Annals of Nuclear Energy 47 (2012) 85–90

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Annals of Nuclear Energy

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Experimental study of transition from laminar to turbulent flow in verticalnarrow channel

Wang Chang, Gao Pu-zhen ⇑, Wang Zhan-wei, Tan Si-chaoKey Discipline Laboratory of Nuclear Safety and Simulation Technology, College of Nuclear Science and Technology, Harbin Engineering University, Heilongjiang 150001, PR China

a r t i c l e i n f o

Article history:Received 29 November 2011Received in revised form 10 April 2012Accepted 13 April 2012Available online 20 May 2012

Keywords:Flow characteristicHeat transfer characteristicLaminar to turbulent transitionNarrow channel

0306-4549/$ - see front matter � 2012 Elsevier Ltd. Ahttp://dx.doi.org/10.1016/j.anucene.2012.04.018

⇑ Corresponding author. Tel./fax: +86 451 8256965E-mail address: gaopuzhen@hrbeu.edu.cn (G. Pu-z

a b s t r a c t

Experimental investigation of flow and heat transfer characteristics of a vertical narrow channel with uni-form heat flux condition are conducted to analysis the effect of wall heating on the laminar to turbulenttransition. The friction factor in the heating condition is compared with that in the adiabatic conditionand the results show that wall heating leads to the delay of laminar to turbulent transition. In addition,the heat transfer characteristic indicates that the critical Reynolds number at the point of laminar flowbreakdown increases with the increase of fluid temperature difference, and the local Nusselt numberat the point of laminar breakdown increases with the increase of the inlet Reynolds number. The analysesof the flow and heat transfer characteristics both indicate that the heating has a stabilizing effect on thewater flow at present experimental scale.

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1. Introduction

Compact heat exchangers are widely adopted in nuclear indus-tries due to their high heat transfer performances. More and moredesigners prefer to use the array of rectangular channels with largeaspect ratio in compact heat exchangers. Up to now, most of theinvestigations of friction factor and heat transfer are focused onthe fully developed laminar and turbulent flow, and the designersalways avoid flows in the transition regime due to the considerableuncertainties. However, there are some situations that the transi-tion regime cannot be avoided, such as upgrading the system asit working originally in the laminar flow or in the accidental sce-narios. Until now, limited work in the transition region has beenreported due to the complexity of the influence factors.

Gajusingh and Siddiqui (2008) investigated the impact of wallheating on the flow structure in the near wall region inside a hor-izontal square channel through use PIV measure the two-dimen-sional velocity fields. It was found that when an originallylaminar flow is heated from below, the turbulence is generatedin the flow mainly due to buoyancy. However, as the flow is firstlyin the turbulent regime, additional wall heating from below re-duces the magnitude of turbulent intensity due to the working ofturbulence against the buoyancy forces. In addition, Behzadmehret al. (2008) studied the unsteady phenomena in the case of air-flows approaching transition inside a uniformly heated verticaltube, they found instability occurs in the buffer region and thenpropagates towards the whole section of the tube as the Grashof

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5.hen).

number is increased. Tam and Ghajar (1997) experimentally stud-ied the pressure drop characteristics in the transition region of ahorizontal circular pipe with different inlet shapes under adiabaticand uniform flux boundary conditions. The results indicate that thelower and upper limit of the non-isothermal transition boundariesincreases owing to the effect of secondary flow. Serkan (2004)modified the incompressible stability equations through introduc-ing the variation of fluid properties over the cross-section. The re-sults show that wall heating shifts the neutral stability curvestowards higher Reynolds numbers and hence have a stabilizing ef-fect. In addition, Sameen and Govindarajan (2007) conducted acomprehensive theoretical research on the effect of wall heatingon the linear transient and consequential growth of instability ina channel flow. The results show that the decrease in viscosityhas a substantial stabilizing effect and vice versa.

Recently, Abraham et al. (2008, 2009, 2010, 2011), Minkowyczet al. (2009) conducted a series of theoretical analyses and numer-ical simulations on the laminar flow breakdown in pipe flow. Theydeveloped some models for predicting the heat transfer coefficientand friction factor in the transition region. In addition, Silin et al.(2010a, 2010b) experimentally studied the effect of wall heatingon the laminar to turbulent transition in a rectangular channeland found that the reduction of viscosity has a stabilizing effecton the flow.

The literature survey reveals that there are two typically typesof transition process, one is the buoyancy induced type transitionin a horizontal heated pipe, such as in the case of Taylor-Couetteflow and Rayleigh–Benard flow, and the other is the so-calledbreakdown type transition, such as that in the heated laminarPoiseuille flow. However, as mentioned above, most of the studies

Nomenclature

A area (m2)b half length of the narrow side (m)Cp specific heat (J kg�1 �C�1)Dh equivalent diameter (m)Gr Grashof numberh heat transfer coefficient (W m�2 �C�1)k thermal conductivity (W m�1 �C�1)L length (m)_m mass flow rate (kg s�1)

Nu Nusselt numberP Perimeter (m)q heat flux (kW m�2)Re Reynolds numberT temperature (�C)u velocity (m s�1)us shear velocity (m s�1)y distance perpendicular to the wall (m)

Greek symbola aspect ratiob thermal expansion coefficient (K�1)l viscosity (Pa s)k friction factor

Subscriptsf fluidin inletm cross section averageout outletPLB point of laminar breakdownw wallx location (m)

Superscript� dimensionless parameter

86 W. Chang et al. / Annals of Nuclear Energy 47 (2012) 85–90

on the breakdown type transition are based on theoretical andnumerical investigation. It is the primary motive to experimentallystudy the effect of wall heating on the breakdown type transitionfrom laminar flow to turbulent in the channel.

2. Experimental instruction

The setup of the experimental loop is displayed in Fig. 1. Thecentrifugal pump circulates de-ionized water through the mag-netic flow rate meter, preheater, test section and then the water-cooled condenser at which hot water condensed before it returnedto the pump. A control valve at the inlet of the test section enablesthe accommodation of flow rate.

The detail of the test section can be seen in Fig. 2. The test sec-tion is a single rectangular channel made of stainless steel with theinternal size of 2 mm � 40 mm. The channel is heated directlyusing a DC power supply which provides a uniform heat flux onboth sides. In addition, the channel is electrically and thermallyinsulated through sandwiched by micanite plates. Furthermore,four Teflon washers are used to keep the test section electricallyinsulated from the other parts of experimental loop. The systempressure is controlled by connecting to a high pressure nitrogengas source.

Fluid bulk temperature at the inlet and outlet of the test sectionis measured by two N-type thermocouples inserted into the mainflow. However, wall temperatures at six locations are measuredusing N-type thermocouples which are attached to the exteriorwall surface. The locations of these thermocouples relative to chan-nel hydraulic diameter are as follows: Lx/Dh = 37, 140, 201, 242,284 and 307. All thermocouples used in the experiment have a cal-ibration accuracy of ±0.5 �C. Additionally, the pressure drop at thefully developed flow region is measured by the differential pres-sure transducer, and the absolute pressure at the inlet of the testsection is measured by a pressure gauge. The accuracy of differen-tial pressure transducers is within ±0.2% of the test span. In addi-tion, the accuracy of the water flow meter is within ±0.3% of thetest span.

3. Experimental procedure and data reduction

Prior to conduct the heating condition experiment, the frictionfactor in adiabatic condition is measured to define the transition

boundary and check the reliability of the data collection system.In addition, five sets of experiments are conducted in the wall heat-ing condition as the inlet bulk fluid temperature is fixed at 40 �C.Additionally, as the mass flow rate increases, the heat flux is ad-justed simultaneously to keep the temperature of outlet bulk fluidunvaried in each set of experiment. The fluid temperature differ-ence between the inlet and outlet of the test section approximatelyequals to 20, 32, 53, 60 and 74 �C. At present the system pressure iskept in 0.8 MPa.

The local bulk temperature of the fluid flowing into the test sec-tion at each position is determined as follows,

_q ¼ _mCpmDT=ðPLxÞ ð1Þ

DT ¼ Tout � T in ð2Þ

Tf ;x ¼ T in þ _qPLx=ð _mCpmÞ ð3Þ

where _q is the heat flux, _m is the water mass flow rate, Cpm is thewater mean specific heat at the bulk temperature, Tfx is the bulktemperature of water at position x, Tin and Tout is the measured inletand outlet flow temperature, respectively, P is the perimeter of thechannel cross section and Lx is the distance of a position from theinlet of test section.

Buyukalaca and Jackson (1997), Herwig and Mahulikar (2006)and Liu et al. (2008) theoretically studied the effect of variableproperty on the thermal hydraulics and found the change of prop-erty resulted in marked influence on the velocity profile and heattransfer in the near wall region. In addition, Li et al. (2007) com-pared the ‘‘Average property’’ and ‘‘Variable property’’ method inthe analyses of friction and heat transfer characteristics and foundthe ‘‘Variable property’’ method is superior in engineering applica-tion since it more accurately and reasonably characterizes the ac-tual phenomenon by nature. Therefore, in the present study, thelocal Reynolds number, local heat transfer coefficient and localNusselt number based on the local fluid property are defined asfollows,

Rex ¼ _mDh=ðlxAÞ ð4Þ

hx ¼ _q=ðTw;x � Tf ;xÞ ð5Þ

Nux ¼ hxDh=k ð6Þ

Fig. 1. Experimental loop.

Fig. 2. Cross section of the rectangular channel.

Fig. 3. Effect of natural convection.

W. Chang et al. / Annals of Nuclear Energy 47 (2012) 85–90 87

where Rex and Nux is the local Reynolds number and local Nusseltnumber, respectively, k is the water thermal conductivity, Dh isthe hydraulic diameter, A is the heat transfer area, Tw,x is the localinner surface temperature. lx is the local dynamic viscosity deter-mined by the local fluid temperature Tf,x.

In addition, as shown in Fig. 1, the special layout of the currentexperimental loop gives rise to a natural convection superimposedon the forced convection. However, it is well known that the rela-tive importance of natural and forced convection can be evaluatedby the ratio of Gr/Re2. If Gr/Re2 is on the order of one, the naturalconvection cannot be neglected and the flow is mixed convection.Whereas the ratio of Gr/Re2 is small compared to one, the flow isforced convection (John and John, 2006). Thus the magnitude ofGrashof number should be considered as can be expressed asfollows,

Grx ¼ gbxðTw;x � Tf ;xÞD3h=m

2x ð7Þ

In which, bx is the local thermal expansion coefficient, K�1, mx isthe kinematic viscosity, m2/s.

Fig. 4. Comparison of the experimental data and the predicted values.

4. Results and discussion

Fig. 3 demonstrated that the natural convection can be ruledout in present study due to the effect of buoyancy is very weak,therefore, the flow in essentially is forced circulation. The acceptedfriction factor and Nusselt number prediction correlations for lam-

Fig. 5. Friction characteristic with different heat flux in transition regime.

88 W. Chang et al. / Annals of Nuclear Energy 47 (2012) 85–90

inar flow of forced circulation in the rectangular channels were re-ported by Hartnett and Kostic (Hartnett and Kostic, 1989),

k ¼ ð96=ReÞð1� 1:3553aþ 1:9467a2 � 1:7012a3 þ 0:9564a4

� 0:2537a5Þ ð8Þ

Nu ¼ 8:235ð1� 2:0421aþ 3:0853a2 � 2:4765a3 þ 1:0578a4

� 0:1861a5Þ ð9Þ

In which, a is the aspect ratio. Re is the Reynolds number basedon the hydraulic diameter.

As seen in Fig. 4, the experimental data agrees well with thepredicted values calculated from Eqs. (7) and (8).

4.1. Friction factor in transition region

As seen in Fig. 5, there is a significant distinction of friction fac-tor between the wall heating condition and isothermal condition inthe transition regime. The larger the temperature difference, thebigger the region of laminar flow. In other words, the wall heating

Fig. 6. Variation of velocity distribution a

introduces an increase of the lower and upper limit of the transi-tion boundaries.

As we know, the wall heating affects the flow characteristic viatwo approaches. One is the wall heating changes the water’s tem-perature and then the viscosity of the water changes greatly, theother is the velocity profile alters due to the variation of fluid prop-erties On considering this, we will analyse this two influential fac-tors separately.

4.1.1. The effect of viscosity variationAs concluded by Schlichting and Gersten (1999), the laminar-

turbulent transition can be described as a stability problem. It iswell known that the viscosity has two effects on the stability phe-nomenon. Firstly, it diffuses the vortices created by high shearforces near the wall and appears as a destabilizing effect. Secondly,it dissipates the disturbance energy and presents as a stabilizingeffect.

As the Reynolds numbers are small, the stabilizing effect of theviscosity is large enough to ensure the small perturbations dieaway. However, as the Reynolds number is large enough, the vis-cosity is no longer sufficient to damp the disturbance energy andthe perturbations are accumulated, thus eventually initiate thetransition to turbulent flow.

Therefore, if the effect of viscosity variation is in the highestflight of the transition process, the decreased kinematic viscositynear the wall as a result of heating will destabilize the flow andintroduce the transition appears earlier than that of the isothermalcondition. However, as seen in Fig. 4, the initiation of transitionReynolds number increases with the increase of temperature dif-ference. As mentioned in the experimental procedure, the viscosityof water will decrease with the increasing temperature differenceat a given inlet fluid temperature. Therefore, the variation of vis-cosity is not the dominant factor that influences the flowtransition.

4.1.2. The effect of velocity profile variationThe typical velocity profiles under different heat flux conditions

at a fixed mass flow rate are simulated through the CFD. The veloc-ity profiles shown in Fig. 6 reveals the remarkably difference ofvelocity profile between the heated and isothermal condition.

nd its derivatives with wall heating.

Fig. 7. The axial distribution of local Nusselt number.

Fig. 8. Local Reynolds number at the point of laminar breakdown.

Fig. 9. Local Nusselt number at the point of laminar break down.

W. Chang et al. / Annals of Nuclear Energy 47 (2012) 85–90 89

Due to the reduced kinematic viscosity, the velocity profile be-come steeper in the near wall region, accordingly, the velocity de-fects f(y⁄) become significantly less when the heat transfer rate isincreased.

f ðy�Þ ¼ ðu�y�¼0 � u�mÞ=u�s ð10Þ

y� ¼ y=b ð11Þ

u� ¼ uy�=uy�¼0 ð12Þ

In which, b is the half length of the narrow side, m; u is the velocity,m, u� is dimensionless fluid velocity in the channel; u�m the dimen-sionless cross-section average velocity; u�s is dimensionless shearvelocity; y is length perpendicular to the wall, m; y⁄ is the dimen-sionless distance from the wall.

As concluded by Serkan (2004), velocity profiles with smallervelocity defects are more stable as demonstrated by Falkner-Skanprofiles. Therefore, one of the reasons that the stabilizing effectin heated water flows may be attributed to this factor.

In addition, as mentioned by Schlichting and Gersten (1999)and Serkan (2004), there is an inflection point (@u�2=@y�2 ¼ 0) oc-curs in the boundary-layer profile which is named Rayleigh insta-bility when the water flows with cooled pipe wall, and thepresences of a point of inflection in the velocity profile in theboundary layer is the adequate and essential conditions for theinstability. However, it can be seen from Fig. 5c that the curvatureof the velocity profile is negative over the whole boundary layerthickness and its moves away gradually towards the point of@u2�=@y�2 ¼ 0 with the increase of heat flux. Therefore, the flow be-comes more stable as the heat flux increases within certain limits.

As the fact mentioned above that the change of viscosity in thenear wall region due to the high heat flux on the wall will lead tothe variation of velocity profile, the curvature of the velocity profileat the wall can be expressed as (1999)

@2u�

@y�2

!w

¼ � 1lw

@l@y�

� �w

@u�

@y�

� �w

ð13Þ

90 W. Chang et al. / Annals of Nuclear Energy 47 (2012) 85–90

Here, lw is the fluid viscosity near the wall, Pa.The flow in present large aspect ratio rectangular channel can

be deem as a two dimensional shear flow, thus the variable of�@u�=@y� can be approximately regard as the vortices distribution.As the physical explanation for Rayleigh’s inflection-point theorempresented by Lin (1966), if fluid with lower vorticity moves up to aregion of higher vorticity the net feedback is to force the fluid backto its original location. Similarly, if fluid of high vorticity movesdown into a region of lower vorticity, the net feedback forces thefluid back to the zone of higher vorticity. Thus, as long as the vor-ticity is monotonically increasing, the vorticity feedback providesstability.

4.2. Local heat transfer characteristic

The local heat transfer characteristic can be seen in Fig. 6, thelocal Nusselt number decreases gradually along the channel inthe entrance region owing to the increasing thickness of theboundary layer, and then it increases sharply in the further down-stream. As demonstrated by Silin et al. (2010a, 2010b), the localReynolds number of the water increases gradually along the flowdirection in a heated channel. So after reaching the critical Rey-nolds number, the turbulence intensity will become significantlyimportant and lead to the laminar breakdown, then the flow willentrance the fully developed intermittent or turbulent flow,accordingly, the heat transfer will be obviously changed in thisprocess. In addition, from Fig. 6b and c one can find that the localNusselt number has a significant decrease at the end of the channelfor certain conditions. The results can be attributed to the effect ofaxial conduction (Tiselj et al., 2004).

To be in accordance with the criteria introduced by Abrahamet al. (2008) and Silin et al. (2010a, 2010b), we also believe thelaminar breakdown takes place where the convection coefficienthas a steep increase. From Fig. 6 one can find that the Reynoldsnumber at the point of laminar breakdown RePLB increases withthe increasing temperature difference. It means that heating onthe water has a stabilizing effect. In addition, it also indicates thatthe change of viscosity is not the predominant factor in the transi-tion process as referred in the above section.

As shown in Fig. 7, the local Nusselt number at the point of lam-inar breakdown does not change with the increase of heat flux for agiven inlet Reynolds number. However, the comparison of Fig. 6a, band c indicates that the local Nusselt number at the point of lam-inar breakdown increases with the increase of the inlet Reynoldsnumber. The phenomenon can be attributed to the difference of in-let velocity profile and turbulence intensity (Minkowycz et al.,2009).

Furthermore, as seen in Figs. 8 and 9, the comparison of presentdata and Silin et al. (2010a, 2010b) data shows a consistent of ten-dency, both of the experimental results shows a stability effect.

5. Conclusions

From the above discussions, we can get the conclusions that theheating on the water flow in a channel has a significant effect onthe location of transition initiation and shifts it downstream,

delaying the beginning of the turbulent flow. The local Nusseltnumber at the point of laminar breakdown depends on the inletReynolds number. In addition, the results also manifest that the lo-cal Reynolds number at the point of laminar breakdown dependson the inlet Reynolds number and the heat flux. Both the flowand heat transfer characteristics in the transition regime indicatesthe change of viscosity is not the dominant factor that introducesthe delay of transition.

Acknowledgment

This work is financial supported by the Fundamental ResearchFunds for the Central Universities (Program No. HEUCFZ1008).

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