Equations of a new puff model for idealized urban canopy

Highlights

• Relations between short and long term releases are presented.

• The model outputs are probability density functions (pdfs) of puff characteristics.

• The pdfs enable to calculate the most probable as well as extreme situations.

Abstract

During a leakage of hazardous materials, emergency services need to predict the evolution of the accident. In such situations, fast models are used. Such models can produce reasonable results for long-term leakages, but short-term leakage results can be underestimated by as much as a full order of magnitude (shown in the COST ES1006 project). Hence, the main aim of this paper is to present equations for recalculating the continuous source results to achieve results valid for the short-term source. The model would consist of a sub-model utilized for the continuous source in combination with the equations introduced in the paper. The outputs obtained are the probability density functions of the puff characteristics: dosage, maximum concentration, and 99th and 95th percentiles of concentrations. These functions can help to estimate the situation not only for the mean case, but also for the extreme cases.

Introduction

Chemical industry products simplify people’s lives on a daily basis; however, the chemical industry also possesses a darker, less visible side. Chemical plant accidents are one such negative aspect of the industry. Inhabitants of areas close to chemical plants are particularly threatened by spills and accidents, often accompanied by large fires (Scott, 2016; Tullo, 2018) or by the leakage of toxic gases into the air (Varma and Varma, 2005; Lees, 1996). Such leakages often last less than one hour, and the dispersion of the toxic material is strongly influenced by turbulence (Zimmerman and Chatwin, 1995; Chaloupecká et al., 2017a).

Emergency services need to be able to predict the evolution of a hazardous situation to perform actions necessary to prevent loss of life and environmental disasters. Such predictions can be performed using mathematical models. The direct numerical simulation (DNS) model solves the Navier–Stokes equations without any turbulence model. It provides accurate results (Moser et al., 1999; SCHLATTER and ÖRLÜ, 2010), but its demands on calculations are for high Reynolds numbers out of range even for available supercomputers (VKI, 2016). The large eddy simulation (LES, (Piomelli, 1999; Kobayashi, 2006)) computes only large-scales, which are affected considerably more by boundary conditions than the small-scales, and utilizes a subgrid-scale model for the small scales. Though LES imposes a lower processing load than DNS, its processing demand is still very high (Zhiyin, 2015). Further decrease of the calculation time can be achieved by Reynolds’ averaging (Stull, 2012), utilizing averaging over a time interval much longer than all the time scales of the turbulent flow (Pal Arya, 1999). Applying this averaging to the Navier–Stokes equations, one obtains the Reynolds averaged Navier–Stokes equations (RANS, (Neofytou et al., 2006; Kajishima and Taira, 2017)). These equations can be utilized in combination with the LES, as performed in the detached eddy simulation (DES, (Spalart, 2009; Özgür Yalçın and Cengiz, 2018)). Nevertheless, RANS are usually used independently in engineering practice (Zhiyin, 2015).

In operational practice, usage of a much simpler and faster approach is more common (Pal Arya, 1999; Şahin and Ali, 2016). This approach is called Gaussian dispersion modelling. Apart from the time issue, one of the reasons for the usage of Gaussian models is their recommendation in regulatory guidelines (Hanna et al., 1982; Jeff Bluett, 2004). Gaussian models can be divided into two main types, called the plume and puff models. The plume type (Pal Arya, 1999) assumes a constant mean transport wind in the horizontal plane and Gaussian concentration distributions in directions perpendicular to the wind direction. It is applicable for accidents in which gas leaks for a relatively long time (e.g. hours to days). The puff type (Pal Arya, 1999) assumes a Gaussian concentration distribution in all three directions, and it is useful for those cases in which the duration of the leakage is on the time scale for which the turbulent motions in flow are crucial.

Results of the COST ES1006 project revealed that fast models utilized for the actual emergency phase for long-term gas leakages (plume models) can achieve reasonable results, but that the results for short-term leakages (puff models) can be underestimated even up to a full order of magnitude (Baumann-Stanzer et al., 2015). The solution to this problem might be to find relations for the recalculation of the results for the short-term sources from those for the long-term sources. The reason why such relations could exist is the hypothesis as follows. Both releases, the continuous and the puff, are set in the same mean turbulent flow. Conditions for both releases are similar in the lateral and vertical directions. In the longitudinal direction, the only difference is that the puff is surrounded by clear air. In contrast, if we imagined a small internal volume of the plume, the contaminant (not the clear air) would surround it in the longitudinal direction. The puff Gaussian model assumes a Gaussian concentration distribution in this direction (Pal Arya, 1999). However, the underestimation of its results (Baumann-Stanzer et al., 2015) indicates that this might not be a good assumption and the dispersion seems to be far more complex. Differences between dispersion characteristics of continuous and puff releases might be given by “edge effects” (puff releases are confined in space and time). These “edge effects” cannot be captured by models that use averaged flow field. Because the duration of the release is short by the puffs and the dispersion is dependent on the actual phase of turbulent flow in the time and the place of the release, many dispersion scenarios exist for an exposed position under the same mean conditions (Zimmerman and Chatwin, 1995; Baumann-Stanzer et al., 2015). Hence, many release realisations under the same mean conditions are needed to get statistically representative datasets. If one randomly chosen puff realisation and the continuous release were compared, no relations would probably be found. But taking into account statistically representative datasets for the puffs and considering the sameness of the mean turbulent flow, one could find the relations between the short-term and the long-term releases. In this paper, we present such relations for a built-up environment consisting of closed courtyards with pitched roofs. To find the relations, wind tunnel experiments were utilized. Because of the many possible dispersion scenarios existence, the result of our recalculation is not one value for a quantity describing the short-term leakage at the exposed location, but instead, a probability density function of the quantity. The probability density function enables one to count the most probable value as well as the extreme cases which can occur. This distinguishes our model from those usually utilized during accidents in which only the ensemble-averaged puff outline and concentration field can be predicted (Pal Arya, 1999). The main aim of this paper is to present the relations for recalculation of the result from the long-term to the short-term sources for the variables: dosage, maximum concentrations, 99th percentiles of concentrations and 95th percentiles of concentrations. These variables are important for the emergency assessment of how hazardous an incident may be (Chaloupecká et al., 2018).

The rest of the paper is organized as follows. Section 2 explains the methodology. Its subsections describe the wind-tunnel experiments, data processing, utilized puff characteristics, uncertainties, and the special functions utilized. Then, the method of validation is introduced. At the end, the entire approach utilized is summarized in a short paragraph and visualization of the approach is facilitated by the presentation of a scheme. Section 3 summarizes the results that are being discussed in two subsections. The first presents the results for the variable dosage; the second describes the results for maximum and high percentiles of concentrations. The main findings are concluded in Section 4.