Minimum gas speed in heat exchangers to avoid particulate fouling

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3952 M.S. Abd-Elhady et al. / International Journal of Heat and Mass Transfer 47 (2004) 3943–3955Fig. 10. Scanning electron microscope photos for the particles at the bottom (left) and top (right) of the fouling layer. The fouling layeris composed of a mixture of copper and bronze particles.Fig. 11. Scanning electron microscope photos for the particles at the bottom (left) and top (right) of the fouling layer. The particles aremade of glass.bronze and copper particles. Fig. 11 shows SEM photosfor the particles at the bottom (near the heat exchangertube) and top of the fouling layer. At the top of thefouling layer large particles have accumulated with smallparticles in between. In the fouling layer near the tube ofthe heat exchanger, the finest particles in the flow haveagglomerated together to form islands of fine particlesconnected to bigger particles. Fig. 12 and Table 2 show acomparison between the particles size distribution of theinjected glass particles in the airflow and the glass particlesin the fouling layer near the HE tube. It is shownthat the average diameter of the glass particles has reducedfrom 20.4 lm in the airflow to 14.7 lm inthefouling layer near the HE tube. 90% of the injected glassparticles in the airflow have a diameter less than 43.1 lmwhile 90% of the glass particles in the fouling layer nearthe HE tube have a diameter less than 25.2 lm. Thereduction in particle size in the fouling layer near the HEtube from the particle size in the airflow is due to thehigher sticking velocity of small particles compared tolarge particles as defined by Rogers and Reed [7].Rogers and Reed [7] developed a model that describesthe adhesion of a particle to a surface following anelastic–plastic impact. The model is based upon considerationof the energy balance during a normal impactbetween a sphere and a massive plane. The model describesthe adhesion of a particle arising from only elasticdeformations occurring during the approach of the particleto the surface. When the particle velocity is reducedto zero during the approach phase, part of the particleinitial kinetic energy, Q k , is converted into stored elasticenergy, Q E , while the remainder, Q L , is dissipated. This isthen followed by the recovery of the stored elastic energy,which is converted into kinetic energy of the reboundingparticle. For a particle of mass m impacting a surfacenormally with a velocity V im we have1mV 22 im þ Q A ¼ Q E þ Q L ;ð2Þwhere Q A is the energy due to the attractive forces betweenthe incoming particle and the surface. If the storedelastic energy, Q E , is greater than the adhesive energyrequired to separate the particle from the surface, Q 0 A ,then the particle will rebound otherwise it sticks to thesurface. The rebound speed, V r , is calculated from1mV 22 r¼ Q E Q 0 A : ð3ÞThe mentioned energy terms are described in detail byRogers and Reed and in van Beek [11]. The maximum
M.S. Abd-Elhady et al. / International Journal of Heat and Mass Transfer 47 (2004) 3943–3955 3953Fig. 12. A comparison between the particle size distribution of the injected glass particles in the airflow and the glass particles in thefirst fouling layers deposited on the HE tube.Table 2A comparison between the particle size distribution of the injected glass particles in the airflow and the glass particles in the first foulinglayers deposited on the HE tubea b cMean diameter (d M ) Standard deviation (SD) D 10 D 50 D 90Injected glass particlesin airflowGlass particle in thefouling layer nearthe HE tube20.4 16.2 3.6 16.2 43.114.7 8.4 5.9 13.3 25.2All dimensions are in micrometers.a The particle diameter at which 10% of the particles are smaller than it.b The particle diameter at which 50% of the particles are smaller than it.c The particle diameter at which 90% of the particles are smaller than it.impact speed at which an incident particle will stick tothe impacted surface, i.e. V r ¼ 0, is defined as the criticalsticking velocity. To show the variation of the stickingvelocity with the incident particle diameter the Rogersand Reed model is solved to calculate the stickingvelocity for copper particles of diameters 10 and 4 lmhitting a solid steel surface. Fig. 13 shows the variationof the coefficient of restitution, e, with the impact speed,V im , for copper particles of diameters 10 and 4 lm. Thecoefficient of restitution is defined as the ratio betweenthe normal rebound speed, V r , and the normal impactspeed, V im , for a particle hitting a solid surface. Fig. 13shows that if a copper particle of diameter 10 lm hits asteel surface at a speed lower than 0.025 m/s it will stick,while a copper particle of diameter 4 lm sticks if it hitsat a velocity lower than 0.12 m/s. Therefore, if we have amixture of particles of diameters 10 and 4 lm in air,which is flowing with an average speed of 1 m/s over aHE tube, there will be a larger number of particles thathit the HE tube with a speed lower than 0.12 m/s thanthe number of particles that hits with a speed lower than0.025 m/s. This can explain why small particles are likelyto dominate at the beginning of the fouling process.3.4. Sintering of fouling layersOnce fouling has started and particles accumulate tobuild up the fouling layer, sintering takes place. Sinteringchanges the fouling layer structure from a weakpowdery layer to a solid stable structure strongly attachedto the heat exchanger tubes [12]. Sintering is afunction of time and of the hot gas temperature flowingover the fouling layer [13]. Fig. 14 shows a cross sectionalview for a fouling layer taken from the previousexperiments mentioned above. The particles in the layerare bronze and were subjected to hot air at 200 °C for
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Minimum gas speed in heat exchangers to avoid particulate fouling

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