DOI: 10.3303/CET2188104 Paper Received: 24 June 2021; Revised: 19 September 2021; Accepted: 7 October 2021 Please cite this article as: Strouhal J., Juřena T., Jegla Z., 2021, Fouling Simulations of a Passive Part of the Testing Combustion Facility, Chemical Engineering Transactions, 88, 625-630 DOI:10.3303/CET2188104 CHEMICAL ENGINEERING TRANSACTIONS VOL. 88, 2021 A publication of The Italian Association of Chemical Engineering Online at www.cetjournal.it Guest Editors: Petar S. Varbanov, Yee Van Fan, Jiří J. Klemeš Copyright © 2021, AIDIC Servizi S.r.l. ISBN 978-88-95608-86-0; ISSN 2283-9216 Fouling Simulations of a Passive Part of the Testing Combustion Facility Jiří Strouhal*, Tomáš Juřena, Zdeněk Jegla Brno University of Technology, Institute of Process Engineering, Technická 2, 61669 Brno, Czech Republic * strouhal@fme.vutbr.cz Results from the previous work of Strouhal et al. (2020) suggest that the used CFD fouling model together with user-implemented subroutines is not sufficient for obtaining satisfactory agreement with deposits observed in a described experimental device. The objective of this work is to create a basis for qualitative improvements of the simulation results. This includes using more detailed geometry and testing an influence of variation of parameters of two implemented fouling models. An accurate estimation of these parameters requires either empirical evidence from device operation or detailed information about fly ash composition and properties, which is usually accessible only for individual fly ash constituents. The goal of the sensitivity analysis was to show influence of these parameters on deposition rates, identify insignificant parameters for the tested range of particle properties and diameters and the most significant parameters for each of the six tested fly ash size fractions. To the authors’ knowledge, such an analysis is not present in available literature. The first tested model shown that one parameter to be significantly higher compared to other, except for the smallest particles. For the second model, all parameters were found to be significant at least for one examined particle diameter. Elastic deformation, plastic deformation and adhesion are thus considered important across the tested range of particle properties and sizes, at least for the fouling model used. 1. Introduction Usage of alternative solid fuels provides savings in primary fuels due to using renewable sources. Variability in composition and amounts of waste combustion products causes difficult predictability of instant release of these products, which causes difficulties in usage of these fuels (Stančin et al., 2020). Fouling has to be considered when designing devices such as heat exchangers used in industrial boilers. It influences size and total cost of the facility (Stehlík, 2011). CFD in fouling prediction was used by many authors. A list of various examples of fouling models based on CFD can be found in an extensive review done by Cai et al. (2018). Models of particulate matter fouling can differ among other by purpose of their usage. The most advanced models are useful for (possibly dynamic) simulation of deposit growth and its influence on the flow field, heat transfer and pressure loss. Often it is desirable to determine conditions, for which particle deposition can be significantly reduced by adjusting the heat transfer surface design or operating conditions (Jegla et al., 2010). Fouling in an experimental device installed on the Institute of Process Engineering is modelled. This device consists of three main parts: a rotary kiln, deposition chamber and a heat exchanger. The chamber represents a passive mechanical part for retaining of the PM. Modelling focused on the chamber and rear part of the kiln. The present study extends the authors’ previous work on development of a CFD model for the prediction of fouling in heat exchangers by particulate matter (PM). This model should be applicable to typical fouling problems on the flue gas side on industrial scale. Hence, cost-effective models were adopted from literature. Preliminary simulation results were not satisfactory compared to experimental findings, which was most obvious for the bottom of a part of an experimental device. The predicted deposition flow rate was very low compared to other surfaces, while experiment has shown this surface to be the most fouled part of the chamber. The objective of this work is to investigate sensitivity of the predicted deposition mass flow rate on variation of parameters of two fouling models. To best authors’ knowledge, such an analysis is not present in available literature. Reference values were chosen with respect to typical fly ash components and conditions inside convective sections of industrial boilers. 625 2. Model All simulations were conducted on a single model of the kiln and chamber assembly. The initial stage of fouling was considered, for which the internal geometry is not affected by accumulated matter. Two models are described, each using small number of parameters describing properties of particles and wall surface. Figure 1: Geometry of the kiln outlet and deposition chamber with illustrative particle trajectories and location of particle injection plane, used in CFD simulations (left); observed deposit after combustion tests in 2020, showing approximately symmetric pattern (right). In order to reduce the time required for simulations, only half of the geometry was modelled, assuming planar symmetry of the investigated flow and particle trajectory patterns. This assumption is partially supported by the symmetry of deposits formed in the chamber during the combustion tests. The generated mesh consisted of 2⋅106 cells. For near wall regions, 6 to 12 prismatic layers were used, with uniform height of boundary cells’ layer. Polyhedral cells were used for the rest of the domain. The smallest boundary cell height was set to 0.15 mm, which presents a value larger than the radius of the largest injected particle, preventing an unrealistic “submersion” of the particle under the wall surface. The average value of y+ at boundary cell centroids was 0.59 for the whole domain and 0.56 for the chamber, with 0.05 % of cells with y+ ≥ 4 in the whole domain and zero in the chamber. The whole fouling model was implemented in Ansys® Fluent 2020 R2 (Ansys, 2020), combined with User Defined Functions, including C routines for modelling of the particle deposition. 2.1 Flow model and DPM For modelling of the turbulence, the Realizable k-ε model combined with an Enhanced Wall Treatment was used. Note, that although the use of the RANS models in general leads to shorter computational time, it often overpredicts the deposition flow rates (Weber et al., 2013). For simulations of PM transport, the steady Discrete Phase Model (DPM) was used. Influence of the turbulence on the particle motion was simulated by using Discrete Random Walk Model (DRWM) combined with Random Eddy Lifetime model using Time Scale Constant 0.15. The number of tries was set to 25, providing a compromise between detailed picture of deposition mass flux and the required computational time. The total number of injected particles. Investigation of the exact location of PM source was not among objectives of this work. Particles were injected from a plane located 0.4 m from the kiln hopper, as shown on Figure 1. 2.2 Model WK12 This fouling model can be found in the work of Wacławiak and Kalisz (2012). It was originally designed for simulations of fouling of superheater tubes in a convective part of industrial boiler. The criterion for particle deposition is based on a force balance, derived from energy balance. Particle sticks if a sum of normal components (relative to the wall or deposit surface) of a gravitational force 𝐹𝑔,𝑛 = 𝑚𝑝 𝑔 𝑐𝑜𝑠 𝛼 and Van der Waals force 𝐹𝑉𝑊 = 2 𝐵/(3 𝑑𝑝) acting on a particle exceeds so-called elastic rebound force, expressed by Eq(1). The g is gravitational acceleration, θ is the impact angle, dp is the particle diameter and B is an empirical constant. Particle sticking probability is expressed by Eq(2). Only B, n and dref were selected for factorial analysis. heat exchanger deposition chamber injection plane rotary kiln 626 The effect of change of a constant G can be substituted by variation of dref, requiring eight instead of 16 simulations. 𝐹𝑒𝑙 = 𝐺 (𝑑𝑝/𝑑ref) 𝑛 𝑑𝑝 2 |𝑣𝑖,𝑛 | 1.2 (1) 𝑃 = { 1, 0, 𝐹𝑉𝑊 + 𝐹𝑔,𝑛 ≥ 𝐹𝑒𝑙 (2) Figure 2: Forces considered in the WK12 model (left) and kinematics in the TN98X18 model (right). 2.3 Model TN98X18 The model described by authors Thornton and Ning (1998) was derived for normal impacts of adhesive particles on a smooth surface, assuming elastic deformations of the impacted surface and elastic or perfectly plastic deformation of the particle. In this work, their model was used for calculation of the rebound velocity normal component. Adhesion occurs during the contact, causing energy losses, further increased if the plastic deformation occurs. Model further assumes the particle geometry changes only negligibly. The expression for the normal restitution coefficient differs between three impaction regimes, determined by velocity values. The first is the sticking velocity vs, which is the minimum velocity, for which the particle rebounds. The second is the yield velocity vy, over which a plastic deformation occurs. These velocities can be obtained from particle and surface properties (Eq(3) and Eq(4)). 𝑣𝑠 = 1.84 ((Γ 𝑟𝑝⁄ ) 5 (𝜌𝑝 3 𝐸∗ 2 )⁄ ) 1 6⁄ (3) 𝑣𝑦 = 1.56 (𝑝𝑦 5 (𝜌𝑝 𝐸 ∗4)⁄ ) 0.5 (4) Unlike the WK12 model, which was designed and tested even for oblique impacts by Wacławiak and Kalisz (2012), the original model of Thornton and Ning (1998) was originally proposed and tested for normal impacts and so, it was adjusted by adding sub-model for calculation of a tangential component of the rebound velocity, described by Xie et al. (2018), also accounting for the particle rotation. Assumptions of the sub-model include spherical shape of particles, particle rotation axis normal to impact and rebound velocity vectors, Coulombic friction during the impact and the independency of the normal restitution coefficient on the impact angle. Expressions for the ratio of the dynamic friction coefficient and impulse ratio required for the momentum balance of the particle during impact were determined for ash particles and smooth steel surface. Experiments were conducted for fly-ash diameters in range (47 to 53) μm, impact velocities (2.2, 3.4 and 4.22) m/s and impact angles in range (15 to 75) °. 3. Model setup and results The average value of the measured flue gas mass flow rate was 0.120 kg s-1. The gas density and temperature were 0.343 kg m-3 and 752 °C, estimated from the average of series of measurements at the kiln outlet. The gas dynamic viscosity 4.227 10-5 Pa s was estimated from the temperature assuming similar temperature dependency as air. A uniform mass flux was defined at the kiln inlet, with turbulence intensity and hydraulic diameter set to 5 % and 0.4 m, respectively. With respect to absence of heat transfer surfaces in investigated parts of the experimental device and neglecting the combustion process in the kiln, the flow was modelled as isothermal. As in the previous work of Strouhal et al. (2020), the ash properties were taken from work of Raclavská et al. (2017), describing fly ash from the municipal solid waste combustion, providing a particle size distribution, composition and density. Six size fractions were assumed, each with uniform size distribution, with diameter 627 equal to arithmetic mean of every interval reported by Raclavská et al. (2017), yielding six particle diameters: 6, 14, 19.5, 28.5, 41.5 and 74.5 μm. For each fouling model, nine simulations were conducted. The observed quantity was the total deposition mass flow rate in the rear part of kiln and the deposition chamber. Both series of simulations present sensitivity analysis of the model with respect to variation of selected model parameters. The analysis required one simulation with parameters set to reference values, followed by eight simulations for all combinations of maxima and minima of these parameters, representing their variation of 50 % of reference values. Table 1: Mean values of model parameters with references to literature Model Parameter Value Reference Note WK12 B 10-17 (Wacławiak and Kalisz 2012) - n 2 (Wacławiak and Kalisz 2012) - dref 17.53⋅10-6 (Raclavská et al. 2017) Average diameter of six smallest diameters from samples FA1 – FA3 TN98X18 E* 5⋅1010 (Kleinhans et al. 2018) Chosen from range of values in Table 29 (page 161) Γ 0.2 (Thornton and Ning 1998) - py 5⋅108 (Kleinhans et al. 2018) Chosen from range of values in Table 20 (page 130) Both models are reported separately as both groups of parameters do not necessarily describe identical properties of fly ash. For each set of nine simulations investigating the influence of parameter variation, factorial analysis was done for all individual size fractions using the Minitab 19 (Minitab, 2019). 3.1 WK12 The results of the factorial analysis show, that the dref (C) is significant for all six fractions. Constant in the Van der Walls force has significant effect only on smaller particles (6 μm and 19.5 μm), possibly showing low significance of the Van der Waals force on particle deposition. Figure 3: WK12 model. Standardized effects of significant terms of the model obtained by factorial analysis of data from simulations. Term (A) represents constant B, (B) exponent n and (C) reference diameter dref. (BC) represents interaction of factors (B) and (C). Figure 4: WK12 using reference values of parameters. Contours of deposition mass flux divided by the maximum flux value. Fluxes are reported separately for three size fractions. 19.5 μm 6.0 μm 14.0 μm 28.5 μm 41.5 μm 74.5 μm Relative deposition mass flux [-] dp = 6.0 μm dp = 28.5 μm dp = 74.5 μm 628 3.2 TN98X18 The effect of the yield limit can be considered as the smallest for middle size fractions, while E* and γ are significant for all investigated particle sizes. The only exception is the diameter 41.5 μm, for which no parameter was identified as statistically significant. In contrast to WK12 model, only a modest deposition flux was observed on the chamber bottom and the baffle for the coarse fractions, at all tested combinations of parameters. Figure 5: Standardized effects of significant terms of the model obtained by factorial analysis of data from simulations using TN98X18 model. (A) represents effective Young modulus E*, (B) yield limit py and (C) interface energy γ. Figure 6: Model TN98X18 using reference values of parameters. Contours show deposition mass flux divided by the maximum flux value. Fluxes are reported separately for three size fractions. 4. Conclusions WK12 – The results showed low sensitivity to value of the parameter B for larger particle diameters. Parameters n and dref express the elasticity of both the particle and surface and influence the particle regardless of its diameter. For the larger particles, the gravitational force is more prominent, which can be seen on the simulated deposition fluxes on the chamber bottom and upper side of the baffle. The dref was identified as the most significant parameter for middle values of particle diameters. Maximum variation of the predicted deposition mass flow rate was 38.8 % for the particle with diameter 14 μm. Least affected were particles with diameter 28.5 μm and 41.5 μm, where the difference between maximum and minimum deposition flow rate was 10.5 % and 11 %. TN98X18 – Compared to the previous model, none of the parameters shown higher significance for any of particle fractions. For the diameters between 19.5 μm and 41.5 μm, the interface energy was shown to be insignificant. Total deposition rate of particles with diameter 41.5 μm was reported to be insensitive to all three parameters. From the obtained results it can be seen, that only for the first model, a general recommendation can be made. The reference diameter has the strongest influence for all tested particle diameters except for the largest diameter. When using the second model, the most important parameter depends on the particle diameter, implying the necessity of information about the size distribution. 19.5 μm 6.0 μm 14.0 μm 28.5 μm 74.5 μm Relative deposition mass flux [-] dp = 6.0 μm dp = 28.5 μm dp = 74.5 μm 629 Nomenclature B – constant in WK12 model, kg·m2/s2 dp – particle diameter, m dref – reference diameter WK12 model, m E* – effective Young modulus, Pa Fel – elastic rebound force, N Fg – gravitational force, N FVW – Van der Waals force, N g – gravity acceleration, m/s2 G – constant in WK12 model, kg/(m2.2·s0.8) mp – particle mass, kg n – exponent in WK12 model, - v – velocity, m/s vs – sticking velocity, m/s vy – yield velocity, m/s py –yield limit, Pa α – angle, rad γ – interface energy, J/m2 ρ – density, kg/m3 θ – angle, rad ω – angular velocity, rad/s Subscripts i – impact n – normal component r – rebound t – tangential component Acknowledgements The authors gratefully acknowledge the financial support provided by the Technology Agency of the Czech Republic (TACR) within the research project National centers of competence, specifically through the project National Centre for Energy (TN1000007). 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