAS’s path and altitude via control of throttle and aerodynamic surfaces. To stabilize the UAS’s attitude, the autopilot would counteract true airspeed with the AoA. By doing this, the autopilot inherently stabilizes the volumetric flow of the pod. The averaged vertical profile of the measured true airspeed, AoA, and volumetric flow for each leg height is shown in Fig. 9. The vertical profile of the volumetric flow shows little correlation to altitude, and the deviations can be attributed to the flight attitude, particularly the AoA and the airspeed of the UAS. The autopilot setting heavily influences the balance of flight attitude and airspeed. This effect can be seen in the difference between the ascent and descent flight phases in Fig. 9, which had different autopilot settings.

Fig. 11

Vertical profile flight: volumetric flow L/min for the wing pods, altitude m, true airspeed m/s, and angle of attack over time s starting at the time of the first flight measurement leg. Each of the flight legs is marked in greyscale. All values in the plot are averaged using a moving window of 5 s

Fig. 12

Vertical profile flight: volumetric flow L/min for the wing pods, altitude m, true airspeed m/s, and AoA over time s starting at the time of the first measurement leg for the first flight legs, which are also marked in a greyscale. All values in the plot averaged using a moving window of 5 s except for volumetric flow

4 Discussion

This section will further elaborate on the presented results, by quantifying the volumetric flow of the simulation model, quantifying the isokinetic efficiency of flight measurements, and evaluating the constitutive relationship between the flight attitude and the measured volumetric flow. Finally, possible improvements for future development of wing pod are discussed.

4.1 Volumetric flow of the 2D simulation

The average airspeed $u_{\text {avg}}$ over the cross-section of the inlet of the wing pod tubes (not the diffuser’s inlet) is chosen as a proxy for the volumetric flow ($Q = u_{\text {avg}} \; A$) for the 2D simulation. Since the inlet surface under the 2D symmetry condition is infinitely long, the calculation of the cross-section area A would not be representative of an actual use case. Therefore, the comparison with $u_{\text {avg}}$ is valid since A is a constant which scales the volumetric flow.

Figure 13 shows the average airspeed at the inlet of the pod as a measure of the 2D-volumetric flow as well as the lift and the drag for each AoA for the simulated wing pods and compares them to values of the NACA4525 airfoil using the XFOIL model. Considering the generated lift, for the pod without the diffuser, Fig. 13 shows a positive correlation of volumetric flow to the AoA. Figure 13 also indicates that the pump effect would increase the drag and decrease the generated lift compared to the wing pod without the inner tubing. This can be explained by the changes in the pressure field around the pod with the inner flow, added resistance of internal tube geometry, and the viscous mixing of the two flows. If the dissipative viscous losses were ignored, the conservation of energy would dictate that the resulting difference between generated lift and added drag of the closed pod compared to the pod with the inner tubes would equal the energy translated to the pump effect. Due to the limitations of the 2D simulation results of the pod with a diffuser and the backward flow described in Section 3.2, the results of the diffuser pod are only valid for a qualitative comparison. Similar considerations regarding the validity of the simulation can be made for the reduction of the average speed of the inlet compared to the freestream due to the simplifications made, such as the 2D symmetry and the sharp corners at inlets. Still, for all AoA, the average flow speed for the pod with the diffuser is, as expected, much lower.

Fig. 13

The left figure shows the simulations result for the average flow speed at the inlet of each pod for different angles of attack. The middle and right figures compare the lift and the drag for each of the simulated wing pods’ geometries to the values of a NACA4525 airfoil of the XFOIL model with an angle of incidence of $5 ^{\circ }$

Furthermore, the effect of coaxiality of flow through the diffuser can be seen in Fig. 13 as the flow speed has a maximum at an AoA of $0 ^{\circ }$. Moreover, the influence of the extended chord length of the pod with the diffuser is also visible, as the flow speed is more bounded over the range of the AoA. As discussed in Section 3.1, these results can be explained by the fact that the pressure minimum point moves further to the front of the profile for larger AoA, thus increasing the pressure at the outlet, as can be seen in Fig. 18. The result underlines the observations of the previous Section 3.1 that an outlet at a further back chord length would be less sensitive to changes in the AoA.

Interestingly, Fig. 13 also shows that for a positive AoA of $\alpha = 7 ^{\circ }$, the lift of both the closed pod and the pod with internal flow match, which suggests that the internal flow contributes positively at higher AoA to the flow around the upper side of the wing pod. Comparing the streamlines at the AoA of $5 ^{\circ }$ and $7 ^{\circ }$, the effect of increased lift can be seen in the reattached streamlines at $\alpha = 7 ^{\circ }$ towards the back of the pod, which indicates that the added impulse of the internal flow could stop flow separation around the airfoil and thus increases the aerodynamic efficiency.

Finally, Fig. 13 shows that the wing pod, compared to the NACA4525 airfoil of XFOIL analysis with a similar chord length, is aerodynamically less efficient, as it has a higher drag and a lower lift. The closed pod geometry has a higher lift than the NACA4525 airfoil, which is a result of the UAS’s airfoil extending beyond the wing pod’s geometry and functioning as a trailing edge flap (Fig. 4). The higher drag of the closed-wing pod can be partly attributed to the different turbulence modeling (see Section 3.2). Yet, the decrease in aerodynamic efficiency was expected since the pod’s geometry was chosen based on practical considerations, such as fitting the sensors, aircraft safety, and not interfering with the flaps of the UAS’s wings. For the pod with the diffuser, the drag results are found to be closer to those of the closed pod, which can be explained by the lower volumetric flow, the increased chord length, and the more aerodynamic shape of the pod with a diffuser. The lift results of the wing pod with the diffuser show a significant variance over the range of attack angles attributed to the discussed second stagnation point and backward flow. At $\alpha = 0 ^{\circ }$, the higher lift can also be explained by the higher average airspeed at the inlet, which positively contributes to the flow speeds on the top side of the pod.

Fig. 14

Measurement flight: heat map of volumetric flow L min$^{-1}$ as function of the angle of attack $^{\circ }$ and the true airspeed ms$^{-1}$. All volumetric flow values of all flight legs are interpolated linearly within a grid of 0.5 $^{\circ }$ or ms$^{-1}$ for the ascent and the descent

4.2 Constitutive relationship

To establish a constitutive relationship between the UAS’s flight mechanics and the pod’s volumetric flow, the resulting volumetric flow of the wing pod was plotted as a function of the AoA and true airspeed. All volumetric flow values are plotted as a color map in Fig. 14 with linear interpolation for binned values of a bin size of 0.5 ms$^{-1}$ for the airspeed and $0.5 ^{\circ }$ for the AoA. The advantage of such a plot is that it illustrates the system’s behavior at extreme values regardless of their statistics. Since the autopilot actively controls both the AoA and true airspeed to hold a constant lift or flight attitude depending on parameters set by the user, the graph illustrates the relationship of volumetric flow to the autopilot’s behavior. Two graphs are plotted because the autopilot controls the UAS differently during the ascent or descent. Figure 14 shows that during the ascent and descent, the UAS relied on different ranges of AoA and wind speeds to hold its attitude and mission targets, as can also be seen in Fig. 9. Figure 14 shows that the volumetric flow would generally increase for higher AoA and airspeeds during the ascent and descent. Deviation from this relationship can be attributed to several reasons, including the reaction of the autopilot to extremes such as sudden turbulence and the necessity to hold the course. Other factors that might also influence the relationship are drift angles, which are not studied here under the assumption that they would average out throughout the course of the flight. Due to the autopilot setting, which favors attitude control through airspeed during the descent, the influence of the AoA becomes marginal compared to changes in the airspeed.

Table 2 Correlation matrix for the volumetric flow, angle of attack, and the true air speed during both flight phases of the measurement fight, which used different autopilot settings

The dependency of the volumetric flow on the autopilot settings and flight attitude can also be seen in the correlation matrix of the volumetric flow, AoA, and the true airspeed ($v_{\text {TAS}}$) in Table 2, which only uses values during the leg sections of the flight. The table shows that the setting chosen for the autopilot especially during the ascent had a positive effect on stabilizing the volumetric flow, as seen in the lower correlation of Q to $\alpha$ and $v_{\text {TAS}}$, compared to the correlation of $\alpha$ to $v_{\text {TAS}}$. During the descent, the autopilot setting favored stabilizing the flight attitude using $v_{\text {TAS}}$ rather than AoA, hence the high correlation of $v_{\text {TAS}}$ to Q, and the low correlation of $\alpha$ to Q. The autopilot setting during the ascent resulted in a more favorable smaller standard deviation of volumetric flow $\sigma _{Q} = 0.25$ compared to $\sigma _{Q} = 0.35$ for the descent.

4.3 Effective sampling diameter

To evaluate if the sampling was isokinetic, the effective diameter $D_{\text {Effective}}$ and the effective area $A_{\text {Effective}}$ were calculated using Eq. 7 and the measured volumetric flow Q and true airspeed $v_{\text {TAS}}$.

$$\begin{aligned} Q = A_{\text {Effective}} \cdot v_{\text {TAS}}= & {} 0.5 \; \pi D_{\text {Effective}} \cdot v_{\text {TAS}} \nonumber \\ D_{\text {Effective}}= & {} 2 \sqrt{\frac{Q}{\pi \; v_{\text {TAS}}}} \end{aligned}$$

(7)

The quantity gives a measure of the aerodynamically effective fraction of the wing pod’s inlet nozzle diameter used for isokinetic sampling. For an ideal isokinetic sampling, the fraction of the effective diameter to the actual diameter should be one. It is a useful alternative to the measurement of flow speed at the inlet $v_{\text {Inlet}}$. Based on continuity and the assumption of an isokinetic flow given by Eq. 3, the value of effective area $A_{\text {Effective}} \equiv A_{\infty }$ would be equal to the inlet area $A_{\text {Inlet}}$ (see Eq. 8). As can be seen in the results of the 2D simulation, the sampling diameter can be measured by the cross-section size of the sampled streamlines in the freestream away from the pod. Due to pressure gradients, the diameter of the sampled cross-section could differ from the actual diameter of the inlet. In Fig. 19, this effect can be seen as the streamlines slightly diverge at the inlet, which can be attributed to positive pressure gradients toward the inlet.

$$\begin{aligned} \text {Continuity: } \, Q= & {} A_{\text {Effective}} \cdot v_{\text {TAS}} = A_{\text {Inlet}} \cdot v_{\text {Inlet}} \nonumber \\ \text {Isokentic: } \, v_{\text {Freestream}}= & {} v_{\text {TAS}} = v_{\text {Inlet}} \nonumber \\ A_{\text {Effective}}= & {} A_{\text {Inlet}} \end{aligned}$$

(8)

Fig. 15

The fraction of the effective diameter to the actual diameter of the inlet nozzle $D_{\text {Nozzel}}=2.75$ mm over the angle of attack for the wing pod with the diffuser during the ascent and the descent of measurement flight. The normalized density of the measured points is plotted as color map

$D_{\text {Effective}}$ is calculated for the flight measurements by dividing the measured volumetric flow by the true airspeed of the UAS, with the used inlet nozzle diameter $D_{\text {Inlet}} = D_{\text {Nozzle}}=2.75$ mm. Figure 15 shows the fraction of the effective diameter to the used nozzle diameter over the AoA. Since the autopilot during the flight phases used a different parameter for ascent and descent, the results are plotted separately. Figure 15 shows the general independence of $D_{\text {Effective}}$ of the AoA, which can be attributed to the active control of autopilot. For the ascent phase, a slight positive correlation to the AoA can be observed and explained by the autopilot’s parameters used during this phase. Effects of the by-pass ratio of the diffuser nozzle are not considered, as the nozzle is out of the scope of this study. Still, if the by-pass ratio were considered, it would positively affect the calculated effective diameter ratio in Fig. 15 because the by-pass flow would be added to the measured volumetric flow. Since the by-pass flow was not measured, the calculated effective diameter values are the minimal possible values.

Figure 15 shows a concentricity of values around $D_{\text {Effective}}$ / $D_{\text {Nozzle}} \approx 0.9$, with a slight tendency to higher ratios and AoA during the descent phase. The plot shows the pump effect concept’s potential for the wing pod as it shows near-constant isokinetic flow rates with a ratio of an effective sampling diameter to inlet diameter close to 1, which was necessary because the wing pod was intended for aerosol measurements. A smaller $D_{\text {Effective}}$ value (less than one) would result in under-sampling or a deviation from an isokinetic sampling, thus negatively influencing measurements.

4.4 Possible improvements

The connection of the pump effect to the lift generated by the profile for a given geometry can be described as a function of the surrounding pressure coefficient distribution and the flight attitude (AoA and airspeed). Because the UAS would need to maintain a flight attitude to guarantee the required lift, the UAS, thus, subsequently creates and stabilizes the pump pressure of the wing pod. While this connection was shown for the results of all methods, each method exemplifies a different aspect of the pump effect and the relationship to the flight attitude that could later be used to improve the pump effect’s design or adapt it for other applications. A brief discussion of the germane possible improvements of each of the methods is therefore summarized:

• 1. While the XFOIL model does not consider the momentum impulses and friction loss effects of the internal flow, the model establishes and compares the possible maxima of generated pump effect for different airfoils and AoA. The method helps develop considerations to achieve a stable pump pressure by choosing the outlet position, e.g., slightly behind the pressure minima. Furthermore, an angle of incidence is needed for a symmetrical airfoil since an AoA of $0^{\circ }$ would generate the least pump pressure. Similarly, negative AoA would severely diminish the pump pressure. For the next development iteration, other high-lift airfoils should be considered to achieve higher pump ratios and find configurations less sensitive to AoA variations.

• 2. The 2D CFD simulation mediates many of the shortcomings of the XFOIL method in modeling the wing pod’s pump effect and accounting for the internal flow and adherent viscous effects. The simulation also establishes the pump effect for a practical geometry that can house sensors and be mounted on a UAS wing, thus creating an asymmetrical airfoil with a non-convex shape. The 2D simulation does not model the complexity of the inner tubing, sensors, and the 3D flow effects, e.g., attributed to the rotational symmetry of the final design. However, the simulation was able to compare the aerodynamic characteristics of the studied geometries and establish the relationship to the generated lift in terms of a positive correlation to the AoA, the increase of total aerodynamic drag, and the reduction of lift compared to the geometry without the inner tubing. The established 2D simulation model can be generalized to consider any arbitrary 2D shape for future pod designs. Furthermore, the simulation can optimize different parameters for a given geometry, e.g., the inlets and the outlet’s shape, position, and flow coaxiality. Further studies should investigate the mixing of the internal and external flows, e.g., by optimizing the angle and shape of the outlet to improve the aerodynamic and the pump efficiency. Similar consideration could be made for the position and shape of the inlet to better adapt to the stagnation point’s position at different AoA. To promote further discussions and improvements, Fig. 19 in the appendix shows a comparison of the pressure field for both the closed pod and the pod with tubes for different AoA. Finally, given enough computational resources, the 2D simulation model can be expanded to a 3D simulation that resolves the 3D flow effects around the pod and validates the simulation using flight measurements.

• 3. The flight measurements showed the pump effect potential under actual flight conditions in the ABL. The conducted measurements deviate from the first two methods in terms of the increased complexity due to the incorporation of sensors, rotational symmetry of the flown geometry, and the turbulent conditions in the ABL. Yet it was possible to achieve and characterize the constant volumetric flow rate required by the sensor system. The method establishes the correlation between the AoA, airspeed, and the generated pump effect for practical applications. Due to the coupling of the sampling flow to the UAS flight attitude, the autopilot plays a central role in controlling the volumetric flow. While the measured volumetric flow of the pod showed a positive correlation to both changes in the AoA and airspeed, this correlation differed in magnitude and dynamics for the different flight phases. The optimization of the autopilot parameters was not part of this study. The only parameters and settings changed were those crucial to the flown mission profile. Yet measurement results suggest that these settings would significantly influence the efficiency of the pump effect. Optimizing the autopilot setting would improve the reaction to turbulence in the ABL, reduce variance, and thus increase measurement fidelity. Future measurement studies of the pump effect should focus on the autopilot since it has the highest potential for determining the sampling’s efficiency and dynamic performance under a wide range of measurement conditions in the ABL.

5 Conclusion

Using the concept discussed in the study, it was possible to generate a passive pump effect based on an airfoil-derived geometry for (isokinetic) gas sampling applications onboard a fixed-wing UAS. The concept can create a pump pressure that is a multiple of the freestream dynamic pressure because it takes advantage of both the stagnation pressure and the suction pressure on the top side of the airfoil. A simulation model and flight experiment were conducted, which characterized and validated the pump effect and its correlation to the flight attitude. Within this study’s scope, the pump concept’s development resulted in a simple, lightweight system capable of passive isokinetic sampling, which can facilitate airborne aerosol and gas measurements.

An outline of the development process and the methods used were presented to give an insight into the theory and application of the concept. Further improvements to optimize the efficacy of the pump effect for a given geometry can be achieved by revisiting each method and the germane discussion. More importantly, the presented methods and the development process are intended to be generalized to other geometries and motivate further development of the pump effect and its applications.

Fig. 16

Path of the pod testing flight during the VALUAS campaign over map (OpenStreetMap 2017). The tower of the German Weather Service’s (DWD) boundary-layer field-site at Falkenberg (Germany) is also marked as a reference point

In terms of establishing a constitutive relationship between the measurement system and the measured quantity for the scope of this study, respectively, the UAS and the sampled air volume, it was possible to establish the pump effect’s correlation to the flight attitude and wind speed. Subsequently, the correlation of the pump effect to the system’s generated lift and flight mechanics is valid. While this relationship is, for the scope of this study, only valid under steady-state consideration, it can be hypothesized, under the assumption that the autopilot accounts for perturbations such as turbulence to hold flight attitude, that the established results can be extended for instationary effects for both the measurement system and the measured quantity. Future studies should thus investigate the influence of instationary effects and develop a comprehensive definition of the constitutive relationship of the UAS’s ability to sample air volumes in the ABL. Ultimately, these definitions should be translated to the sensor system, UAS flight, and autopilot parameters due to the essential role of such parameters in implementing meteorological airborne measurement systems that minimize perturbations to the measured environment and improve the measurements’ fidelity.

Appendix

1.1 A.1 Flight measurements

1.2 A.2 Simulation model

Table 3 The OpenFOAM boundary conditions and values used in the simulation model

1.3 A.3 Simulation model evaluation

A quantitative evaluation of the used simulation model is given in Fig. 17 by comparing the resulting lift and drag forces of the NACA0024 and NACA4525 airfoils to values of the XFOIL model. These airfoils are chosen as they give a good approximation of the wing pod in terms of thickness and asymmetry in the case of the NACA4525. The deviations to the XFOIL lift forces are systematic and show a slight dependency on AoA, especially for higher values. The drag forces exhibit a similar systematic, relatively constant deviation. Thus, these differences can be attributed to the underlying, e.g., the turbulence, modeling of each method. Yet, these results show that the model can give a good representation of the pressure field and the resulting forces, which is adequate for a comparative analysis between the different wing pod configurations.

Fig. 17

Comparison of the lift and drag forces over the angle of attack of the 2D simulation (solid) and the XFOIL (dashed line) models for the NACA4525 and the NACA0024 airfoils

1.4 A.4 Simulation results

 

Fig. 18

The dynamic pressure field in Pa of the wing pod with the diffuser at an AoA $\alpha = 3 ^{\circ }$. The velocity vector field (arrows) and the streamlines passing through the inner tubes are colored by velocity magnitude in m/s

Fig. 19

The simulated dynamic pressure field in Pa and the streamlines passing through the inner tubes (colored by velocity magnitude m/s) for a pitched wing pod without a diffuser (left) and the wing pod without inner tubes (right) for AoA of $\alpha \in [-7,-3,-1,3, 5,7]$ degrees from bottom to top. The inner tubes are also shown in the right plots as a reference