High-fidelity simulations of Chemical Plume Tracing in the planetary boundary layer
Introduction
Locating a gas-emitting source is a challenge encountered in many environmental monitoring and hazard assessment applications. It can be used for finding gas leaks in landfills and industrial compounds, for the early monitoring of fire outbreaks, and for mitigating accidental or deliberate release of toxic gas to the atmosphere. Historically, this general problem has been addressed by two fundamentally different approaches.
The first approach, often referred to as Source Term Estimation (STE) or Reversed Modeling, takes into account concentration measurements from a net of stationary sensors (Hutchinson et al., 2017). Combined with a dispersion model, these readings are utilized to determine the most probable source location. Although this technology is mature are applied for ranges of few hundred meters (Yee, 2012) to thousands of kilometers (Seibert and Frank, 2004), it demands deployment of a complex system at the site of interest.
An alternative method is the Chemical Plume Tracing (CPL), in which a robotic platform, equipped by a chemical sensor, and potentially with anemometry capability, is designed to autonomously navigate towards the source of the sensed gas. The robotic platform can be wheeled, aerial or underwater (Arrieta, 2003), and are easily deployable. Potentially, the search can be conducted by a swarm of collaborating robots (see e.g. Marjovi, 2010). CPT approaches benefit relative portability and fast deployment. Also, in contrast to classical STE, no coupling to a dispersion model is inherently necessary.
Many CPL algorithms are essentially inspired by searching strategies of moths, dung beetles and lobsters seeking for food or mating by navigating upwind along an odor plume (Kuwana, 1999). Other algorithms relay on Bayesian inference, to deduce the source location given concentration measurements conducted along the platform trajectory (Vergassola, 2007). For a review of the subject, the reader is referred to, e.g., Kowadlo and Russel (2008).
Often, field experimentation is conducted to validate, compare and optimize CPT algorithms. Aside from the high cost involved, the limited number of experimental repetitions is normally insufficient for proper averaging considering the turbulent, constantly changing environment.
Consequently, numerical simulations of CPT are also commonly conducted. Such experiments involve simulating both the background Flow and Dispersion (F&D) of gas, the sensors measurements and the resulting motion of the robotic platform. Numerical simulations can be repeated many times for different initial conditions, source characteristics, and algorithm tuning parameters, while maintaining controlled background conditions. This provides a solid qualitative ground for algorithm evaluation and development.
Dispersion from localized sources in a turbulent atmospheric boundary layer flow, has some properties which have to be taken into account in order to properly simulate the background environment and consequently, the CPT process. Atmospheric turbulence promotes great temporal variability of the instantaneous concentrations. Moreover, the concentration at a point can zero out for significant periods due to turbulent plume meandering (Wilson, 2010). As a consequence, CPT algorithms should provide robustness under frequent concentration signal losses, and should be numerically evaluated within a simulated environment which expresses the turbulent nature of the real atmosphere with high fidelity.
A pioneering study testing CPT algorithms based upon realistically-simulated turbulent F&D was done by Farrel (Farrel et al., 2002). The horizontal flow in this study was calculated on a two dimensional grid on which the Reynolds Averaged Navier Stokes (RANS) equations were solved. By construction, the RANS model only solves for the temporally average flow, which excludes the turbulent eddies that promotes plume meandering motion. For this reason Farrel et al. used prescribed time-varying Boundary Conditions to artificially create the needed motions. The concentration field in this work was comprised of puffs, or filaments, which were advected by the flow. The turbulent effects on the filaments were modeled by gradually enlarging them according to a prescribed diagnostic formula, mimicking the effect of puff scale turbulent eddies. The effect of eddies larger than the filaments was taken into account by adding a random velocity perturbation to the velocity of each specific puff.
The modeling approach developed by Farrel et al. was subsequently used by several authors as a framework to preform CPT simulations. Zarzhitsky et al. (2010) conducted simulations to study CPT conducted by a swarm of searchers. Pashami et al. (2010) integrated the model suggested by Farrel into the framework of the OPENFOAM CFD software. Neumann et al. (2013) used this work for a comparative study of several CPT algorithms.
This work makes another step in the direction of improving the simulation of the environmental conditions, to allow better CPT development and evaluation. Within the last few decades, major advancement in the availability of computational resources has made high fidelity, turbulent resolving CFD within reach even for the high resolution needed for simulating CPT algorithms. The relevant scales of turbulent flow can now be directly modeled, using the Large Eddy Simulation (LES) turbulence modeling method (Sagaut, 2006). F&D fields, simulated by LES, exhibit not only qualitatively, but also quantitatively realistic behavior, supplying the adequate simulated environment for conducting multiple reliable CPT simulations.
In the current study, we demonstrate how high-fidelity LES calculations of flow and dispersion in the atmospheric boundary layer can be used for the development of better CPT. The algorithm chosen for the demonstration is the surge-cast algorithm, inspired by search strategies applied by male moths to find a mate. Section 2 is dedicated to the description and testing of the F&D models used to simulate the environment in which the CPT takes place. It is shown that the concentration field agrees well with other state of the art models in terms of the average concentration, its relation to the concentration standard deviation, and the frequency distribution of instantaneous concentration values.
In section 3 the applied surge-cast algorithm is described and illustrated. Section 4 exemplifies the advantage of the proposed method by focusing on two issues. The first is the evaluation of the optimal platform velocity, and the second one is the extension of the CPT to three-dimensions, to enable localization of elevated sources. Both issues are addressed by statistically analyzing multiple CPT simulations. Section 5 summarizes and points at future directions of development.
Section snippets
Turbulent boundary layer simulation
To generate the background flow, the Navier Stokes equations were numerically integrated using the Large Eddy Simulation (LES) method. Here we use the PALM model (Maronga et al., 2015), an advanced, state of the art LES modeling system for atmospheric and oceanic boundary-layer flows, specially designed for massively parallel runs over multiple nodes. The PALM model utilizes an eddy-dissipation, 1.5-order SGS model. i.e., an equation for the SGS Turbulent Kinetic Energy (TKE) is prognostically
General structure
The CPT algorithm applied here is a variant of the surge-cast algorithm suggested by Lochmatter (2010), inspired by the behavior of silkworm moths navigating a pheromone plume to locate a female. Denoting the local horizontal wind vector at time t , the local simulated concentration , the sensitivity threshold , and the velocity of the platform is v, the algorithm for a single time step is described in the flowchart below.
The algorithm is comprised of alternating phases of surging
Numerical experiments
In the following, the advantage of LES modeling for CPT development and testing is demonstrated. First, it is shown that in respect to a given scenario, there exists an optimal platform speed. The optimal value is assessed and the reason for its existence is explained. Additionally, the CPT algorithm is extended to a three dimensional search, i.e., the height of the source above ground is treated as an unknown to be found by an aerial robotic platform.
Conclusions and future prospects
A novel framework for the high-fidelity simulation of CPT algorithms using LES modeling was presented. CPT is conducted by an autonomous robotic platform equipped by a chemical sensor and an anemometric instrument that is designed to navigate towards a localized gas source. Testing CPT algorithms by numerical simulations is a common practice, aimed to avoid, as much as possible, the difficulties involved in real-life experimentation. However, accurately simulating the planetary boundary layer,
Acknowledgements
This work has been supported by the Israel Ministry of Defense (IMOD). The authors would like to express their gratitude to Dr. A. Lacser for his important comments and suggestions.
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