旋转条件下U形通道转弯段形状对流动和传热特性的影响.pdf

Chinese Journal of Turbomachinery第65卷，2023年第3期Http:/turbo- Vol.65，2023,No.3Effects of Turn Shapes on Flow and Heat TransferEffects of Turn Shapes on Flow and Heat Transfer CharacteriCharacteri-stics in U-shaped Channel Under Rotating Conditionsstics in U-shaped Channel Under Rotating Conditions*Ru-quan You1,2Ze-xuan Liu1,2,*Hai-wang Li1,2Jin-cheng Shi1,2Zhi Tao1,2（1.ResearchInstituteofAero-Engine,BeihangUniversity；2.NationalKeyLaboratoryofScienceandTechnologyonAero-EnginesAero-Thermodynamics,BeihangUniversity)Abstract：In this paper,the flow and heat transfer characteristics in U-shaped channel with three different turnshapes are studied.The rotation number ranges from 00.251,Reynolds number are 11500,23000,34500,respectively.The results show that the flow separation and reattachment in the turning section are the key factors affecting the localheat transfer and pressure loss of U-shaped channel.The square turn will generate corner vortices at the outside of theturning section,and the size of the inner separation vortex and reattachment vortex is larger than that of the other twoturnshapes.Theexistenceofvortexsystemwillincreasethemixingandenhanceheattransfer,butincreasethepressureloss,so its relative Nusselt number and pressure loss are the largest.There are corner vortices on the outside of theturning section of the channel with a inner circle turn and outer square turn,but the arc-shaped inner edge makes itsseparation delay and the separation vortex decrease,and the size of the reattachment vortex also decreases.The arc-shaped outer edge of the channel with circle turn in both inner and outer further inhibits the generation of cornervortices,soitsrelativeNusseltnumberandpressurelossarethelowest.Rotationwillcausethefluidtodeflectundertheinfluence of Coriolis force,strengthen the heat transfer on the trailing surface of radial outflow and the leading surfaceofradialinternalflow,andgeneratesecondaryflowandseparationvortexintheturningsection,resultinginthechangeof vortex structure in the turning section.With the increase of rotation number,the Nusselt number of the three types ofturningsectionstructuresincreases.Thethermalperformancefactorofthethreechannelsincreaseswiththeincreaseofrotatingspeed,andthechannelwithainnercircleturnandoutersquareturnisthehighest,whichis9.6%higherthanthechannel with circle turn in both inner and outer on average,and 17.8%higher than the channel with square turn in bothinnerandouter.Keywords：Rotation；U-shaped Channel；Pressure Loss；Nusselt NumberDOI:10.16492/j.fjjs.2023.03.00061IntroductionAt present,the thrust of the aero-engine is increasing,and the temperature before the turbine is getting higher andhigher,which also has higher requirements on the materialand cooling technology of the turbine blade.Internal bladecooling channels are now widely used in turbine blades as amajor internal cooling method.The internal cooling channelof the real blade is generally a serpentine curved channel,and the cold air flows in the curved channel,so that the inter-nal cooling of the blade can be achieved by exchanging heatwith the wall surface.In experiments or numerical simula-tions,a U-shaped channel with a rectangular section and a180 turning structure is often studied as a unit of the serpen-tine turning channel.Under the rotating condition of the U-shaped channel,due to the existence of the additional rotat-ing force and the turning section,the cold air distributionwill be uneven,resulting in the temperature in some areas be-ing too high,which cannot meet the cooling requirements.The flow mechanism in the U-shaped channel is particularlyimportant.At present,most scholars have carried out a seriesof experimental and numerical studies on the stationary androtating conditions of the U-shaped channel and the U-shaped turning section.1.1Research on Stationary Condition of U-shapedChannelWhen the smooth U-shaped channel in stationary condi-tion,the existence of the turning section is the main factor af-fecting its heat transfer and pressure loss.To this end,schol-ars have studied it through experiments and numerical simu-*Funding：National Natural Science Foundation of China（51906008）*Corresponding author:Ze-xuan Liu,liuzx_ 33Chinese Journal of Turbomachinerylations.M.Gallo et al.1 used PIV(Particle Image Velocime-try)technology to photograph the flow field in the smooth U-shaped channel in detail,and found that there are three highheat transfer areas in stationary condition,which are mainlycaused by turning.It is caused by the vortex system generat-ed by the segment and the impact of the fluid on the wall.Tong-Miin Liou et al.2-3 used PIV technology to cap-ture the flow fields of U-shaped channels with parallelogramand square cross-sections,and conducted a comparison.Theresults indicate that in the turning section,the turbulent flowexhibits anisotropy,with a stronger impact of the secondaryflow on the outer wall of the parallelogram channel com-pared to the square channel.Runzhou Liu et al.4 used TR-PIV(Time-resolved Parti-cle Image Velocimetry)technology to photograph the flowfields of three smooth U-shaped channels with different turn-ing section structures,and used POD method to determinethe spatial characteristics of the flow field.Square channelshave fewer and smaller separate vortices,but their secondaryflow is more complex.Numerous scholars have also been involved in the fieldof numerical simulation.Tom Shin5 used numerical simula-tion methods to study the heat transfer and flow resistance ofU-shaped channels in stationary condition respectively.Theflow of the channel is mainly determined by the flow direc-tion separation and the secondary flow generated by the 180turning section.Some scholars add fins in the stationary U-shaped chan-nel in order to obtain better heat transfer effect.Chia,Kai-Chieh 6 also studied the U-shaped channel with 45 in-clined ribs under stationary conditions,and found that add-ing fins can reduce the rotation effect,and the arrangementof the fins has a significant impact on the heat transfer at thetop of the channel.Prashant Singh7 added V-shaped fins inthe channel with AR=1:2 and compared it with the smoothchannel,and found that the heat transfer level of the firstchannel with ribs increased by more than 30%comparedwith the smooth channel.T.M.Liou et al.8 added airfoilribs in the channel and found that the addition of airfoil ribscan induce Fujiwhara co-rotating vortices,which can effec-tively eliminate the wake in the channel.The wake regioncan effectively enhance the heat exchange effect of the twochannels.1.2Research on Rotation Condition of U-shapedChannelRotation will generate Coriolis force and buoyancy.Therefore,in a smooth U-shaped channel with rotation,theadditional force of rotation coupled with the curve effect ofthe 180 turning section will make the flow field inside thechannel more complicated,which will affect the U channel,heat transfer characteristics and pressure loss losses.Bons and Kerrebrock 9 used PIV(particle image velo-cimetry)technology to photograph the flow in the coolingchannel of a smooth-walled turbine blade with or withoutheating,and observed that the velocity vector was deflectedtoward the trailing surface.Dimitra Tsakmakidou10 alsoused the PIV technique to photograph the flow field of theribbed U-shaped channel,and they mainly focused on the ef-fect of the additional force generated by the rotation on thereattachment vortex of the U-shaped channel.Chuankai Liu et al.11-12 conducted experiments andnumerical simulations on the rotating smooth U-shaped chan-nel with square inside and outside of the turning section.Their research shows that the relative Nusselt number gener-ally increases with the rotation.The increase in the numberof rotations has a greater impact on the radial outflow sec-tion of the U-shaped channel.In the radial inflow section,due to the Coriolis force and the curve effect of the turningsection,the heat transfer increase effect is not very large.Na-ris Pattanaprates et al.13 used numerical simulation methodto study the effect of changing the geometry of multi-chan-nel U-shaped channel and turning section on pressure lossand heat transfer,and found that with the increase of rotationnumber,the heat transfer performance was slightly en-hanced,but the pressure loss is reduced,while the pressureloss isreduced.Mandana S.Saravani et al.14 and Jiangtao Bai et al.15 used numerical simulation to verify that for a smooth U-shaped channel,the increase ofRoandRewill lead to the in-crease of the overall heat transfer coefficient of the channel,and the increment of the turning segment will be more obvi-ous.The numerical simulation results of the U channel by Y.L.Lin et al.16 also confirmed that the rotation will in-crease the heat transfer effect of the trailing surface of thefirst channel due to the Coriolis force and the buoyancy,andthe heat transfer effect of the leading surface of the secondchannel enhanced.In the 1980s and 1990s,J.C.Han et al.17-19 conducted a detailed and in-depth study on smoothchannels and ribbed channels by combining experiments andnumerical simulations,and found that the heat transfer effectof the ribbed channel is better than that of the smooth chan-nel,but the pressure loss is also much larger;The basicsource of the pressure loss of the smooth channel is the im-pact at its turning section and the generation of secondaryflow.In addition,Michael Huh and Han 20 and BerrabahBrahim 21 studied the placement inclination of the smoothU channel and found that when the U channel was placed atan inclination of 45,the rotation had a significant effect onthe rib-induced secondary flow and the rotation.The heattransfer difference between leading and trailing surfaces dueto the Coriolis force will be reduced.Wenlung Fu 22 con-ducted a numerical study on smooth U channels with differ-ent aspect ratios and placement angles,and the resultsshowed the effect of rotation in the second channel of chan-nels with aspect ratios of 1:2 and 1:4.The non-uniformity ofheat transfer when the U channel is placed at 90 is largerthan that when placed at 45,which is consistent with thelaw studied by Han.Scholars have done relatively researches on the heattransfer and flow characteristics of the U-channel under sta-tionary conditions,while the rotating research is still insuffi-cient in recent years due to the harsh experimental conditionsEffects of Turn Shapes on Flow and Heat Transfer Characteri-stics in U-shaped Channel Under Rotating Conditions 34Chinese Journal of Turbomachinery第65卷，2023年第3期Http:/turbo- Vol.65，2023,No.3and the complex internal flow state,and the research on theinfluence of the geometric shape change of the turning sec-tion in the rotating condition is even more lacking;this paperstudies the influence on the flow characteristics,heat transfercharacteristics and pressure loss characteristics of the U chan-nel turning section when the geometric shape changes,andhow these properties change under rotating condition.2Materials and Methods2.1Problem DescriptionThe models studied in this paper are shown in Fig.1.The cross-sectional shapes of the three models are all square,and their hydraulic diameter is 60 mm.They all have a radialouter flow channel,a radial inner flow channel and a turningsection.The shapes of the turning sections are different.Theinside and outside of the turning section of(a)are circulararcs with radius of 30mm and 90mm,respectively;The in-side and outside of the turning section of(b)are square;theinside of the turning section of(c)is arc shape of radius=30mm,the outer side is square.The distance from the inlet tothe farthest end of the inlet is the same for the three chan-nels,and the distance between the radial inflow channel andthe radial outflow channel is 60mm.In order to ensure thefull development of turbulence,an extension section withthree times the diameter of hydraulic diameter is set at the in-let and outlet.The overall shape of the model is consistentwith that of Runzhou Liu4.In this paper,the SSTk-(Shear Stress Transport)tur-Fig.1Geometric model(a)The channel with circle turnin both inner and outer(b)The channel with squareturn in both inner and outer(c)The channel with a innercircle turn and outer square turnModelAModel BModel Cbulence model is used to simulate the flow and heat transferprocesses in the U-channel with three different geometricshapes.Y plus 0.8 for the first mesh node.The conver-gence criterion is the scale residual for which all governingequations are less than10-5.The specific boundary condi-tions of the calculation model are shown in Tab.1.2.2Data ReductionSince this study involves rotation,the rotation numberRoneeds to be introduced,such as formula(1),is the rota-tional angular velocity,Dhis the hydraulic diameter,andvisthe inlet velocity.Ro=ReRe=Dhv(1)The Nusselt number is obtained from the wall heattransfer coefficient h,whereqwis the local wall heat flow,Twis the wall temperature,andTbis the average temperatureof the local cold air in the channel.k is the thermal conduc-tivity of air,take 0.025h=qw(TwTb)(2)Nu=hDhk(3)When studying the heat transfer performance of thechannel,the normalized Nusselt numberNu/Nu0is usuallyused,which is the ratio of the relative Nusselt number,Nu0isthe average Nusselt number that fully develops the turbulentflow of the stationary smooth circular tube of the same hy-draulic diameter.Nu0=0.023Re0.8Pr0.4(4)Introduce the friction factor f and normalize it asf/f0todetermine the size of the channel pressure loss,pis the in-let and outlet pressure difference over the lengthx,andis the average density and average velocity of the inlet fluid.According to the Karman-Nikuradse equation,f0is frictionfactor for a smooth stationary tube.f=p/0.524x/Dh(5)f0=0.046Re0.2(6)The Thermal Performance Factor(TPF)is the ratio ofthe normalized Nusselt number to the normalized pressureloss coefficient,which can reflect the comprehensive charac-teristics of channel heat transfer and pressure loss,and canbetter reflect the comprehensive cooling efficiency of thechannel.ParameterInlet Reynolds numberRotation number rangeInlet cold air temperature/KInlet turbulence degree/%Outlet average static pressure/PaWall conditionsSetting11500，23000，3450000.2513005101325No-slip boundaryWall temperature 350KTab.1Boundary conditions setting 35Chinese Journal of TurbomachineryTPF=Nu/Nu0(f/f0)13(7)2.3Computational Rationality and Grid Indepen-denceThe grid division results of this study are shown in Fig.3.In order to ensure the accuracy of the calculation and therationality of the number of grids,a grid-independent analy-sis is carried out in this paper.Different mesh numbers canverify the rationality of the other two mesh divisions.The fol-lowing takes the grid numbers of 4 million,8 million and 11million of the inner and outer models,and calculates the cor-responding average Nusselt numbers along the route,asshown in Fig.4.The results show that the 4 million gridsand the 8 million grids.T