Modelling of particles deposition in an environment relevant to solid fuel boilers
Introduction
Deposit formation on heat transfer surfaces is one of the most acute problems encountered in biomass-fired boilers. Depending on operational conditions, fuel characteristics and geometry of the boiler, ash particles entrained by the flue gases can impact and adhere to solid surfaces, aggregate and accumulate in form of a solid deposit that severely affects the boiler operation. Heat transfer is usually strongly impaired, but thick deposits may also reduce the flow passage areas and thus affect and even substantially alter the flow pattern, with grave consequences on the combustion process itself. While the heavy fouling problem is particularly common in equipments exposed to flue gases laden with particles coming from the combustion of biomass, it is also frequent in boilers fired by coal or wastes.
The classical approach to estimate the deposit formation is based on empirical correlations deduced mainly from experiments. A number of indicators were established and used in the past to predict the propensity of a given fuel (especially coal) to form deposit [1], [2], [3], [4]. In recent years the numerical modelling and simulation of particle-laden flows and deposit formation have become the standard tool for design, development and optimisation of the operating conditions of various combustion and heat exchange devices (e.g. [5], [6], [7].), thus replacing, at least in part, the traditional but outdated correlation/indicators approach.
Particle deposition is affected by a number of factors, such as particle size and shape, composition, turbulent dispersion and particle interactions, temperature, mechanics of impact/adhesion, etc. Depending on their size and shape, particles can be influenced by gravity, drag and/or other mass forces and the particles governing equation should account for all of these forces, if relevant, in order to correctly predict their dynamics [8], [9], [10]. On the other hand, particles composition influences strongly their interaction with solid surfaces affecting their propensity to stick or rebound, especially in hot flows [1]. Two-phase flows are usually turbulent, and then identical particles starting from the same position but at different time instants, are spread by turbulence and follow different trajectories. In order to predict particle deposition accounting for this phenomenon, a huge number of particles need to be tracked to obtain statistically independent results. This in turn requires a huge computational time. Different models are available to handle this problem (i.e., Eddy Lifetime model [9], [11], Particle Cloud Tracking model [12], [13], Particle Number Density model [14], etc.). Finally, temperature becomes important in two-phase flows simulations when it affects the flow or particles viscosity. As a matter of fact, particle deposition within a combustion device occurs in zones exposed to both high and relatively low temperatures, thus the impact/adhesion mechanism can be significantly different. For deposition in relatively cold flows, however, it is the impact mechanics and adhesion energy that govern the deposit formation, and these need to be appropriately modelled, [15], [16], [17].
In a recent paper [18], we compared the numerical results obtained with some of these models with very limited experimental data that could be traced in the literature, and identified the models that seem to give the most realistic results. The temperature variation in the flow was accounted for, but considered as not to be excessive and the thermal effects on the deposition thus regarded as marginal. However, when particles are entrained by a hot fluid flow, temperature becomes an important factor, especially for particle adhesion, and different models have to be considered. In another companion publication [19], we applied a model that accounts for the temperature effect in particle deposition to predict the deposit formation within a biomass-fired furnace. In that work the Particle Cloud Tracking (PCT) model [12], [13] was adopted to simulate the turbulent dispersion of particles. The PCT model can represent a useful approach for the solution of real industrial situations, especially when the field can be considered as statistically steady and if only an overall (bulk) description of the deposit layer is required. Otherwise, where a more accurate and more detailed results are needed, all the particles should be individually tracked (Single Particle Tracking - SPT) but this approach usually requires very large computational resources and time.
Some rationing is, however, possible. In the present work we selected carefully the elements in which particles enter the domain and this allowed us to obtain statistically independent results requiring a computational time that is much shorter than in a general SPT approach. Details of this procedure will be discussed below. The impact mechanism was then analysed aimed at understanding the occurrence of deposition and rebound of impacting particles based on the criteria related to the temperature. To this purpose, we considered deposit formation on a long cylinder subjected to a particle-in-gas cross flow for which some experimental (mainly visual) data are available [20].
In the next paragraphs the particle transport and deposit growth modelling as well as the temperature effect on ash sticking are outlined. Then the details of the experimental test case will be described, followed by presentation and discussion of some of the simulation results. The paper is closed by some conclusions.
Section snippets
Particle transport modelling
In particle-laden flows one of the most important parameter to chose the right coupling between the flow and particle motion is the solid volume fraction (VF), that is the volume fraction of solid particles dispersed within a unit volume of fluid. When the volume fraction is very high (VF ≥ 1.0E-3) particle motion affects the flow field, otherwise this effect can be neglected. Besides, particle motion is also affected by interaction with other particles. For smaller value of volume fraction
Deposit growth modelling
In order to evaluate the deposit thickness, particles arrangement in the deposit layers should be analysed and modelled. However, modelling the real arrangement is not trivial because particles of different sizes can deposit simultaneously thus resulting in a very irregular arrangement. Moreover, in hot flows sintering and melting effects could play a role in the deposit growth. Hence, for a real industrial application in complex configuration, it is unavoidable to introduce some modelling
Temperature effect on ash sticking
In most industrial applications involving combusting particles in a gas flow, and especially in biomass-fed boilers, ash composition is a very important parameter in deposit formation. Substances such as potassium, calcium and silicon are prone to form oxides which have softening temperature about 650–700 °C. These oxides remain in the ash making it to become sticky even at relatively low temperature.
This phenomenon can be accounted for by introducing a quantity named sticking probability p(T)
Computational details
The results of Zhou et al. [20] are adopted as a reference for validating the approach here considered. Zhou et al. studied deposit growth on a tube in cross flow within a small laboratory combustor fed with straw. A cylindrical probe in cross flow (Fig. 1) was placed at a certain distance from the flame. Further details on the experimental apparatus can be found [20] and [31].
The flow field used for determining the particles trajectories was calculated by a prior U-RANS computation. A 3D
Conclusions
Computational modelling of the complex phenomenon of particle deposition on solid obstacles was considered aimed at assessing various models and modelling assumptions reported in the literature, as well as at identifying the dominant process elements in the deposition dynamics. The present investigation is confined to only few issues which are believed to constitute the main elements of a comprehensive model that could be used for practical prediction of deposit formation in realistic
Acknowledgements
The work of Prof. K. Hanjalic was supported by EU under the project Marie Curie Chair ‘COMSITA’.
Part of the computations was carried out on Matrix Supercomputing Cluster at CASPUR under the HPC Grant 2009.
Nomenclature
- CD
- drag coefficient
- dp
- particle diameter, m
- gravity acceleration, m/s2
- hdep
- deposit thickness, m
- mp
- particle mass, kg
- np
- number of particles
- p(T)
- sticking probability
- Rep
- particle Reynolds number
- T
- temperature, K
- Tcv
- temperature of critical viscosity, K
- t
- time, s
- fluid velocity, m/s
- particle velocity, m/s
- particle position vector, m
- η
- particle viscosity, Pa s
- ηref
- particle critical viscosity, Pa s
- ρdep
- deposit bulk density, kg/m3
- ρf
- fluid density, kg/m3
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