Study of Nucleate Boiling Heat Transfer to Slush Hydrogen andSlush Nitrogen

Katsuhide OhiraNagasaki R & D Center, Mitsubishi Heavy Industries, Ltd., Nagasaki, 851-0392 Japan

Slush hydrogen is a mixture of liquid hydrogen and solid hydrogen particles,and is being considered as a spaceplane fuel or as a means of transport for hydrogenused as a source of clean energy. This paper describes nucleate boiling heat transfercharacteristics of slush hydrogen and slush nitrogen. For the visual observation of heattransfer states, a heat transfer unit was placed in a glass Dewar designed to minimizethe heat loss from an atmospheric environment. The heat transfer unit used was acircular flat plate 0.025 m in diameter made of electrolytic tough pitch copper. Duringtesting, three different orientations of the heat transfer surface were used: horizontalfacing up, vertical, and horizontal facing down. Heat transfer data for the normalboiling point (NBP) of liquid hydrogen, the triple point (TP) of liquid hydrogen, theNBP of liquid nitrogen, and the TP of liquid nitrogen were obtained up to the criticalheat flux (burnout). These data for slush hydrogen and nitrogen, including the resultsof observation of the heat transfer surface were compared. This clarified the nucleateboiling heat transfer characteristics of slush hydrogen and slush nitrogen, which haverarely been investigated. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(1):13–28, 2003; Published online in Wiley InterScience (www.interscience.wiley.com).DOI 10.1002/htj.10068

Key words: cryogenics, heat transfer, liquid fuel, rocket, nucleate boiling,liquid hydrogen, slush hydrogen, liquid nitrogen, slush nitrogen

1. Introduction

Slush hydrogen is a mixture of liquid hydrogen and solid hydrogen particles. Compared withthe normal boiling point (NBP) of liquid hydrogen, slush hydrogen with a 50% solid weight fractioncan be expected to increase cooling capacity about 18% and about 16% in density. Thus, practicaldevelopment of the slush hydrogen technology as a fuel for a completely reusable space shuttle(spaceplane) is now in progress for the future space transportation age.

When slush hydrogen is used as a spaceplane fuel, it can be expected to decrease the fuel tankvolume (lightweight design of the airframe) due to the increased density of hydrogen and to increasethe cryogenic energy source to the Liquid Air Cycle Engine using liquefied air as an oxidizer.Cryogenic energy sources are also available for cooling of the engines and aerodynamic heating of

© 2002 Wiley Periodicals, Inc.

Heat Transfer—Asian Research, 32 (1), 2003

13

the vehicle airframe. Development of the slush hydrogen technology has become an important factorfor the spaceplane with a nondisposable propulsion system unlike the multistage rocket now in use.

Furthermore, the use of slush hydrogen is drawing attention to decrease the boil-off gas andto improve the transport efficiency due to the increased density of hydrogen during its transport fromabroad to Japan. Here hydrogen is used as a clean energy source in the WE-NET (World EnergyNetwork System) Project as part of MITI’s ongoing New Sunshine Program.

If slush hydrogen is used as a rocket fuel, the cryogenic energy held by it would first berecovered and then its pressurized hydrogen vapor would be fired with an oxidizer in a combustor toachieve rocket propulsion. In order to effectively use slush hydrogen for engine cooling or coolingof the aerodynamic heating, etc., it becomes an important practical issue to obtain experimentally theheat transfer characteristics of slush hydrogen.

The heat transfer characteristics of liquid hydrogen have been examined by Coeling and others[1–3], and the experimental investigation of slush hydrogen’s transfer characteristics is limited to theone report of Sindt [4]. Required data, including the heat transfer characteristics of the triple-point(TP) liquid hydrogen, still need to be defined. Solid nitrogen has been used as a cooling medium forinstrumentation equipment mounted on meteorological satellites to improve its accuracy. The heattransfer characteristics of the TP liquid nitrogen and slush nitrogen are still relatively undefined.

In Sindt’s experiment, a circular flat plate of stainless steel 0.0254 m in diameter was used asthe heat transfer surface to obtain the heat transfer data in a region of relatively small heat fluxes fromthe natural convection region to the nucleate boiling region in three aspects of the heat transfer surface:horizontal surface facing up, vertical surface, and horizontal surface facing down. The heat transfercharacteristics from a large heat flux region to the critical heat flux point (burnout point) have not yetbeen obtained.

The present study detailed measurements of heat transfer characteristics for slush hydrogen,NBP liquid hydrogen, and TP liquid hydrogen. These were conducted by varying the orientation ofthe heat transfer surface in the nucleate boiling region, like Sindt’s experiment, and their critical heatflux points were verified. The shape of the heat transfer surface tested was much the same one as usedfor Sindt’s experiment, but an electrolytic tough pitch copper was used. The heat transfer charac-teristics of slush nitrogen, NBP liquid nitrogen, and TP liquid nitrogen were also measured, using thesame heat transfer surface for slush hydrogen. The systematic investigation of the nucleate boilingheat transfer characteristics for slush nitrogen and slush hydrogen including differences due tovariations in the orientations of the heat transfer surface is presented in this paper. The heat transfercharacteristics of slush hydrogen, liquid hydrogen, slush nitrogen, and liquid nitrogen were, respec-tively, compared with Rohsenow’s equation for nucleate boiling heat transfer coefficients and theircritical heat flux values with Kutateladze’s equation.

Nomenclature

c: specific heat (J/(kg⋅K))

g: gravitational acceleration (m/s2)

h: heat transfer coefficient (W/(m2⋅K))

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k: thermal conductivity (W/(m⋅K))P: pressure (Pa, Torr)q: heat flux (W/m2)q*: critical heat flux (burnout) (W/m2)T: temperature (K)∆T: temperature difference (degrees of superheat) at heat transfer surface (Tw − Ts) (K)∆T* temperature difference at critical heat flux (K)X: [σg(ρl − ρv) / ρv

2]1 / 4 (m/s)Y: q∗

/ λρv (m/s)λ: latent heat of vaporization (J/kg)µ: viscosity (Pa⋅s)ρ: density (kg/m3)σ: surface tension (N/m)φ: angle of inclination (deg)

Subscripts

c: critical pointl: liquids: saturation temperaturev: vaporw: wall surface

2. Test Apparatus and Method

2.1 Test apparatus

Figure 1 shows a schematic diagram of the test apparatus. The test apparatus consists of a heattransfer unit, a glass Dewar vessel for slush hydrogen, a pressure controller in the glass Dewar vessel,a measurement and data processor, a measuring device for the heater current/voltage, and a densimeter

Fig. 1. Test apparatus for slush hydrogen.

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for slush hydrogen. The glass Dewar vessel is composed of three glass Dewar vessels nested together;its outer vessel contains liquid nitrogen, its intermediate vessel liquid hydrogen, and its inner vesselslush hydrogen. The purpose of the outer and intermediate vessels is to minimize heat leakage intothe inner vessel. The three vessels use double vacuum-jacketed structures fabricated of Pyrex glassand the internal surface of the vacuum chamber is lined with silver to prevent heat leakage due toradiation. A slitted observation window not coated with silver has been provided looking upward inthe Dewar vessel to enable observations of the heat transfer surface and slush hydrogen duringexperiments. The volume capacity of the inner vessel is about 14 liters; with the inner vessel filledwith liquid hydrogen, the heat leakage into the liquid hydrogen was about 1.2 W when measuredunder experimental conditions.

For production of slush hydrogen, the freeze–thaw (intermittent evacuation) method wasemployed. After evacuating the inner vessel containing liquid hydrogen up to the triple-point pressureusing the vacuum pump, a further evacuation would produce solid hydrogen over the liquid surface.After production of this solid hydrogen, evacuation is suspended to break the produced solid hydrogeninto fine particles using a stirrer (propeller). Slush hydrogen is produced by repeating this processperiodically. The stirrer is located at two positions (upper and lower) inside the vessel, driven by amotor placed on top of the Dewar vessel. A vacuum pump with a discharge rate of 10,000 liters/minfor liquid hydrogen evacuation and a pressure gauge, a pressure controller, and a solenoid valve,required for the periodic evacuation, were provided to the vacuum line. Hydrogen vapor is producedduring the nucleate boiling experiment while the pressure in the inner vessel can be held constantwithin an error of ±0.5 Torr using the vacuum pump and the pressure controller, etc., based on theoutput signal from the pressure gauge.

2.2 Heat transfer unit

Details of the heat transfer unit are shown in Fig. 2. The heat transfer surface was a circularflat plate made of electrolytic tough pitch copper 0.025 m in diameter. The connection between theheat transfer surface and the flange retaining it used a sheet design 0.1 mm thick to minimize the heatloss from the heat transfer surface. The heat transfer surface was finished with emery paper (#1000)and cleaned after each experiment. The surface roughness of the heat transfer surface was measured;

Fig. 2. Heat transfer unit.

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Ra = 0.2 µm. For heating of the heat transfer surface, a manganese wire (50 Ω) wound around theheater block was used and the wall temperature of the heat transfer surface was measured using agermanium resistance thermometer inserted into the wall center. The measuring accuracy of thisthermometer is within ±0.01 K and the lead wire to the thermometer was provided with a thermalanchor to prevent heat leakage into the heat transfer surface. To improve thermal conduction betweenthe heater block and the thermometer, Apiezon grease was used to minimize the measuring error. Inorder to minimize leakage of the heat from the heater to areas other than the heat transfer surface, theinterior of the cell casing made of stainless steel was evacuated by a vacuum pump. The circumferenceof the heater block was provided with multilayer insulation to prevent heat loss due to radiation. Theelectric power supply to the heater was calculated from the current flowing through a standard resistorplaced in the room-temperature area and from the voltages measured at both ends of the manganesewire used as the heating value of the heater.

2.3 Experimental method

Experiments were conducted on six types of fluids: triple-point (TP) slush hydrogen (52.8Torr, 13.8 K), liquid hydrogen at normal boiling point (NBP; 1 atm, 20.3 K), TP liquid hydrogen(52.8 Torr, 12.8 K), NBP liquid nitrogen (1 atm, 77.4 K), TP liquid nitrogen (94.0 Torr, 63.2 K), andslush nitrogen (TP; 94.0 Torr, 63.2 K), using the same heat transfer unit. In a series of the experiments,the mean solid weight fractions of the slush hydrogen and the slush nitrogen were in the range from20 to 35% at the start of the experiment and from 10 to 20% at the end of the experiment. In theseexperiments, the effect of the solid weight percentage on the heat transfer characteristics was not takeninto consideration. The mean solid weight fraction at the start of the experiment was obtained fromboth the measurement by a capacitance-type density sensor placed in the glass Dewar vessel and thecalculation from the liquid decrement during slush hydrogen production and those at the end of theexperiment were measured, using a capacitance-type density sensor [5]. Three different inclinationsof the heat transfer surface were used: horizontal surface facing up (φ = 0°), vertical surface (90°),and horizontal surface facing down (180°).

The experimental method on slush hydrogen is described below. After evacuating the innervessel containing liquid hydrogen to the triple-point pressure using the vacuum pump, slush hydrogenis produced by means of the freeze–thaw method already described. After a given solid weight fractionhas been reached, slush hydrogen production is stopped. After confirming stabilization of slushhydrogen in the inner vessel, the heat transfer surface is heated by the heater placed in the heat transferunit and the heating value is controlled by checking current and voltage to the heater. After thetemperature of the heat transfer surface has been stabilized at its steady state, data such as temperature,pressure, current, and voltage to the heater are measured. The critical heat flux was determined fromcalculation using the electric power value immediately before the burnout of the heat transfer surface.

The temperature difference (degrees of superheat) at the heat transfer surface ∆T = Tw − Ts

must be obtained from the measured wall temperature Tw and the saturated temperature Ts. Thesaturated temperature changes for each experiment or during the experiment because the liquid leveldepth (hydrostatic pressure) of the heat transfer surface changes due to vaporization. The temperaturechange due to the hydrostatic pressure is large especially in the case of liquid nitrogen because it hasa large density. Accordingly, the saturated temperature was corrected by measuring the liquid leveldepth through the observation window during the experiment. Because the measurement error of the

17

level depth is ±1 mm at maximum, this error can be converted to ±0.005 K at maximum for thecalculational error of the saturated temperature for liquid nitrogen. The liquid temperature during theexperiment was measured using the germanium resistance thermometer placed at the same height ofthe heat transfer surface level in the Dewar vessel, and the difference between the measuredtemperature difference and the calculated result from the saturated temperature as described abovewas within 5% in the nucleate boiling region.

In the experiment with slush nitrogen, the intermediate vessel and the inner vessel are filledwith liquid nitrogen to produce slush nitrogen in the inner vessel. The subsequent test method is thesame one used for slush hydrogen.

2.4 Physical properties of slush nitrogen and slush hydrogen

The liquid hydrogen used for the experiments was para-hydrogen with its para-hydrogenconcentration 95% or more, and for the thermophysical properties of the hydrogen and the nitrogen,the thermophysical property values published by NIST in the USA (former NBS) were used [6, 7].

3. Experimental Results and Discussion

3.1 Heat transfer characteristics of liquid hydrogen and slush hydrogen

Figure 3 shows experimental results of liquid hydrogen at the normal-boiling-point pressureand at the triple-point pressure and slush hydrogen at the triple-point pressure. In each figure, the heatflux q is shown along the axis of ordinates and the temperature difference ∆T along the axis ofabscissas. The open symbols refer to the case of increased heat flux and the closed symbols to thecase of decreased heat flux. The starting point of the observed bubbling during transition from thenatural convection region to the nucleate boiling region by increasing the heat flux in the observationof the heat transfer surface during the experiment has been labeled the Initial Vapor. The lastobservation point of bubbling from the heat transfer surface during decrease of the increased heat fluxhas been labeled the Last Vapor. Because slush showed an appearance of white turbidity due to solidparticles, there are some cases where the start and stop of actual bubbling could not be visualized.The values of the critical heat flux q* and the critical temperature difference ∆T∗ calculated from theequation of Kutateladze [2] often used for the estimated critical heat fluxes in the nucleate boilingregion are shown in Figs. 3(a) and 3(d). [For q*, K = 0.16 was used for calculation of Eq. (3) asdescribed later.]

Figures 3(a) through 3(c) summarize heat transfer characteristics of liquid hydrogen at NBP,liquid hydrogen at TP, and slush hydrogen for the horizontal surface facing up (0°), the vertical surface(90°), and the horizontal surface facing down (180°). Also, Figs. 3(d) through 3(f) are a rearrangementof Figs. 3(a) through 3(c) for better understanding of the above heat transfer characteristics accordingto the orientations (0°, 90°, and 180°) of the heat transfer surface.

Figures 3(a) and 3(d) show the results of Coeling and Merte [1] obtained from the flat plateheat transfer surface (Ra = 0.13 µm) 0.0254 m in diameter in liquid hydrogen for comparison betweencopper and stainless steel used for the heat transfer surface. Figures 3(a) through 3(f) also show theresults of Sindt [4] using a heat transfer surface made of stainless steel 0.0254 m in diameter (theroughness of the heat transfer surface is unknown).

18

The results obtained from the present experiments in the nucleate boiling region of liquidhydrogen at NBP tend to be similar to the results of Coeling and Merte for the copper heat transfersurface and show a trend similar to Sindt’s boiling curve. Deviation of the present results to the leftfrom Sindt’s curve is probably due to the differences in the materials used for the heat transfer surfaceand the surface roughness.

The relationship between the heat flux q and the heat transfer coefficient h, as obtained fromthe present investigation, is shown in Fig. 5.

From the experimental results shown in Figs. 3(a) through 3(c) and in Fig. 5, the followingcan be observed.

In Sindt’s experiment, if the orientation of the heat transfer surface in the nucleate boilingregion remains the same, the value of heat flux q corresponding to the same value of ∆T becomes thelargest with liquid hydrogen, showing equal values of heat flux for liquid hydrogen at TP and slushhydrogen. In the current experiments, on the other hand, the value of heat flux q to the same value of∆T becomes smaller in the order of liquid hydrogen at NBP, liquid hydrogen at TP, and slush

Fig. 3. Heat transfer of hydrogen. (a) Horizontal surface facing up; (b) Vertical surface; (c) Horizontal surface facing down; (d) Liquid at NBP; (e) Liquid at TP; (f) Slush at TP.

19

Fig. 4. Heat transfer of nitrogen. (a) Horizontal surface facing up; (b) Vertical surface;(c) Horizontal surface facing down; (d) Liquid at NBP; (e) Liquid at TP; (f) Slush at TP.

Fig. 5. Relation between heat flux and heat transfer coefficient.

20

hydrogen. Although the difference in heat flux value between liquid hydrogen at TP and slushhydrogen is small, this difference is clearly recognized.

As compared with the cases of horizontal surface facing up and vertical surface in Figs. 3(a)and 3(b), the case of horizontal surface facing down in Fig. 3(c) shows a marked variance in theexperimental data particularly in the high-heat-flux regions of liquid hydrogen at TP and slushhydrogen. The reason for this may be that movement of bubbles near the heat transfer surface mayhave influenced the heat transfer, unlike the cases of horizontal surface facing up and vertical surface,since bubbles produced over the heat transfer surface were observed to move along the heat transfersurface toward its periphery. In Sindt’s results (solid line) of liquid hydrogen at TP and slush hydrogen,shown in Fig. 3(c), a jump-over is seen in the heat transfer data, probably caused by the transitionfrom the natural convection region to the nucleate boiling region, and a small jump-over is also seennear ∆T = 1 K in the present experiment.

When the angle of inclination of the heat transfer surface is increased in cryogenic fluids,previous reports found that the heat transfer coefficient (heat flux) increased in the low-heat-fluxnucleate boiling region whereas it remains nearly unchanged. In the report by Nishio and Chandra-tilleke [8] on the measurement of liquid helium, the heat transfer coefficient increased if the angle ofinclination increased (φ = 0° → 175°) whereas Lyon [9] only found a slight difference between φ =90° and 180° although the heat transfer coefficient increased at φ = 90°. In the measurement by Classand colleagues [3] for liquid hydrogen, the heat transfer coefficient remained almost unchanged evenif the angle of inclination of the heat transfer surface increased (φ = 0° → 90°).

When the experimental results in Figs. 3(d) through 3(f) and in Fig. 5 are checked, it is seenthat liquid hydrogen at NBP and liquid hydrogen at TP hardly show a difference between φ = 90° and180° but clearly show a higher value than at φ = 0°. Although a large variance in the experimentaldata is seen in slush hydrogen, the values at φ = 90° and 180° tend to show values higher than thevalue at φ = 0° in the low-heat-flux region as seen in the cases of liquid hydrogen at NBP and liquidhydrogen at TP.

The results of Sindt show a remarkable hysteresis between increasing and decreasing the heatflux. In the current experiments, hysteresis was observed in the case of the vertical heat transfer surfacein liquid hydrogen at NBP and in the case of the horizontal surface facing down in slush hydrogen.The reason for hysteresis of the horizontal surface facing down in slush hydrogen may be theinsufficient supply of solid hydrogen near the heat transfer surface due to the orientation of the heattransfer surface, accompanied with decreased weight fraction of solid hydrogen, because the data[symbol E in Fig. 3(f)] in the natural convection region, obtained during the decrease of heat flux, arevery similar to the data on liquid hydrogen at TP [Fig. 3(e)].

3.2 Heat transfer characteristics of liquid nitrogen and slush nitrogen

Figure 4 shows the experimental results of nitrogen plotted as for hydrogen. The symbols andthe like in the figure are the same ones used for the case of hydrogen. Figure 4(d) shows the resultsof Marto and colleagues [10] obtained from a flat plate heat transfer surface made of copper (mirrorfinish) 0.0252 m in diameter. The relationship between the heat flux q and the heat transfer coefficienth in the nucleate boiling region, based on the experimental results of nitrogen, is shown in Fig. 6.

21

From the experimental results presented in Figs. 4(a) through 4(c) and in Fig. 6, the followingcan be seen. Compared with the results of hydrogen, there exists a marked hysteresis. The heat transfercharacteristics in the natural convection region are nearly equal, regardless of the orientation of theheat transfer surface and the different types of fluids. If the orientation of the heat transfer surfaceremains the same in the nucleate boiling region after transition, the heat transfer coefficient of liquidnitrogen at NBP is the largest whereas the heat transfer coefficients of liquid nitrogen at TP and slushnitrogen are nearly equal or the heat transfer coefficient of slush nitrogen is somewhat lower.

Although no sufficient experimental data have been obtained regarding the changes of heattransfer coefficients according to the angle of inclination of the heat transfer surface in the low heatnucleate boiling region, the experimental results of Figs. 4(d) through 4(f) and Fig. 6 reveal hardlyany changes of the heat transfer coefficients unlike the case of hydrogen. In liquid nitrogen at NBP,transition from the natural convection region to the nucleate boiling region took place at a temperaturedifference ∆T = 3 to 7 K whereas it occurred at ∆T = 5 to 30 K in liquid nitrogen at TP and slushnitrogen at TP. The critical radius of the bubble nucleus formed in the state of nucleate boiling isgiven by rc = 2σ / ∆P. ∆P is the pressure difference between inside and outside of the bubble and σ isthe surface tension. If critical radii of liquid nitrogen at NBP and liquid (slush) nitrogen at TP areestimated, using ∆T = 5 K and 18 K, they are, respectively, calculated to be rc = 0.25 µm and 0.17µm. Since the states of the heat transfer surfaces are almost identical to each other, it is inferred thattransition to the nucleate boiling region occurs at ∆T where the critical radii become nearly equal toeach other. In Fig. 4(f) referring to the case of slush nitrogen (symbol ") with horizontal surfacefacing down, the fluid goes into the burnout state directly from the natural convection region.

3.3 Study on nucleate boiling heat transfer coefficients

From experimental data on noncryogenic liquids such as water, Rohsenow derived thefollowing equation for the nucleate boiling heat transfer coefficient h [11, 12]:

Fig. 6. Relation between heat flux and heat transfer coefficient.

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cl∆T

λ = Csf

q

µlλ

σg(ρl − ρv)

12

0.33

Prls

(1)

where cl, µl, and Prl are, respectively, the specific heat, the viscosity, and the Prandtl number of theliquid and λ and σ are the latent heat of vaporization and the surface tension. The factor Csf is a valuedecided by the combination of the heat transfer surface material and the liquid, and the same valuecan apply to different pressures. For the exponent s of Prl, 1.7 is usually used. Clark proposed thefollowing equation for the heat transfer coefficient of cryogenic fluids by modifying Eq. (1) [11]:

cl∆T

λ =

13.25 × 105

12.89

TTc

−1.18

q

µlλ

σg(ρl − ρv)

12

0.33

Prl1.18

(2)

The differences from Eq. (1) are addition of the term T / Tc taking the effect of pressure into accountand predeterminations of the Csf value and the exponent of Prl. It has been reported that Eq. (2) agreeswell in the case of methane [13].

The present experimental results were examined by comparison with calculations using Eqs.(1) and (2). The thermophysical property values used were values of saturated temperatures at NBPand at TP.

In the case of Eq. (1), 1.0, 1.18, and 1.7 were chosen as the value of the exponent s. Csf and swere decided so as to be representative of the experimental results of the liquid at NBP. BecauseCsf and s are the same value if the combination of the heat transfer surface and the liquid remains thesame, even with different pressures, the heat transfer coefficients of the liquid at TP and the slush canbe predicted, using the experimental results of the liquid at NBP. Predictability of the heat transfercoefficients for slush can be important in consideration of its experimental difficulties. For slush, thevalue including the heat of fusion of the solid in the latent heat of vaporization λ was used. Figures5 and 6 plot the calculated results as solid lines.

The heat transfer coefficients calculated from Eq. (2) were significantly lower than theirexperimental results in both hydrogen and nitrogen, as shown in Figs. 5 and 6. Figure 5 also showsheat transfer coefficients (Facing Up, Vertical) calculated from Sindt’s experiments. When the heattransfer coefficients of the liquid at TP and the slush at TP were calculated from Eq. (1) using theexperimental results of the liquid at NBP, calculations on hydrogen in Fig. 5 showed a lower valuethan its experimental value, and this agrees with Sindt’s experimental results. (If 1.7 is used as theexponent s, the calculated result further decreases.) Meanwhile, calculations on nitrogen in Fig. 6agree well with the experimental results of the liquid at TP and slush nitrogen at TP.

3.4 Study on critical heat fluxes

Kutateladze gives the equation for the critical heat flux q* in the nucleate boiling heat transferof the horizontal heat transfer surface facing up in the following form [11]:

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q∗

λρv = K

σg(ρl − ρv)ρv

2

14

(3)

Although the factor K differs (0.095 ≤ K ≤ 0.20), depending on conditions of heat transfer, etc., K =0.16 proposed by Kutateladze is generally recommended as a mean value and is in good agreementwith the experimental value.

Figures 7 and 8 plot the value of X for the right side and Y for the left side of Eq. (3) from thecritical heat fluxes q* of the liquid at NBP, the liquid at TP, and slush at TP as obtained from thepresent experiments. The cases of 0.16 and of 0.20 and 0.095 for the value K in Eq. (3) are shown bythe solid line and by the dashed lines in the figures. It is seen that the critical heat flux shows the sametrend for both hydrogen and nitrogen. The symbol # refers to calculations including the heat of fusionof the solid in the latent heat of vaporization λ regarding the horizontal surface facing up in slush.

Calculations of the factor K in Eq. (3) from the critical heat flux values of the horizontal surfacefacing up for the liquid at NBP, the liquid at TP, and slush at TP are shown in Fig. 9. The ratios(P / Pc) of pressures to critical pressures in the respective fluids are shown along the abscissa. Thecalculations for slush including the heat of fusion of the solid in the latent heat of vaporization arealso plotted. Figure 9 also shows the experimental results of Bewilogua and colleagues [14 ,15] nearthe λ point (P / Pc = 0.02) of liquid helium. There were no measurements in the region ofP / Pc < 0.02, and in the present experiment, the K value tends to increase in the order of the liquid atTP and the slush over the liquid at NBP in both cases of hydrogen and nitrogen, and for the slush,approximately K = 0.23(H2), 0.19(N2) (when the heat of fusion of the solid is included in the latentheat of vaporization).

Fig. 7. Comparison of critical heat fluxes with Kutateladze correlation for liquid and slushhydrogen.

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Subsequently, changes of the critical heat flux q* according to the inclination of the heattransfer surface are shown in Figs. 10 and 11. For reference, the figures also show the calculatedresults of q* for the horizontal surface facing up using the factor K = 0.16 in Eq. (3). For the slush,the calculations include the heat of fusion of the solid in the latent heat of vaporization λ. Figures 10and 11 also show the correlation of Vishnev [15] based on the horizontal surface facing up. Thecorrelation of Vishnev uses K′ = K(190 − φ)0.5

/ 1900.5 instead of the factor K of Eq. (3).

Lyon [9] conducted his experiment in liquid helium from the critical point to the λ point andshowed that the critical heat flux decreases with an increase of the angle (φ) of inclination of the heat

Fig. 8. Comparison of critical heat fluxes with Kutateladze correlation for liquid and slush nitrogen.

Fig. 9. Comparison of Kutateladze correlation factor K with reduced pressure (horizontal surfacefacing up).

25

transfer surface. There have been no published data on experiments systematically covering changesof the critical heat fluxes near the triple-point pressure according to the inclination of the heat transfer

surface for liquid hydrogen and liquid nitrogen, but the experiments of Class and colleagues [3] usingangles of inclination φ = 0°, 45°, and 90° in liquid hydrogen at 0.82 atm, show hardly any difference

in the critical heat flux. The present experiments show that the liquid at TP and slush at TP exhibit

slightly higher values in the vertical orientation rather than in the horizontal orientation with the

surface facing up. The comparison with the correlation of Vishnev shows that the experimental results

for both orientations of the vertical surface and the horizontal surface facing down are higher than the

calculations. The critical heat flux values of slush hydrogen and slush nitrogen in the case of the heattransfer surface in its horizontal upward-facing surface decreased to 0.45 and 0.62 times those of the

liquid at NBP. In the case of the horizontal surface facing down, the respective values decreased to

0.33 and 0.43 times the critical heat flux values of slush in the case of the horizontal surface facing

up.

Fig. 10. Orientation dependence to critical heat flux in liquid and slush hydrogen.

Fig. 11. Orientation dependence to critical heat flux in liquid and slush nitrogen.

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4. Conclusions

The author conducted experimental investigations on nucleate boiling heat transfer charac-teristics of slush hydrogen and slush nitrogen at the triple-point pressure, including the effect ofinclination of the heat transfer surface. Nucleate boiling heat transfer characteristics of liquid hydrogenand liquid nitrogen at the normal-boiling-point and at the triple-point pressure were measured, usingthe same heat transfer surface, for comparison with the heat transfer characteristics of slush hydrogenand slush nitrogen. From the experimental results, the following conclusions on the heat transfercharacteristics of slush hydrogen and slush nitrogen are drawn.

(1) The heat transfer coefficients of slush hydrogen and slush nitrogen in the high-heat-fluxregion decrease, respectively, to about 0.5 times those of liquid hydrogen and liquid nitrogen at thenormal-boiling-point pressure.

(2) The heat transfer coefficients of slush hydrogen in the low-heat-flux region increase withan increase of the angle of heat transfer surface as seen in liquid hydrogen at the normal-boiling-pointand at the triple-point pressure; however, the difference is small between the vertical surface and thehorizontal surface facing down. Although this tendency yet remains unclear regarding slush nitrogendue to limited experimental data, it is inferred that its heat transfer coefficient remains almostunchanged even with an increase of the heat transfer surface angle as seen in liquid nitrogen at thenormal-boiling-point and at the triple-point pressure.

(3) Prediction of the heat transfer coefficients for slush hydrogen and nitrogen using theequation of Rohsenow from the experimental results of the liquids at the normal-boiling-pointpressure, shows that the calculated result agrees well with the experiment on nitrogen although thecalculations on hydrogen are lower than the experimental results.

(4) The critical heat flux value in the horizontal surface facing up, decreases in the followingorder: liquid at the normal-boiling-point pressure, slush and liquid at the triple-point pressure in bothcases of hydrogen and nitrogen. Meanwhile, the factor K of Kutateladze’s correlation increases in theorder of the liquid at the normal-boiling-point pressure, the liquid at the triple-point pressure, and theslush. For slush, approximately, K = 0.23 (H2), 0.19 (N2).

(5) The critical heat flux values of slush hydrogen and slush nitrogen decrease to 0.45 and0.62 times those of the liquids at the normal-boiling-point pressure in the case of the horizontal surfacefacing up. The critical heat flux values of slush hydrogen and slush nitrogen in the case of thehorizontal surface facing down, decrease to 0.33 and 0.43 times those of slush hydrogen and slushnitrogen in the case of the horizontal surface facing up.

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"F F F"

Originally published in Trans JSME Ser B 65, 1999, 4055–4062.Translated by Katsuhide Ohira, Nagasaki R & D Center, Mitsubishi Heavy Industries, Ltd., 5-717-1

Fukahori-machi, Nagasaki, 851-0392 Japan.

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