**1. Background and Objectives**

It is well documented that aircraft of all sizes are adversely affected by turbulence and gusts; as identified by the Federal Aviation Administration (FAA) and the US Transportation Safety Board as a leading cause of accidents—costing over USD 100M p.a. [1]. Severe injuries are reported, such as those in the 2015 Air Canada flight AC088, which injured 21 passengers, including three children [2]; and 2019 Qantas Flight QF108 whereby 3 cabin staff had head and neck injuries [3]. Accidents still continue to occur with more recent ac-cidents that resulted in injured passengers [4] and even a passenger death [5]. As the size, mass and speed of aircraft decrease, the susceptibility to turbulence and gusts increases [6,7]; or in sum, due to lower wing loading [8]. Smaller general aviation aircraft and helicop-ters also tend to fly more at lower altitudes within the Atmospheric Boundary Layer (ABL) which is dominated by high turbulence intensities from ground protruding structures [7,9]. This has led to reported accidents directly relating to turbulence [10–13]. Even the tran-sition through the ABL can be detrimental to aircraft that are designed to fly at very high altitudes such as Facebook's Aquila Uncrewed Air Vehicle (UAV) and Airbus' Zephyr UAV, whereby both had fatal crashes due to turbulence and/or gusts [14,15].

The advent of Advanced Air Mobility (AAM) vehicles involves operating fleets of UAVs in urban environments far more frequently than we have ever anticipated, for the purpose of transporting parcels and passengers. This exposes the fleet of aircraft to a wide range of challenging flow conditions; specifically large-scale gusts induced by

**Citation:** Mohamed, A.; Marino, M.; Watkins, S.; Jaworski, J.; Jones, A. Gusts Encountered by Flying Vehicles in Proximity to Buildings. *Drones* **2023**, *7*, 22. https://doi.org/ 10.3390/drones7010022

Academic Editors: Ivana Semanjski, Antonio Pratelli, Massimiliano Pieraccini, Silvio Semanjski, Massimiliano Petri and Sidharta Gautama

Received: 27 October 2022 Revised: 19 December 2022 Accepted: 23 December 2022 Published: 28 December 2022 Corrected: 31 May 2023

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

urban infrastructure which can persist up to several kilometers away from the source and interact in complex ways. AAM will more than often involve operation in closeproximity to physical structures (e.g., inspection of infrastructure, or take-off and landing operations from building rooftops). In the presence of large-scale gusts, significant flight path deviations can occur, increasing risk of collision with objects. Aircraft collisions with high-rise buildings is not unheard of [16], and the routine operation of UAVs in cities further increases the risk of collisions. There is a need for both research and regulation efforts to enhance safety and minimize the risk through considering vertiport and vehicular design.

The most relevant aspect of aviation to AAM is the operation of helicopters which also fly in urban environments, albeit less frequently and with a human pilot onboard. Landing on buildings poses a specific challenge in some cases, warranting further aerodynamic studies and field wind measurements being prudent [17]. From a vehicular design standpoint, the AAM vehicles' design and flight dynamics are different from the conventional helicopter and airplane design which warrants an exploration into novel design features and technologies that enable lower sensitivity to turbulence and precise maneuvering [1]. From a vertiport standpoint, the existing heliport infrastructure can potentially support AAM; however there is a need for purpose-built buildings (for ease of public access and to account for the autonomy of UAVs). The characterization of the flow fields for different wind conditions around vertiports is warranted, similar to those conducted for heliports [18–21]. New research is, thus, required to characterize the temporal and spatial variation in the flow fields around buildings and vertiports. This will inform vertiport design and site selection to minimize the risk imposed by the local wake of the building from affecting flight safety as well as passenger ride quality.

In recent years, considerable attention has focused on measurements in ground-test facilities or computations that replicate some idealized flow unsteadiness such as a pitching and/or plunging maneuver or an imposed well-characterized gust [22–29]. However, perhaps the most obvious gust problem for UAV flight is steady level operation, or at least, intended steady level operation through the atmospheric boundary layer (ABL), where no discrete obstacle (or associated wake) is present. Previous studies on UAV flight through the ABL [30,31] have shown that three-dimensional (3-D) turbulent structures induce particularly strong disturbances in UAV roll response owing to variation in effective angle of attack along the wingspan. This disturbance in roll was also noted in comments from pilots attempting to hold steady level flight in well-mixed turbulence [32]. Roll disturbances not only degrade payload performance (particularly the blurring of images from optical sensors) but may also lead to undesired flight path deviations. The most critical parts of UAV urban operations entail flight in very close proximity to buildings and may include entering buildings through windows or air vents or landing on their rooftops (see Figure 1). Whilst the flow field around buildings has been extensively studied from a fixed reference frame (e.g., by wind engineers for the purposes of structural loadings [33,34], dispersion of pollutants [35,36], pedestrian wind comfort [37,38], etc.), there appear to be very few studies from the reference frame of the moving aircraft and at the relevant frequencies [39]. We therefore examine this relative flow field with an overall aim to reveal the characteristics of a "severe" gust for UAVs in close proximity to buildings.

In this paper we first review turbulence in the ABL to frame a taxonomy of gusts and consider their relevance to UAVs. The more challenging flight environment for vehicles passing through the local wakes of buildings is then considered and compared to flight in the ABL. Flight in the urban environment is expected to yield gusts of high severity (frequency and/or amplitude), most likely leading to unwanted, severe force spikes and flow separation about the aircraft wing. While the problem is inherently 3D, we first investigate a 2D longitudinal-only case by examining the relative flow near the centerplane of the building. The outcome of this work is an assessment of the most basic research question to characterize the urban environment: What are the disturbances in effective angle of attack and relative flight speed magnitude in a flight-relevant urban gust encounter?

**Figure 1.** Notional flow field about a building generated by atmospheric winds.

#### **2. Turbulence**

Turbulence is defined as a chaotic, random, highly nonlinear and unpredictable flow [40]. In the atmosphere, the characteristics of turbulence are influenced by the thermal stability of the ABL (adiabatic, or various degrees of stability). However, under strong winds mechanical mixing tends to dominate the turbulence generation mechanisms and thermal stability plays a smaller role. Thus, in the current work we ignore thermally driven turbulent flows, as they only tend to dominate under light winds, which are unlikely to generate severe gusts. The ABL extends from the Earth's surface up to an altitude where the wind is no longer influenced by the roughness of the ground, which may include geological or civil structures. The mean wind speeds increase from zero at the Earth's surface up to the "gradient" wind speed, i.e., that which occurs at the gradient height, typically 1–2 km depending upon terrain roughness. Above this height the air is generally smooth, except for bursts of "clear air turbulence," which are not considered here. The ABL is well documented from stationary measurements for various purposes, including meteorological and wind engineering studies (e.g., [41–43]). The interaction of the ABL with obstacles such as buildings, bridges and other infrastructure will generate coherent turbulence structures with length scales of a similar size to the obstacle, as depicted in a 3-D computational fluid dynamics (CFD) simulation shown in Figure 2, from [44]. The building shown is nominally a cuboid of dimension 43 m, and the simulation includes a representation of the velocity and intensity profiles in the approaching ABL. Figure 3 further illustrates the decaying nature of turbulence in an urban scenario, whereby the coherent structures dissipate downstream of obstacles, and a well-mixed turbulent wake then develops (as can be seen downstream of the building in the figure). These flow features yield a velocity field with a broad spectral content that contains a wide range of length and time scales.

**Figure 2.** Instantaneous velocities in the atmosphere in an urban environment. Flow travels from left to right. With the reference height and velocity as *U*<sup>∞</sup> = 3 m/s and *y*<sup>∞</sup> = 10 m, this results in a domain (average) Re of approximately 2.05 <sup>×</sup> <sup>10</sup><sup>6</sup> [44].

**Figure 3.** The atmospheric environment in an urban location.

#### **3. Prior Gust Models**

Aircraft encounter different types of turbulence while flying through the ABL, and there exists a significant body of knowledge relevant to manned flight focused on the temporal and spatial characteristics of the flow environment that is well-removed from local effects and (usually) from the influence of the ground. These prior works include continuous gust models that represent the structure of the statistically random flow fluctuations in the atmosphere as power spectral functions. These spectra allow for predictions of the mean-square values of the flight vehicle and aeroelastic responses, provided that a

transfer function between the gust and response can be established from deterministic or other means [45,46].

The most common continuous gust spectra of Von Karman [47], as well as those of Diederich and Drischler [48], Dryden [49]) are one-dimensional, i.e., they yield three orthogonal velocity components at a single point, a restriction that neglects gradients in the gust across the aircraft as well as any altitude-dependent wind shear effects. These gust models are built up from the statistical theory and measurements of isotropic turbulence. The von Kármán model form interpolates between the isotropic scaling results of Heisenberg [50] at low frequency and the higher-frequency scaling of Kolmogorov [51] in the inertial subrange. The Dryden model instead assumes a functional form that fits experimental measurements of the isotropic turbulent energy spectrum in the early stages of decay; see Liepmann, Laufer [52] for further discussion and comparison of these gust models. The choice of the simpler Dryden form over the more theoretically-grounded von Kármán model is largely a matter of engineering convenience; the correctness advantage of the von Kármán model is important only if significant spectral content relevant also to the flight and aeroelastic dynamics is centered in the microscale range, a decade or more above the integral scale break frequency where the isotropic inertial subrange begins [53]. The isotropic turbulence assumption, central to both models, is valid for turbulence at high altitude. However, at lower altitudes relevant to UAVs/AAM (less than about 2000 ft), anisotropic effects of the ABL without the influence of urban structures may be modeled by adjusting the turbulence intensity and turbulence length scales in the isotropic models according to empirical design specifications. Such specifications at low altitude for the von Kármán and Dryden models, as well as a discussion of more sophisticated gust models, are organized by Standard [53]. Continuous gust models may be compared with traditional discrete gust models including the sharp-edged gust and "1-cosine" gust used to establish severe aeroelastic scenarios. However, if desired, one may readily construct a continuous gust from a known series of discrete gusts [54], and the continuous and discrete models may be superposed provided that the flow disturbances and resulting structural motions are sufficiently small to retain linearity.

Flows within an urban environment are generally inhomogeneous, anisotropic, and time-varying and, therefore, violate many of the core assumptions of traditional gust models. Near the ground, turbulence length scales and intensities vary rapidly with altitude and depend strongly on the terrain [55]; there is a lack of viable models to describe the broad range of general turbulent flows possible in this environment. The introduction of AAM and UAVs further complicates the modelling challenge of the urban environment. Wind shears from the terrain and from multi-scale arrays of buildings produce longitudinal and vertical gusts that generate significant roll and yaw moments, which must be characterized and accounted for in the gust and vehicle dynamics models [56]. In the absence of buildings and terrain, the length scales of the most energetic eddies in the ABL are much larger than the UAV feature lengths, and the high-frequency content of the turbulence spectrum is therefore expected to play a more significant role in the vehicle gust response. However, the urban landscape affects this turbulent flow and can introduce gust length scales pertinent to the air vehicle response. Furthermore, the gusts encountered by UAVs near buildings may be large relative to the local background flow and can lead to catastrophic nonlinear effects, such as stall-induced pitch-up. In light of these challenges, the next sections survey experimental measurements and computational simulations to characterize the three-dimensional gust fields of canonical urban landscapes and investigate scenarios of vehicle trajectories in this environment.

#### **4. Turbulence Experienced by Moving Vehicles (Relative Turbulence)**

Turbulence Intensity (*Ti*) is defined as the standard deviation of the fluctuating component of wind velocity (*u'*) divided by the mean wind velocity (*U*),

$$Ti = \frac{\sqrt{\overline{(u')}^2}}{\overline{\mathcal{U}}} = \frac{\sigma\_{(u')}}{\overline{\mathcal{U}}} \tag{1}$$

The variation in the intensities and scales with height from the ground from a stationary perspective (i.e., with reference to the ground) is described in Watkins, Thompson [30], and a database compiled from a wide range of measurements can be found in ESDU 85020 [57]. Movement through the turbulence field at different speeds and directions changes how the turbulence is perceived by moving vehicles. The effect of a moving measurement reference frame has been explored by Watkins and Cooper [58] for ground-based vehicles, where two-component data (in the horizontal plane) obtained from hot-wire anemometers mounted above a vehicle were compared for fixed and moving vehicle frameworks. Turbulence intensities measured from the moving vehicle were found to be in good agreement with those predicted from the measured vehicle-fixed data in relatively smooth domains, well-removed from local wakes such as buildings. However, when data were obtained in rougher terrains, which included traversing local wakes, a significant increase in turbulence intensity was found in the data from the moving vehicle. The lateral intensities were considerably higher than values predicted from ground-fixed data, whereas only slight increases in longitudinal intensities were noted. This result was attributed to the fact that turbulence from a stationary perspective (referenced to the ground) was measured at locations specifically chosen to be removed from local wakes.

Watkins, Milbank [6] extended this work to include three-component data obtained from four laterally spaced, dynamically calibrated, multi-hole Cobra probes. This extension was carried out to understand the turbulent flow environment of UAVs, whereby the lateral separation between the probes could be altered to document the flow impinging at different spanwise locations on a UAV wing. Data were collected over various types of terrain, and under a range of wind speeds and vehicle speeds that included some data closer to buildings than in earlier hot-wire measurements. The closest that the measurement tracks came to buildings was about 5 m due to the vehicle being driven on public roads. The study provided data relating the measured turbulence intensities to relative flight velocity (Figure 4), demonstrating a reduction with increasing freestream speed. In the moving case, the denominator in the turbulence intensity (Equation (1)), *U*, becomes *Vr*, which is the vehicle speed relative to the air (i.e., the wind speed). Figure 5 illustrates the vector addition used to compute *Vr*,

$$V\_r = \sqrt{V\_w^2 + V\_w^2 - 2\, V\_w \, V\_v \cos \theta} \tag{2}$$

It is therefore important to differentiate between *Ti* and the Relative Turbulence Intensity (*J*), which takes into account the relative velocity, *Vr*:

$$J = \frac{\sqrt{\left(V\_W\right)^2}}{\overline{V\_r}} = \frac{\sigma\_{V\_W}}{\overline{V\_r}}\tag{3}$$

**Figure 4.** The relationship between relative turbulence intensity *J* and flight velocity *VV* [6].

**Figure 5.** Aircraft and wind velocity vectors.

#### **5. Relevant Gust Characteristics**

Excessively large gusts (i.e., those with length scales significantly larger than the vehicle's characteristic dimension) can often be considered quasi-steady, and their effects are relatively easily compensated for [6]. Gust scales equivalent to or smaller than the characteristic length are more deleterious and introduce significant asymmetrical forces and moments. As a gust impacts the leading edge of an aerodynamic surface such as a wing, the flow angle and velocity are altered, inducing variations in the load distribution as illustrated in Figure 6. Gusts of a 3-D nature that are smaller than the wing span will lead to uneven lift distribution over the wings, inducing a rolling motion. Lissaman [59] demonstrated that a sinusoidal load distribution with a period relating to a dimension that is slightly larger than the span of the aircraft results in the maximum roll moment.

**Figure 6.** Effect of gust length scale on wing loading. Adapted from Lissaman [59].

Gusts in well-mixed turbulence are highly three-dimensional in nature and it has been shown that out of the possible six degrees of freedom, rolling motion is the most significant disturbing factor for UAVs [6]. Atmospheric measurements in well-mixed turbulence removed from building wakes illustrate the three-dimensionality of gusts, whereby significant flow pitch variations are evident across typical UAV wingspans or rotor diameters. Figure 7a shows a typical time record of the angle of attack, *α*, recorded by four laterally separated probes during a two-second sampling time, showing large fluctuations of the order of ±10◦. At first, it might seem that there is a strong correlation between the pitch angles measured from the four probes. However, closer examination of the data presented in Figure 7b reveals that there are considerable differences, and at some instances the variation is ≈15◦ across probes with a lateral separation of 150 mm.

**Figure 7.** Pitch angle variation: (**a**) 2-s sample (**b**) 0.2-s sample [6].

For fixed wings, Thompson, Watkins [60] showed that typical lateral variations in *α* are more significant than the associated velocity magnitude variations in generating potential rolling moments (using data from measurements of well-mixed atmospheric turbulence close to the ground applied to simple wing strip theory). The experimental work by Mohamed, Watkins [31] confirmed the high sensitivity of the roll axis to *α* variation. For rotary wings, among the most relevant work was that conducted by Wang, Dai [61] in which it was found that a variable pitch helicopter blade encountering a downward gust experiences a significant reduction in thrust force. It was also found that the sharper the gust, the more adverse the response is with respect to aerodynamic forces and structural deflection. This behavior is particularly relevant when travelling through shear layers at higher speeds, causing the relative encountered gust front to be perceived as a sharp gust front.

#### **6. Gust Taxonomy**

It is desirable to approximate gusts as quasi 1-D or 2-D (see Figure 8) for fundamental studies on the transient flow field around airfoils through, for example, pitch and/or plunge motions in fundamental experiments. However, the reality of well-mixed atmospheric turbulence is intrinsically three-dimensional in nature. Discrete gusts can be categorized as either 1-D or 2-D in the streamwise or transverse directions. Streamwise 1D gusts involve a momentary change in streamwise velocity. For example, as streamwise velocity increases, the corresponding lift over an airfoil also increases, which if not corrected, will result in a translation of the airfoil upwards (due to lift) and backwards (due to the increased drag). Non-symmetric velocity changes along the span of a wing will result in a rolling and yawing motion if not taken into consideration. It is worth noting that Thompson, Watkins [60], using a simple strip theory model, found that angular flow changes typically have a tenfold greater effect on lift compared to the magnitude changes in atmospheric turbulence. This behavior implies that travelling through a transverse gust will result in a stronger generation of lift than from a streamwise gust.

**Figure 8.** Dimensionality of gusts (modified from Diederich [62]).

#### **7. Severe Gusts around Buildings: Case Studies**

Let us now consider the flow field around a nominally cuboid building in a suburban environment. At the juncture between the building and the ground plane, there is the usual horseshoe vortex, perhaps with associated finer structures [63]. Near the building rooftop, there is expected to be a separated flow with meandering shear layers of timevarying position, width, and intensity. Depending on the building's geometry and wind direction, vortices may also be present near the rooftop. Using the taxonomy discussed in the previous section, possible gust encounters by UAV flight in urban environments are illustrated in Figure 9. Given that the angular flow changes typically have a greater effect on sectional lift coefficient in contrast to magnitude changes [31], the most detrimental case in this set is likely to be a transverse gust given the rapidity of the encounter with respect to the flight trajectory. The latter scenario will therefore be the focus of a case study presented in the remainder of this paper, whereby we use the flow field around a representative cuboid building computed by Mohamed, Carrese [44] (see Figure 2) to estimate variations in the lift and rolling moment coefficients of representative UAVs. The CFD simulation representing an urban environment uses an Improved Delayed Detached Eddy Simulation (IDDES) turbulence model. Mohamed, Carrese [44] validated the simulation by demonstrating excellent agreement of the solution strategy with the experimental and large eddy simulation (LES) data of similar but simpler cases. The validation cases examined were: (1) developed channel flow, (2) flow over a backward-facing step, (3) flow over periodic 2D hills, (4) wall-mounted hump flow, and (5) trailing-edge separation over a hydrofoil. Full details of the basis of these simulations can be found in [44] and comparison with point-probe atmospheric measurements is carried out in [39,64].

**Figure 9.** Schematics of possible gust encounters by a fixed wing UAV flying in the vicinity of buildings. Note drawn to scale for illustration purposes.

In the simulation, inflow boundary conditions replicate the relevant velocity and intensity profiles of a suburban ABL. Due to the mesh resolution near the building (~0.05 m), the scales of the resolved turbulence are suitable for the UAV spans discussed in this paper. Initialization of the IDDES simulation was provided using a steady-state *k*—*ω* SST model. The RANS momentum field is converted to an instantaneous momentum field before commencing the transient run. The pressure-based Non-Iterative Time-Advancement (NITA) fractional-step solver is utilized, with bounded second-order temporal discretization. The time step is normalized by the ratio of (*l*∞*/U*∞) with a non-dimensional time-step of Δ*t* ∗ = 0.003 for the total time of the simulation *t* ∗ *T* = 600 with sampling statistics collected from *t* <sup>∗</sup> *>* 200. An average wind speed of 3 m/s at a height of 10 m was used in the upstream boundary condition representing the ABL, and the mean wind direction was normal to the southerly face (i.e., along the *x*-axis in the figures below). The modelling requirements and profiles for the ABL were obtained from the work of Blocken, Stathopoulos [65], and the ABL velocity profile *U*(*y*) was estimated using

$$
\mathcal{U}I(y) = \frac{\mu^\*}{\kappa} \cdot \ln\left(\frac{y}{y\_0}\right) \tag{4}
$$

where *u*\* is the friction velocity, *U*<sup>∞</sup> and *y*<sup>∞</sup> are the reference velocity and height, *κ* is the von Kármán constant, and *y*<sup>0</sup> is the equivalent aerodynamic roughness height. The profiles for the turbulence kinetic energy *k* and specific dissipation *ω* were estimated using:

$$k(y) = \mu^{\*2} \cdot \mathbb{C}\_{\mu}^{-0.5} \tag{5}$$

$$
\omega(y) = \mu^\* \cdot \mathbb{C}\_{\mu}^{-1.5} \cdot \frac{\kappa}{y} \tag{6}
$$
