Experimental Thermal and Fluid Science 61 (2015) 144–152

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Experimental Thermal and Fluid Science

journal homepage: www.elsevier .com/locate /et fs

Heat transfer to supercritical pressure hydrocarbons flowingin a horizontal short tube

http://dx.doi.org/10.1016/j.expthermflusci.2014.10.0240894-1777/� 2014 Elsevier Inc. All rights reserved.

⇑ Corresponding author. Tel./fax: +86 029 82665287.E-mail address: qcbi@mail.xjtu.edu.cn (Q. Bi).

Zhuqiang Yang, Qincheng Bi ⇑, Zhaohui Liu, Yong Guo, Jianguo YanState Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, No. 28 Xianning West Road, Xi’an 710049, PR China

a r t i c l e i n f o

Article history:Received 12 April 2014Received in revised form 27 October 2014Accepted 28 October 2014Available online 6 November 2014

Keywords:HydrocarbonsHeat transferSupercritical pressureHorizontal tube

a b s t r a c t

The heat transfer characteristics of hydrocarbon fuel were investigated in a short horizontal tube with a1.0 mm inside diameter. The experiments were conducted in test tubes that were 46 mm and 116 mm inlength at a supercritical pressure of 3.0 MPa. The experimental parameters included a liquid velocity of0.21–1.20 m/s, an inlet fluid temperature of 298–673 K, and various heat fluxes. Different heat transferregions were designated based on the heat transfer behavior. The mechanisms of heat transfer enhance-ment and deterioration are discussed. Heat transfer was improved by thermophysical property variation,thermoacoustic oscillation, and endothermic reactions of the hydrocarbons in the respective processes.Heat transfer deterioration was characterized by gas resistance and coke deposition in the boundary fluid.Heat flux, fluid velocity, and inlet temperature were studied in depth as effective parameters. The allowedmaximum ratios between heat flux and mass flow rate at various velocities and inlet fluid temperaturesare given and could be used as criteria for future applications.

� 2014 Elsevier Inc. All rights reserved.

1. Introduction

The supercritical heat transfer of hydrocarbon fuel plays a keyrole in heat management technology for liquid rocket and scramjetengines [1–3], which endure high heat loads from aerodynamicheating, high temperature engine components, and other heat pro-ducers [3]. Regenerative fuel cooling has been considered the mosteffective cooling method for both the liquid rocket engine [4,5] andthe scramjet [6,7]. In a regenerative cooling system, hydrocarbonfuel absorbs the heat by physical sensible heat and endothermicchemical reactions in the flow channel, resulting in a reductionin the engine wall temperatures. Meanwhile, the fuel’s enthalpyincreases and the ignition is improved in the combustor. In thisprocess, the hydrocarbon fuel needs a remarkable endothermiccooling ability, with high stability and low coking [1,8]. Depositformation on the wall surface causes an increase in thermal resis-tance, leading to a progressive increase in the wall temperatureand, ultimately, failure [9].

Thus, extreme operating conditions, such as high heat flux, alarge temperature difference between the engine wall and thefluid, severe composition variation, and limited flow rate, exist ina regenerative cooling system [3,10–12]. A fundamental under-standing of the heat transfer characteristics of the hydrocarbon

fuel under different conditions is required, and would be beneficialfor the design and management of the regenerative cooling system.

A series of studies have been carried out on heat transfer ofsupercritical fluid. Most have focused on the supercritical water[13–15] and the refrigerants [16–18], due to their practicalapplications in the power industry and refrigeration fields. A num-ber of theories and computational formulas have been developedto interpret the various phenomena.

Due to the particular application of hydrocarbon fuel, the heattransfer characteristics of supercritical hydrocarbon fuel haveattracted the attention of researchers in the aerospace and powerengineering industries. Yanovskii and Kamenetskii [19] conductedexperiments on the heat exchange of RT and T-6 fuel oil in forcedflow, at supercritical pressure. They summarized the limit condi-tion of impaired heat transfer as a dimensionless relationship.Hitch and Karpuk [20] studied the heat transfer of JP-7 hydrocar-bon fuel in a supercritical flow. They found that tube wall temper-ature above pseudocritical temperature could cause significantpressure and temperature oscillations when reduced pressurevalues (the ratio of operating pressure to critical pressure) werebelow 1.5. However, no significant heat transfer enhancementwas observed under the oscillating conditions. Kelbaliev [21]investigated a mode transition from improved heat transfer todeteriorated heat transfer for toluene at supercritical pressures insmall tubes. Chen and Dang [22] conducted experiments on thesupercritical heat transfer of JP-7 and ascertained the characteris-tics of the heat transfer and the coking properties of the fuel.

Nomenclature

Abbreviationsd diameter of the tube (mm)g gravitational constant (m/s2)l length of test section (mm)u fuel velocity (m/s)p pressure (MPa)q heat flux (kW/m2)T temperature (K)Q absorbed heat (W)x location from inlet of the tube (mm)h heat transfer coefficient (W/(m2 K))G mass velocity (kg/(m2 s))

Greekq density (kg/m3)l dynamic viscosity (Pa s)k thermal conductivity (W/(m K))

Subscriptsb bulkf filminl inlet of tubein inside of tubeout outside of tubepc pseudocriticalw tube wall

Z. Yang et al. / Experimental Thermal and Fluid Science 61 (2015) 144–152 145

Edwards [8] reviewed progress in the thermal instability of super-critical hydrocarbon aviation fuels in the cracking process. Huaet al. [23] simulated the forced convective heat transfer ofn-heptane inside a horizontal mini-tube. Heat transfer deteriora-tion occurred when tube wall or fluid temperature reached thepseudocritical temperature, while high pressure enhanced the heattransfer. Jiang et al. [24] tested a series of model compounds(n-octane, n-decane, n-dodecane, cyclohexane, methylcyclohex-ane) and RP-3 in a heated tube at supercritical pressure andobtained their critical points of thermal cracking and deposition.

Although numerous studies have been done on supercriticalhydrocarbons, there have been few investigations into the heattransfer characteristics at practical conditions, an area that needsto be addressed. In this paper, the heat transfer behavior of a ker-osene-based hydrocarbon fuel was studied in a short horizontaltube at supercritical pressure. The improved and deteriorated heattransfer characteristics of the respective mechanisms areexpounded. The effects of fluid velocity, inlet temperature, andheat flux are discussed.

2. Experimental apparatus and procedure

2.1. Experimental apparatus

The experiments were conducted in our laboratory using ahome-designed hydrocarbon fuel test loop. The schematic diagramof the experimental system is shown in Fig. 1. Each kerosene fuelwas driven by high pressure nitrogen. The fuel passed the flowregulating valve and mass flow meter and flowed into a horizontal

Fig. 1. Schematic diagram o

tube (inner diameter, 1.0 mm; wall thickness, 0.5 mm) made ofGH3128 high temperature nickel alloy. The tube was in series con-nected in power circuit to heat the fuel by its joule heat. Two low-voltage AC power supplies (40 V, 250 A) were available in the pre-heated section and the test section, respectively. Following the testtube, a circular quartz silica tube with the same diameter wasinstalled, to visualize the flow [25]. Finally, the fluid was cooledby a condenser and separated by a gas–liquid separator. A backpressure valve was used to control the work pressure.

In the test section, two U 1.5 mm K-type armored thermocoupleswere installed at the inlet and outlet to measure the bulk tempera-ture. Eight pairs of U 0.2 mm K-type thermocouples were uniformlywelded on the outside surface of the test tube to measure wall tem-peratures. The distribution of these thermocouples is shown inFig. 2. Work pressure was measured by a Rosemount 3051 capaci-tance-type pressure transmitter at the outlet and the pressure dropwas obtained by a Rosemount 3051 differential pressure transducer.In the visualization section, flow images were recorded by a high-speed camera (1000 flames per second). The terminology used byWojtan et al. [26] was applied to characterize the flow patterns inthe images. All information was recorded using a computerized dataacquisition system (IMP3595). Specific experimental parametersare listed in Table 1 and the estimated uncertainties of the measuredand calculated parameters are presented in Table 2.

2.2. Experimental material

Hydrocarbon fuel is made up of a blend of hydrocarbons, withcycloalkanes comprising 30.50 wt.%, alkanes 20.06 wt.%, and

f experimental system.

Fig. 2. Structure of the test section and distribution of measurement points.

Table 2Uncertainties in measured and calculated parameters.

Value Uncertainty (%)

Pressure (MPa) 0.78Differential pressure (kPa) 1.5Electrically-heated power (W) 2.7Mass flow rate (g/s) 0.03Fluid temperature (K) 0.4Wall temperature (K) 0.58Heat flux (kW/m2) 4.2Heat transfer coefficient 4.29

Table 1Parameters of the test condition.

Parameters Test range or value

Pressure (MPa) 3.0Velocity (m/s) 0.21–1.20Inlet fluid temperature (K) 298–673Length of test tube (mm) 46, 116

146 Z. Yang et al. / Experimental Thermal and Fluid Science 61 (2015) 144–152

aromatics 49.42 wt.%. The average molecular formula is C11.9H23.4

[27]. The fuel’s critical pressure and temperature are 2.35 MPaand 674.1 K, according to the critical opalescence phenomenon.

2.3. Experimental procedure

In each run, the mass velocity and pressure were firstly set togiven values. Preheating and heating power was then regulatedto adjust fluid temperature. Data were collected when fluid tem-perature reached a steady state. The heating power was increasedstepwise and more data recorded. Once the tube wall temperaturewas over 1173 K, or rose rapidly at a constant heat flux, the testwas terminated. The heat flux corresponding to the final value inthe experiment was defined as the maximum heat flux and couldbe used as a criterion for engineering design. The effects of massvelocity and inlet fluid temperature were studied by repeatingthe above processes.

Coolant side wall temperature was calculated from the outsidewall temperature using Eq. (1) [28]. The calculation was based onthe direct radial conduction, assuming equal power distributionalong the tube.

Tw;in ¼ Tw;out �Q

2pkxln

dout

dinð1Þ

where Tw,in and Tw,out are the inside and outside tube wall temper-ature respectively, din and dout stand for the inside and outsidediameter of the tube, Q represents the heat energy absorbed bythe fuel, and k stands for the thermal conductivity of the tubematerial.

The local heat transfer coefficient h at location x along the testtube is defined as:

h ¼ qTw;in � Tb

ð2Þ

where q represents the heat flux over the inside wall of the tube.Thus, the local Nusselt number Nu is calculated by Eq. (3),

where kb is the local thermal conductivity of bulk fluid:

Nu ¼ hdkb

ð3Þ

3. Results and discussion

In these experiments, a hydrodynamic stabilization section of60 diameters was installed before the heated section, to supplydeveloped flow. In the test section, variations in the temperatureand heat transfer coefficient of the fluid were investigated. Theheat transfer mechanism was analyzed in different regions. Thevariation in heat transfer in the cross section played an importantrole in the experiments.

3.1. Region dividing of the heat transfer characteristics

The inside wall, bulk, and film temperatures of the test pointswere used in the experimental analysis. The inside wall tempera-ture was calculated from the measured outside wall temperatureusing Eq. (1). The local bulk temperature of the test point was cal-culated using the specific heat and the local enthalpy obtainedfrom the inlet enthalpy, heat flux, and axial location. [18] In heattransfer and fluid mechanics, the film temperature is an approxi-mation of the temperature of a fluid inside a convection boundarylayer. In this work, it is calculated as the arithmetic mean of theinside wall temperature and the bulk temperature of the fluid,using Eq. (4).

Tf ¼Tw;in þ Tb

2ð4Þ

In tests, the inside wall temperatures along the tube varied withthe increase in heat flux. However, the trends of all tested temper-atures at different points exhibited good unanimity. As a typicalrepresentation, the curves for the inside wall, bulk, and filmtemperatures at test point x/d = 24 were plotted in Fig. 3, and vari-ations in superheat, defined as the difference between the insidewall temperature and the fluid pseudocritical temperature, andheat transfer coefficient at test point x/d = 24 were plotted inFig. 4. The divisions of the different heat transfer regions werebased on the behavior shown in Figs. 3 and 4.

In the low heat flux region (segment AB), inside wall tempera-ture and superheat increased linearly with the increase of heatflux. The heat transfer coefficient was proportional to the fluidenthalpy. In this region, the heat transfer of the fuel was controlledby the conventional law of convection flow [19]. It occurred whenfilm temperature was lower than the pseudocritical temperature.

The heat transfer was improved in segment BC. The inside walltemperature remained unchanged while the superheat of the fluidgradually decreased. A number of studies [19,23,29] have beenconducted on the mechanisms of heat transfer enhancement witha temperature distribution of Tw > Tpc and Tf < Tpc. To further under-stand the mechanisms, we reviewed the variation in the thermalproperties of hydrocarbon fuel (density, isobaric specific heat,

Fig. 5. Thermophysical properties ratio of the hydrocarbon fuel vs. temperature atp = 3.0 MPa.

Fig. 3. Variation of inside wall, bulk fluid and film temperature vs. heat flux atx/d = 24, u = 1.03 m/s and Tb,in = 298 K.

Z. Yang et al. / Experimental Thermal and Fluid Science 61 (2015) 144–152 147

and thermal conductivity) in our previous work. The dimensionlessvalue of each property was obtained by dividing its maximumvalue, as shown in Fig. 5. When the bulk temperature was above850 K, the isobaric specific heat capacity increased rapidly andthe density decreased monotonously, leading to a rapid increasein absorbed heat in the boundary layer and an enhancement ofthe flow turbulence. More energy was taken from the boundarylayer into the bulk fluid and, thus, the heat transfer was improved.

Following the improved region, some impaired heat transferbehavior occurred in segment CD, accompanied by a sharp increasein inside wall temperature and a decrease in the heat transfer coef-ficient. In this process, the film temperature was in the vicinity ofthe pseudocritical temperature. Thermal conductivity of the bulkfluid decreased, as evident in Fig. 4(b), increasing the thermal resis-tance of the fluid and playing a dominant role in heat transfer inthis region. Therefore, the heat transfer deteriorated and the walltemperature increased sharply.

As seen in Figs. 3 and 4, the increase in the inside wall temper-ature and superheat slowed down in segment EF. The secondimproved heat transfer region with thermoacoustic oscillation[28,30–33] observed in the tests. The temperature and pressuredevelopment with time are shown in Fig. 6. An intermittentdecrease in inside wall temperature and a subsequent up rush ofbulk temperature were observed in Fig. 6(a). Oscillation of thepress drop was also observed in Fig. 6(b). With the heat fluxincreasing, the frequency and amplitude of the variations changeddrastically. The thermoacoustic oscillations disrupted flow stabilityand enhanced turbulence in bulk flow. This phenomenon is

Fig. 4. Heat transfer behaviors at x/d = 24, u = 1.03 m/s and Tb,in = 298 K. (a

somewhat similar to the subcritical boiling process of a steamchirp. Some researchers have claimed that the thermoacousticoscillation is related to the formation and collapse of pseudobub-bles, propagated in the fluid with the speed of sound [30,34]. Oth-ers have attributed the phenomenon to large variations inthermophysical properties [28,33], or the phonon carriers of acous-tical energy in the molecular lattice [35]. These opinions are incon-sistent with each other. In our experiments, a visualization methodwas used to explore this phenomenon. In the initial visualizationprocess, the acoustic chirp was faint. With the increase in heat flux,the chirp gradually became raspy. A few microbubbles wereobserved in the visualization image shown in Fig. 7(a). In the tests,microbubbles formed on the gasification cores of the heated tubewall and absorbed an amount of heat. When the bubbles were car-ried into the bulk fluid, they collapsed and condensed rapidly inthe subcooling fluid with the heat release. Thus, the inside walltemperature and bulk temperature varied in succession. Heattransfer was improved by the thermoacoustic oscillation.

When the oscillation disappeared, the impaired heat transfercharacteristics reappeared in segment FG. At that moment, largebubbles were observed in the visualization test, as shown inFig. 7(b), indicating that the non-condensing gas formed in thefluid could not improve the heat transfer as the microbubbles had.

At high temperature, the macromolecule hydrocarbons beganto crack and dehydrogenize into small molecule materials. Thechemical reactions were accompanied by a large amount of heat,which was absorbed and transferred to the bulk fluid. Thus, thewall temperature and superheat decreased significantly in seg-ment GH, the third heat transfer enhancement observed. Using this

) Superheat vs. heat flux and (b) heat transfer coefficient vs. Enthalpy.

Fig. 8. Variations of top and bottom wall temperature along tube with d = 1.0 mmand Tb,in = 298 K.

Fig. 6. Oscillation phenomenon at x/d = 24, u = 1.03 m/s, Tb,in = 298 K and q = 2800 kW/m2. (a) Fuel and tube-wall temperature oscillation and (b) pressure drop oscillation intest tube.

Fig. 7. Visualization experiment at l = 46 mm, u = 1.03 m/s and Tb,in = 298 K.

148 Z. Yang et al. / Experimental Thermal and Fluid Science 61 (2015) 144–152

process, plenty of gas was generated and the color of the fuel beganto change (Fig. 7(c)).

However, too much gas generated near the hot wall cannot bedelivered into the bulk fluid and removed in time, causing forma-tion of a gaseous layer and fuel coking in the boundary layer(Fig. 7(d)). As a result, heat transfer deteriorated in segment HI. Itwas a very rapid process from the gaseous layer formation to thehydrocarbon fuel coking. A slight increase in the heat flux wouldcause a surge of wall temperature and could even burst the tube.

3.2. Influence of the free convection

In previous studies, free convection proved to be an importantmechanism in the heat transfer of various flow passageways andmediums [14,21]. In this paper, gravitational effect was alsostudied in a horizontal mini-tube. Groups of thermocouples wereidentically spot-welded on the top and bottom surface of the test

tube. As shown in Fig. 8, the temperature measurement for eachsurface was almost identical at every point in the temperatureranges. The Grashof number, the ratio of buoyancy to viscousforces, is based on the integrated density and defined in Eq. (5).

Grb ¼q2

f ðqb � �qÞd3ing

l2f qb

ð5Þ

with

�q ¼R Tw

TbqdT

Tw � Tb� qf ð6Þ

Here, q is the fuel density, l is the dynamic viscosity, g is the grav-itational constant, T is the temperature, and din is the inside diam-eter of the tube. The subscripts w, b, and f stand for inside wall,bulk, and film respectively. The Grashof numbers under differentconditions were calculated according to Eq. (5). We found that themaximum Grashof number was in the order of 103. It proved thatfree convection had no effect on heat transfer characteristics inour experiments [19].

3.3. The effect of parameters on the heat transfer

Operating parameters affected the heat transfer process of thefuel, including the thermophysical property variation, thermoacou-stic oscillation, and hydrocarbons decomposition. The effects of heatflux, fluid velocity, and inlet temperature were studied.

Fig. 10. Variation of Nusselt number vs. Reynolds number at different locationwhen l = 46 mm, m = 1.03 m/s and Tb,in = 298 K.

Z. Yang et al. / Experimental Thermal and Fluid Science 61 (2015) 144–152 149

3.3.1. The effect of heat flux on the heat transfer behaviorThe effect of heat flux on the heat transfer characteristics is

plotted in Fig. 9. The variation in the inside wall temperature andheat transfer coefficient with reduced length x/d is shown. Withan increase in heat flux, the wall temperature and heat transfercoefficient varied regularly, with all the test points exhibiting agood unanimity over the whole process. Along the length of thetube, the heat transfer coefficients were almost the same for lowheat flux. With the increase in heat flux, the heat transfer coeffi-cients varied. The maximum value appeared in the outlet of thetube, due to the increase in the Reynolds number and endothermicreactions in the boundary layer.

When inlet temperature and fluid velocity were constant, theReynolds number increased with increased heat flux, due todecreased viscosity. The correlation of the Nusselt number withthe Reynolds number at different axial locations was plotted inFig. 10. In the initial stage, Nu increased with the increase in Re,showing a linear relationship. When Re was larger than 2000, Nudeviated from the original trend, indicating a different heat trans-fer mechanism dominated. It increased rapidly in the improvedheat transfer region and decreased in the deteriorated region.

Comparison of the experimental heat transfer data with empir-ical correlations was performed at Tb < Tpc < Tw. Due to a largertemperature difference between the tube wall and bulk fluid, thecorrelations modified by the thermophysical properties wereadopted as follows.

The rewritten Dittus–Boelter correlation with viscosity modifi-cation [36] is shown in Eq. (7):

Nu ¼ 0:023Re0:8b Pr0:4

blb

lw

� �0:11

ð7Þ

The Stiegemeier [37] correlation in Eq. (8) was proposed fromthe experimental data of five hydrocarbon fuels:

Nu ¼ 0:016Re0:862Pr0:4 1þ 2ðx=dÞ

� �ð8Þ

Hu [38] proposed a correlation (Eq. (9)) for a kerosene hydro-carbon fuel in a 1.7 mm test tube:

Nu ¼ 0:008Re0:873b Pr0:451

b ð9Þ

Krasnoshchekov [39] modified the original correlation forforced convective heat transfer of water and carbon dioxide atsupercritical pressures as:

Nu ¼ Nu0qw

qb

� �Cp

Cpb

!n

ð10Þ

Fig. 9. Heat transfer behavior vs. reduced length x/d with various heat flux at l = 46 mm, mcoefficient vs. x/d.

where Nu0 was define as:

Nu0 ¼ðn=8ÞRebPr

12:7ffiffiffiffiffiffiffiffin=8

pðPr2=3 � 1Þ þ 1:07

ð11Þ

and

n ¼ 1

ð1:82log10Reb � 1:64Þ2ð12Þ

Exponent n is n = 0.22 + 0.18 (Tw/Tpc) at 1 6 (Tw/Tpc) 6 2.5.Jackson [40] modified the original correlation of Krasnoshchekov

and used a Dittus–Boelter type form for Nu0 (Eq. (13)):

Nu ¼ 0:0183Re0:82b Pr0:5 qw

qb

� �0:3 Cp

Cpb

!n

ð13Þ

Exponent n is: n = 0.4 for Tb < Tw < Tpc and 1.2Tpc < Tb < Tw;n = 0.4 + 0.2(Tw/Tpc � 1) for Tb < Tpc < Tw.

Fig. 11 shows a comparison of the calculated Nusselt numberwith the experimental data in the tests. The calculated values byDittus–Boelter and Stiegemeier correlations were all much largerthan the experimental data. The correlations of Hu, Krasnoshche-kov, and Jackson agreed with the data well within a ±50% errorband. Most of the calculated points were within a ±30% error band.The correction factor of thermophysical properties proved to beimportant in the heat transfer calculation.

= 1.03 m/s and Tb,in = 298 K. (a) Inside wall temperature vs. x/d and (b) heat transfer

Fig. 11. Comparison of calculated Nusselt numbers by correlations with theexperimental data.

Fig. 13. Variation of Nusselt number with the ratio of heat flux to mass velocity q/Gat various fluid velocities and l = 116 mm.

150 Z. Yang et al. / Experimental Thermal and Fluid Science 61 (2015) 144–152

3.3.2. The effect of fluid velocity on heat transfer behaviorThe effect of inlet fuel velocity on heat transfer is shown in

Fig. 12. The heat transfer behavior of fluid at high and low veloci-ties shows obvious differences. It indicates that fluid velocity playsan important role in the dynamic and heat transfer of the fluid. Theincreased flow velocity enhanced the fluid turbulence and reducedboundary layer thickness, so heat transferred from the boundarylayer to the bulk fluid increased and, thus, greater heat flux wasobtained with the increased velocity. Note that fluid velocity alsoaffected the occurrence of thermoacoustic oscillation in theimproved heat transfer region. At low velocities, the thermoacou-stic oscillation was not observed and the inside wall tempera-ture increased with heat flux. Once the inlet velocity exceeded0.81 m/s, the oscillation phenomenon appeared and the heat trans-fer was improved by bubble generation. The same phenomenonwas also observed in the tube of 46 mm length, with the fluidvelocity increasing to 1.03 m/s.

The Nusselt number variation with q/G (G is mass flow rate) atdifferent velocities is shown in Fig. 13. There was no obviousdecrease in the Nusselt number at low velocities. The tests wereterminated at q/G = 3.0–4.0 kJ/kg to avoid the bursting of tubesdue to high wall temperature. When fluid velocity was higher than0.62 m/s, the heat transfer deteriorated. The experiments were ter-minated at a lower ratio, q/G = 2.0–2.5 kJ/kg. As a conservativedesign for all velocities, q/G less than 2.0 kJ/kg is recommended.

Fig. 12. Effect of fuel velocity on heat transfer at l = 116 mm, x/d = 64 and Tb,in = 298 K

3.3.3. The effect of inlet fluid temperature on heat transfer behaviorFig. 14 shows the variations in inside wall temperature and

Nusselt number with the increase of heat flux at different inletfluid temperatures. High inlet temperature results in a large Rey-nolds number for inlet fluid. Therefore, with the increase in inletfluid temperature, Nu increased in the initial experimental stageas the Reynolds number took a dominant role in this process. How-ever, with the heat flux further increasing, the distinct heat trans-fer behavior occurred at different inlet temperatures, indicatingthat inlet temperature affects not only the Reynolds number, butalso other parameters in the process. When the inlet fluid temper-ature was between 298 K and 373 K, the heat transfer process wasenhanced by variation of the thermal properties, thermoacousticoscillations, and endothermic cracking of the hydrocarbons. Asthe inlet temperature increased to 473 K and 573 K, heat transferwas only enhanced by thermoacoustic oscillation. When the inletfuel temperature was 673 K, the inside wall temperature variedmonotonously and no enhancement phenomenon occurred. Thiswas because the high inlet temperature reduces the temperaturegradient in the boundary layer, which hinders bubble generationand makes the heat resistance more significant. Thus, the thermoa-coustic oscillations only occurred at the lower inlet temperatureand the wall temperature monotonously increased at the higherinlet temperature. The Nusselt number variation with q/G at differ-ent inlet temperatures was plotted in Fig. 15. The maximum q/Gdecreased with the increase in inlet temperature.

. (a) Inside wall temperature vs. heat flux and (b) Nusselt number vs. heat flux.

Fig. 14. Effect of inlet liquid temperature on heat transfer at l = 46 mm, x/d = 24 and u = 1.03 m/s. (a) Inside wall temperature vs. heat flux and (b) Nusselt number vs. heatflux.

Fig. 15. Variation of Nusselt number with the ratio of heat flux to mass velocity q/Gat various inlet fluid temperatures and l = 46 mm.

Fig. 16. The maximum value of q/G with various fluid velocities and different inlettemperatures at l = 46 mm.

Z. Yang et al. / Experimental Thermal and Fluid Science 61 (2015) 144–152 151

In Fig. 16, the maximum values of q/G for the 46 mm test tubewere given at different inlet temperatures and velocities. This fig-ure could be used as a criterion for future applications. When thefluid velocity was lower than 0.62 m/s, the maximum value of q/G remained almost the same at the high inlet temperatures of

573 K and 673 K. The maximum value of q/G significantlydecreased with the increased fluid velocity when the inlet temper-ature was lower than 573 K. At low velocity, the residence time ofthe fluid in the tube increased, which in turn increased the endo-thermic reactions at the boundary layer. At a velocity of 0.81–1.20 m/s, higher fluid velocity was found to have a larger maxi-mum value of q/G at different inlet temperatures. The maximumq/G value decreased with the increase in inlet temperature, indicat-ing that the increase in velocity and the reduction in inlet temper-ature could improve the heat transfer.

4. Conclusions

Heat transfer characteristics of supercritical pressure hydrocar-bon fuel were studied in a short horizontal tube with a 1.0 mminner diameter. Different heat transfer regions are designatedbased on their distinct heat transfer behavior. The heat transferis improved by thermophysical property variation, thermoacousticoscillation, and endothermic chemical reactions of the hydrocar-bons in the respective processes. The deteriorated heat transfer ischaracterized by a sharp rising of the wall temperature, due togas-resistance and coking of the hydrocarbons formed on the tubesurface. A visualization method was used to identify the flow phe-nomenon in different heat transfer regions. Free convection provednegligible in a small horizontal tube.

The effects of heat flux, fluid velocity, and inlet temperature onthe heat transfer were studied. High fluid velocity and low inletfluid temperature were beneficial for the occurrence of thermoa-coustic oscillation, which could enhance the heat transfer bygrowth and collapse of condensable bubbles. Finally as a criterionfor engineering design, the maximum value of q/G was given atvarious fluid velocities and inlet temperatures.

Acknowledgements

This work is supported by the National Natural Science Founda-tion of China (Grant No. 21306147), the National Science Founda-tion for Post-doctoral Scientists of China (Grant No. 2013M532044)and the Fundamental Research Funds for the Central Universities.Their financial supports are grateful acknowledged.

References

[1] H. Lander, A.C. Nixon, Endothermic fuels for hypersonic vehicles, J. Aircraft 8(1971) 200–207.

152 Z. Yang et al. / Experimental Thermal and Fluid Science 61 (2015) 144–152

[2] D.R. Sobel, L.J. Spadaccini, Hydrocarbon fuel cooling technologies for advancedpropulsion, J. Eng. Gas Turb. Power 119 (1997) 344–351.

[3] H. Huang, L.J. Spadaccini, D.R. Sobel, Fuel-cooled thermal management foradvanced aeroengines, J. Eng. Gas Turb. Power 126 (2004) 284–293.

[4] D.K. Huzel, D.H. Huang, Modern Engineering for Design of Liquid-PropellantRocket Engines, AIAA, Washington, 1992.

[5] M. Naraghi, S. Dunn, D. Coats, A model for design and analysis of regenerativelycooled rocket engines, in: 40th AIAA/ASME/SAE/ASEE Joint PropulsionConference and Exhibit, AIAA, 2004.

[6] E.T. Curran, Scramjet engines: the first forty years, J. Propul. Power 17 (2001)1138–1148.

[7] D. Emeric, B. Marc, H. Olivier, M. Paul-Marie, N. Gascoin, P. Gillard, Fuelreforming for scramjet thermal management and combustion optimization, in:AIAA/CIRA 13th International Space Planes and Hypersonics Systems andTechnologies Conference, AIAA, 2005.

[8] T. Edwards, Cracking and deposition behavior of supercritical hydrocarbonaviation fuels, Combust. Sci. Technol. 178 (2006) 307–334.

[9] A.J. Giovanetti, L.J. Spadaccini, E.J. Szetela, Deposit formation and heat-transfercharacteristics of hydrocarbon rocket fuels, J. Spacecraft Rockets 22 (1985)574–580.

[10] O.A. Powell, J.T. Edwards, R.B. Norris, K.E. Numbers, J.A. Pearce, Development ofhydrocarbon-fueled scramjet engines: the hypersonic technology (HyTech)program, J. Propul. Power 17 (2001) 1170–1176.

[11] N. Mohammad, D. Stu, C. Doug, Dual regenerative cooling circuits for liquidrocket engines, in: 42nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference &Exhibit, AIAA, 2006.

[12] R.S. Fry, A century of ramjet propulsion technology evolution, J. Propul. Power20 (2004) 27–58.

[13] J.G. Wang, H.X. Li, S.Q. Yu, T.K. Chen, Investigation on the characteristics andmechanisms of unusual heat transfer of supercritical pressure water invertically-upward tubes, Int. J. Heat Mass Transfer 54 (2011) 1950–1958.

[14] I.L. Pioro, R.B. Duffey, Experimental heat transfer in supercritical water flowinginside channels (survey), Nucl. Eng. Des. 235 (2005) 2407–2430.

[15] I.L. Pioro, H.F. Khartabil, R.B. Duffey, Heat transfer to supercritical fluidsflowing in channels – empirical correlations (survey), Nucl. Eng. Des. 230(2004) 69–91.

[16] C.H. Son, S.J. Park, An experimental study on heat transfer and pressure dropcharacteristics of carbon dioxide during gas cooling process in a horizontaltube, Int. J. Refrig. 29 (2006) 539–546.

[17] J.R. Thome, G. Ribatski, State-of-the-art of two-phase flow and flow boilingheat transfer and pressure drop of CO2 in macro- and micro-channels, Int. J.Refrig. 28 (2005) 1149–1168.

[18] C. Zhang, G. Xu, L. Gao, Z. Tao, H. Deng, K. Zhu, Experimental investigation onheat transfer of a specific fuel (RP-3) flows through downward tubes atsupercritical pressure, J. Supercrit. Fluids 72 (2012) 90–99.

[19] L.S. Yanovskii, B.Y. Kamenetskii, Heat exchange during the forced flow ofhydrocarbon fuels at supercritical pressures in heated tubes, J. Eng. Phys.Thermophys. 60 (1991) 38–42.

[20] B. HItch, M. Karpuk, Experimental investigation of heat transfer and flowinstabilities in supercritical fuels, AIAA 3043 (1997).

[21] R.F. Kelbaliev, Experimental investigation of changes in the wall temperaturein different regimes of motion of supercritical-pressure liquids, J. Eng. Phys.Thermophys. 75 (2002) 1037–1042.

[22] A.Y. Chen, L. Dang, Characterization of supercritical JP-7’s heat transfer andcoking properties, AIAA 5 (2002).

[23] Y.X. Hua, Y.Z. Wang, H. Meng, A numerical study of supercritical forcedconvective heat transfer of n-heptane inside a horizontal miniature tube, J.Supercrit. Fluids 52 (2010) 36–46.

[24] R.P. Jiang, G.Z. Liu, Z.Q. You, M.J. Luo, X.Q. Wang, L. Wang, X.W. Zhang, On thecritical points of thermally cracked hydrocarbon fuels under high pressure,Ind. Eng. Chem. Res. 50 (2011) 9456–9465.

[25] Z. Yang, Q. Bi, Y. Guo, Z. Liu, J. Yan, Visualization and flow boiling heat transferof hydrocarbons in a horizontal tube, AIP Conf. Proc. 1547 (2013) 432–441.

[26] L. Wojtan, T. Ursenbacher, J.R. Thome, Investigation of flow boiling inhorizontal tubes: part I—A new diabatic two-phase flow pattern map, Int. J.Heat Mass Transfer 48 (2005) 2955–2969.

[27] Z. Liu, Q. Bi, Y. Guo, Q. Su, Heat transfer characteristics during subcooled flowboiling of a kerosene kind hydrocarbon fuel in a 1mm diameter channel, Int. J.Heat Mass Transfer 55 (2012) 4987–4995.

[28] D.L. Linne, M.L. Meyer, D.C. Braun, D.J. Keller, Investigation of instabilities andheat transfer phenomena in supercritical fuels at high heat flux andtemperatures, in: NASA/TM-2000-210345, 2000.

[29] F.Q. Zhong, X.J. Fan, G. Yu, J.G. Li, C.J. Sung, Heat transfer of aviation kerosene atsupercritical conditions, J. Thermophys. Heat Transfer 23 (2009) 543–550.

[30] V.D. Vas’yanov, N.L. Kafengauz, A.G. Lebedeva, A.V. Timakov, V.V. Chekanov,Mechanism of thermoacoustic self-oscillations, J. Eng. Phys. Thermophys. 34(1978) 525–527.

[31] I.T. Alad’ev, V.D. Vas’yanov, N.L. Kafengauz, A.G. Lebedeva, A.V. Timakov,Characteristics of self-excited thermoacoustic oscillations in heat transfer to n-heptane, J. Eng. Phys. Thermophys. 33 (1977) 752–755.

[32] R. Friedman, R.C. Hendricks, R.J. Simoneau, Heat-transfer characteristics ofcryogenic hydrogen from 1000 to 2500 psia flowing upward in uniformlyheated straight tubes, in: NASA-TN-D-2977, 1965.

[33] G.H. Ackerman, L.E. Faith, H.T. Henderson, Heat sink capability of jet A fuel –heat transfer and coking studies, in: NASA-CR-72951, 1971.

[34] W.S. Hines, H. Wolf, Pressure oscillations associated with heat transfer tohydrocarbon fluids at supercritical pressures and temperatures, ARS J. 3 (1962)361–366.

[35] G. Bisio, G. Rubatto, Sondhauss and Rijke oscillations—thermodynamicanalysis, possible applications and analogies, Energy 24 (1999) 117–131.

[36] F. Dittus, L. Boelter, Heat transfer in automobile radiators of the tubular type,Int. Commun. Heat Mass 12 (1985) 3–22.

[37] B. Stiegemeier, M.L. Meyer, R. Taghavi, A thermal stability and heat transferinvestigation of five hydrocarbon fuels: JP-7, JP-8, JP-8+ 100, JP-10, and RP-1,in: 38th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, AIAA,2002.

[38] H. Zhihong, C. Tingkuan, L. Yushan, Z. Jianxue, T. Min, Heat transfercharacteristics of kerosene at supercritical pressure, J. Xi’an Jiaotong Univ. 9(1999) 62–65.

[39] E. Krasnoshchekov, V. Protopopov, F. Van, I. Kuraeva, Experimentalinvestigation of heat transfer for carbon dioxide in the supercritical region,in: Proceedings of the 2nd All-Soviet Union Conference on Heat and MassTransfer, Minsk, Belarus, 1964.

[40] J. Jackson, Consideration of the heat transfer properties of supercriticalpressure water in connection with the cooling of advanced nuclear reactors,in: The 13th Pacific Basin Nuclear Conference, Shenzhen City, China, 2002.