flow and heat transfer in narrow channels with corrugated walls a cfd code application

FLOW AND HEAT TRANSFER IN NARROWCHANNELS WITH CORRUGATED WALLS

A CFD Code Application

A. G. KANARIS, A. A. MOUZA and S. V. PARAS�

Department of Chemical Engineering, Aristotle University of Thessaloniki, Thessaloniki, Greece

In an effort to obtain information on the local flow structure inside compact heatexchangers made of corrugated plates, a commercial CFD code (CFXw) is employedto simulate the flow through an element of this type of equipment. For simplicity, the

channel used for the simulation is formed by only one corrugated plate, while the otherplate is flat. A two-equation turbulence model (SST) is used for the calculations and, inaddition to isothermal flow, heat transfer simulations are conducted for a Reynolds numberrange (400–1400), for the case of hot water (608C) in contact with a constant-temperaturewall (208C). The results, presented in terms of friction factor, wall shear stress, wall heatflux and local Nusselt numbers, are consistent with the description of the fluid motioninside similar conduits by other investigators. The calculated mean heat transfer coefficientsand friction factors are found to be in reasonable agreement with the limited publishedexperimental data.

Keywords: compact heat exchanger; narrow channel; corrugation; CFD; Nusselt number;pressure drop.

INTRODUCTION

The development of compact heat exchangers has beenmainly driven by the need for economical, high performance,yet small in size and light weight equipment. Novel compactheat exchangers made of corrugated plates hold significantadvantages over conventional equipment. Plate exchangerswith corrugated walls provide a large surface area tovolume ratio and enhanced heat transfer coefficients, whileallowing ease of inspection and cleaning (Kays andLondon, 1998; Shah and Wanniarachchi, 1991). Such typesof exchangers, like the herringbone or the chevron type, arebeing rapidly adapted by food, chemical and refrigerationprocess industries replacing shell-and-tube exchangers.Unfortunately, unlike the conventional heat exchangers,there is lack of a generalized design method for plate heatexchangers. Variations in design of the basic geometricalfeatures (e.g., aspect ratio, inclination angle of the corruga-tions) make it almost impossible to generate an adequateheat transfer database covering all possible configurations.The heat transfer augmentation in conduits with corru-

gated walls is accompanied by a substantial increase inpressure drop. An optimum design must involve a balancebetween friction losses and heat transfer rates and thus the

designer must decide how to trade off between these twofactors. Nevertheless, the requirement for detailed andaccurate measurement of the design parameters (e.g.,temperature, pressure and velocity fields) is very difficultto be achieved, because the flow passages in compactheat exchangers are complex in geometry and of relativelysmall dimensions. The rapid development of computationaltools permits the prediction of flow characteristics usingCFD code simulation which is considered an effectivetool to estimate momentum and heat transfer rates in thistype of process equipment. Consequently, as CFD ismore widely used in engineering design, it is becomingof essential importance to know how reliably the flowfeatures and the hydrothermal behaviour can be reproducedin such conduits.

Kays and London (1998) state that the applicable rangeof Reynolds numbers for compact heat exchangers isbetween 500 and 15 000. In addition, when these equip-ments are used as reflux condensers the limit imposed bythe onset of flooding reduces the maximum Reynoldsnumber to a value less than 2000 (Paras et al., 2001).The type of flow prevailing in such narrow passages isstill an open issue. Shah and Wanniarachchi (1991) declarethat, for the Reynolds number range 100–1500, there isevidence that the flow is turbulent. Heggs et al. (1997)suggest that pure laminar flow does not exist in theReynolds number range they tested (150–11,500) and sup-port their conclusion by studying local transfer coefficients.Ciofalo et al. (1998), in a comprehensive review article

�Correspondence to: Professor S. V. Paras, Department of ChemicalEngineering, Aristotle University of Thessaloniki, Univ. Box 455, GR54124 Thessaloniki, Greece.E-mail: [email protected]

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0263–8762/05/$30.00+0.00# 2005 Institution of Chemical Engineers

www.icheme.org/journals Trans IChemE, Part A, May 2005doi: 10.1205/cherd.04162 Chemical Engineering Research and Design, 83(A5): 460–468

concerning modelling heat transfer in narrow flowpassages, state that, in the Reynolds number range of1500–3000, transitional flow is expected, a kind of flowamong the most difficult to simulate using conventionalturbulence models. Recently, Vlasogiannis et al. (2002),who experimentally tested a plate heat exchanger undersingle and two-phase flow conditions, verify that the flowis turbulent for Re . 650. Lioumbas et al. (2002), whostudied experimentally the flow in narrow passagesduring counter-current gas–liquid flow, suggest that theflow exhibits the basic features of turbulent flow evenfor the relatively low gas Reynolds numbers tested(500 , Re , 1200). Focke and Knibbe (1986) performedflow visualization in narrow passages with corrugatedwalls using an electrode-activated pH reaction. They con-cluded that the flow patterns in such geometries are verycomplex and suggested that the local flow structure controlsthe heat transfer process in the narrow passages. The salientfeature of the flow is the existence of secondary swirlingmotions along the furrows of their test section.The choice of the most appropriate turbulence model

for CFD simulation is another open issue in the literature.The most common two-equation model, based on theequations for the turbulence energy k and its dissipation1, is the k–1 model (Davidson, 2001). Ciofalo et al.(1998) state that the standard k–1 model using ‘wallfunctions’ overpredicts both wall shear stress and wallheat flux, especially for the lower range of the Reynoldsnumber encountered in this kind of equipment. Menterand Esch (2001) note that the overprediction of heattransfer is caused by the overprediction of turbulentlength scale in the region of flow reattachment, which isa characteristic phenomenon appearing on the corrugatedsurfaces in these geometries.An alternative to the k–1 model is the k–v model devel-

oped by Wilcox (1988). The k–v model, which uses theturbulence frequency v in place of turbulence dissipation1, appears to be more robust, even for complex appli-cations, and does not require very fine grid near the wall(Davidson, 2001). The main disadvantage of k–v modelis its sensitivity to the free stream values of turbulence fre-quency v outside the boundary layer, which affects thesolution and, in order to avoid this, a combination of thetwo models, k–1 and k–v, i.e., the SST (Shear-StressTransport) model is proposed (Menter and Esch, 2001).The SST model can switch automatically between thetwo aforementioned turbulence models using specific‘blending functions’ that activate the k–v model near thewall and the k–1 model for the rest of the flow. Althoughthe SST model combines the most widely usedtwo-equation turbulence-models, other models, like LES(Large-Eddy Simulation) is considered more appropriatein turbulent flow simulation. However, the LES model isconsidered less robust and requires high-computationalpower (Ciofalo et al., 1998).Due to the modular nature of a compact heat exchanger,

a common practice for computational expense reasons is tothink of it as composed of a large number of unit cells(RES, Representative Elementary Unit). The results areobtained using a single cell as the computational domainand imposing periodicity conditions across its boundaries(e.g., Ciofalo et al., 1998; Mehrabian and Poulter, 2000;Blomerius and Mitra, 2000). However, since the validity

of this assumption is not generally accepted in the literature(Ciofalo et al., 1998), an alternative method is to considerthe complete corrugated plate as the computational domain,but this results in an increase of both computational spaceand time.

In a previous work in this Laboratory (Paras et al., 2001)the flow in a vertical channel of a model plate heatexchanger was studied. This model, manufactured byVICARB-Alfalaval, comprises of two plates havingcorrugations machined at a 458 angle and two side-channels[Figure 1(a)]. The experiments revealed that, duringcounter-current gas–liquid flow (which resembles the flowwhen this equipment is used as a condenser), the sidechannels play a significant role in the liquid flow throughthe furrows of the corrugations, promoting even distri-bution. The lateral drainage into the side-channels tends toincrease with increasing gas flow rate, leading to a progress-ive elimination of the liquid film. This situation, referred toas ‘maldistribution’, is considered favourable for the oper-ation of such a device as a condenser, because of theexposure of nearly ‘fresh’ wall to the condensing vapours.

In this paper, CFD modelling is employed to investigatethe flow and thermal characteristics within the complicatedpassages of a plate heat exchanger as described above.The approach used here is based on a more complex geo-metry consisting of a whole channel instead of a singlecell. More specifically, the solution domain employed,due to computational power limitations, is a simplificationof the real conduit and comprises of one corrugated and oneflat plate, adjacent to each other. Nevertheless, the resultsfrom this simplified geometry can be used to study thebasic features of the flow inside narrow channels with cor-rugated walls and to validate the CFD code. Experimentalresults on overall pressure drop, obtained from a Plexiglasw

test section of the same geometry, are compared to thecalculated values. Information on local heat transfer coeffi-cients is also obtained and validated with data from theliterature, in order to quantitatively evaluate the thermalperformance of a corrugated-plate compact heat exchangerwith side-channels. In addition, the flow pattern prevailinginside the furrows and the side-channels of the conduit,which affects the local momentum and heat transfer ratesof this type of equipment, is predicted.

MODEL PARAMETERS AND SOLUTIONPROCEDURE

The geometry studied in the present simulations isconsistent with an existing compact heat exchangerdescribed in detail elsewhere (Paras et al., 2001). ThePlexiglasw text section is formed by two plates, 70 cmhigh and 15 cm wide, which simulates a vertical channelof a corrugated plate heat exchanger. On each plate, corru-gations are machined at a 458 angle, as well as side-chan-nels [Figure 1(a)]. The two plates were superposed so thatthe opposite corrugations formed a cross-type pattern withthe crests of the corrugations nearly in contact. However,in order to keep the computational demands at acceptablelevels, a simpler channel is studied. This channel is formedby only one of the corrugated plates [Figure 1(b)], which iscomprised of fourteen equal sized and uniformly spacedcorrugations and two side-channels (Figure 2), while thesecond plate is flat. Details of the corrugated plate

Trans IChemE, Part A, Chemical Engineering Research and Design, 2005, 83(A5): 460–468

FLOW AND HEAT TRANSFER IN NARROW CHANNELS 461

geometry are presented in Figure 2 and Table 1. Thesimpler case of single-phase flow of water is investigatedhere.The Reynolds number is defined at the conduit

entrance as:

Re ¼ u � d � rm

(1)

where u is the fluid velocity defined as Q/A, Q is the volu-metric flow rate, A is the flow cross section at the entrance,d is the distance between the plates at the conduit entrance(d ¼ 10 mm), while r and m are the density and theviscosity of the fluid respectively, at entrance conditions,calculated by the CFD code. The Reynolds numbers exam-ined (400, 900, 1000, 1150, 1250, 1400) lay at the lowerpart of the compact heat exchanger operability range andcorrespond to the working conditions of reflux condensers.It must be noted that the definition of Reynolds number isan open issue in literature, as the geometry of these devicesdo not allow a unique calculation method.

In this study, in addition to isothermal flow, heat transfersimulations are carried out for the same Reynolds numbers,where hot water (608C) is cooled in contact with a constant-temperature wall (208C). The latter case is realized incondensers and evaporators. Additionally, it is assumed

Figure 1. Model plate heat exchanger: (a) view of two superposed corrugated plates; (b) detail of a single plate with side channels.

Figure 2. Geometry of the CFD model and sectional view of a corrugation.

Table 1. Plate geometric characteristics.

Plate length 0.200 mPlate width 0.110 mMaximum spacing between plates, d 0.010 mNumber of corrugations 14Corrugation angle 458Corrugation pitch, h 0.005 mCorrugation width, w 0.014 mPlate length before and after corrugations 0.050 mChannel (groove) width 0.005 mHeat transfer area 2.7 � 1022 m2


462 KANARIS et al.

that heat is transferred only through the corrugated plate,while the rest of the walls are considered adiabatic.A commercial CFD code, namely CFXw version 5.6,

developed by AEA Technology, was employed to exploreits potential for computing detailed characteristics of thiskind of flow. The code uses a finite volume approach,and the simulation is performed in steady state. The gridsize used is chosen by performing a grid dependencestudy, since the accuracy of the solution depends onthe number and the size of the cells (Versteeg andMalalasekera, 1995). The grid dependence study wasconducted by altering the cell size inside the channel, andby refining the grid size on the corrugated wall.To overcome computer power limitation, a compromise

was made and the SST model was preferred to LESmodel in the calculations, as mentioned previously. Themean velocity of the liquid phase was applied as boundarycondition at the channel entrance (i.e., Dirichlet boundarycondition on the inlet velocity) and no-slip conditions onthe channel walls. A constant temperature boundarycondition was applied only at the wall of the plate withthe corrugations (including the flat entry and exit sections),whereas the rest of the plate walls are considered adiabatic.The choice of constant temperature on the wall wasselected for simplicity, by assuming that on the other sideof the wall, the flow rate of the cool fluid is high enoughto ensure this condition.Calculations were performed on a SGI O2 R10000 work-

station with a 195MHz processor and 448 Mb RAM. TheCFXw 5.6 code uses a finite volume method on a non-orthogonal body-fitted multi-block grid. Unstructuredtetrahedral mesh was used, modified near the walls byapplying prism layers, in order to simulate the wall bound-ary layer accurately. The use of prism layers on the walls isadvised for confined geometries (CFXw Manual, 2003).The mesh was also checked for inappropriate generatedcells (e.g., tetrahedral cells with sharp angles) and fixedand the final number of cell elements was 870,000. In thepresent calculations, the CFD code uses a method similarto that used by Rhie and Chow (CFXw Manual, 2003)with the SIMPLEC algorithm for pressure-velocity decou-pling and the QUICK scheme for discretisation of themomentum equations (Versteeg and Malalasekera, 1995;CFXw Manual, 2003). The grid was constructed usingCFXw-Build 5.6 and ICEM CFD 4.CFX, while CFXw-Post was used for post-processing. The normalized massresidual, i.e., the measure of the local imbalance of eachconservative volume equation (CFXw Manual, 2003) isused by the CFD code as the convergence criterion andits value was set to be less than 1028.

RESULTS AND DISCUSSION

The results of the present study confirm the dominantrole of the side-channels in flow distribution and suggestthat fluid flow is mainly directed to the right side-channelof this model plate (Figure 3). Part of the fluid flows overthe corrugation crests and after being ‘reflected’ on theright side wall, follows the furrows and reaches the oppo-site side-channel. It appears that if two corrugated plateswith angles þ458 and 2458 were superposed (as in a realheat exchanger) part of the fluid phase would also bedirected to the right channel, creating a symmetrical overall

flow distribution. Experiments performed in this Labora-tory (Paras et al., 2001) suggest that the above flow distri-bution promotes the drainage of the liquid phase throughthe side-channels in counter-current two-phase flow.

This type of flow behaviour is also described by Fockeet al. (1985), who made visual observations of the flowbetween two superposed corrugated plates without sidechannels. They confirm that the fluid, after entering afurrow, mostly follows it until it reaches the side wall,where it is reflected and enters the anti-symmetricalfurrow of the plate above, a behaviour similar to the onepredicted by the CFD simulation. More specifically, thevelocity inside the left side-channel progressively increases[Figure 4(a)], while that in the right side-channel decreases[Figure 4(b)]. It seems that most of the flow passes throughthe furrows, where enhanced heat transfer characteristicsare expected, a fact that is also reported by Heggs et al.(1997).

Figure 5 shows details of the flow inside a furrow, wheresecondary, swirling flow is identified. It is suggested(Heggs et al., 1997) that this kind of secondary flow isthe result of interaction between the flow inside thenarrow channel and the highly accelerated flow over thecrest. This flow is considered capable of bringing newfluid from the main stream close to the walls, augmentingheat transfer rates. Focke and Knibbe (1986) describealso this kind of swirling flow. Blomerius and Mitra(2000) have also observed longitudinal vortices in narrowchannels, while Won et al. (2003) consider this secondaryflow responsible for the increase in turbulence shearstress and turbulence production.

A typical distribution of the z-component of shearstress is presented in Figure 6 for Re ¼ 1400, since the

Figure 3. Typical flow pattern (streamlines) inside the channel, predictedby CFD; Re ¼ 900.



distribution is similar for all Re numbers. Shear stressincreases with Reynolds number, as expected, and it attainsits maximum value at the crests of the corrugations. It maybe argued here that, during gas–liquid counter-current flowin such geometries, this shear stress distribution tends toprevent the liquid layer from falling over the crest of thecorrugations and to keep it inside the furrows. The visualobservations of Paras et al. (2001) seem to confirm theabove behaviour.Wall heat flux through the corrugated plate was predicted

by the CFD code [Figure 7(a)]. The local Nusselt number,

Nux, was then calculated (by means of a Fortran subroutine)using the expression:

Nux ¼ q � d(Tb � Tw)k

(2)

where q is the local wall heat flux, d the distance betweenthe plates at entrance, Tw the wall temperature, Tb

Figure 4. Velocity vectors inside channels: (a) left-side channel; (b) right-side channel.

Figure 5. Swirling flow inside a furrow; Re ¼ 900.Figure 6. Wall y-shear stress distribution on the corrugated plate;Re ¼ 1400.


464 KANARIS et al.

the local fluid temperature and k the thermalconductivity of the fluid. The local fluid temperatureover a point of the plate wall, Tb, is the average fluidtemperature calculated by numerical integration of thefluid temperature across a line vertical to the corrugatedwall at this point. In addition to the local Nusseltnumber various modified ‘Nusselt numbers’ were evalu-ated as follows:

. a mean Nusselt number, Nuc, calculated by numericallyintegrating the local Nu over the corrugated area only;

. an overall average Nusselt number, Nuave, calculated bynumerically integrating the local Nu over the wholeplate;

and their values are presented in Table 2. These ‘Nusseltnumbers’ were calculated in CFXw-Post using a functionthat computes the average value of a variable by takinginto account the mesh element sizes. It must be notedthat in an effort to validate the CFD code predictions,values of Nuave for the smooth plate were computed byCFXw and are found to be in accordance with analyticallyobtained results. These non-dimensional quantities are alsocalculated in order to study the effect of non-corrugatedarea to the whole heat transfer augmentation.

Figure 7 shows typical wall heat flux and local Nusseltnumber distributions over the corrugated wall forRe ¼ 1400. The distributions of heat flux and Nu aresimilar for all Reynolds numbers studied. It is noticeablethat on the top of the corrugations the local Nusseltnumber attains its maximum value. Heggs et al. (1997)also notice that the mass and heat transfer performance exhi-bits peaks on the crests of the corrugations. This confirms thestrong effect of the corrugations, not only on the flow distri-bution, but also on the heat transfer results. Ligrani and Oli-veira (2003) also denote that vortices and secondary flows ingeneral contributes in heat transfer augmentation, as theyincrease secondary advection of fluid between the centralparts of the channel and the near-wall region, and provideregions of high turbulence production. Secondary flowsalso decrease the probability of appearance of stagnationareas that promote heat and mass transfer.

To the best of the authors’ knowledge, experimentalmeasurements of heat transfer and pressure drop for thecorrugated plate geometry under consideration are notavailable in the open literature. In an effort to validatethe simulation results, data by Heavner et al. (1993),Vlasogiannis et al. (2002) and Ligrani and Oliveira(2003) are used. The data by Vlasogiannis et al. (2002)concern measurements of the heat transfer coefficientsboth for single (Re , 1200) and two-phase flow in aplate heat exchanger with two corrugated walls and acorrugation inclination angle of 608. It should be alsonoted that heat exchangers used in Vlasogiannis et al.(2002) and Heavner et al. (1993) experiments lack theside channels employed in the present simulation.The results presented by Ligrani and Oliveira (2003) con-cern geometries with rib turbulators in 458 continuousarrangements.

In heat exchanger analysis j-Colburn factor, commonlyused to express the heat coefficients, is defined as (Blomeriusand Mitra, 2000):

j ¼ Nu

Re Pr1=3(3)

Figure 7. Heat transfer results for Re ¼ 1400: (a) wall heat flux distri-bution on the corrugated plate; (b) local Nu distribution on the corrugatedplate.

Table 2. Nusselt number: calculated and experimental data (Vlasogianniset al., 2002).

Re Nuave Nuc Nuvlasog 65% Nuvlasog Nusm Nu/Nusm

400 20.7 20.5 13.2 8.6 — —900 27.5 27.3 38.0 24.7 9.4 2.91000 28.8 28.6 41.2 26.8 10.2 2.81150 30.0 28.8 44.2 28.7 11.0 2.71250 31.1 30.9 46.8 30.4 11.7 2.71400 32.2 32.0 49.5 32.2 12.5 2.6



In Figure 8 the j-Colburn factor values, calculated usingNuc, are compared with experimental values for variousReynolds numbers. Focke et al. (1985), who measuredheat transfer coefficients in a corrugated plate heatexchanger by placing a partition of celluloid sheetbetween the two plates, report that the overall heat trans-fer rate is reduced to 65% of the value for the plates with-out the partition. This statement was taken into account, inan effort to compare the CFD results of this study with theexperimental data by Vlasogiannis et al. (2002), which areacquired in similar geometries but with two corrugatedplates. Thus, the results are found to be in good agreementwith the 65% of the corresponding experimental values.The exponent of Re in the resulting correlation has avalue 0.42 which agrees with that proposed in the litera-ture. The above remark holds true for all Reynolds num-bers except for the smallest one (Re ¼ 400). In the lattercase the Nusselt number, and consequently the j-factor, isgreatly overpredicted by the CFD code. This is not unex-pected, since a two-equation turbulence model is notcapable of correctly predicting the heat transfer character-istics for such low Reynolds numbers.Since the Nusselt numbers for the corrugated area (Nuc)

and the overall average Nuave (Table 2) have practicallythe same value, it can be concluded that the presenceof the smooth part of the plate does not significantly influ-ence the heat transfer coefficient. Consequently, the pre-sence of the side-channels, whose area is only a smallpercentage of the total plate area, apart from inhibitingflooding (Paras et al., 2001), seems to have practically noeffect on the thermal behaviour of the plate in singlephase flow.In an effort to validate the CFXw code, the CFD predic-

tions were checked against the corresponding values for thesmooth wall plate calculated by an analytical method(White, 1991) and found to be in excellent agreement, asexpected. The pressure drop for the corrugated plate wasalso predicted by the CFD code, converted into terms offriction factor and compared with experimental datacollected in this Laboratory (Table 3). Figure 9 presents

the friction factor experimental data and CFD predictionsfor the corrugated plate as a function of the Reynoldsnumber. It appears that the experimental values follow apower law of the form:

f ¼ mRe�n (4)

where m and n are constants with values 0.27 and 0.14,respectively. Heavner et al. (1993) propose a similarempirical correlation based on their experimental resultson a plate heat exchanger with 458 corrugation angle, butwith two corrugated plates and without side channels. Itmust be noted that, in spite of the differences in geometry,the slope of the correlation derived from the present datahas the same value with the one proposed by Heavneret al. (1993).

Figure 10 presents the normalized values of Nuave and fobtained both from the present study (Tables 2 and 3) andthe work by Taslim and Wadsworth, as referred by Ligraniand Oliveira (2003), concerning a 458 continuous ribarrangement. Values of Nuave and f are normalized by thecorresponding values from a smooth plate heat exchanger,in order to evaluate the heat transfer augmentation versusthe friction losses increase due to the existence of corruga-tions. The CFD results are once more in agreement with theexperimental results taking under consideration that the ribarrangement setup, justifies an increase in heat transfer,which is attributed to the existence of ribs on both sidesof the plate heat exchanger.

Table 3. Friction factor: calculated and corresponding experimental data.

Re fexp fcfx fsm f/fsm

900 0.1044 0.0915 0.0074 12.41000 0.1025 0.0886 0.0069 12.81150 0.1020 0.0866 0.0064 13.51250 0.0984 0.0850 0.0061 13.91400 0.0981 0.0839 0.0058 14.5

Figure 9. Friction factor vs. Reynolds number.

Figure 8. j-Colburn factor vs. Reynolds number.


466 KANARIS et al.

CONCLUDING REMARKS

The present work examines the ability of a commercialCFD code to predict the flow and heat transfer character-istics in a narrow channel with corrugated wall, with acertain corrugation angle, width and height. The use of aCFD code allows computation for various geometricalconfigurations, in order to evaluate their effects and tostudy them closely. In this way the engineer is able to opti-mize the efficiency (i.e., maximize the ratio of heat transferto friction losses) for a given geometry.The simulation results reveal that, compared to a

smooth-wall plate heat exchanger, corrugations improveboth flow distribution and heat transfer. The comparisonof Nusselt number values for the simplified model showsthat the side-channels, besides improving the operabilityof the heat exchanger by shifting the flooding limit tohigher gas velocities when used as reflux condensers(Paras et al., 2001), do not affect the overall heat transferaugmentation negatively. Pressure drop, a variable thatcould also trigger interest on economically optimizinga plate heat exchanger, has, as expected, higher valuescompared to a smooth plate channel.Additional experimental work is needed, and indeed is in

progress in this laboratory, to obtain more data in order tovalidate the results of the present work. More specifically,local velocity profile determination will clarify the type offlow prevailing in such geometries, while local temperaturemeasurements will allow the prediction of heat transfer rates.

NOMENCLATURE

A cross section area at the entrance of the channeld distance between the plates at the entrance of the channel,

equation (1)f friction factork fluid thermal conductivitym constantn constantNux local Nusselt number

Nuc mean Nu calculated by numerical integration over thecorrugated area

Nuave average Nu calculated using the total wall heat flux through thewhole corrugated plate

Nusm average Nu calculated using the total wall heat flux through thewhole smooth plate

Pr Prandtl numberQ volumetric flow rateq local wall heat fluxRe Reynolds numberTb local fluid temperatureTw wall temperatureu mean velocity at channel entrance

Greek letters1 turbulence energy dissipationm viscosityr densityf corrugation angle

REFERENCES

Blomerius, H. and Mitra, N.K., 2000, Numerical investigation of convec-tive heat transfer and pressure drop in wavy ducts, Numerical HeatTransfer, Part A, 37: 37–54.

CFXw Release 5.6 User Guide, 2003, AEA Technology, CFX Inter-national, Harwell, Didcot, UK.

Ciofalo, M., Collins, M.W. and Stasiek, J.A., 1998, Flow and heat transferpredictions in flow passages of air preheaters: assessment of alternativemodeling approaches, in Sunden, B. and Faghri, M. (eds). ComputerSimulations in Compact Heat Exchangers (Computational MechanicsPubl., UK).

Davidson, L., 2001, An Introduction to Turbulence Models, Department ofThermo and Fluid Dynamics, Chalmers University of Technology,Publication 97/2 (Goteborg, Sweden).

Focke, W.W. and Knibbe, P.G., 1986, Flow visualization in parallel-plateducts with corrugated walls, J Fluid Mech, 165: 73–77.

Focke, W.W., Zachariades, J. and Olivier, I., 1985, The effect of thecorrugation inclination angle on the thermohydraulic performance ofplate heat exchangers, Int J Heat Mass Transfer, 28: 1469–1497.

Heavner, R.L., Kumar, H. and Wanniarachchi, A.S., 1993, Performanceof an industrial plate heat exchanger: effect of chevron angle, AIChESymp Ser No 295, Vol 89, Heat Transfer, Am Inst Chem Eng, Atlanta,GA, 262–267.

Heggs, P.J., Sandham, P., Hallam, R.A., Walton, C., 1997, Local transfercoefficients in corrugated plate heat exchangers channels, TransIChemE, Part A, Chem Eng Res Des, 75(A7): 641–645.

Kays, W.M. and London, A.L., 1998, Compact Heat Exchangers, 3rdedition (Krieger Publ. Co., Florida, USA).

Ligrani, P.M. and Oliveira, M.M., 2003, Comparison of heat transferaugmentation techniques, AIAA Journal, 41(3): 337–362.

Lioumbas, I.S., Mouza, A.A. and Paras, S.V., 2002, Local velocities insidethe gas phase in counter current two-phase flow in a narrowvertical channel, Trans IChemE, Part A, Chem Eng Res Des, 80(6):667–673.

Mehrabian, M.A. and Poulter, R., 2000, Hydrodynamics and thermalcharacteristics of corrugated channels: computational approach, AppliedMathematical Modeling, 24: 343–364.

Menter, F. and Esch, T., 2001, Elements of industrial heat transfer predic-tions, 16th Brazilian Congress of Mechanical Engineering (COBEM),26–30 Nov. 2001, Uberlandia. Brazil.

Paras, S.V., Drosos, E.I.P., Karabelas, A.J. and Chopard, F., 2001,Counter-current gas/liquid flow through channels with corrugatedwalls—visual observations of liquid distribution and flooding, WorldConference on Experimental Heat Transfer, Fluid Mechanics &Thermodynamics, September 24–28, Thessaloniki, Greece.

Shah, R.K. and Wanniarachchi, A.S., 1991, Plate heat exchanger designtheory, in Buchlin, J.M. (ed.). Industrial Heat Exchangers, vonKarman Institute Lecture Series 1991–2004.

Versteeg, H.K. and Malalasekera, W., 1995, An Introduction to Compu-tational Fluid Dynamics (Longman Press, London, UK).

Vlasogiannis, P., Karagiannis, G., Argyropoulos, P. and Bontozoglou, V.,2002, Air–water two-phase flow and heat transfer in a plate heatexchanger, Int J Multiphase Flow, 28(5): 757–772.

Figure 10. Globally averaged Nusselt number ratio vs. friction factor ratio.



White, F.M., 1991, Viscous Fluid Flow, 2nd edition (McGraw-Hill Inc.,New York, USA).

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Won, S.Y., Mahmood, G.I. and Ligrani, P.M., 2003, Flow structure andlocal Nusselt number variations in a channel with angled crossed-ribturbulators, Int J Heat Mass Transfer, 46: 3153–3166.

ACKNOWLEDGEMENTS

The authors wish to thank Professor A.J. Karabelas for his helpfulcomments and suggestions and Mr A. Lekkas for the technical support.

The manuscript was received 2 June 2004 and accepted for publicationafter revision 17 February 2005.


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flow and heat transfer in narrow channels with corrugated walls a cfd code application

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