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J. of Supercritical Fluids 72 (2012) 90– 99

Contents lists available at SciVerse ScienceDirect

The Journal of Supercritical Fluids

jou rn al h om epa ge: www.elsev ier .com/ locate /supf lu

xperimental investigation on heat transfer of a specific fuel (RP-3) flowshrough downward tubes at supercritical pressure

hunben Zhanga,b,∗, Guoqiang Xua, Lin Gaoa, Zhi Taoa, Hongwu Denga, Kun Zhua

National Key Laboratory of Science and Technology on Aero-Engine Aero-Thermodynamics, School of Jet Propulsion, Beijing University of Aeronautics and Astronautics, Beijing00191, PR ChinaXi’an Aerospace Propulsion Institute, Xi’an 710100, PR China

r t i c l e i n f o

rticle history:eceived 14 February 2012eceived in revised form 21 May 2012ccepted 26 July 2012

a b s t r a c t

The heat transfer characteristics of a specific hydrocarbon fuel RP-3 flowing through vertically down-ward miniature tubes (din = 1.8 mm) were experimentally investigated at supercritical pressure (P = 5 MPa,PR = 2.15) based on measured thermophysical properties under the fuel temperature ranged from 373 to800 K. Test results indicated that: in the initial heating region, wall temperature increased dramatically

eywords:upercriticalydrocarbon fueleat transfereteriorationorrelation

from the initial heating point and then decreased rapidly at higher heat flux, but this phenomenon dimin-ished when the inlet Reynolds number reached to 10,000. In addition, heat transfer deterioration occurredwhen thermal acceleration parameter (Kv) was less than 1.5 × 10−8 or buoyancy factor (Bo*) was less than1.6 × 10−10. Finally, a new heat transfer correlation was developed based on the experimental data andwhich predicted the heat transfer for RP-3 well.

Crown Copyright © 2012 Published by Elsevier B.V. All rights reserved.

. Introduction

In order to solve the cooling problem of the aircrafts operat-ng under high supersonic and hypersonic regime, the engine fuel

ill be used as the primary coolant to cool hot engine components.he fuel-cooled thermal management systems will be popularlysed with a minimum weight penalty and technical risk [1]. Forhe advanced gas turbine engines, the engine fuel is first pumpednto an air/fuel heat exchanger to cool the cooling air (CCA) fromompressor at supercritical pressures and the fuel is heated up overts critical temperature at the same time. It is then injected into theombustor while the cooled cooling air is led to the turbine for bladend disk cooling. For liquid oxygen–kerosene rocket engines andupersonic combustion ramjet (scramjet), so-called Active Regen-rative Cooling (ARC) technology has been used for a long time, thats: the fuel is first used for thrust chamber or combustor cooling,

nd the heat absorbed by the fuel will be released in combustorgain.

∗ Corresponding author at: National Key Laboratory of Science and Technologyn Aero-Engine Aero-Thermodynamics, School of Jet Propulsion, Beijing Universityf Aeronautics and Astronautics, Beijing 100191, PR China. Tel.: +86 10 82314545;ax: +86 10 82314545.

E-mail address: zhang cb@sjp.buaa.edu.cn (C. Zhang).

896-8446/$ – see front matter. Crown Copyright © 2012 Published by Elsevier B.V. All rittp://dx.doi.org/10.1016/j.supflu.2012.07.011

Hence, the flow and heat transfer characteristics of supercriticalhydrocarbon fuel play a key role in future CCA technology and ARCtechnology development for advanced gas turbine engines, rocketengines and supersonic combustion ramjet (scramjet). The exist-ing investigations into supercritical fluids are mainly focused onwater and carbon dioxide. Mokry et al. [2] confirmed that therewere three heat-transfer regimes for forced-convective heat trans-fer to water flowing inside tubes at supercritical pressures: namely,normal heat-transfer regime, deteriorated heat-transfer regimeand improved heat-transfer regime. The appearance and magni-tude of the deteriorated and improved heat-transfer regimes wereaffected by pressure, bulk fluid temperature, mass flux and heatflux. Kim et al. [3] found that heat transfer deterioration occurredwhen q > 0.2G.2.0 regardless of the cross-sectional shapes of tubes.Bazargan and Mohseni [4] numerically studied the significanceof the buffer zone in the boundary layer by using carbon diox-ide in a round tube at supercritical pressure. They concluded thatheat transfer deterioration was due to the turbulence reductionand flow laminarization. Sharabi and Ambrosini [5] also stud-ied heat transfer enhancement and deterioration numerically andcompared with experimental data from other researchers. Theymaintained that heat transfer enhancement was purely due to the

lambda-shaped trend of specific heat as a function of tempera-ture, whenever buoyancy effects were relatively important; andheat transfer deterioration was caused by laminarization effectsand occurred only in upward flow when buoyancy effects were

ghts reserved.

C. Zhang et al. / J. of Supercritic

Nomenclature

Bo* buoyancy factor, Bo∗ = Gr∗Re3.425Pr0.8

cp isobaric specific heat capacity (J/(kg K))d diameter (m)G mass flux (kg m−2 s−1)g acceleration of gravity (kg m−2 s−1)

Gr Grashof number, Gr = D3gˇ�T�2

Gr* Grashof number, Gr∗ = ˇgd4qw

��2

H enthalpy (J/kg)h heat transfer coefficient (W/(m2 K))I electrical current (A)k thermal conductivity (W/(m K))ks roughness (m)Kv thermal acceleration parameter, Kv = 4qwˇ

�ubcpRe

L length (m)m mass flow rate (kg/s)Nu Nusselt numberP pressure (Pa)Pr Prantl number, Pr = �cp

�Q heat (W)R reducedP pressurePc pseudo-criticalS smoothT temperature (K)X local positionW wallq heat flux (W/m2)r radius (m)Re Reynolds number, Re = �UD

�

U voltage (V)x local position (m)

Greekˇ isobaric thermal expansivity (K−1)� density (kg/m3)� dynamic viscosity (Pa s)� kinetic viscosity (m2/s)� thermal conductivity (W/(m K))� relative error volume heat source (W/m3)

SubscriptsB bulkC criticalF filmin insideout outside

AbbreviationsCCA cool the cooling airARC Active Regenerative CoolingDHT deteriorated heat transferHT heat transferHTC heat transfer coefficientNHT normal heat transfer

rfa[

upstream of the flow control valve (Model: SS-426F3, Swagelok)

elatively important. Bazargan indicated that criterion developed or buoyancy-free regions in a near-constant property flow is notdequate for predicting supercritical flows. Many other researchers6–15] also conducted supercritical CO2 and H2O investigations.

al Fluids 72 (2012) 90– 99 91

Brad and Michael [16,17] conducted experimental studies onthe supercritical fluid flow and heat transfer of a hydrocarbonfuel, JP-7, in a vertical tube, aiming to facilitate the technologi-cal development of the cooling strategies in future air-breathingpropulsion systems. When the reduced pressures (P/Pc) were below1.5 and the tube wall temperatures were above the correspond-ing pseudo-critical temperature, they observed significant pressureand temperature oscillations along with declined local heat trans-fer coefficients. Linne et al. [18] performed a series of heatedtube experiments to investigate fluid instabilities that occurredwhen heating supercritical fluids. In the tests, JP-7 flowed verti-cally through small diameter tubes at supercritical pressures. Alltests of theirs at the highest velocity were stable, but there was nofunctional relationship found between the instability and velocity,or a combination of velocity and temperature ratio. In addition, allof the unstable tests had significant buoyancy at the inlet of thetest section, however, many stable tests also showed significantbuoyancy forces. Li et al. [19] conducted the flow and heat transfercharacteristics of China No. 3 aviation kerosene in a heated curvedtube numerically under supercritical pressure. They concluded thatheat transfer was enhanced after the wall temperature was overthe pseudo-critical temperature, and the centrifugal force causeda strong secondary flow, which not only enormously enhanced theheat transfer, but also greatly increased the friction factors through-out the flow process. Edwards and his team [20–23] devoted tothe mechanisms of hydrocarbon fuel deposition at supercriticalpressures and a series of additives have been developed to min-imize cracking and coking in supercritical jet fuels.

Compared to pure fluids, due to the scarcity of properties ofhydrocarbon fuel such as vapor pressure, specific heat, density,viscosity, surface tension, and critical parameters, the theoreticalresearch on hydrocarbon fuel is still not deep enough and manyproblems remain to be solved. Based on the measured thermo-physical property data of RP-3 in our previous works [24–27],heat transfer of RP-3 flow through downward miniature tubes hasbeen experimentally studied under supercritical pressure in thisresearch, and this paper is organized as follows: firstly, the experi-mental apparatus and procedures are described in Section 2. Thenthe test results are analyzed in Section 3. Finally, a conclusion withsome major findings of this paper is reached in Section 4.

2. Experimental

2.1. Experimental system and test section

Fig. 1 shows the experimental system. It consists of preparativesystem, measured system and reclaimed system.

In preparative system, the fuel in tank 1 is pumped up to 12 MPaby a piston pump (Model: 2J-Z 104/16, Ailipu). A 45 �m filter (filter1 of Fig. 1) is attached to the suction side of the piston pump bothto protect the pump from any entrained debris and to serve as aninlet accumulator to ensure that the pump is not starved on the suc-tion stroke. The pre-pressed fuel from the piston pump was pushedinto an attached airbag pulsation damper (Model: NXQ-L04/16-H,Ailipu) to reduce the pressure pulsation to lower than 0.5% of thetest section inlet pressure. The fuel from the damper is dividedinto a major path fuel and a bypass fuel: the latter was collectedfor reuse and its pressure was controlled by a back pressure valve(0–15 MPa) in the bypass system; the mass flow rate of the majorpath fuel was measured using a Coriolis-force flow meter (Model:DMF-1-1, 0.15%, Sincerity) and a 30 �m filter was installed to the

to protect the fine passages in it. In order to achieve the requiredinlet fuel temperature of the test section, the pre-pressurized majorpath fuel was heated (up to 830 K) by two pre-heaters (Pre-heater 1

92 C. Zhang et al. / J. of Supercritical Fluids 72 (2012) 90– 99

Fig. 1. Schematic diagram of experimental system.

agram

ac

RtoA

3fswc

s1srttpito

nes, 4.39% naphthalenes and 1.46% other elements. The detailedcompositions of RP-3 were reported in our previous work [24].

Fig. 3 shows the density, dynamic viscosity, isobaric spe-cific heat capacity and thermal conductivity of RP-3 at 5 MPa

Table 1Experimental parameters.

Inside diameter of the test tube (mm) 1.805Heated length of the test section (mm) 300Inlet pressure (MPa) 5

Fig. 2. Schematic di

nd Pre-heater 2) which were controlled by independent availableurrent power supplies with a capacity of 20 kW.

In the test section, a pressure gage transducer (Model 3051CA4,osemount) is used to measure the static pressure at the inlet of theest section. The fuel temperature is measured at the inlet and outletf the test tube with K-type armored thermocouples respectively.ll data were recorded using computer system.

After each test, the hot fuel is cooled downed to lower than10 K by water cooled shell and tube heat exchanger, and then theuel pressure releases to ambient pressure through a back pres-ure valve. The fuel is collected into tank 2 for other usages and theater out from heat exchanger is cooled in cooling tower and then

ollected into tank 3 for recycling.Fig. 2 shows the details of the test section. The inside and out-

ide diameters of the test tube (Stainless Steel 1Cr18Ni9Ti) are.805 mm and 2.20 mm, which are measured by field emissioncanning electron microscope (Model: CamScan3400) and vernier,espectively. The test tube and the copper electrode are clamped bywo bolts. An electrical resistance wire is wrapped around the elec-rode and used to heat the test tube. An insulated length of 90 mm

recedes the heated tube length of 300 mm, which is followed by an

nsulated length of 60 mm. The outside wall temperature of the testube is measured by 20 K-type thermocouples with the diameterf 0.1 mm which are distributed uniformly. The whole test section

of the test section.

is insulated by Aspen (an insulating compound). The experimentcovers a wide range of parameters as listed in Table 1.

2.2. Coolant and properties

A typical jet fuel RP-3 is used here. The critical point of RP-3 is (Tc = 645.04 K, Pc = 2.33 MPa) which was identified by criticalopalescence phenomenon in our previous work [25]. Composi-tion analysis by using GC6890-MS5975 shows that RP-3 consists of52.44% alkanes, 7.64% alkenes, 18.53% benzenes, 15.54% cycloalka-

Mass flux (kg m−2 s−1) 786.5–2359Inlet temperature (K) 373–800Inlet Reynolds number 3500–10,000Heat flux (kW/m2) 300–550

C. Zhang et al. / J. of Supercritic

F

(cfdSaedFe3ct±it

2

h

we

q

w

flae

q

T

T

ig. 3. Physical parameters ratio of RP-3 vs. temperature at 5 MPa (TPc = 716.57 K).

TPc = 716.57 K, H(TPc ) = 1285.18 kJ/kg). The density, dynamic vis-osity and isobaric specific heat capacity used here were calculatedrom the equations obtained from our previous experimentalata [24,26,28]. Thermal conductivity was first calculated by NISTupertrapp based on 10-compositions substitute kerosene [29],nd then the pseudo-critical point was revised based on thexperimental value, which ensured that the trend of thermal con-uctivity variation coincides with the other three parameters.or RP-3: the combined standard uncertainty and the relativexpanded uncertainty (coverage factor k = 2) of the density of RP-

were calculated as ±0.683% and ±1.37%, respectively [24]; theombined standard uncertainty of the dynamic viscosity was iden-ified as ±(1.07–3.21)% and the relative expanded uncertainty was(2.14–6.42) %, respectively [26]; for isobaric specific heat capac-

ty, ±2.11% and ±4.22% (k = 2), respectively [28]. The uncertainty ofhe thermal conductivity is considered ±2.5% in this paper.

.3. Data analysis method

The local heat transfer coefficient (HTC) hx is defined by

x = qx

Twx,in − Tb,x(1)

here the effective heat flux qx is the difference of local electricalnergy and heat losses, and it was calculated by

x = I2R(T)/[(d2o − d2

i)]

d− qloss,x (2)

here R(T) is the electronic resistivity of stainless steel.The local fuel temperature Tb,x was determined by the local heat

ux, the inlet and outlet fuel enthalpy, and the inside wall temper-ture Twx,in is determined by solving the 1-D thermal conductivityquation under the cylindrical coordinate system as

k

r

d

dr

(r

dT

dr

)+ = 0 (3)

The boundary conditions were

loss = −kdT

dr

∣∣∣r=routo

(4)

hen Twx,in is given by

wx,in = Twx,out −[((r2

out/2) − qx,lossrout ) ln(rout/rin) − (/4)(r2out − r2

in)]

kx(5)

al Fluids 72 (2012) 90– 99 93

And then the local Nusselt number is calculated as follows

Nux = hxd

�x(6)

where �x is the local thermal conductivity of fluid.Based on the experimental parameters range in Table 1, the

minimum temperature difference between the inside wall and thebulk fluid is 27 K. The uncertainties of local wall temperature andbulk fluid temperature are ±0.87 K and ±0.85 K, respectively. Themaximum relative error of the effective heat flux qx is ±0.46%. Themaximum uncertainties of HTC and Nusselt number are identifiedas ±6.83% and ±8.33%, respectively.

3. Results and discussion

3.1. Effect of heat flux

Fig. 4 shows the variations of inside wall temperature(Twx,in) and the heat transfer coefficient (HTC) of RP-3 vs. fluidenthalpy for downward flow. In the experiments, the inletfuel pressure is fixed at 5 MPa, the inlet fluid temperatureranges from 373 to 800 K and the mass flux is maintained at1572.7 kg m−2 s−1; the heat flux changes from 300 to 550 kW/m2;and the corresponding local Reynolds number ranges from 5000to about 87,000. The enthalpy in Fig. 4 is defined by bulk fluidtemperature.

It can be seen that differences of wall temperatures at variousheat fluxes decrease with the increase of fluid enthalpy; at thesame enthalpy point, HTC decreases with the increase of heat flux.In addition, Fig. 4 shows that there are four heat transfer regions:(1) initial heating region, featuring a local peak value of wall tem-perature; (2) normal heat transfer region, featuring a linearly riseof Twx,in and HTC; (3) enhanced heat transfer region, featuringnonlinear increase of HTC; (4) deteriorated heat transfer region,featuring the decrease of HTC with the increase of enthalpy, andthe increase of Twx,in. In the following sections, the fundamentalmechanisms of these four heat transfer regions will be discussed indetail.

3.1.1. Heat transfer mechanism of the initial heating region (IHR)Fig. 5(a) and (b) presents the variations of local Nusselt num-

ber (Nux) with reduced temperature Tb/TPc and reduced length x/din the initial heating region, respectively. It is shown that deterio-rated heat transfer fist appears from the initial heating point. Heattransfer recovers after Nux reaches to the minimum value. The rea-son is that in the initial heating region, thermal boundary layer isin the developing stage, the thickness of thermal boundary layerincreases along flow direction. Meanwhile, the thermal conductiv-ity of RP-3 decreases with the increase of fluid temperature in thisregion, which results in the increase of thermal resistance and thethickness of that increases along flow direction. Hence, the bulkfluid temperature and velocity change slightly. As a consequence,the trend of the increase of heat transfer is greater than the trendof the decrease of heat transfer, which finally leads to the rapidincrease of wall temperature (see Fig. 3) and heat transfer deterio-ration from the initial heating point. According to Hall and Jackson’s[9,30] explanation of this phenomenon, when temperature gradi-ent was large near wall layer, buoyancy force caused the decreaseof wall shear stress and then caused the fluid in the wall layerto be laminarized, and wall temperature further increased evena peak value occurred. Zhou [31] also found this phenomenon insupercritical water investigation and as he has explained, thermal

boundary layer was laminar-like at the beginning and the thicknessof thermal boundary layer increased along flow direction, whichcaused the heat transfer intensity to decrease and the wall temper-ature to increase. As thermal boundary layer developed and Grashof

94 C. Zhang et al. / J. of Supercritical Fluids 72 (2012) 90– 99

Fig. 4. Variations of HTC and wall temperature with bulk fluid enthalpy at various heat fluxes. (�, �) q = 300 kW/m2; (�, ©) q = 400 kW/m2; (�, �) q = 500 kW/m2; (�, �)q = 550 kW/m2.

a b

F q = 400 kW/m2; (�) q = 500 kW/m2; (�) q = 550 kW/m2. (a) Nu vs. Tb/TPc and (b) Nu vs. x/d.

nllwoa

tohmquth

ifMot

ig. 5. Variation of Nusselt number (P = 5 MPa, Tf,in = 373 K). (�) q = 300 kW/m2; (�)

umber (Gr) reached to a certain value, the thermal boundaryayer transited from laminar-like to turbulent-like. The thickness ofaminar boundary layer was reduced and heat transfer intensity

as enhanced. He also stated that this phenomenon not onlyccurred at supercritical pressures but also at subcritical pressurest any fluid temperature conditions.

Fig. 5(a) also indicates that the corresponding bulk tempera-ure of the minimum value of Nux increases with the increasef heat flux. Before the minimum Nux point, Nux increases witheat flux at the same fluid temperature, it is opposite beyond theinimum value point, but this phenomenon is not obvious when

> 500 kW/m2. Similarly, Fig. 5(b) indicates that the minimum val-es of Nux at various heat fluxes occur at the same tube position,hat is x/d ≈ 30. When x/d > 30, Nux increases with the increase ofeat flux at the same tube position.

In addition, Fig. 6 shows that the wall temperature regionnfluenced by the development of the thermal boundary layer is dif-erent: the higher the heat flux, the wider the temperature region.

oreover, it can be seen from Fig. 5(a) and (b) that the positionf the minimum value of Nux is not the local peak value of wallemperature, this phenomenon can be explained by variation of

Fig. 6. Variation of Twx,in vs. x/d in initial heating region (P = 5 MPa, Tf,in = 373 K). (�)q = 300 kW/m2; (�) q = 400 kW/m2; (�) q = 500 kW/m2; (�) q = 550 kW/m2.

C. Zhang et al. / J. of Supercritic

Fig. 7. Variation of (Twx,in − Tbx) vs. x/d in initial heating region (P = 5 MPa,T 2 2 2

q

tsl

3

atphtiim3vf

3

tiewtptT1ictavT(twioo

1a

f,in = 373 K). (�) q = 300 kW/m ; (�) q = 400 kW/m ; (�) q = 500 kW/m ; (�) = 550 kW/m2.

emperature difference (Twx,in − Tbx) along tube (see Fig. 7). Fig. 7hows that (Twx,in − Tbx) reaches to the peak value at x/d ≈ 30, whicheads to the lowest HTC at this position.

.1.2. Mechanism of the normal heat transfer region (NHTR)Fig. 11(a) and (b) is sub-figures of Fig. 7 when q = 300 kW/m2

nd q = 550 kW/m2, respectively. In the two figures, each heatransfer region is divided and marked. It can be seen that the initialoint of normal heat transfer (NHT) region is different for variouseat flux whilst the ending point of NHT region is the same. Forhe experimental runs in this work, the ending point correspond-ng to the fluid enthalpy is 930 kJ/kg or reduced fluid temperatures 0.85. In NHT region, both wall temperature and HTC increase

onotonously. The main reason is that physical parameters of RP- change linearly when Tb/TP < 0.85 (see Fig. 3). Beyond this point,ariations of the physical parameters are nonlinear. This region isollowed by enhanced heat transfer region.

.1.3. Mechanism of the enhanced heat transfer region (EHTR)As aforementioned, the initial point of EHT region corresponds

o the fluid enthalpy of 930 kJ/kg. It can be seen from Fig. 8 that HTCn this region increases significantly compared to NHT region. How-ver, the fluid enthalpy at the ending point of EHT region increasesith heat flux, which changes from about 1580 kJ/kg at 300 kW/m2

o 1700 kJ/kg at 550 kW/m2, and the corresponding reduced tem-eratures are 1.1–1.15 respectively. It can be seen from Fig. 3 thathe variation of physical parameters of RP-3 is increased whenb/TPc = 0.85. When reduced fluid temperature rises from 0.85 to.1, the density of RP-3 decreases by 7 times; isobaric specific capac-

ty increases by a factor of 1.33; dynamic viscosity and thermalonductivity decrease by a factor of 2.6 and 1.08, respectively. Inhe four basic physical parameters, variations of density, viscositynd specific capacity are beneficial to enhance heat transfer; onlyariation of thermal conductivity would reduce the heat transfer.he variations of physical parameters cause the thermal diffusivity

= (�/�cp)) increases by about 6 times, the increase of indicateshe increase of the ability of fluid temperature evened out, in otherords, the momentum and thermal diffusivity of the fluid at var-

ous velocity layers are enhanced. Thus, the comprehensive effectf the four physical parameters leads to a significant enhancement

f heat transfer.

When the reduced fluid temperature of RP-3 rises from 1.1 to.24, density decreases by a factor of 1.33; heat capacity, viscositynd thermal conductivity increase as well. For the four parameters,

al Fluids 72 (2012) 90– 99 95

variations of density, heat capacity and thermal conductivity arebeneficial to heat transfer; only variation of viscosity is detrimentalto heat transfer. The heat transfer should have been enhanced butthe result is opposite. The thermal diffusivity decreases 1.26 timesdue to variations of physical parameters, which further enlargesthe temperature differences at various fluid layers. Thus, the effectof buoyancy force in radial direction is enhanced. In addition, atTb/TPc = 1.1, the corresponding fluid temperature is about 788 K,the chemical reaction of hydrocarbon fuel is enhanced significantly.Thus, enhancements of buoyancy force and chemical reaction maybe the reasons for heat transfer deterioration. In the following sec-tion, the mechanism of heat transfer deterioration will be analyzedby the variations of dimensionless parameters.

3.1.4. Mechanism of the deteriorated heat transfer region (DHTR)Re, Pr, Gr are the three basic dimensionless parameters that

reflect the characteristics of flow and heat transfer. Generallyspeaking, these parameters are defined by bulk fluid temperature,so variations of Re, Pr and Gr are invariable for various heat fluxes atthe same fluid temperature. However, the beginning point of DHTregion is different for various heat fluxes. McEligot et al. [32] andJackson and Hall [33] promoted a heating acceleration parameterKv and a buoyancy parameter Bo*, respectively. Among them, Bo*is defined as follows [33]:

Bo∗ = Gr∗

Re3.425Pr0.8(7)

where is Grasholf number too, which is calculated by Gr∗ =(ˇgd4qw/��2); � is kinetic viscosity (m2/s); is thermal expansivity(K−1); qw and is the wall heat flux (W/m2).

And Kv is defined as [33]:

Kv = vb

u2b

dub

dx= 4q+

Re= 4qwˇ

�ubcpRe(8)

Variations of local Kv, Bo* and Nu with reduced fluid temper-ature at different heat fluxes are given in Fig. 9. It should benoted that Kv and Bo* increase significantly before pseudo-criticalpoint and then decrease when Tb/TPc > 1. Combine the trend ofNusselt number variation, the changes of Kv and Bo* in the pseudo-critical region (0.95 < Tb/YPc < 1.05) promote heat transfer. Thisphenomenon indicates that variations of thermophysical proper-ties near pseudo-critical point result in an enhanced turbulenceintensity. In addition, when Kv is near 1.5 × 10−8 or Bo* is near1.6 × 10−10, heat transfer deterioration (HTD) appears for all exper-imental runs, which is the beginning point of DHT region. After HTDoccurs, Kv and Bo* decrease dramatically until an inflection pointappears. The appearance of the inflection point indicates that heattransfer is totally deteriorated. The reason that Kv and Bo* can reflectHTD is that both of them include the effect of wall heat flux on flowand heat transfer. However, the criterion for HTD prediction in thiswork is different from McEligot’s [32], who concluded that: whenKv ≤ 3 × 10−6, the flow was maintained as turbulent flow; whenKv > 3 × 10−6, HTC decreased and the flow may be laminarized. Mur-phy et al. [34] argued that the flow would also be maintained asturbulent flow when Kv ≤ 9.5 × 10−7 while it was laminarized whenKv ≥ 4 × 10−6. In our experiments, all the values of Kv in the DHTregion are far less than 3 × 10−6, or even lower than 9.5 × 10−7. Theprobable reason for this difference could be that the fluid used hereis a multi-component mixture, at the same time chemical reactionsexist in the whole heating process.

3.2. Effect of inlet Reynolds number

Fig. 10 shows the effects of inlet Reynolds numbers onheat transfer. In these experiments, the inlet fluid pressure and

96 C. Zhang et al. / J. of Supercritical Fluids 72 (2012) 90– 99

id ent

ttc7iwH

baRl

Fig. 8. Variations of HTC and wall temperature with bulk flu

emperature are maintained at 5 MPa (PR = 2.15) and 373 K, respec-ively; the heat flux is 550 kW/m2; the inlet Reynolds numberhanges from 3500 to 10,000, and the corresponding mass flux is86–2359 kg m−2 s−1; the local Reynolds number in the test section

s up to 1.7 × 105. It can be seen from Fig. 10(a) that HTC increasesith the increase of inlet Reynolds number. Besides, the slope ofTC vs. fluid enthalpy is higher at higher Rein.

Fig. 10(b) shows the effect of Rein on wall temperature. It cane seen that the local peak value characteristic of wall temper-

ture in the initial heating region decreases with the increase ofein. When Rein reaches to 104 and the inlet fluid temperature is

ower than its pseudo-critical temperature, the local peak value of

Fig. 9. Variations of local Kv , Bo* and Nu with reduced fluid temperature

halpy (P = 5 MPa). (a) q = 300 kW/m2 and (b) q = 500 kW/m2.

wall temperature will disappear except the point is close to copperelectrode. This phenomenon illustrates that the increase of Rein notonly changes the boundary layer development of velocity, but alsochanges the boundary layer development of temperature.

To further discuss the effect of Rein on heat transfer character-istics of RP-3, Fig. 10(c) and (d) shows the variations of Nu vs. Reand Tb/TPc , respectively. It can be seen that if the initial heatingeffect is neglected, Nu increases with the increase of Re and it hasa linear relationship with Re at logarithmic coordinates. However,

at the same local Reynolds number position, the higher the inletReynolds number, the higher the Nusselt number. It indicates thatNu is not only affected by Re but also by other parameters. Similarly,

(P = 5 MPa, Tf,in = 373 K). (a) q = 300 kW/m2 and (b) q = 550 kW/m2.

C. Zhang et al. / J. of Supercritical Fluids 72 (2012) 90– 99 97

a b

c d

F 2 (�) Rein = 3500; (�) Rein = 5000; (�) Rein = 6500; (�) Rein = 10,000. (a) HTC vs. enthalpy; (b)i

Nifpfaphh

3

mcvtac1Ja

fome

Fig. 11. Comparison of the calculated Nusselt numbers by using the classical cor-relations with the experimental data. (a) No buoyancy: (�) Jackson and Hall (nobuoyancy) [33,35]; (�) Krasnoshchekov [36], Protopopov [37] and Grigoriev [38];

ig. 10. The effects of Rein on heat transfer (P = 5 MPa, Tf,in = 373 K, q = 550 kW/m ).

nside wall temperature vs. enthalpy; (c) Nu vs. Re and (d) Nu vs. Tb/TPc .

u increases linearly with the increase of fluid temperature untilt is close to pseudo-critical point. As aforementioned, heat trans-er will be enhanced when fluid temperature nears pseudo-criticaloint. At the same time, Fig. 10(d) further indicates that heat trans-er enhancement point is presented at higher Rein. Thus, higher Reinnd significant variations of thermophysical properties close toseudo-critical point are two main factors that influence flow andeat transfer in miniature tubes. The fitting method for establishingeat transfer correlation will be discussed in the following part.

.3. Heat transfer correlation for hydrocarbon fuel

The existing heat transfer correlations for supercritical fluids areainly divided into two types: one is the convective heat transfer

orrelation that takes into account the thermophysical propertiesariation; the other is the correlation that considers the effects ofhermal acceleration and buoyancy force. Both of the two typesre listed in Table 2. For the sake of convenient comparison, theorrelations (JH-1 and JH-2) are proposed by Petukhov [35–37] (No.

in Table 2), Stiegemeier [38] (No. 2), Protopopov [39] (No. 3) andackson and Hall [33,40] (No. 4). The details of these correlationsre in Table 2.

Fig. 11 exhibits comparison of the calculated Nusselt number

rom the four correlations in Table 2 and the experimental resultsf RP-3 which flows through downward tubes. It can be seen thatost of the calculated value by the six correlations are within ±30%

rror band in the NHT region (Nu < 200) and POV is better compared

(�) Krasnoshchekov, Protopopov and Petukhov; (b) considering buoyancy: (�)Stiegemeier et al. [39]; (©) Jackson and Hall [33,35]; (�) Protopopov [37].

to the others; in the region of Nu < 300, KPP is much better; but in

EHT and DHT regions, calculated values by JH-1, JH-2, KPG, KPPand POV are far from the experimental values, only SMT is rela-tively close to the experimental values. It indicates that large error

98 C. Zhang et al. / J. of Supercritical Fluids 72 (2012) 90– 99

Table 2Selected heat transfer correlations of supercritical fluids.

Author and No. Correlation Fluid

No. 1 Petukhov Nu = Nu0

(�b�w

)0.11( kbkw

)−0.33( cpcpb

)0.35

where,

Nu0 = (�/8)RebPr

12.7√

�/8(Pr2/3−1)+1.07

� ={ 1

(1.82 log10Reb − 1.64)2, Re < 105

0.02 Re > 105

2 × 104 < Reb < 8.6 × 105, 0.85 < Pr < 65, 0.90 <�b�w

< 3.6,

1.00 <kbkw

< 6.00, 0.07 <cpcpb

< 4.50

H2OCO2

No. 2 Stiegemeier Nu = 0.016[

1 + 2(x/d)

]Re0.862Pr0.4 JP-7

JP-8JP-8+100JP-10 RP-1

No. 3 Protopopov Nufx = Nuf0x˚(K)

where, K =(

1 − �w�b

)· Gr

Re2

when 0.01 < K < 0.4:˚(K) = 0.79782686 − 1.6459037lnK − 2.7547316(lnK)2

− 1.7422714(lnK)3 − 0.54805506(lnK)4 − 0.086914323(lnK)5

− 0.0055187343(lnK)6

when K > 0.4:˚(K) = 1.4K0.37

Application condition :(

xd

)>

(xd

)in

≈ 2(

xd

)max tw

subscript “in” represents “inlet”,(

xd

)max tw

= 95K−0.25 − 15

H2ORe2

No. 4Jackson and Hall NuNuf

=[∣∣∣1 ± 8×104Gr∗

Re3.425Pr0.8

(NuNuf

)−2∣∣∣]0.46

, Bo∗ = Gr∗Re3.425Pr0.8

where, “+” and “−” represent downward and upward flowrespectively; and Nufis calculated as:

Nub = 0.0183Re0.82b

Pr0.5b

(�w�b

)0.3( cpcpb

)n

n ={

0.40.4 + 0.2[(Tw/Tpc) − 1]0.4 + 0.2(Tw/Tpc − 1)[1 − 5(Tb/Tpc − 1)]

,

Tw

H2OCO2

ocptlop8

eif

waca(

N

w

bw

Tb < Tw < Tpc, 1.2Tpc < Tb <Tb < Tpc < Tw

Tpc < Tb < 1.2TpcTb < Tw

ccurs when correlations obtained by pure fluids are used to HTCalculation of multi-component hydrocarbon fuel which accom-anies chemical reaction. At the same time, deviations betweenhe calculated values by SMT and experimental values are alsoarge when Nuexp < 120, the main reason is that SMT correlation isbtained based on a small temperature range: the outlet fuel tem-erature is maintained at 568 K; the wall temperature at 707 K or46 K. Thus, the scope of SMT is limited.

Based on the measured thermophysical properties and thexperimental data for the circular tube of d = 1.8 mm, the follow-ng correlation is obtained for forced convection of hydrocarbonuel in miniature tubes heated at supercritical pressures:

Nu

Nu0= 0.125

( �f

�b

)0.12( �f

�b

)0.153(

1 + 7.558(

Nu

Nu0

)0.989)

(9)

here subscript “b” indicates that the thermophysical propertiesre calculated based on bulk fluid temperature; subscript “f” indi-ates that the thermophysical properties are the weightedverage properties in boundary layer, e.g. �f =(∫ Tw,in

Tb�(T)dT)/(Tw,in − Tb)); Nu0 is defined as follows:

u0 = 0.0113Re0.862Pr0.4f (10)

�f cp,f

here Prf = �f.

Fig. 12 shows the comparison of the calculated Nusselt numbersy Eq. (9) with the experimental values. All the 1380 points areithin the ±8% error band.

Fig. 12. Comparison of the calculated Nusselt number (Eq. (9)) with the experimen-tal value.

4. Conclusion

The heat transfer characteristics of a specific hydrocarbon fuelRP-3 flowing through downward vertical straight tubes wereexperimentally investigated at supercritical pressure based on

measured thermophysical properties. Test results demonstrate thatheat transfer (HT) of RP-3 in heated miniature tubes can be dividedinto four regions: (1) initial heating region; (2) normal HT region;

rcritic

(ismitebtdce

R

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

C. Zhang et al. / J. of Supe

3) enhanced HT region; (4) deteriorated HT region. The dramaticncrease from the initial heating point and the later decrease of thelope of wall temperature are caused by the development of ther-al boundary layer, but this phenomenon disappears when Rein is

ncreased to 10,000. The mechanics of normal and enhanced heatransfer regions depend on the variations of thermophysical prop-rties of RP-3. In addition, deteriorated heat transfer is caused byuoyancy force and thermal acceleration. When thermal accelera-ion parameter Kv < 1.5 × 10−8 or buoyancy factor Bo* < 1.6 × 10−10,eteriorated heat transfer occurs. Finally, a new heat transferorrelation is developed based on the experimental data, whichxhibits a good predictive capability for RP-3.

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