Comparisons of two numerical approaches to simulate slatted floor of a slurry pit model – Large eddy simulations

Abstract

For dairy cattle buildings with slatted floor systems, about 40% of the ammonia emission originates from the slurry pit. In order to find a solution to abate this part of emission, a better understanding of the ammonia transportation from the pit to the room space is crucial. Large eddy simulation (LES) was adopted to investigate the transportation of airflow and ammonia under slatted floor. To tackle the involvement of the slatted floor, two approaches were proposed: modelling slatted floors directly with geometrical details (LESD) and treating them as porous media (LESP). The main purpose of this work was to study the potential of using porous media to model the slatted floor. The LES results were validated by the air velocities measured using a LDA (Laser Doppler Anemometer) in a 1:8 scale pit model placed in a wind tunnel. The results showed that LESP was able to estimate the mean air velocities and turbulence kinetic energy in the core of the pit headspace; but it cannot well predict the mean air velocities and turbulence kinetic energy in the space next to the upwind wall. Clear vertical air motion in the top surface of the slot was observed for LESD results. There was not such trend found for LESP results. Both the air velocity and NH₃ fraction fluctuated weaker for LESP results. By spectral analysis, LESP was able to capture the entire power spectrum compared with LESD. A dominant Strouhal number 0.23 was found for LESD results but no dominant Strouhal number was found for LESP results. The emission rate and total mass of NH₃ in the pit headspace calculated by LESD was double of those calculated by LESP. Pollutants were confined in the headspace for longer time by means of using LESP than using LESD. For both LESD and LESP, turbulence transportation was the dominant removal mechanism to transport pollutants from the headspace to the free stream.

Introduction

Dairy cow buildings constitute one of the largest sources of ammonia emissions among various animal husbandry operations in Denmark (Pedersen, 2006). Solutions to curtail the dairy cow emissions include changes in housing and floor design. Slatted floor with scrapers on the floor surface as well as channel scraper show the potential to keep ammonia emissions at a low level (Zhang et al., 2005, Wu et al., 2012a). For a cattle building with slatted floors, about 60% of the total ammonia emission originates from floor surface, whereas 40% is released from the slurry pit (Braam et al., 1997). In order to find a solution to abate the portion of emission coming from the slurry pit and improve the design of the floor system, a better understanding of the ammonia transportation mechanism from the pit to the room space is necessary. So far, some studies regarding airflow patterns and pollutant dispersion in dairy cow buildings have been limited to the space above the slatted floor (Norton et al., 2010a, Norton et al., 2010b, Wu et al., 2012b). However, the knowledge of the characteristics of the airflow and mass transport under the slatted floor is still missing, although it is crucial to estimate the ammonia emission from the slurry pit correctly (Morsing et al., 2008). Wu et al. (2012c) applied CFD to study the airflow characteristics under slatted floor in a 1:2 pit model of a cattle building, in which the slatted floor was simulated in geometrical detail. However, the measured air velocities were limited due to the spatial resolution of the sensors and the experimental facilities (Wu et al., 2012d). Considering that obtaining the characteristics of the air motion under slatted floor in a full scale livestock building is the final research goal, modelling of slatted floor in reality becomes the main concern. The slot width in a real cattle building is about 0.02 m, while the shortest building dimension is generally longer than several metres. The small ratio of slot width and building dimension prevents a direct modelling of the geometrical details. Therefore, slatted floor is usually handled as porous media (Sun et al., 2004, Bjerg et al., 2008a, Bjerg et al., 2008b). However, up to date, the information on the difference that might exist between simulations using geometrical details and porous media cannot be found in the literature. The uncertainty of using porous media to replace the slatted floor above the slurry pit in simulations should be investigated.

The crucial prerequisite of an investigation on the difference between modelling slatted floors with geometrical details and treating them as porous media is to accurately simulate the flow passing by the pit headspace – a cubic cavity. The flow in such a cavity is featured with separation. The phenomenon is known to be difficult to model. The research of similar cavity flow can be found in the area of modelling airflow in street canyons (Vardoulakis et al., 2003). Reynolds-averaged Navier–Stokes (RANS) models are the most commonly adopted turbulence models in calculating street canyon wind flow. The RANS models ever employed in street canyon field are the standard k–ε model (Johnson and Hunter, 1998, Baik and Kim, 2002, Kim and Baik, 2003, Neofytou et al., 2006) and its variants, RNG k–ε model (Tsai and Chen, 2004) as well as realisable k–ε model (Sagrado et al., 2002). Despite of the widely utilisation of k–ε models, the main deficiency pointed out by Solazzo et al. (2009) is the underestimation of the turbulence kinetic energy and air velocities within some parts of the cavity. The experimental and computational studies of Chang and Meroney (2003) revealed that the dispersion of gaseous pollutants within the street cavity was essentially unsteady. Johnson and Hunter (1998) also reported that the transient flow was a very important factor in quantifying the gas dispersion from street canyon. Hence, the precise prediction of gas dispersion from a cavity may not be reached by assuming a steady state process. A pilot CFD simulation using a k–ε model (Zong, 2012) on air motion in pit airspace showed a large discrepancy comparing with the measurement results. Because there is no vertical mean flow at the floor level and the conventional k–ε turbulence model does not account for the detailed turbulent transport in a transient manner, it is unable to calculate the air ventilation and pollutant dilution rates. Due to the weakness of RANS models, large eddy simulation (LES) was used to examine the flow features in street canyons by Liu et al. (2005) and the LES results agreed reasonably well with wind tunnel measurements. Walton et al. (2002) compared the accuracy of k–ε and LES turbulence closure schemes against experimental results and found that the LES results exhibited the best agreement with measured results.

The cavity flow in this study is much more complicated than the above mentioned studies on street canyon due to the involvement of a porous layer (the slatted floor). The main purpose of this work is to use LES to compare the difference of modelling slatted floor directly and modelling slatted floor as porous media.