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  1. 1. This article was downloaded by: [Indest open Consortium] On: 14 May 2009 Access details: Access Details: [subscription number 907749878] Publisher Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK Aerosol Science and Technology Publication details, including instructions for authors and subscription information: Miniature Pipe Bundle Heat Exchanger for Thermophoretic Deposition of Ultrafine Soot Aerosol Particles at High Flow Velocities A. Messerer a; R. Niessner a; U. Pöschl a a Technical University of Munich, Institute of Hydrochemistry, Munich, Germany First Published on: 01 May 2004 To cite this Article Messerer, A., Niessner, R. and Pöschl, U.(2004)'Miniature Pipe Bundle Heat Exchanger for Thermophoretic Deposition of Ultrafine Soot Aerosol Particles at High Flow Velocities',Aerosol Science and Technology,38:5,456 — 466 To link to this Article: DOI: 10.1080/02786820490449449 URL: PLEASE SCROLL DOWN FOR ARTICLE Full terms and conditions of use: This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, re-distribution, re-selling, loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.
  2. 2. Aerosol Science and Technology, 38:456–466, 2004 Copyright c American Association for Aerosol Research ISSN: 0278-6826 print / 1521-7388 online DOI: 10.1080/02786820490449449 Miniature Pipe Bundle Heat Exchanger for Thermophoretic Deposition of Ultrafine Soot Aerosol Particles at High Flow Velocities A. Messerer, R. Niessner, and U. P¨ schl o Technical University of Munich, Institute of Hydrochemistry, Munich, Germany high investment and running costs. Due to the limitations of par- ticle loading by their size, small particles between 10 and 30 nm The deposition of submicrometer soot aerosol particles in a Downloaded By: [Indest open Consortium] At: 10:37 14 May 2009 miniature pipe bundle heat exchanger system has been investi- cannot be removed reliably. Furthermore, electrostatic precip- gated under conditions characteristic for combustion exhaust from itators can generate undesired gaseous components, especially diesel engines and oil or biomass burning processes. The system has when operated with negative voltage (Yehia et al. 2000). Turbu- been characterized for a wide range of aerosol inlet temperatures lent precipitators showed particle deposition efficiencies of up (390–510 K) and flow velocities (1–4 m s−1 ), and particle deposition to 35% with significantly reduced removal of particles in the efficiencies up to 45% have been achieved over an effective deposi- tion length of 27 cm. Thermophoresis was the dominant deposition range between 80 and 300 nm (van Gulijk et al. 2001). Shi and mechanism, and its decoupling from isothermal deposition was con- Harrison (2001) report on thermophoretic deposition of diesel sistent with the assumption of independently acting processes. The soot in a water-cooled fluidized bed. In diesel processes (Shi measured deposition efficiencies can be described by simple linear et al. 1999) nearly all particles are in the submicrometer size parameterizations based on an approximation formula for ther- range based on particle mass; in the case of biomass burning mophoretic plate precipitators. The results of this study support the development of modified heat exchanger systems with enhanced (Baumbach 1993) it is more than 80%. Messerer et al. (2003) capability for filterless removal of combustion aerosol particles. could show that the thermophoretic coefficient of ultrafine soot agglomerate particles exhibits no significant dependency on ag- glomerate size. Therefore, thermophoretic soot particle removal can provide a reliable solution for filterless combustion aerosol INTRODUCTION deposition in the submicrometer size range. Sufficient tempera- Ultrafine combustion aerosol particles pose a potential threat ture gradients for particulate removal can be established in heat to human health since they can enter the alveolar system of exchangers, so that future engineering could focus on the paral- human lungs. Therefore, public authorities and industry aim lel optimization of heat transfer and submicrometer particulate to reduce particle emissions by means of combustion process removal in one device. development and exhaust gas treatment. In many applications, Byers and Calvert (1969) were the first to perform exper- conventional filter systems lead to an undesired increase of pres- iments and analyses of thermophoretic deposition of particles sure drop and are prone to clogging by soot and oil ashes (Neeft in a hot turbulent gas stream from the aspect of air cleaning. et al. 1996). Electrostatic filtration has found wide application Nishio et al. (1974) investigated the thermophoretic deposition to remove combustion particles; however, this method imposes of aerosol particles in a heat exchanger pipe, in particular the influence of fouling on the long-term heat exchange behavior of the tube. Further studies of thermophoretic particle deposi- Received 17 September 2003; accepted 19 February 2004. tion in externally cooled tubes include Stratmann and Fissan This work is part of the project “Katalytisches System zur filter- (1989), Chang et al. (1990), Montassier et al. (1991), Sasse and losen kontinuierlichen Rußpartikelverminderung f¨ r Fahrzeugdiesel- u Nazaroff (1994), Chang et al. (1995), and Lin and Tsai (2003). motoren,” supported by the Bavarian Research Foundation, Mu- nich. Additional funding from the Max-Buchner-Forschungsstiftung Sasse and Nazaroff (1994) performed a numerical simulation and technical support by Sebastian Wiesemann are gratefully of a tobacco smoke particle filter based on thermophoretic de- acknowledged. position from natural convection flow. They emphasize the ne- Address correspondence to Reinhard Niessner, Technical Univer- cessity for a proof-of-principle experiment for the validation of sity of Munich, Institute of Hydrochemistry, Marchioninistrasse, 17, their simulation results. Up to now little information about the Munich D-81377, Germany. E-mail: 456
  3. 3. 457 THERMOPHORETIC DEPOSITION IN A HEAT EXCHANGER thermophoretic deposition of submicrometer aerosol particles tigate particle deposition at high gas flow rates and temperature at high flow velocities in the temperature gradient field around gradients. Twenty seven stainless steel tubes with an inner diam- internally cooled tubes is available. eter of 0.99 mm and an outer diameter of 1.59 mm are arranged in a near-quadratic area of 10.4 · 10.5 mm such that the axes of Thermophoretic particle motion can be described by (Talbot et al. 1980) all tubes are near-equidistant. At their ends 5 mm of each tube are fitted into 10 mm stainless steel blocks, which are inserted µg ∇T into a stainless steel channel. The top of the channel can be re- vth = −K th , [1] ρg T p moved to control the alignment of the tubes as well as the soot deposition (Figure 2). The 2 mm viton sealing in the top was where K th is the thermophoretic coefficient, vth is the ther- found to be leak proof for the experimental conditions of this mophoretic particle velocity, and ∇T represents the temperature study. Along the 300 mm effective length of the tubes between gradient in the vicinity of the particle. µg is the gas dynamic vis- the two blocks the bottom area of the channel as well as the top cosity, T p is the particle temperature, and ρ g is the gas density. were formed in a way that reduces the free space towards the For the free molecular regime (Kn 1), Waldmann and Schmitt tubes, simulating half-perimeter tubes directly mounted at the (1966) derived a thermophoretic coefficient that is independent bottom and top plate. of particle size: K th = 0.55. For the transition (Kn ≈ 1) and con- The hot aerosol was led into the channel by a 8 mm di tube at tinuum (Kn 1) regimes, however, the thermophoretic coeffi- an angle of 35◦ as a compromise between engineering require- cient generally depends on particle size, and different formulae ments and a high fluid impulse in axial direction to minimize for the calculation of K th as a function of the Knudsen num- Downloaded By: [Indest open Consortium] At: 10:37 14 May 2009 turbulences in the entry region of the tube channel (Figure 3). The ber have been derived (e.g., Brock 1962; Derjaguin et al. 1976; aerosol outlet was designed symmetrically. The cooling fluid— Kousaka et al. 1976; Talbot et al. 1980). In accordance with a in the study presented here pressurized air—was added by 8 mm theoretical study by Rosner and Khalil (2000), we demonstrated di tubes through the top plate and by a smooth 90◦ curvature that the thermophoretic coefficient of agglomerate soot parti- directed into the steel blocks supporting the 27 heat exchanger cles in the transition regime can be approximated by K th ≈ 0.55 tubes. The pipe inlets were conical to minimize pressure build up (Messerer et al. 2003). For the simple case of a constant tem- by the inflowing cooling gas. The outlet was symmetrical. The perature gradient along a flown-through rectangular channel in whole heat exchanger was thermally insulated to reduce heat thermophoretic plate precipitators, the thermophoretic deposi- transfer to and from the channel. Therefore the aerosol flow- tion efficiency εth can be efficiently approximated by (Tsai and ing between the outer tubes and the walls of the heat exchanger Lu 1995; Messerer et al. 2003) heated up the channel walls, and so no significant undesired thermal gradients that would increase thermophoretic deposi- L µg,0 T vth L εth = = K th , [2] tion towards a cooler channel wall were established. The walls vx,0 H ρg,0 vx,0 H 2 T of the upper and lower plate were adopted to the void space to reduce the aerosol flow between the channel walls and the where H and T are the distance and temperature difference between the plates, respectively; and µg,0 , ρg,0 , and vx,0 are the outer tubes. At the same time there was still space between the outer tubes and the channel walls to avoid direct thermal con- gas properties (dynamic viscosity, density, and axial velocity) at tact and conductive heat transfer between the wall and tubes. the average temperature in the precipitator. According to the cross-sectional areas (Figure 1) only about Miniaturized heat exchanger systems provide a high surface- 10% of the aerosol flow passed between the outer tubes and the to-volume ratio and therefore lead to high heat transfer rates wall. Therefore, the particle deposition effects observed in this even under laminar flow conditions. The heat transfer behavior study were not significantly influenced by these boundary phe- in these devices has been investigated by a number of researchers nomena. The internal cooling of the 27 tubes lead to a smaller over the last decade, e.g., Peng et al. (1995). Due to high tem- thermal axial expansion of the tubes in comparison to the channel perature gradients thermophoresis is expected to be significantly housing the steel blocks. Therefore the tubes were equidistantly higher than in conventional heat exchangers for particle-loaded distributed over the whole heat exchanger length. The effective flows. To our knowledge this is the first study on the removal deposition length can be calculated from the tube length between of aerosol particles in the external flow around cooling tubes in the stainless steel blocks, the distance between the blocks, and a miniature heat exchanger under experimental conditions rele- the axial position where the inflowing aerosol comes in contact vant for modern combustion exhaust systems with aerosol flow with the cooling tubes: L = 300 − 2 · (15) = 270 mm. The velocities between 1 and 4 m s−1 . relative error in the determination of the deposition length re- sulting from the diameter of the inflowing aerosol tube (8 mm) is METHODS ±3%. High Temperature Gradient Pipe Bundle Heat Exchanger Temperatures of the system were measured with four K- type thermocouples (accuracy ±0.1 K). The thermocouples for Figure 1 shows the cross-sectional area of the miniature pipe bundle heat exchanger that has been designed and used to inves- the aerosol inlet and outlet were placed in the center of the
  4. 4. 458 A. MESSERER ET AL. Downloaded By: [Indest open Consortium] At: 10:37 14 May 2009 Figure 1. Cross-sectional area of the miniature pipe bundle heat exchanger. Pipe inner diameter di = 0.99 mm, outer diameter do = 1.59 mm. Aerosol flow around the cooling tubes flown through by cooling air. Experimental Setup and Measurement Procedure 8 mm tubes about 2 mm before the tube bundle. The ther- mocouples for the cooling gas inlet and outlet were mounted The complete experimental setup applied in this study is in the center of the tube blocks at a distance of about outlined in Figure 4. The test aerosol particles were produced 3 mm. by a spark discharge between graphite electrodes (Alfa Aesar, Karlsruhe, Germany, purity 99.9995%) in a 3.7 l min−1 argon flow (Messer Griesheim, Krefeld, Germany, purity 4.6). The primary carbon particles produced with the applied spark dis- charge aerosol generator are known to have a diameter of ∼5 nm (PALAS GfG 1000, Karlsruhe, Germany; Evans et al. 2003). Af- ter passing through an agglomeration reservoir (2 l glass flask), the aerosol flow was diluted with 4.4 l min−1 of filtered nitro- gen and led through a Kr 85 aerosol neutralizer (10 mCi). The aerosol flow through the pipe bundle heat exchanger was con- trolled by venting the excess through an outlet valve into the ex- haust line. Before entering the heat exchanger system the aerosol was heated to the desired inlet temperature. The symmetric sampling setup at ambient temperature and equal flow conditions enabled near-identical aerosol sampling conditions before and after the heat exchanger. Thus the signifi- Figure 2. Photograph of the pipe bundle heat exchanger inlet cant thermophoretic losses which are known to occur upon cool- section. ing of a hot aerosol flow to ambient temperature in a sampling
  5. 5. 459 THERMOPHORETIC DEPOSITION IN A HEAT EXCHANGER Downloaded By: [Indest open Consortium] At: 10:37 14 May 2009 Figure 3. Longitudinal section of the pipe bundle heat exchanger. Note the symmetrical design of the deposition device. line (Berger et al. 1995) could be avoided. Other potential ef- ment range 20–300 nm). Before the SMPS, the particle con- fects of the sampling process on the aerosol properties can be centration in the sample flow was reduced by a ratio of 1:20 assumed to cancel out and were neglected in the measurement in a dynamic dilution system (TOPAS DDS 560) to minimize data analysis. soiling and transient particle deposition in the measurement de- Particle number size distributions were measured with a scan- vice. The particle size spectra were analyzed with a resolution ning mobility particle sizer (SMPS) system consisting of an of 16 particle size classes i per decade, providing sufficient in- electrostatic classifier (TSI 3071) and a condensation particle formation on the size distribution of the sparkdischarge soot counter (TSI 3025) operated with a sample flow of 1 l min−1 , a aerosol and maintaining a high signal-to-noise level at the same sheath air flow of 10 l min−1 , and a scan time of 120 s (measure- time. Figure 4. Schematic flow diagram of the experimental setup for counterflow heat exchanger particle deposition measurements.
  6. 6. 460 A. MESSERER ET AL. Table 1 Experimental parameters for the investigation of the particle deposition mechanisms in the miniature pipe bundle heat exchanger vx,hot,in Vh,out Th,in Th,out Tc,in Tc,out T log,mean Vc,in [l min−1 ] [m s−1 ] [l min−1 ] Exp. [K] [K] [K] [K] [K] Re Ia 3 1.31 403.5 301.9 300.5 329.5 18.30 64.8 5 Ib 3 1.41 436.0 302.8 301.0 338.8 23.92 63.1 5 Ic 3 1.49 460.5 303.5 301.4 346.5 28.02 62.0 5 Id 3 1.58 489.0 304.1 301.5 356.0 33.14 60.8 5 II a 4 1.73 400.2 301.1 300.0 333.1 16.04 86.7 5 II b 4 1.79 414.0 303.5 299.5 342.5 23.40 85.4 5 II c 4 2.05 474.8 303.3 300.1 363.2 30.60 81.8 5 II d 4 2.16 499.0 300.4 297.8 373.0 32.80 81.0 5 III a 5 2.17 401.5 301.3 300.5 330.4 15.64 108.2 10 III b 5 2.37 440.1 301.6 300.7 341.0 20.87 105.0 10 III c 5 2.55 473.0 302.8 301.7 352.5 25.42 102.5 10 III d 5 2.74 507.9 304.4 303.0 364.5 30.69 100.1 10 IV a 6 2.55 393.5 302.4 297.6 344.7 18.97 130.5 5 Downloaded By: [Indest open Consortium] At: 10:37 14 May 2009 IV b 6 2.64 407.3 303.7 302.3 339.8 17.06 128.8 10 IV c 6 2.86 442.5 304.9 303.2 352.1 22.32 125.2 10 IV d 6 3.03 468.0 300.8 298.9 359.0 26.45 123.8 10 IV e 6 3.2 494.7 301.0 299.3 367.1 29.23 121.6 10 Va 8 3.35 387.5 302.3 300.3 339.9 14.36 174.9 10 Vb 8 3.86 447.0 303.8 300.7 366.5 23.77 166.7 10 Vc 8 4.16 482.1 304.0 300.2 381.0 29.63 162.8 10 Volumetric flow rates at ambient temperature and pressure: 300 K, 950 mbar bution ε th ,i . ε iso,i is the deposition efficiency measured when The parameters describing flow and temperature properties of the different experiments are summarized in Table 1. After the heat exchanger was operated under isothermal but other- every experiment the pipe bundle heat exchanger was flushed wise unchanged conditions. It was generally in the range of with pressurized air at flow velocities of about 40 m s−1 to reli- 2–20%. ably remove soot deposits on the tubes, which influence particle The small volume of the heat exchanger necessitates a macro- deposition and heat transfer properties. scopic description of the thermal gas properties by measuring The spark-discharge soot aerosol exhibited an approximated temperatures at the hot aerosol inlet, Th,in , the aerosol outlet, log-normal size distribution with a median particle diameter of Th,out , the cooling gas inlet, Tc,in , and the cooling gas outlet, about 82 nm, a geometric standard deviation of 1.64, and a num- Tc,out . The logarithmic mean temperature difference, T log,mean ber concentration between 6 and 9 · 106 cm−3 . It is similar to which is generally used to describe heat transfer characteristics, those encountered in the exhaust of modern heavy duty diesel is given by engines (Shi et al. 1999). The average particle size distribution Tlog,mean before and after the heat exchanger for experiment Id is given Tinlet − Toutlet (Th,in − Tc,out ) − (Th,out − Tc,in ) in Figure 5. = = . ln Th,in −Tc,out For each set of parameters the heat exchanger system was Tinlet ln Toutlet Th,out −Tc,in heated up by the aerosol flow until thermal equilibrium was [3] reached. Then 12 consecutive particle size distribution mea- surements were taken, alternatingly before and after the heat RESULTS AND DISCUSSION exchanger. For every switching, the particle concentration dif- In Figure 6 the measured εtot,i and εiso,i are displayed for the ference was divided by the particle concentration measured be- conditions of experiment series I with average aerosol flow ve- fore the precipitator. The arithmetic mean of the 11 values per locities vx,0 between 1.15 and 1.28 m s−1 . Small particles in the particle size class i obtained by this procedure was taken as the (size-dependent) total deposition efficiency, εtot,i . The measured size range of 34 to 70 nm are found to exhibit significant particle deposition up to 20% in the case of small aerosol flows through total deposition efficiency can be split into an isothermal con- tribution εiso,i caused by diffusion, impaction, and interception the heat exchanger when no temperature gradients are estab- lished. This observation can be attributed to diffusion processes under isothermal flow conditions and a thermophoretic contri-
  7. 7. 461 THERMOPHORETIC DEPOSITION IN A HEAT EXCHANGER Downloaded By: [Indest open Consortium] At: 10:37 14 May 2009 Figure 5. Soot-particle size distributions measured before and after the heat exchanger in experiment Ia (arithmetic mean ± standard deviation of 6 measurements each). Figure 6. Total particle deposition efficiencies εtot,i and isothermal losses εiso,i in the pipe bundle heat exchanger for experiments Ia–Id. Data points with error bars represent the arithmetic mean ± standard deviation of 11 differential measurement values.
  8. 8. 462 A. MESSERER ET AL. εtot,i and εiso,i measured in experiment Ia and thermophoretic occuring in the heat exchanger, leading to an increased particle contribution εth,i calculated from Equation (4) for the different deposition with decreasing d p . Increasing Th,in leads to signif- icantly enhanced particle deposition εtot,i , indicating that ther- assumptions outlined above. With f iso,th = −εiso,i · εth,i , εth,i mophoretic deposition occurs. exhibits no significant size dependency, as expected from ear- To investigate the contribution of thermophoresis to the total lier experimental results and theory calculations (Messerer et al. particulate deposition εtot,i , the different deposition mechanisms 2003). With f iso,th = 0, on the other hand, εth,i exhibits a pro- nounced decrease towards smaller particle size at d p < 100 nm, have to be decoupled. The first step in decoupling the ther- mophoretic deposition component εth,i is to determine how the which is not consistent with earlier investigations (Messerer mechanisms couple together. A general expression for combin- et al. 2003). Similar effects were observed for all experiments ing the mechanisms occuring in this study is given by performed in this study (more pronounced at low and less pro- nounced at high aerosol flow rates). Therefore, all further values εtot,i = εiso,i + εth,i + f iso,th , of εth,i presented in this study have been calculated from [4] εth,i = (εtot,i − εiso,i )/(1 − εiso,i ). [5] where f iso,th is a function of the mechanisms involved in the de- position process describing the interaction between the different Particle removal efficiencies representative for the investigated deposition mechanisms. A detailed description of the different size range were calculated by concentration-weighted averaging, methods of decoupling thermophoresis from other deposition 19 mechanisms is given in Romay et al. (1998). Still, the determi- ci εtot,avg = εtot,i , [6] nation of f iso,th is a matter worthy of discussion. For their studies Downloaded By: [Indest open Consortium] At: 10:37 14 May 2009 cint i=1 on the contribution of thermophoresis to particle deposition in 19 ci tubes, Nishio et al. (1974) and Romay et al. (1998) simply added εth,avg = εth,i , [7] εiso,i and εth,i with f iso,th = 0. On the other hand, Brockmann cint i=1 (2001) proposed f iso,th = −εiso,i · εth,i for independently act- ing deposition processes. The experimental data of this study where ci represents the particle number concentration per size allow the testing different coupling approaches. Figure 7 shows class averaged over the 12 consecutive SMPS measurements, Figure 7. Total particle deposition efficiencies εtot,i , isothermal losses εiso,i , and thermophoretic deposition efficiencies εth,i calculated with f (iso,th) = −εth,i · εiso,I and f (iso,th) = 0, respectively, for experiment Ia. Data points with error bars represent the arithmetic mean ± standard deviation of 11 differential measurement values; dashed line illustrates εth,avg calculated with f (iso,th) = −εth,i · εiso,i .
  9. 9. 463 THERMOPHORETIC DEPOSITION IN A HEAT EXCHANGER and cint is the particle number concentration integrated over the temperatures in the middle of the flow channels and minimum investigated size range. temperatures at the cooling pipe surfaces. For each of the investigated cooling air flow rates (5 L min−1 A detailed mathematical model of particle deposition in the and 10 L min−1 ), εtot,avg exhibits a near-linear increase with the pipe bundle heat exchanger would require solving a complex set of differential equations describing fluid flow, heat trans- precipitator number. The increase is steeper for the higher cool- fer, and particle motion by extensive numerical calculations for ing air flow, but the linear least-squares fits to both measure- ment data sets intercept the y axis ( T = 0 K) at εtot ≈ 4%, every relevant set of experimental conditions. To find a sim- ple semiempirical parameterization of deposition efficiency as which is consistent with the particle deposition observed under isothermal conditions averaged over all experiments (εiso,avg = a function of temperature and flow conditions, we tested the 4.5 ± 2.5%). applicability of the plate precipitator formula in Equation (2). In Figure 8 the average total particle deposition efficiencies Figure 9 shows the average thermophoretic deposition effi- εtot,avg from all experiments are plotted against the dimensionless ciencies, εth,avg , plotted against the precipitator number. Again, a “precipitator number” (Lµ0 Tlog,mean )/(vx,0 ρ0 TH2 ). µ0 , vx,0 near-linear increase is observed for each of the cooling air flows. ch and ρ0 are the arithmetic mean values of the gas properties cal- The linear least-squares fits intercept the y axis ( T = 0 K) at εth,avg ≈ 0, as expected for isothermal conditions. The slopes culated for the temperatures of the aerosol flow at the inlet and outlet of the heat exchanger (Th,in , Th,out ), respectively. L and of the fit lines (0.42 and 0.34, respectively) are fairly close to Tlog,mean are the effective deposition length and logarithmic the value of 0.55, which can be observed in plate precipitators mean temperature difference as defined above. Hch is the char- and equals the thermophoretic coefficient applicable for soot Downloaded By: [Indest open Consortium] At: 10:37 14 May 2009 acteristic distance for particle deposition along the temperature agglomerates in the investigated range of particle size and ex- gradient perpendicular to the gas flow. In a plate precipitator it perimental conditions (Tsai and Lu 1995; Messerer et al. 2003). is the distance between the hot and cold plates. For the minia- If the dimensionless precipitator numbers were calculated with characteristic distances of Hch,1 ∗ = Hch sqrt (0.55/0.32) = ture pipe bundle heat exchanger it was calculated as the arith- 0.79 mm and Hch,2 ∗ = Hch sqrt (0.55/0.42) = 0.69 mm, which metic mean of vertical and horizontal half-distances between the outer surfaces of the cooling pipes: Hch = 0.25 · (0.51 mm + are well within the range of different half-distances occurring 1.88 mm) = 0.60 mm (Figure 1). This is assumed to be a char- between the outer surfaces of the cooling pipes in heat exchanger acteristic average for the varying distances between maximum (0.26–0.94 mm), the slopes of the linear least-squares fit would Figure 8. Total particle deposition efficiency εtot,avg plotted against the dimensionless precipitator number calculated from average flow parameters, (Lµ0 Tlog,mean )/(v0 ρ0 T0 Hch ). The lines are linear least-squares fits to the data sets with different cooling air flow 2 −1 −1 rates (5 l min dotted; 10 l min dashed). Error bars represent the standard deviation (±1 s.d.) of the averaged values εtot,i .
  10. 10. 464 A. MESSERER ET AL. Downloaded By: [Indest open Consortium] At: 10:37 14 May 2009 Figure 9. Thermophoretic particle deposition efficiency εth,avg plotted against the dimensionless precipitator number calculated from average flow parameters, (Lµ0 Tlog,mean )/(v0 ρ0 T0 Hch ). The lines are linear least-squares fits to the data sets with different 2 −1 −1 cooling air flow rates (5 l min dotted; 10 l min dashed) and the theoretical relation for a plate precipitator (solid). Error bars represent the standard deviation (±1 s.d.) of the averaged values εth,i . Figure 10. Thermophoretic particle deposition efficiency εth,i plotted against the dimensionless precipitator number calculated from effective flow parameters at the hot inlet, (L ∗ µh,in Th,in )/(vh,in ρh,in Th,in Hch ). The line is the theoretical relation for a plate 2 precipitator. Error bars represent the standard deviation (±1 s.d.) of the averaged values εth,i .
  11. 11. 465 THERMOPHORETIC DEPOSITION IN A HEAT EXCHANGER be identical to K th ≈ 0.55. The results confirm that plate pre- Overall, the results of our study confirm the high potential of cipitator formula can be regarded as a physically reasonable miniature pipe bundle heat exchangers for combustion exhaust and a consistent basis for simple semiempirical parameteriza- treatment systems combining efficient heat recovery and aerosol tions of εth,avg as a function of temperature and flow conditions particle deposition. in miniature pipebundle heat exchangers. For a given geome- ∗ try and cooling gas flow the characteristic distance, Hch can NOMENCLATURE be determined from a few measurements and used to estimate Cross-sectional area of heat exchanger (m2 ) AHE deposition efficiencies for varying thermal conditions. Particle number concentration (cm−3 ) cp To investigate the influence of deposited soot on the depo- dp Particle diameter (nm) sition efficiency, experiment Ic was extended over a time span Hydraulic diameter,4AHE /PHE of 13 h. εtot,avg was near-constant at (37 ± 1)%. After the long- Dh term experiment the isothermal deposition efficiencies εiso,i were fiso,th Coupling term of deposition mechanisms Hch Characteristic distance (m) found to be 5–10% higher than at the beginning. Apparently ∗ Hch Modified characteristic distance (m) the deposited soot led to enhanced nonthermophoretic deposi- HP Plate distance (m) tion and reduced the contribution of thermophoresis, while the Kn Knudsen number, 2λ/d p overall deposition efficiency remained near-constant. Substan- K th Thermophoretic coefficient tial blackening of the heat exchanger tubes was observed upon L Deposition length (m) visual inspection after the long-term experiment. The blacken- L∗ Downloaded By: [Indest open Consortium] At: 10:37 14 May 2009 Modified deposition length (m) ing was most intense at the beginning of the heat exchanger and PHE Perimeter of heat exchanger (m) strongly decreased along the flow direction, indicating that the Heat exchanger Reynolds number, vh,0 Dh ρg,h,0 / Re particle removal was dominated by deposition over the first few µg,h,0 centimeters of the heat exchanger, where the highest temperature T Gas temperature (K) gradients and thermophoretic forces occur. Tp Particle temperature (K) The dominant influence of the conditions at the aerosol inlet Thermophoretic velocity (m s−1 ) vth was confirmed by test calculations in which the inlet temperature Axial velocity (m s−1 ) vx and flow parameters ( Th,in , µh,in , vx,h,in , Th,in ) instead of the average parameters ( Th,0 , µh,0 , vx,h,0 , Th,0 ) and an effective deposition length L ∗ = 0.1 · L = 30 mm were inserted in Greek Lettters Equation (2). The assumption L ∗ = 0.1 · L = 30 mm is based εiso Isothermal particle deposition on observed deposition patterns and is consistent with basic εth Thermophoretic particle deposition efficiency temperature profile calculations. With these parameters the data εtot Measured particle deposition efficiency points plotted against the precipitator number converged towards Tlog,mean Mean logarithmic temperature difference (K) the theoretical line for a simple plate precipitator with K th ≈ 0.55 λ Mean free path of gas molecules (m) (Figure 10). Dynamic viscosity of the gas (kg m−1 s−1 ) µ Density of the gas (kg m−3 ) ρg ∇T CONCLUSIONS Temperature gradient in the heat exchanger (K m−1 ) The results of this study demonstrate the applicability of miniature pipe-bundle heat exchangers for efficient particle de- position under typical combustion exhaust conditions. At aerosol Additional Subscripts inlet temperatures of 390–510 K, flow velocities of 1–4 m s−1 , i Particle size class and cooling air inlet temperatures around 300 K, deposition ef- avg Weighted average over particle spectrum ficiencies of up to 45% have been achieved for submicrometer 0 Arithmetic mean of inlet and outlet aerosol proper- spark discharge soot aerosol particles. ties Thermophoresis was the dominating particle deposition h Hot aerosol mechanism, and its decoupling from isothermal mechanisms c Cooling air was consistent with the assumption of independently acting pro- cesses (Brockmann 2001). Simple parameterizations derived from plate-precipitator the- REFERENCES ory and experiments (Tsai and Lu 1995; Messerer et al. 2003) Batchelor, G. K., and Shen, C. (1985). Thermophoretic Deposition of Par- ticles in Gas Flowing over Cold Surfaces, J. 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