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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
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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: reinhard.niessner@ch.tum.de

456

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-

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

458 A. MESSERER ET AL.

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

459

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.


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

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-

461

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.


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

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 .

463

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

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 .


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 .

465

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∗

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).
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