Experimental study on heat transfer of thermally developingand developed, turbulent, horizontal pipe flowof dilute air-solids suspensions

T. Aihara, K. Yamamoto, K. Narusawa, T. Haraguchi, M. Ukaku, A. Lasek, F. Feuillebois

Abstract Heat transfer characteristics of a turbulent, diluteair-solids suspension ¯ow in thermally developing/devel-oped regions were experimentally studied, using a uni-formly heated, horizontal 54.5 mm-ID pipe and 43-lm-diameter glass beads. The local heat transfer was measuredat 27 locations from the inlet to 120-dia downstream of theheated section over a range of Reynolds numbers 3� 104

ÿ1:2� 105 and solids loading ratio 0±3, and the fully de-veloped pro®les of air velocity/temperature and particlemass ¯ux were measured at a location 140-dia downstreamof the heated section using specially designed probes, in-serted into the suspension ¯ow. The effects of the Reynoldsnumber, solids loading ratio, and azimuthal/longitudinallocations on the heat transfer characteristics and their in-teractions are discussed through comparison of the presentresults with the data obtained by other investigators.

List of symbolsca speci®c heat of air, J/(kg á K)cp speci®c heat of glass beads, J/(kg á K)

d inner diameter of pipe, mdp Sauter diameter, or surface mean diameter, of test

particles, m_Ga mass ¯ow rate of air, kg/s_Gp mass ¯ow rate of solid particles, kg/s

hx;u local heat transfer coef®cient, de®ned by Eq. (1),W=(m2 á K)

M solids loading ratio, _Gp= _Ga, dimensionlessmp local mass ¯ux of solid particles, kg=(m2 á s)Nux;u local Nusselt number, de®ned by Eq. (2), dimen-

sionlessDp pressure drop, Paq wall heat ¯ux, W=m2

Rea air Reynolds number, uad=ma, dimensionlessr radial distance from the pipe central axis, mrw inner radius of pipe, d=2, mTa air temperature, KTb;x local equilibrium suspension bulk temperature,

given by Eq. (3), KTa;0 inlet equilibrium suspension bulk temperature, KTw inside wall temperature, Kua air velocity, m/sx distance from the inlet of heated section, my radial distance from the inside wall of pipe, m

Greek symbolska thermal conductivity of air, W/(m á K)ma kinematic viscosity of air, m2=sqa density of air, kg=m3

qp true density of glass beads, kg=m3

sw wall shear stress, N=m2

u azimuthal angle measured from the pipe bottom,rad

Subscriptsa airp solid particles air-solid suspensionx local value at location xw inside wall of pipeu local value at angle u0 inlet of heated section or evaluation of ¯uid physical

properties at T0

1 asymptotic value in thermally developed region

Superscript) average value

Heat and Mass Transfer 33 (1997) 109±120 Ó Springer-Verlag 1997

109

Received on 14 October 1996

T. Aihara, M. UkakuInstitute of Fluid Science, Tohoku University2-1-1 Katahira, Aoba-ku, Sendai 980-77, Japan

K. YamamotoComponent and Dynamics Dept 2Engine Engineering Div 1, Toyota Motor Corp. 1Toyota-cho, Toyota 471, Japan

K. NarusawaEngine Sect, Traf®c Nuisance Div,Traf®c Safety and Nuisance Research Institute6-38-1 Shinkawa, Mitaka, Tokyo 181, Japan

T. HaraguchiDepartment of System Engineering,Faculty of Engineering, Ibaraki University4-12-1 Naka Narusawa-cho, Hitachi 316, Japan

A. LasekLaboratoire d'Aerothermique, CNRS 4 ter, route des Gardes,F-92190 Meudon, France

F. FeuilleboisLaboratoire de Physique et Mecaniquedes Materiaux Heterogenes,CNRS Ecole Superieure de Physique et Chemie Industrielles10, rue Vauquelin, F-75231 Paris, Cedex 05, France

Correspondence to: T. Aihara

1IntroductionHeat and mass transfer of turbulent pipe ¯ows ofgas-solid suspensions is of prime interest to chemical,mechanical, nuclear, automobile, combustion,gasi®cation, and environmental engineers. Since the late1950s, a great deal of effort has been expended to clarifythe mechanisms and characteristics of heat and masstransfer of vertical or horizontal turbulent pipe ¯ows ofgas-solid suspensions experimentally and theoretically.Depew and Kramer extensively reviewed papers on heattransfer to ¯owing gas-solid mixtures, published before1970 [1].

A great number of reports on experimental studies ofsuspension heat transfer have been published; however,the majority of these studies focus on heat-transfercharacteristics of vertical ¯ows, and average ones at that.Experimental research on convective heat transferof horizontal ¯ows has not been as extensive [2±9].Several theoretical approaches [1, 10±16] have also beenattempted on the many assumptions, most of which arevalid only for vertical ¯ows. Rigorous theoretical approachseems dif®cult, particularly for horizontal ¯ows, becauseof the statistical nonlinearity arising from the randomnature and complexity of particle-¯uid, particle-particle,and particle-wall interactions in turbulent pipe ¯owsof suspensions.

Recently, a new concept of heat transfer control [17]using an intelligent multiphase ¯uid [18] has been pro-posed; an intelligent multiphase ¯uid is de®ned as a sus-pension of ¯uid and special solid particles with sensingfunctions for ambient parameters such as temperature andactive functions. For realization of the new concept, it isnecessary to obtain further information on the heat-transfer characteristics of a turbulent suspension pipe ¯owwith a comparatively low solids loading ratio, in particular,on the distribution of the local heat-transfer coef®cientswith respect to azimuthal and longitudinal directions ofthe pipe, because a suspension ¯ow has a very long en-trance length and excellent heat transfer in there. More-over, there is a dearth of experimental heat-transfer dataobtained using a large test pipe.

We have carried out an experimental study on heattransfer of turbulent, dilute air-solids suspension ¯ow inboth thermally developing and thermally developed re-gions, using a uniformly heated, long horizontal pipe withan inner diameter of 54.5 mm and 43 lm-diameter glassbeads. In this paper, the major emphasis is placed on heattransfer rather than pressure loss because the latter hasalready been investigated in detail by many researchers.The experimental results are presented for the respectivefully developed pro®les of particle mass ¯ux and air ve-locity/temperature, and the local and asymptotic Nusseltnumbers for air-solids suspension ¯ow, along with theuniversal velocity/temperature distributions and local andasymptotic Nusselt numbers of pure air ¯ow. The in¯u-ences of the Reynolds number, solids loading ratio, andazimuthal/longitudinal locations on the heat transfercharacteristics and their mutual interactions are discussedthrough comparison of the present results with the dataobtained by other investigators.

2Experimental apparatus and procedures1

2.1General arrangement of flow system

2.1.1Air flow systemA schematic of the gas-solids system used in this inves-tigation is shown in Fig. 1. Humidity-controlled air 2 wasdrawn into the inlet port 1 of a large concrete silencer;after it was passed through a glass wool silencer 2 of di-ameter 80 mm and length 580 mm and a ®lter 3, it waspressurized by a 11 kW Roots blower 4 (0.068 m3=s at69 kPa). After damping of the pressure pulsation withsurge tanks 5 and 7, the mass ¯ow rate of air _Ga wasmeasured with a quadrant-edge ori®ce 10 with an area-contraction ratio of 0.25, located downstream of a wire netscreen and a straightener 9. A check valve 8 was also in-stalled for preventing back ¯ow.

The top-to-base amplitude of pressure pulsation, D~p, inthe discharge of the Roots blower increases with the dis-charge pressure. The damping system which included twosurge tanks was designed to have a Hodgson number of16±90 in the present experimental range. Pulsation-wavemeasurement with a memory-oscilloscope showed that thepresent system effectively damped the pressure pulsationeven in the case of maximum discharge pressure, where D~preached up to 45 kPa at the discharge port of the Rootsblower, and that the pulsation waves at the ori®ce 10 werealmost triangular. It is well known that the in¯uence ofpulsation with triangular wave forms on the accuracy of¯ow-rate measurement is minimal in comparison with thatof pulsation with other wave forms [20]. Thus the air ¯owrate was measured with the calibrated ori®ce 10 within anerror of �3%. The air ¯ow rate was regulated with a mainvalve 11 and bypass valve 12.

2.1.2Particle feeding and recovery systemsSolid particles ¯owed down from an 800 mm-diameterfeed hopper 23 into a heat exchanger 25, in which theparticle temperature was regulated to be equal to the air-¯ow temperature. Then, the solid particles were added tothe air¯ow through a slit in the throat wall of a 2-dimen-sional Venturi mixing tube 13, at a constant feed rateregulated by an electromagnetic, amplitude-controlled vi-bration feeder 27. The Venturi mixing tube 13 was spe-cially designed so that the throat width and wall pro®lecould be varied for control of the throat static pressure.The mass rate of air leakage from the Venturi mixing tube13 to the hopper 23 via the sampling valve 24, heat ex-

1The details of the present experimental apparatus and proce-dures are described in Ref. [19].2The motion of solid particles is in¯uenced by their electrostaticcharge, which is strongly related to air humidity. Hence, the inlethumidity and temperature of the air introduced into the testsections (described later) were regulated to be approximately 70%and 7±9�C using an air-water mist tunnel [21] and a heatexchanger 6, respectively.

110

changer 25, and gate valve 26 was less than 0.1% of themass rate of air ¯ow.

After a heat-transfer test, the solid particles were sepa-rated from the air-solid suspension by a cyclone separator15; then, the air was exhausted to the atmosphere througha bag ®lter 14 after dedusting. The recovered particlesnormally passed through a dust bunker 16 and measure-ment hopper 18, and ¯owed into the feed hopper 23; thus,the solid particles circulated in the experimental appara-tus.

The measurement hopper 18 was mounted on a cali-brated, electric-recording platform-balance 21. Hence, theparticle circulation rate _Gp was measured by closing aquick-acting valve 19, accumulating the solid particles inthe measurement hopper 18, and continuously monitoringtheir weight with the automatic balance 21. Stainless-steelbellows 17 and 20, connecting the moving parts with thestationary parts, were designed to be very ¯exible, with aspring constant of 0.392 kN/m. Piping 22 was adopted forpressure balancing.

2.1.3Air-solid suspension flow systemThe air-solid suspension ¯ow system was composed of a¯ow-development section, heated section, and returningsection. Every section was made of polished, stainless-steelseamless pipe with an inner diameter of 54.5 mm andlength of 4 m; the pipe wall thickness was 3 mm in thedevelopment and returning sections 28, 32 and 1.18 mmin the heated section 30. All the pipes were ¯ange-jointed smoothly on the inside, and the joints were madeairtight with Te¯on O-ring. The horizontal pipe lineswere supported by the following mechanisms at 1 mintervals.

The test section pipe was held in position in the air bytwo 0.25 mm-dia-wires which were tight-stretched in aV-shape and a K-shape between the arms of an adjustableU-shaped stand; this stand was attached to a small truckmovable on horizontal rails. This mechanism was adoptedfor minimizing heat-leakage through itself. On the other

hand, the returning pipe 32 was suspended by a pulley andbeam-balance mechanism from the room ceiling; hence,the returning pipes were movable both horizontally andvertically.

Thus, the longitudinal thermal expansion was absorbedby a stainless-steel bellows 31 having a spring constant of6.1 kN/m. Care was taken in pipe alignment to attainsuf®cient straightness and collinearity of pipes, particu-larly in the test sections, for avoiding irregularity of heattransfer characteristics [4].

2.2Test solid particlesThe solid particles used in the experiment were near-perfectly spherical glass beads, which were screened bymeans of standard sieves. The size distribution was mea-sured from micrographs of particles both before testrunning and after 200 h running.

According to the measurements, the test solid particleshad a nearly monodisperse size distribution, expressed bythe mass-basis Rosin-Rammler equation with a dispersionparameter 6.7 or 7.6 and a size parameter (36.8%-dia-meter) of 43.5 lm. The size distribution was almost un-changed by 200 h running, except for some very smallparticles which had been trapped in low velocity or stag-nant zones in the ¯ow system, such as the hopper and heatexchanger. No further change in the size distribution wasfound after running for longer than 200 h. Thus, it may besaid that particle-size reduction during the present ex-periment was negligible.

Based on these data, the Sauter diameter of the testparticles, or surface mean diameter, was determined to be43.4 lm. Particles of such small size were used due toconsideration of Depew and Cramer's experimental ®nd-ings [4] that heat transfer data differ signi®cantly betweenthe top and bottom of a pipe in the case of 30 lm diameterglass beads, but not in the case of 200 lm-diameter glassbeads. According to additional measurements, the truedensity qp and speci®c heat cp of the test glass beads were2440 kg=m3 and 828 J/(kg á K), respectively.

Fig. 1. General arrangement of equipment(not to scale; dimensions in mm)

111

2.3Test sectionsThe test sections were composed of the development sec-tion 28 and heated section 30. The heated section wasjoined to both the development and returning sections28, 32 smoothly on the inside using ¯anges and C-clamps,but electrically insulated with Te¯on gaskets for applica-tion of an electric current for Joule-heating of the heatedsection. The test sections were thermally insulated alongtheir entire length with 30 or 50 mm-thick foam polyester-isocyanate insulators 29.

The 78 calibrated 0.1 mm-diameter copper-constantanthermocouples were attached to the outside of the heated-section pipe around its circumference at each of 27 axiallocations, as follows. The hot junction was soft-soldered toa small copper piece of 3�3�0.1 mm3, which was attachedto the pipe wall with adhesive so as to be thermally con-ductive but electrically insulated. The lead wires of thethermocouples were also attached to the pipe wall for adistance of 20 mm and coated with the adhesive.

The development section was 147-dia long, enough toprovide a fully developed, isothermal air-solid suspension¯ow before reaching the heated section. Hence the equi-librium bulk temperature, Ta;0, of the air-solid suspensionentering the heated section was measured at a position0.5 m upstream of the joint of the development and heatedsections and 5 mm below the top of the pipe, using a0.1 mm-diameter copper constantan thermocouple. Thethermocouple hot junction was exposed to the ¯ow out ofthe downstream-facing slant-cut end of a 0.5 mm-diameterprotective support tube. The estimated error in tempera-ture measurement by the above-mentioned methods waswithin �0.2 K.

The test section pipes were also equipped with four0.5 mm-diameter pressure taps around their circumferenceat 1 m intervals in the axial direction, except near the outlet.

2.4Instruments for local measurementThe air-solid suspension ¯ow was both hydrodynamicallyand thermally developed before it reached a position140-dia downstream of the inlet of the heated section.Hence, the velocity and temperature distributions in thesuspension ¯ow were measured at this position. The crosssection at this position, hereafter called the ``traverse sec-tion'', was explored by traversing probes of several typeswith a mechanism having a micrometer with 10 lm grad-uations. Figure 2 shows details of the traversing mechanism,which was electrically and thermally insulated and keptairtight by sandwiching mica rings between a brass clampand the heated pipe and pasting them with liquid packing.

According to results of preliminary measurement with a0.4 mm-diameter static pressure tube, the radial distribu-tion of static pressure was almost uniform over the tra-verse section. Hence, the local air velocity ua was cal-culated from the measured total pressure and the extrap-olated value of the static pressures, measured with thepressure taps at three locations 530, 1130, and 2130 mmupstream of the traverse section. The total pressure wasmeasured using a calibrated 3 mm-OD total pressure tube,which had a ¯attened tube head with a slit opening of

30 lm � 4.5 mm for preventing particle irruption into theinside. In an air-alone test (single phase), ua was measuredwith a calibrated hot-wire anemometer.

The local mass ¯ux of solid particles, mp, in the sus-pension ¯ow was measured by isokinetic sampling with astainless-steel probe having an outside diameter of 3.0 mmand thickness of 0.5 mm, the tip mouth of which wassharp-edged inward. The air-solid suspension was sam-pled for 5±20 min with the air suction velocity at the probemouth, regulated to be equal to the local air velocity ua bymonitoring with a constriction ¯ow meter. Large particleswere collected by inertia and gravitation in a 300 cm3-¯ask, and then the residual ®ne particles were collected ina 1000 cm3-¯ask. The value of mp was determined by di-viding the mass of the collected particles by the samplingtime and the frontal area of the probe mouth. According tothe results of our calibration test and studies by Davies[22] and Badzioch [23], the measurement error of mp dueto slightly erroneous anisokinetic sampling was negligiblein the present experimental range.

The local air temperature Ta was measured using astainless-steel temperature probe, shown in Fig. 3; in thismeasurement, only the carrier air was drawn through thedownstream intake, its ¯ow rate was monitored with theconstriction ¯ow meter, and its temperature was measuredwith a calibrated 25 mm-dia chromel-alumel thermocou-ple placed in the probe head. The measurement error bythis method was within 2% in terms of �Tw ÿ Ta�=�Tw

ÿTb� for y=rw � 0:06 and about )10% at y=rw � 0:055. Inan air-alone test, Ta was measured with a 25 lm-diachromel-alumel thermocouple which was tight-stretchedbetween a couple of 0.3 mm-dia glass tubes.

2.5Experimental proceduresThe inside wall temperature of the pipe, Tw;x;u, at a posi-tion of distance x and angle u was estimated from themeasured outside wall temperature with correction for thethermal resistance across the pipe wall and the thin ad-hesive ®lm. All the pressures, as well as the pressure dropacross the ori®ce, were measured with pressure trans-ducers and Betz manometers.

Fig. 2. Cut-away view of a traverse mechanism for a measuringprobe (not to scale)

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The Joule-heating of the heated section was performedby direct application of alternating current (150±200 A by6±8 V) through the 1.18 mm-thick pipe wall; and theJoule-heating rate was measured by the three-ammetermethod. The Joule-heating of the pipe wall was con®rmedto be satisfactorily uniform in the axial direction.

The local net wall heat ¯ux qx was determined by sub-tracting the local heat loss to the surroundings from theJoule-heating rate per unit heat-transfer area and cor-recting for the conduction loss through the pipe wall. Theheat loss to the surroundings was estimated on the basis ofthe local temperature difference between the pipe wall andthe surroundings, using a precise empirical formula whichwas derived from the results of a preliminary experiment.

The local conduction loss was theoretically predictedusing the measured neighboring wall temperatures. Theconduction loss at both ends of the heated section wasmore precisely estimated from the temperatures measuredwith the thermocouples, which were attached to the re-spective pipes at distances of 0.5-dia and 3-dia from the¯ange joints. According to the measurement results, therewas no discontinuity in the axial temperature distributionnear the joints.

A run of the heat-transfer test was performed as follows:First, the respective mass ¯ow rates of air and solid par-ticles, _Ga and _Gp, were established; then, the electric cur-rent for Joule-heating was applied to the heated section.The heating power was regulated automatically using thesensors and microcomputers. After overall thermal equi-librium of the experimental apparatus/system and steadystate ¯ows of the air and solids had been established, thedata recording was started under steady conditions for allinstruments. The output signals from the pressure trans-ducers, thermocouples, and electric/electronic measure-ment instruments were recorded using self-balancingelectronic potentiometers, except for the solids mass ¯owrate _Gp which was measured ®ve or seven times duringeach run. Time-averaged values of the measured data wereused for the data analysis described in the following sec-tion, though ¯uctuations in the measured values were verysmall.

However, a small temperature variation due to non-uniformity of the pipe wall thickness was found in theazimuthal direction at a given axial location, though it wasless than 1 K even in the air alone tests. Accordingly, in theanalysis of the data obtained in the air-solid suspensiontests, the local wall temperature Tw;x;u was determined asan average of the values which were measured four timesevery p=2-turn of the pipe.

After the desired number of runs for several air mass¯ow rates had been completed at the same solids mass ¯owrate, other series of runs were conducted, during which thesolids mass ¯ow rate was varied at random. During the air-solids runs, check runs were always performed with airalone for detection of any change and substantiation of thereproducibility of the calibration results.

2.6Analysis of dataThe local heat transfer coef®cient hx;u and local Nusseltnumber Nux;u of an air-solid suspension ¯ow are de®nedas

hx;u � qx=�Tw;x;u ÿ Tb;x� �1�Nux;u � hx;ud=ka �2�Here, d is the inner diameter of the pipe, ka the thermalconductivity of air, and Tb;x is the local equilibrium sus-pension bulk temperature, given as

Tb;x � Ta;0 � pdRqxDx=�Gaca � Gpcp� �3�where x is the downstream distance from the inlet, ca andcp the speci®c heat of air and glass beads, respectively.Equation (3) is based on an energy balance between theinlet and location x of the heated section and on the as-sumption that the phases are in thermal equilibrium.

The air Reynolds number Rea is used for the dataanalysis.

Rea � uad=ma �4�where ua is the average air velocity and ma the kinematicviscosity of air. The solids loading ratio, or mass ¯ow-rateratio, M is de®ned as

M � _Gp= _Ga : �5�In this paper, all ¯uid physical properties are evaluated atTb;x, unless otherwise speci®ed.

3Experimental results and discussionExperiments were performed under the conditions ofsteady state, uniform wall heat ¯ux q � 600ÿ2000 W/m2,and a temperature excess of Ts;0 over the ambient tem-perature of 2 K or less. Hence, the radiation effect was notconsidered in the data analysis.

3.1Single-phase flow of air aloneFor ensuring the reliability of the apparatus and veri®ca-tion of the phenomenological performance of the system,several test runs with air alone were initially carried out atvarious Reynolds numbers.

Fig. 3. Air-temperature probe (not to scale; dimensions in mm)

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As for the universal temperature/velocity distributionsin the fully developed region of pure air ¯ow, the mea-sured values for q � 848 and 1670 W/m2 agree well withthose obtained by other investigators [24±31]. It was foundthat such a low heating rate as in the present experimenthas little in¯uence on the universal temperature/velocitydistributions. As to the wall shear stress, the present dataagree with Blasius' empirical formula within a difference of3% .

As for the asymptotic Nusselt number �Nu1�a in athermally fully developed region, the present data showexcellent agreement with the constant property solutionsobtained by Sparrow et al. [32] and are well correlated withthe following equation in the range of Rea � 3� 104ÿ1:2� 105:

�Nu1�a�Tw=Tb�0:55 � 0:0176 Re0:8a : �6�

The local heat transfer coef®cients �hx�a, measured inthe thermally developing region, are plotted in the form ofan azimuthal average in Fig. 4, where �h1�a is the as-ymptotic value for a thermally fully developed ¯ow andRea;o the air Reynolds number, evaluated at the inlet bulktemperature Ta;0. The present data fall within the dataobtained by Sparrow et al. [32] and Mills [33].

Thus, it was concluded that the performance of theexperimental apparatus was suf®cient for the presentpurpose. The details of the experimental results of uni-versal temperature/velocity distributions and asymptoticNusselt numbers for pure air ¯ows are given in Ref. [19].

3.2Air-solids suspension flow

3.2.1Temperature and velocity distributionsin fully developed regionFigures 5a and 5b show the vertical and horizontal dis-tributions, respectively, of the solids mass ¯ux mp in the

both thermally and hydrodynamically developed region ofthe air-solids suspension ¯ow. These were measured atx=d � 140 for q � 896 W/m 2; the average mass ¯ux mp iscalculated from the solids mass ¯ow rate _Gp. At a highReynolds number, both the distributions of mp have apeak or plateau near the pipe center, though the values ofpeak and plateau ¯uctuate within �0:1 approximately; thedistribution pro®les are roughly axisymmetric. The ex-trapolated value of mp=mp is not zero at the wall surface,but 0.53 at u � 0 (bottom wall), approximately 0.2 at�p=2 (side wall), and 0.06 at p (top wall). This may be dueto some particles having been transported by rolling andsliding along the wall surface. At a low Reynolds number,the air ¯ow can hardly induce suf®cient lift of the particlesto prevent their sedimentation due to gravity; conse-quently, larger particles are barely air-conveyed by rollingand bouncing along the bottom wall, and only smallerparticles are suspended and carried by the air ¯ow. Hence,as the Reynolds number decreases, the denser solid phaseshifts to the pipe bottom, and the extrapolated value ofmp=mp varies to be about 1.5 at the bottom, 0.1 at bothsides �u � �p=2�, and almost zero at the top.

A typical vertical distribution of air velocity ua atx=d � 140 is shown in Fig. 6a, in which the data obtained inthe air alone test �M � 0� are also plotted with a dashedline. It is seen by inspection of the ®gure that the location ofthe maximum air velocity shifts from the center to the tophalf of the pipe, as the solids loading ratio M�� _Gp= _Ga� isincreased, and that this tendency is more remarkable at alow Reynolds number. The reason for this is that air ismore apt to ¯ow through the diluter solid phase which

Fig. 4. Local heat transfer coef®cients �hx�a of pure air vs.dimensionless distance x=d. �h1�a: the asymptotic value for athermally fully developed ¯ow

Fig. 5. a Vertical distribution of solids mass velocity mp in boththermally and hydrodynamically developed region of air-solidssuspension ¯ow, measured at x=d � 140 for q � 896 W/m2;b horizontal distribution of mp in fully developed air-solidssuspension ¯ow, measured at x=d � 140 for q � 896 W/m2

114

occurs in the top half, as Rea is decreased. Figure 6b showsthe horizontal distribution of ua having a dual-peak pro®le,which becomes more pronounced with increasing solidsloading ratio M or decreasing Reynolds number Rea. Thisarises from the horizontal distribution of solids mass ¯uxhaving the denser phase around the pipe center, shown inFig. 5b. It should be pointed out that even a low loading-ratio ¯ow of M � 0:16 has a horizontal pro®le of ua whichis appreciably different from that of pure air ¯ow.

Depew and Kramer [1] derived theoretically universalsuspension velocity pro®les on the assumptions valid foraxisymmetric vertical ¯ows, including uniform particledistribution. However, it was impossible to derive suchuniversal pro®les from the present data on horizontal¯ows, as can be seen from Figs. 5±6.

Fully developed vertical and horizontal distributions ofthe air temperature Ta, measured at x=d � 140 forq � 896 W/m 2, are shown in the dimensionless form inFigs. 7a and 7b, respectively. The air velocity near the pipewall, excluding the bottom, is higher than in the case ofpure air ¯ow at the same Rea, owing to the existence of thedenser phase around the pipe center. Generally, the higherthe velocity, the lower is the air temperature for a givenenthalpy. Since the air velocity is lower near the bottom,the air temperature tends to be higher than that in the caseof pure air ¯ow. However, as Rea decreases, the densephase with a great effective heat capacity moves towardthe bottom and suppresses an increase in the local airtemperature there. Consequently, with increasing Rea andM, the distribution of dimensionless temperature�Tw ÿ Ta�=�Tw ÿ Tb� shows such complicated variationsas shown in Figs. 7a and 7b.

It should be added that the measured values of thepressure-loss ratio of suspension ¯ow to pure air ¯ow

Dps=Dpa are in good agreement with Ikemori's empiricalformula [35], as listed in Table 1.

3.2.2Asymptotic Nusselt numberfor fully developed suspension flowFrom an inspection of its axial distribution, the localNusselt number Nux;u is found to be almost constant forx=d of approximately 120 and higher. Hence in this paper,the measured values at x=d � 120 are regarded as the as-ymptotic Nusselt numbers Nu1;u for a suspension ¯ow,though the temperature and velocity distributions weremeasured3 at x=d � 140, as described above.

Figure 8 shows the in¯uence of the solids loadingratio M and air Reynolds number Rea on the asymptoticNusselt number Nu1;u. The Nu1;u which is based on theequilibrium suspension bulk temperature,4 decreases at®rst upon addition of ®ne glass beads to air¯ow; however,after reaching a minimum at a critical loading ratio Mcr, it

Fig. 6. a Typical vertical distribution of air velocity ua in fullydeveloped air-solids suspension ¯ow, measured at x=d � 140 forq � 896 W/m2; b horizontal distribution of air velocity ua in fullydeveloped air-solids suspension ¯ow, measured at x=d � 140 forq � 896 W/m2

Fig. 7. a Vertical distribution of air temperature Ta in fully de-veloped air-solids suspension ¯ow, measured at x=d � 140 forq � 896 W/m2; b horizontal distribution of air temperature Ta infully developed air-solids suspension ¯ow, measured atx=d � 140 for q � 896 W/m2

Table 1. Pressure-loss ratios of suspension ¯ow to pure air ¯ow

Rea M Dps=Dpa

Measured Predicted [35]

6:7� 104 0.16 1.05 1.086:9� 104 1.00 1.28 1.524:1� 104 1.00 1.81 1.91

3The reason for this is that a thermal entrance length based on theconstancy of the heat transfer coef®cient is slightly shorter thanone based on the invariability of the temperature pro®le.4If Nu1;u is de®ned on the basis of air bulk temperature, itincreases upon addition of glass beads [36].

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begins to increase with increasing the loading ratio M.This reduction in Nu1;u at a loading ratio of around Mcr

can be attributed to the action of ®ne solid particles ondamping of the turbulent air ¯uctuations, but little onbreaking up of the viscous sublayer for the present rangeof Reynolds numbers. Han et al. [15] also found theoret-ically for vertical suspension ¯ows of dp=d � �2ÿ6� � 10ÿ4

and Rea � 5:3� 104 that the Nusselt number reaches aminimum at a loading ratio of around unity, mainly due toan increase in the viscous sublayer thickness caused by theturbulence suppression near the pipe wall.

The critical value Mcr depends on both the azimuthalangle u and Reynolds number Rea. Consequently, theNusselt number �Nu1�top for the pipe top �u � p� isgreater than the Nusselt number �Nu1�botm for the pipebottom (u � 0� within the range of M < �Mcr�side. How-ever, at a loading ratio of over �Mcr�side, �Nu1�botm is al-ways greater than �Nu1�top owing to the denser phase nearthe bottom, except in the case of heavy sedimentation.

The in¯uence of M and Rea is more clearly shown inFig. 9, in which the ratio of the suspension Nusselt numberNu1;u to the air Nusselt number �Nu1�M�0 is plotted.Most of the data for Rea � 5:5� 104 and 1:2� 105 fall onor near the respective single curves for the top and side(dashed line) and the bottom (solid line), while the datafor Rea � 3� 104 fall adjacent to the other differentcurves. This indicates that ¯ow and heat transfer mecha-nisms change considerably when Rea exceeds approxi-mately 4� 104, as can be seen from Figs. 5a and 5b. Nev-ertheless, the increasing slope of �Nu1�botm= �Nu1�M�0with M is almost identical for every Reynolds number inthe range of M > �Mcr�botm:

Briller and Peskin [3] performed a heat transfer ex-periment using an isothermal pipe of 78-mm-ID. In Figs. 8and 9, some of their data on the circumferential averageNusselt number are also plotted for the case of 28 lm-diameter glass beads. Their measured values agree com-paratively well with the present data on the uniform heat¯ux pipe of 54.5 mm-ID, though there exist some dis-crepancies owing to the differences between both the ex-perimental conditions. Two years later, they [11] proposeda dimensionless group, n2=3

p dvlp; on the assumptions ofuniform particle distribution and no slip between thephases, and made a comparison with experimental dataobtained by a large number of investigators principally onvertical ¯ows. Here, np is the particle number density, dv

the viscous sublayer thickness of a clear gas ¯ow, and lp

the particle penetration depth into the boundary layer.Since their assumptions do not hold for the present hor-izontal ¯ows, no close correlation with their parameter isfound for the present data of n

2=3p dvlp � 150ÿ1240.

Figure 10 shows the azimuthal distribution of the as-ymptotic Nusselt numbers Nu1;u for M � 0:56 andRea � 8:5� 104. In Fig. 11, the ratios of �Nu1�botm=

Fig. 8. In¯uence of solids loading ratio M�� Gp=Ga� onasymptotic Nusselt number Nu1;u, measured at x=d � 120

Fig. 9. In¯uence of loading ratio M and Reynolds number Rea onthe ratio of suspension Nusselt number Nu1;u to air Nusseltnumber �Nu1�M�0

Fig. 10. Azimuthal distribution of asymptotic Nusselt numbersNu1;u for M � 0:56 and Rea � 8:5� 104

116

�Nu1�top are plotted against the solids loading ratio Malong with Depew and Cramer's data [4], which were ob-tained using an 18 mm-ID uniformly heated pipe and30 lm-dia glass beads. It is seen by inspection of thesedata for M � 2 that none of Depew and Cramer's data arelower than unity, while most of the present data on the54.5 mm-dia pipe are below unity. Moreover, their dataindicates that �Mcr�botm � 2:2 for Rea � 3� 104, but thepresent data in Fig. 9 give a much small value of�Mcr�botm � 0:25, though the minimum value of�Nu1�botm=�Nu1�M�0 obtained by them is almost thesame as the present value 0.68. These discrepancies arisefrom the difference in suspension ¯ow patterns, whichcorrespond to the respective test pipe sizes.

Sukomel et al. carried out a series of experiments [2, 6]on suspension ¯ow of air/graphite particles 65±290 lm indiameter at Rea � 104 ÿ 3� 104. From the results ob-tained using comparatively narrow pipes of 5.3±18.8 mm-ID, they concluded that the pipe diameter and ¯ow ori-entation have no signi®cant in¯uence on suspension heattransfer [6]. It can be pointed out from the above dis-cussions on horizontal suspension ¯ows that a criticalpipe-diameter at which noticeable changes in ¯ow patternand heat transfer occur, exists in the range of 18 mm to54 mm.

3.2.3Heat transfer in developing regionFigures 12 through 18 show the axial distribution of thelocal Nusselt numbers Nux;u in the thermally developingregion for various solids loading ratios and air Reynoldsnumbers. In the ®gures, the local values Nux;u are ren-dered non-dimensional in terms of the respective asymp-totic Nusselt numbers Nu1;u.

The following tendencies may be seen from Figs. 12through 14 for Rea;0 � 6:0� 104. At the pipe top, devel-opment of the thermal boundary layer is retarded mo-notonously with increasing M; namely, the top thermalentrance length on the basis of constancy of Nusseltnumber is prolonged. At the bottom, however, the boun-dary-layer development is enhanced upon increase of Mabove 1, though in the range of M � 1 the developmenttendency is similar to that of the top boundary layer. In

Fig. 11. Nusselt number ratios of �Nu1�botm=�Nu1�top vs. solidsloading ratio M

Fig. 12. Axial distribution of the local Nusselt number Nux;u atpipe top in thermally developing region for Rea;0 � 6:0� 104

Fig. 13. Axial distribution of the local Nusselt number Nux;u atpipe side in thermally developing region for Rea;0 � 6:0� 104

Fig. 14. Axial distribution of the local Nusselt number Nux;u atpipe bottom in thermally developing region for Rea;0 � 6:0� 104

117

particular, as M excesses over 1.7, the bottom thermalentrance length becomes shorter indeed than that for apure air ¯ow. At the sides, development tendency of thethermal boundary layer is in between those of the top andbottom. The shortening effect of the thermal entrancelength peculiar to the bottom was also found in Depew andCramer's experiment [4]. This effect may be due to thetransition from a quasi-axisymmetric ¯ow, having themaximum solids mass ¯ux around the pipe axis, to a ¯owhaving the denser solid phase near the bottom. For thecase of a high Reynolds number of 1:2� 105, similartendencies are recognized from Figs. 15 and 16.

Figures 17 and 18 show plots of the Nux;u=Nu1;u-ratiosfor Rea;0 � 3:2� 104, without subtraction of 1 from thembecause of the wide scatter of the data for M � 1:2. Even incases of the lowest Reynolds number, similar prolongationof the thermal entrance region is observed for M � 0:8.However, according to visual observations using trans-parent glass pipes of the same size, the suspension ¯owpattern changed at M � 1:2; namely, small particles aretransported in the form of a heterogeneous suspensionbeing maintained by turbulence, while large particles areconveyed by saltation, i.e., the particles being alternatelypicked up by the airstream and deposited further along thepipe. The dense solid phase near the bottom increases theeffective heat capacity of the suspensions ¯owing there,while the particles deposited on the bottom act as a ther-mal resistance layer. Accordingly, in the case of M � 1:2,the heat transfer rate ¯uctuates, and the distributions of�Nux=Nu1�top and �Nux=Nu1�botm become discontinuous,as shown in the ®gures.

Sukomel et al. [2] correlated their data on the azimuthalaverage Nusselt numbers Nux with the following empiricalexpression:

Nux=�Nux�M�0 � �Nu1=�Nu1�M�0�� �1� Asexp�ÿmx=d�� ; �7�

where As and m are the experimental constants. However,it was almost impossible to correlate the present data inthe form of their expression. The reason for this is that the

¯ow pattern and heat transfer mechanisms of pure air ¯owhave no direct relationship to those of an air-solids sus-pension ¯ow, because the addition of a small quantity of®ne glass beads greatly distorts the velocity and temper-ature pro®les of pure air ¯ow (see Figs. 6 and 7) andmakes the thermal entrance length much longer than thatin the case of pure air ¯ow. The present data could becorrelated with expressions in the following forms, exceptfor those for the pipe bottom at large loading ratios andlow Reynolds numbers.

�Nux=Nu1�u � 1� AA�x=d�ÿn for �x=d� < CA �8��Nux=Nu1�u � 1� BAexp�ÿpx=d� for �x=d� � CA

�9�where AA; BA; CA��6ÿ30�, n and p are experimentalconstants which depend on u; M, and Rea.

4ConclusionsA careful experiment was carried out on heat transfer of ahorizontal air-solids suspension ¯ow over the ranges of

Fig. 15. Axial distribution of the local Nusselt number Nux;u atpipe top in thermally developing region for Rea;0 � 1:2� 105

Fig. 16. Axial distribution of the local Nusselt number Nux;u atpipe bottom in thermally developing region for Rea;0 � 1:2� 105

Fig. 17. Axial distribution of the local Nusselt number Nux;u atpipe top in thermally developing region for Rea;0 � 3:2� 104

118

Reynolds number Rea � 3� 104ÿ1:2� 105 and solidsloading ratio M � 0ÿ3. The results obtained are summa-rized as follows.

The fully developed distributions of solids mass ¯ux areroughly axisymmetric at a high Reynolds number; how-ever, at a low Reynolds number, a dense solid phase ap-pears near the pipe bottom. The radial distributions of airvelocity/temperature in both thermally and hydrodynam-ically developed region are in¯uenced by the location ofthe dense solid phase with a large effective heat capacity;these pro®les are distorted by addition of even a very smallquantity of solid particles to the air ¯ow. As M increases orRea decreases, the highest velocity zone shifts to the tophalf of the pipe, and the horizontal velocity pro®le comesto have dual peaks. Thus, the air temperature distributionshows complicated variations with increasing Rea and M.

Regardless of azimuthal angle u, every asymptoticsuspension Nusselt number ®rst decreases, due to turbu-lence suppression caused by addition of ®ne glass beads;however, after reaching a minimum at a critical loadingratio, it begins to increase with increasing M. The criticalloading ratio depends on both u and Rea. By comparingwith data obtained by others, the in¯uence of the Reynoldsnumber and solids loading ratio on ¯ow and heat transfermechanisms were discussed, and the existence of a criticalpipe-diameter at which noticeable changes in them occurwas predicted.

Various in¯uences of the Reynolds number, solidsloading ratio, and azimuthal/longitudinal locations on thelocal Nusselt numbers in the thermally developing regionwere examined in detail. In the range of Rea � 6� 104ÿ1:2� 105, development of the thermal boundary layer atthe pipe top is retarded monotonously with increasing M.On the other hand, that of the bottom boundary layer isenhanced upon increase of M above 1. The development

tendency of the side thermal boundary layer is betweenthose of the top and bottom.

At a low Reynolds number of 3:2� 104, the suspension¯ow pattern changes so markedly at M � 1:2 that largeparticles are conveyed by saltation and the axial distri-butions of the top and bottom Nusselt numbers becomediscontinuous.

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