Simulations of Unmanned Aerial Systems in Canonical Atmospheric Boundary Layer Turbulence for Sensing and Navigation

Over the past decade, Unmanned Aircraft Systems (UAS) technology has evolved significantly and is on the verge of being a ubiquitous part of any urban landscape. With the FAA announcement of a policy to allow small UAS (sUAS) to operate at low altitudes, it is expected that there will be a flood of UAS models into the market and most importantly into the National Airspace Systems (NAS) for various civilian, military and scientific applications. From a geophysical sciences perspective, such technology would allow for sensing of large-scale atmospheric flows, particularly, atmospheric boundary layer (ABL) turbulence, air quality monitoring in urban settings where multitude of small, minimally-invasive and mobile sensors can drastically alter our ability to study such complex phenomena. Currently available observational data of atmospheric boundary layer physics is so sparse and infrequent which significantly limits analysis. With the quantity and resolution of the data that can be measured using a swarm of UAS, three-dimensional reconstruction and deduction of coherent structures in ABL turbulence may be feasible. However, key challenges remain in the form of identifying optimal trajectories to fly the UAS to obtain the relevant quantifications of the turbulence, interpretation of the sensor data from mobile sensors and understanding how representative are the sparse measurements of the overall turbulent boundary layer. This leads to many fundamentally interesting questions that are itemized here: (a) How does UAS trajectory influence sensing and measurements of turbulence? (b) How does ABL turbulence impact UAS trajectory? (c) How to design optimal sensing strategy for canonical turbulence? The key to answering these questions requires the study and understanding of the coupled system of sUAS flight dynamics, controller and ABL turbulence. It is also worth mentioning that some of the above are relevant issues only for small UAS such as quadcopters whose trajectory can be modulated to ABL gusts as against medium-scale fixed wing UAS.

One of the key challenges of creating realistic sUAS models is that the flight dynamics and navigation performance of sUAS operating in low altitudes is subject to spatially and temporally varying turbulent gusts in the Atmospheric Boundary Layer (ABL). The turbulent flow in the lower atmosphere is a complex dynamical system characterized by the combined influences of the weather, topography, solar heating and diurnal variations, cloud processes, scalar transport and the prevalent state of the atmosphere at the location and time of interest. This interplay produces highly coherent gust patterns that are unique to the conditions of interest. Thus there exists a need for realistic, physics-inspired models of sUAS-ABL encounters. While sUAS are associated with O(1)m length scales, the most energy containing turbulent motions scale as the distance from the surface at these low-altitude flight trajectories, i.e O(1-100)m. In spite of this disparity in length scales, the spatiotemporally varying microscale turbulence impacts the flight dynamics over sub-minute time-scales during which the sUAS traverses potentially hundreds of meters. The variability in the velocity across these turbulence eddies can go up to 20% of the mean wind at these low altitudes. Further, in the presence of buoyancy-driven motions in the unstable stability regime, turbulent updrafts are correlated with reduced horizontal wind velocity and the sweeping of these eddies across the sUAS trajectory induces strong space-time variability in the gust patterns that are stability state dependent. These factors make it imperative to consider the larger scale spatial heterogeneity of the turbulence over a wide range of scales. This knowledge can potentially be used to develop strategies to mitigate negative impacts of trajectory deviation of sUAS, for example by improved designs or more intelligent controllers.

In this study, we will limit our investigations to modeling sUAS dynamics in a “canonical” horizontally homogeneous ABL operating in quasi-equilibrium over flat topography at a fixed stability state – i.e. combination of steady surface heat flux and steady unidirectional "geostrophic" wind vector operating at the mesoscale. To accomplish this, we will use idealized microscale large eddy simulation (LES) to model the extremely high Reynolds number daytime atmospheric boundary layer that is well resolved to accurately capture the energetic atmospheric turbulence motions. The goal is to characterize the space-time variability of the winds relevance to sUAS flight. The filtered incompressible Navier-Stokes equation for the resolved velocity field in rotational form along with the Poisson equation for the resolved pressure is used to describe the dynamics of the ABL. The resolved momentum equation contains a sub-filter scale (SFS) stress tensor, Coriolis acceleration and buoyancy force based on the Boussinesq approximation. Virtual potential temperature evolves through a transport equation augmented with a SFS temperature flux vector. The SFS stress in the momentum equation is modeled with a one-equation eddy viscosity model with a prognostic equation for SFS kinetic energy. In such atmospheric flows, the roughness elements are unresolved and the first grid level is in the inertial surface layer. As a result, total surface shear stress is modeled using a locally logarithmic velocity profile. The LES algorithm is highly parallelized, employs spectral difference in the horizontal and finite difference in the vertical and RK3 for the time-integration. The simulation of the quadcopter is accomplished using a 6DOF flight dynamics model along with a PID position controller and a PD attitude controller. This integrated system will be leveraged to model a aUAS ABL sensing paradigm to answer the relevant research question posed earlier.