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This article was downloaded by:[2007 King Mongkut's University of Technology Thonburi]On: 31 October 2007Access Details: [subscription number 780012218]Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK
Drying TechnologyAn International JournalPublication details, including instructions for authors and subscription information:http://www.informaworld.com/smpp/title~content=t713597247
HEAT AND MASS TRANSFER IN IMPINGEMENTDRYINGSuna Polat aa Procter & Gamble Company Winton Hill Technical Center 6250 Center HillAvenue, Cincinnati, Ohio
Online Publication Date: 01 January 1993To cite this Article: Polat, Suna (1993) 'HEAT AND MASS TRANSFER INIMPINGEMENT DRYING', Drying Technology, 11:6, 1147 - 1176To link to this article: DOI: 10.1080/07373939308916894URL: http://dx.doi.org/10.1080/07373939308916894
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DRYING TECHNOLOGY, 11(6), 1147-1176 (1993)
HEAT AND MASS TRANSFER IN IMPINGEMENT DRYING
Suna Polat Procter & Gamble Company Winton Hill Technical Center 6250 Center Hill Avenue Cincinnati. Ohio 45224
-and Drying of Paper and Textiles; Impinging lets
In indusoial drying applications, efficient transfer of heat and mass between a drying medium and the material being dried is very critical for the overall economics of the operation. Impinging jets are therefore widely used for their enhanced transport characteristics, especially for drying of continuous sheets of materials such as paper and textiles. In such applications, a thin sheet of material, as wide as 6m in cross machine direction, speeds at velocities as high as 90 kmhr under high velocity jets emerging from a confining surface parallel to the material surface. Many variables and effects need to k considered for proper design of such impinging jet systems: nozzle geometry and sizc. nozzle confieuntion. location of exhaust wns . nozzle-to-surface se~aration. jet-to-je~ separation. &ss flow. jet c x ~ t veloc~ty abd surface motion. For pcrmcnhle mntenals, add~tional cnh~nccmenl of hcat and mass transfer thst occur when some of the mptnglng gas 1s rcmovcd through the mdrenal makes this option an attmctivc one.
Here, we review the above effects and offer predictive correlations from literature which may be used in the design of high velocity impinging jet systems.
In drying of solids, imponant mechanisms that may affect drying are: - Heat transfer . Capillary uanspon of moisture to the surface . Diffusion in liquid phase
Diffusion in gas phase
copytight 0 1993 by Marcel Dckkcr. Ins.
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Phase equilibrium between the gaseous,
liquid and solid phases
Depending on the initial and the final moistures of the material being dried, as
drying proceeds, the controlling mechanism can change from pure heat transfer to some
combination of the above mechanisms. For example, drying of unbound water is a
heat mnsfer controlled phenomena. During this regime, generally called the "constant
drying rate period", drying rate increases with the heat wnsfer rate. Drying of bound
water, on the other hand, is generally limited by phase equilibrium and transpon
phenomena insidc the material. During this latcr stage, the drying rate continuously
decreases as the name "falling ratc period" implics. At thc constant drying rate period,
the temperature of the material stays nearly constant - at thc adiabatic saturation
temperature of the drying medium - and sharply increases during the falling rate period.
If the product to be dried is temperature sensitive, drying conditions at this stage must
be adjusted carefully to avoid product degradation.
If the product is in a form that is amenable to direct exposure to hot gases, heat and
mass transfer rates at the material surface can be enhanced significantly using
impinging jets. Impinging jets are thus particularly useful for drying unbound moisture.
However, should the drying continue to rrmove a significant portion of the bound
moisture, additional advantage of impinging jets is the potential for fine control of local
transfer rates, not only by varying flow ratc and AT, but by a number of geometric jet
parameters: nozzle type, jet diameter (or width), jet-to-surface distance, jet-to-jet
separation and configuration. This many design parameters complicates the design, and
requires more careful fabrication of the equipment to avoid undesired non-uniformities.
At the same time, it provides flexibility: with prior knowledge of these effects, a dryer
can be designed in several stages where drying rate and product temperature can be
controlled to achieve the best product quality.
In industry, impinging jets are used to dry materials in the form of continuous
sheets, i.e. paper and textiles, photographic film, veneer and carpets, or in the form of
granules or pallets, i.e. food and pharmaceulical products. In some cases hot jets are
insened in a bed of particles moving on a conveyor belt, fluidizing the particles.
Tnnspon propenies at particle surfaces in such systems differ from those produced by
impingement and thus will not be pan of this paper.
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IMPINGEMENT DRYING 1149
With enhanced transport characteristics of impinging jets, large drying duties can be
achieved in smaller size equipment. Because large volumes of air or hot gases are used
for rcasons of thermal efficiency, gases have to be recovered and reci~ulated. This
adds new considerations to the design, i.c. confinement and location of exhaust pons.
Cost increases because of more complex fabrication and increased air handling systems.
Dryer designs are based on heat and mass transfer measurements done in laboratory
equipment. Although most industrial uses are with systems of multiple jets. most
laboratory investigations have been with single jets. In a multiple jet system when the
jets are spaced widely and therefore not interacdng, use of single jet data is expected to
be valid. However, when the jets are spaced closely and therefore highly interacting.
special multiple jet data must be used in the design. Knowledge of geomeuic and flow
conditions at which jets in a multiple impinging jet system no longer behave as
independent single jets is required to make the distinction between the non-interacting
and interacting jet systems. n e case of multiple jets thus introduces the design
variables like jet-to-jet separation, exhaust flow location and cmssflow.
In drying of continuous sheets of materials, an added variable is the machine speed
relative to velocity of jets. For example, in impingement drying of paper (e.g. Yankee
dryer), the paper moves at speeds as high as 90 km/hr under impinging jets with nozzle
exit velocity of about I00 mls. With large changes in boundary layer conditions at a
moving surface, it is expccted that transfer rates would be significantly different than
those measured in laboratory studies with a stationary surface.
Again, for drying of permeable continuous sheets such as paper or textiles.
impingement drying rates can be increased funher by drawing some of the hot gases
through the product. This type of drying then combines two very effective modes of
heat and mass m s f e r mechanisms: impingement and through flow. Because only a
fraction of hot gases is drawn thmugh the pmduct, this combination drying can be
applied to even low permeability materials as opposed to pure through flow drying
which is only practical to use for drying of highly permeable webs.
This many design variables both simplifies and aggravates the design of an
impinging system. On one hand, understanding and quantification of these multiple
effects - individually or in combination - is critical for an accurate design. On the other
hand, it seems that a wrong choice for cenain design variables can be compensated by
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adjusting others. The difficulty is to find the optimal system design that will satisfy the
requirements of both the product and process simultaneously.
In this presentation, the effects of various design variables on impingement heat
transfer are discussed, and design correlations from literature are given. The equivalent
mass transfer coefficients can be obtained using analogy beween heat and mass
transfer. The intent is to provide a practical framework for the design of impinging jet
dryers.
Heat transfer coefficient, h, is a measure of the heat transfer efficiency. It is
commonly expressed as heat transferred per unit time per unit area per degree
temperature driving force (AT). The AT on which "h" is based naturally affects its
value. Hence, it is very imponant that the AT used between the reporting studies and
the applications should bc consistent. For impingement systems, AT is the difference
between the impingement surface temperature and a reference fluid temperature. fl,- T,). The reference temperature. T,, can be the nozzle exit temperature, Ti, a film
temperature based on the jet and impingement surface temperatures, e.g. (T,+T.) 01
~T,+zT,), or the adiabatic surfacc temperature. 3
Impingement heat transfer is actually a three temperature problem, i.e. in addition to
the jet and surfacc temperatures, the temperature of the surrounding gas, via
entrainment, also affects heat uansfer rates at the surface. Several authors including Goldstein et a1. (1990) and Hollwonh and Wilson (1984) defined correction factors in
terms of adiabatic surface temperature for h (or Nu) calculated using AT=(T.-Tj). The
intent is to quantify entrainment effects on impingement heat transfer. As the definition
of the adiabatic surface temperature by each author differs slightly, such correction
factors may be confusing. The adiabatic surface temperature is also a function of all of
the flow and geometric parameters that affect impingement heat uansfer. Moreover.
measuring or predicting the adiabatic surface temperature disuibution in actual
applications is difficult. Therefore, its use is not very practical.
For close jet-to-nozzle spacings, i.e. <8d, the nozzle exit temperature is generally the
preferred T,. For an isothermal impingement surface, with this choice of T,, local h
profiles then in fact become profiles of heat flux divided by a constant. Hence, local h - or in non-dimensional form "Nu" -does not account for changes in local AT that may
result due to effects on the boundary layer of various flow and gwmemc variables.
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IMPINGEMENT DRYING
Potential Core
Free Jet Region -- Impingement Region
Figure 1. n o w ficld of an impinging jet
These effects need to be quantificd in the range of geometric and flow variables for
practical applications.
A shon revicw of the flow smcture of impinging jets would be beneficial to
understand the discussions that follow.
Row field of an impinging jet may be dividcd into t h m characteristic regions:
Free jet
Stagnation flow - Wall jet
Depending on nozzle shape, its characteristic dimension and nozzlc-to-surfacc distance.
h e fra jet may display a potcntial core, a developing flow and a developed flow
regions. Figure I.
The potential core is characterized by a constant jet centerline velocity nearly equal
to the nozzle cxit velocity. The length of the potential core rrgion is determined by the
rate of gmwth of the mixing layer at the jet boundary. For a contoured jet nozzle,
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because i t produces nearly a flat velocity profile and low nozzle exit turbulence, the
potential core length is significantly larger than any other nozzle types (6-8d).
D o s d o p (1969) and O b t (1980). However, for a particular nozzle type, the actual
length of the potential core may dccrcase as the turbulence level at the nozzle exit
increases, Saad ct al. (1992). For a commonly used nozzle type, i.e. square-edged
orifice. Hollwonh and Wilson (1984) repon a third length which agrees with those
reponed by O b t for an orifice of similar design. The% flow measurements were
mostly done at low temperatures. The centerline velocity of heated impinging jets in
industrial applications decays faster, hence resulting in shoner potential core lengths.
Kataoka et al. (1984).
In thedeveloping flow region. axial velocity decays as the jet spreads. Eventually, a
bell shaped profile is approached which can be described by a Gaussian disuibution,
Manin (1977). I t has been shown by several investigators that the turbulence level
continues to increase beyond the potential core region in the developing and developed
free jet regions. For closely spaced multiple jets, the turbulence intensity at the
centerline increases more rapidly and to higher values as compared with those for single
jets. Saad el a1.(1992).
The nozzle-to-jet spacing at which the maximum stagnation point heat transfer
occurs relates to the velocity and turbulence development at the centerline of the jet.
Heat transfer under jets emerging from contoured nozzles displays a maximum when
the impingement surface is at 6-8d away from nozzles. Gardon and Akfirat (1965)
proposed that the maximum occurred at the location of maximum centerline turbulence
The data by various researchers, more recently by Kataoka et al. (1987). confirms this.
Hence, the location of the maximum heat uansfer may be closer to the nozzle exit, or
may not exist at all, if the turbulence level at the nozzle exit is already high.
In the stagnation region, flow makes a W rum. Here, static pressure first increases
sharply with the corresponding drop in axial velocity, then drops as the flow accelerates
along the impingement surface. Hence, in this region, there is significant favorable
pressure gradient on the surface. Studies by Gutmark et al. (1978) and Saad (1981)
with slot jets consistently reported that effect of stagnation on free jet mean flow is not
felt bcyond 0.2H from the impingement surface, and on axial turbulence velocity
beyond O.OSH which is also in agreement with the results of Obot (1980) for circular
jets.
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IMPINGEMENT DRYING 1153
The end of stagnation region in the lateral direction, defined as the location where
pressure gradient becomes rcro. is reported to be 0.35-0.5H from the impingement
point, Schaucr and Eustis (1963). Gardon and Akfirat (1965). Kumada and Mabuchi
(1970). Cadek (1968) and Saad ct al. (lW2). Beyond the stagnation region. in the wall
jet region, the pressure gradient in the lateral flow d i c t i o n is essentially rcro while the
fluid boundary layer over the impingement surface grows. Of the two sides of the wall
jet boundary layer, the impingement surface side shows typical effects of a
conventional boundary layer while the outer region has features of a free turbulent jet.
For a confined jet, if the confinement and impingement surfaces are sufficiently long,
the wall jet boundary layer grows to reach the confinement surface, thereby enclosing a
recirculating flow.
For a multiple jet system, another region of interest is the location where the wall
jets fmm adjacent jets meet. Characteristics of this region, as expected, highly depend
on the type of outflow used. This is a region of high turbulence; therefore, heat transfer
is enhanced, Saad et al. (1992). For slot impinging jets, if symmemcal exhaust pons in
the confinement surface are available, Saad et al. (1992) and Polat and Douglas (1990).
then the spent flow is directed upwards in the mid point between the jets without
causing cross flow effects on adjacent jets. Saad et al. reports that when the flow aspect
ratio, S N , is greater than 1.5, individual jets in such a system behave like independent
single jets, i.e. non-interacting.
Effects that are present in the industrial systems of impinging jets, such as surface
motion, exhaust port location, cross flow, entrainment and surface through flow
significantly change the boundary layer development over the impingement surface.
Moreover, due to the same effects, local temperature driving force for heat transfer is
also modified. Consequently, heat transfer rates at industrial impingement surfaces
reflect the combined effects of change in local shear rates and temperature driving
force.
Local Profiles
It is frequently said that the local dismbution of impingement uansfer rates has little
engineering value because a moving impingement surface, typical of industrial systems,
automatically integrates the local profiles. This is generally m e . However, for cases
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e 30 q i m o ~ l aqi j o pua aqi si3aUal em!u!m al(L 'aueld aizzou aql WOIJ ieme mg ueqi
ssai asepns e uo sa%u!dm! la1 asualnq1nl le!i!u! mole aiaqm maisB e ~ o j @s!dB are
ain%!cl j o salgo~d ~ajsuen ieaq [em1 aql u! em!xem pue em!u!m uo!leu%eis-jjo a u
.sa[zzou iuaserp aqi uaamiaq aJepns luwrauguo~ aq1 U! L lpx iyaumis
qe iuads Bu!lsneqxa i q paieu!m!ja s! maisk iacald!l[nm s!qlloj moU ssou
JO i m g a a q ~ .asepns luama%u!dm! aql mo l j ieme ms palem1 pue ap!m m u 01 are
salzzou 'maisis ~ajBu@u!dm! s!q~ 10s '(0661) selsnoa pue lelod 'eue uado 191 %OZ
q1!m s ~ a l ald!ilnm Bu!iswnu! alojaraqi p m d s L laso l~ l o j an salgo~d E un%!d 'aJepns
~uama%u!dm! aql m o l j ieme m q z paieml an ' m u OZ=M ' S ~ Z Z O U i a ~ h u a ~!id
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IMPINGEMENT DRYING 1155
purely laminar boundary layer from its minimum thickness at the stagnation point. The
increase from the minimum to the secondary maximum is due to the enhanced uansport
characteristics of a boundary layer in transition to turbulence. Beyond thc off-
stagnation maximum, fhc Nu profiles decline again with growing fhickncss of the
turbulent boundary layer.
4 I 4- - - -7- r/L R J L d L
Although the jet-to-surface spacing is still less than 8w, because of the very close
jct-to-jet spacing, these off-stagnation minima and maxima disappear in the profile
under the jets with 20% open area. Figure 3. This is typical of a syslcm where jet-to-jet
interaction is significant. Saad ct al. (1992).
60
20
H / v . 5 Re - S I H = 0.5 - E l 0 0 ..... 1 2000 - 20600 --- 25800
- ,**--.. - / - - - - I - Id---C' -- '- I \----- CZC-- ._ -.
8 0 , , ' - \.--*- 0--- 0' x-
.- /' ----a'
... k. , .--0-*
0
-
-7 .5 - 5 . 0 -2.5 0.0 2.5 5.0 7.5
Distance f r o m niddle J e t Centerllne, y l w
Figure 3. h f i l e s of local Nusselt number for interacting multiplc impinging slot
jets
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1156 POL AT
Distance t ram Nozzle Centerline, y / w
Figure 4. Profiles of surface p n s s u n relative to nozzle exit pressure for a single
slot jet atH=2.5w
Average Coeficieno Average Nusselt number. G, correlation for the jet system shown in Figure 2 is
- Nu =0.0314 Re0.76
valid in the ranges 3.2 5S/HS.4 and 16.000<Re<58.000.
And for the jet system shown in Figure 3 is
- Nu =0.094 ~ e ~ . ~ ~
valid for 8,00O<ReQ6,000.
A comparison of the average heat transfer rates on the basis of equal fan energy
requires that the jet Reynolds number for the f=3% system be 6.7 times higher than that
for f=ZO% system, provided nozzle discharge coefficients are equal. Within the range
of applicabilily of these correlations. Re=58.000 and 8.700 satisfy this requiremcnr
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IMPINGEMENT DRYING 1157
0 1 I 10 5 0 5 10
Dlrlance from Stagnation Polnt. r/d
700
li r 600 - C
500 U - -
400 V L w -
300 u
+ ; 200 w I - 0 100- " 0 A
Figure 5. Pmfiles of local Nusselt number for a single round impinging jet: Effect
of jet-trnsurface distance, Gardon and Akfirat(1965)
0 - 6 J m m
- PI= 28.000 AT. ZO'C
- .
- - -
Using the above correlations, the correspondingG values are 83 and 44 for the f=3% and 20% systems respectively. Economic considerations would dictate the use of the
3% open area system because of higher heat wnsfer rates. However, relatively uniform
local profiles under the 20% open area system can be of interest if the product is
susceptible to deformation under high pressure gradients at the surface for the 3% open
area system. Figure 4.
Another option for providing more uniform, but lower, heat transfer at the surface is
to increase nozzle-to-surlace distance. As depicted in Figure 5 for round jets, when
H%-8w, the secondary p e a s disappear. A more bell-shaped heat transfer profile is
%en at the surface. In parallel, forces applied on the product due lo deceleration and
acceleration of the flow alsn decrease.
Jer Flow
Like any boundary layer flow, for a given set of geometric conditions, impingement
heat mnsfer rates increase as jet flow increases. m e dependency of an averdge Nusselt
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Figure 6a. Correlation of impinging slot jct data as a function of flow aspect ratio.
S/H. Sad(1981)
1.0
0.8
0 .6
0.4
0.2 - Nu
~ e " ( H / W ) ~
0 .10
0.08
0.06
0 . 0 4
0.02
number on Reynolds number is expressed as Nu = b Rea. Depending on the study, the
- - 0.33 ! SIH ! 1.33 1.51 SIH ! 4 - - 8 S H I V ! 2 4 8 ! H l v ! 2 4 - 3.3301Rc129.160 f<;:,&! 20,740 - - -O.ZIS(SIH~. - n . " ( ~ l v ) ~
. - - =
1 RP65(H,v)-0.80
- - /' - 0 .63 ( s I H ) ~ ~ ~ - - - I - I -
I I I I 1 1 1 1 1 I I I I , I
0.2 0 . 4 0 .6 0.8 1 0 2.0 4 .0 6.0
proportionality constant " b andthe exponent "a" are reported as functions of geometric
parameters. Ww. SiH. Slw or I. In thc stagnation region, when H <8w (or 8d), it is
generally observed that "a" is close to 0.5, a value typical of laminar boundary layer flows. With increasing averaging distance from stagnation point, i.e. Slw, for reasons
explained earlicr, Re exponent becomes higher, indicating a boundary layer in transition to turbulent flow.
Flow Cell Proportion. S/H
For single slot jets, or non-interacting multiplc jets, i.e. S/H>1.5, and for 8 W w
524. Saad (1981) found that the exponent "a" was constant for all practical purposes at
a value 0.65, Figure 6a. This agrees well with the value 0.67 reported by Martin (1977)
for 2cWw<80. As S/H decreases, i.e. the jets become more closely spaced, the turbulence created in the rcgion where the wall jets from the adjacent jets approach
each other affects heal Wnsfer. Saad repons an increase in the Re exponent from 0.65
to 0.8 almost linearly as S N decreased from 1.5 to 0.375. Figure 6b.
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f low Ce l l Proporl lon. S/H
Figure 6b. Dependency of avenge Nuswll number on Reynolds number for slot
jets
Figure 6c. Dependency of average Nusselt number on Ww for slot jcls
. 1.0
-0.8
-0.6-
m - 0 .4 -
-0.2
0
0 0
8 ! Hlv ! 24 - m
F " = c ( H / v ) -
- / - PC
0 5,500 - - 0 11.000
15.000
I I I 1 1 1 1 1 I I I I I
0.3 0.4 0.5 1 .O 1.5 2.0 3.0 4.0 5.0
Flow C e l l Proportion, S/H
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Obot et al. (1980) reports an extensive list of design correlations available for round
jets. The Re cxponent in the correlations range from as low as 0.33 to as high as 1.06.
However. Obot et al. note anomaly of such low and high Re exponents. The majority
of studies reported values ranging from 0.5 to 0.8.
Nozzle Geomerry
I t is generally recognized that the nozzle design appreciably affects the
impingement surface heat and mass transfer profiles. Different nozzle designs produce
different nozzle exit velocity and turbulence profiles. Moreover. the nozzle exit
turbulence is also affected by the nozzle design. As free stream turbulence enhances
heat transfer in a laminar boundary layer, it is then expected that the nozzle geometry
effect be more imponant for H<8w (or d).
A majority of laboratory studies have used contoured entry nozzles, Cadek (1968).
van Heiningen (1982). Saad et al. (1992). Polat et al. (1991a). Although this type of
nozzle is impractical for industrial use, for study of the effects on impingement
transport phenomena of other design variables, and also for computer simulation
studies, i t provides uniform nozzle exit conditions, i.e. flat velocity and turbulence profiles with low nozzle exit turbulence.
Using contoured entry slot nozzles. Saad et al. varied the nozzle width from 3 mm to
13.3 mm. A consistent increase in turbulence intensity at the nozzle exit plane. I, from
0.65% for the narrowest nozzle to 0.8% for the widest one was measured. perhaps
specific to his equipment. With increasing distance from nozzle exit, these small differences in I were shown to grow into big differences. Consquently, at H=8w, Nuo
was 17% higher for the widest nozzle than that for the narrowest nozzle.
Hardisty and Can (1980) studied heat transfer characteristics of impinging slot jets using 8 different typcs of nozzles in thc range 3.000<Re<13.000. They measured the
discharge coefficients of the nozzles, Figure 7, and found that the centerline Nu from
different nozzles can bc correlated using the effective slot width (w'=Cow) as the
characteristic dimension instead of the nozzle width, w. It is unlikely that the use of w'
would completely eliminate variation in Nu due to the nozzlc design. This variation is
partially due to the turbulence effects, discussed above. Some researchen tried to
incorporate a turbulence enhancement factor to their correlations. Kataoka et al. (1987).
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IMPINGEMENT DRYING 1161
1.0 - NOZZIC wldth
D v.3 m m (conrtsnt) U
; 0 9 - c Nozzle u - shape Sqrnbol
a, 0
li U . a y 0.7 - 1J a = i r . ?2 ', 7 r 0 6 0.6 - \I A
-- 0
0.5 , 7
0 I I I I I , , I I I 1 I L I I I I I I ,
I 2 s 5 7 1 0 ~ 2 3 s 7 t 0 5 z 3 s
Reynolds number. Re
Figure 7. Discharge coefficients for various type slot nozzles. Hardisty and Can(1980)
For indusmal applications, however, such correlations are not practical: turbulence is
not an easily measurable or prrdictable quantity.
Consistent with the theory, both Hardisry and Can, and Saad (1980) repon that, for
geometrically similar nozzles, narrower nozzles gave higher heat transfer coefficients.
Obot (1980) has compared heat transfer and discharge coefficients for round jets
issuing fmm various types of nozzles and orifices. He also repons higher average heat
transfer coefficients for jets emerging from sharp entry nozzles when H<8d.
Differences between the uansfer coefficients from different types of nozzles tend to
decrease with increasing H, when H>8d.
Jet-lo-Surface Separalion
The effect on impingement hear transfer of the jet-to-surface distance is again
related to the flow and turbulence characteristics of a free jet. Figure 5 shows the
general characteristics of local profiles at various distances away from the nozzle exit
for a round jet. For especially close spacings, because of the influence of the nozzle
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Extent or Heat Transfer Surrace. S/H 4 3.2 2 1.33 t too I I I
Figure 8. Effect of nozzle-to-surface distance on average Nusselt number for slot
jets
: 80 i (U n
5 Z
= 60 a '9 ," > Z a rn a
40 > a
20
geometry and size on velocity and turbulence development, the effect of jet-to-surface
distance on Nu could vary depending on the nozzle design.
P d ~ t el a t . ( 1 9911) Slnqlr Jet v a n t l t l n i n p t n (1982) Sinpl. Jet
A Cobk(1968)SlnplrJ1t - 0 $806 ( 198 1 ) M u l l l p l e Jet1
-
S I W . 8 ( r . 6 . z ~ ~ ) - Re .21,000
I I I I I I I I I 0 2 4 6 8
For contoured entry slot nozzles in a multiple jet system. Saad repons that average
Nu in the range 4w<H<8w is almost independent of Ww. Figure 8. The trend
displayed by average Nu for single jets from contoured slot nozzles. Polat ct al.
(1991a,b), van Heiningen (1982), Cadek (1968). is to increase with increasing distance
from the nozzle exit for Ww values of up to 6w. In contradiction to bath of h e w
uends, not shown in Figure 8, Wedel's (1980) data for sharp entry multiple slot nozzles
show a continuous decrease with increasing Ww.
Nozzle-to-Surface Spaclng, H/w
For non-interacting impinging jets, for H/w>8. Saad's analysis indicates that
logarilhniic dependency of average heat transfer on Ww is a linear decrease with slope
-0.8. For interacting jets, the linear dependency on Ww is still valid: however, the
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IMPINGEMENT DRYING 1163
slope becomes less sensitive to Ww as S/H ratio becomes smaller, Figure 6c. This is
opposite of the trend that is reported by Manin (1977) for arrays of round nozzles.
Journeaux ct al. (1992) repons that for round jets for 1dUdc4 and 35.000<Rc
<I 17,003, average Nu is almost independent of Wd. This agrees well with thc data of
Wedel for multiplc round jcts. For 2dUd<l2 and 15,WO<Re<60,000. Obot (1980)
found a steady decrease in average Nu with increasing distance from the nozzlc cxit.
Hc reports a value of -0.2 for the (Hld) exponent.
Jet-to-Jet Separation
The effect ofjet-to-jet separation distance, 2S/w, is naturally coupled with other
effects that exist in a multiple jet system. In a confined mulliplc jet system with spent
flow exhausting from one cnd of the channel that is formed between confinement and
impingement surfaces. cross flow effects exist. Although there is less concern for cross
flow, a discussion on unconfined impingement systems is not useful because, for
thermal efficiency reasons, they are not commonly used in commercial systems.
The studies by Saad et al. (1992) and Polat and Douglas (1990), and Polar et al.
(1991a.b) isolated the effects ofjet-to-jet separation from the cross flow effects by
providing symmetrical exhaust ports in between slot nozzles at the confinement surface.
Saad et al. showed that this system can be thought of as an assembly of repeated flow
cells with an aspect ratio of S/H. They classified the multiple jets as "non-interacting"
when the internozzle spacing, 2S, is sufficiently wide and "interacting" when the
internozzle spacing is not wide enough. Their data indicated that for 4dUw<24 when
S/H>1.5, a multiple impinging jet system without cross flow effects is effectively an
assembly of single jets, therefore single jet transfer data can be used just as effectively.
For S/H<1.5, because the hcat uansfer profiles changed significantly due to jet-to-jet
interactions, special multiple jct data is needed. This is also evident from Manin's
correlation results displayed in Figure 9. Polat and Douglas (1990) reported heat
uansfer results for the Ww and S/H combination. 5 and 0.5, that Saad (1981) predicted
as being the combination that would give the highest heat transfer for a system of slot
impinging jets without cross flow effects, Figure 9.
T-T Sriegl and Diller (1984a.b) proposed to use an entrainment factor, F = 2 . 1 0 TI-T,
predict heat transfer in a multiple jet system from the single jet data. This method was
successful only for widely spaced jas , indicating that interactions in a closely spaced
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FIOV c e l l Ratio, S I H
Figure 9. Effect of flow cell ratio on average Nusselt number as a function of
nozzle-to-surface distance. Hlw: Comparison of the data and predictions
jet system affect both the temperature and flow fields. Journeaux et al. (1992) applied
the approach to the case of unconfined round jets and correlated their results in terms of
F.
A heat balance for the control volume shown in Figure 10, gives the following
As indicated by this relation. F increases with decreasing percent jet open area, f.
i.e. with increasing jet-to-jet separation distance. Hence, as SW increases for a fixed
HJw. the F value for h e cell increases indicating that the spent fluid temperature,T,, is
approaching toT,. Figure 1 I compares average Nu under round impinging jets
predicted using correlations by Martin (1977) for a single round jet and arrays of round
jets, and by Journeaux et al. for a row of round jets using F values of =0.0.3 and 0.5. , The Manin's single jet correlation results agree well with the results of Journeaux et al.
at F=O, i.e. for a case where the nozzle exit temperature is the same as that of the
environment. Figure I I results also show that when the isothermal jet results of
Journeaux et al. are corrected for enuainmenl in a multiple jet system, using F as a
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IMPINGEMENT DRYING
Figure 10. Control column for heat balance in a flow cell
.......... Mnnin11977). S indc .......... Manin (1977). Multiple c I
Jovmcalu ecd. (1-2) 0 t, 120- ,, ----- Jomeaux e~a1. (1992) 09 .......... Joumuur =I a1.0992) 03
E, roo- z - - g 80
- YI ..-. 5 60 -
40 4 I 1.0 2.0 3.0 4.0 5.0
Flow Cell Ratio. SM
Figure 11. Effect of flow cell ratio on average heat transfer for round jets:
Entrainment factor, F
comction factor, they agree very well with the predictions for multiple jets. It is
interesting to note that, as expected, the multiple jet results approach the F 4 . 3 line at
small SM values and the F 4 . S line at higher S/H values.
Spenr (oi Cross) Flow Effects
In a confined jet system, without symmetrical exhaust of spent flow between jet
nozzles, cross flow effects on heat transfer should be considered. In such systems, the
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flow from the intermediatc jets has to cross the jet flow from nozzles closer to the
exhaust pons. As cwler spent flow from the intermediate jets accumulates and flows
across other jet flows, significant changes in heat transfer is expected to occur as both
local shear rates and temperatures are modificd by this superimposed flow.
Saad (1981) measured local and average heat transfer profiles under impinging slot
jets with and without the effects of cross flow. Hc noted a 15% to 30% decrease in
average Nu when cross flow was only I to 2 times the jet flow. This decrease was
found to be insensitive to Re and f in the ranges 5.700<ReQ0,7W and 3<1<8.
Saad et al. (1980b) reported local and average Nu numbers for staggered anays of circular jets for 2<Syld<4, 3<Sx/d<6 and 3,35O<RcQ1,500. They found that, in the
range I d / d < 3 , the cross flow effect does not significantly affect heat aansfer for up to 3-5 jet rows. In industrial systems, exhaust pons are typically provided at every 3 to 10
rows of jets. Hencc thc effects may be greater for larger number of rows in a group.
The correlation based on a one-dimensional model presented by Galant and Martinez
(1982) for cross flow effects may then be used to predict the extent of such effects.
Jet Temperature and Hwridiry
In impingement drying, the variation in fluid properties from nozzle exit to the
surface is substantial and thus must be considered. In their study of superhcated steam
drying of paper. Bond el al. (1990) used Manin's correlation for anays of round jets to
calculate impingement heat transfer coefficients in their system. With fluid properties evaluated at a reference temperature given by the one-third mle suggested by Chow and Chung (1983),T, = fi+ :T.. and transpiration effects included using the film theory correction for heat transfer, given laier, they obwincd good agreement between the
predictions and their data, Figure 12.
Richards and Florschuetz (1986) measured impingement heat transfer coefficients
under conditions of varying humidity at the jet nozzles. Their primary objective was to
evaluate existing mcthods to calculate viscosity and thermal conductivity of airlwaar
vapor mixtures. Their results indicate that neglecting the effect of humidity does not
produce large errors. < 10% for humidity ratios up to 0.25 (kg waterkg dry air).
Evaporation at rhe Surfoce
In drying, especially during the constant rate period, evaporation rate at the surface
is high. The reported impingement heat and mass transfer coefficients do not include
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IMPINGEMENT DRYING 1167
Temperature. Deg. C
,025 r
E \ rn .02 Y
a- " ,015
rn C .- 2 & .o 1
D a N .-
,005
E D
0
Figure 12. Impingement drying using superheated steam: Comparison between the
data and Manin's cornlalion with and without transpiration corrections
,' , - Bond el al. (1990) - Corrected lor Transpilalion /' - ,
No1 Correcled lor Transpiralion 4
#' 4'
#'
evaporation effects. Therefore, these coefficients should k corrected appropriately
when used i n the design o f dryers. Bird. Steward and Lightfoot (1960) describe several
approaches to determine the form o f the comction factors. Here, only the comction
factors based on the f i lm theory, which wen: successfuUy applied to impingement flows
by Crotogino and Allenger (1979) and Bond et al. (1990). are given.
0 : , 100 , / ZOO 300 400 SO0
Heat transfer coefficient with evaporation at the surface:
Mass transfer coefficient with evaporation at the surface:
Surfnce Morion
Impingement drying of continuous sheets of material involves impingement to take
place on a rapidly moving surface, a feature which may change heat and mass transfer
characteristics substantially.
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Rej -35400 H/v -2 .5
100
-16 - 1 2 - 8 - 4 0 4 8 I Z 16
Otstance from Nozzle Centerllne. y /w
Figure 13. Profiles of local Nusselt number for a single slor jet impinging on a
moving surface: Effect of surface motion
Polar and Douglas (1990) and Polat et al. (1991b) provided the local heat transfer
profiles at a rapidly moving surface under confined slot jets for interacting multiple jets
and a single jet respectively. They expressed surface motion non dimensionally as the surface-to-jet mass velocity ratio, MvS. For the jet Reynolds numbers in the range
18.000-35,400, Mvs was varied from 0.029 to 0.34 by varying the surface speed from
0.5 ro 9 m/s. Figure 13 profiles at HJw=2.5 and Re=35,400 indicate that for this close
jet-lo-surface spacing, the largest effect on the local hear transfer is felt in the wall jet
region of the side where surface motion is towards the nozzle centerline. This was
perhaps due to the dominating effect of reduction in local AT near the surface when
cooler temperature spent fluid is dragged by the surface motion into the jet region. 7he
net effect of surface motion on average hear transfer rates was found to decrease heat
transfer. For both interacting and non-interacting jets, this reduction was correlated only as a function of MvS as ( I + M V ~ ) - ~ . ~ .
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IMPINGEMENT DRYING 1169
Journeaux et al. (1992) more recently reponed a similar analysis for an array of
confined and unconfined round jets impinging on a rapidly moving surface. Their conclusion was that the impingement heat transfer was not appreciably affected for Mvs
values up to 0.6, i.c. twice the maximum value that was obtained by Polat et al. for slot
jets. Insensitivity to swiacc motion in h e case of round jets may be explained with the
fact that, in this case, the spent flow has a higher degree of freedom to spread on the
surface.
Surface Throughflow
At a permeable impingement surface, such as paper and textiles, convective
transpon rates can be enhanced funher by withdrawing some of the jet flow through the
surface. Baines and Keffer (1976. 1979) measured the effect of through flow on local
shear stress, and by analogy reponed enhancement in heat transfer due to through flow.
Because analogy between momentum and heat transfer does not hold for the stagnation
region of impinging flows, validity of those results is questionable. Saad (1981) and
Obot (1982) measured increase in impingement heat transfer for a limited set of
conditions for slot and round jets, thus, they did not repon any correlations. However.
both noted a uniform, linear increase in local heat transfer profiles with through flow.
Enhancement in local impingement heat transfer due to through flow was measured
for multiple. Polar and Douglas (1990), as well as a single impinging jet, Polat et al.
(l991a.b) using a permeable heat flux sensor, Polat et al. (1990). They expressed through flow non-dimensionally as the through flow-to-jet mass velocity ratio, MuS.
Figure 14 shows enhancement of local heat transfer profiles with increasing MuS for the
single jet case. As reponed by Saad and Obot, enhancement is nearly uniform
everywhere in the profiles.
Polar el al. noted that, based on a heat balance near the surface, enhancement due to
through flow is best expressed in terms of Stanton number. They found that increase in
Stanton number due to through flow is proportional only to the through flow parameter Mus with a proportionality constant of about 0.17 for both interacting and non-
interacting jets. Their maximum Mus value was 0.023. These results indicate that the proponionality constant may be valid even in a much wider range of geometric and
flow parameters.
Referring to Figure 14, the significance of the surface through flow effect for industrial applications is apparent that by using Mu, = 0.0121. heat transfer is nearly
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0 1 -16 - 1 2 - 8 - 4 0 4 8 I2 16
Distance from Nozzle Centerline, y/w
Figure 14. Profiles of local Nusselt number for a single slot jet impinging on a
permeable surface: Effect of surface through flow
doubled for heat transfer surfaces of any half-width. S, over the broad range 0.8 - 6.4.
In this range. f=25%-3%. the through flow rate is only 4.8% to 38.7% of the jet flow
rate. Adding to this impressive enhancement of convective heat transfer at the surface.
there is funher enhancement inside the permeable smcture due to intimate contact with
gas, Polat. 0. (1989). With such impressive enhancement features, the combined
impingement and through flow drying c e d n l y opens possibilities for even low
permeability media.
Because impingement heat and mass transfer has attracted the attention of many
researchers, there are quite a few correlations available in literature for this type of
flow. Obot et a1.(1980). The majority are limited to a narrow range of flow and
geometric variables. The Figure 6 correlation by Saad (1980) for multiple slot jet
systems without cross flow effects, and the following correlations by Manin (1977) are
therefore suggested.
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IMPINGEMENT DRYING
where f. = (60 + ~ ( W Z W - ~ ) ~ ) ~ ~ ~ .
Range of applicability is
I ,500<Re<40,000 0.008<f<2.Sf0
2<Ww<80
Note that the cornlation by Martin for slot jet systems was developed using data for
a system where spcnt flow was allowed along the length of the nozzles. This outflow
arrangement natl~rally imposed three-dimensional effects on heat transfer rates.
Therefore the predictions using Martin correlation on Figure 9 are lower than the
cxpcrimental data for slot jets where exit pons were provided symmetrically on both
sides of the jets. In the range that is most relevant for industrial applications, however.
Martin's correlation agrees reasonably well with the data.
Although Saad's correlation is valid in the range 8<Ww<24, he observed that for
4 W w < 8 , his results were relatively insensitive to Ww showing only about 5% increase with decreasing H.
For arrays of round jets, again the following correlation by Martin is suggested
Range of validity
102,000<Re<100.000
O.W4<f<0.04
2cH/d<12
Correction factors that are suggested for the effects of surface motion, evaporation.
and/or through flow in the above sections can be applied to these Nu correlations when
such effects are present.
Due to the complex interaction on impingement heat transfer of turbulence, mean
flow and temperature fields, modified due to the effects of flow and geometric
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variables, these correlations should still be used cautiously. Once the conceptual dryer
design is completed, it is common practice to check the validity of the results using a
small scale dryer.
P E W CONSIDERATIONS
Economic reasons dictate maximizing the heat transfer per unit fan energy per unit
heat mnsfer area. Assuming the jet nozzles m the major resislance to flow, h e
following relation between the fan energy, nozzle discharge coefficient and the nozzle
exit velocity is valid.
Using this relation, an optimal spatial arrangement for jet nozzles can be determined
while keeping one of the characteristic lengths, i.e. w. H or S, constant. Manin (1977).
using his comlations for impingement heat transfer, gives the following optimal values
on the basis of a constant H.
Staggered Array of Round Array of lets Slot lets
0.015 0.072
It is interesting to nore that the optimal S/H value for both types of nozzles is the
same and very close to rhe value that Saad et al. (1992) reported to be a critical value,
S/H=0.75, where jet-to-jet interactions start affecting hear transfer at the stagnation
point.
One scenario for the design procedure would bc to choose the values of H and d to
achieve the optimal Wd value while keeping the maintenance and operation constraints
for a particular application in mind. The S value is thus fixed by the optimal S/H and H
values. With the selection of the nozzle type and nozzle exit velocity - which
determines the total volume of gas for the system - the dryer area is found from the total
drying requirements of the system. The drycr design is completed with the layour and
sizing of the duct work.
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IMPINGEMENT DRYING 1173
The nozzle exit velocity could be limited if the product is susceptible to deformation
under the hydrodynamic force by the jets. In this case, slot jets should be preferred
over round jeu. This is because, for the same blower rating, slot jets give about the
same heat transfer as the round jets at lower jet velocities. On the other hand, with slot
jets, the total volume of gas recirculated in the system is almost three times greater.
CONCLUSIONS
High drying rates achieved with impinging jets make this technology attractive for a
number of industrial applications. Sensitivity of heat and mass transfer rates, however,
in such applications to a number of flow and geometrical parameten makes the design
engineer's job difficult as to the selection of a design basis and control strategy. Here a
concise review ofthe imponant effects on impingement transport phenomena is given. Although the dixussions are based on impingement heat transfer, as analogy to mass
transfer is well established, they equally apply to both.
Remember that, because of the interactive nature of a number of effects, laboratory
investigations directed to quantify certain effects may sometimes produce results and
conclusions that are not directly relevant to indusmal use. On the other hand, because
the numbcr of effects is high, an experimental program to fully characterize and
develop general correlations for impingement flows would be an impossible task.
Correlations by Manin (1977) for arrays of slot and round jets when moderate cross
flow effecu are present, and by Saad (1980) for arrays of slot jets without cross flow
effects are given here because of the wider range of variables they covered.
The same Nu correlations can be used to predict impingement transfer coefficients if
surface motion and through flow effects are important with the multiplication or
addition of appropriate facton. For slot jets, as suggested by Polat and Douglas (1990) and Polat et al. (1991b). multiplying average Nu with the factor ( I + M V , ) - ~ . ~ would
account for the surface motion effecu. For round jets this effect is not important even
for quite high values of Mv,. Joumeaux et al. (1992) . For surface through flow effects,
average Nu number under both slot and round jets can be modified by adding the term
0.17 Mv, Re R, Polat and Douglas (1990) and Polar et a1.(1991a). These correction
factors can be used either alone or in combination depending on the casc.
Based on the discussions provided here on general mechanisms of effects, design
engineers should usc their best judgement to account for other effects specific to a
particular case.
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NOMENCLATURE
CD : nozzle discharge coefficient
d :jet nozzle diameter
f : fraction open area (T-T,) F : enuainment factor. 1 (Tj-TA
: heat transfer coefficient
: nozzle-ro-surface distance
: volumeuic gas flow rate per unit heat transfer area
:radial direction
: jet-to-jet separation distance in flow direction for a two dimensional jet m y
: jet-to-jet separation distance in lateral direction for a two dimensional jet m y
: jet-to-jet separation half distance : nozzle exit temperature
:Reference temperature
: surface temperature
: nozzle exit velocity
: nozzle exit velocity for slot jet
: nozzle width
: fan energy
Non-dimensional numbers
Ww : nozzle-to-surface distance
Re : Reynolds number, = P V,=i(or w) P
Mv, : surface motion parameter, surface-to-jet mass velocity ratio
Mu, : surface through flow parameter, through flow-to-jet mass velocity
ratio h d(or w)
Nu : Nusselt number,= - k
h : Prandtl number SiH : flow cell ratio
S/w : averaging distance from jet centerline
w12S : fraction open area for slot jet systems
REFERENCES
Baines, W.D. and J.F. Keffer (1976), Shear Smss and Heat Transfer at a Stagnation Point, Int. Heat Mass Transfer, Vol. 19, pp.21-26.
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IMPINGEMENT DRYING 1175
Baincs. W.D. and J.F. Keffer (1979). Shear S a s s Measurements for an lmpinging Air Jct, Transactions of the Technical Section, Canadian Pulp and Paper Assoc. Vol. 5, pp. 39-44.
Bird. R.B., W.E. Steward and E.N. Lightfoot (1960). Transpon Phenomena. John Wiley & Sons. Inc., New York.
Bond. J.F., R.H. Crotogino, W.J.M. Douglas. A.S. Mujumdar, and A.R.P. van Heiningen (1990). Impingement Drying of Paper in Supcrhcated Steam in the Constant Rate Period. Presented in lntemational Drying Symposium. Prague.
Cadek. F.F. (1968). A Fundamental Investigation of Jet Impingement Heat Transfer, Ph.D. Thesis, University of Cincinnati.
Chow. L.C. and 1.N Chung (1983). Evaporation of Waar into a Laminar Stream of Air and Supcrhcalcd Slcam. Int. J Hcat Mass Transfcr. Vol. 26. No. 3. pp. 373-380.
Crotogino. R.H. and V. Allcngcr (1979). Mathematical Model of the Papridryer Process. Transaction of thc Technicvl Section. Canadian Pulp and Paper Association, Vol. 5, No. 4, pp. 84-91.
Dosdogru, G.A. (1969). Uber die Ausfuhrung von Schlitzdusen im Untershallbereich. Mitteilungen Heft 2, Forschungsgesell schaft Dnrckmachinen e.V.
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