Abstract A film boiling heat transfer model is

developed for cryogenic chilldown at low mass flux

inside a horizontal pipeline. It incorporates the strati-

fied flow structure and is based on conservation prin-

ciples of mass, momentum, and energy. Simplifying

assumptions lead to an expression for the local film

boiling heat transfer coefficient which varies with the

azimuthal angle. The efficacy of the model is assessed

by comparing the predicted wall temperature histories

with those measured at several azimuthal positions and

various mass fluxes. Good agreement is observed at

low flux, G = 13–54 kg/m2 s.

List of symbols

Bo boiling number

cp heat capacity (J/kg K)

D pipe diameter (m)

d thickness of pipe wall (m)

G mass flux (kg/m2 s)

g gravity (m/s2)

h heat transfer coefficient (W/m2 K)

hfg latent heat (J/kg)

Ja Jakob number

k thermal conductivity (W/m K)

Nu Nusselt number

p pressure (Pa)

R radius of pipe (m)

Ra Rayleigh number

Re Reynolds number

T temperature (K)

Tw wall temperature (K)

t time (s)

U velocity (m/s)

u and v vapor film velocity (m/s)

x and y vapor film coordinates

z, r, and u cylindrical coordinates

Greek symbolsav vapor thermal diffusivity (m2/s)

al liquid volume fraction

d vapor film thickness (m)

vtt Martinelli parameter

m kinematic viscosity (m2/s)

q density (kg/m3)

Subscripts

v vapor

sat saturated

1 Introduction

Cryogenic chilldown is the process in which an idle

system at ambient temperature is cooled down to the

bulk cryogen temperature. It is encountered in many

applications, but it is of particular importance during

cryogenic transport in pipelines. In order to avoid an

J. Liao Æ R. Mei Æ J. F. Klausner (&)Department of Mechanical and Aerospace Engineering,University of Florida, P.O. Box 116300, Gainesville,FL 32611-6300, USAe-mail: klaus@ufl.edu

Heat Mass Transfer (2006) 42:891–900

DOI 10.1007/s00231-006-0143-5

123

SPECIAL ISSUE

A film boiling model for cryogenic chilldown at low mass fluxinside a horizontal pipeline

Jun Liao Æ Renwei Mei Æ James F. Klausner

Received: 11 January 2006 / Accepted: 8 May 2006 / Published online: 28 June 2006� Springer-Verlag 2006

excessive loss of cryogen to evaporation and dangerous

pressure fluctuations in the pipeline, a basic under-

standing of the chilldown process is needed.

Usually, film boiling, transient boiling, flow boiling,

and forced convection heat transfer all contribute to

removing heat from the pipe wall at different wall

superheats during the chilldown process. Film boiling

plays a dominant role since large wall superheats

characterize the longest time span of the chilldown

process. This investigation focuses on developing a

reliable predictive model for the local film boiling heat

transfer coefficient in the low mass flux range, which is

essential for chilldown simulations.

Existing models for heat transfer in the film boiling

regime are relatively limited, because (1) historically,

film boiling has not been of central concern in

industrial applications; and (2) high temperature dif-

ferences create numerous experimental challenges

such as large material expansions, incompatibility of

materials, excessive heat loss, dangerous operating

conditions, among others. For film boiling on vertical

surfaces, early work was reported by Bromley [1],

Dougall and Rohsenow [2] and Laverty and Rohse-

now [3]. Film boiling over a horizontal cylinder was

first studied by Bromley [1], and the reported heat

transfer correlation has been widely used. Breen and

Westwater [4] modified Bromley’s equation to ac-

count for very small and large tubes. When the tube

diameter exceeds the wavelength associated with

Taylor instability, the heat transfer correlation re-

duces to the result of an earlier work by Berenson [5]

for a horizontal surface.

Empirical correlations for cryogenic flow film boil-

ing have been proposed by Hendrick et al. [6, 7], El-

lerbrock et al. [8], von Glahn [9], and Giarratano and

Smith [10]. These correlations relate a simple or

modified Nusselt number ratio to the Martinelli

parameter. Giarratano and Smith [10] provide a de-

tailed assessment of these correlations for steady flow

cryogenic film boiling. These flow film boiling corre-

lations are difficult to use for chilldown simulations

because they do not account for local variations of heat

transfer associated with the two-phase flow structure.

In reality, for the same vapor quality, the local heat

transfer rate for annular flow is significantly different

from that for stratified flow. Simulations for chilldown

in a horizontal pipeline require the local heat transfer

coefficient in order to incorporate the thermal inter-

action with the pipe wall. Since the two-phase flow

regime encountered for horizontal chilldown is strati-

fied at low mass flux, a reliable heat transfer model is

needed to account for the flow structure and local

variations in heat transfer.

Available models for pool film boiling are based on

boundary layer analysis of the vapor film and provide

local film boiling heat transfer coefficients for

quenching in a pool of cold liquid. Such correlations

include those of Bromley [1] and Breen and Westwater

[4] for film boiling on the outer surface of a hot tube

and Frederking and Clark [11] and Carey [12] for film

boiling on the surface of a sphere. The ideas presented

in those works will prove to be useful for the current

analysis.

In order to accurately evaluate the local film boiling

heat transfer coefficient during chilldown in a hori-

zontal pipeline, a stratified flow film boiling model is

developed using conservation principles of mass,

momentum, and energy in the low mass flux regime.

An appropriate chilldown numerical simulation is used

as the testing platform to validate the model for the

flow film boiling heat transfer regime. In the results

section, detailed assessments of the heat transfer pre-

diction are provided by comparing the computed

temporal and spatial temperature variations with those

measured experimentally. Satisfactory results are ob-

tained for chilldown at low mass flux.

2 Formulation

A schematic diagram depicting the liquid/vapor struc-

ture for stratified flow film boiling inside a horizontal

pipe is shown in Fig. 1. The bulk liquid is near the

bottom of the pipe. Beneath the liquid is a thin vapor

film of thickness d(u). Due to gravitational stratifica-

liquid

vapor

δ

ϕ0

ϕ

x, u

Rg

y, v

Fig. 1 Schematic diagram of film boiling in stratified flow in apipe. Vapor film thickness d (d > R) is enlarged to clearly showthe structure of the thin vapor film beneath the liquid

892 Heat Mass Transfer (2006) 42:891–900

123

tion, the vapor in the film flows upward along the

azimuthal direction. Heat is transferred through the

thin vapor film from the solid to the liquid in the lower

portion of the pipe and to the bulk vapor in the upper

portion of the pipe. Therefore, a reliable heat transfer

model for film boiling in pipes or tubes requires

knowledge of the thin vapor film thickness, which can

be obtained by solving the film layer mass, momentum,

and energy equations.

To simplify the analysis for vapor film heat transfer,

it is assumed the liquid velocity in the azimuthal

direction is zero. Both the liquid and vapor flow are

assumed to be locally fully developed in the axial

direction. It is further assumed that the vapor film

thickness is small compared with the pipe radius and

the vapor flow is quasi-steady, incompressible, and

laminar. The laminar flow assumption can be con-

firmed post priori as the Reynolds number, Re, based

on the film velocity and film thickness is typically of

O(100~ 102). In terms of the x- and y-coordinates and

(u, v) velocity components shown in Fig. 1, the gov-

erning equations for the vapor flow are similar to

boundary-layer equations:

@u

@xþ @v

@y¼ 0; ð1Þ

u@u

@xþ v

@u

@y¼ � 1

qv

@p

@xþ mv

@2u

@y2� g sin u; ð2Þ

u@Tv

@xþ v

@Tv

@y¼ av

@2Tv

@y2; ð3Þ

where the subscript v denotes the properties of vapor.

Because the length scale in the azimuthal (x)

direction is much larger than the length scale in the

normal (y) direction, the v-component may be ne-

glected. Furthermore, the convection terms are as-

sumed small and are neglected. The resulting

momentum equation simplifies to

0 ¼ � 1

qv

@p

@xþ mv

@2u

@y2� g sin u: ð4Þ

The vapor pressure is evaluated by considering the

hydrostatic pressure from the liquid core as:

p ¼ p0 þ qlgR cosx

R

� �� cos u0

� �; ð5Þ

where u0 is the azimuthal position where the film

merges with the vapor core, and p0 is the pressure in

the vapor core. The momentum equation transforms

to,

ql � qvð Þqv

g sinx

R

� �þ mv

@2u

@y2¼ 0: ð6Þ

The vapor velocity boundary conditions are u = 0 at

y = 0 and u = ul = 0 at y = d. The resulting vapor

velocity profile is

u ¼ ql � qvð Þ2mvqv

g sinx

R

� �ðdy� y2Þ: ð7Þ

The average velocity �u in the vapor film is

�u ¼ 1

d

Zd

0

udy ¼ ql � qvð Þd2g

12mvqv

sinx

R

� �: ð8Þ

The energy and mass balances on the vapor film re-

quire that

kv

hfg� @Tv

@y

� �

y¼d

" #dx ¼ d _m ¼ qvdð�udÞ: ð9Þ

With negligible convection in the vapor energy equa-

tion, the vapor temperature profile is linear. The tem-

perature at the liquid–vapor interface is the vapor

saturation temperature, Tsat. For simplicity, the tem-

perature at the vapor–solid interface is assumed con-

stant, Tw. The following linear temperature profile is

obtained,

Tv � Tsat

Tw � Tsat¼ 1� y

d: ð10Þ

Substituting the temperature and velocity profiles into

Eq. 9 yields

dR

d

dudR

� �3

sin u

!¼ 12kvmv

hfgðql � qvÞgR3Tw � Tsatð Þ:

ð11Þ

This equation has an analytical solution for the vapor

thickness, d,

dR¼ 12kvmv Tw � Tsatð Þ

hfg ql � qvð ÞgR3

� �14 43

R u0 sin1=3 u0du0 þ const

sin4=3 u

!14

:

ð12Þ

A finite film thickness at u = 0 requires that const = 0.

Thus the solution may be cast as,

dR¼ 2

6Ja

Ra

� �14

F uð Þ; ð13Þ

where Ja is Jakob number and Ra is Raleigh number

and are expressed as,

Heat Mass Transfer (2006) 42:891–900 893

123

Ja ¼ cp;v Tw � Tsatð Þhfg

; ð14Þ

Ra ¼ gD3 ql � qvð Þmvavqv

; ð15Þ

and, cp is the heat capacity, D is the pipe diameter, and

F(u) is a geometrical factor,

F uð Þ ¼43R u

0 sin1=3 u0du0

sin4=3 u

!14

: ð16Þ

The average velocity �u of the vapor film at any azi-

muthal position is

�u uð Þ ¼ Tw � Tsatð Þ ql � qvð ÞgkvR

12mvq2vhfg

� �12

F2 uð Þ sin uð Þ:

ð17Þ

A closed form approximation for F(u) can be obtained

using a four-term Taylor series expansion for the

integrand in Eq. 16. This results in

F uð Þ � usin u

� �13

1� 1

45u2 � 1

12960u4 � 53

6735960u6

� �14

:

ð18Þ

Equation 18 agrees with the results from numerical

integration of Eq. 16 within 0.53% for 0 £ u < p.

This accurate closed form approximation is con-

venient for the evaluation of the local heat transfer

coefficient.

Curves for F(u) and F2(u)sin u based on the

numerical integration are shown in Fig. 2. The vapor

film thickness has a minimum at u = 0 and is nearly

constant for u < p/2. It rapidly grows when u > p/2.

The singularity at the top of tube when u fi p is of

no practical significance since the film will merge

with the vapor core at the vapor–liquid interface.

The vapor velocity is controlled mainly by

F2(u)sin u, which is zero at the bottom of the tube

and increases almost linearly in the lower part of the

tube where the vapor film thickness does not change

substantially. In the upper part of the tube, due to

the increase in the vapor film thickness, the vapor

velocity gradually drops back to zero at the very top.

Thus a maximum velocity may exist in the upper

part of the tube.

The local film boiling heat transfer coefficient is

easily obtained from the linear temperature profile.

It is

h uð Þ ¼ kv

d¼ 0:6389

kv

DF uð ÞRa

Ja

� �14

: ð19Þ

A further simplification can be made on Eq. 19 for

F(u) using a Taylor series expansion so that

h uð Þ � 0:6389kv

D

Ra

Ja

� �14

1� 1

20u2 � 1

1920u4 � 4:65593� 10�5u6

� �:

ð20Þ

The above agrees with the numerical integration

results within 1 and 3% for u < 2.4 and u < 2.64,

respectively. The heat transfer rate per unit length

from the wall to the liquid is obtained by integrating

the heat flux around the wall,

q0 ¼ 2

Zu0

0

kvðTw � TsatÞdðuÞ Rdu

¼ kv Tw � Tsatð Þ 6Ja

Ra

� ��14

G u0ð Þ;

ð21Þ

where

G u0ð Þ ¼Zu0

0

1

F uð Þ du: ð22Þ

Using Eq. 20, a simple approximation for G(u0) can be

obtained as

G u0ð Þ � u0 �1

60u3

0 �1

9600u5

0 � 6:5133� 10�6u70;

ð23Þ

0

1

2

3

4

5

0 0.5 1 1.5 2 2.5 3 3.5

ϕ, ϕ0 (radians)

F2(ϕ)sin(ϕ)

F(ϕ)

G(ϕ0)

Fig. 2 Curves for functions F(u), F2(u)sin u, and G(u0)

894 Heat Mass Transfer (2006) 42:891–900

123

which agrees with the results of numerical integration

using Simpson’s rule within 1.7% for 0 £ u0 £ p. For

u0 < 3.05, the difference is less than 1%. The variation

of G based on numerical integration with respect to the

azimuthal angle u0 is also shown in Fig. 2, together

with F(u) and F2(u)sin u.

The average heat transfer coefficient in the lower

portion of the tube (0 £ u £ u0) is represented by the

Nusselt number,

Nu ¼ hD

kv¼ q0D

pDkv Tw � Tsatð Þ

¼ Ra

Ja

� �14 6�

14

pG u0ð Þ ¼ 0:2034

Ra

Ja

� �14

G u0ð Þ:

ð24Þ

Using Eq. 23, the Nusselt number, Nu, can be simpli-

fied to

Nu ¼ 0:2034Ra

Ja

� �14

u0 �1

60u3

0 �1

9600u5

0 � 6:5133� 10�6u70

� �:

ð25Þ

The Nu number in the lower portion of the tube is only

a function of liquid level, characterized by the azi-

muthal angle, u0. When the liquid volume fraction al is

known, geometric considerations allow u0 to be com-

puted from,

al ¼2u0 � sin 2u0ð Þ

2p: ð26Þ

It is important to recognize that in the upper portion

of the tube (u0 < u £ p) there is convective heat

transfer to the vapor core from the wall. It is computed

separately.

3 Results and discussions

In this section, the flow film boiling heat transfer

coefficient is applied to predict the cryogenic chilldown

temperature fields with mass flux ranging from 13.7 to

54.49 kg/m2 s. A comparison with experimental mea-

surements is examined.

3.1 Chilldown model

Cryogenic chilldown is a highly transient heat transfer

process. To gain a fundamental insight into the film

boiling process between the wall and the cryogenic

fluid and to avoid complicated hydrodynamics in the

pipeline, a pseudosteady chilldown model [13, 14], is

adopted. In this model, a liquid wave front speed is

assumed to be constant and is the same as the bulk

liquid speed [15]. It is also assumed that steady state

thermal fields for both the liquid and the solid exist in a

reference frame that is moving with the wave front.

The governing equation for the solid thermal field

becomes a parabolic equation and can be efficiently

solved. In the lower portion of the pipe (0 £ u £ u0),

the local film boiling heat transfer coefficient (Eq. 19)

is used. In the vapor core the flow is turbulent, and the

Dittus–Boelter correlation for single phase flow is used

to evaluate the vapor core heat transfer coefficient

based on the average vapor velocity.

3.2 Comparison of predicted pipe wall temperature

history with experiment of Chung et al.

Chung et al. [16] studied cryogenic chilldown with

nitrogen at low mass flux in a horizontal pipe. Their

study includes a visual recording of the chilldown

process in a transparent Pyrex tube, identification of

flow and heat transfer regimes, and a collection of

temperature histories at different positions along the

wall during chilldown. Their results provide the nec-

essary information that can be used to assess the effi-

cacy of the film boiling heat transfer coefficients for the

present study.

The experimental test section consists of an inner

Pyrex tube surrounded by an outer Pyrex tube. The

chamber between the inner and outer tubes is vacuum

sealed with an absolute pressure of 0.2 atm. The inner

diameter (I.D.) and outer diameter (O.D.) of the inner

tube are 11.1 and 15.9 mm, respectively. The I.D. and

O.D. of the outer tube are 95.3 and 101.6 mm,

respectively. Numerous thermocouples are placed at

different locations along the inner tube. Experiments

were carried out at room temperature and atmospheric

pressure. Liquid nitrogen flows from a reservoir to the

test section driven by gravity. The average nitrogen

mass flux G is 13.7 kg/m2 s and the measured average

liquid nitrogen velocity is U ~ 5 cm/s. As the liquid

nitrogen flows through the pipe, it evaporates and chills

the pipe.

Although a vacuum insulation chamber between the

inner and outer tubes is used in the cryogenic transport

line in Chung et al. [16], the heat loss to the environ-

ment is non-negligible due to the large temperature

difference between the cryogenic fluid and the envi-

ronment. Radiation heat transfer exists between the

inner and outer pipe and the residual air in the vacuum

Heat Mass Transfer (2006) 42:891–900 895

123

section undergoes free convection between the inner

and outer pipe. Evaluation of the heat loss has been

incorporated in the pseudo-steady chilldown model

[13].

The computation for the solid wall thermal field

includes 40 grids along the radial direction and 40 grids

along the azimuthal direction as shown in Fig. 3. The

characteristic liquid volume fraction for the pseudo-

steady chilldown model is 0.3 based on recorded video

images. The characteristic time used for the computa-

tion is t0 = 100 s. The axial vapor velocity is estimated

to be approximately 0.5 m/s [13]. The average vapor

kinematic viscosity from the beginning of the chilldown

to the end of film boiling is 1.19 · 10– 6m2/s, and the

vapor phase hydraulic diameter is 8.58 mm based on

the characteristic vapor volume fraction 0.7. The vapor

core Reynolds number is thus 3,603. The average

liquid kinematic viscosity during the same period is

2.00 · 10– 7/s, and the liquid phase hydraulic diameter

is 4.77 mm based on the characteristic liquid volume

fraction. The liquid core Reynolds number is thus 1,192.

Figures 4 and 5 compare the measured and com-

puted wall temperature as a function of time at posi-

tions 11, 12, 14, and 15 shown in Fig. 3. The overall

temperature histories agree well in the film boiling

regime. The slight discrepancy between wall tempera-

tures in the upper wall (Fig. 5) is due to the uncertainty

in estimating the vapor velocity.

The wall temperature history is also computed using

the steady flow film boiling heat transfer correlation of

Giarratano and Smith [10]. The correlation is given by

Nu

Nucalc

� �Bo�0:4 ¼ f ðxÞ ¼ exp

2:83þ 0:317 ln xþ 0:000569 ln2 x� �

;

ð27Þ

where Nucalc is the Nusselt number for the single-phase

forced convection heat transfer, Bo is the Boiling

number, and x is the vapor quality. In this correlation,

the heat transfer coefficient is the averaged value for

the whole cross section. The computed wall tempera-

ture histories using the film boiling correlation of

Giarratano and Smith [10] are shown in Fig. 4.

Apparently, the correlation of Giarratano and Smith

[10] gives a very low heat transfer rate so that the

predicted wall temperature is excessively high. This

comparison elucidates the need to account for local

variations in heat transfer. It is appropriate to point out

that the correlation was developed using turbulent flow

film boiling data, and the current experiment [16] in-

cludes laminar liquid flow and turbulent vapor flow.

Figure 6 shows the variation of the computed vapor

film thickness, d, at the bottom of the pipe (u = 0) as a

function of time during chilldown for the experimental

thermal and flow reported in Chung et al. [16]. As the

wall chills down significantly, the vapor film thickness

decreases as d P (Tw – Tsat)1/4. As the Leidenfrost

temperature is reached, the film collapses and liquid

wets the wall, setting the stage for transitioning to the

nucleate boiling regime.

Figure 7 shows the computed temperature distribu-

tion at a given cross-section at different times during

film boiling chilldown. Because the upper part of pipe

120°

T 11

T 14

T 12 T 15

Fig. 3 Computational grid arrangement and position of thermo-couples in experiment of Chung et al. [16]

0 10 20 30 40 50 60t(s)

100

125

150

175

200

225

250

275

300

T(K

)

T 12 predictedT 15 predictedT 12 experimentalT 15 experimentalT 12 predicted using film boiling correlation [10]

Fig. 4 Comparison between measured and predicted transientwall temperatures at positions 12 and 15 near the bottom of thepipe during flow film boiling chilldown for experiment in Chunget al. [16], average mass flux G = 13.7 kg/m2 s

896 Heat Mass Transfer (2006) 42:891–900

123

wall is exposed to the nitrogen vapor, and the bottom

part of pipe wall is quenched with film boiling, the heat

transfer in the bottom portion is significantly more

effective.

In the derivation for the film boiling heat transfer

coefficient in Sect. 2, the flow in the thin vapor film is

assumed to be laminar. For the experimental condi-

tions reported by Chung et al. [16], the maximum va-

por film thickness is estimated to be d = 0.15 mm and

the maximum vapor velocity in azimuthal direction is

estimated to be �u ¼ 1:65 m=s using Eqs. 13 and 17,

respectively. Since the measured liquid velocity in the

axial direction is around 0.05 m/s, the vapor film

velocity in the axial direction should be on the same

order and less than the vapor velocity in azimuthal

direction. The maximum vapor film Reynolds number

during the film boiling stage of chilldown is on the

order of Re = 200. Hence, the flow within the thin

vapor film is primarily azimuthal and laminar.

3.3 Comparison of predicted pipe wall temperature

history with experiment of Velat

Next, the chilldown experiment of Velat [17] is mod-

eled and the predicted wall temperature histories

during chilldown are compared with those experi-

mentally measured. Velat [17] and Velat et al. [18]

studied cryogenic chilldown in a well-controlled

experiment with nitrogen flow from low to high mass

flux in a horizontal tube. Velat’s study included visual

recordings of the chilldown process in a transparent

Pyrex tube, an identification of flow and boiling

regimes, and a collection of temperature histories on

the outside surface of a stainless tube downstream of

the Pyrex test section.

The test section for temperature measurements

consists of a 304 stainless steel tube with a 12.5 mm

I.D. and a 16.0 mm O.D. The liquid nitrogen supply

is stored in a 1,580 kPa (230-psi) Dewar. The pres-

sure in the Dewar drives liquid nitrogen through the

test section. There are three thermocouples for tem-

perature measurements that are located on the top,

side, and bottom of outer surface of the tube wall

(Fig. 8).

The heat transfer test section is surrounded by

insulation material instead of a vacuum chamber. The

measured overall heat transfer coefficient though the

insulation to the ambient is 4.38 W/m2 K. The com-

putational mesh is the same as that used in the simu-

lation for the experiment of Chung et al. [16]. The

liquid and vapor volume fractions, liquid and vapor

velocity, liquid temperature, pressure, and Reynolds

number for the computation are provided from

experimental measurements [17].

Figure 9 compares temperatures at a relatively low

mass flux G = 37.52 kg/m2 s, which is experiment #9

in Velat [17]. The average axial liquid and vapor

velocities are 0.175 and 1.89 m/s, respectively. The

liquid temperature at the entrance is 85 K, and the

average pressure is 717 kPa. The average vapor core

and liquid core Reynolds numbers are 17,000 and

10,241, respectively. Liquid volume fraction as a

function of time fitted from the experimental mea-

surements is given as al = 0.05 + 0.0033t – 7 · 10– 6 t2.

The solid line is the computed wall temperature and

the dashed line is the measured wall temperature. The

comparisons of the temperatures are at the top, side,

0 10 20 30 40 50 60t(s)

100

125

150

175

200

225

250

275

300

T(K

)

T 11 predictedT 14 predictedT 11 experimentalT 14 experimental

Fig. 5 Comparison between measured and predicted transientwall temperatures at positions 11 and 14 in the upper portionof the pipe. Average mass flux in experiment [16] isG = 13.7 kg/m2 s

0.116

0.118

0.12

0.122

0.124

0.126

0.128

0.13

0.132

0.134

0.136

0.138

0 10 20 30 40 50 60t(s)

δ (m

m)

Fig. 6 Computed variation of vapor film thickness d duringchilldown in experiment [16]

Heat Mass Transfer (2006) 42:891–900 897

123

and bottom of the tube. Figure 9 shows the overall

temperature histories agree well in the film boiling

regime.

Figure 10 shows the comparison of temperatures

at a higher mass flux, G = 54.49 kg/m2 s, experiment

#3 in Velat [17]. The average axial liquid and vapor

velocity are 0.29 and 2.30 m/s, respectively. The li-

quid temperature at the entrance is 98 K, and the

average pressure is 679 kPa. The average vapor core

and liquid core Reynolds numbers are 18,000 and

17,600, respectively. Liquid volume fraction as a

function of time fitted from the experimental mea-

surement is given as al = 0.0848 + 0.0012t + 5 · 10– 5

t2. The predicted temperatures generally agree with

the measured temperatures but are slightly higher

than the measured temperatures. This is indicative

that the predicted film boiling heat transfer coeffi-

cient is slightly lower than the actual heat transfer

coefficient.

For film boiling experiment #9 reported by Velat

[17], the estimated maximum vapor film thicknesses is

d = 0.18 mm, and the estimated maximum vapor

velocity in azimuthal direction is 2.22 m/s. The cor-

responding maximum vapor film Reynolds numbers is

thus 481. The vapor film velocity in axial direction is

on the same order as the azimuthal velocity, and

laminar film flow is confirmed. For film boiling

experiment #3 reported by Velet [17], the maximum

vapor film Reynolds numbers is 482, also in the

laminar flow regime.

At higher mass flux, G > 55 kg/m2 s, the film boiling

correlation is not successful in predicting the temper-

ature histories reported by Velat [17]. At high mass

flux the vapor film transitions to turbulent flow and the

t=0s t=20s

t=60st=40s

300295290285280275270265260255250245240235230225220215210205200195190185180

Ts (K)

300295290285280275270265260255250245240235230225220215210205200195190185180

Ts (K)

'X

'Y'

-0.005 0 0.005'X

-0.005 0 0.005

'X-0.005 0 0.005

'X-0.005 0 0.005

-0.006

-0.004

-0.002

0

0.002

0.004

0.006

300295290285280275270265260255250245240235230225220215210205200195190185180

Ts (K)

300295290285280275270265260255250245240235230225220215210205200195190185180

Ts (K)'Y

'

-0.006

-0.004

-0.002

0

0.002

0.004

0.006

'Y'

-0.006

-0.004

-0.002

0

0.002

0.004

0.006

'Y'

-0.006

-0.004

-0.002

0

0.002

0.004

0.006

Fig. 7 Spatial variation of wall temperature at t = 0, 20, 40, and 60 s

898 Heat Mass Transfer (2006) 42:891–900

123

current model is not valid. An investigation of higher

mass flux flow film boiling will be considered in another

work.

4 Conclusions

A new film boiling heat transfer model for cryogenic

chilldown has been developed using conservation

principles and incorporating the stratified flow struc-

ture at low mass flux. The new film boiling heat

transfer model, together with a pseudo-steady chill-

down computational model, was successfully applied to

predict chilldown in a cryogenic transfer line at low

mass flux. The predicted wall temperature histories,

based on the local film boiling heat transfer coefficient,

match well with the experimental results during the

chilldown process.

Acknowledgements This work was supported by NASA GlennResearch Center under contract NAG3-2930 and NASA Ken-nedy Space Center. The authors wish to thank Professor JacobN. Chung and PhD student Kun Yuan at the University ofFlorida for many useful discussions.

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T top

T side

T bottom

Fig. 8 Computational grid arrangement and position of thermo-couples for experiment of Velat [17]

100.00

120.00

140.00

160.00

180.00

200.00

220.00

240.00

260.00

280.00

300.00

0 20 40 60 80 100 120 140

t(s)

T(K

)

experimental

predictedbottom of pipe

side of pipe

top of pipe

Fig. 9 Comparison between measured and predicted transientwall temperatures, experiment #9 in Velat [17], average mass fluxG = 37.52 kg/m2 s

100.00

120.00

140.00

160.00

180.00

200.00

220.00

240.00

260.00

280.00

300.00

0 10 20 30 40 50 60 70 80 90t(s)

T(K

)

experimental

predicted

bottom of pipe

side of pipe

top of pipe

Fig. 10 Comparison between measured and predicted transientwall temperatures, experiment #3 in Velat [17], average mass fluxG = 54.49 kg/m2 s

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