Heat transfer augmentation in a circular tube with winglet vortex generators☆

Suriya Chokphoem phun,M onsak Pim sarn,Chinaruk Thianpong,Pongjet Prom vonge*

Department of Mechanical Engineering,Faculty of Engineering,King Mongkut's Institute of Technology Ladkrabang,Bangkok 10520,Thailand

Keyw ords:Nusselt number Friction factor Therm al enhancement factor winglet Vortex generator

ABSTRACT The article presents the influence of winglet vortex generators(W VGs)placedin the core flow area on thermal performance enhancement of a tube heat exchanger.The experiment was carried out in a uniform wall heat-fluxed tube by varying turbulent airflow for Reynolds number ranging from 5300 to 24000.In the present work,the WVGs with an attack angle of 30°were insertedin to the test tube at four different winglet pitch ratios(R P=P/D)and three winglet-width or blockage ratios(R B=e/D).The experimental results at various R P and R B values were evaluated and com pared with those for smooth tube and tubes with twisted tape or wire coil.The measurement reveals that the W VGs enhance considerably the heat transfer and friction loss above the plain tube,wire coil and twisted tape.The Nusselt number and friction factor increase with the increment of R B and Re bu t with the decreasing R P.The average Nusselt numbers for the WVGs with various R B are in the range of 2.03-2.34 times above the plain tube.The thermal performance for the WVGs is found to be much higher than that for the wire coil and twisted tape andis in a range of 1.35-1.59.Also,an umerical investigation is conducted to study the flow structure and heat transfer enhancement mechanism s in the winglet-inserted tube.

1.Introduction

Passive enhancement techniques by tube inserts are widely used for augmenting the heat transfer rate in a heat exchanger because this method can be easily em ployedin an existing heat exchanger without requiring an additional power source.Insertion of devices to generate the vortex/swirl flow such as twisted tapes,wire coils,ribs,fins,baffles,wing lets etc.,in the flow passage to enhance the convective heat transfer rate is the most comm only know n in many thermal system s.In general,the objective of enhanced heat transfer is to make the heat exchangers mo re com pact to reduce overall sizes of the heat exchanger,possibly their cost or to reduce the pumping power required for a given heat transfer target,which can result in a saving of operating costs.Therefore,m any investigations have been carried out to study the effect of tu rbu lators on heat transfer enhancement in the heat exchanger.The con jugate heat transfer and thermal stress in a tube with coiled wire inserted under a uniform wall heat-flux was numerically investigated by Ozceyhan[1],while the heat transfer and pressure drop characteristics in a horizon tal doub le pipe with coiled wire inserts were studied experimentally by Naphon[2].Prom vonge[3]reported a com parative study of effect of square-wire and circular-wire coils on heat transfer and turbulent flow friction characteristics in a uniform heat-fluxed tube.

Rahimi et al.[4]examined the heat transfer,friction factor and thermal hyd rau lic performance in a round tube with the classic and the modified twisted tape inserts.Murugesan et al.[5]conducted an experimental work on heat transfer rate and friction facto r characteristics in a double pipe heat exchanger fitted with plain twisted tapes and square-cu t twisted tapes.Sharma et al.[6]investigated the heat transfer coefficient and friction factor in a round tube with twisted-tape inserts in the transition range of flow with Al2O3nanofluid for different twist ratios.Yuxiang et al.[7]perform ed a numerical simulation of turbulent flow and heat transfer in converging-diverging tubes equipped with twin counter-swirling twisted tapes.Influences of the b roken twisted tapes with various twist ratios on the heat transfer and friction facto r were also studied by Chang et al.[8].The effect of insertion of twisted tape with wirenails and plain twisted-tapes at three different twist ratios in a doub le pipe heat exchanger on thermal characteristics was studied experimentally by Mu rugesan et al.[9].Sivashanm ugamet al.[10]examined the heat transfer and friction factor characteristics in a tubefitted with righ t-left helical screw tapes of equal length,and unequal length at different twist ratios.A comparison of the thermal and hyd rau lic performances between twisted-tape inserts and coil-wire inserts was in troduced by W ang and Sunden[11]for both lam inar and turbulent flow regimes.Prom vonge[12]used wire-coil inserts in con junction with twisted tapes for heat transfer augmentation in a tube.Bharadw aj et al.[13]investigated the heat transfer and pressure dropin a spirally grooved tube with twisted-tape insert for lam inar tofully turbulent regions.Prom vonge[14]perform ed a measurement to investigate the e ffect of the converging and diverging conical-ring arrangements on the heat transfer enhancement in a tube.Du rm us[15]em ployed con ical-ring tu rbu lators with different conical angles for enhancing heat transfer in a tube.Prom vonge and Eiam sa-ard[16]experimentally studied the effect of the conical-nozzle turbulat or combined with the snail en trance on heat transfer rate and flow friction in a heat exchanger tube.The influence of the flow geometry parameters on transient forced convection heat transfer for turbulent flowin a tube with baffle inserts was reported by Tandiroglu[17].Kongkaitpaiboon et al.[18]presented the effect of the circular-ring turbula tor on the heat transfer and flu id friction characteristics in a heat exchanger tube.

For wing let applications,Allison and Dally[19]studied experim entally the heat transfer performance of a fin-and-tube radiator with delta-wing let vo rtex generators by full scale measurements and d ye v isualization.Tian et a l.[20]numerically examined the air-side heat transfer and flu id flow characteristics of w avy finand-tube heat exchanger with delta wing lets;having three-row round tubes in staggered or in line arrangements.Chom pookhamet a l.[21]carried out measurements to study the effect of com bined w edge ribs and winglet vo rtex generators(W VGs)on heat transfer and friction loss behaviors for turbulent airflow through a constan t heat flux channe l.Zhou and Ye[22]experimentally investigated the thermal and flow characteristics in a duct fitted with curved trapezoidal,rectangu lar,trapezoidal and delta wing lets.Sinha et al.[23]provided anumerical result pertaining to heat transfer enhancement of a plate-fin heat exchanger using two rows of WVGs with five different strategies on placing the WVGs.Effects of com bined ribs and WVGs on convection heat transfer and friction loss behaviors for turbulent airflow through aconstan the atfl uxed channel were experimentally investigated by Prom vonge et a l.[24].Tw o pairs of W VGs at different attack ang les(α)were moun ted on the test duct en trance to create longitudinal vo rtexflow s through the test channel.Experiment was conducted to study heat transfer behavio rs of a solar air heater channel with com bined ribs and delta-wing let type vortex generators(DW s)[25].Ten pairs of DWs with three attack angles(α)of 60°,45°and 30°are in troduced and moun ted on the low er plate en trance of the tested channel.

According to the literature review above,the application of winglets has been show n more attractive than other vortex-flow devices due to lower pressure loss.How ever,the wing lets cited above,in general,have been used by placing on flat surfaces of ducts or channels and rarely been found to be usedin round tubes.To em ploy winglets in a circular tube,the modification of winglet placements is needed by placing the W VGs repeated ly on the core flow of the tube in the cu rren t work.Therefore,the objective of the present work is to exam ine the influence of the em ployed WVGs as a turbulence prom o ter(called turbulator)on enhanced heat transfer andflow characteristics in turbulent flow region,where air is used as the test fluid.The effect of the winglet width and pitch length is determined and the results are com pared with the results of the typical twisted-tape at y/w=4 and the wire coil at RC=H/d=5 under similar operating conditions.The W VGs are moun ted on the core flow with attack angle of 30°with respect to the main flow direction.The choice of this attack angle is that it provides the op tim um thermal performance w hen com pared to other angles of attack as suggestedin the literature[24,25].The larger angle of attack(45°-60°)provides higher heat transfer with ex trem e pressure loss,leading to low er thermal performance while the sm aller attack angle(20°-15°)yields low er heat transfer rate.

2.Experimental Setup

The detail of the experimental apparatus usedin the present work is displayed schem atically in Fig.1.In the apparatus,the air from a 1.5 kW high pressure b low er was directed through an orificeflow-meter and passed to the heat transfer test section.The airflow rate was measured by the orifice-meter,built according to ASME standard[26]and calib rated by using a hot-wire anem ometer to measure flow velocities across the tube section.M anometric fluid was usedin an inclined manometer with a specific gravity(SG)of 0.826 to ensure a reasonably accurate measurement of pressure drop across the orifice.The desired volumetric airflow rate from the b low er was obtained by con trolling the motor speed of the b lower through an inverter.The inner(D)and outer diameters of the copper test tube were,respectively,50.8 and 54.8 mm and the tube was 3000 mm long,including the test section(L)of 1000 mm.The test tube was heated by con tinually winding flexib le electrical wire on the outer tube wall.The electrical outpu t power was con tro lled by a variac transform er to obtain a uniform heat-flux along the en tire length of the test section.The outer surface of the test tube was w ell insu lated to minim ize heat loss to surroundings.The in let and outlet air temperatures in the tube were measured by RTD-type(Pt100)therm ocouples positioned upstream and dow nstream of the test tube while the surface temperatures(Tw)were measured by 24 K-type therm ocouples located equally on the top and one side of test tube along the test section.The 24 K-type therm ocouples were installedin ho les d rilled from the rear surface and centered of the tube walls with the respective jun ctions positioned with in 1 mm of the inside wall and axial separation was 90 mm apart.All of the temperature readings from the measurement system were consisten tly recorded using a data logger.The pressure drop across the test section was measured by a digital manometer.Reynolds numbers for the air flowing through the test section were con trolledin the range of 5300 to 24000.

A detail of the test tube inserted with 30°W VGs is depictedin Fig.2.All WVGs made of alum inum strip were 0.3 mm thick and 99 mm long with rounded ends and variab le width e.The W VGs were moun ted repeated ly along the core flow at α =30°with respect to the main flow direction as depictedin Fig.2(a).As seen in figure,the W VG elements were tied together by putting two straight steel wires into the ho les d rilled on both end areas of the winglets with two semicircular rod-supports on bo th ends of the inserted.The WVGs were insertedin the test tube with three different wing let widths,e=5,7.5 and 10 mm(RB=e/D=0.1,0.15 and 0.2)and with four pitch lengths;P=25,50,75 and 100 mm(RP=P/D=0.5,1.0,1.5 and 2.0).

For comparison,the twisted-tape made of alum inum sheet was in troduced and its size was 0.8 mm thick,42 mm wide(w)and 1200 mm long with a twist length(y)of 168 mm(twist ratio,y/w=4).Also,the wire coil[3]with 3 mm wire thickness(d)and 15 mm coil pitch length(H)at coil pitch ratio,RC=H/d=5 was offered andits data were taken from Ref.[3].

To quantify the uncertainties of measurements,the reduced dataobtained experimentally were determined.The uncertainty in the data calculation was based on Ref.[27].The maxim um uncertain ties of non-dim ensional parameters were±5%for Reynolds number,±7.6%for Nusselt number and±9.5%for friction.The uncertainty in the axial velocity measurement was estimated to be less than±5%,and the pressure has a corresponding estimated uncertainty of±5%,whereas the uncertainty in temperature measurement at the tube wall was about±0.5%.

3.Data Reduction

In the present work,the air used as the test fluid flow ed through a uniform heat-fluxed and insulated tube.The steady state heat transfer rate is assumed to be equal to the heat loss in the test section,which can be expressed as

Fig.1.Schem atic diagram of experim ental apparatus.

Fig.2.(a)Test tube fitted with 30°WVGs and(b)photograph of test section.

where

The heat supplied by the electrical winding in the test tube is found to be 3%-5%higher than the heat absorbed by the fluid for the thermal equilibrium test due to convection and radiation heat losses from the test section to the surrounding.Thus,only the heat transfer rate absorbed by the fluidis taken for the internal convective heat transfer coefficient calculation.The convection heat transfer in the test tube can be written as

in which

where Twis the local wall temperature evaluated at the outer wall surface of the tested copper tube.The average wall temperature,˜Tw,is calculated from 24 pointsofsurface temperatures lined atequalinterval between the in let and the exit of the tested tube.The average heat transfer coefficient(h)and the mean Nusselt number(Nu)are estimated as follow s:

The heat transfer is calculated from the Nusselt number which can be obtained by

The Reynolds number based on tube diameter is given by

The friction factor(f)computed by pressure drop across the test tube length(L)is written as

in which U is mean air velocity in the tube.All of therm o-physical properties of the air are determined at the overall bulk air temperature(Tb)from Eq.(4).

To assess the practical use of the enhanced tube,the performance of the enhanced tube is evaluated relatively to the smooth tube atan identical pumping power in the form of thermal performance enhancement factor(η)which can be expressed as

4.Numerical Simulation

4.1.winglet geometry and mathematical modeling

The system of in terest is a circular tube inserted with 30°WVGs as show n in Fig.3.The full-length tube was divided in to 3 parts:en try,test section and exit.The detail of the full-length winglet-inserted tube is displayed in Fig.3(a),whereas a module of one periodic flow,computational domain and its grid is show n in Fig.3(b).The periodic flow tube attains a periodical fully developed flow and thermal condition where the velocity field and heat transfer pattern repeat itself from one module to another.The concep t of periodical fully developedflow andits solution procedure has been describedin Ref.[28].In the periodic flow module,the air en ters the tube at an in let temperature(Tin)and flow s over a 30°winglet where e is the winglet width,the tube diameter(D)is set to 50 mm,and e/dis know n as the b lockage ratio(RB).The axial pitch spacing(P)is a distance between the winglet cells,in which P/dis defined as the pitch ratio(RP).To investigate the flow structure and heat transfer mechanism for the W VGs,RBof 0.1,0.15 and 0.2 is simulated and the results are validated with the measurement in the present work.

The numerical model for fluid flow and heat transfer in the inserted tube is developed under the fo llowing assum ptions:steady,threedim ensional,turbulent andincom pressib le flow;constant fluid properties;and ignored body forces,viscous dissipation and radiation heat transfer.Based on the above assumptions,the tube flow model is governed by the Reynolds averaged Navier-Stokes(RANS)equations with the RNG k-εturbulencem odel and theenergy equation.The details on mathematical modeling can be foundin Ref.[29].In the present sim ulation,the commercials of tware ANSYS FLUENT is em ployed.

4.2.Boundary conditions

For a full-length circular tube fitted with winglets,a uniform air velocity was in troduced at the in let while a pressure outlet condition was applied at the exit.For a periodic flow module,periodic boundaries were used for the in let and outlet of the flow domain.A constant massflow rate of air at 300 K was assum edin the flow direction.The physical properties of the air were assum ed to rem ain constan t at mean bu lk temperature.Im perm eab le boundary and no-slip wall conditions were implementedinside the tube walls as w ell as the winglet surface.The constan t wall heat flux of the tube was main tained at 600 W·m-2while the winglet strip was assum ed at adiabatic wall condition.

Fig.3.(a)full-length tube geometry and(b)computational dom ain of periodic flow.

4.3.Gridindependence test

The com putational domain of a periodic flow module is resolved by regu lar Cartesian elements or hexahedron elements.A gridindependence procedure was implemented by using Richardson extrapolation technique over grids with different numbers of cells,about 32000,64000,128000 and 255000.The variation in Nu and f values is found to be less than 0.3%for the increment of the number of cells from 128000 to 255000.with consideration in both com puting time and solution precision,the grid of 128000 cells was adopted while similar grid density was also applied for the full-length flow model.

4.4.fully developed periodic condition

To investigate a fully developed periodic condition,the full-length tubefitted with multiple wing lets as depicted in Fig.3(a)wassim ulated for Re=10000,RB=0.2 and RP=0.1.The fully developed periodic flow and heat transfer in the winglet-inserted tube can be examined by considering the axial Nuxand velocity distributions.For brevity,both the axial distributions are not displayed here.The sim ulation revealed that the fully developed periodic condition occurs at about the 5 th module/period or at x/D≈5.In addition,the preliminary study indicates that the fully developed periodicflow condition dependson thewinglet width and pitch ratios where the higher RBand the sm aller RPlead tofaster developm ent of the fully periodic flow.Therefore,the concept of fully developed periodic flow can be applied efficien tly to turbulent tube flow through winglets.Again,by considering both convergent time and solution precision,only a fully developed periodic flow model(one periodic flow module)is em ployedin the subsequen t com putation.

5.Results and Discussion

5.1.Validation of smooth tube

The present experimental results on the heat transfer and friction characteristics in a smooth wall tube are first validated in terms of Nusselt number(Nu)and friction factor(f).The simulated results of Nu and f for the present smooth tube are,respectively,com pared with those from correlations of Dittus-Boelter and Blasius found in the open literature[30]for turbulent flow in circular ducts in Fig.4.

Fig.4.Verification of Nusselt number and friction factor for smooth tube.Dittus and Boelter;Nu smooth tube;Blasius;○f smooth tube.

Dittus and Boelter correlation:

Blasius correlation:

In Fig.4,the present sim ulations agree reasonab ly w ell within±6%with the Blasius correlation and the Dittus-Boelter correlation.

5.2.Effect of WVGs on heat transfer

Fig.5.Variation of(a)Nu and(b)Nu/Nu0 with Re for WVG inserts.R B=0.20,R P=0.5;R B=0.20,R P=1.0;R B=0.20,R P=1.5;R B=0.20,R P=2.0;R B=0.15,R P=0.5;R B=0.15,R P=1.0; R B=0.15,R P=1.5;R B=0.15,R P=2.0;R B=0.10,R P=0.5;R B=0.10,R P=1.0;R B=0.10,R P=1.5;R B=0.10,R P=2.0;wire coil,R C=5;twisted tape,y/w=4;sm oo th tube.

The effect of four different pitch ratios(RP=0.5,1,1.5 and 2)and three b lockage ratios(RB=0.1,0.15 and 0.2)on the heat transfer is examined and presentedin the form of Nu.The relationships between heat transfer(Nu)and Reynolds numbers(Re)of the tube inserted with WVGs are demonstratedin Fig.5(a).According to the figu re,W VG tu rbu lators yield considerab le heat transfer enhancement with a similar trendin comparison with the smooth tube,twisted tapes and thewire coil.This isdue to the in terrup tion of theflow by the tu rbu lator results in the destruction of thermal boundary layer near the tube wall.The Nusseltnumber increaseswith the rise ofReynolds number and the b lockage ratio and with the decreasing of the pitch ratio.

The ratio of augm ented Nu of inserted tube to Nu of smooth tube,Nu/Nu0plotted against the Reynolds number(Re)is displayedin Fig.5(b).In the figure,the Nu/Nu0tends to decrease slightly with the rise of Re for all cases studied.The heat transfer values of the tube with WVGs are found to be better than that of the smooth tube with/without the twisted tapesbecause theWVGsp rovide the strong mixing or tu rbu lence in tensity leading to destruction of thermal boundary layer and the vortex flow creating better flow mixing between thefluid at the core and the tube wall.Both flow phenom ena prom ote an increase in the tangen tialand radial turbu len tfluctuationsor the turbulence in tensity,thinning the boundary layer,and therefore causing the rise in heat transfer rate inside a tube.The average increases in Nu for using the 30°WVGs with RP=0.5,1,1.5 and 2 are about 218%,208%,200%and 186%;234%,222%,215%and 202%;and 251%,240%,229%and 217%at RB=0.1,0.15 and 0.2,respectively while the wire coil and twisted tape inserts yield the mean increase in Nu of 212%and 129%above the smooth tube.

The variation of surface temperature along the inserted tube at RB=0.10,RP=1.5 for Re=11660 and 15442 is displayedin Fig.6 where x is the location of therm ocouples starting from the en try of test section.In the figu re,the surface temperature show s an increase tendency with the increment of x/D for both the Re values and a sligh t drop at the last two locations(x/D≈18 and 20)due to the radiation and the exit effect.The wall temperature in the Re=11660 case is higher than that of Re=15442 because of low er heat rem oval from the tube wall.

5.3.Effect of WVGs on friction factor

Fig.7(a)show s the relationship between the friction factor and the Reynolds number obtained with 30°W VGs inserted.It is observed that the friction factor tends to decrease with raising the Reynolds number.The WVGs provide a substantial increase in f over the smooth tube,due to the dissipation of dynam ic pressure of the fluid due to higher surface area and the reverse/swirl flow.The WVGs give much higher f than that of the twisted tape but considerab ly low er than the wire coil.f decreases with the decrease of RBbut the rise of RP.

Fig.7(b)p resen ts the variation of friction factor ratio(f/f0)with Re for various RBand RPvalues:f/f0tends to increase sligh tlywith the increment of Re for all the W VGs applied and to decrease sligh tly with the rise of Re for using the twisted tape and wire coil.The maxim um f/f0of about 5.63 times is seen for the WVG insert at RB=0.2 and RP=0.5 w h ile that of about 7.5 times is for the wire coil insert.

Fig.6.Variation of wall temperature along inserted tube,R B=0.1 and R P=1.5.Re=11660;Re=15442.

5.4.Effect of RP on heat transfer and friction factor

Fig.8(a)displays the plot of the Nu/Nu0against the RPfor various RBand Re values:Nu/Nu0tends to decrease with the increment of Re and RP.The WVGs at RP=0.5,1,1.5 and 2 provide the mean increase in Nu up to 234%,223%,215%and 202%above the plain tube.

Fig.8.Variation of(a)Nu/Nu0 and(b)f/f0 with R P for WVG inserts.R B=0.20,Re=5363;R B=0.20,Re=13236;R B=0.20,Re=21042;R B=0.15,Re=5363;R B=0.15,Re=13236;R B=0.15,Re=21042;R B==5363;R B=0.10,Re236;R B=0.10,Re=21042.

The effect of RPon f/f0is depictedin Fig.8(b):f/f0show s a decrease trend with the increment of RPfor all RBandit is nearly free from Re.The maxim um friction loss in the present study is found for the WVGs with RP=0.5.The mean f values for the WVGs at RP=0.5 are seen to be higher than those at RP=1.0,1.5 and 2.0 at about 22%,48%and 65%,respectively.

5.5.Effect of WVGs on thermal performance

In thermal performance evaluation,the thermalenhancement factor(η)under constan t pumping power conditions is taken in to accoun t by using Eq.(10).The variation of the η with Re is depictedin Fig.9.The η valuesgenerally are above unity for theWVG inserts,indicating that the use of W VGs is advantageous over the smooth tube.η tends to decrease with the increase of Re and RBvalues for all WVG inserts.The maxim um η is between 1.45-1.59 for the WVGs with RB=0.1 and RP=1.5 while them inim um isbetween 1.35-1.49 for theoneswith RB=0.2 and RP=0.5.The highest η of 1.59 is found for the W VGs at RB=0.1 and RP=1.5 at low er Re.

Fig.9.Variation of η with Re for W VG inserts.R B=0.10,R P=1.5;R B=0.10,R P=1.0;○R B=0.10,R P=2.0;●R B=0.10,R P=0.5;R B=0.15,R P=1.5;R B=0.15,R P=1.0;R B=0.15,R P=2.0;■R B=0.15,R P=0.5;R B=0.20,R P=1.5;R B=0.20,R P=1.0;R B=0.20,R P=2.0;♦R B=0.20,R P=0.5;✚wire coil,R C=5;twisted tape,y/w=4.

In addition,the em pirical correlations for WVGs developed by relating the Re,RBand RPtogether are com pared with experimental data within±5%and±6%for Nusselt number and friction factor,as can be seen in Fig.10(a)and(b),respectively.

5.6.Numerical results of inserted-tube flow

The flow and vortex coherent structure in the inserted tube is displayed by stream lines superim posed with temperature field at various locations in transverse planesasdepictedin Fig.11.The stream lines of the W VG flow model are presented for Re=10000,RP=1.0 and RB=0.2,showing that there are two main coun ter-rotating vortexflow s appearing on the low er and upper parts along the tube.The appearance of the two vortex flow s can help to increase higher heat transfer in the tube because of higher transport of the fluid from the central core to the near-wall regimes as can be observed from the major change in the temperature field over the tube.This means that the vortex flow s provide a significan t influence on the temperaturefield,because it can induce better fluid mixing between the wall and the core flow regions,leading to a high temperature gradient over the heated wall,especially in the dow nstream winglet-end region.

Fig.10.Variation tests of(a)Nusselt number and(b)friction factor correlations.

Fig.11.Stream lines and temperature contours in transverse planes for WVGs at Re=10000,R P=1.0 and R B=0.2.

The local Nu con tou r including the stream lines showing the impingement on the tube wall for Re=10000,RP=1.0 and RB=0.2 is presentedin Fig.12.In the figu re,it is apparent that the h igh Nu values for the inserted tube are seen in large areas over the tube wall.The peaks can be observedin the sidewall area around the dow nstream winglet-end where the red area show s the im pingement region of the secondary flow providing higher heat transfer rate than other areas.This means that the vortex-inducedim pingement flowis responsib le to heat transfer enhancement in the tube,apart from fast fluid mixing between the core and the near-wall regions.

Fig.12.Stream lines of im pinging jets on tube wall and Nu con tou rs for WVGs at Re=10000,R P=1.0 and R B=0.2.

The results of Nusselt number and friction factor from simulation with RP=1.0 and RB=0.1,0.15 and 0.2 are validated by comparison with experimental data under similar operating conditions as show n in Fig.13(a)and(b),respectively.It is w orth noting that the numerical results are in good agreement with experimental data.The average deviations of the results are less±9%for Nusselt number and±12%for friction factor.

6.Conclusions

The heat transfer and the friction factor characteristics in a round tube inserted with 30°W VGs at three RBand four RPvalues have been investigated for the turbulent regim e,Re=5300-24000 under a uniform heat-flux condition.In the present study,the following conclusions can be d raw n.

Fig.13.Variation of(a)Nu/Nu0 and(b)f/f0 with Re for WVG inserts at R P=1.0 and R B=0.2.R B=0.20,experimental;R B=0.15,experim ental;R B=0.10,experim ental;R B=0.20,simulated;R B=0.15,simulated;R B=0.10,simulated.

·The use of the 30°WVGs leads to considerable heat transfer enhancementover the plain tubeatabout186 to 251%depending on the Re,RBand RPvalues.

·The sm aller RPyields higher heat transfer rate than the larger one but the sm aller RBprovides an opposite trend.

·The friction factor of the WVGs is found to be 2.07-5.63 times above that of the plain tube.The f tends to decrease with the rise of RPbu t with decreasing RB.

·The η for the W VGs investigatedis in a range of 1.35-1.59 which is much higher than that for the coil wire and the twisted tape.The maxim um η of around 1.59 is found for the WVGs with RB=0.1 and RP=1.5 at low er Re.Thus,the WVG insert is a prom isingmethod to im prove thermal system s in industrial applications.

Acknowledgments

The authors w ou ld like to gratefully acknow ledge M r.Som bat Tam na,lecturer of the Facu lty of Engineering,Thai-Nich i Institu te of Technology,Thailand for the support in numericalwork of this research.

Nomenclature

Subscripts